Determinacacao do ponto de referencia inicial: TRANSITION 1 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables, all linear 211995 constraints, all linear; 563706 nonzeros 100200 equality constraints 111795 inequality constraints 1 linear objective; 1398 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 16062.94221 43541 dual simplex iterations (0 in phase I) Funcao Ojetivo($)/ Investment/ O&M: 16062.94 2821.97 13240.61 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2168.47/ 1962.06/ 700.12 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 2316.43 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 0.00 0.00 0.00 0.00 0.00 1172.97 51 0.00 0.00 0.00 0.00 0.00 0.00 64 1353.84 0.00 744.03 1500.00 1500.00 1500.00 PV systems (kW): Node T1 T2 T3 35.00 619.07 0.00 0.00 46.00 283.51 0.00 0.00 64.00 582.26 217.74 0.00 67.00 0.00 800.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 0.00 522.30 428.48 50.00 0.00 0.00 0.00 69.00 0.00 0.00 0.00 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 0.00 5.67 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 21.26 8.20 Conductors 0.00 0.00 16.66 6.43 Structures 0.00 0.00 14.60 5.63 Fixed CBs 3.36 3.36 5.21 7.46 Switchable CBs 5.04 10.08 19.06 18.64 PV systems 919.51 1387.85 1387.85 2316.33 Wind systems 0.00 366.05 619.89 466.28 EES systems 0.00 0.00 3.11 1.20 Total invesment cost 927.91 1767.34 2087.65 2830.17 Purchased energy cost 5645.06 6106.96 7298.35 12250.83 Carbon tax payment 194.95 341.77 718.28 684.09 O&M PV cost 89.99 121.64 114.79 209.77 O&M wind cost 0.00 72.87 130.83 95.69 O&M EES cost 0.00 0.00 0.61 0.24 Total O&M cost 5929.99 6643.23 8262.86 13240.61 Total cost 6857.91 8410.57 10350.51 16070.78 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 14814.89 0.00 130306.45 0.00 0.00 2 112549.13 24968.95 5579.32 141404.09 1693.31 0.00 3 131557.56 24969.12 10156.23 161754.72 2491.22 3.58 CO2 Emissions (Ton): Period Distribution EV 1 9751.97 4980.53 2 9841.45 4906.75 3 9887.75 4780.66 4 9911.42 4659.94 5 9980.06 4476.17 6 8517.11 4266.91 7 8592.80 4025.47 8 8661.49 3733.05 9 8706.60 3403.07 10 8825.28 2999.31 11 8856.03 2539.22 12 8985.47 2025.48 13 9113.01 1443.32 14 9198.73 753.85 15 9401.86 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 187.89 4445.21 -908.72 1520.01 0.90 1.00 0.95 1.00 2 0.00 5163.77 -1288.49 1435.32 0.90 1.00 0.95 1.00 3 0.00 8834.79 -2903.85 1689.85 0.90 1.00 0.95 1.00 Reactive Power by DG Period PV Wind min max min max 1 -150.84 221.42 0.00 0.00 2 -200.42 304.93 -94.66 116.99 3 -207.91 286.95 -173.22 216.47 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 0.00 0.00 4.53 4.53 22.66 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 5.67 5.67 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 0.00 0.00 187.89 4445.21 -908.72 1520.01 | 4( 2)| 0.00 0.00 0.00 5163.77 -1288.49 1435.32 | 4( 2)| 0.00 300.00 -2.51 8832.28 -2905.31 1689.85 2- 3 | 4( 2)| 0.00 0.00 180.65 4421.19 -920.58 1500.08 | 4( 2)| 0.00 300.00 -14.29 5135.35 -1307.36 1416.52 | 4( 2)| 0.00 300.00 -12.05 8789.93 -2934.44 1666.04 3- 4 | 4( 2)| 0.00 0.00 731.67 3925.26 -1152.47 1291.96 | 4( 2)| 0.00 0.00 246.70 4547.48 -1676.72 1226.13 | 4( 2)| 0.00 300.00 -1075.80 5741.33 -4008.76 1032.72 4- 5 | 3( 1)| 0.00 0.00 471.32 3061.03 -1529.75 647.53 | 3( 1)| 0.00 0.00 -21.03 3525.94 -2277.53 526.39 | 3( 1)| 0.00 230.00 -1087.79 4412.64 -4840.28 262.72 5- 6 | 3( 1)| 0.00 0.00 464.08 3037.01 -1541.61 627.60 | 3( 1)| 0.00 230.00 -69.48 3497.52 -2296.41 504.75 | 3( 1)| 0.00 230.00 -1128.10 4339.55 -4881.54 238.91 6- 7 | 3( 1)| 0.00 0.00 456.84 3012.99 -1553.46 607.67 | 3( 1)| 0.00 230.00 -119.08 3469.10 -2315.28 483.10 | 3( 1)| 0.00 230.00 -1169.56 4304.37 -4907.02 215.09 7- 8 | 3( 1)| 0.00 0.00 445.17 2974.30 -1570.96 577.77 | 3( 1)| 0.00 230.00 -131.98 3423.31 -2343.12 450.64 | 3( 1)| 0.00 230.00 -1179.74 4247.71 -4945.24 179.37 8- 9 | 2( 1)| 0.00 0.00 401.17 2828.41 -1634.71 468.82 | 2( 1)| 0.00 180.00 -200.02 3250.68 -2444.60 347.01 | 2( 1)| 0.00 180.00 -1184.04 4034.06 -5084.52 49.19 9- 10 | 1( 1)| 0.00 0.00 299.11 1002.96 322.99 715.07 | 1( 1)| 0.00 140.00 -327.88 1101.07 82.90 884.56 | 1( 1)| 0.00 140.00 -660.90 1354.20 -529.37 1025.62 10- 11 | 1( 1)| 0.00 0.00 291.07 975.97 314.32 695.91 | 1( 1)| 0.00 140.00 -336.93 1069.40 73.56 866.52 | 1( 1)| 0.00 140.00 -661.24 1314.46 58.37 1001.59 11- 12 | 1( 1)| 0.00 0.00 238.62 800.12 254.89 564.46 | 1( 1)| 0.00 140.00 25.08 914.20 176.61 631.95 | 1( 1)| 0.00 140.00 -162.68 1118.34 93.12 727.12 12- 13 | 1( 1)| 0.00 0.00 180.54 605.37 189.08 418.89 | 1( 1)| 0.00 140.00 -51.17 681.16 100.81 472.45 | 1( 1)| 0.00 140.00 -277.73 827.80 13.14 553.15 13- 14 | 1( 1)| 0.00 0.00 169.01 566.69 177.83 393.68 | 1( 1)| 0.00 140.00 -77.15 635.08 87.85 444.82 | 1( 1)| 0.00 140.00 -347.36 770.36 -0.53 523.63 14- 15 | 1( 1)| 0.00 0.00 157.47 528.02 165.37 366.11 | 1( 1)| 0.00 140.00 -88.52 589.01 73.49 414.96 | 1( 1)| 0.00 140.00 -355.29 712.92 -15.68 490.96 15- 16 | 1( 1)| 0.00 0.00 150.23 503.73 156.10 345.94 | 1( 1)| 0.00 140.00 -95.58 560.08 62.81 393.87 | 1( 1)| 0.00 140.00 -360.21 676.85 -26.95 467.34 16- 17 | 1( 1)| 0.00 0.00 137.08 459.65 142.42 315.68 | 1( 1)| 0.00 140.00 -130.42 507.58 47.06 362.24 | 1( 1)| 0.00 140.00 -369.14 611.39 -43.39 431.91 17- 18 | 1( 1)| 0.00 0.00 119.65 401.18 126.76 280.72 | 1( 1)| 0.00 140.00 -147.41 437.94 29.02 325.70 | 1( 1)| 0.00 140.00 -380.99 524.57 -62.41 390.97 18- 19 | 1( 1)| 0.00 0.00 102.21 342.72 111.11 245.75 | 1( 1)| 0.00 140.00 -164.40 368.29 10.99 289.15 | 1( 1)| 0.00 140.00 -412.23 437.74 -81.44 350.03 19- 20 | 1( 1)| 0.00 0.00 94.97 318.43 106.85 236.00 | 1( 1)| 0.00 140.00 -171.46 339.36 6.09 278.96 | 1( 1)| 0.00 140.00 -417.15 401.67 -86.61 338.62 20- 21 | 1( 1)| 0.00 0.00 86.25 289.19 98.80 217.85 | 1( 1)| 0.00 140.00 -179.96 304.54 -3.19 259.98 | 1( 1)| 0.00 140.00 -423.07 358.26 -96.40 317.36 21- 22 | 1( 1)| 0.00 0.00 53.12 178.10 61.86 136.16 | 1( 1)| 0.00 140.00 -218.05 174.36 -45.74 174.58 | 1( 1)| 0.00 140.00 -446.98 193.95 -141.29 242.44 22- 23 | 1( 1)| 0.00 0.00 38.63 129.53 45.90 100.86 | 1( 1)| 0.00 140.00 -236.98 117.42 -64.12 144.25 | 1( 1)| 0.00 140.00 -464.19 122.39 -160.69 220.56 23- 24 | 1( 1)| 0.00 0.00 31.39 105.24 36.63 80.69 | 1( 1)| 0.00 140.00 -246.45 88.96 -74.80 131.52 | 1( 1)| 0.00 140.00 -472.79 87.94 -171.95 211.76 24- 25 | 1( 1)| 0.00 0.00 23.34 78.26 27.51 60.51 | 1( 1)| 0.00 140.00 -257.14 56.80 -85.30 122.35 | 1( 1)| 0.00 140.00 -498.97 49.04 -183.04 199.36 25- 26 | 1( 1)| 0.00 0.00 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 140.00 -266.61 28.33 -95.98 113.01 | 1( 1)| 0.00 140.00 -507.58 14.59 -194.31 190.55 26- 27 | 1( 1)| 0.00 0.00 8.05 26.99 9.12 20.17 | 1( 1)| 0.00 140.00 -277.30 -2.57 -106.49 103.84 | 1( 1)| 0.00 140.00 -517.30 -22.10 -205.39 181.89 3- 28 | 1( 1)| 0.00 0.00 -424.00 186.81 -135.69 268.38 | 1( 1)| 0.00 140.00 -376.62 222.10 -116.78 297.07 | 1( 1)| 0.00 140.00 -356.30 2204.60 -88.95 669.38 28- 29 | 1( 1)| 0.00 0.00 -431.51 161.90 -145.75 254.49 | 1( 1)| 0.00 140.00 -387.13 192.62 -128.10 280.27 | 1( 1)| 0.00 140.00 -369.50 2163.67 -100.90 644.80 29- 30 | 1( 1)| 0.00 0.00 -439.03 136.99 -155.82 240.60 | 1( 1)| 0.00 140.00 -397.64 163.15 -139.42 267.50 | 1( 1)| 0.00 140.00 -382.69 2102.47 -112.85 615.62 30- 31 | 1( 1)| 0.00 0.00 -446.27 112.98 -166.78 225.73 | 1( 1)| 0.00 140.00 -407.77 134.73 -151.75 258.47 | 1( 1)| 0.00 140.00 -395.42 2062.00 -125.87 589.14 31- 32 | 1( 1)| 0.00 0.00 -453.51 88.96 -177.75 210.85 | 1( 1)| 0.00 140.00 -417.91 106.31 -164.08 245.84 | 1( 1)| 0.00 140.00 -408.15 2005.66 -138.89 559.07 32- 33 | 1( 1)| 0.00 0.00 -461.56 62.27 -188.53 195.97 | 1( 1)| 0.00 140.00 -429.36 74.21 -176.21 226.74 | 5( 1)| 0.00 400.00 -422.53 1561.98 -151.69 494.26 33- 34 | 1( 1)| 0.00 0.00 -469.61 35.58 -199.32 181.09 | 1( 1)| 0.00 140.00 -446.87 42.10 -194.03 196.05 | 5( 1)| 0.00 400.00 -472.66 700.99 -189.30 333.08 34- 35 | 1( 1)| 0.00 0.00 -475.11 17.35 -214.95 159.77 | 1( 1)| 0.00 140.00 -484.41 20.53 -212.54 164.88 | 5( 1)| 0.00 400.00 -489.60 25.55 -206.04 164.45 3- 36 | 1( 1)| 0.00 0.00 -134.27 285.11 16.33 203.29 | 1( 1)| 0.00 140.00 -124.83 337.36 23.47 280.01 | 1( 1)| 0.00 140.00 -150.19 792.84 5.84 373.82 36- 37 | 1( 1)| 0.00 0.00 -141.78 260.20 6.26 191.59 | 1( 1)| 0.00 0.00 -132.23 307.88 14.43 261.27 | 1( 1)| 0.00 140.00 -154.70 752.46 -3.07 349.24 37- 38 | 1( 1)| 0.00 0.00 -149.29 235.29 -3.80 179.89 | 1( 1)| 0.00 140.00 -139.63 278.41 5.38 242.53 | 1( 1)| 0.00 140.00 -159.21 715.98 -11.17 324.06 38- 39 | 1( 1)| 0.00 0.00 -156.53 211.27 -14.77 167.15 | 1( 1)| 0.00 0.00 -146.76 249.99 -4.47 222.45 | 1( 1)| 0.00 140.00 -163.56 680.81 -20.40 298.18 39- 40 | 1( 1)| 0.00 0.00 -163.51 188.15 -23.93 156.49 | 1( 1)| 0.00 140.00 -153.62 222.62 -13.71 205.39 | 1( 1)| 0.00 140.00 -167.74 642.53 -28.78 275.52 40- 41 | 1( 1)| 0.00 0.00 -170.48 165.02 -33.10 145.84 | 1( 1)| 0.00 140.00 -167.53 195.26 -31.74 188.32 | 4( 1)| 0.00 394.31 -218.03 266.05 -36.17 200.83 41- 42 | 1( 1)| 0.00 0.00 -177.73 141.00 -44.07 133.10 | 1( 1)| 0.00 140.00 -190.41 166.84 -45.79 168.25 | 1( 1)| 0.00 140.00 -217.90 216.22 -49.19 177.02 42- 43 | 1( 1)| 0.00 0.00 -184.97 116.98 -55.03 120.36 | 1( 1)| 0.00 140.00 -194.79 138.42 -55.64 148.54 | 1( 1)| 0.00 140.00 -220.41 181.34 -58.62 154.14 43- 44 | 1( 1)| 0.00 0.00 -190.20 99.63 -62.04 112.21 | 1( 1)| 0.00 140.00 -197.95 117.89 -61.94 136.19 | 1( 1)| 0.00 140.00 -220.31 155.27 -64.47 140.10 44- 45 | 1( 1)| 0.00 0.00 -197.44 75.61 -73.00 99.47 | 1( 1)| 0.00 140.00 -206.53 89.47 -71.79 117.20 | 1( 1)| 0.00 140.00 -220.18 114.22 -74.69 119.61 45- 46 | 1( 1)| 0.00 0.00 -208.71 37.81 -87.20 84.47 | 1( 1)| 0.00 140.00 -217.03 44.74 -84.96 92.20 | 1( 1)| 0.00 140.00 -224.38 55.69 -87.13 93.17 4- 47 | 1( 1)| 0.00 0.00 253.11 849.59 285.90 632.03 | 1( 1)| 0.00 140.00 152.04 1010.91 249.93 723.08 | 1( 1)| 0.00 140.00 12.13 1286.78 188.72 823.89 47- 48 | 1( 1)| 0.00 0.00 245.86 825.31 276.63 611.86 | 1( 1)| 0.00 140.00 148.16 981.98 240.79 700.01 | 1( 1)| 0.00 140.00 12.26 1245.43 182.72 797.59 48- 49 | 1( 1)| 0.00 0.00 222.93 748.40 250.79 554.71 | 1( 1)| 0.00 140.00 119.16 890.38 214.85 634.62 | 1( 1)| 0.00 140.00 -4.07 1114.47 162.30 723.09 49- 50 | 1( 1)| 0.00 0.00 111.46 374.20 125.40 277.36 | 1( 1)| 0.00 0.00 59.58 445.19 107.43 317.31 | 1( 1)| 0.00 140.00 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 0.00 0.00 22.27 74.66 25.23 55.81 | 1( 1)| 0.00 140.00 13.45 88.93 22.14 63.85 | 1( 1)| 0.00 140.00 -0.41 110.87 16.43 72.75 51- 52 | 1( 1)| 0.00 0.00 10.46 35.08 12.31 27.23 | 1( 1)| 0.00 140.00 5.59 41.79 10.55 31.15 | 1( 1)| 0.00 0.00 -0.19 52.10 8.07 35.50 9- 53 | 1( 1)| 0.00 0.00 93.34 1807.62 -2063.32 -259.66 | 1( 1)| 0.00 140.00 -20.08 2138.34 -3096.64 -227.75 | 1( 1)| 0.00 140.00 -599.87 2656.18 -4974.06 -581.77 53- 54 | 1( 1)| 0.00 0.00 80.73 1765.81 -2089.12 -294.87 | 1( 1)| 0.00 140.00 -40.04 2088.87 -3129.94 -265.98 | 1( 1)| 0.00 140.00 -611.98 2594.60 -5016.35 -623.84 54- 55 | 1( 1)| 0.00 0.00 73.09 1740.46 -2102.99 -308.98 | 1( 1)| 0.00 140.00 -61.40 2058.87 -3147.85 -286.54 | 1( 1)| 0.00 140.00 -611.84 2557.26 -5039.10 -646.47 55- 56 | 1( 1)| 0.00 0.00 66.11 1717.33 -2115.64 -321.61 | 1( 1)| 0.00 140.00 -82.36 2031.50 -3164.18 -305.30 | 1( 1)| 0.00 140.00 -611.72 2523.19 -5059.84 -667.11 56- 57 | 1( 1)| 0.00 0.00 59.14 1694.20 -2128.30 -334.24 | 1( 1)| 0.00 140.00 -180.00 2004.14 -3180.52 -324.06 | 1( 1)| 0.00 140.00 -611.59 2489.12 -5080.59 -687.74 57- 58 | 1( 1)| 0.00 0.00 51.89 1670.18 -2142.90 -348.80 | 1( 1)| 0.00 140.00 -223.78 1975.72 -3199.68 -345.70 | 1( 1)| 0.00 140.00 -611.46 2453.74 -5104.53 -711.56 58- 59 | 1( 1)| 0.00 0.00 44.65 1646.16 -2157.50 -363.37 | 1( 1)| 0.00 140.00 -245.78 1947.30 -3218.84 -367.34 | 1( 1)| 0.00 140.00 -611.32 2418.37 -5128.47 -735.37 59- 60 | 1( 1)| 0.00 0.00 15.68 1550.09 -2210.06 -415.82 | 1( 1)| 0.00 140.00 -286.19 1833.62 -3286.70 -444.29 | 1( 1)| 0.00 140.00 -633.71 2276.85 -5214.64 -821.11 60- 61 | 1( 1)| 0.00 0.00 8.43 1526.07 -2224.66 -430.39 | 1( 1)| 0.00 140.00 -290.57 1805.20 -3305.86 -461.94 | 1( 1)| 0.00 140.00 -633.58 2241.48 -5238.58 -844.92 61- 62 | 1( 1)| 0.00 0.00 -352.11 330.03 -2878.90 -1078.49 | 1( 1)| 0.00 0.00 -508.31 390.51 -4144.30 -1103.88 | 1( 1)| 0.00 140.00 -632.29 480.45 -6303.43 -1759.34 62- 63 | 1( 1)| 0.00 0.00 -361.50 299.34 -2896.01 -1095.24 | 1( 1)| 0.00 140.00 -513.90 354.20 -4166.39 -1118.01 | 1( 1)| 0.00 140.00 -632.12 435.25 -6330.96 -1772.53 63- 64 | 1( 1)| 0.00 0.00 -368.75 275.32 -2910.88 -1109.81 | 1( 1)| 0.00 140.00 -559.70 325.78 -4186.46 -1130.50 | 1( 1)| 0.00 140.00 -631.99 399.87 -6354.90 -1786.30 64- 65 | 1( 1)| 0.00 0.00 17.17 57.57 19.15 42.36 | 1( 1)| 0.00 140.00 9.18 68.57 16.41 48.46 | 1( 1)| 0.00 140.00 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 0.00 10.46 35.08 11.86 26.22 | 1( 1)| 0.00 140.00 -624.01 41.05 -273.51 214.30 | 1( 1)| 0.00 140.00 -628.34 51.10 -269.94 216.62 66- 67 | 1( 1)| 0.00 0.00 5.23 17.54 5.93 13.11 | 1( 1)| 0.00 140.00 -626.80 20.53 -279.90 205.66 | 1( 1)| 0.00 140.00 -632.66 25.55 -277.46 211.77 12- 68 | 1( 1)| 0.00 0.00 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 140.00 8.75 65.36 15.80 46.15 | 1( 1)| 0.00 140.00 0.68 81.48 11.80 52.59 68- 69 | 1( 1)| 0.00 0.00 8.05 26.99 9.12 20.17 | 1( 1)| 0.00 140.00 4.37 32.68 7.81 23.08 | 1( 1)| 0.00 140.00 -0.15 40.74 5.90 26.29 Voltage p.u. min max 1 0.95 1.01 2 0.95 1.02 3 0.95 1.04 Elapsed AMPL time : 2.641s Elapsed Solve time : 21.563s Elapsed CPU time: 24.204s Sumatorio de erros e2 10610.67399 Sumatorio de erros pq 52252.20950 Sumatorio de erros vi 105.03091 Maximum Psae error 5.37524 Maximo erro superior 8466.4269 Maximo erro inferior -6524.5245 TRANSITION 2 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables, all linear 211995 constraints, all linear; 886868 nonzeros 100200 equality constraints 111795 inequality constraints 1 linear objective; 1398 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 15228.08625 1951 simplex iterations (150 in phase I) 99 barrier iterations Funcao Ojetivo($)/ Investment/ O&M: 15228.09 2188.57 13039.52 Required investment at the beginning of T1/T2/T3/Total (10^3$) 1587.53/ 1931.67/ 0.00 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 788.21 0.00 0.00 419.94 405.11 0.00 51 0.00 0.00 0.00 166.29 0.00 0.00 64 0.00 0.00 0.00 0.00 0.00 0.00 PV systems (kW): Node T1 T2 T3 35.00 0.00 310.58 0.00 46.00 0.00 661.61 0.00 64.00 535.92 264.08 0.00 67.00 454.38 345.62 0.00 Wind systems (kW): Node T1 T2 T3 27.00 0.00 138.26 0.00 50.00 0.00 0.00 0.00 69.00 0.00 0.00 0.00 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 0.00 0.00 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 34.93 34.93 34.93 70.08 Structures 24.21 24.21 24.21 48.58 Fixed CBs 1.96 1.96 1.96 3.93 Switchable CBs 1.97 3.33 3.33 5.32 PV systems 613.26 1341.20 1341.20 1963.13 Wind systems 0.00 96.90 96.90 97.52 EES systems 0.00 0.00 0.00 0.00 Total invesment cost 676.33 1502.53 1502.53 2188.57 Purchased energy cost 5621.84 6089.91 7143.93 12157.49 Carbon tax payment 194.95 341.59 706.87 679.59 O&M PV cost 60.02 125.02 117.98 183.13 O&M wind cost 0.00 19.29 19.03 19.31 O&M EES cost 0.00 0.00 0.00 0.00 Total O&M cost 5876.81 6575.81 7987.82 13039.52 Total cost 6553.13 8078.34 9490.35 15228.09 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 9880.60 0.00 130306.45 477.86 0.00 2 112453.50 25663.41 1476.92 141404.09 1773.78 0.00 3 129384.81 25663.59 1476.90 161754.72 3052.43 0.00 CO2 Emissions (Ton): Period Distribution EV 1 9756.52 4980.53 2 9842.63 4906.75 3 9886.82 4780.66 4 9909.72 4659.94 5 9976.96 4476.17 6 8541.12 4266.91 7 8600.67 4025.47 8 8652.67 3733.05 9 8686.70 3403.07 10 8785.32 2999.31 11 8768.56 2539.22 12 8868.17 2025.48 13 8961.34 1443.32 14 9028.29 753.85 15 9176.36 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 537.71 4281.65 260.42 2046.55 0.90 0.97 Infinity -Infinity 2 0.00 4803.54 -201.85 2326.46 0.90 1.00 0.99 1.00 3 0.00 5458.27 0.00 2619.13 0.90 0.97 Infinity -Infinity Reactive Power by DG Period PV Wind min max min max 1 -71.20 201.39 0.00 0.00 2 -206.94 295.32 -23.00 36.92 3 -188.74 296.60 -25.19 30.27 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 0.00 0.00 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 5( 2)| 16.49 200.22 537.70 4280.96 260.42 2045.95 | 5( 2)| 0.00 400.00 -4.46 4803.06 -201.90 2325.89 | 5( 2)| 0.00 400.00 -4.46 5459.78 -2.59 2619.29 2- 3 | 5( 2)| 15.68 198.81 530.44 4255.25 251.01 2025.19 | 5( 2)| 0.00 203.93 -14.60 4773.47 -214.50 2303.40 | 5( 2)| 0.00 201.09 -12.96 5428.23 -14.35 2594.21 3- 4 | 5( 2)| 0.00 168.71 381.19 3757.48 67.23 1643.34 | 5( 2)| 0.00 177.90 322.13 4184.27 -283.63 1885.56 | 5( 2)| 0.00 170.64 280.04 4725.07 -442.83 2134.96 4- 5 | 5( 2)| 0.00 121.07 120.70 2892.08 -232.00 1028.82 | 5( 2)| 0.00 121.35 65.65 3161.91 -681.15 1203.17 | 5( 2)| 0.00 121.65 22.20 3428.61 -658.77 1330.90 5- 6 | 5( 2)| 0.00 120.27 113.94 2867.67 -241.37 1008.40 | 5( 2)| 0.00 120.66 59.05 3146.75 -694.35 1182.25 | 5( 2)| 0.00 120.59 15.42 3433.72 -667.34 1312.09 6- 7 | 5( 2)| 0.00 119.49 107.19 2843.42 -250.73 987.98 | 5( 2)| 0.00 119.98 52.49 3132.21 -707.57 1161.41 | 5( 2)| 0.00 119.54 8.66 3440.29 -675.90 1293.38 7- 8 | 5( 2)| 0.00 117.77 95.64 2804.73 -264.59 960.60 | 5( 2)| 0.00 118.47 41.14 3089.99 -726.17 1129.89 | 5( 2)| 0.00 117.47 -2.79 3392.83 -688.61 1265.10 8- 9 | 5( 2)| 0.00 110.70 51.77 2659.39 -148.82 990.16 | 5( 2)| 0.00 112.12 -21.40 2921.00 -627.11 1098.79 | 5( 2)| 0.00 109.44 -65.53 3183.94 -709.20 1280.22 9- 10 | 5( 2)| 0.00 12.37 -52.04 1004.39 -828.40 -249.98 | 5( 2)| 0.00 20.15 -277.39 1166.24 -1361.19 -288.60 | 5( 2)| 0.00 400.00 -312.28 1464.53 -1461.48 -87.05 10- 11 | 5( 2)| 0.00 54.55 -59.92 977.37 212.23 647.69 | 5( 2)| 0.00 400.00 -283.21 1133.61 36.52 724.86 | 5( 2)| 0.00 76.52 -316.76 1423.44 130.98 845.48 11- 12 | 3( 1)| 16.13 46.22 239.91 810.86 255.25 567.19 | 3( 1)| 9.36 53.44 203.36 958.50 219.42 644.78 | 3( 1)| 0.00 230.00 166.16 1201.99 226.56 736.97 12- 13 | 3( 1)| 12.10 34.94 181.61 614.21 189.34 420.89 | 3( 1)| 0.00 230.00 157.28 722.85 153.21 477.26 | 3( 1)| 0.00 230.00 97.03 907.15 143.12 545.80 13- 14 | 1( 1)| 11.36 32.78 169.67 572.14 177.99 394.91 | 1( 1)| 0.00 140.00 135.24 672.32 141.89 447.40 | 1( 1)| 0.00 140.00 89.10 843.00 121.28 511.47 14- 15 | 1( 1)| 10.57 30.54 157.77 530.49 165.44 366.67 | 1( 1)| 0.00 140.00 77.79 622.33 129.35 414.97 | 1( 1)| 0.00 140.00 29.81 779.66 98.38 473.82 15- 16 | 1( 1)| 10.03 29.05 150.47 505.71 156.16 346.39 | 1( 1)| 0.00 33.40 72.60 592.75 120.02 391.74 | 1( 1)| 0.00 40.88 27.78 742.61 91.91 447.32 16- 17 | 1( 1)| 9.16 26.51 137.23 460.84 142.45 315.95 | 1( 1)| 0.00 30.44 63.20 539.22 106.40 356.89 | 1( 1)| 0.00 140.00 24.10 675.60 82.47 407.54 17- 18 | 1( 1)| 8.07 23.29 119.78 402.25 126.80 280.96 | 1( 1)| 0.00 140.00 50.77 469.42 90.65 316.85 | 1( 1)| 0.00 32.58 19.22 588.53 71.54 361.91 18- 19 | 1( 1)| 6.99 20.07 102.29 343.38 111.13 245.91 | 1( 1)| 0.00 22.90 38.34 399.26 74.89 276.73 | 1( 1)| 0.00 27.90 14.34 500.93 60.62 316.16 19- 20 | 1( 1)| 6.62 18.86 95.02 318.87 106.87 236.11 | 1( 1)| 0.00 140.00 32.64 370.04 70.61 265.51 | 1( 1)| 0.00 26.11 12.31 464.44 57.64 303.36 20- 21 | 1( 1)| 6.07 17.23 86.26 289.33 98.80 217.88 | 1( 1)| 0.00 140.00 24.14 334.83 62.50 244.65 | 1( 1)| 0.00 140.00 -10.40 420.44 47.42 279.57 21- 22 | 1( 1)| 3.78 10.67 53.13 178.24 61.87 136.19 | 1( 1)| 0.00 140.00 -8.14 203.04 25.33 151.19 | 1( 1)| 0.00 14.29 -19.64 256.13 21.64 173.08 22- 23 | 1( 1)| 2.78 7.82 38.64 129.63 45.91 100.88 | 1( 1)| 0.00 140.00 -31.95 145.14 9.27 110.80 | 1( 1)| 0.00 10.07 -30.27 183.94 10.50 127.05 23- 24 | 1( 1)| 2.23 6.31 31.39 105.30 36.63 80.70 | 1( 1)| 0.00 6.78 -39.01 116.17 -0.06 87.71 | 1( 1)| 0.00 140.00 -38.88 147.81 4.03 100.74 24- 25 | 1( 1)| 1.67 4.71 23.34 78.27 27.51 60.52 | 1( 1)| 0.00 4.83 -46.98 83.44 -9.24 64.62 | 1( 1)| 0.00 140.00 -54.03 107.01 -2.33 74.43 25- 26 | 1( 1)| 1.13 3.21 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 140.00 -54.85 54.79 -18.57 41.54 | 1( 1)| 0.00 140.00 -58.95 70.94 -13.00 48.14 26- 27 | 1( 1)| 0.56 1.60 8.05 26.99 9.12 20.17 | 1( 1)| 0.00 0.46 -65.54 22.63 -27.75 31.51 | 1( 1)| 0.00 0.00 -66.92 30.19 -19.37 33.85 3- 28 | 1( 1)| 0.00 10.88 56.34 188.91 72.50 159.36 | 1( 1)| 0.00 12.70 -149.47 222.38 -11.09 180.58 | 1( 1)| 0.00 140.00 -129.18 276.48 0.20 190.75 28- 29 | 1( 1)| 0.00 9.49 48.82 163.72 63.99 140.53 | 1( 1)| 0.00 11.08 -159.98 192.88 -21.86 173.29 | 1( 1)| 0.00 12.95 -142.38 239.79 -10.77 177.66 29- 30 | 1( 1)| 0.00 8.11 41.31 138.53 55.48 121.70 | 1( 1)| 0.00 9.47 -170.49 163.30 -33.20 166.00 | 1( 1)| 0.00 140.00 -155.58 203.10 -21.74 170.47 30- 31 | 1( 1)| 0.00 6.72 34.07 114.24 46.21 101.53 | 1( 1)| 0.00 7.85 -180.63 134.87 -45.56 158.06 | 1( 1)| 0.00 9.16 -168.31 167.73 -33.69 164.44 31- 32 | 1( 1)| 0.00 5.33 26.83 89.95 36.93 81.36 | 1( 1)| 0.00 6.24 -190.76 106.41 -57.91 150.11 | 1( 1)| 0.00 7.27 -181.04 132.35 -48.55 158.41 32- 33 | 1( 1)| 0.00 3.85 18.78 62.97 27.81 61.19 | 1( 1)| 0.00 140.00 -202.21 74.25 -70.06 142.30 | 1( 1)| 0.00 140.00 -195.41 92.38 -63.91 144.00 33- 34 | 1( 1)| 0.00 2.38 10.73 35.98 18.70 41.02 | 1( 1)| 0.00 140.00 -213.66 42.11 -87.30 111.70 | 1( 1)| 0.00 140.00 -209.79 52.42 -79.26 112.72 34- 35 | 1( 1)| 0.00 0.94 5.23 17.54 5.47 12.10 | 1( 1)| 0.00 140.00 -241.63 20.53 -105.25 80.65 | 1( 1)| 0.00 140.00 -245.67 25.55 -103.69 84.27 3- 36 | 1( 1)| 0.00 16.18 85.71 288.65 99.56 218.94 | 1( 1)| 0.00 18.63 -473.87 337.89 -121.07 228.90 | 1( 1)| 0.00 22.28 -493.97 420.51 -166.77 262.11 36- 37 | 1( 1)| 0.00 14.77 78.20 263.42 91.04 200.10 | 1( 1)| 0.00 17.02 -477.89 308.36 -130.11 209.21 | 1( 1)| 0.00 20.35 -494.29 383.80 -172.64 241.11 37- 38 | 1( 1)| 0.00 13.35 70.69 238.18 82.53 181.26 | 1( 1)| 0.00 15.40 -481.93 278.82 -139.17 189.51 | 1( 1)| 0.00 18.42 -494.60 347.09 -178.51 235.58 38- 39 | 1( 1)| 0.00 11.93 63.44 213.88 73.26 161.09 | 1( 1)| 0.00 13.78 -485.81 250.38 -149.02 168.42 | 1( 1)| 0.00 16.49 -494.90 311.72 -184.90 229.55 39- 40 | 1( 1)| 0.00 10.62 56.47 190.47 65.51 143.94 | 1( 1)| 0.00 13.85 -489.56 222.98 -157.26 150.49 | 1( 1)| 0.00 14.91 -495.19 277.65 -190.24 224.51 40- 41 | 1( 1)| 0.00 9.30 49.49 166.92 57.76 126.76 | 1( 1)| 0.00 14.66 -493.69 195.35 -165.61 132.51 | 1( 1)| 0.00 140.00 -523.32 243.20 -205.38 209.67 41- 42 | 1( 1)| 0.00 7.87 42.25 142.58 48.49 106.57 | 1( 1)| 0.00 140.00 -497.77 166.85 -175.52 111.41 | 1( 1)| 0.00 140.00 -523.60 207.71 -211.82 203.55 42- 43 | 1( 1)| 0.00 6.48 35.01 118.29 39.21 86.40 | 1( 1)| 0.00 16.67 -501.67 138.43 -185.38 90.32 | 1( 1)| 0.00 20.98 -523.53 172.32 -218.22 197.51 43- 44 | 1( 1)| 0.00 5.51 29.78 100.75 33.29 73.29 | 1( 1)| 0.00 17.09 -504.48 117.90 -191.68 76.61 | 1( 1)| 0.00 20.90 -523.45 146.76 -222.31 193.65 44- 45 | 1( 1)| 0.00 4.13 22.53 76.46 24.02 53.12 | 1( 1)| 0.00 17.81 -508.43 89.47 -203.63 55.53 | 1( 1)| 0.00 20.78 -523.46 111.38 -228.72 187.59 45- 46 | 1( 1)| 0.00 2.06 11.27 38.23 12.01 26.56 | 1( 1)| 0.00 140.00 -514.60 44.74 -219.79 27.76 | 1( 1)| 0.00 20.75 -523.35 55.69 -237.01 179.76 4- 47 | 5( 2)| 17.51 48.43 253.26 850.74 285.96 632.47 | 5( 2)| 12.85 56.27 135.37 1012.45 244.96 723.67 | 5( 2)| 8.44 68.31 -4.59 1262.60 185.84 824.71 47- 48 | 3( 1)| 16.97 47.00 245.98 826.16 276.67 612.18 | 3( 1)| 12.44 54.61 131.48 983.13 237.01 700.44 | 3( 1)| 8.16 66.32 -4.46 1225.97 179.80 798.20 48- 49 | 3( 1)| 15.39 42.65 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.56 119.16 890.51 214.86 634.65 | 3( 1)| 7.44 230.00 -4.07 1110.27 163.09 723.14 49- 50 | 1( 1)| 7.70 21.33 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 140.00 59.58 445.19 107.43 317.31 | 1( 1)| 3.72 140.00 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 0.00 4.16 22.27 74.66 -141.06 51.67 | 1( 1)| 0.00 4.85 24.94 88.94 -140.28 58.34 | 1( 1)| 0.00 5.89 18.98 110.88 -145.46 66.80 51- 52 | 1( 1)| 0.74 2.05 10.46 35.08 12.31 27.23 | 1( 1)| 0.79 140.00 5.59 41.79 10.55 31.15 | 1( 1)| 0.78 140.00 -0.19 52.10 8.07 35.50 9- 53 | 5( 2)| 0.00 54.52 96.73 1637.59 424.55 1332.61 | 5( 2)| 0.00 55.08 83.97 1739.82 381.85 1531.12 | 5( 2)| 0.00 21.44 58.42 1798.39 309.03 1783.13 53- 54 | 5( 2)| 0.00 50.41 85.11 1602.03 408.29 1297.20 | 5( 2)| 0.00 52.06 73.40 1704.63 366.93 1492.80 | 5( 2)| 0.00 0.00 48.54 1761.54 298.09 1738.25 54- 55 | 5( 2)| 0.00 48.30 78.82 1585.16 399.60 1278.04 | 5( 2)| 0.00 50.37 68.30 1694.10 359.02 1472.17 | 5( 2)| 0.00 0.00 44.12 1749.17 292.34 1715.41 55- 56 | 5( 2)| 0.00 46.67 73.22 1570.52 391.69 1260.57 | 5( 2)| 0.00 48.81 63.88 1686.30 351.81 1453.38 | 5( 2)| 0.00 0.00 40.35 1739.53 287.11 1694.78 56- 57 | 5( 2)| 0.00 45.97 74.01 1595.85 384.22 1242.37 | 5( 2)| 0.00 400.00 -284.60 1771.16 259.97 1434.63 | 5( 2)| 0.00 400.00 -531.52 1937.03 113.72 1684.40 57- 58 | 5( 2)| 0.00 44.50 70.64 1595.85 375.10 1222.09 | 5( 2)| 0.00 46.75 -279.57 1798.60 252.37 1413.10 | 5( 2)| 0.00 400.00 -552.88 2035.15 107.95 1664.29 58- 59 | 5( 2)| 0.00 42.61 64.91 1581.09 365.81 1202.06 | 5( 2)| 0.00 44.88 -280.27 1791.81 244.57 1391.54 | 5( 2)| 0.00 400.00 -549.57 2052.52 101.80 1640.40 59- 60 | 5( 2)| 0.00 34.00 38.04 1496.96 332.68 1130.40 | 5( 2)| 0.00 400.00 -292.75 1706.50 174.08 1313.48 | 5( 2)| 0.00 0.00 -545.98 1980.48 79.49 1548.90 60- 61 | 5( 2)| 0.00 31.80 33.58 1488.68 323.48 1110.66 | 5( 2)| 0.00 34.29 -291.28 1715.55 166.39 1292.10 | 5( 2)| 0.00 400.00 -539.87 2036.90 73.53 1526.79 61- 62 | 5( 2)| 0.00 0.00 -325.96 296.14 -87.62 277.98 | 5( 2)| 0.00 0.00 -506.46 309.32 -180.94 329.49 | 5( 2)| 0.00 0.00 -554.60 322.63 -205.96 358.13 62- 63 | 5( 2)| 0.00 0.00 -333.64 271.36 -98.13 258.57 | 5( 2)| 0.00 0.00 -509.02 287.22 -189.79 304.72 | 5( 2)| 0.00 0.00 -553.17 298.56 -213.02 329.55 63- 64 | 5( 2)| 0.00 0.00 -332.79 275.36 -106.96 242.05 | 5( 2)| 0.00 400.00 -524.48 325.82 -197.09 296.59 | 5( 2)| 0.00 400.00 -573.26 405.60 -218.57 311.08 64- 65 | 1( 1)| 1.17 3.41 17.17 57.57 19.15 42.36 | 1( 1)| 1.35 140.00 9.18 68.57 16.41 48.46 | 1( 1)| 1.24 140.00 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 1.97 -342.09 34.69 -143.79 40.04 | 1( 1)| 0.00 140.00 -623.87 41.05 -284.82 217.24 | 1( 1)| 0.00 140.00 -632.57 51.10 -269.89 201.82 66- 67 | 1( 1)| 0.00 0.99 -347.32 17.35 -153.51 34.03 | 1( 1)| 0.00 29.64 -626.80 20.53 -290.08 212.07 | 1( 1)| 0.00 140.00 -632.66 25.55 -277.46 194.39 12- 68 | 1( 1)| 1.12 3.15 16.10 53.97 18.24 40.34 | 1( 1)| 0.80 140.00 8.75 65.36 15.63 46.15 | 1( 1)| 0.50 140.00 -0.30 81.49 11.80 52.59 68- 69 | 1( 1)| 0.56 1.57 8.05 26.99 9.12 20.17 | 1( 1)| 0.41 140.00 4.37 32.68 7.81 23.08 | 1( 1)| 0.27 140.00 -0.15 40.74 5.90 26.29 Voltage p.u. min max 1 0.97 1.00 2 0.97 1.01 3 0.96 1.01 Elapsed AMPL time : 5.501s Elapsed Solve time : 48.531s Elapsed CPU time: 54.032s Sumatorio de erros e2 33926.36316 Sumatorio de erros pq 45106.12098 Sumatorio de erros vi 197.55451 Maximum Psae error 0.00000 Maximo erro superior 8765.9449 Maximo erro inferior -6.0105 TRANSITION 3 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886891 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 16458.45 44 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 16129.83 2884.42 13245.42 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2205.89/ 2057.96/ 650.42 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 0.00 112.06 132.33 959.01 303.90 0.00 51 0.00 0.00 0.00 230.97 0.00 0.00 64 60.85 0.00 0.00 1180.08 0.00 0.00 PV systems (kW): Node T1 T2 T3 35.00 81.49 81.69 0.00 46.00 75.25 393.36 0.00 64.00 800.00 0.00 0.00 67.00 459.35 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 0.00 530.95 0.00 50.00 0.00 0.00 166.30 69.00 0.00 411.20 213.88 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 0.00 86.42 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 34.60 34.60 42.81 72.59 Structures 21.57 21.57 25.68 44.87 Fixed CBs 0.15 0.43 0.76 0.71 Switchable CBs 7.96 8.98 8.98 17.00 PV systems 876.93 1095.54 1095.54 1979.56 Wind systems 0.00 660.30 885.53 751.41 EES systems 0.00 0.00 47.42 18.28 Total invesment cost 941.22 1821.43 2106.73 2884.42 Purchased energy cost 5640.47 6089.14 7282.91 12229.22 Carbon tax payment 194.93 341.89 719.19 684.49 O&M PV cost 85.82 91.92 86.74 176.34 O&M wind cost 0.00 131.44 181.96 151.77 O&M EES cost 0.00 0.00 9.33 3.60 Total O&M cost 5921.22 6654.39 8280.13 13245.42 Total cost 6862.44 8475.81 10386.86 16129.83 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 14128.86 0.00 130306.45 685.02 0.00 2 112610.17 18868.42 10064.31 141404.09 1047.98 0.00 3 131749.94 18868.55 14125.27 161754.72 1873.29 57.97 CO2 Emissions (Ton): Period Distribution EV 1 9741.36 4980.53 2 9835.80 4906.75 3 9887.38 4780.66 4 9916.83 4659.94 5 9991.28 4476.17 6 8504.95 4266.91 7 8589.51 4025.47 8 8665.82 3733.05 9 8717.00 3403.07 10 8849.49 2999.31 11 8849.34 2539.22 12 8991.13 2025.48 13 9125.81 1443.32 14 9219.78 753.85 15 9435.66 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 243.67 4505.03 118.01 2025.36 0.90 0.98 Infinity -Infinity 2 0.00 5192.15 -14.00 2318.80 0.90 1.00 1.00 1.00 3 0.00 6470.72 -6.09 2632.77 0.90 0.97 0.95 1.00 Reactive Power by DG Period PV Wind min max min max 1 -70.07 166.68 0.00 0.00 2 -200.42 169.57 -81.78 91.83 3 -207.91 173.74 -78.96 94.21 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 0.00 0.00 69.14 69.14 345.69 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 86.42 86.42 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 0.00 224.62 243.67 4504.11 118.01 2024.62 | 4( 2)| 0.00 257.91 0.00 5190.89 -14.09 2317.78 | 4( 2)| 0.00 314.86 0.00 6468.74 -6.09 2631.23 2- 3 | 4( 2)| 0.00 223.26 236.45 4477.82 108.62 2003.49 | 4( 2)| 0.00 256.32 -8.01 5158.85 -26.80 2294.16 | 4( 2)| 0.00 312.83 -8.18 6427.78 -14.59 2601.96 3- 4 | 4( 2)| 3.64 195.78 208.78 3979.44 -22.22 1624.86 | 4( 2)| 0.00 225.84 94.07 4617.85 -206.21 1875.23 | 4( 2)| 0.00 275.46 -278.33 5735.59 -458.12 2124.01 4- 5 | 4( 1)| 9.54 149.11 -51.71 3113.77 -321.45 1009.56 | 4( 1)| 5.10 169.72 -159.74 3575.94 -554.87 1192.40 | 4( 1)| 0.00 206.55 -244.70 4448.77 -660.62 1304.70 5- 6 | 4( 1)| 9.59 147.74 -59.01 3081.93 -330.89 986.25 | 4( 1)| 4.14 168.08 -166.84 3535.73 -568.24 1163.67 | 4( 1)| 0.00 204.68 -244.41 4393.61 -669.03 1267.59 6- 7 | 4( 1)| 9.66 146.38 -66.31 3050.05 -340.34 962.89 | 4( 1)| 2.97 166.45 -173.94 3495.55 -581.63 1134.87 | 4( 1)| 0.00 202.82 -244.08 4338.56 -677.89 1236.70 7- 8 | 4( 1)| 9.81 144.28 -78.00 3009.44 -354.22 934.77 | 4( 1)| 0.00 163.96 -185.33 3446.21 -600.28 1101.38 | 4( 1)| 0.00 199.74 -244.41 4275.85 -690.68 1204.56 8- 9 | 4( 1)| 0.00 137.15 -122.01 2862.45 -255.82 965.74 | 4( 1)| 0.00 156.90 -228.22 3268.84 -502.95 1075.50 | 4( 1)| 0.00 190.47 -246.12 4053.85 -737.11 1266.55 9- 10 | 4( 1)| 0.00 47.56 -55.74 1002.27 -551.15 556.89 | 4( 1)| 0.00 59.11 -450.49 1091.47 -1272.06 423.54 | 4( 1)| 0.00 69.13 -663.96 1377.07 -1416.86 289.19 10- 11 | 4( 1)| 11.42 53.80 -63.81 975.28 211.04 647.45 | 4( 1)| 7.17 58.57 -456.44 1058.52 95.22 710.42 | 4( 1)| 5.45 72.35 -666.47 1335.96 84.79 830.51 11- 12 | 3( 1)| 16.01 45.42 239.68 808.74 255.23 566.96 | 3( 1)| 0.00 49.63 -243.35 890.98 207.07 617.34 | 3( 1)| 0.00 60.24 -423.06 1114.39 163.12 703.13 12- 13 | 2( 1)| 12.00 34.25 181.38 612.21 189.32 420.70 | 3( 1)| 0.00 38.09 -91.79 688.29 162.35 463.68 | 3( 1)| 0.00 46.73 -153.24 868.55 155.53 532.30 13- 14 | 2( 1)| 11.27 32.19 169.65 571.95 177.99 394.87 | 3( 1)| 0.00 35.71 -102.92 640.49 147.27 434.09 | 3( 1)| 0.00 43.84 -156.42 808.42 147.68 498.35 14- 15 | 1( 1)| 10.49 29.99 157.77 530.40 165.44 366.65 | 1( 1)| 0.00 33.15 -114.44 590.98 130.54 401.75 | 3( 1)| 1.25 195.87 -161.58 748.62 135.99 461.02 15- 16 | 1( 1)| 9.95 28.52 150.47 505.64 156.16 346.37 | 1( 1)| 0.00 31.44 -121.52 561.49 118.12 378.54 | 3( 1)| 0.00 38.79 -166.49 712.17 129.99 434.57 16- 17 | 1( 1)| 9.08 26.04 137.23 460.80 142.45 315.94 | 1( 1)| 0.00 28.53 -134.38 508.09 99.80 343.72 | 1( 1)| 0.00 35.23 -175.44 645.32 121.23 394.82 17- 18 | 1( 1)| 8.01 22.87 119.78 402.21 126.79 280.95 | 1( 1)| 0.00 24.83 -151.37 438.31 78.83 303.69 | 1( 1)| 0.00 30.65 -187.29 558.28 111.10 349.20 18- 19 | 1( 1)| 6.94 19.70 102.29 343.36 111.13 245.90 | 1( 1)| 0.00 21.12 -168.40 368.24 57.86 263.59 | 1( 1)| 0.00 26.06 -199.15 470.78 92.58 303.48 19- 20 | 1( 1)| 6.57 18.52 95.02 318.86 106.87 236.10 | 1( 1)| 0.00 19.73 -175.48 339.07 52.16 252.38 | 1( 1)| 0.00 24.31 -204.08 434.34 85.56 290.69 20- 21 | 1( 1)| 6.02 16.92 86.26 289.33 98.80 217.88 | 1( 1)| 0.00 17.86 -184.01 303.93 41.36 231.53 | 1( 1)| 0.00 22.00 -210.02 390.42 72.28 266.91 21- 22 | 1( 1)| 3.75 10.48 53.13 178.23 61.87 136.19 | 1( 1)| 0.00 10.32 -222.59 173.84 -8.11 139.57 | 1( 1)| 0.00 12.79 -232.44 226.11 11.40 160.42 22- 23 | 1( 1)| 2.76 7.67 38.64 129.63 45.91 100.88 | 1( 1)| 0.00 7.36 -241.54 116.88 -29.49 124.67 | 1( 1)| 0.00 8.81 -247.65 153.94 -14.90 114.39 23- 24 | 1( 1)| 2.22 6.20 31.39 105.30 36.63 80.70 | 1( 1)| 0.00 7.53 -251.04 88.39 -41.91 116.01 | 1( 1)| 0.00 7.08 -256.31 117.83 -30.19 104.68 24- 25 | 1( 1)| 1.66 4.63 23.34 78.27 27.51 60.52 | 1( 1)| 0.00 7.80 -261.83 56.20 -54.22 107.47 | 1( 1)| 0.00 8.11 -266.16 77.04 -45.22 97.30 25- 26 | 1( 1)| 1.12 3.15 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 8.03 -271.35 27.73 -66.79 98.81 | 1( 1)| 0.00 8.26 -274.83 42.51 -60.50 89.81 26- 27 | 1( 1)| 0.56 1.58 8.05 26.99 9.12 20.17 | 1( 1)| 0.00 8.35 -282.07 -3.11 -79.29 90.29 | 1( 1)| 0.00 8.69 -284.59 3.60 -75.54 82.46 3- 28 | 1( 1)| 0.00 10.87 -6.89 187.02 42.86 156.19 | 1( 1)| 0.00 12.69 -41.16 222.38 29.65 167.45 | 1( 1)| 0.00 15.35 -57.02 626.43 33.87 259.21 28- 29 | 1( 1)| 0.00 9.49 -14.40 162.09 34.23 137.36 | 1( 1)| 0.00 11.08 -51.46 192.88 20.44 147.30 | 1( 1)| 0.00 13.39 -65.37 626.10 23.07 253.67 29- 30 | 1( 1)| 0.00 8.10 -21.91 137.10 25.61 118.52 | 1( 1)| 0.00 9.47 -61.97 163.30 11.22 132.78 | 1( 1)| 0.00 12.67 -73.73 625.78 12.27 248.11 30- 31 | 1( 1)| 0.00 6.72 -29.16 113.08 16.21 98.35 | 1( 1)| 0.00 7.85 -72.10 134.87 1.19 124.75 | 1( 1)| 0.00 12.29 -81.79 625.48 0.51 242.08 31- 32 | 1( 1)| 0.00 5.33 -36.40 89.03 6.81 78.17 | 1( 1)| 0.00 6.23 -82.24 106.41 -8.85 116.72 | 1( 1)| 0.00 11.92 -89.86 625.18 -11.25 236.03 32- 33 | 1( 1)| 0.00 3.85 -44.45 62.30 -2.43 57.99 | 1( 1)| 0.00 4.49 -93.68 74.25 -19.23 108.82 | 1( 1)| 0.00 6.19 -99.00 624.84 -22.83 230.10 33- 34 | 1( 1)| 0.00 2.38 -52.49 35.59 -11.67 37.98 | 1( 1)| 0.00 140.00 -117.86 42.11 -38.24 78.13 | 4( 1)| 0.00 359.08 -123.64 52.42 -34.41 74.26 34- 35 | 1( 1)| 0.00 0.94 -57.99 17.35 -25.08 11.21 | 1( 1)| 0.00 140.00 -125.63 20.53 -52.50 46.95 | 1( 1)| 0.00 140.00 -129.12 25.55 -51.19 45.97 3- 36 | 1( 1)| 2.50 15.98 27.32 285.50 78.58 215.92 | 1( 1)| 0.00 18.63 -321.82 337.89 -69.21 228.90 | 1( 1)| 0.00 22.63 -370.77 420.73 -104.84 262.16 36- 37 | 1( 1)| 1.69 14.60 19.81 260.55 69.95 197.09 | 1( 1)| 0.00 17.01 -325.86 308.36 -76.59 209.21 | 1( 1)| 0.00 20.66 -370.69 383.97 -110.72 239.60 37- 38 | 1( 1)| 0.00 13.21 12.30 235.59 61.32 178.25 | 1( 1)| 0.00 15.40 -329.94 278.82 -83.97 189.51 | 1( 1)| 0.00 18.70 -370.65 347.17 -116.60 217.04 38- 39 | 1( 1)| 0.00 11.82 5.06 211.56 51.92 158.08 | 1( 1)| 0.00 14.16 -333.83 250.38 -92.01 168.42 | 1( 1)| 0.00 17.68 -370.55 311.77 -123.00 192.89 39- 40 | 1( 1)| 0.00 10.54 -1.92 188.41 44.07 140.92 | 1( 1)| 0.00 14.44 -337.60 222.98 -98.73 150.49 | 1( 1)| 0.00 17.57 -370.49 277.65 -128.36 175.42 40- 41 | 1( 1)| 0.00 9.26 -8.89 165.09 36.21 123.74 | 1( 1)| 0.00 14.71 -341.81 195.35 -105.55 132.51 | 1( 1)| 0.00 16.85 -370.99 243.20 -133.82 168.10 41- 42 | 1( 1)| 0.00 7.87 -16.14 141.01 26.81 103.56 | 1( 1)| 0.00 15.01 -345.89 166.85 -113.63 111.41 | 1( 1)| 0.00 16.72 -371.12 207.71 -140.27 159.42 42- 43 | 1( 1)| 0.00 6.48 -23.38 116.99 17.42 83.39 | 1( 1)| 0.00 15.32 -349.80 138.43 -121.67 90.32 | 1( 1)| 0.00 16.60 -371.02 172.32 -146.67 150.79 43- 44 | 1( 1)| 0.00 5.51 -28.61 99.64 11.41 70.27 | 1( 1)| 0.00 15.54 -352.60 117.90 -126.81 76.61 | 1( 1)| 0.00 16.53 -370.94 146.76 -150.76 145.27 44- 45 | 1( 1)| 0.00 4.12 -35.85 75.61 1.48 50.10 | 1( 1)| 0.00 15.85 -356.55 89.47 -136.25 55.53 | 1( 1)| 0.00 16.41 -370.89 111.38 -157.17 137.42 45- 46 | 1( 1)| 0.00 2.06 -47.12 37.81 -12.72 24.59 | 1( 1)| 0.00 16.32 -362.71 44.74 -150.97 27.76 | 1( 1)| 0.00 16.27 -370.74 55.69 -165.46 129.60 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.94 67.58 -36.91 1249.49 196.46 819.31 47- 48 | 4( 1)| 16.97 46.97 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.57 131.48 983.13 237.01 700.44 | 4( 1)| 8.66 65.58 -36.78 1213.21 190.43 792.82 48- 49 | 3( 1)| 15.39 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.89 59.41 -36.40 1097.57 173.72 717.78 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 0.00 29.39 -39.81 542.34 74.48 356.19 8- 51 | 1( 1)| 0.00 8.97 22.27 74.66 -205.74 42.95 | 1( 1)| 0.00 8.88 11.90 88.94 -205.58 51.78 | 1( 1)| 0.00 9.06 -0.41 110.88 -206.85 53.02 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 9.27 98.72 -75.09 1829.35 -269.21 1214.92 | 4( 1)| 9.76 115.59 58.19 2179.78 34.25 1380.63 | 4( 1)| 12.40 133.96 34.45 2682.96 254.54 1698.39 53- 54 | 4( 1)| 7.21 96.29 -87.64 1786.06 -293.48 1178.40 | 4( 1)| 8.15 112.77 45.21 2127.44 5.04 1338.59 | 4( 1)| 11.14 130.57 21.84 2616.17 237.87 1649.99 54- 55 | 4( 1)| 5.83 94.88 -95.22 1758.81 -306.46 1158.07 | 4( 1)| 6.90 111.17 37.33 2093.73 -10.76 1315.01 | 4( 1)| 10.42 128.82 14.09 2572.09 228.91 1622.45 55- 56 | 4( 1)| 4.27 93.60 -102.12 1733.87 -318.27 1139.46 | 4( 1)| 5.57 109.71 30.14 2062.83 -25.18 1294.35 | 4( 1)| 9.75 127.36 7.02 2531.60 220.73 1597.18 56- 57 | 4( 1)| 0.00 92.48 -108.67 1702.43 -329.44 1115.94 | 4( 1)| 4.11 400.00 -353.47 2019.48 -40.26 1270.47 | 4( 1)| 9.18 400.00 -493.02 2468.52 151.99 1561.07 57- 58 | 4( 1)| 0.00 91.17 -115.71 1674.84 -343.06 1092.93 | 4( 1)| 0.00 107.25 -357.90 1984.29 -57.33 1246.41 | 4( 1)| 8.40 126.65 -493.82 2421.18 145.40 1528.50 58- 59 | 4( 1)| 0.00 89.79 -122.88 1649.54 -356.92 1071.73 | 4( 1)| 0.00 105.68 -361.98 1953.46 -74.16 1223.87 | 4( 1)| 7.55 124.93 -494.31 2381.64 138.93 1499.88 59- 60 | 4( 1)| 0.00 84.38 -151.77 1552.10 -406.32 1000.99 | 4( 1)| 0.00 99.40 -377.74 1837.21 -133.43 1144.61 | 4( 1)| 3.26 117.51 -495.75 2235.80 116.19 1402.59 60- 61 | 4( 1)| 0.00 83.04 -158.92 1526.51 -420.00 980.02 | 4( 1)| 0.00 97.88 -381.96 1805.89 -150.20 1121.72 | 4( 1)| 0.00 115.90 -496.38 2195.89 109.67 1373.00 61- 62 | 1( 1)| 0.00 22.92 -519.60 330.41 -1061.47 122.66 | 1( 1)| 0.00 27.36 -574.79 391.12 -896.97 239.85 | 1( 1)| 0.00 25.48 -528.92 469.13 -453.82 234.61 62- 63 | 1( 1)| 0.00 23.48 -529.24 299.65 -1078.13 100.48 | 1( 1)| 0.00 27.43 -579.93 354.69 -916.53 230.50 | 1( 1)| 0.00 25.65 -530.28 425.44 -475.86 227.74 63- 64 | 1( 1)| 0.00 23.86 -537.69 275.36 -1092.87 81.18 | 1( 1)| 0.00 27.48 -585.29 325.82 -933.82 221.94 | 1( 1)| 0.00 25.86 -532.53 390.76 -495.34 221.44 64- 65 | 1( 1)| 1.18 3.34 17.17 57.57 19.15 42.36 | 1( 1)| 0.88 3.89 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 140.00 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 15.97 -345.89 34.69 -145.56 31.32 | 1( 1)| 0.00 11.17 -355.91 41.05 -159.08 125.83 | 1( 1)| 0.00 12.22 -363.38 51.10 -154.01 122.25 66- 67 | 1( 1)| 0.21 16.68 -351.17 17.35 -155.31 25.30 | 1( 1)| 0.00 11.52 -358.71 20.53 -164.33 118.36 | 1( 1)| 0.00 12.53 -363.30 25.55 -159.54 114.74 12- 68 | 1( 1)| 1.11 3.10 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 1.74 -205.35 35.98 -43.51 85.43 | 1( 1)| 0.00 0.88 -327.05 36.25 -60.59 102.48 68- 69 | 1( 1)| 0.56 1.55 8.05 26.99 9.12 20.17 | 1( 1)| 0.00 0.00 -216.04 4.27 -57.15 76.92 | 1( 1)| 0.00 0.75 -336.77 -2.66 -77.40 90.31 Voltage p.u. min max 1 0.97 1.01 2 0.97 1.01 3 0.95 1.02 Elapsed AMPL time : 9.626s Elapsed Solve time : 101.093s Elapsed CPU time: 110.719s Sumatorio de erros e2 1529.74871 Sumatorio de erros pq 1756.41462 Sumatorio de erros vi 97.76620 Factor de erro e2 0.10 Factor de erro pq 0.10 Factor de erro vi 1.00 Maximum Psae error 81.99331 Maximo erro superior 8343.8472 Maximo erro inferior -1.2489 TRANSITION 4 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886866 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 16509.81937 45 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 16345.32 3059.56 13285.76 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2393.62/ 2168.92/ 461.66 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 298.91 0.00 0.00 538.13 380.22 197.35 51 0.00 0.00 0.00 198.72 59.52 0.00 64 45.78 0.00 0.00 652.88 134.93 0.00 PV systems (kW): Node T1 T2 T3 35.00 99.61 0.00 0.00 46.00 168.18 196.07 0.00 64.00 800.00 0.00 0.00 67.00 488.91 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 0.00 793.80 0.00 50.00 0.00 0.00 0.00 69.00 0.00 398.40 308.21 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 0.00 5.13 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 33.57 33.57 39.59 69.68 Structures 18.47 18.47 23.75 39.10 Fixed CBs 0.86 0.86 0.86 1.72 Switchable CBs 4.67 6.60 7.26 11.57 PV systems 964.01 1054.24 1054.24 2025.06 Wind systems 0.00 835.55 1018.14 911.35 EES systems 0.00 0.00 2.81 1.09 Total invesment cost 1021.58 1949.28 2146.65 3059.55 Purchased energy cost 5648.90 6088.62 7289.65 12239.93 Carbon tax payment 194.94 341.88 719.20 684.50 O&M PV cost 94.34 85.19 80.40 178.24 O&M wind cost 0.00 166.33 206.47 182.88 O&M EES cost 0.00 0.00 0.55 0.21 Total O&M cost 5938.18 6682.03 8296.26 13285.76 Total cost 6959.76 8631.31 10442.92 16345.32 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 15531.80 0.00 130306.45 913.85 0.00 2 112603.24 17487.83 12735.38 141404.09 1214.10 0.00 3 131748.61 17487.95 16027.51 161754.72 1856.30 3.30 CO2 Emissions (Ton): Period Distribution EV 1 9747.35 4980.53 2 9839.62 4906.75 3 9888.13 4780.66 4 9913.43 4659.94 5 9984.12 4476.17 6 8508.11 4266.91 7 8591.24 4025.47 8 8664.48 3733.05 9 8713.86 3403.07 10 8846.41 2999.31 11 8851.72 2539.22 12 8993.42 2025.48 13 9125.51 1443.32 14 9217.24 753.85 15 9433.36 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 135.67 4498.94 65.71 2004.97 0.90 0.98 Infinity -Infinity 2 0.00 5165.93 -0.00 2303.56 0.90 1.00 1.00 1.00 3 0.00 6520.69 -0.00 2633.75 0.90 1.00 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 -22.01 198.98 0.00 0.00 2 -206.94 186.36 -118.90 136.90 3 -207.91 187.23 -105.61 125.81 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 0.00 0.00 4.10 4.10 20.52 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 5.13 5.13 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 4.16 224.33 135.67 4498.07 65.71 2004.23 | 4( 2)| 0.00 257.15 0.00 5164.78 -0.00 2302.56 | 4( 2)| 0.00 320.71 0.00 6518.88 -0.00 2632.18 2- 3 | 4( 2)| 3.31 222.99 128.43 4471.88 56.31 1983.13 | 4( 2)| 0.41 255.54 -8.01 5133.02 -10.04 2279.02 | 4( 2)| 0.00 318.76 -8.18 6478.34 -11.76 2602.81 3- 4 | 4( 2)| 8.63 195.56 186.76 3973.60 -42.62 1607.78 | 4( 2)| 0.00 224.87 -21.54 4576.11 -207.05 1860.14 | 4( 2)| 0.00 280.87 -545.96 5770.81 -452.31 2117.20 4- 5 | 4( 1)| 12.06 149.01 -73.73 3108.01 -341.86 992.53 | 4( 1)| 7.01 169.11 -275.36 3534.38 -466.11 1177.34 | 4( 1)| 9.95 212.72 -573.19 4471.45 -644.19 1291.71 5- 6 | 4( 1)| 12.16 147.74 -81.07 3077.38 -351.33 968.02 | 4( 1)| 6.97 167.64 -282.61 3497.16 -474.37 1148.96 | 4( 1)| 10.66 211.00 -575.63 4421.57 -650.57 1256.85 6- 7 | 4( 1)| 12.28 146.47 -88.42 3046.66 -360.81 944.26 | 4( 1)| 6.97 166.16 -289.88 3459.83 -482.64 1120.50 | 4( 1)| 11.36 209.26 -578.08 4371.49 -656.95 1229.58 7- 8 | 4( 1)| 12.49 144.40 -100.12 3006.34 -374.70 916.17 | 4( 1)| 7.04 163.70 -301.31 3411.19 -494.67 1087.09 | 4( 1)| 12.25 206.25 -581.50 4309.98 -669.72 1197.59 8- 9 | 4( 1)| 5.30 137.84 -144.14 2859.61 -226.52 962.63 | 4( 1)| 0.00 156.68 -344.20 3234.45 -418.50 1056.56 | 4( 1)| 4.71 197.11 -593.90 4089.12 -680.62 1257.34 9- 10 | 3( 1)| 0.00 46.54 -78.44 1004.36 -538.46 105.90 | 3( 1)| 0.00 54.88 -562.34 1071.30 -1147.47 162.01 | 3( 1)| 0.00 71.64 -810.27 1355.35 -1425.73 262.74 10- 11 | 3( 1)| 11.02 53.94 -86.52 976.91 209.55 647.58 | 3( 1)| 6.06 57.65 -568.32 1037.79 62.10 700.39 | 3( 1)| 7.66 71.49 -813.16 1313.32 -16.85 815.19 11- 12 | 3( 1)| 16.04 45.58 239.89 810.44 255.24 567.09 | 3( 1)| 0.00 48.99 -365.21 872.86 106.72 608.99 | 3( 1)| 4.98 59.42 -592.26 1094.18 127.76 692.33 12- 13 | 2( 1)| 12.03 34.38 181.59 613.89 189.34 420.82 | 3( 1)| 0.00 37.30 -221.03 669.16 97.71 454.93 | 3( 1)| 3.98 46.16 -274.90 854.45 131.06 524.14 13- 14 | 1( 1)| 11.28 32.18 169.66 571.95 177.99 394.87 | 1( 1)| 0.90 34.74 -233.16 619.39 85.24 425.22 | 1( 1)| 3.67 42.97 -283.62 791.20 119.39 490.00 14- 15 | 1( 1)| 10.50 29.98 157.77 530.40 165.44 366.65 | 1( 1)| 0.00 32.18 -245.29 570.10 71.41 392.93 | 1( 1)| 2.52 51.76 -292.36 728.72 106.47 452.52 15- 16 | 1( 1)| 9.97 28.52 150.47 505.64 156.16 346.37 | 1( 1)| 0.00 30.47 -252.49 540.64 61.12 369.73 | 1( 1)| 1.55 37.63 -297.43 691.83 96.87 426.05 16- 17 | 1( 1)| 9.09 26.03 137.23 460.80 142.45 315.94 | 1( 1)| 0.00 27.57 -265.56 487.31 45.94 334.92 | 1( 1)| 0.00 34.08 -306.65 625.07 82.70 386.32 17- 18 | 1( 1)| 8.02 22.86 119.78 402.21 126.79 280.95 | 1( 1)| 0.00 23.87 -282.61 417.59 28.58 294.89 | 1( 1)| 0.00 29.51 -318.55 538.04 62.53 340.70 18- 19 | 1( 1)| 6.95 19.70 102.29 343.36 111.13 245.90 | 1( 1)| 0.00 20.18 -301.71 348.65 11.20 254.80 | 1( 1)| 0.00 24.95 -330.66 450.60 42.16 294.99 19- 20 | 1( 1)| 6.58 18.52 95.02 318.86 106.87 236.10 | 1( 1)| 0.00 18.80 -311.29 319.96 6.47 243.59 | 1( 1)| 0.00 23.21 -335.75 414.19 36.48 282.20 20- 21 | 1( 1)| 6.03 16.92 86.26 289.33 98.80 217.88 | 1( 1)| 0.00 16.93 -322.89 285.40 -2.48 222.76 | 1( 1)| 0.00 20.91 -341.95 370.33 26.10 258.44 21- 22 | 1( 1)| 3.75 10.48 53.13 178.23 61.87 136.19 | 1( 1)| 0.00 16.53 -366.20 155.71 -51.71 176.97 | 1( 1)| 0.00 16.76 -374.81 206.02 -23.22 155.80 22- 23 | 1( 1)| 2.76 7.67 38.64 129.63 45.91 100.88 | 1( 1)| 0.00 16.84 -385.26 98.75 -73.66 162.05 | 1( 1)| 0.00 16.97 -392.16 133.85 -49.53 142.91 23- 24 | 1( 1)| 2.22 6.20 31.39 105.30 36.63 80.70 | 1( 1)| 0.00 16.99 -395.02 70.26 -86.43 153.33 | 1( 1)| 0.00 17.14 -401.07 98.41 -64.82 135.37 24- 25 | 1( 1)| 1.66 4.62 23.34 78.27 27.51 60.52 | 1( 1)| 0.00 17.24 -406.38 38.09 -99.02 144.67 | 1( 1)| 0.00 17.54 -411.48 59.48 -79.90 127.88 25- 26 | 1( 1)| 1.12 3.15 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 17.66 -416.14 10.30 -111.80 135.96 | 1( 1)| 0.00 17.90 -420.39 25.03 -95.20 120.34 26- 27 | 1( 1)| 0.56 1.58 8.05 26.99 9.12 20.17 | 1( 1)| 0.33 18.15 -427.01 -19.30 -124.36 127.41 | 1( 1)| 0.00 18.32 -430.29 -12.74 -110.25 112.96 3- 28 | 1( 1)| 1.71 10.87 -20.82 187.02 36.08 147.64 | 1( 1)| 0.88 12.70 1.01 222.38 47.24 170.41 | 1( 1)| 0.00 38.91 -10.39 834.48 50.36 280.52 28- 29 | 1( 1)| 1.42 9.49 -28.33 162.09 27.45 130.15 | 1( 1)| 0.00 11.08 -7.30 192.88 38.48 149.77 | 1( 1)| 0.00 38.83 -18.74 834.35 42.26 274.92 29- 30 | 1( 1)| 1.23 8.11 -35.85 137.10 18.83 112.70 | 1( 1)| 0.00 9.47 -15.60 163.30 29.72 129.12 | 1( 1)| 0.00 38.75 -27.09 832.66 34.15 268.97 30- 31 | 1( 1)| 0.94 6.72 -43.09 113.08 9.43 94.03 | 1( 1)| 0.00 7.85 -25.28 134.87 20.18 107.02 | 1( 1)| 0.00 38.68 -35.15 832.46 23.13 262.87 31- 32 | 1( 1)| 0.18 5.33 -50.34 89.03 0.03 75.34 | 1( 1)| 0.00 6.24 -35.41 106.41 10.63 86.30 | 1( 1)| 0.00 38.59 -43.20 831.05 11.37 256.49 32- 33 | 1( 1)| 0.00 3.85 -58.40 62.30 -9.22 56.66 | 1( 1)| 0.00 4.49 -46.86 74.25 1.20 78.39 | 1( 1)| 0.00 38.52 -52.30 827.46 -0.20 249.71 33- 34 | 1( 1)| 0.51 3.06 -66.50 35.59 -18.47 37.98 | 1( 1)| 0.00 140.00 -69.41 42.11 -15.49 47.70 | 4( 1)| 0.00 400.00 -74.97 52.42 -16.03 57.74 34- 35 | 1( 1)| 0.00 3.52 -72.05 17.35 -31.88 11.21 | 1( 1)| 0.00 74.91 -75.59 20.53 -29.75 30.50 | 1( 1)| 0.00 140.00 -78.85 25.55 -28.63 29.45 3- 36 | 1( 1)| 0.00 15.98 -44.76 285.50 53.45 208.89 | 1( 1)| 0.00 18.63 -240.03 337.89 -52.45 228.90 | 1( 1)| 0.00 22.64 -288.69 420.73 -66.24 262.16 36- 37 | 1( 1)| 0.00 14.60 -52.27 260.55 44.83 190.06 | 1( 1)| 0.00 17.01 -244.07 308.36 -59.83 209.21 | 1( 1)| 0.00 20.67 -288.58 383.97 -72.11 239.60 37- 38 | 1( 1)| 0.00 13.21 -59.78 235.59 36.20 171.22 | 1( 1)| 0.00 15.40 -248.12 278.82 -67.21 189.51 | 1( 1)| 0.00 18.71 -288.51 347.17 -77.99 217.04 38- 39 | 1( 1)| 0.00 11.82 -67.03 211.56 26.49 151.75 | 1( 1)| 0.00 13.78 -252.00 250.38 -75.25 168.42 | 1( 1)| 0.00 16.75 -288.39 311.77 -84.39 192.89 39- 40 | 1( 1)| 0.00 10.54 -74.00 188.41 17.32 135.36 | 1( 1)| 0.00 12.29 -255.76 222.98 -81.97 150.49 | 1( 1)| 0.00 14.93 -288.31 277.65 -89.74 172.36 40- 41 | 1( 1)| 0.00 9.26 -80.98 165.09 8.15 118.94 | 1( 1)| 0.00 11.90 -259.80 195.35 -88.75 132.51 | 1( 1)| 0.00 13.90 -288.61 243.20 -95.16 151.75 41- 42 | 1( 1)| 0.00 7.87 -88.23 141.01 -2.81 99.65 | 1( 1)| 0.00 12.19 -263.81 166.85 -96.81 111.41 | 1( 1)| 0.00 13.77 -288.66 207.71 -101.59 133.96 42- 43 | 1( 1)| 0.00 6.48 -95.47 116.99 -13.78 80.38 | 1( 1)| 0.00 12.50 -267.71 138.43 -104.85 90.32 | 1( 1)| 0.00 13.65 -288.55 172.32 -107.98 125.33 43- 44 | 1( 1)| 0.00 5.51 -100.70 99.64 -20.79 67.86 | 1( 1)| 0.00 12.72 -270.51 117.90 -109.99 76.61 | 1( 1)| 0.00 13.58 -288.46 146.76 -112.07 119.81 44- 45 | 1( 1)| 0.00 4.12 -107.95 75.61 -31.75 49.18 | 1( 1)| 0.00 13.03 -274.43 89.47 -118.03 55.53 | 1( 1)| 0.00 13.47 -288.39 111.38 -118.48 111.17 45- 46 | 1( 1)| 0.00 4.47 -119.22 37.81 -45.95 24.59 | 1( 1)| 0.00 13.49 -280.57 44.74 -128.44 27.76 | 1( 1)| 0.00 13.33 -288.22 55.69 -126.77 102.47 4- 47 | 4( 1)| 17.50 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.24 135.36 1012.21 244.96 723.65 | 4( 1)| 8.17 68.27 -4.60 1262.32 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.56 131.48 983.13 237.01 700.44 | 4( 1)| 7.89 66.26 -4.47 1226.01 178.93 798.20 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.10 60.08 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.29 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 2.92 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 0.00 7.95 22.27 74.66 -173.49 46.77 | 1( 1)| 0.00 10.63 11.90 88.94 -232.85 51.78 | 1( 1)| 0.00 10.66 -0.41 110.88 -234.12 53.02 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.88 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 7.84 96.71 -75.11 1823.16 78.32 1112.76 | 4( 1)| 9.17 115.50 -7.74 2163.51 111.63 1324.64 | 4( 1)| 9.84 142.44 23.05 2703.03 161.41 1658.50 53- 54 | 4( 1)| 6.26 94.31 -87.69 1780.52 59.56 1077.80 | 4( 1)| 7.80 112.72 -20.88 2112.73 89.82 1282.68 | 4( 1)| 8.58 139.01 9.78 2639.10 144.73 1610.19 54- 55 | 4( 1)| 5.26 92.93 -95.30 1754.07 49.45 1058.29 | 4( 1)| 6.88 111.14 -28.99 2080.99 78.00 1259.20 | 4( 1)| 7.88 137.07 1.24 2598.62 135.76 1582.76 55- 56 | 4( 1)| 4.24 91.67 -102.24 1729.87 40.23 1040.42 | 4( 1)| 6.00 109.70 -36.40 2051.93 67.21 1237.69 | 4( 1)| 7.23 135.29 -6.56 2561.47 127.57 1557.59 56- 57 | 4( 1)| 3.02 90.54 -109.02 1700.88 30.91 1017.38 | 4( 1)| 5.07 400.00 -353.07 2015.10 55.79 1209.47 | 4( 1)| 6.56 400.00 -632.17 2510.05 119.34 1521.76 57- 58 | 4( 1)| 0.00 89.21 -116.17 1674.07 20.07 995.09 | 4( 1)| 3.89 106.94 -357.92 1982.14 42.94 1182.49 | 4( 1)| 5.76 132.03 -633.22 2466.31 109.73 1489.26 58- 59 | 4( 1)| 0.00 87.83 -123.37 1649.02 9.27 974.69 | 4( 1)| 2.35 105.34 -362.16 1952.02 30.32 1157.96 | 4( 1)| 4.92 130.08 -633.54 2427.80 100.13 1460.65 59- 60 | 4( 1)| 0.00 82.41 -152.31 1551.78 -34.18 904.03 | 4( 1)| 0.00 98.97 -378.10 1836.41 -14.04 1072.86 | 4( 1)| 0.00 122.26 -633.59 2282.67 66.16 1363.35 60- 61 | 4( 1)| 0.00 81.04 -159.50 1526.29 -46.81 883.14 | 4( 1)| 0.00 97.36 -382.56 1805.54 -26.71 1047.72 | 4( 1)| 0.00 120.27 -634.20 2242.71 56.56 1333.72 61- 62 | 3( 1)| 0.00 32.23 -520.14 330.23 -670.37 35.93 | 3( 1)| 0.00 33.10 -575.39 390.82 -723.32 260.87 | 3( 1)| 3.40 32.56 -627.78 481.60 -623.67 236.02 62- 63 | 3( 1)| 0.00 33.38 -529.68 299.51 -689.30 16.96 | 3( 1)| 0.00 34.27 -580.53 354.45 -744.70 250.21 | 3( 1)| 2.92 32.55 -627.87 436.29 -644.87 229.12 63- 64 | 3( 1)| 0.00 34.33 -537.69 275.36 -706.16 1.31 | 3( 1)| 0.00 35.26 -585.29 325.82 -764.01 241.86 | 3( 1)| 1.42 32.74 -628.94 400.47 -663.98 222.72 64- 65 | 1( 1)| 1.17 3.33 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.91 9.18 68.57 16.41 48.46 | 1( 1)| 0.56 4.82 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 17.14 -368.82 34.69 -156.24 24.28 | 1( 1)| 0.00 18.32 -379.11 41.05 -176.07 97.96 | 1( 1)| 0.42 19.07 -386.69 51.10 -179.50 119.75 66- 67 | 1( 1)| 0.00 17.81 -374.12 17.35 -166.04 12.14 | 1( 1)| 0.00 18.55 -381.98 20.53 -181.22 91.85 | 1( 1)| 0.08 19.14 -386.68 25.55 -183.38 115.11 12- 68 | 1( 1)| 1.11 3.11 16.10 53.97 18.24 40.34 | 1( 1)| 0.40 9.03 -198.27 36.87 -47.08 53.50 | 1( 1)| 0.02 16.96 -372.17 30.83 -79.64 101.99 68- 69 | 1( 1)| 0.56 1.55 8.05 26.99 9.12 20.17 | 1( 1)| 0.16 9.48 -208.98 5.06 -57.58 42.91 | 1( 1)| 0.30 17.34 -381.95 -7.55 -85.54 95.62 Voltage p.u. min max 1 0.97 1.00 2 0.97 1.01 3 0.96 1.02 Elapsed AMPL time : 13.236s Elapsed Solve time : 154.499s Elapsed CPU time: 167.735s Sumatorio de erros e2 1374.89259 Sumatorio de erros pq 270.12236 Sumatorio de erros vi 56.54185 Factor de erro e2 0.10 Factor de erro pq 0.10 Factor de erro vi 1.00 Maximum Psae error 3.07339 Maximo erro superior 8590.1118 Maximo erro inferior -824.5092 TRANSITION 5 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886870 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 16513.46406 48 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 16371.22 3081.63 13289.59 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2420.22/ 2165.70/ 465.14 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 322.13 0.00 0.00 332.61 476.51 250.48 51 7.04 0.00 0.00 237.38 26.96 0.00 64 17.18 0.00 0.00 869.83 0.00 27.48 PV systems (kW): Node T1 T2 T3 35.00 61.10 0.00 0.00 46.00 155.50 153.57 0.00 64.00 800.00 0.00 0.00 67.00 563.05 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 0.00 944.39 4.57 50.00 0.00 0.00 0.00 69.00 0.00 274.07 309.72 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 0.00 0.00 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 30.68 30.68 36.70 63.88 Structures 18.47 18.47 23.75 39.10 Fixed CBs 0.86 0.86 0.86 1.73 Switchable CBs 4.84 6.53 7.46 11.77 PV systems 978.23 1048.90 1048.90 2033.90 Wind systems 0.00 853.95 1040.14 931.25 EES systems 0.00 0.00 0.00 0.00 Total invesment cost 1033.08 1959.39 2157.81 3081.63 Purchased energy cost 5650.89 6086.25 7287.55 12239.64 Carbon tax payment 194.94 341.78 719.06 684.39 O&M PV cost 95.73 84.24 79.50 178.69 O&M wind cost 0.00 169.99 210.91 186.87 O&M EES cost 0.00 0.00 0.00 0.00 Total O&M cost 5941.56 6682.27 8297.03 13289.59 Total cost 6974.64 8641.66 10454.84 16371.22 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 15760.85 0.00 130306.45 1006.40 0.00 2 112571.26 17292.86 13015.87 141404.09 1226.52 0.00 3 131724.04 17292.98 16372.80 161754.72 1875.78 0.00 CO2 Emissions (Ton): Period Distribution EV 1 9749.94 4980.53 2 9840.86 4906.75 3 9887.95 4780.66 4 9912.08 4659.94 5 9981.82 4476.17 6 8505.20 4266.91 7 8588.59 4025.47 8 8661.99 3733.05 9 8711.52 3403.07 10 8844.49 2999.31 11 8849.32 2539.22 12 8991.49 2025.48 13 9123.80 1443.32 14 9215.60 753.85 15 9432.54 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 117.93 4500.55 57.12 1999.99 0.90 0.97 Infinity -Infinity 2 0.00 5167.94 -0.00 2288.75 0.90 1.00 1.00 1.00 3 0.00 6518.36 -0.00 2628.45 0.90 0.97 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 -3.91 204.30 0.00 0.00 2 -206.94 214.61 -139.31 180.55 3 -207.91 215.62 -145.12 154.00 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 0.00 0.00 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 5.91 224.27 117.93 4499.67 57.12 1999.26 | 4( 2)| 0.00 257.03 0.00 5166.79 -0.00 2287.75 | 4( 2)| 0.00 320.52 0.00 6516.57 -0.00 2626.88 2- 3 | 4( 2)| 5.42 222.93 110.69 4473.48 47.72 1978.16 | 4( 2)| 0.41 255.42 -8.01 5135.01 -10.04 2264.21 | 4( 2)| 0.27 318.56 -8.18 6476.08 -11.76 2597.52 3- 4 | 4( 2)| 5.82 195.51 129.39 3975.19 -54.69 1604.88 | 4( 2)| 2.43 224.31 -68.47 4569.08 -194.79 1845.34 | 4( 2)| 0.00 280.22 -636.10 5759.84 -428.17 2107.70 4- 5 | 4( 1)| 10.87 148.98 -131.10 3109.60 -353.93 985.96 | 4( 1)| 9.32 168.58 -322.29 3527.34 -453.85 1162.53 | 4( 1)| 14.61 212.09 -813.11 4460.56 -666.03 1282.22 5- 6 | 4( 1)| 11.07 147.68 -138.46 3078.92 -363.41 961.45 | 4( 1)| 9.40 167.02 -329.56 3489.96 -462.12 1134.17 | 4( 1)| 14.28 210.19 -818.96 4411.10 -675.02 1250.10 6- 7 | 4( 1)| 11.29 146.37 -145.82 3048.17 -372.90 937.90 | 4( 1)| 9.51 165.46 -336.84 3452.51 -470.39 1105.73 | 4( 1)| 13.98 208.30 -824.84 4361.51 -684.04 1222.82 7- 8 | 4( 1)| 11.63 144.30 -157.53 3007.84 -386.79 909.80 | 4( 1)| 9.72 162.98 -348.27 3403.84 -482.43 1072.32 | 4( 1)| 13.53 205.26 -833.11 4300.12 -696.87 1190.82 8- 9 | 4( 1)| 2.25 139.01 -201.55 2861.05 -192.90 1039.51 | 4( 1)| 1.48 155.89 -391.15 3227.06 -273.43 1037.84 | 4( 1)| 8.06 196.08 -863.19 4079.37 -655.92 1246.56 9- 10 | 3( 1)| 4.23 45.58 -135.67 1006.21 -446.67 152.37 | 3( 1)| 2.99 53.52 -619.11 1064.09 -1096.70 116.71 | 3( 1)| 0.01 73.86 -869.92 1349.17 -1433.92 192.44 10- 11 | 3( 1)| 10.07 54.09 -143.72 978.75 199.29 647.73 | 3( 1)| 7.59 57.31 -625.17 1030.56 26.85 695.59 | 3( 1)| 8.95 71.13 -872.69 1307.12 -57.94 808.58 11- 12 | 3( 1)| 16.05 45.72 240.13 812.40 255.26 567.25 | 3( 1)| 2.84 49.01 -375.52 872.64 80.62 608.19 | 3( 1)| 7.08 59.36 -605.26 1094.72 116.37 691.44 12- 13 | 1( 1)| 12.03 34.43 181.60 613.95 189.34 420.84 | 1( 1)| 0.69 36.79 -294.86 657.02 65.52 449.84 | 1( 1)| 4.84 45.56 -350.75 842.28 96.65 519.07 13- 14 | 1( 1)| 11.29 32.30 169.66 571.99 177.99 394.88 | 1( 1)| 0.00 34.31 -307.41 607.35 52.99 420.15 | 1( 1)| 3.84 42.50 -360.00 779.15 84.94 484.96 14- 15 | 1( 1)| 10.51 30.09 157.77 530.42 165.44 366.65 | 1( 1)| 0.00 31.74 -319.97 558.16 39.11 387.88 | 1( 1)| 2.66 39.35 -369.27 716.77 71.97 447.50 15- 16 | 1( 1)| 9.97 28.62 150.47 505.65 156.16 346.37 | 1( 1)| 0.00 30.03 -327.25 528.73 28.82 364.68 | 1( 1)| 1.90 37.27 -374.43 679.89 62.36 421.03 16- 17 | 1( 1)| 9.10 26.13 137.23 460.81 142.45 315.94 | 1( 1)| 0.00 27.12 -340.48 475.82 13.62 329.88 | 1( 1)| 1.69 33.70 -383.84 613.15 48.17 381.31 17- 18 | 1( 1)| 8.02 22.95 119.78 402.22 126.79 280.95 | 1( 1)| 0.00 23.42 -360.48 407.16 -3.75 289.85 | 1( 1)| 0.00 29.10 -395.78 526.14 31.97 335.69 18- 19 | 1( 1)| 6.95 19.77 102.29 343.36 111.13 245.90 | 1( 1)| 0.00 19.89 -383.58 338.24 -25.71 249.77 | 1( 1)| 0.00 24.51 -408.06 438.71 11.90 289.98 19- 20 | 1( 1)| 6.58 18.58 95.02 318.86 106.87 236.10 | 1( 1)| 0.00 20.07 -393.25 309.56 -31.84 239.65 | 1( 1)| 0.00 22.76 -413.26 402.32 5.88 277.20 20- 21 | 1( 1)| 6.04 16.98 86.26 289.33 98.80 217.88 | 1( 1)| 0.00 20.22 -404.99 275.01 -43.05 232.04 | 1( 1)| 0.00 21.05 -420.64 358.47 -5.14 253.43 21- 22 | 1( 1)| 3.75 10.51 53.13 178.23 61.87 136.19 | 1( 1)| 0.00 20.80 -448.31 145.32 -94.33 197.58 | 1( 1)| 0.00 21.37 -459.86 194.16 -55.53 195.52 22- 23 | 1( 1)| 2.76 7.70 38.64 129.63 45.91 100.88 | 1( 1)| 0.00 21.11 -467.46 88.37 -116.52 182.64 | 1( 1)| 0.00 21.56 -477.29 122.57 -78.15 182.61 23- 24 | 1( 1)| 2.22 6.22 31.39 105.30 36.63 80.70 | 1( 1)| 0.00 21.27 -477.39 59.89 -129.45 173.88 | 1( 1)| 0.00 21.71 -486.38 88.09 -93.47 175.03 24- 25 | 1( 1)| 1.66 4.64 23.34 78.27 27.51 60.52 | 1( 1)| 0.00 21.74 -489.14 27.72 -142.25 165.14 | 1( 1)| 0.00 22.12 -497.20 49.16 -108.58 167.44 25- 26 | 1( 1)| 1.12 3.16 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 22.16 -499.07 1.03 -155.19 156.39 | 1( 1)| 0.00 22.48 -506.28 14.71 -123.90 159.87 26- 27 | 1( 1)| 0.56 1.58 8.05 26.99 9.12 20.17 | 1( 1)| 1.28 22.64 -510.04 -28.57 -167.89 147.82 | 1( 1)| 0.92 22.89 -516.29 -21.99 -138.97 152.46 3- 28 | 1( 1)| 1.79 10.87 8.94 187.02 50.52 151.63 | 1( 1)| 2.72 12.77 24.81 222.38 57.88 174.99 | 1( 1)| 2.40 41.37 16.85 865.98 57.10 270.75 28- 29 | 1( 1)| 1.18 9.49 1.43 162.09 41.90 132.80 | 1( 1)| 2.15 11.11 16.50 192.88 49.12 153.45 | 1( 1)| 1.85 41.30 9.41 865.81 48.17 265.14 29- 30 | 1( 1)| 0.33 8.11 -6.09 137.10 33.27 113.95 | 1( 1)| 1.56 9.47 8.19 163.30 40.36 131.89 | 1( 1)| 1.27 41.23 1.28 863.89 39.24 259.14 30- 31 | 1( 1)| 0.00 6.72 -13.33 113.08 23.87 94.16 | 1( 1)| 0.87 7.85 0.18 134.87 30.82 108.81 | 1( 1)| 0.53 41.16 -6.78 863.64 29.51 253.02 31- 32 | 1( 1)| 0.00 5.33 -20.57 89.03 14.48 75.34 | 1( 1)| 0.00 6.23 -7.83 106.41 21.26 86.70 | 1( 1)| 0.00 41.08 -14.83 862.03 19.79 246.60 32- 33 | 1( 1)| 0.00 3.85 -28.62 62.30 5.23 56.66 | 1( 1)| 0.00 4.58 -18.52 88.32 11.49 66.61 | 1( 1)| 0.00 41.01 -23.93 857.94 10.22 239.70 33- 34 | 1( 1)| 0.00 2.38 -36.67 35.59 -4.01 37.98 | 1( 1)| 0.00 140.00 -40.08 42.11 -2.52 43.23 | 4( 1)| 0.00 400.00 -45.52 52.42 -3.44 49.10 34- 35 | 1( 1)| 0.00 1.42 -42.18 17.35 -17.42 11.21 | 1( 1)| 0.00 61.57 -45.29 20.53 -15.97 20.54 | 1( 1)| 0.00 140.00 -48.41 25.55 -16.03 19.44 3- 36 | 1( 1)| 2.22 15.98 -34.89 285.50 42.48 203.15 | 1( 1)| 1.95 18.63 -196.80 337.89 -31.47 228.90 | 1( 1)| 2.02 22.64 -245.27 420.73 -42.83 262.68 36- 37 | 1( 1)| 2.06 14.60 -42.40 260.55 33.85 185.28 | 1( 1)| 1.65 17.01 -200.83 308.36 -38.84 209.21 | 1( 1)| 1.46 20.67 -245.16 383.97 -48.70 239.60 37- 38 | 1( 1)| 1.86 13.21 -49.91 235.59 25.23 167.84 | 1( 1)| 1.29 15.40 -204.87 278.82 -46.22 189.51 | 1( 1)| 0.95 18.70 -245.07 347.17 -54.58 217.04 38- 39 | 1( 1)| 1.67 11.82 -57.16 211.56 15.83 149.16 | 1( 1)| 1.09 13.78 -208.75 250.38 -54.25 168.42 | 1( 1)| 0.76 16.75 -244.95 311.77 -60.97 192.89 39- 40 | 1( 1)| 1.35 10.54 -64.13 188.41 7.97 133.28 | 1( 1)| 0.98 12.29 -212.50 222.98 -60.97 150.49 | 1( 1)| 1.04 14.93 -244.86 277.65 -66.32 172.36 40- 41 | 1( 1)| 1.08 9.26 -71.13 165.09 0.11 117.36 | 1( 1)| 0.87 10.79 -216.45 195.35 -67.74 132.51 | 1( 1)| 0.61 13.12 -245.06 243.20 -71.73 151.75 41- 42 | 1( 1)| 0.78 7.87 -78.39 141.01 -9.29 98.67 | 1( 1)| 0.74 10.38 -220.42 166.85 -75.79 111.41 | 1( 1)| 0.75 12.08 -245.06 207.71 -78.14 127.58 42- 43 | 1( 1)| 0.74 6.48 -85.63 116.99 -18.69 80.00 | 1( 1)| 0.53 10.67 -224.31 138.43 -83.83 90.32 | 1( 1)| 0.50 11.96 -244.95 172.32 -84.54 111.87 43- 44 | 1( 1)| 0.33 5.51 -90.86 99.64 -24.69 67.86 | 1( 1)| 0.00 10.88 -227.11 117.90 -88.96 76.61 | 1( 1)| 0.00 11.89 -244.86 146.76 -88.63 106.35 44- 45 | 1( 1)| 0.39 4.69 -98.11 75.61 -34.09 49.18 | 1( 1)| 0.00 11.18 -231.02 89.47 -97.00 55.53 | 1( 1)| 0.00 11.78 -244.77 111.38 -95.03 97.72 45- 46 | 1( 1)| 0.00 5.37 -109.39 37.81 -46.27 24.59 | 1( 1)| 0.00 11.63 -237.15 44.74 -107.41 27.76 | 1( 1)| 0.00 11.64 -244.59 55.69 -103.32 88.13 4- 47 | 4( 1)| 17.50 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.27 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.58 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.47 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.08 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.29 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 0.00 9.82 22.27 74.66 -219.17 35.43 | 1( 1)| 0.00 11.28 11.90 88.94 -249.48 49.21 | 1( 1)| 0.00 11.31 -0.41 110.88 -247.28 47.23 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.88 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 8.55 94.50 -74.86 1822.85 36.24 1010.79 | 4( 1)| 8.28 113.93 -6.62 2163.23 118.11 1272.85 | 4( 1)| 7.65 141.06 -62.95 2702.89 120.96 1625.59 53- 54 | 4( 1)| 7.36 92.10 -87.45 1780.21 14.18 975.88 | 4( 1)| 6.87 111.11 -19.82 2112.41 100.21 1230.93 | 4( 1)| 6.65 137.54 -70.30 2639.11 104.27 1577.31 54- 55 | 4( 1)| 6.67 90.70 -95.06 1753.77 2.16 956.43 | 4( 1)| 6.02 109.46 -28.01 2080.64 90.57 1207.49 | 4( 1)| 6.10 135.48 -75.68 2598.88 95.30 1549.93 55- 56 | 4( 1)| 6.04 89.42 -102.01 1729.59 -8.82 938.63 | 4( 1)| 5.18 107.96 -35.50 2051.55 81.77 1186.02 | 4( 1)| 5.60 133.60 -81.52 2562.00 87.11 1524.80 56- 57 | 4( 1)| 5.41 88.21 -108.84 1700.77 -20.99 915.95 | 4( 1)| 4.28 400.00 -353.65 2014.85 72.85 1158.06 | 4( 1)| 5.10 400.00 -638.44 2512.58 78.86 1489.36 57- 58 | 4( 1)| 4.70 86.86 -116.01 1674.06 -34.25 893.83 | 4( 1)| 2.99 104.90 -358.24 1981.99 62.50 1131.21 | 4( 1)| 4.50 129.83 -639.14 2469.87 69.24 1457.06 58- 59 | 4( 1)| 3.97 85.48 -123.23 1649.03 -47.08 873.50 | 4( 1)| 0.00 103.27 -362.38 1951.92 50.67 1106.73 | 4( 1)| 3.88 127.79 -639.32 2431.75 59.64 1428.53 59- 60 | 4( 1)| 0.00 80.11 -152.18 1551.83 -96.92 802.92 | 4( 1)| 0.01 96.94 -378.21 1836.36 6.92 1021.69 | 4( 1)| 1.35 120.05 -639.19 2287.10 25.66 1331.32 60- 61 | 4( 1)| 0.00 78.74 -159.39 1526.39 -112.50 782.14 | 4( 1)| 0.01 95.32 -382.52 1805.56 -5.44 996.62 | 4( 1)| 0.00 118.08 -639.57 2247.75 16.06 1301.82 61- 62 | 3( 1)| 0.00 33.58 -520.03 330.32 -774.78 -33.71 | 3( 1)| 0.00 35.00 -575.35 390.84 -759.23 288.00 | 3( 1)| 4.10 36.44 -633.13 486.65 -693.79 264.65 62- 63 | 3( 1)| 0.88 34.71 -529.60 299.59 -792.01 -51.54 | 3( 1)| 0.00 36.03 -580.49 354.47 -780.61 278.84 | 3( 1)| 2.39 36.52 -633.18 441.36 -715.01 257.74 63- 64 | 3( 1)| 2.74 35.64 -537.69 275.36 -807.66 -67.09 | 3( 1)| 0.00 36.96 -585.29 325.82 -799.97 270.46 | 3( 1)| 0.98 36.76 -634.07 405.60 -734.22 251.33 64- 65 | 1( 1)| 1.18 3.33 17.17 57.57 19.15 42.36 | 1( 1)| 0.87 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.76 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.21 19.73 -426.32 34.69 -181.56 24.28 | 1( 1)| 0.28 21.73 -437.42 41.05 -204.32 96.55 | 1( 1)| 0.49 22.05 -445.28 51.10 -207.89 97.14 66- 67 | 1( 1)| 0.20 20.49 -431.64 17.35 -192.94 12.14 | 1( 1)| 0.17 21.95 -440.32 20.53 -209.48 90.43 | 1( 1)| 0.00 22.13 -445.30 25.55 -211.77 91.69 12- 68 | 1( 1)| 1.11 3.11 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 5.01 -129.73 45.43 -50.17 37.76 | 1( 1)| 0.00 13.65 -304.11 39.00 -114.48 80.03 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 0.00 5.55 -140.43 13.28 -58.68 27.18 | 1( 1)| 0.00 14.03 -313.87 0.09 -121.83 69.40 Voltage p.u. min max 1 0.97 1.00 2 0.97 1.02 3 0.96 1.02 Elapsed AMPL time : 16.783s Elapsed Solve time : 211.452s Elapsed CPU time: 228.235s Sumatorio de erros e2 1344.59238 Sumatorio de erros pq 77.80573 Sumatorio de erros vi 13.65006 Factor de erro e2 0.10 Factor de erro pq 0.10 Factor de erro vi 1.00 Maximum Psae error 0.00001 Maximo erro superior 8599.4880 Maximo erro inferior -213.2119 TRANSITION 6 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886867 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17074.86168 44 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 16823.29 3495.50 13327.79 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2503.54/ 2195.74/ 2099.95 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 337.28 0.00 0.00 302.43 807.57 0.00 51 0.00 0.00 0.00 206.07 76.56 0.00 64 0.00 0.00 0.00 753.03 133.56 68.99 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 200.76 0.00 0.00 64.00 800.00 0.00 0.00 67.00 296.92 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 250.95 874.05 0.00 50.00 0.00 0.00 0.00 69.00 0.00 453.90 155.06 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 874.51 46.00 0.00 0.00 74.50 64.00 0.00 0.00 552.78 67.00 0.00 0.00 251.37 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 33.57 36.19 36.19 70.00 Structures 18.47 20.77 20.77 39.37 Fixed CBs 0.84 0.84 0.84 1.68 Switchable CBs 4.24 7.66 7.89 12.03 PV systems 803.61 803.61 803.61 1612.42 Wind systems 207.83 1138.52 1230.38 1389.12 EES systems 0.00 0.00 961.96 370.88 Total invesment cost 1068.56 2007.58 3061.63 3495.50 Purchased energy cost 5640.80 6073.15 7141.22 12165.00 Carbon tax payment 194.94 341.92 719.65 684.70 O&M PV cost 78.65 63.07 59.52 140.76 O&M wind cost 35.58 220.28 238.60 264.35 O&M EES cost 0.00 0.00 189.31 72.99 Total O&M cost 5949.96 6698.42 8348.30 13327.79 Total cost 7018.52 8706.00 11409.93 16823.29 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 12947.51 2680.58 130306.45 876.53 0.00 2 112616.94 12947.32 16866.21 141404.09 1014.89 0.00 3 131828.21 12947.41 18522.22 161754.72 1217.70 756.07 CO2 Emissions (Ton): Period Distribution EV 1 9745.54 4980.53 2 9839.39 4906.75 3 9888.47 4780.66 4 9913.72 4659.94 5 9985.53 4476.17 6 8508.33 4266.91 7 8592.39 4025.47 8 8664.66 3733.05 9 8713.42 3403.07 10 8850.58 2999.31 11 8856.23 2539.22 12 9007.50 2025.48 13 9129.69 1443.32 14 9209.32 753.85 15 9446.07 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 289.41 4448.17 104.39 2001.64 0.90 0.97 Infinity -Infinity 2 0.00 5177.44 -0.00 2271.65 0.90 0.99 1.00 1.00 3 0.00 6478.80 -6.49 2624.45 0.90 1.00 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 0.00 210.28 -43.29 49.75 2 -206.94 161.24 -187.18 197.19 3 -207.91 118.15 -187.40 178.98 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 874.51 699.61 3498.05 46 0.00 0.00 0.00 0.00 0.00 0.00 74.50 59.60 297.99 64 0.00 0.00 0.00 0.00 0.00 0.00 442.22 442.22 2211.11 67 0.00 0.00 0.00 0.00 0.00 0.00 251.37 201.10 1005.49 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 531.60 814.73 46 0.00 0.00 0.00 0.00 47.66 74.50 64 0.00 0.00 0.00 0.00 320.43 483.04 67 0.00 0.00 0.00 0.00 248.58 251.37 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 11.45 221.63 289.40 4447.33 104.39 2000.96 | 4( 2)| 0.00 257.24 0.00 5176.28 -0.00 2270.68 | 4( 2)| 0.00 318.78 0.00 6477.04 -6.49 2622.90 2- 3 | 4( 2)| 10.89 220.29 282.15 4421.22 94.99 1979.09 | 4( 2)| 0.00 255.63 -7.06 5144.50 -8.74 2247.21 | 4( 2)| 0.00 316.82 -6.85 6436.62 -15.32 2593.58 3- 4 | 4( 2)| 10.92 192.87 288.50 3923.00 -21.80 1603.86 | 4( 2)| 0.00 223.71 -394.72 4562.28 -304.65 1828.40 | 4( 2)| 0.00 278.80 -661.03 5731.15 -198.72 2096.17 4- 5 | 4( 1)| 11.66 146.36 28.02 3057.44 -321.04 962.10 | 4( 1)| 8.05 168.04 -580.39 3520.54 -563.72 1145.61 | 4( 1)| 11.12 210.68 -656.32 4431.89 -483.86 1270.69 5- 6 | 4( 1)| 12.02 145.08 20.79 3027.34 -330.48 937.81 | 4( 1)| 8.54 166.49 -586.08 3483.22 -572.14 1117.58 | 4( 1)| 11.74 208.79 -656.25 4382.77 -495.68 1241.48 6- 7 | 4( 1)| 12.17 143.80 13.55 2997.18 -339.92 914.66 | 4( 1)| 9.05 164.94 -591.81 3445.83 -580.57 1089.48 | 4( 1)| 12.36 206.89 -656.19 4333.52 -507.50 1214.08 7- 8 | 4( 1)| 12.28 141.73 1.89 2956.99 -353.80 886.61 | 4( 1)| 9.82 162.46 -600.27 3397.17 -592.66 1056.15 | 4( 1)| 13.27 203.85 -655.99 4272.22 -524.87 1182.06 8- 9 | 4( 1)| 1.94 136.27 -42.11 2810.36 -198.27 981.51 | 4( 1)| 0.00 155.29 -631.74 3220.40 -508.06 1015.66 | 4( 1)| 0.00 194.65 -655.18 4051.53 -491.66 1232.62 9- 10 | 3( 1)| 6.32 44.37 19.20 963.43 -416.24 46.47 | 3( 1)| 0.00 59.62 -642.82 1058.36 -1269.78 37.23 | 3( 1)| 3.13 65.02 -798.24 1342.15 -1135.29 143.51 10- 11 | 3( 1)| 6.56 52.36 11.07 935.80 214.69 653.23 | 3( 1)| 7.03 57.30 -651.11 1024.82 47.29 714.05 | 3( 1)| 0.00 70.90 -804.15 1300.10 69.70 820.40 11- 12 | 3( 1)| 14.42 44.74 167.74 792.78 264.71 558.71 | 3( 1)| 0.00 47.75 -554.68 842.05 55.85 600.42 | 3( 1)| 5.68 58.48 -704.09 1075.48 78.48 684.60 12- 13 | 2( 1)| 10.04 33.61 102.46 596.40 185.54 412.48 | 2( 1)| 2.56 36.23 -383.11 642.42 59.38 443.73 | 2( 1)| 3.61 45.06 -436.75 828.43 75.03 513.31 13- 14 | 1( 1)| 9.18 31.47 87.94 554.61 171.93 386.55 | 1( 1)| 1.42 33.74 -396.24 593.17 47.28 414.07 | 1( 1)| 3.17 42.00 -446.61 765.44 63.26 479.23 14- 15 | 1( 1)| 8.26 29.26 73.46 513.19 156.87 358.37 | 1( 1)| 0.00 31.16 -409.40 544.73 33.87 381.82 | 1( 1)| 2.49 38.83 -456.49 703.18 50.23 441.80 15- 16 | 1( 1)| 7.59 27.79 64.48 488.46 145.71 338.09 | 1( 1)| 0.00 29.45 -418.03 515.75 23.93 358.63 | 1( 1)| 1.75 36.75 -461.77 666.32 40.61 415.33 16- 17 | 1( 1)| 6.33 25.29 48.19 443.66 129.26 307.67 | 1( 1)| 0.00 26.54 -435.65 463.30 9.25 323.84 | 1( 1)| 0.00 33.16 -471.39 599.63 26.41 375.62 17- 18 | 1( 1)| 4.46 22.10 26.64 385.08 110.26 272.68 | 1( 1)| 0.00 24.05 -458.54 394.65 -7.53 306.61 | 1( 1)| 0.00 28.56 -483.38 512.62 9.56 330.00 18- 19 | 1( 1)| 2.03 18.92 5.08 326.26 91.26 237.64 | 1( 1)| 0.00 24.33 -481.79 325.75 -25.07 291.87 | 1( 1)| 0.00 25.14 -497.28 425.23 -12.04 284.30 19- 20 | 1( 1)| 0.00 17.73 -3.88 301.77 85.97 227.85 | 1( 1)| 0.00 24.51 -491.57 297.09 -31.13 287.81 | 1( 1)| 0.00 25.27 -506.22 388.85 -18.07 274.46 20- 21 | 1( 1)| 0.00 16.12 -14.66 272.27 76.29 209.63 | 1( 1)| 0.00 24.67 -503.49 262.56 -42.21 280.15 | 1( 1)| 0.00 25.37 -517.14 345.03 -29.10 267.82 21- 22 | 1( 1)| 0.00 9.63 -55.89 161.18 31.90 131.57 | 1( 1)| 0.00 25.24 -546.81 132.87 -95.57 245.69 | 1( 1)| 0.00 25.69 -556.36 180.71 -79.50 238.05 22- 23 | 1( 1)| 0.00 6.79 -76.56 112.58 11.58 103.93 | 1( 1)| 0.21 25.55 -566.05 75.92 -121.72 230.73 | 1( 1)| 0.00 25.87 -573.89 110.84 -101.30 225.12 23- 24 | 1( 1)| 0.00 5.29 -86.90 88.26 -0.81 88.13 | 1( 1)| 0.62 25.69 -576.20 47.44 -136.96 221.92 | 1( 1)| 0.00 25.95 -583.19 76.38 -114.69 217.49 24- 25 | 1( 1)| 0.00 3.68 -98.39 61.25 -12.99 72.71 | 1( 1)| 0.41 26.06 -588.42 16.11 -152.04 213.07 | 1( 1)| 0.00 26.35 -594.47 37.45 -130.77 209.80 25- 26 | 1( 1)| 0.00 2.13 -108.72 36.96 -25.38 62.30 | 1( 1)| 0.36 26.50 -598.55 -10.10 -167.28 204.28 | 1( 1)| 0.00 26.72 -603.75 3.01 -147.05 202.18 26- 27 | 1( 1)| 0.00 0.00 -120.21 10.34 -37.56 52.79 | 1( 1)| 1.84 27.00 -609.63 -39.70 -182.26 195.69 | 1( 1)| 1.47 27.15 -613.87 -32.48 -163.04 194.75 3- 28 | 1( 1)| 3.47 11.26 56.34 189.11 72.50 159.40 | 1( 1)| 2.64 14.64 45.99 454.60 68.53 182.76 | 1( 1)| 0.00 32.89 -437.65 760.10 48.19 207.82 28- 29 | 1( 1)| 2.82 9.82 48.83 163.91 63.99 140.57 | 1( 1)| 1.93 14.12 39.89 449.21 60.50 161.22 | 1( 1)| 0.00 32.88 -450.25 760.05 42.64 183.27 29- 30 | 1( 1)| 2.09 8.39 41.31 138.64 55.48 121.73 | 1( 1)| 0.97 13.61 33.78 443.63 52.47 143.08 | 1( 1)| 0.00 32.89 -462.85 758.87 36.87 158.69 30- 31 | 1( 1)| 1.10 6.94 34.07 114.34 46.21 101.55 | 1( 1)| 0.00 13.17 27.90 438.43 43.72 134.87 | 1( 1)| 0.00 32.89 -474.78 758.76 30.82 132.39 31- 32 | 1( 1)| 0.00 5.48 26.83 90.02 36.93 81.37 | 1( 1)| 0.00 12.73 22.01 433.11 34.98 126.64 | 1( 1)| 0.00 32.90 -486.72 757.78 24.59 106.08 32- 33 | 1( 1)| 0.00 3.93 18.78 63.00 27.81 61.19 | 1( 1)| 0.00 12.26 15.36 426.92 26.38 118.50 | 1( 1)| 0.00 32.94 -500.20 755.19 18.14 79.77 33- 34 | 1( 1)| 0.00 2.41 10.73 35.98 18.70 41.02 | 2( 1)| 0.00 283.99 5.74 42.86 16.15 47.31 | 2( 1)| 0.00 10.83 -513.76 754.75 12.20 53.47 34- 35 | 1( 1)| 0.00 0.94 5.23 17.54 5.47 12.10 | 1( 1)| 0.00 1.10 2.80 20.89 4.69 13.85 | 1( 1)| 0.00 5.93 -522.98 754.85 3.54 15.78 3- 36 | 1( 1)| 1.86 15.98 -69.95 285.50 33.90 202.72 | 1( 1)| 0.00 18.63 -112.03 337.89 27.23 230.59 | 1( 1)| 0.00 22.64 -105.40 420.73 -5.79 267.57 36- 37 | 1( 1)| 1.65 14.60 -77.46 260.55 25.28 185.28 | 1( 1)| 0.00 17.01 -116.05 308.36 19.20 209.95 | 1( 1)| 0.00 20.67 -106.28 384.91 -11.66 243.77 37- 38 | 1( 1)| 1.37 13.21 -84.98 235.59 16.65 167.84 | 1( 1)| 0.00 15.40 -120.06 278.82 11.17 189.51 | 1( 1)| 0.00 18.70 -107.17 349.52 -17.53 219.96 38- 39 | 1( 1)| 1.30 11.82 -92.22 211.56 7.25 149.16 | 1( 1)| 0.00 13.78 -123.93 250.38 2.43 168.42 | 1( 1)| 0.00 16.78 -108.01 315.48 -23.92 194.48 39- 40 | 1( 1)| 0.96 10.54 -99.20 188.41 -0.61 133.28 | 1( 1)| 0.00 12.29 -127.66 222.98 -4.89 150.49 | 1( 1)| 0.00 15.02 -108.81 282.68 -29.26 172.81 40- 41 | 1( 1)| 0.74 9.26 -106.22 165.09 -8.47 117.36 | 1( 1)| 0.00 10.79 -131.39 195.35 -12.20 132.51 | 1( 1)| 0.00 13.26 -111.79 249.53 -34.61 151.75 41- 42 | 1( 1)| 0.55 7.87 -113.49 141.01 -17.88 98.67 | 1( 1)| 0.00 9.18 -135.26 166.85 -20.95 111.41 | 1( 1)| 0.00 11.37 -115.05 217.05 -41.00 127.58 42- 43 | 1( 1)| 0.00 6.48 -120.74 116.99 -27.27 80.00 | 1( 1)| 0.00 7.56 -139.14 138.43 -29.69 90.32 | 1( 1)| 0.00 9.48 -118.34 184.80 -47.39 103.43 43- 44 | 1( 1)| 0.00 5.71 -125.97 99.64 -33.28 67.86 | 1( 1)| 0.00 6.43 -141.93 117.90 -35.96 76.61 | 1( 1)| 0.00 8.16 -121.85 161.51 -51.48 87.73 44- 45 | 1( 1)| 0.00 6.16 -133.22 75.61 -43.40 49.18 | 1( 1)| 0.00 4.82 -145.81 89.47 -45.96 64.34 | 1( 1)| 0.00 6.37 -126.72 129.25 -57.87 67.79 45- 46 | 1( 1)| 0.10 6.85 -144.50 37.81 -57.61 24.59 | 1( 1)| 0.00 5.61 -151.90 44.74 -58.90 53.80 | 1( 1)| 0.00 6.01 -141.94 80.14 -66.15 59.98 4- 47 | 4( 1)| 17.50 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.27 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.58 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.47 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.08 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.29 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 1.80 8.30 22.27 74.66 -180.84 39.74 | 1( 1)| 0.00 11.79 11.90 88.94 -257.23 51.51 | 1( 1)| 0.00 11.83 -0.41 110.88 -259.48 53.02 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.88 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 9.09 93.06 -74.53 1823.64 95.74 929.07 | 4( 1)| 8.67 112.54 -278.51 2162.62 119.61 1210.98 | 4( 1)| 12.18 139.69 -270.80 2697.48 91.18 1584.19 53- 54 | 4( 1)| 7.93 90.67 -87.13 1780.97 72.57 894.19 | 4( 1)| 7.60 109.73 -285.60 2111.83 101.72 1169.09 | 4( 1)| 10.89 136.27 -270.29 2633.77 74.46 1535.94 54- 55 | 4( 1)| 7.27 89.28 -94.77 1754.48 60.08 874.78 | 4( 1)| 6.84 108.09 -289.51 2080.11 92.07 1145.70 | 4( 1)| 10.13 134.27 -269.76 2593.63 65.44 1508.60 55- 56 | 4( 1)| 6.66 88.00 -101.74 1730.26 48.69 857.01 | 4( 1)| 6.09 106.59 -293.04 2051.07 83.28 1124.28 | 4( 1)| 9.41 132.44 -269.25 2556.84 57.21 1483.52 56- 57 | 4( 1)| 6.05 86.77 -108.67 1701.19 37.10 834.54 | 4( 1)| 5.90 212.18 -353.71 2014.61 74.36 1096.58 | 4( 1)| 8.67 130.65 -267.44 2507.99 48.73 1448.31 57- 58 | 4( 1)| 5.39 85.42 -115.89 1674.35 23.68 812.53 | 4( 1)| 5.26 103.54 -358.27 1981.87 64.00 1069.86 | 4( 1)| 7.80 128.69 -267.97 2465.57 39.00 1416.11 58- 59 | 4( 1)| 4.72 84.06 -123.13 1649.28 10.33 792.24 | 4( 1)| 4.60 101.93 -362.40 1951.84 53.69 1045.42 | 4( 1)| 6.86 126.72 -268.68 2427.57 29.36 1387.62 59- 60 | 4( 1)| 2.21 78.72 -152.10 1552.02 -36.85 721.70 | 4( 1)| 1.81 95.61 -378.21 1836.33 14.11 960.44 | 4( 1)| 0.00 118.99 -271.82 2283.07 -4.66 1290.47 60- 61 | 4( 1)| 1.55 77.36 -159.34 1526.51 -50.21 700.97 | 4( 1)| 0.00 94.00 -382.50 1805.61 1.75 935.44 | 4( 1)| 0.00 117.02 -272.36 2243.90 -14.31 1261.03 61- 62 | 3( 1)| 5.49 33.59 -519.99 330.44 -693.93 -89.94 | 3( 1)| 2.41 35.50 -575.34 390.88 -769.42 305.19 | 3( 1)| 0.00 37.64 -411.93 482.81 -759.97 281.26 62- 63 | 3( 1)| 6.44 34.71 -529.56 299.68 -713.53 -107.78 | 3( 1)| 1.59 36.52 -580.48 354.50 -790.80 296.03 | 3( 1)| 0.00 37.75 -427.27 437.51 -784.67 274.46 63- 64 | 3( 1)| 7.36 35.65 -537.69 275.36 -730.95 -123.33 | 3( 1)| 0.00 37.45 -585.29 325.82 -810.17 287.64 | 3( 1)| 0.00 38.02 -439.69 401.77 -807.00 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.87 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.75 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 5.68 -219.91 34.69 -99.56 24.28 | 1( 1)| 0.00 5.50 -228.08 41.05 -102.91 67.91 | 1( 1)| 0.00 11.87 -280.71 170.06 -106.00 66.63 66- 67 | 1( 1)| 0.00 6.29 -225.15 17.35 -105.57 12.14 | 1( 1)| 0.00 5.91 -230.88 20.53 -108.04 61.81 | 1( 1)| 0.00 12.71 -294.10 153.61 -109.85 61.19 12- 68 | 1( 1)| 1.11 3.11 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 9.56 -228.87 33.04 -94.26 36.14 | 1( 1)| 0.31 14.54 -318.06 37.32 -67.00 89.66 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 0.00 10.10 -239.59 1.64 -102.77 14.04 | 1( 1)| 0.28 14.93 -327.83 -1.59 -79.86 83.28 Voltage p.u. min max 1 0.97 1.00 2 0.97 1.02 3 0.96 1.02 Elapsed AMPL time : 20.549s Elapsed Solve time : 265.780s Elapsed CPU time: 286.329s Sumatorio de erros e2 222.32222 Sumatorio de erros pq 292.52455 Sumatorio de erros vi 27.22028 Factor de erro e2 1.00 Factor de erro pq 0.10 Factor de erro vi 1.00 Maximum Psae error 643.71268 Maximo erro superior 6162.0580 Maximo erro inferior -754.8586 TRANSITION 7 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886912 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17034.80019 43 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 16857.44 3528.66 13328.78 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2567.63/ 2197.40/ 1993.18 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 317.66 0.00 0.00 195.50 1083.99 0.00 51 0.00 0.00 0.00 223.61 46.56 0.00 64 0.00 0.00 0.00 874.31 16.56 88.15 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 132.59 0.00 0.00 64.00 800.00 0.00 0.00 67.00 165.08 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 440.04 684.96 0.00 50.00 0.00 0.00 0.00 69.00 0.00 642.06 198.55 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 632.20 46.00 0.00 0.00 10.91 64.00 0.00 0.00 814.77 67.00 0.00 0.00 139.78 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 28.38 31.48 31.48 60.07 Structures 18.47 21.19 21.19 39.80 Fixed CBs 0.79 0.79 0.79 1.58 Switchable CBs 4.35 8.20 8.50 12.71 PV systems 679.75 679.75 679.75 1363.89 Wind systems 364.44 1294.47 1412.10 1712.62 EES systems 0.00 0.00 876.63 337.98 Total invesment cost 1096.17 2035.88 3030.44 3528.66 Purchased energy cost 5633.87 6067.61 7099.57 12138.57 Carbon tax payment 194.93 342.02 719.99 684.89 O&M PV cost 66.52 53.35 50.35 119.06 O&M wind cost 62.39 246.53 270.48 319.74 O&M EES cost 0.00 0.00 172.52 66.51 Total O&M cost 5957.72 6709.51 8312.91 13328.78 Total cost 7053.89 8745.39 11343.35 16857.44 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 10951.89 4700.52 130306.45 894.46 0.00 2 112650.19 10951.73 18876.18 141404.09 1032.85 0.00 3 131894.69 10951.80 20996.77 161754.72 1272.50 963.19 CO2 Emissions (Ton): Period Distribution EV 1 9742.41 4980.53 2 9838.38 4906.75 3 9888.86 4780.66 4 9914.85 4659.94 5 9988.15 4476.17 6 8512.21 4266.91 7 8595.82 4025.47 8 8666.85 3733.05 9 8714.45 3403.07 10 8852.84 2999.31 11 8858.54 2539.22 12 9011.71 2025.48 13 9134.19 1443.32 14 9213.65 753.85 15 9453.74 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 409.48 4414.70 193.46 2035.90 0.90 0.97 Infinity -Infinity 2 0.00 5187.05 -0.00 2254.90 0.90 0.99 1.00 1.00 3 0.00 6412.28 -28.61 2617.42 0.90 1.00 0.99 1.00 Reactive Power by DG Period PV Wind min max min max 1 -5.49 181.26 -5.40 87.23 2 -206.94 141.71 -187.18 197.19 3 -207.91 117.91 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 568.53 505.76 2528.79 46 0.00 0.00 0.00 0.00 0.00 0.00 8.73 8.73 43.65 64 0.00 0.00 0.00 0.00 0.00 0.00 651.81 651.81 3259.07 67 0.00 0.00 0.00 0.00 0.00 0.00 123.85 111.82 559.11 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 335.98 632.20 46 0.00 0.00 0.00 0.00 10.91 10.91 64 0.00 0.00 0.00 0.00 466.97 795.04 67 0.00 0.00 0.00 0.00 139.78 139.78 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 19.50 220.01 409.47 4413.86 193.45 2035.20 | 4( 2)| 0.00 257.39 0.00 5185.90 -0.00 2253.94 | 4( 2)| 0.00 315.84 0.00 6410.55 -28.62 2615.89 2- 3 | 4( 2)| 18.99 218.64 402.21 4387.78 184.04 2013.30 | 4( 2)| 0.00 255.78 -7.06 5154.11 -8.65 2230.50 | 4( 2)| 0.00 313.88 -4.92 6370.23 -37.24 2586.65 3- 4 | 4( 2)| 15.77 191.43 355.73 3889.58 46.49 1630.30 | 4( 2)| 4.26 223.57 -463.98 4565.33 -307.18 1811.72 | 4( 2)| 0.00 277.33 -560.19 5700.75 -232.59 2086.22 4- 5 | 4( 1)| 11.52 144.69 95.25 3024.02 -252.75 977.32 | 4( 1)| 10.99 167.95 -631.55 3523.58 -562.89 1128.94 | 4( 1)| 12.10 209.21 -571.03 4401.50 -507.28 1261.01 5- 6 | 4( 1)| 11.83 143.39 88.00 2993.94 -262.18 952.14 | 4( 1)| 11.51 166.40 -637.21 3486.21 -571.30 1101.02 | 4( 1)| 12.57 207.32 -571.52 4352.58 -516.03 1233.83 6- 7 | 4( 1)| 12.14 142.10 80.75 2963.81 -271.62 926.93 | 4( 1)| 12.04 164.85 -642.89 3448.75 -579.73 1073.05 | 4( 1)| 13.05 205.42 -572.01 4303.54 -524.78 1206.59 7- 8 | 4( 1)| 12.58 140.03 69.08 2923.63 -285.49 895.45 | 4( 1)| 12.84 162.37 -651.34 3400.08 -591.68 1039.75 | 4( 1)| 13.75 202.38 -572.55 4242.28 -537.55 1174.61 8- 9 | 4( 1)| 1.69 135.06 25.08 2776.96 -112.41 1008.15 | 4( 1)| 5.51 155.12 -682.82 3223.30 -611.38 994.04 | 4( 1)| 0.00 193.15 -574.39 4021.62 -480.20 1220.54 9- 10 | 1( 1)| 7.76 44.52 57.37 962.59 -276.01 170.04 | 1( 1)| 5.02 66.03 -670.73 1058.25 -1368.24 6.50 | 1( 1)| 2.44 64.08 -852.28 1352.09 -1149.89 128.87 10- 11 | 3( 1)| 10.53 52.31 48.60 934.97 228.47 663.76 | 3( 1)| 7.39 57.18 -679.02 1024.72 70.59 725.59 | 3( 1)| 7.38 71.26 -858.44 1310.01 65.58 829.76 11- 12 | 3( 1)| 11.51 44.18 83.15 781.28 228.16 552.50 | 3( 1)| 3.40 47.24 -651.64 831.21 51.59 595.26 | 3( 1)| 5.56 57.61 -820.11 1060.91 58.02 677.61 12- 13 | 1( 1)| 7.37 32.88 11.19 583.15 158.49 406.17 | 1( 1)| 3.79 36.16 -382.82 642.38 62.17 443.72 | 1( 1)| 4.27 44.83 -436.41 828.27 65.91 513.29 13- 14 | 1( 1)| 6.36 30.75 -3.22 541.50 144.51 380.28 | 1( 1)| 3.15 33.67 -396.01 593.15 50.07 414.06 | 1( 1)| 4.10 41.77 -446.33 765.34 54.14 479.22 14- 15 | 1( 1)| 5.28 28.55 -17.61 500.22 129.03 352.12 | 1( 1)| 2.22 31.10 -409.23 544.72 36.65 381.82 | 1( 1)| 3.17 38.61 -456.29 703.14 41.10 441.79 15- 16 | 1( 1)| 4.48 27.08 -26.58 475.50 117.55 331.85 | 1( 1)| 1.69 29.39 -417.91 515.75 26.71 358.63 | 1( 1)| 2.38 36.54 -461.58 666.29 31.48 415.33 16- 17 | 1( 1)| 3.19 24.58 -42.85 430.75 100.62 301.44 | 1( 1)| 1.73 26.48 -435.55 463.30 12.03 323.84 | 1( 1)| 1.50 32.97 -471.22 599.61 17.27 375.61 17- 18 | 1( 1)| 1.51 21.40 -64.40 372.18 81.06 266.46 | 1( 1)| 1.88 24.42 -458.44 394.65 -5.28 306.64 | 1( 1)| 0.00 28.38 -483.22 512.60 0.60 330.00 18- 19 | 1( 1)| 0.00 18.23 -85.97 313.38 61.50 231.42 | 1( 1)| 1.92 24.69 -481.70 325.75 -26.57 291.89 | 1( 1)| 0.42 25.56 -497.19 425.21 -21.00 284.30 19- 20 | 1( 1)| 0.00 17.04 -95.05 288.91 55.75 221.63 | 1( 1)| 2.04 24.87 -491.48 297.09 -32.83 287.84 | 1( 1)| 1.14 25.68 -506.13 388.84 -27.03 274.49 20- 21 | 1( 1)| 0.00 15.44 -107.52 259.43 44.79 203.42 | 1( 1)| 1.64 25.02 -503.41 262.56 -44.67 280.17 | 1( 1)| 1.48 25.77 -517.07 345.02 -38.06 267.84 21- 22 | 1( 1)| 0.00 8.97 -154.81 148.33 -4.55 121.72 | 1( 1)| 1.38 25.58 -546.74 132.87 -98.88 245.71 | 1( 1)| 1.02 26.09 -556.29 180.71 -90.01 238.08 22- 23 | 1( 1)| 0.00 6.87 -175.50 99.74 -25.88 86.79 | 1( 1)| 1.17 25.88 -565.99 75.92 -122.33 230.75 | 1( 1)| 1.04 26.27 -573.83 110.85 -117.21 225.14 23- 24 | 1( 1)| 0.00 7.28 -185.90 75.43 -38.27 66.86 | 1( 1)| 1.18 26.02 -576.15 47.44 -136.95 221.94 | 1( 1)| 0.77 26.34 -583.14 76.38 -133.48 217.51 24- 25 | 1( 1)| 0.00 7.79 -197.52 48.43 -50.46 46.92 | 1( 1)| 0.84 26.32 -588.40 16.11 -152.03 213.08 | 1( 1)| 0.71 26.60 -594.45 37.45 -149.57 209.80 25- 26 | 1( 1)| 0.00 8.27 -207.92 24.42 -62.86 26.99 | 1( 1)| 0.72 26.76 -598.54 -10.10 -167.28 204.28 | 1( 1)| 0.47 26.97 -603.74 3.01 -165.85 202.18 26- 27 | 1( 1)| 0.00 8.82 -219.45 -1.08 -75.05 14.91 | 1( 1)| 1.93 27.25 -609.63 -39.70 -182.26 195.69 | 1( 1)| 1.57 27.39 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.76 24.20 46.02 506.38 68.53 182.76 | 1( 1)| 0.00 29.28 -211.25 644.77 49.70 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 3.31 23.91 39.91 502.03 60.50 163.12 | 1( 1)| 0.00 29.25 -223.85 644.30 44.16 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.85 23.62 33.80 497.10 52.47 155.60 | 1( 1)| 0.00 29.23 -236.47 642.95 38.42 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.37 23.33 27.91 492.88 43.73 147.54 | 1( 1)| 0.00 29.20 -248.41 642.46 32.34 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.89 23.05 22.02 488.23 34.98 139.38 | 1( 1)| 0.00 29.18 -260.38 641.28 25.87 106.08 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.39 22.75 15.37 482.30 26.38 131.19 | 1( 1)| 0.00 29.17 -273.99 638.79 19.49 79.77 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 3( 1)| 0.90 303.30 5.74 42.86 16.15 47.31 | 3( 1)| 0.00 29.26 -299.04 636.41 13.05 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.00 29.25 -318.40 632.41 3.54 15.78 3- 36 | 1( 1)| 0.38 15.98 -17.16 285.50 54.66 202.98 | 1( 1)| 0.69 18.63 -58.31 337.89 49.86 233.76 | 1( 1)| 1.46 22.64 -95.36 420.73 45.61 270.64 36- 37 | 1( 1)| 0.00 14.60 -24.67 260.55 46.03 185.28 | 1( 1)| 0.00 17.01 -62.33 308.36 41.83 213.12 | 1( 1)| 1.17 20.67 -95.23 383.97 37.80 246.84 37- 38 | 1( 1)| 0.00 13.21 -32.18 235.59 37.40 167.84 | 1( 1)| 0.00 15.40 -66.35 278.82 33.81 192.48 | 1( 1)| 0.00 18.70 -95.10 347.17 29.99 223.04 38- 39 | 1( 1)| 0.00 11.82 -39.42 211.56 28.01 149.16 | 1( 1)| 0.00 13.78 -70.22 250.38 25.06 170.37 | 1( 1)| 0.00 16.75 -94.97 311.77 21.49 197.55 39- 40 | 1( 1)| 0.00 10.54 -46.40 188.41 20.15 133.28 | 1( 1)| 0.00 12.29 -73.96 222.98 17.75 151.58 | 1( 1)| 0.00 14.93 -94.85 277.65 14.38 175.89 40- 41 | 1( 1)| 0.00 9.26 -53.37 165.09 12.29 117.36 | 1( 1)| 0.00 10.79 -77.72 195.35 10.44 132.74 | 1( 1)| 0.00 13.11 -94.79 243.20 7.27 154.15 41- 42 | 1( 1)| 0.00 7.87 -60.62 141.01 2.90 98.67 | 1( 1)| 0.00 9.18 -81.61 166.85 1.69 111.41 | 1( 1)| 0.00 11.16 -94.68 207.71 -1.24 128.65 42- 43 | 1( 1)| 0.00 6.48 -67.86 116.99 -6.50 80.00 | 1( 1)| 0.00 7.56 -85.48 138.43 -7.05 90.32 | 1( 1)| 0.00 9.20 -94.55 172.32 -9.74 103.43 43- 44 | 1( 1)| 0.00 5.51 -73.09 99.64 -12.51 67.86 | 1( 1)| 0.00 6.43 -88.28 117.90 -12.64 76.61 | 1( 1)| 0.00 7.83 -94.46 146.76 -15.18 87.73 44- 45 | 1( 1)| 0.00 4.12 -80.34 75.61 -21.91 49.18 | 1( 1)| 0.00 4.82 -92.15 89.47 -21.56 55.53 | 1( 1)| 0.00 5.87 -94.48 111.38 -23.68 63.58 45- 46 | 1( 1)| 0.00 3.62 -91.61 37.81 -34.08 24.59 | 1( 1)| 0.00 3.73 -98.25 44.74 -34.51 44.70 | 1( 1)| 0.00 4.63 -95.80 57.14 -34.69 42.27 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.46 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 2.04 9.09 22.27 74.66 -198.38 39.74 | 1( 1)| 0.00 11.22 11.90 88.94 -244.78 54.14 | 1( 1)| 0.75 11.26 -0.41 110.88 -247.03 52.94 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.88 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 7.14 91.59 -74.55 1823.38 -9.65 834.49 | 4( 1)| 6.26 111.25 -333.99 2162.38 115.13 1154.93 | 4( 1)| 10.65 137.91 -171.02 2672.92 94.89 1545.30 53- 54 | 4( 1)| 6.57 89.23 -87.14 1780.74 -31.69 800.60 | 4( 1)| 5.26 108.45 -340.87 2111.61 97.23 1113.07 | 4( 1)| 9.60 134.51 -170.83 2609.36 78.12 1497.08 54- 55 | 4( 1)| 6.31 87.84 -94.76 1754.28 -43.69 782.22 | 4( 1)| 4.74 106.81 -345.15 2079.90 87.59 1089.71 | 4( 1)| 9.00 132.51 -171.21 2569.42 69.03 1469.77 55- 56 | 4( 1)| 6.10 86.58 -101.72 1730.09 -54.66 765.39 | 4( 1)| 4.27 105.32 -349.08 2050.88 78.79 1068.32 | 4( 1)| 8.44 130.68 -172.08 2532.84 60.73 1444.73 56- 57 | 4( 1)| 5.92 85.36 -108.57 1701.17 -66.71 743.96 | 4( 1)| 3.77 103.86 -354.01 2014.54 69.87 1040.82 | 4( 1)| 7.96 128.92 -173.23 2485.07 51.89 1409.70 57- 58 | 4( 1)| 5.45 84.02 -115.77 1674.40 -79.93 723.06 | 4( 1)| 3.15 102.27 -358.47 1981.86 59.52 1014.19 | 4( 1)| 7.31 126.98 -174.23 2443.17 41.98 1377.60 58- 59 | 4( 1)| 4.78 82.67 -122.99 1649.36 -92.74 703.84 | 4( 1)| 2.52 100.67 -362.56 1951.85 49.21 989.79 | 4( 1)| 6.57 125.02 -175.12 2405.36 32.27 1349.14 59- 60 | 4( 1)| 2.29 77.37 -151.95 1552.13 -137.54 637.11 | 4( 1)| 0.86 94.37 -378.32 1836.37 12.77 904.85 | 4( 1)| 2.88 117.30 -178.54 2261.09 -1.84 1252.03 60- 61 | 4( 1)| 1.64 76.03 -159.17 1526.65 -150.45 617.46 | 4( 1)| 0.00 92.77 -382.55 1805.67 2.46 879.90 | 4( 1)| 0.00 115.34 -179.45 2222.23 -11.60 1222.64 61- 62 | 3( 1)| 10.09 33.95 -519.84 330.56 -768.64 -149.58 | 3( 1)| 2.37 35.60 -575.38 390.94 -771.41 305.18 | 3( 1)| 0.00 38.85 -389.03 467.89 -797.74 281.44 62- 63 | 3( 1)| 10.81 35.28 -529.44 299.79 -785.87 -167.42 | 3( 1)| 0.00 36.63 -580.52 354.55 -792.79 296.02 | 3( 1)| 0.00 39.16 -404.34 424.34 -822.45 274.60 63- 64 | 3( 1)| 10.78 36.39 -537.69 275.36 -801.53 -182.99 | 3( 1)| 0.00 37.56 -585.29 325.82 -812.16 287.64 | 3( 1)| 0.00 39.88 -416.58 389.98 -844.82 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.75 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 2.78 -117.62 34.69 -50.02 24.28 | 1( 1)| 0.00 3.19 -124.32 41.05 -52.65 43.17 | 1( 1)| 0.00 6.55 -178.60 142.92 -55.51 49.71 66- 67 | 1( 1)| 0.00 3.39 -122.86 17.35 -56.03 13.53 | 1( 1)| 0.00 3.58 -127.12 20.53 -57.79 37.07 | 1( 1)| 0.00 7.42 -191.97 131.22 -59.36 45.62 12- 68 | 1( 1)| 1.12 3.11 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 14.58 -332.60 20.08 -138.56 30.23 | 1( 1)| 0.00 19.42 -446.42 21.92 -98.24 118.92 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 0.00 15.09 -343.34 -9.95 -147.08 7.21 | 1( 1)| 0.00 19.85 -456.23 -15.53 -114.59 112.55 Voltage p.u. min max 1 0.97 1.00 2 0.97 1.02 3 0.96 1.03 Elapsed AMPL time : 24.251s Elapsed Solve time : 317.671s Elapsed CPU time: 341.922s Sumatorio de erros e2 167.38745 Sumatorio de erros pq 99.69788 Sumatorio de erros vi 13.20316 Factor de erro e2 1.00 Factor de erro pq 0.10 Factor de erro vi 1.00 Maximum Psae error 532.57050 Maximo erro superior 6576.2434 Maximo erro inferior -360.3901 TRANSITION 8 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886922 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17030.36824 45 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 16884.40 3543.44 13340.96 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2617.68/ 2189.00/ 1867.12 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 345.58 0.00 0.00 237.36 1004.53 0.00 51 0.00 0.00 0.00 213.59 36.95 0.00 64 0.00 0.00 0.00 782.72 109.24 98.56 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 57.80 0.00 0.00 64.00 800.00 0.00 0.00 67.00 94.25 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 574.92 550.08 0.00 50.00 0.00 0.00 0.00 69.00 0.00 773.84 194.00 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 417.71 46.00 0.00 0.00 0.00 64.00 0.00 0.00 999.85 67.00 0.00 0.00 68.63 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 28.38 30.76 30.76 59.33 Structures 18.47 20.56 20.56 39.16 Fixed CBs 0.86 0.86 0.86 1.72 Switchable CBs 4.14 8.01 8.34 12.33 PV systems 589.57 589.57 589.57 1182.96 Wind systems 476.14 1404.00 1518.93 1933.53 EES systems 0.00 0.00 815.48 314.40 Total invesment cost 1117.57 2053.76 2984.50 3543.44 Purchased energy cost 5628.79 6063.42 7107.03 12133.76 Carbon tax payment 194.93 342.10 720.23 685.02 O&M PV cost 57.70 46.27 43.67 103.27 O&M wind cost 81.51 264.92 287.99 357.03 O&M EES cost 0.00 0.00 160.48 61.87 Total O&M cost 5962.93 6716.71 8319.39 13340.96 Total cost 7080.50 8770.46 11303.89 16884.40 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 9499.02 6141.29 130306.45 859.70 0.00 2 112673.83 9498.88 20283.91 141404.09 1023.88 0.00 3 131939.98 9498.94 22355.83 161754.72 1233.96 896.15 CO2 Emissions (Ton): Period Distribution EV 1 9740.20 4980.53 2 9837.67 4906.75 3 9889.14 4780.66 4 9915.65 4659.94 5 9989.99 4476.17 6 8515.03 4266.91 7 8598.29 4025.47 8 8668.39 3733.05 9 8715.17 3403.07 10 8854.37 2999.31 11 8860.12 2539.22 12 9014.36 2025.48 13 9137.30 1443.32 14 9216.91 753.85 15 9458.84 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 497.92 4398.94 233.13 2021.84 0.90 0.97 Infinity -Infinity 2 0.00 5190.40 -0.00 2238.30 0.90 0.99 1.00 1.00 3 0.00 6358.41 -0.00 2610.71 0.90 1.00 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 -1.93 215.38 0.00 113.97 2 -206.94 145.09 -187.18 197.19 3 -207.91 122.57 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 355.80 334.17 1670.85 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 0.00 0.00 799.88 799.88 3999.40 67 0.00 0.00 0.00 0.00 0.00 0.00 54.91 54.91 274.54 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 229.37 417.71 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 0.00 566.79 956.78 67 0.00 0.00 0.00 0.00 68.63 68.63 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 24.68 219.79 497.91 4398.09 233.12 2021.13 | 4( 2)| 0.00 257.30 0.00 5189.25 -0.00 2237.35 | 4( 2)| 0.00 313.45 0.00 6356.71 -0.00 2609.21 2- 3 | 4( 2)| 24.19 218.42 490.64 4371.80 223.70 1999.21 | 4( 2)| 0.41 255.69 -7.06 5157.47 -8.65 2213.93 | 4( 2)| 0.27 311.49 -4.92 6316.45 -7.47 2580.02 3- 4 | 4( 2)| 17.77 190.88 386.14 3875.15 61.61 1606.70 | 4( 2)| 5.43 223.13 -450.24 4561.49 -267.91 1795.17 | 4( 2)| 0.00 275.48 -396.59 5661.30 -163.30 2076.24 4- 5 | 4( 1)| 11.70 143.73 125.37 3002.51 -237.62 953.71 | 4( 1)| 12.83 167.57 -635.89 3519.75 -524.26 1112.40 | 4( 1)| 13.78 207.35 -426.75 4362.07 -401.62 1253.24 5- 6 | 4( 1)| 11.92 142.42 118.02 2972.16 -247.06 928.54 | 4( 1)| 13.39 166.02 -641.47 3482.46 -532.78 1084.60 | 4( 1)| 14.01 205.46 -427.78 4313.45 -410.30 1226.24 6- 7 | 4( 1)| 12.16 141.10 110.66 2941.75 -256.50 903.32 | 4( 1)| 13.95 164.48 -647.08 3445.09 -541.32 1056.74 | 4( 1)| 14.25 203.57 -428.83 4264.72 -418.99 1199.18 7- 8 | 4( 1)| 12.30 139.01 98.87 2901.23 -270.38 871.84 | 4( 1)| 13.92 162.00 -655.51 3396.43 -553.43 1023.47 | 4( 1)| 14.60 200.53 -430.25 4203.54 -431.73 1167.24 8- 9 | 4( 1)| 4.87 133.98 54.43 2753.37 -107.33 969.82 | 4( 1)| 6.11 154.67 -686.93 3219.67 -597.24 972.51 | 4( 1)| 0.00 191.28 -435.37 3982.93 -467.78 1208.61 9- 10 | 1( 1)| 5.57 44.91 46.86 958.58 -256.51 179.43 | 1( 1)| 3.02 66.41 -701.56 1054.77 -1345.34 3.18 | 1( 1)| 3.35 64.41 -884.41 1349.25 -1132.95 87.92 10- 11 | 3( 1)| 11.06 52.71 36.89 930.96 230.15 668.26 | 3( 1)| 8.11 57.31 -709.87 1021.25 81.52 724.69 | 3( 1)| 8.11 71.26 -890.55 1307.18 71.42 853.89 11- 12 | 2( 1)| 9.21 43.82 18.44 771.87 190.66 548.01 | 3( 1)| 5.08 46.77 -724.13 822.26 50.68 585.39 | 3( 1)| 6.63 57.34 -884.28 1051.48 49.30 673.31 12- 13 | 1( 1)| 3.73 32.57 -53.50 573.81 114.11 401.69 | 1( 1)| 3.87 36.35 -382.88 642.48 62.23 443.74 | 1( 1)| 4.15 45.14 -436.50 828.46 63.90 513.33 13- 14 | 1( 1)| 2.74 30.43 -67.91 532.21 101.02 375.82 | 1( 1)| 3.25 33.85 -396.05 593.21 50.12 414.08 | 1( 1)| 4.00 42.06 -446.40 765.45 52.13 479.24 14- 15 | 1( 1)| 1.60 28.21 -82.31 490.99 86.53 347.67 | 1( 1)| 2.58 31.27 -409.26 544.75 36.71 381.83 | 1( 1)| 2.99 38.88 -456.34 703.19 39.09 441.80 15- 16 | 1( 1)| 0.00 26.73 -91.28 466.29 75.74 327.41 | 1( 1)| 2.10 29.55 -417.95 515.77 26.76 358.64 | 1( 1)| 2.23 36.80 -461.63 666.33 29.47 415.34 16- 17 | 1( 1)| 0.00 24.23 -107.57 421.55 59.84 297.00 | 1( 1)| 1.86 26.62 -435.58 463.31 11.96 323.84 | 1( 1)| 1.45 33.20 -471.27 599.63 15.26 375.62 17- 18 | 1( 1)| 0.00 21.03 -130.07 362.98 41.45 262.02 | 1( 1)| 1.90 24.35 -458.47 394.66 -5.42 306.63 | 1( 1)| 1.20 28.58 -483.26 512.62 -1.05 330.00 18- 19 | 1( 1)| 0.00 17.85 -155.01 304.20 23.07 226.98 | 1( 1)| 1.94 24.63 -481.72 325.76 -24.82 291.89 | 1( 1)| 1.17 25.46 -497.24 425.23 -22.65 284.30 19- 20 | 1( 1)| 0.00 16.66 -165.39 279.74 17.94 217.19 | 1( 1)| 2.05 24.80 -491.50 297.09 -30.88 287.83 | 1( 1)| 1.42 25.58 -506.17 388.85 -28.68 274.48 20- 21 | 1( 1)| 0.00 15.05 -177.90 250.27 8.56 198.98 | 1( 1)| 1.79 24.96 -503.43 262.56 -42.16 280.17 | 1( 1)| 1.52 25.67 -517.10 345.03 -39.71 267.83 21- 22 | 1( 1)| 0.00 9.86 -225.19 139.18 -34.39 117.73 | 1( 1)| 1.39 25.51 -546.75 132.87 -96.24 245.70 | 1( 1)| 1.03 25.99 -556.32 180.71 -94.98 238.07 22- 23 | 1( 1)| 0.00 10.74 -245.92 90.59 -52.96 82.84 | 1( 1)| 1.18 25.81 -566.00 75.92 -121.71 230.74 | 1( 1)| 1.04 26.17 -573.86 110.85 -120.25 225.13 23- 24 | 1( 1)| 0.00 11.21 -256.38 66.28 -64.96 62.91 | 1( 1)| 1.19 25.95 -576.15 47.44 -136.95 221.93 | 1( 1)| 0.78 26.25 -583.17 76.38 -134.97 217.50 24- 25 | 1( 1)| 0.00 11.74 -268.18 39.28 -77.18 42.97 | 1( 1)| 0.85 26.28 -588.40 16.11 -152.03 213.08 | 1( 1)| 0.71 26.48 -594.46 37.45 -149.57 209.80 25- 26 | 1( 1)| 0.00 12.24 -278.66 16.27 -89.59 23.04 | 1( 1)| 0.72 26.72 -598.54 -10.10 -167.28 204.28 | 1( 1)| 0.49 26.86 -603.75 3.01 -165.85 202.18 26- 27 | 1( 1)| 0.17 12.80 -290.23 -9.23 -101.79 3.11 | 1( 1)| 1.94 27.22 -609.63 -39.70 -182.26 195.69 | 1( 1)| 1.57 27.28 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.76 20.07 46.02 418.70 68.53 182.76 | 1( 1)| 0.00 19.66 -89.87 429.07 47.83 207.83 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 3.31 19.72 39.92 414.38 60.50 161.22 | 1( 1)| 0.66 19.59 -102.46 428.12 42.31 183.28 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.85 19.38 33.80 409.68 52.47 139.65 | 1( 1)| 0.00 19.52 -115.07 426.77 36.73 158.70 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.37 19.04 27.91 405.50 43.73 127.72 | 1( 1)| 0.00 19.46 -127.00 425.85 30.72 132.40 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.89 18.71 22.03 401.03 34.98 119.61 | 1( 1)| 0.00 19.40 -138.95 424.62 24.65 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.39 18.40 15.37 395.55 26.38 111.51 | 1( 1)| 0.00 19.35 -164.76 422.73 18.60 79.78 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 2( 1)| 0.90 273.99 5.74 42.86 16.15 47.31 | 2( 1)| 0.00 19.28 -192.65 420.59 12.47 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.00 19.25 -211.66 418.32 3.54 15.78 3- 36 | 1( 1)| 2.87 15.98 40.87 285.50 79.18 211.60 | 1( 1)| 2.60 18.86 0.48 338.40 74.70 243.17 | 1( 1)| 1.89 23.03 -47.26 423.55 71.39 278.28 36- 37 | 1( 1)| 2.10 14.60 33.35 260.55 70.56 192.76 | 1( 1)| 1.92 17.20 -3.54 308.36 66.67 221.62 | 1( 1)| 1.10 21.00 -47.12 386.07 63.58 253.72 37- 38 | 1( 1)| 1.05 13.21 25.84 235.59 61.93 173.92 | 1( 1)| 1.03 15.54 -7.56 278.82 58.65 200.06 | 1( 1)| 0.00 18.97 -46.98 348.55 55.77 229.15 38- 39 | 1( 1)| 0.00 11.82 18.60 211.56 52.53 153.75 | 1( 1)| 0.00 13.88 -11.43 250.38 49.90 176.98 | 1( 1)| 0.00 16.96 -46.85 312.46 47.27 202.85 39- 40 | 1( 1)| 0.00 10.54 11.62 188.41 44.68 136.60 | 1( 1)| 0.00 12.34 -15.16 222.98 42.59 157.36 | 1( 1)| 0.00 15.09 -46.72 277.68 40.16 180.49 40- 41 | 1( 1)| 0.00 9.26 4.65 165.09 36.82 119.41 | 1( 1)| 0.00 10.81 -18.89 195.35 35.28 137.69 | 1( 1)| 0.00 13.21 -46.61 243.20 33.05 158.07 41- 42 | 1( 1)| 0.00 7.87 -2.59 141.01 27.42 99.23 | 1( 1)| 0.00 9.18 -22.76 166.85 26.53 114.60 | 1( 1)| 0.00 11.19 -46.48 207.71 24.54 132.02 42- 43 | 1( 1)| 0.00 6.48 -9.84 116.99 18.03 80.00 | 1( 1)| 0.00 7.56 -26.63 138.43 17.79 91.99 | 1( 1)| 0.00 9.20 -46.35 172.32 16.04 106.54 43- 44 | 1( 1)| 0.00 5.51 -15.07 99.64 12.02 67.86 | 1( 1)| 0.00 6.43 -29.43 117.90 12.20 77.62 | 1( 1)| 0.00 7.83 -46.25 146.76 10.60 89.97 44- 45 | 1( 1)| 0.00 4.12 -22.31 75.61 2.62 49.18 | 1( 1)| 0.00 4.82 -33.30 89.47 3.45 55.53 | 1( 1)| 0.00 5.87 -46.12 111.38 2.10 64.49 45- 46 | 1( 1)| 0.00 2.06 -33.58 37.81 -9.55 24.59 | 1( 1)| 0.00 2.41 -39.39 44.74 -7.87 27.76 | 1( 1)| 0.00 2.94 -45.91 55.69 -8.91 31.79 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.46 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 2.05 8.66 22.27 74.66 -188.36 39.74 | 1( 1)| 0.35 10.31 11.90 88.94 -225.15 56.34 | 1( 1)| 0.75 10.35 -0.41 110.88 -227.40 52.94 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.88 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 7.01 90.62 -74.25 1823.90 87.57 781.85 | 4( 1)| 2.35 110.14 -333.91 2162.24 105.77 1103.33 | 4( 1)| 10.68 136.08 -153.87 2645.87 106.65 1507.92 53- 54 | 4( 1)| 6.47 88.27 -86.86 1781.23 64.39 748.86 | 4( 1)| 1.27 107.36 -340.82 2111.48 88.40 1061.50 | 4( 1)| 9.64 132.67 -155.42 2582.38 89.89 1459.72 54- 55 | 4( 1)| 6.23 86.89 -94.51 1754.75 51.91 730.50 | 4( 1)| 0.72 105.72 -345.13 2079.80 79.07 1038.17 | 4( 1)| 9.05 130.67 -156.44 2542.53 80.80 1432.45 55- 56 | 4( 1)| 6.05 85.63 -101.49 1730.52 40.51 713.69 | 4( 1)| 0.22 104.23 -349.07 2050.79 70.55 1016.82 | 4( 1)| 8.48 128.84 -157.37 2506.04 72.49 1407.43 56- 57 | 4( 1)| 5.91 84.40 -108.49 1701.46 28.95 692.37 | 4( 1)| 0.00 117.05 -354.01 2014.53 62.06 989.49 | 4( 1)| 7.96 127.06 -158.89 2458.79 63.64 1372.59 57- 58 | 4( 1)| 5.64 83.07 -115.74 1674.62 15.53 671.52 | 4( 1)| 0.52 101.19 -358.46 1981.88 52.07 962.94 | 4( 1)| 7.30 125.12 -160.06 2417.15 53.72 1340.57 58- 59 | 4( 1)| 4.97 81.73 -122.99 1649.55 2.18 652.32 | 4( 1)| 0.00 99.59 -362.56 1951.89 42.08 938.57 | 4( 1)| 6.57 123.16 -161.03 2379.45 44.01 1312.14 59- 60 | 4( 1)| 2.45 76.47 -151.97 1552.29 -44.99 585.61 | 4( 1)| 0.35 93.32 -378.32 1836.42 6.69 853.67 | 4( 1)| 2.89 115.45 -164.54 2235.30 9.90 1215.07 60- 61 | 4( 1)| 1.78 75.14 -159.23 1526.77 -58.35 565.99 | 4( 1)| 0.00 91.72 -382.55 1805.75 -3.30 828.77 | 4( 1)| 0.00 113.49 -165.57 2196.59 -0.01 1185.74 61- 62 | 3( 1)| 0.00 34.47 -519.89 330.67 -705.37 -194.55 | 3( 1)| 1.24 35.69 -575.38 391.01 -773.17 305.18 | 3( 1)| 0.00 39.31 -362.64 478.56 -809.21 281.37 62- 63 | 3( 1)| 3.35 35.78 -529.48 299.87 -724.97 -212.40 | 3( 1)| 0.00 36.71 -580.52 354.61 -794.56 296.02 | 3( 1)| 3.21 39.71 -371.46 437.26 -833.93 274.54 63- 64 | 3( 1)| 4.85 36.88 -537.69 275.36 -742.40 -227.99 | 3( 1)| 1.23 37.64 -585.29 325.82 -813.93 287.64 | 3( 1)| 4.44 40.43 -380.55 408.35 -856.31 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.74 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 1.96 -62.67 34.69 -23.40 24.28 | 1( 1)| 0.00 2.28 -68.58 41.05 -25.66 30.97 | 1( 1)| 0.00 4.25 -90.93 91.24 -28.38 42.12 66- 67 | 1( 1)| 0.00 1.90 -67.90 17.35 -29.41 12.14 | 1( 1)| 0.00 2.13 -71.38 20.53 -30.79 23.78 | 1( 1)| 0.00 3.39 -104.28 75.21 -32.24 27.80 12- 68 | 1( 1)| 1.12 3.12 16.10 53.97 18.24 40.34 | 1( 1)| 0.00 18.07 -405.23 11.53 -151.76 22.08 | 1( 1)| 0.31 23.14 -516.91 13.46 -112.23 135.00 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 0.65 18.59 -416.00 -18.07 -160.28 -0.51 | 1( 1)| 1.00 23.57 -526.75 -23.12 -129.05 128.62 Voltage p.u. min max 1 0.97 1.00 2 0.97 1.02 3 0.96 1.03 Elapsed AMPL time : 27.986s Elapsed Solve time : 372.421s Elapsed CPU time: 400.407s Sumatorio de erros e2 139.93954 Sumatorio de erros pq 60.24529 Sumatorio de erros vi 4.25515 Factor de erro e2 1.00 Factor de erro pq 0.10 Factor de erro vi 1.00 Maximum Psae error 744.16416 Maximo erro superior 5948.1600 Maximo erro inferior -361.6533 TRANSITION 9 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886925 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17074.99441 44 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 17066.65 3711.90 13354.75 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2641.16/ 2666.06/ 1366.48 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 294.27 36.06 0.00 172.12 975.51 0.00 51 0.00 0.00 0.00 229.01 0.90 0.00 64 0.00 0.00 0.00 867.65 23.46 105.47 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 18.34 0.00 0.00 64.00 800.00 0.00 0.00 67.00 63.75 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 639.38 485.62 0.00 50.00 0.00 0.00 0.00 69.00 0.00 832.84 197.52 ESS systems (kW): Node T1 T2 T3 35.00 0.00 193.85 69.21 46.00 0.00 0.00 0.00 64.00 0.00 223.48 904.30 67.00 0.00 0.00 42.40 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 28.38 28.38 28.38 56.94 Structures 18.47 18.47 18.47 37.06 Fixed CBs 0.73 0.82 0.82 1.56 Switchable CBs 4.26 7.62 7.98 12.07 PV systems 546.25 546.25 546.25 1096.02 Wind systems 529.52 1453.56 1570.57 2037.59 EES systems 0.00 254.12 811.55 470.68 Total invesment cost 1127.61 2309.22 2984.01 3711.92 Purchased energy cost 5626.28 6026.25 7110.59 12109.55 Carbon tax payment 194.93 342.16 720.37 685.12 O&M PV cost 53.46 42.87 40.46 95.68 O&M wind cost 90.65 273.15 296.59 374.60 O&M EES cost 0.00 48.54 154.76 89.81 Total O&M cost 5965.31 6732.98 8322.77 13354.75 Total cost 7092.92 9042.19 11306.78 17066.67 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 8800.95 6829.78 130306.45 854.98 0.00 2 112684.31 8800.82 20914.12 141404.09 898.16 209.46 3 131965.73 8800.88 23023.63 161754.72 1215.05 865.17 CO2 Emissions (Ton): Period Distribution EV 1 9739.21 4980.53 2 9837.35 4906.75 3 9889.26 4780.66 4 9916.01 4659.94 5 9990.81 4476.17 6 8525.33 4266.91 7 8604.24 4025.47 8 8668.14 3733.05 9 8709.82 3403.07 10 8847.76 2999.31 11 8861.37 2539.22 12 9016.02 2025.48 13 9139.07 1443.32 14 9218.61 753.85 15 9461.36 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 539.10 4400.46 261.10 2009.02 0.90 0.97 Infinity -Infinity 2 0.00 5131.86 -0.00 2222.61 0.90 1.00 1.00 1.00 3 0.00 6297.82 -0.00 2602.92 0.90 0.99 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 -4.02 186.71 0.00 146.07 2 -197.29 143.30 -149.43 197.19 3 -207.91 122.06 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 193.85 155.08 775.40 214.86 210.44 1052.22 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 178.78 178.78 893.91 902.22 902.22 4511.09 67 0.00 0.00 0.00 0.00 0.00 0.00 33.92 33.92 169.58 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 90.40 193.85 176.82 263.06 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 167.42 223.48 640.39 1041.98 67 0.00 0.00 0.00 0.00 42.40 42.40 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 27.26 219.48 539.09 4399.62 261.09 2008.31 | 4( 2)| 0.00 254.59 0.00 5130.74 -0.00 2221.69 | 4( 2)| 0.00 310.76 0.00 6296.15 -0.00 2601.45 2- 3 | 4( 2)| 26.77 218.12 531.74 4373.33 251.78 1986.39 | 4( 2)| 0.41 252.98 -7.06 5099.05 -8.65 2198.34 | 4( 2)| 0.27 308.80 -4.92 6255.97 -7.47 2572.32 3- 4 | 4( 2)| 18.33 190.40 394.52 3872.85 67.11 1588.86 | 4( 2)| 6.27 220.85 -285.68 4514.04 -180.99 1779.63 | 4( 2)| 5.10 273.73 -268.72 5624.11 -156.75 2066.79 4- 5 | 4( 1)| 11.64 143.33 131.52 3000.21 -232.13 935.87 | 4( 1)| 9.57 165.28 -471.31 3472.33 -456.44 1096.87 | 4( 1)| 12.00 205.59 -344.07 4324.89 -394.49 1245.44 5- 6 | 4( 1)| 11.84 142.02 124.16 2969.88 -241.56 910.71 | 4( 1)| 10.10 163.75 -476.42 3435.55 -465.29 1069.29 | 4( 1)| 12.19 203.70 -352.88 4276.48 -402.10 1218.51 6- 7 | 4( 1)| 12.07 140.71 116.81 2939.50 -251.01 885.50 | 4( 1)| 10.51 162.22 -481.53 3398.70 -474.17 1041.66 | 4( 1)| 12.40 201.81 -361.70 4227.95 -409.72 1191.51 7- 8 | 4( 1)| 12.25 138.62 105.01 2898.99 -264.88 854.03 | 4( 1)| 11.16 159.75 -489.84 3350.17 -486.99 1008.45 | 4( 1)| 12.74 198.77 -375.78 4166.82 -421.34 1159.59 8- 9 | 4( 1)| 4.17 133.50 60.57 2751.13 -86.41 965.51 | 4( 1)| 0.00 152.35 -521.15 3173.51 -511.73 952.85 | 4( 1)| 0.00 189.48 -428.10 3946.23 -461.22 1196.32 9- 10 | 1( 1)| 4.27 45.28 31.10 956.31 -225.05 223.02 | 1( 1)| 2.56 60.62 -716.98 1053.09 -1232.41 3.71 | 1( 1)| 2.48 64.56 -897.90 1340.76 -1124.14 53.28 10- 11 | 3( 1)| 10.86 52.89 21.13 928.69 210.01 669.97 | 3( 1)| 8.29 57.59 -725.28 1019.57 92.98 729.26 | 3( 1)| 8.42 70.89 -903.92 1298.71 76.09 848.93 11- 12 | 2( 1)| 7.60 43.59 -12.36 767.32 149.84 545.86 | 2( 1)| 4.72 46.57 -756.57 818.20 49.11 583.42 | 2( 1)| 5.92 57.09 -915.86 1046.71 43.44 671.30 12- 13 | 1( 1)| 2.31 32.34 -84.29 569.30 73.63 399.55 | 1( 1)| 3.82 36.35 -383.59 642.48 61.85 443.74 | 1( 1)| 4.01 45.13 -436.50 828.46 58.71 513.34 13- 14 | 1( 1)| 1.69 30.20 -98.72 527.75 60.60 373.68 | 1( 1)| 3.19 33.85 -396.60 593.21 49.74 414.08 | 1( 1)| 3.88 42.06 -446.41 765.45 48.35 479.24 14- 15 | 1( 1)| 1.51 27.98 -113.14 486.58 46.17 345.55 | 1( 1)| 2.49 31.27 -409.65 544.75 36.33 381.83 | 1( 1)| 2.81 38.88 -456.34 703.18 36.87 441.80 15- 16 | 1( 1)| 1.70 26.50 -122.12 461.88 35.43 325.28 | 1( 1)| 2.02 29.55 -417.96 515.77 26.38 358.64 | 1( 1)| 2.04 36.79 -461.63 666.33 28.36 415.34 16- 17 | 1( 1)| 1.76 24.00 -138.67 417.15 19.59 294.88 | 1( 1)| 1.86 26.62 -435.58 463.31 11.70 323.84 | 1( 1)| 1.26 33.19 -471.27 599.63 14.33 375.62 17- 18 | 1( 1)| 0.85 20.81 -163.57 358.59 1.29 259.89 | 1( 1)| 1.90 23.37 -458.47 394.66 -5.36 283.81 | 1( 1)| 1.25 28.57 -483.26 512.62 -3.10 330.00 18- 19 | 1( 1)| 1.20 17.62 -188.53 299.81 -17.02 224.86 | 1( 1)| 1.61 23.71 -481.73 325.76 -25.54 254.09 | 1( 1)| 1.17 25.45 -497.24 425.22 -24.70 284.30 19- 20 | 1( 1)| 1.45 16.44 -198.92 275.36 -22.13 215.07 | 1( 1)| 1.88 23.90 -491.50 297.09 -32.00 250.03 | 1( 1)| 1.42 25.57 -506.18 388.85 -30.73 274.48 20- 21 | 1( 1)| 1.42 14.83 -211.47 245.89 -31.47 196.87 | 1( 1)| 1.79 24.09 -503.42 262.56 -43.81 242.38 | 1( 1)| 1.52 25.66 -517.10 345.03 -41.76 267.83 21- 22 | 1( 1)| 0.00 11.68 -258.76 134.80 -74.24 115.84 | 1( 1)| 1.39 24.77 -546.75 132.87 -97.90 207.92 | 1( 1)| 1.03 25.98 -556.33 180.71 -97.75 238.07 22- 23 | 1( 1)| 0.77 12.61 -279.51 86.21 -92.73 80.96 | 1( 1)| 1.18 25.35 -566.00 75.92 -121.71 192.96 | 1( 1)| 1.04 26.16 -573.86 110.85 -122.21 225.13 23- 24 | 1( 1)| 0.00 13.10 -290.02 61.91 -103.50 61.02 | 1( 1)| 1.19 25.79 -576.15 47.44 -136.95 184.16 | 1( 1)| 0.78 26.24 -583.17 76.38 -136.47 217.50 24- 25 | 1( 1)| 0.57 13.65 -301.93 35.33 -114.15 41.09 | 1( 1)| 0.84 26.29 -588.40 16.11 -152.03 175.32 | 1( 1)| 0.71 26.47 -594.46 37.45 -150.58 209.80 25- 26 | 1( 1)| 0.37 14.16 -312.46 12.38 -124.92 21.16 | 1( 1)| 0.72 26.73 -598.54 -10.10 -167.28 166.53 | 1( 1)| 0.49 26.84 -603.75 3.01 -165.85 202.18 26- 27 | 1( 1)| 0.58 14.73 -324.06 -13.12 -135.51 1.23 | 1( 1)| 1.94 27.24 -609.63 -39.70 -182.26 157.94 | 1( 1)| 1.58 27.28 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 1.35 13.32 -2.22 227.64 62.26 182.77 | 1( 1)| 1.70 17.02 -15.73 329.41 47.34 207.84 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 0.00 11.66 -8.32 221.68 54.96 161.22 | 1( 1)| 0.99 15.23 -28.32 295.93 41.83 183.29 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 0.00 9.99 -14.43 217.42 47.67 139.66 | 1( 1)| 0.37 13.43 -40.92 269.16 36.29 158.71 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 0.00 8.32 -20.31 213.32 39.72 116.58 | 1( 1)| 0.00 11.66 -60.10 268.30 30.29 132.41 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 0.00 6.64 -26.20 209.22 31.78 93.49 | 1( 1)| 0.00 9.96 -84.63 267.36 24.26 106.10 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 0.00 4.84 -32.85 204.59 23.97 70.40 | 1( 1)| 0.00 9.91 -112.40 266.17 18.31 79.78 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 1( 1)| 0.00 3.04 -39.49 199.93 16.15 47.31 | 1( 1)| 0.00 9.85 -140.29 264.73 12.29 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.00 1.73 -53.73 196.81 4.69 13.85 | 1( 1)| 0.00 9.86 -159.11 263.66 3.54 15.78 3- 36 | 1( 1)| 5.21 16.29 71.51 286.05 93.28 216.62 | 1( 1)| 4.13 19.06 31.54 342.20 89.82 248.18 | 1( 1)| 2.84 23.22 -16.07 427.25 68.98 283.19 36- 37 | 1( 1)| 4.67 14.86 64.00 260.90 84.76 197.78 | 1( 1)| 3.73 17.39 27.52 312.14 82.53 226.63 | 1( 1)| 2.56 21.20 -15.93 389.76 63.47 258.63 37- 38 | 1( 1)| 4.12 13.42 56.48 235.74 76.24 178.94 | 1( 1)| 3.32 15.73 23.51 282.06 75.23 205.08 | 1( 1)| 2.28 19.17 -15.79 352.24 57.96 234.06 38- 39 | 1( 1)| 3.54 11.98 49.23 211.56 66.96 158.77 | 1( 1)| 2.87 14.07 19.63 253.12 67.29 182.00 | 1( 1)| 1.96 17.16 -15.66 316.15 51.96 207.76 39- 40 | 1( 1)| 3.02 10.65 42.26 188.41 59.20 141.62 | 1( 1)| 2.48 12.54 15.90 225.22 60.65 162.37 | 1( 1)| 1.68 15.29 -15.53 281.37 46.94 185.40 40- 41 | 1( 1)| 2.49 9.33 35.27 165.09 51.44 124.43 | 1( 1)| 2.08 11.00 12.17 197.10 53.40 142.70 | 1( 1)| 1.38 13.42 -15.41 246.24 41.93 162.97 41- 42 | 1( 1)| 1.84 7.90 28.02 141.01 42.16 104.24 | 1( 1)| 1.57 9.34 8.29 168.09 44.65 119.60 | 1( 1)| 0.97 11.40 -15.28 210.05 35.93 136.65 42- 43 | 1( 1)| 1.08 6.49 20.78 116.99 32.88 84.07 | 1( 1)| 0.97 7.67 4.42 139.15 35.38 96.52 | 1( 1)| 0.35 9.38 -15.15 173.97 29.93 110.35 43- 44 | 1( 1)| 0.00 5.51 15.55 99.64 26.94 70.96 | 1( 1)| 0.00 6.51 1.62 118.25 29.08 81.52 | 1( 1)| 0.00 7.97 -15.05 147.92 25.44 93.26 44- 45 | 1( 1)| 0.00 4.12 8.30 75.61 17.66 52.01 | 1( 1)| 0.00 4.85 -2.25 89.47 19.22 58.44 | 1( 1)| 0.00 5.95 -14.92 111.84 16.94 66.96 45- 46 | 1( 1)| 0.00 2.06 -2.96 37.81 5.56 28.02 | 1( 1)| 0.00 2.41 -8.34 44.74 6.38 29.52 | 1( 1)| 0.00 2.94 -14.71 55.69 5.93 32.72 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.46 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 2.05 9.33 22.27 74.66 -203.78 39.74 | 1( 1)| 0.00 9.41 11.90 88.94 -206.11 57.47 | 1( 1)| 0.75 9.41 -0.41 110.88 -206.77 54.05 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.88 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 6.52 89.77 -74.23 1823.99 -2.29 734.86 | 4( 1)| 4.65 107.50 -207.13 2121.59 91.98 1057.75 | 4( 1)| 15.69 134.25 -104.60 2618.23 106.82 1472.87 53- 54 | 4( 1)| 6.00 87.44 -86.84 1781.33 -24.34 701.89 | 4( 1)| 3.62 104.73 -214.65 2071.06 74.70 1015.94 | 4( 1)| 15.07 130.85 -110.39 2554.80 91.79 1424.69 54- 55 | 4( 1)| 5.79 86.07 -94.49 1754.85 -36.35 683.54 | 4( 1)| 3.06 103.11 -219.14 2039.67 65.40 992.64 | 4( 1)| 14.72 128.85 -113.99 2515.03 83.68 1397.45 55- 56 | 4( 1)| 5.63 84.82 -101.46 1730.62 -47.31 666.75 | 4( 1)| 2.54 101.64 -223.22 2010.96 56.92 971.31 | 4( 1)| 14.40 127.02 -117.29 2478.60 76.27 1372.46 56- 57 | 4( 1)| 5.51 83.59 -108.45 1701.57 -59.39 645.53 | 4( 1)| 2.02 100.24 -226.70 1976.28 48.37 944.13 | 4( 1)| 14.11 125.24 -121.28 2431.77 68.64 1337.78 57- 58 | 4( 1)| 5.39 82.27 -115.70 1674.73 -72.61 624.73 | 4( 1)| 1.34 98.69 -230.71 1944.39 38.41 917.65 | 4( 1)| 13.78 123.32 -124.96 2390.33 59.21 1305.84 58- 59 | 4( 1)| 4.89 80.93 -122.95 1649.67 -85.42 605.55 | 4( 1)| 0.34 97.10 -234.94 1914.68 28.46 893.31 | 4( 1)| 13.46 121.42 -128.38 2352.70 49.41 1277.45 59- 60 | 4( 1)| 2.38 75.72 -151.93 1552.40 -130.62 538.87 | 4( 1)| 0.00 90.86 -252.25 1799.55 -6.71 808.43 | 4( 1)| 12.22 113.97 -141.62 2208.64 14.88 1180.41 60- 61 | 4( 1)| 1.73 74.40 -159.18 1526.88 -143.82 519.27 | 4( 1)| 0.00 89.29 -256.37 1769.31 -16.65 783.57 | 4( 1)| 11.92 112.06 -145.13 2170.05 5.04 1151.12 61- 62 | 3( 1)| 13.34 35.94 -519.85 330.77 -758.20 -235.48 | 3( 1)| 3.49 35.76 -474.14 379.30 -774.83 294.13 | 3( 1)| 0.00 39.55 -362.63 486.96 -815.27 281.45 62- 63 | 3( 1)| 14.03 37.24 -529.44 299.96 -777.82 -253.33 | 3( 1)| 3.39 36.79 -479.77 344.00 -796.22 285.13 | 3( 1)| 2.06 39.98 -371.45 453.51 -839.99 274.61 63- 64 | 3( 1)| 14.38 38.34 -537.69 275.36 -795.34 -268.94 | 3( 1)| 3.86 37.71 -484.36 316.09 -815.59 277.11 | 3( 1)| 3.13 40.70 -378.61 450.84 -862.38 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.74 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 1.96 -39.00 34.69 -11.94 24.28 | 1( 1)| 0.00 2.28 -44.57 41.05 -14.03 27.41 | 1( 1)| 0.00 3.62 -46.05 76.41 -13.09 39.19 66- 67 | 1( 1)| 0.00 1.82 -44.23 17.35 -17.95 12.14 | 1( 1)| 0.00 1.98 -47.37 20.53 -19.16 18.08 | 1( 1)| 0.00 2.70 -59.40 58.88 -17.39 22.10 12- 68 | 1( 1)| 1.12 3.12 16.10 53.97 18.24 40.34 | 1( 1)| 0.52 19.78 -437.75 7.90 -142.86 20.32 | 1( 1)| 0.56 24.85 -551.54 9.30 -121.67 121.33 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 0.99 20.30 -448.53 -21.70 -151.39 -2.27 | 1( 1)| 1.25 25.28 -561.41 -26.84 -138.49 114.94 Voltage p.u. min max 1 0.97 1.01 2 0.97 1.02 3 0.96 1.03 Elapsed AMPL time : 31.798s Elapsed Solve time : 425.656s Elapsed CPU time: 457.454s Sumatorio de erros e2 0.22961 Sumatorio de erros pq 60.49310 Sumatorio de erros vi 6.44603 Factor de erro e2 10.00 Factor de erro pq 0.10 Factor de erro vi 1.00 Maximum Psae error 930.53843 Maximo erro superior 2.1830 Maximo erro inferior -217.3915 TRANSITION 10 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886926 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17071.16137 43 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 17067.68 3712.04 13355.64 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2655.34/ 2652.63/ 1342.06 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 344.05 0.00 0.00 227.09 903.80 0.00 51 0.00 0.00 0.00 209.15 4.24 0.00 64 0.00 0.00 0.00 781.32 114.46 104.44 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 800.00 0.00 0.00 67.00 44.80 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 677.10 447.90 0.00 50.00 0.00 0.00 0.00 69.00 0.00 877.21 187.59 ESS systems (kW): Node T1 T2 T3 35.00 0.00 90.45 67.82 46.00 0.00 0.00 0.00 64.00 0.00 306.50 917.24 67.00 0.00 0.00 20.93 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 0.85 0.85 0.85 1.71 Switchable CBs 4.09 7.53 7.88 11.80 PV systems 523.16 523.16 523.16 1049.70 Wind systems 560.76 1489.46 1600.59 2102.69 EES systems 0.00 241.72 793.70 456.10 Total invesment cost 1133.75 2307.60 2971.07 3712.06 Purchased energy cost 5625.06 6021.33 7112.88 12106.15 Carbon tax payment 194.93 342.19 720.45 685.16 O&M PV cost 51.20 41.06 38.75 91.63 O&M wind cost 96.00 279.34 301.33 385.62 O&M EES cost 0.00 46.17 151.49 87.08 Total O&M cost 5967.18 6730.09 8324.90 13355.64 Total cost 7100.92 9037.69 11295.97 17067.70 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 8428.96 7232.72 130306.45 868.27 0.00 2 112691.67 8428.83 21388.14 141404.09 903.52 235.92 3 131981.43 8428.89 23391.53 161754.72 1225.64 847.09 CO2 Emissions (Ton): Period Distribution EV 1 9738.53 4980.53 2 9837.14 4906.75 3 9889.35 4780.66 4 9916.25 4659.94 5 9991.38 4476.17 6 8525.65 4266.91 7 8604.72 4025.47 8 8668.67 3733.05 9 8710.37 3403.07 10 8848.71 2999.31 11 8861.93 2539.22 12 9016.91 2025.48 13 9140.15 1443.32 14 9219.79 753.85 15 9463.09 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 557.27 4403.17 269.90 1990.45 0.90 0.97 Infinity -Infinity 2 0.00 5074.58 -0.00 2207.16 0.90 1.00 1.00 1.00 3 0.00 6275.10 -0.00 2594.42 0.90 0.99 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 -1.34 225.19 0.00 154.69 2 -197.29 167.52 -116.37 197.19 3 -207.91 139.39 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 72.36 72.36 361.81 126.62 126.62 633.08 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 245.20 245.20 1226.02 978.99 978.99 4894.97 67 0.00 0.00 0.00 0.00 0.00 0.00 16.75 16.75 83.74 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 53.11 90.45 111.49 158.27 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 217.42 306.50 692.56 1115.59 67 0.00 0.00 0.00 0.00 20.93 20.93 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 28.22 219.18 557.25 4402.33 269.88 1989.74 | 4( 2)| 0.00 251.94 0.00 5073.48 -0.00 2206.26 | 4( 2)| 0.00 309.66 0.00 6273.44 -0.00 2592.96 2- 3 | 4( 2)| 27.74 217.82 549.90 4376.05 260.57 1967.82 | 4( 2)| 0.41 250.33 -7.06 5041.85 -8.65 2182.96 | 4( 2)| 0.27 307.70 -4.92 6233.25 -7.47 2563.86 3- 4 | 4( 2)| 18.55 190.05 399.06 3873.79 79.03 1567.95 | 4( 2)| 6.53 218.83 -202.50 4472.48 -177.98 1764.29 | 4( 2)| 5.48 271.90 -176.98 5584.95 -153.70 2057.53 4- 5 | 4( 1)| 11.66 143.06 136.07 3001.14 -220.08 914.97 | 4( 1)| 10.34 163.27 -406.96 3430.78 -453.43 1081.54 | 4( 1)| 10.75 203.75 -353.94 4285.74 -392.44 1237.73 5- 6 | 4( 1)| 11.85 141.76 128.71 2970.82 -229.52 889.81 | 4( 1)| 10.76 161.73 -414.26 3394.16 -462.29 1054.15 | 4( 1)| 10.90 201.86 -362.73 4237.57 -401.41 1210.83 6- 7 | 4( 1)| 12.07 140.45 121.35 2940.44 -238.96 864.61 | 4( 1)| 11.19 160.19 -421.57 3357.47 -471.17 1026.71 | 4( 1)| 11.07 199.97 -371.55 4189.28 -410.39 1183.88 7- 8 | 4( 1)| 12.23 138.36 109.56 2899.94 -252.84 833.13 | 4( 1)| 11.83 157.72 -433.01 3308.98 -483.99 993.99 | 4( 1)| 11.35 196.93 -385.62 4128.21 -423.58 1151.97 8- 9 | 4( 1)| 4.98 132.93 65.12 2752.09 -94.22 928.53 | 4( 1)| 0.00 150.25 -475.90 3132.34 -487.06 933.47 | 4( 1)| 3.99 187.62 -437.93 3907.66 -458.17 1184.09 9- 10 | 1( 1)| 4.41 45.53 22.48 960.48 -247.79 223.93 | 1( 1)| 1.78 58.61 -729.09 1053.66 -1228.24 -1.90 | 1( 1)| 1.32 64.63 -904.13 1334.23 -1120.12 32.94 10- 11 | 3( 1)| 10.49 53.09 12.51 932.75 203.97 671.26 | 3( 1)| 8.26 57.71 -737.39 1020.13 99.41 729.14 | 3( 1)| 8.64 71.01 -910.22 1292.19 99.92 844.79 11- 12 | 1( 1)| 7.20 43.46 -30.40 764.66 141.29 544.60 | 1( 1)| 5.10 46.41 -780.97 815.14 49.40 581.94 | 1( 1)| 6.04 56.95 -933.17 1044.07 60.71 670.19 12- 13 | 1( 1)| 3.03 32.21 -102.33 566.67 65.07 398.29 | 1( 1)| 3.86 36.35 -384.09 642.47 62.11 443.74 | 1( 1)| 4.00 45.13 -436.51 828.46 57.65 513.34 13- 14 | 1( 1)| 2.92 30.06 -116.75 525.15 52.04 372.43 | 1( 1)| 3.22 33.85 -396.97 593.21 50.00 414.08 | 1( 1)| 3.87 42.05 -446.41 765.45 47.29 479.24 14- 15 | 1( 1)| 3.14 27.85 -131.18 483.99 37.60 344.30 | 1( 1)| 2.53 31.27 -409.90 544.75 36.59 381.83 | 1( 1)| 2.78 38.88 -456.35 703.18 35.81 441.80 15- 16 | 1( 1)| 2.86 26.37 -140.16 459.30 26.87 324.04 | 1( 1)| 2.05 29.55 -417.96 515.77 26.64 358.64 | 1( 1)| 2.01 36.79 -461.63 666.33 27.30 415.34 16- 17 | 1( 1)| 1.96 23.86 -158.26 414.58 11.02 293.64 | 1( 1)| 1.86 26.62 -435.58 463.31 11.67 323.84 | 1( 1)| 1.23 33.19 -471.27 599.63 14.73 375.62 17- 18 | 1( 1)| 1.66 20.67 -183.17 356.02 -7.28 258.65 | 1( 1)| 1.90 22.90 -458.47 394.66 -5.71 283.81 | 1( 1)| 1.25 28.57 -483.26 512.62 -2.29 330.00 18- 19 | 1( 1)| 1.58 17.49 -208.15 297.25 -25.60 223.62 | 1( 1)| 1.67 23.06 -481.72 325.76 -25.86 243.73 | 1( 1)| 1.17 25.44 -497.25 425.22 -23.89 284.30 19- 20 | 1( 1)| 1.81 16.30 -218.55 272.79 -30.71 213.83 | 1( 1)| 1.93 23.27 -491.50 297.09 -31.92 232.53 | 1( 1)| 1.42 25.56 -506.19 388.85 -30.06 274.48 20- 21 | 1( 1)| 1.71 14.70 -231.11 243.33 -40.05 195.63 | 1( 1)| 1.79 23.48 -503.42 262.56 -42.99 211.70 | 1( 1)| 1.52 25.66 -517.11 345.03 -42.41 267.83 21- 22 | 1( 1)| 1.18 12.64 -278.40 132.24 -82.82 114.74 | 1( 1)| 1.39 24.49 -546.74 132.87 -97.02 174.83 | 1( 1)| 1.03 25.98 -556.33 180.71 -98.97 238.07 22- 23 | 1( 1)| 1.01 13.60 -299.17 83.65 -101.32 79.85 | 1( 1)| 1.18 25.36 -565.99 75.92 -121.71 159.87 | 1( 1)| 1.04 26.15 -573.87 110.85 -123.44 225.13 23- 24 | 1( 1)| 0.87 14.11 -309.71 59.35 -112.10 59.92 | 1( 1)| 1.19 25.81 -576.15 47.44 -136.95 151.08 | 1( 1)| 0.78 26.23 -583.17 76.38 -137.69 217.50 24- 25 | 1( 1)| 0.68 14.67 -321.68 33.05 -122.76 39.99 | 1( 1)| 0.84 26.31 -588.40 16.11 -152.03 142.25 | 1( 1)| 0.71 26.46 -594.46 37.45 -151.80 209.80 25- 26 | 1( 1)| 0.49 15.19 -332.24 10.10 -133.54 20.05 | 1( 1)| 0.72 26.76 -598.54 -10.10 -167.28 133.46 | 1( 1)| 0.49 26.84 -603.75 3.01 -166.07 202.18 26- 27 | 1( 1)| 0.71 15.77 -343.86 -15.40 -144.13 0.12 | 1( 1)| 1.94 27.28 -609.63 -39.70 -182.26 124.87 | 1( 1)| 1.58 27.28 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.09 13.60 21.54 235.30 62.25 182.77 | 1( 1)| 2.24 16.91 28.65 326.06 47.02 207.83 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.63 11.93 15.43 205.75 54.95 161.23 | 1( 1)| 1.95 15.12 17.08 292.58 41.51 183.28 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.18 10.26 9.32 176.10 47.66 139.66 | 1( 1)| 1.67 13.32 4.48 258.93 36.00 158.70 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 1.68 8.59 3.44 147.61 39.72 116.58 | 1( 1)| 1.20 11.55 -7.45 226.65 30.00 132.40 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.18 6.91 -2.45 119.80 31.77 93.49 | 1( 1)| 0.00 9.78 -19.69 194.31 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 0.00 5.10 -9.10 103.94 23.96 70.40 | 1( 1)| 0.00 7.85 -47.39 160.75 18.10 79.78 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 1( 1)| 0.00 3.40 -18.53 98.10 16.15 47.31 | 1( 1)| 0.00 5.92 -75.12 159.64 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.00 2.89 -36.26 94.18 4.69 13.85 | 1( 1)| 0.00 5.49 -93.78 158.87 3.54 15.78 3- 36 | 1( 1)| 5.98 16.54 85.76 288.71 99.57 218.95 | 1( 1)| 4.40 19.22 45.98 343.96 85.30 250.52 | 1( 1)| 2.87 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.46 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.01 17.55 41.97 313.91 78.00 228.96 | 1( 1)| 2.61 21.28 -1.43 391.48 58.92 260.91 37- 38 | 1( 1)| 4.93 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.63 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.35 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.39 12.23 63.48 213.94 73.27 161.10 | 1( 1)| 3.21 14.21 34.08 254.88 62.77 184.33 | 1( 1)| 2.06 17.24 -1.16 317.86 47.41 210.05 39- 40 | 1( 1)| 3.91 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.85 12.67 30.35 226.99 56.13 164.70 | 1( 1)| 1.81 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.42 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.49 11.13 26.60 198.86 49.48 145.03 | 1( 1)| 1.57 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.87 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.07 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.26 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.31 6.69 35.01 118.29 39.21 86.40 | 1( 1)| 1.63 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 0.93 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 1.93 5.69 29.78 100.75 33.29 73.29 | 1( 1)| 1.34 6.62 16.06 120.01 28.52 83.85 | 1( 1)| 0.70 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.35 4.25 22.53 76.46 24.02 53.12 | 1( 1)| 0.86 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.15 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.32 2.11 11.27 38.23 12.01 26.56 | 1( 1)| 0.00 2.47 6.09 45.54 10.29 30.38 | 1( 1)| 0.00 3.02 -0.21 56.77 7.77 34.62 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.46 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 1.42 8.42 22.27 74.66 -183.92 39.74 | 1( 1)| 0.00 8.65 11.90 88.94 -189.59 58.18 | 1( 1)| 0.75 8.72 -0.41 110.88 -190.25 55.24 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.88 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 6.23 89.06 -74.20 1824.09 100.14 692.30 | 4( 1)| 6.99 106.36 -178.31 2097.35 104.42 1015.23 | 4( 1)| 19.60 133.37 -140.86 2596.24 102.40 1438.18 53- 54 | 4( 1)| 5.72 86.75 -86.82 1781.42 77.98 659.34 | 4( 1)| 6.00 103.66 -185.88 2048.12 87.14 973.43 | 4( 1)| 18.86 130.08 -146.66 2535.03 87.36 1390.03 54- 55 | 4( 1)| 5.51 85.38 -94.47 1754.94 66.06 641.01 | 4( 1)| 5.45 102.07 -190.43 2017.41 77.82 950.16 | 4( 1)| 18.46 128.14 -150.27 2496.51 79.22 1362.82 55- 56 | 4( 1)| 5.37 84.14 -101.45 1730.72 55.18 624.24 | 4( 1)| 4.95 100.62 -194.57 1989.29 69.33 928.85 | 4( 1)| 18.11 126.37 -153.57 2461.21 71.80 1337.86 56- 57 | 4( 1)| 5.27 82.91 -108.45 1701.68 44.24 603.10 | 4( 1)| 4.46 99.20 -198.40 1954.26 60.69 901.80 | 4( 1)| 17.76 124.63 -157.60 2414.65 64.05 1303.34 57- 58 | 4( 1)| 5.06 81.60 -115.70 1674.84 31.47 582.34 | 4( 1)| 3.88 97.66 -202.59 1922.65 50.68 875.38 | 4( 1)| 17.35 122.74 -161.29 2374.07 55.24 1271.48 58- 59 | 4( 1)| 4.56 80.28 -122.95 1649.78 18.71 563.18 | 4( 1)| 3.29 96.10 -206.89 1893.58 40.72 851.07 | 4( 1)| 16.95 120.83 -164.72 2337.60 46.54 1243.12 59- 60 | 4( 1)| 2.49 75.11 -151.94 1552.51 -26.42 496.51 | 4( 1)| 1.12 90.02 -224.29 1781.59 5.53 766.22 | 4( 1)| 15.57 113.39 -177.97 2198.75 15.91 1146.11 60- 61 | 4( 1)| 1.83 73.80 -159.20 1526.99 -39.16 476.94 | 4( 1)| 0.00 88.48 -228.54 1751.86 -4.44 741.40 | 4( 1)| 15.20 111.49 -181.49 2161.20 6.34 1116.87 61- 62 | 3( 1)| 0.00 36.06 -519.86 330.87 -704.73 -272.62 | 3( 1)| 5.96 35.82 -458.99 379.36 -776.06 294.16 | 3( 1)| 0.00 39.75 -362.62 493.47 -819.85 281.51 62- 63 | 3( 1)| 3.32 37.36 -529.45 300.04 -724.32 -290.48 | 3( 1)| 6.00 36.84 -466.62 344.05 -797.45 285.16 | 3( 1)| 0.81 40.14 -371.44 475.89 -843.61 274.66 63- 64 | 3( 1)| 4.82 38.45 -537.69 275.36 -741.74 -306.10 | 3( 1)| 6.37 37.77 -473.01 316.09 -816.82 277.11 | 3( 1)| 1.83 40.87 -390.79 473.20 -866.01 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.87 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.74 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 1.96 -24.30 34.69 -4.82 24.28 | 1( 1)| 0.00 2.28 -29.67 41.05 -6.81 35.59 | 1( 1)| 0.00 3.09 -30.29 61.81 -6.06 39.05 66- 67 | 1( 1)| 0.00 1.23 -29.53 17.35 -10.83 12.14 | 1( 1)| 0.00 1.38 -32.46 20.53 -11.94 20.91 | 1( 1)| 0.00 1.89 -34.26 40.26 -10.58 23.57 12- 68 | 1( 1)| 1.12 3.12 16.10 53.97 18.24 40.34 | 1( 1)| 0.50 20.92 -462.20 5.17 -134.39 18.99 | 1( 1)| 0.52 25.73 -570.62 7.01 -125.89 115.98 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.13 21.44 -473.00 -24.44 -142.92 -3.59 | 1( 1)| 1.36 26.16 -580.50 -28.89 -142.71 109.60 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 35.611s Elapsed Solve time : 477.749s Elapsed CPU time: 513.360s Sumatorio de erros e2 0.01987 Sumatorio de erros pq 32.78536 Sumatorio de erros vi 4.55312 Factor de erro e2 10.00 Factor de erro pq 0.10 Factor de erro vi 1.00 Maximum Psae error 1062.91723 Maximo erro superior 2.3364 Maximo erro inferior -358.1427 TRANSITION 11 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886922 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17070.32117 46 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 17067.39 3710.69 13356.70 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2659.57/ 2644.93/ 1337.28 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 294.08 34.05 0.00 168.55 981.70 0.00 51 0.00 0.00 0.00 212.63 0.00 0.00 64 0.00 0.00 0.00 869.29 28.44 105.34 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 800.00 0.00 0.00 67.00 30.39 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 690.08 434.92 0.00 50.00 0.00 0.00 0.00 69.00 0.00 890.93 186.99 ESS systems (kW): Node T1 T2 T3 35.00 0.00 33.61 64.99 46.00 0.00 0.00 0.00 64.00 0.00 355.79 935.35 67.00 0.00 0.00 1.96 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 0.73 0.81 0.81 1.55 Switchable CBs 4.20 7.59 7.95 11.98 PV systems 514.23 514.23 514.23 1031.79 Wind systems 571.51 1500.72 1611.50 2124.65 EES systems 0.00 237.12 787.08 450.69 Total invesment cost 1135.55 2305.37 2966.46 3710.71 Purchased energy cost 5624.51 6021.56 7113.67 12106.05 Carbon tax payment 194.92 342.19 720.47 685.17 O&M PV cost 50.33 40.36 38.09 90.07 O&M wind cost 97.84 281.25 303.13 389.34 O&M EES cost 0.00 45.30 150.28 86.06 Total O&M cost 5967.60 6730.66 8325.64 13356.70 Total cost 7103.15 9036.03 11292.11 17067.41 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 8285.14 7371.33 130306.45 873.21 0.00 2 112693.77 8285.02 21534.68 141404.09 896.85 232.09 3 131985.65 8285.07 23531.71 161754.72 1221.81 840.15 CO2 Emissions (Ton): Period Distribution EV 1 9738.33 4980.53 2 9837.07 4906.75 3 9889.37 4780.66 4 9916.32 4659.94 5 9991.55 4476.17 6 8525.73 4266.91 7 8604.85 4025.47 8 8668.82 3733.05 9 8710.53 3403.07 10 8849.00 2999.31 11 8862.09 2539.22 12 9017.16 2025.48 13 9140.44 1443.32 14 9220.10 753.85 15 9463.55 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 564.66 4403.58 273.48 1971.36 0.90 0.97 Infinity -Infinity 2 0.00 5045.10 -0.00 2191.41 0.90 1.00 1.00 1.00 3 0.00 6286.17 -0.00 2585.36 0.90 0.99 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 -4.70 190.99 0.00 156.60 2 -197.29 151.62 -99.51 197.19 3 -207.91 127.00 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 26.89 26.89 134.44 78.88 78.88 394.41 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 284.64 284.64 1423.18 1032.92 1032.92 5164.58 67 0.00 0.00 0.00 0.00 0.00 0.00 1.57 1.57 7.84 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 33.54 33.61 90.77 98.60 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 242.24 355.79 729.43 1182.25 67 0.00 0.00 0.00 0.00 1.96 1.96 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 28.61 218.79 564.65 4402.74 273.47 1970.65 | 4( 2)| 0.00 250.45 0.00 5044.01 -0.00 2190.53 | 4( 2)| 0.00 309.97 0.00 6284.49 -0.00 2583.88 2- 3 | 4( 2)| 28.13 217.43 557.30 4376.47 264.15 1948.73 | 4( 2)| 0.41 248.84 -7.06 5012.40 -8.65 2167.25 | 4( 2)| 0.27 308.01 -4.92 6244.28 -7.47 2554.78 3- 4 | 4( 2)| 18.91 189.70 406.46 3874.21 82.61 1548.87 | 4( 2)| 6.60 216.81 -153.14 4430.56 -177.98 1748.62 | 4( 2)| 5.56 270.54 -169.96 5556.45 -153.70 2048.49 4- 5 | 4( 1)| 11.70 142.79 143.46 3001.57 -215.83 895.88 | 4( 1)| 11.40 161.25 -406.97 3388.87 -453.43 1066.86 | 4( 1)| 10.70 202.39 -356.72 4257.25 -393.79 1230.16 5- 6 | 4( 1)| 11.88 141.49 136.10 2971.28 -225.27 870.74 | 4( 1)| 11.61 159.71 -414.27 3352.45 -462.29 1040.16 | 4( 1)| 10.81 200.49 -365.52 4209.15 -402.76 1203.28 6- 7 | 4( 1)| 12.08 140.18 128.74 2940.92 -234.71 845.55 | 4( 1)| 11.84 158.17 -421.59 3315.96 -471.17 1013.40 | 4( 1)| 10.95 198.60 -374.33 4160.95 -411.74 1176.35 7- 8 | 4( 1)| 12.30 138.11 116.95 2900.42 -248.58 814.07 | 4( 1)| 12.20 155.70 -433.03 3267.52 -483.99 980.98 | 4( 1)| 11.18 195.56 -388.40 4099.90 -424.93 1144.45 8- 9 | 4( 1)| 4.99 132.41 72.51 2752.57 -86.49 899.02 | 4( 1)| 2.06 148.16 -475.93 3090.90 -487.02 914.28 | 4( 1)| 4.05 186.20 -440.71 3879.35 -458.16 1171.98 9- 10 | 1( 1)| 3.64 45.72 23.34 963.40 -219.07 229.49 | 1( 1)| 1.69 58.51 -729.33 1054.02 -1228.23 1.95 | 1( 1)| 0.00 64.72 -907.28 1348.52 -1120.20 47.15 10- 11 | 3( 1)| 10.13 53.24 13.36 935.67 211.07 672.67 | 3( 1)| 8.21 57.86 -737.62 1020.49 102.43 729.06 | 3( 1)| 8.81 71.18 -913.36 1306.43 123.19 841.19 11- 12 | 1( 1)| 7.05 43.50 -36.62 763.78 139.39 544.17 | 1( 1)| 4.85 46.46 -788.56 814.25 47.70 581.49 | 1( 1)| 5.62 57.04 -939.84 1043.18 66.76 669.79 12- 13 | 1( 1)| 3.17 32.23 -108.54 565.79 63.18 397.87 | 1( 1)| 3.82 36.43 -384.51 642.51 61.68 443.75 | 1( 1)| 3.94 45.25 -436.55 828.53 57.23 513.35 13- 14 | 1( 1)| 3.16 30.08 -122.95 524.27 50.15 372.01 | 1( 1)| 3.19 33.92 -397.29 593.23 49.58 414.08 | 1( 1)| 3.82 42.16 -446.44 765.49 46.87 479.25 14- 15 | 1( 1)| 3.45 27.85 -137.38 483.11 35.71 343.88 | 1( 1)| 2.50 31.33 -410.11 544.76 36.16 381.83 | 1( 1)| 2.71 38.98 -456.37 703.20 35.39 441.81 15- 16 | 1( 1)| 2.78 26.38 -146.36 458.42 24.97 323.61 | 1( 1)| 2.02 29.61 -417.98 515.78 26.22 358.64 | 1( 1)| 1.94 36.88 -461.66 666.34 26.88 415.34 16- 17 | 1( 1)| 2.02 23.86 -165.00 413.70 9.12 293.21 | 1( 1)| 1.86 26.68 -435.60 463.31 11.54 323.84 | 1( 1)| 1.22 33.28 -471.29 599.64 14.32 375.62 17- 18 | 1( 1)| 1.73 20.67 -189.90 355.14 -9.18 258.22 | 1( 1)| 1.90 22.95 -458.48 394.66 -5.72 283.81 | 1( 1)| 1.25 28.65 -483.29 512.63 -2.69 330.00 18- 19 | 1( 1)| 1.79 17.48 -214.89 296.36 -27.50 223.19 | 1( 1)| 1.67 22.49 -481.73 325.76 -26.68 243.73 | 1( 1)| 1.17 25.40 -497.27 425.23 -24.43 284.30 19- 20 | 1( 1)| 1.90 16.29 -225.29 271.91 -32.61 213.41 | 1( 1)| 1.94 22.72 -491.50 297.09 -32.74 232.53 | 1( 1)| 1.42 25.51 -506.21 388.85 -30.82 274.47 20- 21 | 1( 1)| 1.83 14.68 -237.85 242.45 -41.95 195.20 | 1( 1)| 1.79 22.95 -503.42 262.56 -43.81 211.70 | 1( 1)| 1.52 25.61 -517.12 345.03 -42.92 267.83 21- 22 | 1( 1)| 1.20 12.98 -285.15 131.36 -84.72 114.36 | 1( 1)| 1.39 24.46 -546.75 132.87 -97.68 152.74 | 1( 1)| 1.03 25.93 -556.35 180.71 -99.22 238.07 22- 23 | 1( 1)| 1.05 13.98 -305.92 82.77 -103.22 79.47 | 1( 1)| 1.18 25.33 -566.00 75.92 -121.71 139.05 | 1( 1)| 1.04 26.10 -573.88 110.85 -123.69 225.13 23- 24 | 1( 1)| 0.91 14.50 -316.47 58.47 -114.00 59.54 | 1( 1)| 1.19 25.78 -576.15 47.44 -136.95 131.06 | 1( 1)| 0.78 26.18 -583.18 76.38 -137.94 217.50 24- 25 | 1( 1)| 0.74 15.08 -328.47 32.26 -124.66 39.61 | 1( 1)| 0.85 26.29 -588.40 16.11 -152.03 123.14 | 1( 1)| 0.71 26.40 -594.47 37.45 -152.05 209.80 25- 26 | 1( 1)| 0.51 15.62 -339.04 9.31 -135.45 19.68 | 1( 1)| 0.73 26.75 -598.54 -10.10 -167.28 115.16 | 1( 1)| 0.49 26.79 -603.75 3.01 -166.32 202.18 26- 27 | 1( 1)| 0.76 16.21 -350.67 -16.18 -146.04 -0.26 | 1( 1)| 1.94 27.27 -609.63 -39.70 -182.26 107.32 | 1( 1)| 1.58 27.23 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.16 13.34 39.51 228.24 62.24 182.77 | 1( 1)| 2.04 15.94 20.98 302.73 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.67 11.68 33.40 198.70 54.95 161.22 | 1( 1)| 1.79 14.14 18.84 269.26 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.14 10.01 27.29 169.05 47.66 139.66 | 1( 1)| 1.54 12.34 16.70 235.64 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 1.50 8.34 21.40 140.57 39.72 116.58 | 1( 1)| 1.26 10.55 14.67 203.37 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 0.49 6.66 15.51 113.94 31.77 93.49 | 1( 1)| 0.98 8.77 1.06 171.05 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 0.00 4.86 8.86 84.54 23.96 70.40 | 1( 1)| 0.62 6.80 -26.66 134.50 18.10 79.77 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 1( 1)| 0.00 3.10 1.03 55.14 16.15 47.31 | 1( 1)| 0.00 4.83 -54.39 103.52 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.00 1.68 -16.68 37.34 4.69 13.85 | 1( 1)| 0.00 4.50 -73.06 100.96 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 1.95 8.62 22.27 74.66 -187.40 39.74 | 1( 1)| 1.14 8.65 11.90 88.94 -188.83 58.34 | 1( 1)| 0.75 8.69 -0.41 110.88 -189.49 55.25 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 6.04 88.47 -74.19 1824.18 -10.25 653.81 | 4( 1)| 10.69 105.61 -164.66 2097.22 93.22 975.66 | 4( 1)| 18.39 132.80 -152.83 2596.00 105.79 1407.18 53- 54 | 4( 1)| 5.54 86.17 -86.80 1781.52 -32.49 620.86 | 4( 1)| 9.56 102.92 -172.25 2048.01 76.08 933.88 | 4( 1)| 17.65 129.51 -158.63 2534.81 90.73 1359.03 54- 55 | 4( 1)| 5.35 84.81 -94.45 1755.04 -44.65 602.55 | 4( 1)| 8.91 101.34 -176.83 2017.31 66.86 910.63 | 4( 1)| 17.25 127.58 -162.23 2496.30 82.58 1331.83 55- 56 | 4( 1)| 5.21 83.57 -101.43 1730.82 -55.77 585.79 | 4( 1)| 8.30 99.89 -181.01 1989.20 58.45 889.35 | 4( 1)| 16.89 125.81 -165.53 2461.02 75.14 1306.89 56- 57 | 4( 1)| 5.12 82.35 -108.43 1701.78 -68.35 564.73 | 4( 1)| 7.68 98.47 -185.02 1954.24 49.97 862.41 | 4( 1)| 16.54 124.06 -169.53 2414.56 67.32 1272.42 57- 58 | 4( 1)| 4.63 81.05 -115.69 1674.95 -81.86 544.00 | 4( 1)| 6.96 96.93 -189.29 1922.67 40.08 836.05 | 4( 1)| 16.13 122.18 -173.20 2374.03 58.47 1240.58 58- 59 | 4( 1)| 4.12 79.74 -122.93 1649.89 -94.83 524.85 | 4( 1)| 6.20 95.39 -193.63 1893.61 30.21 811.75 | 4( 1)| 15.73 120.28 -176.62 2337.58 49.75 1212.23 59- 60 | 4( 1)| 2.35 74.61 -151.92 1552.62 -140.00 458.20 | 4( 1)| 2.64 89.33 -211.07 1781.63 -4.69 726.93 | 4( 1)| 14.35 112.84 -189.86 2198.74 18.92 1115.24 60- 61 | 4( 1)| 1.69 73.31 -159.17 1527.10 -153.12 438.64 | 4( 1)| 0.00 87.79 -215.38 1751.92 -14.55 702.14 | 4( 1)| 13.98 110.95 -193.37 2161.22 9.93 1086.01 61- 62 | 3( 1)| 15.18 36.75 -519.84 330.97 -759.47 -306.26 | 3( 1)| 4.98 35.82 -459.13 379.42 -776.08 294.15 | 3( 1)| 1.63 39.91 -365.56 497.13 -825.34 281.58 62- 63 | 3( 1)| 15.84 38.04 -529.44 300.12 -779.09 -324.11 | 3( 1)| 5.26 36.84 -466.75 344.09 -797.47 285.15 | 3( 1)| 0.00 40.27 -399.59 487.15 -848.69 274.72 63- 64 | 3( 1)| 16.41 39.13 -537.69 275.36 -796.61 -338.81 | 3( 1)| 5.50 37.77 -473.15 316.09 -816.84 277.11 | 3( 1)| 0.00 40.99 -427.66 484.47 -869.85 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.87 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 1.96 -13.12 34.69 0.60 24.28 | 1( 1)| 0.00 2.28 -18.32 41.05 -1.31 32.33 | 1( 1)| 0.00 2.78 -22.26 51.10 -1.45 35.96 66- 67 | 1( 1)| 0.00 0.98 -18.35 17.35 -5.41 12.14 | 1( 1)| 0.00 1.14 -21.12 20.53 -6.45 19.28 | 1( 1)| 0.00 1.39 -22.17 25.55 -5.59 20.65 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.52 21.27 -469.77 4.32 -127.40 18.58 | 1( 1)| 0.52 26.01 -577.89 6.14 -128.83 114.77 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.19 21.78 -480.57 -25.28 -135.93 -4.00 | 1( 1)| 1.40 26.45 -587.77 -29.68 -145.66 108.39 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 39.345s Elapsed Solve time : 532.296s Elapsed CPU time: 571.641s Sumatorio de erros e2 0.03144 Sumatorio de erros pq 26.15953 Sumatorio de erros vi 2.29601 Factor de erro e2 10.00 Factor de erro pq 0.10 Factor de erro vi 1.00 Maximum Psae error 1142.18414 Maximo erro superior 1.1956 Maximo erro inferior -132.0570 TRANSITION 12 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886923 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17070.71731 44 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 17068.13 3710.95 13357.18 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2667.29/ 2635.12/ 1331.74 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 342.82 0.00 0.00 225.02 914.41 0.00 51 0.00 0.00 0.00 202.55 0.00 0.00 64 0.00 0.00 0.00 780.11 119.14 106.45 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 800.00 0.00 0.00 67.00 15.59 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 701.72 423.28 0.00 50.00 0.00 0.00 0.00 69.00 0.00 902.41 185.80 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 54.04 46.00 0.00 0.00 0.00 64.00 0.00 381.42 944.64 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.92 26.92 26.92 54.02 Structures 20.65 20.65 20.65 41.43 Fixed CBs 0.85 0.85 0.85 1.71 Switchable CBs 4.06 7.53 7.89 11.77 PV systems 505.07 505.07 505.07 1013.40 Wind systems 581.15 1510.25 1620.33 2143.61 EES systems 0.00 232.26 780.23 445.03 Total invesment cost 1138.70 2303.53 2961.93 3710.97 Purchased energy cost 5623.98 6021.87 7114.40 12106.00 Carbon tax payment 194.92 342.20 720.49 685.18 O&M PV cost 49.43 39.64 37.41 88.47 O&M wind cost 99.49 282.85 304.55 392.53 O&M EES cost 0.00 44.37 149.03 85.00 Total O&M cost 5967.82 6730.93 8325.87 13357.18 Total cost 7106.52 9034.46 11287.81 17068.15 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 8137.46 7495.73 130306.45 845.25 0.00 2 112695.76 8137.34 21657.31 141404.09 870.14 227.77 3 131988.89 8137.40 23641.60 161754.72 1189.41 833.50 CO2 Emissions (Ton): Period Distribution EV 1 9738.12 4980.53 2 9837.00 4906.75 3 9889.39 4780.66 4 9916.40 4659.94 5 9991.73 4476.17 6 8525.82 4266.91 7 8604.97 4025.47 8 8668.96 3733.05 9 8710.67 3403.07 10 8849.26 2999.31 11 8862.21 2539.22 12 9017.34 2025.48 13 9140.66 1443.32 14 9220.35 753.85 15 9463.89 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 572.16 4403.66 277.11 1952.00 0.90 0.97 Infinity -Infinity 2 0.00 5023.94 0.00 2175.80 0.90 1.00 Infinity -Infinity 3 0.00 6275.85 -0.00 2576.39 0.90 0.98 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 -3.71 228.79 0.00 153.18 2 -197.29 161.01 -99.51 197.19 3 -207.91 128.82 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 43.23 43.23 216.16 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 305.14 305.14 1525.68 1060.85 1060.85 5304.23 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 54.04 54.04 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 257.57 381.42 745.42 1212.84 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 28.99 218.41 572.14 4402.83 277.10 1951.29 | 4( 2)| 0.00 249.31 0.00 5022.86 0.00 2174.92 | 4( 2)| 0.00 309.38 0.00 6274.19 -0.00 2574.93 2- 3 | 4( 2)| 28.51 217.05 564.80 4376.56 267.78 1929.38 | 4( 2)| 0.26 247.70 -7.06 4991.27 -8.65 2151.67 | 4( 2)| 0.27 307.42 -4.92 6234.00 -7.47 2545.83 3- 4 | 4( 2)| 19.28 189.35 413.95 3874.31 86.24 1529.52 | 4( 2)| 6.83 214.84 -153.14 4389.90 -177.98 1733.06 | 4( 2)| 5.65 269.04 -131.35 5524.69 -153.71 2039.56 4- 5 | 4( 1)| 11.76 142.52 150.95 3001.67 -211.58 876.53 | 4( 1)| 12.41 159.28 -406.97 3348.22 -453.43 1053.58 | 4( 1)| 11.01 200.88 -357.99 4225.49 -394.40 1222.61 5- 6 | 4( 1)| 11.92 141.22 143.60 2971.40 -221.02 851.40 | 4( 1)| 12.76 157.74 -414.27 3311.98 -462.29 1026.90 | 4( 1)| 11.10 198.99 -366.78 4177.61 -403.37 1195.74 6- 7 | 4( 1)| 12.10 139.92 136.24 2941.07 -230.46 826.22 | 4( 1)| 13.13 156.20 -421.59 3275.67 -471.17 1000.17 | 4( 1)| 11.22 197.09 -375.59 4129.61 -412.36 1168.81 7- 8 | 4( 1)| 12.38 137.85 124.44 2900.57 -244.34 794.75 | 4( 1)| 12.95 153.74 -433.03 3227.28 -483.99 967.76 | 4( 1)| 11.43 194.05 -389.67 4068.61 -425.55 1136.90 8- 9 | 4( 1)| 5.44 131.92 80.00 2752.73 -92.32 864.97 | 4( 1)| 6.74 146.13 -475.93 3050.68 -487.00 895.30 | 4( 1)| 4.67 184.67 -441.97 3848.09 -458.19 1159.84 9- 10 | 1( 1)| 4.65 45.82 25.03 966.46 -247.21 226.21 | 1( 1)| 1.47 58.41 -728.08 1054.53 -1228.21 -5.66 | 1( 1)| 0.00 64.70 -906.90 1351.05 -1119.95 45.42 10- 11 | 3( 1)| 9.91 53.39 15.06 938.72 211.68 674.16 | 3( 1)| 8.18 58.02 -736.37 1021.00 108.55 730.55 | 3( 1)| 9.01 71.30 -912.98 1308.97 136.14 840.41 11- 12 | 1( 1)| 7.00 43.46 -42.19 762.96 142.83 543.78 | 1( 1)| 5.09 46.42 -794.88 813.46 45.82 581.11 | 1( 1)| 5.85 57.01 -945.03 1042.40 75.46 669.46 12- 13 | 1( 1)| 3.42 32.18 -114.11 564.98 66.61 397.48 | 1( 1)| 3.86 36.43 -384.80 642.51 61.47 443.75 | 1( 1)| 3.96 45.25 -436.55 828.53 58.94 513.35 13- 14 | 1( 1)| 3.44 30.03 -128.51 523.46 53.58 371.62 | 1( 1)| 3.22 33.93 -397.50 593.23 49.37 414.08 | 1( 1)| 3.84 42.17 -446.44 765.49 48.53 479.25 14- 15 | 1( 1)| 3.29 27.81 -142.94 482.31 39.14 343.49 | 1( 1)| 2.53 31.34 -410.25 544.76 35.95 381.83 | 1( 1)| 2.73 38.98 -456.37 703.20 36.56 441.81 15- 16 | 1( 1)| 2.65 26.33 -152.20 457.62 28.40 323.23 | 1( 1)| 2.06 29.61 -417.98 515.78 26.01 358.64 | 1( 1)| 1.96 36.89 -461.66 666.34 27.71 415.34 16- 17 | 1( 1)| 1.99 23.82 -171.04 412.91 12.55 292.83 | 1( 1)| 1.86 26.68 -435.59 463.31 11.33 323.84 | 1( 1)| 1.22 33.28 -471.30 599.64 14.24 375.62 17- 18 | 1( 1)| 1.72 20.63 -195.95 354.34 -5.75 257.84 | 1( 1)| 1.90 22.95 -458.47 394.66 -5.76 283.81 | 1( 1)| 1.25 28.65 -483.29 512.63 -1.97 330.00 18- 19 | 1( 1)| 1.80 17.44 -220.93 295.57 -24.07 222.81 | 1( 1)| 1.67 22.09 -481.73 325.76 -26.61 243.73 | 1( 1)| 1.17 25.39 -497.28 425.23 -24.06 284.30 19- 20 | 1( 1)| 1.89 16.25 -231.34 271.12 -29.18 213.02 | 1( 1)| 1.94 22.33 -491.50 297.09 -32.67 232.53 | 1( 1)| 1.42 25.51 -506.21 388.85 -30.45 274.47 20- 21 | 1( 1)| 1.85 14.64 -243.91 241.66 -38.53 194.82 | 1( 1)| 1.79 22.58 -503.41 262.56 -43.75 211.70 | 1( 1)| 1.52 25.61 -517.12 345.03 -42.65 267.83 21- 22 | 1( 1)| 1.19 13.29 -291.20 130.57 -81.30 114.02 | 1( 1)| 1.39 24.47 -546.74 132.87 -96.80 152.74 | 1( 1)| 1.03 25.92 -556.35 180.71 -99.22 238.07 22- 23 | 1( 1)| 1.08 14.30 -311.98 81.98 -99.79 79.13 | 1( 1)| 1.18 25.35 -565.99 75.92 -121.71 139.05 | 1( 1)| 1.04 26.10 -573.88 110.85 -123.68 225.13 23- 24 | 1( 1)| 0.89 14.83 -322.55 57.68 -110.57 59.20 | 1( 1)| 1.19 25.80 -576.14 47.44 -136.95 131.06 | 1( 1)| 0.78 26.18 -583.18 76.38 -137.94 217.50 24- 25 | 1( 1)| 0.77 15.41 -334.57 31.56 -121.24 39.27 | 1( 1)| 0.85 26.32 -588.39 16.11 -152.03 123.14 | 1( 1)| 0.71 26.40 -594.47 37.45 -152.05 209.80 25- 26 | 1( 1)| 0.51 15.96 -345.14 8.61 -132.02 19.33 | 1( 1)| 0.73 26.78 -598.54 -10.10 -167.28 115.16 | 1( 1)| 0.49 26.79 -603.75 3.01 -166.32 202.18 26- 27 | 1( 1)| 0.79 16.55 -356.78 -16.89 -142.62 -0.60 | 1( 1)| 1.94 27.30 -609.63 -39.70 -182.26 107.32 | 1( 1)| 1.58 27.24 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 2.79 13.15 30.26 226.36 62.24 182.76 | 1( 1)| 2.05 15.54 -2.72 281.75 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.34 11.49 26.25 196.34 54.95 161.22 | 1( 1)| 1.75 13.57 -4.86 248.28 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 1.87 9.82 22.23 166.22 47.66 139.65 | 1( 1)| 1.44 11.59 -7.00 214.68 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 1.30 8.15 18.35 137.28 39.72 116.57 | 1( 1)| 1.08 9.73 -9.03 182.42 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 0.48 6.47 14.48 108.31 31.77 93.49 | 1( 1)| 0.70 7.94 -11.06 150.11 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 0.00 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.00 5.97 -13.35 113.59 18.10 79.77 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 1( 1)| 0.00 2.89 5.74 42.86 16.15 47.31 | 1( 1)| 0.00 3.98 -17.71 77.09 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.00 1.11 2.80 20.89 4.69 13.85 | 1( 1)| 0.00 2.30 -36.33 56.40 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 1.18 8.16 22.27 74.66 -177.32 39.54 | 1( 1)| 1.14 8.18 11.90 88.94 -178.75 58.34 | 1( 1)| 0.75 8.22 -0.41 110.88 -179.41 55.25 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 5.81 87.95 -74.78 1823.82 104.50 619.11 | 4( 1)| 10.41 104.93 -157.43 2096.88 97.40 938.55 | 4( 1)| 17.25 132.24 -114.65 2595.51 110.34 1376.08 53- 54 | 4( 1)| 5.36 85.66 -87.39 1781.16 82.44 586.17 | 4( 1)| 9.41 102.24 -165.03 2047.68 80.03 896.78 | 4( 1)| 16.50 128.96 -120.43 2534.34 94.90 1327.96 54- 55 | 4( 1)| 5.19 84.31 -95.04 1754.69 70.51 567.87 | 4( 1)| 8.85 100.67 -169.63 2016.99 70.68 873.55 | 4( 1)| 16.10 127.03 -124.01 2495.85 86.54 1300.79 55- 56 | 4( 1)| 5.06 83.08 -102.02 1730.47 59.63 551.12 | 4( 1)| 8.33 99.22 -173.82 1988.90 62.15 852.29 | 4( 1)| 15.74 125.26 -127.28 2460.59 78.89 1275.87 56- 57 | 4( 1)| 4.76 81.87 -109.03 1701.45 48.69 530.12 | 4( 1)| 7.82 97.80 -177.92 1954.00 53.58 825.46 | 4( 1)| 15.39 123.52 -131.12 2414.23 70.75 1241.57 57- 58 | 4( 1)| 4.24 80.57 -116.28 1674.64 35.91 509.43 | 4( 1)| 7.25 96.27 -182.24 1922.46 43.56 799.15 | 4( 1)| 14.98 121.63 -134.71 2373.75 61.63 1209.81 58- 59 | 4( 1)| 3.72 79.27 -123.53 1649.57 23.16 490.29 | 4( 1)| 6.67 94.73 -186.59 1893.41 33.56 774.87 | 4( 1)| 14.58 119.74 -138.10 2337.32 52.69 1181.48 59- 60 | 4( 1)| 2.10 74.18 -152.52 1552.31 -21.97 423.65 | 4( 1)| 4.52 88.70 -204.06 1781.45 -1.83 690.07 | 4( 1)| 13.20 112.32 -151.29 2198.51 21.28 1084.53 60- 61 | 4( 1)| 1.79 72.90 -159.78 1526.79 -34.72 404.11 | 4( 1)| 3.95 87.17 -208.39 1751.75 -11.83 665.31 | 4( 1)| 12.83 110.42 -154.74 2161.02 12.28 1055.34 61- 62 | 3( 1)| 0.01 36.75 -520.44 330.66 -716.95 -327.16 | 3( 1)| 4.08 35.83 -459.59 379.25 -776.21 294.14 | 3( 1)| 3.75 39.99 -386.96 505.78 -829.75 281.58 62- 63 | 3( 1)| 3.34 38.05 -530.04 299.79 -737.17 -338.74 | 3( 1)| 4.58 36.85 -467.23 343.91 -797.60 285.13 | 3( 1)| 2.26 40.38 -418.45 503.04 -853.09 274.72 63- 64 | 4( 1)| 4.86 39.11 -537.69 275.36 -755.20 -348.51 | 4( 1)| 4.98 37.78 -473.36 316.09 -816.92 277.11 | 4( 1)| 0.00 41.42 -443.65 500.69 -874.20 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.87 3.87 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.00 1.96 -1.63 34.69 6.16 27.11 | 1( 1)| 0.00 2.28 -6.68 41.05 4.33 28.02 | 1( 1)| 0.00 2.79 -12.52 51.10 3.29 32.93 66- 67 | 1( 1)| 0.00 0.98 -6.86 17.35 0.15 15.26 | 1( 1)| 0.00 1.14 -9.47 20.53 -0.81 15.01 | 1( 1)| 0.00 1.39 -12.42 25.55 -0.85 17.45 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.52 21.56 -476.09 3.61 -120.94 18.24 | 1( 1)| 0.51 26.27 -583.59 5.45 -131.04 113.82 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.22 22.08 -486.90 -25.99 -129.47 -4.34 | 1( 1)| 1.44 26.71 -593.47 -30.29 -146.87 107.44 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 42.985s Elapsed Solve time : 585.234s Elapsed CPU time: 628.219s Sumatorio de erros e2 0.03000 Sumatorio de erros pq 22.86099 Sumatorio de erros vi 2.21962 Factor de erro e2 10.00 Factor de erro pq 0.10 Factor de erro vi 1.00 Maximum Psae error 1138.02708 Maximo erro superior 0.5640 Maximo erro inferior -359.1295 TRANSITION 13 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886931 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17072.8452 44 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 17072.39 3713.18 13359.21 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2674.04/ 2628.23/ 1329.06 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 342.92 0.00 0.00 209.82 931.37 0.00 51 0.00 0.00 0.00 203.20 0.00 0.00 64 0.00 0.00 0.00 789.28 110.14 106.59 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 800.00 0.00 0.00 67.00 5.95 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 715.87 409.13 0.00 50.00 0.00 0.00 0.00 69.00 0.00 915.22 185.45 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 36.78 46.00 0.00 0.00 0.00 64.00 0.00 377.44 959.86 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 0.85 0.85 0.85 1.71 Switchable CBs 4.04 7.54 7.90 11.76 PV systems 499.10 499.10 499.10 1001.42 Wind systems 592.87 1521.03 1630.90 2166.09 EES systems 0.00 229.83 776.69 442.15 Total invesment cost 1141.74 2303.23 2960.31 3713.19 Purchased energy cost 5623.66 6021.89 7114.80 12105.85 Carbon tax payment 194.92 342.18 720.48 685.17 O&M PV cost 48.84 39.17 36.97 87.42 O&M wind cost 101.49 284.64 306.26 396.31 O&M EES cost 0.00 43.90 148.38 84.47 Total O&M cost 5968.92 6731.79 8326.89 13359.21 Total cost 7110.66 9035.03 11287.20 17072.41 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 8041.30 7646.84 130306.45 874.43 0.00 2 112691.65 8041.18 21794.13 141404.09 895.00 225.53 3 131987.62 8041.23 23774.67 161754.72 1218.86 829.75 CO2 Emissions (Ton): Period Distribution EV 1 9738.21 4980.53 2 9837.05 4906.75 3 9889.38 4780.66 4 9916.33 4659.94 5 9991.68 4476.17 6 8525.34 4266.91 7 8604.58 4025.47 8 8668.64 3733.05 9 8710.40 3403.07 10 8849.16 2999.31 11 8861.89 2539.22 12 9017.16 2025.48 13 9140.57 1443.32 14 9220.30 753.85 15 9464.10 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 576.25 4404.70 278.52 1950.09 0.90 0.97 Infinity -Infinity 2 0.00 5023.54 -0.00 2174.30 0.90 0.98 1.00 1.00 3 0.00 6285.49 -0.00 2575.50 0.90 0.98 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 -1.42 217.62 0.00 152.76 2 -197.29 139.34 -99.51 197.19 3 -207.91 125.14 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 29.42 29.42 147.11 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 301.95 301.95 1509.75 1069.84 1069.84 5349.18 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 36.78 36.78 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 255.76 377.44 751.30 1224.69 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 29.19 218.41 576.23 4403.87 278.51 1949.39 | 4( 2)| 0.00 249.27 0.00 5022.46 -0.00 2173.42 | 4( 2)| 0.00 309.78 0.00 6283.82 -0.00 2574.03 2- 3 | 4( 2)| 28.70 217.05 568.88 4377.60 269.20 1927.47 | 4( 2)| 0.15 247.66 -7.06 4990.85 -8.65 2150.17 | 4( 2)| 0.27 307.81 -4.92 6243.61 -7.47 2544.93 3- 4 | 4( 2)| 19.48 189.36 418.04 3875.34 87.66 1527.61 | 4( 2)| 6.98 214.80 -153.14 4389.45 -177.98 1731.56 | 4( 2)| 5.67 268.99 -139.83 5523.91 -153.72 2038.65 4- 5 | 4( 1)| 11.83 142.54 155.04 3002.70 -210.14 874.62 | 4( 1)| 12.41 159.25 -406.97 3347.76 -453.43 1052.28 | 4( 1)| 11.18 200.84 -361.45 4224.70 -396.08 1221.87 5- 6 | 4( 1)| 11.98 141.24 147.68 2972.39 -219.58 849.48 | 4( 1)| 12.77 157.70 -414.27 3311.24 -462.29 1025.61 | 4( 1)| 11.27 198.93 -370.25 4176.55 -405.05 1194.99 6- 7 | 4( 1)| 12.15 139.94 140.32 2942.02 -229.02 824.29 | 4( 1)| 13.14 156.14 -421.59 3274.66 -471.17 998.88 | 4( 1)| 11.38 197.02 -379.06 4128.30 -414.04 1168.06 7- 8 | 4( 1)| 12.40 137.86 128.53 2901.51 -242.90 792.82 | 4( 1)| 12.87 153.67 -433.03 3226.20 -483.99 966.46 | 4( 1)| 11.57 193.97 -393.14 4067.24 -427.23 1136.16 8- 9 | 4( 1)| 5.51 131.92 84.09 2753.66 -90.23 861.68 | 4( 1)| 6.77 146.06 -475.95 3049.54 -487.01 893.42 | 4( 1)| 4.89 184.58 -445.45 3846.66 -458.20 1158.61 9- 10 | 1( 1)| 4.84 45.89 23.06 967.98 -217.36 225.71 | 1( 1)| 1.31 58.36 -729.67 1054.75 -1228.23 -4.06 | 1( 1)| 0.58 64.73 -908.25 1350.98 -1119.97 44.87 10- 11 | 3( 1)| 10.02 53.47 13.08 940.24 212.66 674.91 | 3( 1)| 8.18 58.10 -737.96 1021.70 109.34 731.35 | 3( 1)| 9.17 71.29 -914.34 1308.90 136.75 841.20 11- 12 | 1( 1)| 6.92 43.41 -48.92 761.96 143.27 543.31 | 1( 1)| 5.11 46.38 -801.91 812.58 46.17 580.68 | 1( 1)| 5.85 56.95 -951.31 1041.44 76.82 669.06 12- 13 | 1( 1)| 3.58 32.13 -120.84 563.99 67.05 397.01 | 1( 1)| 3.86 36.43 -384.80 642.51 61.51 443.75 | 1( 1)| 3.96 45.25 -436.55 828.53 59.23 513.35 13- 14 | 1( 1)| 3.68 29.98 -135.26 522.48 54.01 371.15 | 1( 1)| 3.22 33.93 -397.50 593.23 49.40 414.08 | 1( 1)| 3.84 42.16 -446.45 765.49 48.79 479.25 14- 15 | 1( 1)| 3.10 27.76 -149.70 481.34 39.57 343.02 | 1( 1)| 2.54 31.34 -410.25 544.76 35.99 381.83 | 1( 1)| 2.73 38.98 -456.37 703.20 36.82 441.81 15- 16 | 1( 1)| 2.49 26.28 -159.55 456.65 28.83 322.76 | 1( 1)| 2.06 29.61 -417.98 515.78 26.05 358.64 | 1( 1)| 1.96 36.89 -461.66 666.34 27.97 415.34 16- 17 | 1( 1)| 1.97 23.77 -178.39 411.94 12.99 292.36 | 1( 1)| 1.86 26.68 -435.59 463.31 11.37 323.84 | 1( 1)| 1.22 33.28 -471.30 599.64 14.39 375.62 17- 18 | 1( 1)| 1.73 20.58 -203.30 353.38 -5.32 257.38 | 1( 1)| 1.90 22.95 -458.47 394.66 -5.83 283.81 | 1( 1)| 1.25 28.65 -483.29 512.63 -1.82 330.00 18- 19 | 1( 1)| 1.83 17.38 -228.29 294.61 -23.64 222.34 | 1( 1)| 1.67 22.08 -481.72 325.76 -26.55 243.73 | 1( 1)| 1.17 25.39 -497.28 425.23 -24.07 284.30 19- 20 | 1( 1)| 1.87 16.20 -238.70 270.16 -28.75 212.56 | 1( 1)| 1.94 22.32 -491.50 297.09 -32.61 232.53 | 1( 1)| 1.42 25.51 -506.21 388.85 -30.46 274.47 20- 21 | 1( 1)| 1.89 14.59 -251.28 240.70 -38.10 194.35 | 1( 1)| 1.79 22.58 -503.41 262.56 -43.69 211.70 | 1( 1)| 1.52 25.61 -517.12 345.03 -42.65 267.83 21- 22 | 1( 1)| 1.18 13.62 -298.57 129.61 -80.87 113.60 | 1( 1)| 1.39 24.47 -546.74 132.87 -96.72 152.74 | 1( 1)| 1.03 25.92 -556.35 180.71 -99.22 238.07 22- 23 | 1( 1)| 1.11 14.64 -319.36 81.02 -99.37 78.72 | 1( 1)| 1.18 25.35 -565.99 75.92 -121.71 139.05 | 1( 1)| 1.04 26.10 -573.88 110.85 -123.69 225.13 23- 24 | 1( 1)| 0.86 15.16 -329.93 56.72 -110.15 58.79 | 1( 1)| 1.19 25.81 -576.14 47.44 -136.95 131.06 | 1( 1)| 0.78 26.17 -583.18 76.38 -137.94 217.50 24- 25 | 1( 1)| 0.81 15.75 -341.97 30.71 -120.82 38.85 | 1( 1)| 0.85 26.32 -588.39 16.11 -152.03 123.14 | 1( 1)| 0.71 26.40 -594.47 37.45 -152.05 209.80 25- 26 | 1( 1)| 0.51 16.29 -352.56 7.76 -131.60 18.92 | 1( 1)| 0.73 26.78 -598.54 -10.10 -167.28 115.16 | 1( 1)| 0.49 26.79 -603.75 3.01 -166.32 202.18 26- 27 | 1( 1)| 0.84 16.88 -364.20 -17.74 -142.20 -1.01 | 1( 1)| 1.94 27.30 -609.63 -39.70 -182.26 107.32 | 1( 1)| 1.58 27.24 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.18 13.15 30.27 226.37 62.25 182.76 | 1( 1)| 2.17 15.54 -12.92 276.88 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.80 11.49 26.26 196.35 54.95 161.22 | 1( 1)| 1.92 13.57 -15.06 240.16 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.42 9.82 22.24 166.23 47.66 139.65 | 1( 1)| 1.67 11.59 -17.20 206.34 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.01 8.15 18.36 137.29 39.72 116.57 | 1( 1)| 1.39 9.61 -19.23 174.07 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.61 6.48 14.49 108.32 31.77 93.49 | 1( 1)| 1.11 7.66 -21.26 141.77 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.20 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.83 5.70 -23.55 105.26 18.10 79.77 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 1( 1)| 0.79 2.90 5.74 42.86 16.15 47.31 | 1( 1)| 0.55 3.75 -25.85 68.77 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.01 2.08 -27.40 44.27 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.47 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 1.89 8.20 22.27 74.66 -177.97 39.33 | 1( 1)| 1.14 8.24 11.90 88.94 -179.66 58.34 | 1( 1)| 0.75 8.26 -0.41 110.88 -179.93 55.25 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 5.80 87.96 -74.19 1824.94 109.18 616.02 | 4( 1)| 10.40 104.94 -158.15 2098.33 99.30 935.02 | 4( 1)| 17.19 132.26 -102.39 2597.04 110.99 1373.02 53- 54 | 4( 1)| 5.35 85.68 -86.80 1782.23 92.85 583.08 | 4( 1)| 9.41 102.25 -165.81 2049.05 81.92 893.25 | 4( 1)| 16.44 128.97 -108.18 2535.79 95.56 1324.89 54- 55 | 4( 1)| 5.17 84.33 -94.45 1755.69 84.06 564.77 | 4( 1)| 8.85 100.67 -170.49 2018.27 72.57 870.01 | 4( 1)| 16.04 127.03 -111.76 2497.21 87.19 1297.72 55- 56 | 4( 1)| 5.05 83.09 -101.43 1731.42 74.68 548.02 | 4( 1)| 8.33 99.22 -174.76 1990.09 64.03 848.74 | 4( 1)| 15.68 125.27 -115.05 2461.85 79.55 1272.79 56- 57 | 4( 1)| 4.76 81.86 -108.44 1702.10 63.68 527.00 | 4( 1)| 7.82 97.78 -179.29 1954.71 55.43 821.88 | 4( 1)| 15.33 123.49 -118.96 2415.00 71.41 1238.46 57- 58 | 4( 1)| 4.24 80.56 -115.69 1675.14 50.95 506.30 | 4( 1)| 7.25 96.23 -183.81 1922.95 45.39 795.56 | 4( 1)| 14.92 121.60 -122.60 2374.28 62.28 1206.70 58- 59 | 4( 1)| 3.73 79.26 -122.94 1650.03 38.29 487.15 | 4( 1)| 6.68 94.69 -188.25 1893.82 35.39 771.28 | 4( 1)| 14.52 119.70 -126.00 2337.77 53.34 1178.37 59- 60 | 4( 1)| 2.11 74.16 -151.93 1552.71 -6.59 420.51 | 4( 1)| 4.53 88.65 -205.81 1781.76 -0.01 686.47 | 4( 1)| 13.15 112.27 -139.22 2198.86 21.94 1081.41 60- 61 | 4( 1)| 1.82 72.88 -159.18 1527.11 -19.35 400.97 | 4( 1)| 3.96 87.12 -210.27 1751.94 -10.02 661.70 | 4( 1)| 12.78 110.37 -142.70 2161.24 12.94 1052.22 61- 62 | 3( 1)| 15.68 36.73 -519.85 330.98 -716.87 -328.77 | 3( 1)| 5.20 35.82 -461.41 379.44 -776.14 294.15 | 3( 1)| 4.62 40.02 -394.86 514.49 -830.00 281.60 62- 63 | 3( 1)| 16.33 38.02 -529.44 300.13 -737.09 -339.73 | 3( 1)| 5.62 36.85 -469.05 344.11 -797.53 285.15 | 3( 1)| 3.42 40.39 -426.34 513.05 -853.34 274.74 63- 64 | 3( 1)| 16.90 39.14 -537.69 275.36 -755.18 -349.51 | 3( 1)| 5.98 37.78 -475.48 316.09 -816.90 277.11 | 3( 1)| 2.46 41.58 -451.65 512.01 -874.51 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.87 3.87 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.36 1.96 5.85 34.69 9.73 25.47 | 1( 1)| 0.00 2.32 0.91 41.22 7.99 29.25 | 1( 1)| 0.00 2.84 -4.90 51.54 6.37 33.44 66- 67 | 1( 1)| 0.00 0.98 0.61 17.35 3.77 13.15 | 1( 1)| 0.00 1.14 -1.89 20.53 2.92 14.25 | 1( 1)| 0.00 1.40 -4.80 25.55 2.23 16.55 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.53 21.88 -483.15 2.82 -119.86 17.86 | 1( 1)| 0.49 26.58 -590.50 4.62 -131.64 112.51 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.26 22.40 -493.96 -26.78 -128.39 -4.72 | 1( 1)| 1.47 27.02 -600.38 -31.03 -147.47 106.12 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 46.704s Elapsed Solve time : 640.546s Elapsed CPU time: 687.250s Sumatorio de erros e2 0.00082 Sumatorio de erros pq 0.44798 Sumatorio de erros vi 1.75295 Factor de erro e2 10.00 Factor de erro pq 1.00 Factor de erro vi 1.00 Maximum Psae error 1137.51859 Maximo erro superior 1.2180 Maximo erro inferior -16.4183 TRANSITION 14 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886933 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17072.10839 41 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 17071.87 3712.26 13359.61 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2675.75/ 2624.29/ 1327.06 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 342.84 0.00 0.00 198.82 943.93 0.00 51 0.00 0.00 0.00 203.63 0.00 0.00 64 0.00 0.00 0.00 796.20 103.31 106.74 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 800.00 0.00 0.00 67.00 0.00 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 721.22 403.78 0.00 50.00 0.00 0.00 0.00 69.00 0.00 920.37 185.23 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 23.76 46.00 0.00 0.00 0.00 64.00 0.00 374.37 971.31 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 0.85 0.85 0.85 1.71 Switchable CBs 4.03 7.54 7.90 11.76 PV systems 495.41 495.41 495.41 994.03 Wind systems 597.30 1525.32 1635.06 2174.79 EES systems 0.00 227.96 773.95 439.94 Total invesment cost 1142.47 2301.98 2958.06 3712.28 Purchased energy cost 5623.44 6021.99 7115.15 12105.83 Carbon tax payment 194.92 342.19 720.49 685.18 O&M PV cost 48.48 38.88 36.69 86.77 O&M wind cost 102.25 285.36 306.94 397.78 O&M EES cost 0.00 43.55 147.87 84.05 Total O&M cost 5969.10 6731.97 8327.15 13359.61 Total cost 7111.58 9033.95 11285.21 17071.89 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 7981.93 7703.98 130306.45 873.44 0.00 2 112692.66 7981.81 21849.17 141404.09 895.26 223.78 3 131989.38 7981.87 23827.35 161754.72 1218.49 826.84 CO2 Emissions (Ton): Period Distribution EV 1 9738.12 4980.53 2 9837.02 4906.75 3 9889.39 4780.66 4 9916.37 4659.94 5 9991.75 4476.17 6 8525.37 4266.91 7 8604.64 4025.47 8 8668.72 3733.05 9 8710.48 3403.07 10 8849.29 2999.31 11 8861.97 2539.22 12 9017.27 2025.48 13 9140.69 1443.32 14 9220.42 753.85 15 9464.27 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 579.30 4404.77 279.96 1948.21 0.90 0.97 Infinity -Infinity 2 0.00 5020.04 -0.00 2172.77 0.90 0.99 0.98 0.98 3 0.00 6289.72 -0.00 2574.59 0.90 1.00 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 -0.00 222.75 0.00 152.47 2 -197.29 143.42 -99.51 197.19 3 -207.91 125.49 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 19.01 19.01 95.03 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 299.49 299.49 1497.46 1076.54 1076.54 5382.68 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 23.76 23.76 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 254.17 374.37 755.55 1230.64 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 29.34 218.38 579.28 4403.93 279.95 1947.50 | 4( 2)| 0.00 249.10 0.00 5018.96 -0.00 2171.89 | 4( 2)| 0.00 309.94 0.00 6288.04 -0.00 2573.12 2- 3 | 4( 2)| 28.86 217.02 571.93 4377.66 270.64 1925.59 | 4( 2)| 0.26 247.49 -7.06 4987.36 -8.65 2148.65 | 4( 2)| 0.27 307.98 -4.92 6247.83 -7.47 2544.01 3- 4 | 4( 2)| 19.63 189.33 421.09 3875.41 89.10 1525.73 | 4( 2)| 7.05 214.63 -153.14 4385.97 -177.98 1730.04 | 4( 2)| 5.67 268.82 -130.93 5520.26 -153.71 2037.73 4- 5 | 4( 1)| 11.86 142.52 158.09 3002.77 -208.70 872.74 | 4( 1)| 12.41 159.08 -406.97 3344.27 -453.43 1050.97 | 4( 1)| 11.38 200.67 -362.34 4221.06 -396.51 1221.14 5- 6 | 4( 1)| 12.00 141.22 150.73 2972.47 -218.13 847.59 | 4( 1)| 12.77 157.54 -414.27 3308.13 -462.29 1024.30 | 4( 1)| 11.46 198.77 -371.14 4172.95 -405.48 1194.26 6- 7 | 4( 1)| 12.17 139.92 143.37 2942.10 -227.58 822.40 | 4( 1)| 13.14 155.99 -421.59 3272.14 -471.17 997.58 | 4( 1)| 11.57 196.86 -379.95 4124.73 -414.47 1167.33 7- 8 | 4( 1)| 12.43 137.84 131.58 2901.60 -241.45 790.93 | 4( 1)| 12.85 153.52 -433.03 3224.45 -483.99 965.16 | 4( 1)| 11.75 193.82 -394.03 4063.68 -427.66 1135.42 8- 9 | 4( 1)| 5.55 131.88 87.14 2753.75 -88.35 858.41 | 4( 1)| 6.75 145.90 -475.95 3050.59 -487.01 891.53 | 4( 1)| 5.09 184.42 -446.33 3843.11 -458.19 1157.42 9- 10 | 1( 1)| 4.87 45.94 23.44 969.16 -215.21 225.23 | 1( 1)| 1.24 58.31 -729.30 1055.95 -1228.22 -2.42 | 1( 1)| 0.68 64.72 -907.71 1351.16 -1119.93 44.43 10- 11 | 3( 1)| 10.08 53.53 13.47 941.42 212.39 675.48 | 3( 1)| 8.18 58.16 -737.59 1022.90 109.95 731.93 | 3( 1)| 9.23 71.31 -913.80 1309.08 137.09 841.78 11- 12 | 1( 1)| 6.90 43.39 -51.46 761.59 143.56 543.13 | 1( 1)| 5.12 46.36 -804.74 812.22 46.11 580.51 | 1( 1)| 5.84 56.94 -953.79 1041.07 76.74 668.90 12- 13 | 1( 1)| 3.66 32.11 -123.39 563.62 67.34 396.83 | 1( 1)| 3.86 36.43 -384.82 642.51 61.49 443.75 | 1( 1)| 3.96 45.25 -436.55 828.53 59.43 513.35 13- 14 | 1( 1)| 3.78 29.96 -137.81 522.11 54.30 370.97 | 1( 1)| 3.22 33.93 -397.52 593.23 49.39 414.08 | 1( 1)| 3.84 42.17 -446.45 765.50 48.94 479.25 14- 15 | 1( 1)| 3.04 27.74 -152.25 480.98 39.86 342.85 | 1( 1)| 2.54 31.34 -410.26 544.76 35.97 381.83 | 1( 1)| 2.73 38.98 -456.37 703.20 36.97 441.81 15- 16 | 1( 1)| 2.45 26.26 -162.32 456.29 29.12 322.59 | 1( 1)| 2.06 29.62 -417.98 515.78 26.03 358.64 | 1( 1)| 1.95 36.89 -461.66 666.34 28.12 415.34 16- 17 | 1( 1)| 2.00 23.75 -181.17 411.58 13.27 292.18 | 1( 1)| 1.86 26.68 -435.59 463.31 11.35 323.84 | 1( 1)| 1.22 33.28 -471.30 599.64 14.38 375.62 17- 18 | 1( 1)| 1.76 20.56 -206.07 353.01 -5.03 257.20 | 1( 1)| 1.90 22.95 -458.47 394.66 -5.86 283.81 | 1( 1)| 1.25 28.65 -483.29 512.63 -1.83 330.00 18- 19 | 1( 1)| 1.86 17.37 -231.07 294.25 -23.35 222.17 | 1( 1)| 1.67 22.05 -481.72 325.76 -26.67 243.73 | 1( 1)| 1.17 25.39 -497.28 425.23 -24.11 284.30 19- 20 | 1( 1)| 1.88 16.18 -241.49 269.79 -28.46 212.38 | 1( 1)| 1.94 22.29 -491.50 297.09 -32.73 232.53 | 1( 1)| 1.42 25.51 -506.21 388.85 -30.50 274.47 20- 21 | 1( 1)| 1.90 14.57 -254.07 240.34 -37.81 194.18 | 1( 1)| 1.79 22.55 -503.41 262.56 -43.80 211.70 | 1( 1)| 1.52 25.60 -517.12 345.03 -42.65 267.83 21- 22 | 1( 1)| 1.19 13.75 -301.36 129.25 -80.58 113.45 | 1( 1)| 1.39 24.47 -546.74 132.87 -96.65 152.74 | 1( 1)| 1.03 25.92 -556.35 180.71 -99.22 238.07 22- 23 | 1( 1)| 1.13 14.76 -322.14 80.66 -99.08 78.56 | 1( 1)| 1.18 25.35 -565.99 75.92 -121.71 139.05 | 1( 1)| 1.04 26.10 -573.88 110.85 -123.68 225.13 23- 24 | 1( 1)| 0.86 15.29 -332.72 56.36 -109.86 58.63 | 1( 1)| 1.19 25.81 -576.14 47.44 -136.95 131.06 | 1( 1)| 0.78 26.17 -583.18 76.38 -137.94 217.50 24- 25 | 1( 1)| 0.82 15.87 -344.77 30.38 -120.53 38.70 | 1( 1)| 0.85 26.32 -588.39 16.11 -152.03 123.14 | 1( 1)| 0.71 26.40 -594.47 37.45 -152.05 209.80 25- 26 | 1( 1)| 0.51 16.41 -355.37 7.43 -131.32 18.76 | 1( 1)| 0.73 26.78 -598.54 -10.10 -167.28 115.16 | 1( 1)| 0.49 26.79 -603.75 3.01 -166.32 202.18 26- 27 | 1( 1)| 0.85 17.01 -367.01 -18.06 -141.91 -1.17 | 1( 1)| 1.94 27.30 -609.63 -39.70 -182.26 107.32 | 1( 1)| 1.58 27.24 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.18 13.15 30.27 226.37 62.25 182.76 | 1( 1)| 2.19 15.54 -5.38 276.88 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.80 11.49 26.26 196.35 54.95 161.22 | 1( 1)| 1.94 13.57 -7.52 240.16 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.42 9.82 22.24 166.23 47.66 139.65 | 1( 1)| 1.70 11.59 -9.67 203.31 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.01 8.15 18.36 137.29 39.72 116.57 | 1( 1)| 1.43 9.61 -11.70 167.91 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.61 6.48 14.49 108.32 31.77 93.49 | 1( 1)| 1.16 7.63 -13.73 135.12 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.20 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.90 5.50 -16.02 98.62 18.10 79.77 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 1( 1)| 0.79 2.90 5.74 42.86 16.15 47.31 | 1( 1)| 0.66 3.50 -18.31 62.13 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.00 1.80 -19.86 37.64 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 1.91 8.22 22.27 74.66 -178.40 39.11 | 1( 1)| 1.14 8.26 11.90 88.94 -180.09 58.34 | 1( 1)| 0.75 8.28 -0.41 110.88 -180.36 55.24 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 5.79 87.92 -74.18 1824.89 109.18 612.93 | 4( 1)| 10.38 104.88 -159.47 2098.25 100.89 931.53 | 4( 1)| 17.09 132.20 -92.76 2596.93 111.37 1370.04 53- 54 | 4( 1)| 5.34 85.64 -86.80 1782.18 92.85 579.99 | 4( 1)| 9.38 102.19 -167.13 2048.99 83.51 889.76 | 4( 1)| 16.34 128.92 -98.55 2535.70 95.94 1321.91 54- 55 | 4( 1)| 5.16 84.29 -94.45 1755.66 84.06 561.69 | 4( 1)| 8.82 100.61 -171.80 2018.21 74.16 866.53 | 4( 1)| 15.94 126.98 -102.14 2497.13 87.57 1294.74 55- 56 | 4( 1)| 5.04 83.05 -101.43 1731.39 76.05 544.93 | 4( 1)| 8.31 99.16 -176.07 1990.04 65.62 845.26 | 4( 1)| 15.58 125.22 -105.42 2461.78 79.93 1269.82 56- 57 | 4( 1)| 4.74 81.83 -108.43 1702.09 68.01 523.92 | 4( 1)| 7.79 97.72 -180.60 1954.70 57.01 818.41 | 4( 1)| 15.23 123.45 -109.34 2414.97 71.78 1235.50 57- 58 | 4( 1)| 4.22 80.52 -115.69 1675.14 58.60 503.22 | 4( 1)| 7.22 96.18 -185.12 1922.95 46.98 792.09 | 4( 1)| 14.82 121.55 -112.98 2374.27 62.65 1203.74 58- 59 | 4( 1)| 3.70 79.22 -122.94 1650.03 49.19 484.08 | 4( 1)| 6.65 94.64 -189.55 1893.82 36.97 767.82 | 4( 1)| 14.41 119.65 -116.38 2337.76 53.71 1175.42 59- 60 | 4( 1)| 2.09 74.14 -151.93 1552.71 5.01 417.44 | 4( 1)| 4.50 88.61 -207.11 1781.76 1.57 683.01 | 4( 1)| 13.04 112.23 -129.60 2198.85 22.30 1078.46 60- 61 | 4( 1)| 1.79 72.85 -159.19 1527.12 -7.66 397.89 | 4( 1)| 3.93 87.07 -211.57 1751.95 -8.43 658.24 | 4( 1)| 12.68 110.33 -133.08 2161.24 13.30 1049.27 61- 62 | 3( 1)| 15.72 36.73 -519.85 330.99 -716.81 -329.81 | 3( 1)| 5.35 35.82 -462.95 379.45 -776.09 294.15 | 3( 1)| 4.63 40.03 -400.27 517.10 -830.25 281.61 62- 63 | 3( 1)| 16.38 38.02 -529.45 300.14 -737.03 -340.76 | 3( 1)| 5.78 36.85 -470.59 344.12 -797.47 285.15 | 3( 1)| 3.41 40.41 -431.76 516.56 -853.59 274.74 63- 64 | 3( 1)| 16.95 39.11 -537.69 275.36 -755.12 -350.54 | 3( 1)| 6.14 37.78 -477.03 316.09 -816.85 277.11 | 3( 1)| 2.42 41.67 -457.08 515.53 -874.76 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.87 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.69 2.02 10.46 35.08 11.86 26.22 | 1( 1)| 0.48 2.35 5.59 41.79 10.16 30.00 | 1( 1)| 0.27 2.87 -0.19 52.10 7.67 34.18 66- 67 | 1( 1)| 0.28 1.01 5.23 17.54 5.93 13.11 | 1( 1)| 0.14 1.17 2.80 20.89 5.08 15.00 | 1( 1)| 0.00 1.43 -0.10 26.05 3.84 17.09 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.53 22.01 -485.99 2.51 -118.96 17.71 | 1( 1)| 0.49 26.70 -593.23 4.30 -132.07 112.19 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.28 22.53 -496.80 -27.09 -127.55 -4.88 | 1( 1)| 1.49 27.14 -603.11 -31.33 -147.90 105.81 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 50.392s Elapsed Solve time : 692.608s Elapsed CPU time: 743.000s Sumatorio de erros e2 0.00008 Sumatorio de erros pq 0.23937 Sumatorio de erros vi 0.32531 Factor de erro e2 10.00 Factor de erro pq 1.00 Factor de erro vi 1.00 Maximum Psae error 1136.26253 Maximo erro superior 0.3737 Maximo erro inferior -10.9391 TRANSITION 15 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886940 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17072.01514 42 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 17071.85 3712.27 13359.58 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2675.90/ 2624.03/ 1327.03 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 342.87 0.00 0.00 190.01 952.71 0.00 51 0.00 0.00 0.00 203.97 0.00 0.00 64 0.00 0.00 0.00 801.74 97.83 106.89 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 800.00 0.00 0.00 67.00 0.00 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 721.31 403.69 0.00 50.00 0.00 0.00 0.00 69.00 0.00 920.31 185.24 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 12.95 46.00 0.00 0.00 0.00 64.00 0.00 374.34 982.06 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 0.85 0.85 0.85 1.71 Switchable CBs 4.02 7.55 7.91 11.75 PV systems 495.41 495.41 495.41 994.03 Wind systems 597.37 1525.29 1635.03 2174.84 EES systems 0.00 227.95 773.91 439.91 Total invesment cost 1142.54 2301.93 2958.00 3712.29 Purchased energy cost 5623.45 6021.96 7115.13 12105.80 Carbon tax payment 194.92 342.19 720.49 685.18 O&M PV cost 48.48 38.88 36.69 86.77 O&M wind cost 102.26 285.35 306.94 397.78 O&M EES cost 0.00 43.54 147.87 84.05 Total O&M cost 5969.12 6731.93 8327.12 13359.58 Total cost 7111.66 9033.86 11285.11 17071.87 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 7981.93 7704.94 130306.45 873.41 0.00 2 112692.57 7981.81 21848.51 141404.09 895.14 223.84 3 131989.27 7981.87 23826.85 161754.72 1218.07 826.70 CO2 Emissions (Ton): Period Distribution EV 1 9738.13 4980.53 2 9837.02 4906.75 3 9889.39 4780.66 4 9916.36 4659.94 5 9991.75 4476.17 6 8525.37 4266.91 7 8604.64 4025.47 8 8668.71 3733.05 9 8710.47 3403.07 10 8849.28 2999.31 11 8861.97 2539.22 12 9017.27 2025.48 13 9140.69 1443.32 14 9220.40 753.85 15 9464.25 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 579.27 4404.75 280.55 1946.31 0.90 0.97 Infinity -Infinity 2 0.00 5016.27 -0.00 2171.22 0.90 0.99 1.00 1.00 3 0.00 6295.56 -0.00 2573.68 0.90 0.98 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 0.00 211.71 0.00 152.32 2 -197.29 149.22 -99.51 197.19 3 -207.91 128.21 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 10.36 10.36 51.82 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 299.47 299.47 1497.37 1085.12 1085.12 5425.59 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 12.95 12.95 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 254.03 374.34 760.93 1238.13 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 29.35 218.34 579.25 4403.91 280.54 1945.61 | 4( 2)| 0.00 248.92 0.00 5015.19 -0.00 2170.35 | 4( 2)| 0.00 310.17 0.00 6293.88 -0.00 2572.21 2- 3 | 4( 2)| 28.87 216.98 571.90 4377.64 271.23 1923.69 | 4( 2)| 0.28 247.31 -7.06 4983.60 -8.65 2147.11 | 4( 2)| 0.27 308.21 -4.92 6253.67 -7.47 2543.09 3- 4 | 4( 2)| 19.64 189.29 421.06 3875.39 89.68 1523.83 | 4( 2)| 7.05 214.45 -153.14 4382.21 -177.98 1728.50 | 4( 2)| 5.65 268.63 -120.11 5516.04 -153.71 2036.81 4- 5 | 4( 1)| 11.84 142.49 158.06 3002.75 -207.27 870.85 | 4( 1)| 12.42 158.90 -406.97 3344.02 -453.43 1049.67 | 4( 1)| 11.63 200.47 -362.34 4216.84 -396.51 1220.39 5- 6 | 4( 1)| 11.98 141.19 150.70 2972.45 -216.71 845.70 | 4( 1)| 12.77 157.35 -414.27 3308.10 -462.29 1023.00 | 4( 1)| 11.71 198.57 -371.14 4168.76 -405.48 1193.51 6- 7 | 4( 1)| 12.15 139.89 143.35 2942.09 -226.15 820.51 | 4( 1)| 13.15 155.80 -421.59 3272.11 -471.17 996.28 | 4( 1)| 11.81 196.66 -379.95 4120.57 -414.47 1166.57 7- 8 | 4( 1)| 12.41 137.82 131.55 2901.58 -240.03 789.04 | 4( 1)| 12.85 153.34 -433.03 3224.43 -483.99 963.86 | 4( 1)| 11.98 193.62 -394.02 4059.53 -427.66 1134.67 8- 9 | 4( 1)| 5.52 131.83 87.11 2753.73 -86.59 855.18 | 4( 1)| 6.74 145.71 -475.95 3050.57 -487.01 889.67 | 4( 1)| 5.35 184.22 -446.33 3838.96 -458.17 1156.22 9- 10 | 1( 1)| 4.90 45.93 23.39 969.15 -213.96 224.74 | 1( 1)| 1.25 58.31 -729.30 1055.95 -1228.22 -0.77 | 1( 1)| 0.65 64.73 -907.69 1351.16 -1119.90 43.92 10- 11 | 3( 1)| 10.04 53.53 13.42 941.42 212.55 675.48 | 3( 1)| 8.19 58.16 -737.59 1022.91 110.07 731.93 | 3( 1)| 9.23 71.30 -913.77 1309.08 137.09 841.78 11- 12 | 1( 1)| 6.90 43.39 -51.51 761.58 143.71 543.13 | 1( 1)| 5.14 46.36 -804.71 812.23 46.22 580.51 | 1( 1)| 5.83 56.94 -953.77 1041.07 75.12 668.90 12- 13 | 1( 1)| 3.67 32.11 -123.43 563.61 67.49 396.83 | 1( 1)| 3.86 36.43 -384.85 642.51 61.51 443.75 | 1( 1)| 3.96 45.25 -436.55 828.53 59.53 513.35 13- 14 | 1( 1)| 3.79 29.96 -137.86 522.11 54.46 370.97 | 1( 1)| 3.22 33.93 -397.54 593.23 49.41 414.08 | 1( 1)| 3.84 42.17 -446.45 765.49 48.93 479.25 14- 15 | 1( 1)| 3.04 27.74 -152.29 480.97 40.02 342.85 | 1( 1)| 2.54 31.34 -410.27 544.76 35.99 381.83 | 1( 1)| 2.73 38.98 -456.37 703.20 36.96 441.81 15- 16 | 1( 1)| 2.46 26.26 -162.37 456.28 29.28 322.58 | 1( 1)| 2.06 29.62 -417.98 515.78 26.05 358.64 | 1( 1)| 1.95 36.89 -461.66 666.34 28.12 415.34 16- 17 | 1( 1)| 2.00 23.75 -181.21 411.57 13.43 292.18 | 1( 1)| 1.86 26.68 -435.59 463.31 11.37 323.84 | 1( 1)| 1.22 33.28 -471.30 599.64 14.18 375.62 17- 18 | 1( 1)| 1.76 20.56 -206.12 353.01 -4.87 257.20 | 1( 1)| 1.90 22.95 -458.47 394.66 -5.86 283.81 | 1( 1)| 1.25 28.65 -483.29 512.63 -2.03 330.00 18- 19 | 1( 1)| 1.87 17.37 -231.12 294.24 -23.19 222.17 | 1( 1)| 1.67 22.02 -481.72 325.76 -26.64 243.73 | 1( 1)| 1.17 25.39 -497.28 425.23 -24.12 284.30 19- 20 | 1( 1)| 1.88 16.18 -241.53 269.79 -28.31 212.38 | 1( 1)| 1.94 22.26 -491.50 297.09 -32.70 232.53 | 1( 1)| 1.42 25.51 -506.21 388.85 -30.51 274.47 20- 21 | 1( 1)| 1.90 14.57 -254.11 240.33 -37.65 194.17 | 1( 1)| 1.79 22.52 -503.41 262.56 -43.77 211.70 | 1( 1)| 1.52 25.61 -517.12 345.03 -42.65 267.83 21- 22 | 1( 1)| 1.19 13.76 -301.41 129.24 -80.42 113.44 | 1( 1)| 1.39 24.47 -546.74 132.87 -96.62 152.74 | 1( 1)| 1.03 25.92 -556.35 180.71 -99.22 238.07 22- 23 | 1( 1)| 1.13 14.77 -322.19 80.65 -98.92 78.56 | 1( 1)| 1.18 25.35 -565.99 75.92 -121.71 139.05 | 1( 1)| 1.04 26.10 -573.88 110.85 -123.68 225.13 23- 24 | 1( 1)| 0.86 15.30 -332.77 56.35 -109.71 58.63 | 1( 1)| 1.19 25.81 -576.14 47.44 -136.95 131.06 | 1( 1)| 0.78 26.18 -583.18 76.38 -137.94 217.50 24- 25 | 1( 1)| 0.82 15.88 -344.82 30.38 -120.38 38.69 | 1( 1)| 0.85 26.32 -588.39 16.11 -152.03 123.14 | 1( 1)| 0.71 26.40 -594.47 37.45 -152.05 209.80 25- 26 | 1( 1)| 0.51 16.42 -355.41 7.43 -131.16 18.76 | 1( 1)| 0.73 26.79 -598.54 -10.10 -167.28 115.16 | 1( 1)| 0.49 26.79 -603.75 3.01 -166.32 202.18 26- 27 | 1( 1)| 0.85 17.02 -367.06 -18.07 -141.76 -1.17 | 1( 1)| 1.94 27.31 -609.63 -39.70 -182.26 107.32 | 1( 1)| 1.58 27.24 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.18 13.15 30.27 226.37 62.25 182.76 | 1( 1)| 2.16 15.54 4.30 276.88 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.80 11.49 26.26 196.35 54.95 161.22 | 1( 1)| 1.91 13.57 2.16 240.16 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.42 9.82 22.24 166.23 47.66 139.65 | 1( 1)| 1.66 11.59 0.02 203.31 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.01 8.15 18.36 137.29 39.72 116.57 | 1( 1)| 1.39 9.61 -2.01 167.91 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.61 6.48 14.49 108.32 31.77 93.49 | 1( 1)| 1.11 7.63 -4.04 132.48 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.20 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.83 5.50 -6.33 92.58 18.10 79.77 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 1( 1)| 0.79 2.90 5.74 42.86 16.15 47.31 | 1( 1)| 0.57 3.38 -8.62 56.10 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.00 1.55 -10.16 31.61 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 1.92 8.23 22.27 74.66 -178.74 38.88 | 1( 1)| 1.14 8.31 11.90 88.94 -182.12 58.33 | 1( 1)| 0.75 8.29 -0.41 110.88 -180.70 55.24 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 5.77 87.88 -74.18 1824.88 109.18 609.84 | 4( 1)| 10.35 104.81 -159.06 2098.23 102.28 928.10 | 4( 1)| 16.99 132.15 -81.95 2596.90 111.44 1367.09 53- 54 | 4( 1)| 5.32 85.59 -86.80 1782.18 92.84 576.90 | 4( 1)| 9.36 102.13 -166.72 2048.97 84.90 886.33 | 4( 1)| 16.24 128.87 -87.74 2535.67 96.00 1318.97 54- 55 | 4( 1)| 5.16 84.24 -94.45 1755.65 84.06 558.60 | 4( 1)| 8.79 100.55 -171.40 2018.19 75.55 863.10 | 4( 1)| 15.84 126.93 -91.32 2497.10 87.63 1291.80 55- 56 | 4( 1)| 5.03 83.01 -101.43 1731.39 76.04 541.84 | 4( 1)| 8.28 99.10 -175.66 1990.02 67.01 841.83 | 4( 1)| 15.48 125.16 -94.61 2461.75 79.99 1266.88 56- 57 | 4( 1)| 4.71 81.79 -108.43 1702.09 68.00 520.84 | 4( 1)| 7.76 97.66 -180.18 1954.69 58.40 815.00 | 4( 1)| 15.12 123.39 -98.52 2414.96 71.83 1232.58 57- 58 | 4( 1)| 4.19 80.48 -115.69 1675.14 58.59 500.14 | 4( 1)| 7.19 96.12 -184.69 1922.95 48.37 788.68 | 4( 1)| 14.72 121.50 -102.15 2374.26 62.69 1200.83 58- 59 | 4( 1)| 3.68 79.18 -122.94 1650.04 49.19 481.00 | 4( 1)| 6.62 94.58 -189.12 1893.82 38.36 764.41 | 4( 1)| 14.31 119.60 -105.56 2337.76 53.75 1172.50 59- 60 | 4( 1)| 2.06 74.10 -151.93 1552.72 13.90 414.36 | 4( 1)| 4.48 88.55 -206.68 1781.76 2.96 679.60 | 4( 1)| 12.94 112.18 -118.77 2198.85 22.34 1075.55 60- 61 | 4( 1)| 1.77 72.82 -159.19 1527.13 1.24 394.82 | 4( 1)| 3.91 87.01 -211.14 1751.96 -7.05 654.84 | 4( 1)| 12.58 110.28 -122.25 2161.24 13.30 1046.36 61- 62 | 3( 1)| 15.77 36.73 -519.85 331.00 -720.38 -330.89 | 3( 1)| 5.42 35.82 -462.94 379.45 -776.04 294.15 | 3( 1)| 4.49 40.04 -405.63 521.37 -830.50 281.62 62- 63 | 3( 1)| 16.43 38.02 -529.45 300.15 -739.99 -341.84 | 3( 1)| 5.86 36.84 -470.58 344.12 -797.43 285.15 | 3( 1)| 3.26 40.41 -437.12 520.82 -853.84 274.75 63- 64 | 3( 1)| 16.99 39.11 -537.69 275.36 -757.44 -351.62 | 3( 1)| 6.23 37.77 -477.01 316.09 -816.80 277.11 | 3( 1)| 2.27 41.79 -462.45 519.78 -875.02 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.87 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.72 2.02 10.46 35.08 11.86 26.22 | 1( 1)| 0.53 2.35 5.59 41.79 10.16 30.00 | 1( 1)| 0.35 2.87 -0.19 52.10 7.67 34.18 66- 67 | 1( 1)| 0.36 1.01 5.23 17.54 5.93 13.11 | 1( 1)| 0.27 1.18 2.80 20.89 5.08 15.00 | 1( 1)| 0.17 1.43 -0.10 26.05 3.84 17.09 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.53 22.01 -485.96 2.51 -118.30 17.71 | 1( 1)| 0.49 26.70 -593.20 4.30 -132.12 112.27 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.28 22.53 -496.76 -27.09 -127.91 -4.87 | 1( 1)| 1.49 27.14 -603.09 -31.32 -147.95 105.89 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 54.064s Elapsed Solve time : 745.858s Elapsed CPU time: 799.922s Sumatorio de erros e2 0.00001 Sumatorio de erros pq 0.16018 Sumatorio de erros vi 0.23306 Factor de erro e2 10.00 Factor de erro pq 1.00 Factor de erro vi 1.00 Maximum Psae error 1136.13995 Maximo erro superior 0.1644 Maximo erro inferior -10.2854 TRANSITION 16 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886937 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17072.00907 44 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 17071.90 3712.31 13359.58 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2675.98/ 2623.98/ 1327.01 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 342.91 0.00 0.00 182.83 959.85 0.00 51 0.00 0.00 0.00 204.25 0.00 0.00 64 0.00 0.00 0.00 806.30 93.34 107.04 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 800.00 0.00 0.00 67.00 0.00 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 721.36 403.64 0.00 50.00 0.00 0.00 0.00 69.00 0.00 920.31 185.23 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 4.11 46.00 0.00 0.00 0.00 64.00 0.00 374.34 990.89 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 0.85 0.85 0.85 1.71 Switchable CBs 4.01 7.55 7.91 11.74 PV systems 495.41 495.41 495.41 994.03 Wind systems 597.42 1525.30 1635.04 2174.89 EES systems 0.00 227.95 773.90 439.91 Total invesment cost 1142.57 2301.94 2958.00 3712.33 Purchased energy cost 5623.45 6021.95 7115.13 12105.80 Carbon tax payment 194.92 342.19 720.49 685.18 O&M PV cost 48.48 38.88 36.69 86.77 O&M wind cost 102.27 285.35 306.94 397.79 O&M EES cost 0.00 43.54 147.86 84.05 Total O&M cost 5969.13 6731.91 8327.11 13359.58 Total cost 7111.70 9033.86 11285.11 17071.91 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 7981.93 7705.47 130306.45 873.48 0.00 2 112692.52 7981.81 21848.56 141404.09 895.04 223.92 3 131989.23 7981.87 23826.81 161754.72 1217.75 826.66 CO2 Emissions (Ton): Period Distribution EV 1 9738.13 4980.53 2 9837.02 4906.75 3 9889.39 4780.66 4 9916.36 4659.94 5 9991.74 4476.17 6 8525.37 4266.91 7 8604.63 4025.47 8 8668.70 3733.05 9 8710.46 3403.07 10 8849.28 2999.31 11 8861.97 2539.22 12 9017.27 2025.48 13 9140.68 1443.32 14 9220.40 753.85 15 9464.24 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 579.25 4404.72 280.55 1944.42 0.90 0.97 Infinity -Infinity 2 0.00 5012.53 -0.00 2169.68 0.90 0.99 1.00 1.00 3 0.00 6300.41 -0.00 2572.78 0.90 0.98 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 0.00 217.27 0.00 152.20 2 -197.29 146.33 -99.51 197.19 3 -207.91 121.22 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 3.29 3.29 16.43 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 299.47 299.47 1497.37 1092.19 1092.19 5460.94 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 4.11 4.11 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 253.92 374.34 765.72 1244.32 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 29.35 218.30 579.24 4403.89 280.53 1943.72 | 4( 2)| 0.00 248.73 0.00 5011.45 -0.00 2168.80 | 4( 2)| 0.00 310.36 0.00 6298.73 -0.00 2571.30 2- 3 | 4( 2)| 28.87 216.94 571.89 4377.62 271.22 1921.80 | 4( 2)| 0.29 247.12 -7.06 4979.86 -8.65 2145.57 | 4( 2)| 0.27 308.40 -4.92 6258.50 -7.47 2542.18 3- 4 | 4( 2)| 19.64 189.26 421.05 3875.37 89.68 1521.94 | 4( 2)| 7.05 214.27 -153.14 4378.47 -177.98 1726.96 | 4( 2)| 5.64 268.44 -111.25 5511.99 -153.70 2035.89 4- 5 | 4( 1)| 11.84 142.47 158.05 3002.73 -207.20 868.96 | 4( 1)| 12.42 158.72 -406.97 3343.99 -453.43 1048.37 | 4( 1)| 11.84 200.28 -362.36 4212.79 -396.52 1219.65 5- 6 | 4( 1)| 11.98 141.16 150.69 2972.43 -216.64 843.81 | 4( 1)| 12.78 157.17 -414.27 3308.07 -462.29 1021.70 | 4( 1)| 11.91 198.38 -371.16 4164.73 -405.49 1192.77 6- 7 | 4( 1)| 12.15 139.86 143.33 2942.07 -226.08 818.63 | 4( 1)| 13.15 155.62 -421.59 3272.09 -471.17 994.99 | 4( 1)| 12.01 196.47 -379.97 4116.57 -414.48 1165.84 7- 8 | 4( 1)| 12.41 137.79 131.54 2901.57 -239.95 787.16 | 4( 1)| 12.85 153.15 -433.03 3224.40 -483.99 962.57 | 4( 1)| 12.18 193.43 -394.05 4055.53 -427.67 1133.93 8- 9 | 4( 1)| 5.51 131.78 87.10 2753.72 -86.24 851.96 | 4( 1)| 6.74 145.52 -475.95 3050.55 -487.01 887.81 | 4( 1)| 5.56 184.03 -446.35 3834.97 -458.16 1155.02 9- 10 | 1( 1)| 4.93 45.92 23.37 969.15 -213.32 224.22 | 1( 1)| 1.26 58.31 -729.34 1055.95 -1228.22 0.86 | 1( 1)| 0.63 64.73 -907.68 1351.16 -1119.89 43.38 10- 11 | 3( 1)| 10.01 53.53 13.40 941.41 212.66 675.48 | 3( 1)| 8.19 58.16 -737.63 1022.91 110.16 731.93 | 3( 1)| 9.23 71.30 -913.77 1309.08 135.59 841.78 11- 12 | 1( 1)| 6.89 43.39 -51.53 761.58 143.83 543.12 | 1( 1)| 5.15 46.36 -804.72 812.23 46.32 580.51 | 1( 1)| 5.83 56.94 -953.77 1041.07 73.63 668.90 12- 13 | 1( 1)| 3.68 32.11 -123.46 563.61 67.61 396.82 | 1( 1)| 3.86 36.43 -384.87 642.51 61.52 443.75 | 1( 1)| 3.96 45.25 -436.55 828.53 59.58 513.35 13- 14 | 1( 1)| 3.79 29.96 -137.88 522.10 54.57 370.97 | 1( 1)| 3.22 33.93 -397.55 593.23 49.41 414.08 | 1( 1)| 3.83 42.17 -446.45 765.49 48.78 479.25 14- 15 | 1( 1)| 3.04 27.74 -152.32 480.97 40.13 342.84 | 1( 1)| 2.54 31.34 -410.28 544.76 36.00 381.83 | 1( 1)| 2.73 38.98 -456.37 703.20 36.81 441.81 15- 16 | 1( 1)| 2.46 26.26 -162.39 456.28 29.39 322.58 | 1( 1)| 2.06 29.62 -417.97 515.78 26.05 358.64 | 1( 1)| 1.95 36.89 -461.66 666.34 27.96 415.34 16- 17 | 1( 1)| 2.00 23.75 -181.24 411.57 13.55 292.18 | 1( 1)| 1.86 26.68 -435.59 463.31 11.37 323.84 | 1( 1)| 1.22 33.28 -471.30 599.64 14.00 375.62 17- 18 | 1( 1)| 1.76 20.56 -206.15 353.00 -4.76 257.20 | 1( 1)| 1.90 22.95 -458.47 394.66 -5.86 283.81 | 1( 1)| 1.25 28.65 -483.29 512.63 -2.21 330.00 18- 19 | 1( 1)| 1.87 17.37 -231.14 294.24 -23.08 222.16 | 1( 1)| 1.67 21.99 -481.72 325.76 -26.63 243.73 | 1( 1)| 1.17 25.39 -497.28 425.23 -24.13 284.30 19- 20 | 1( 1)| 1.88 16.18 -241.56 269.78 -28.19 212.38 | 1( 1)| 1.94 22.23 -491.49 297.09 -32.69 232.53 | 1( 1)| 1.42 25.51 -506.21 388.85 -30.52 274.47 20- 21 | 1( 1)| 1.90 14.57 -254.14 240.33 -37.54 194.17 | 1( 1)| 1.79 22.51 -503.41 262.56 -43.76 211.70 | 1( 1)| 1.52 25.61 -517.12 345.03 -42.65 267.83 21- 22 | 1( 1)| 1.19 13.76 -301.43 129.24 -80.31 113.44 | 1( 1)| 1.39 24.47 -546.74 132.87 -96.58 152.74 | 1( 1)| 1.03 25.92 -556.35 180.71 -99.22 238.07 22- 23 | 1( 1)| 1.13 14.78 -322.21 80.65 -98.81 78.56 | 1( 1)| 1.18 25.36 -565.99 75.92 -121.71 139.05 | 1( 1)| 1.04 26.10 -573.88 110.85 -123.69 225.13 23- 24 | 1( 1)| 0.86 15.30 -332.79 56.35 -109.59 58.62 | 1( 1)| 1.19 25.81 -576.14 47.44 -136.95 131.06 | 1( 1)| 0.78 26.18 -583.18 76.38 -137.94 217.50 24- 25 | 1( 1)| 0.82 15.89 -344.85 30.37 -120.26 38.69 | 1( 1)| 0.85 26.33 -588.39 16.11 -152.03 123.14 | 1( 1)| 0.71 26.40 -594.47 37.45 -152.05 209.80 25- 26 | 1( 1)| 0.51 16.43 -355.44 7.43 -131.05 18.76 | 1( 1)| 0.73 26.79 -598.54 -10.10 -167.28 115.16 | 1( 1)| 0.49 26.79 -603.75 3.01 -166.32 202.18 26- 27 | 1( 1)| 0.85 17.03 -367.08 -18.07 -141.64 -1.17 | 1( 1)| 1.94 27.31 -609.63 -39.70 -182.26 107.32 | 1( 1)| 1.58 27.24 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.18 13.15 30.27 226.37 62.25 182.76 | 1( 1)| 2.12 15.67 3.08 278.16 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.80 11.49 26.26 196.35 54.95 161.22 | 1( 1)| 1.86 13.65 3.21 240.73 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.42 9.82 22.24 166.23 47.66 139.65 | 1( 1)| 1.61 11.63 3.35 203.31 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.01 8.15 18.36 137.29 39.72 116.57 | 1( 1)| 1.32 9.62 3.08 167.91 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.61 6.48 14.49 108.32 31.77 93.49 | 1( 1)| 1.04 7.63 2.77 132.48 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.20 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.75 5.50 1.61 92.44 18.10 79.77 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 1( 1)| 0.79 2.90 5.74 42.86 16.15 47.31 | 1( 1)| 0.42 3.38 -0.68 52.42 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.00 1.35 -2.22 26.68 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.48 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 1.93 8.24 22.27 74.66 -179.02 38.65 | 1( 1)| 1.14 8.33 11.90 88.94 -182.39 58.34 | 1( 1)| 0.75 8.31 -0.41 110.88 -180.97 55.25 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 5.76 87.83 -74.18 1824.88 109.07 606.78 | 4( 1)| 10.32 104.75 -158.69 2098.21 103.53 924.69 | 4( 1)| 16.89 132.10 -73.09 2596.87 111.00 1364.17 53- 54 | 4( 1)| 5.31 85.55 -86.80 1782.18 92.74 573.84 | 4( 1)| 9.33 102.07 -166.34 2048.95 86.15 882.92 | 4( 1)| 16.14 128.82 -78.88 2535.64 95.57 1316.05 54- 55 | 4( 1)| 5.14 84.20 -94.45 1755.65 83.95 555.54 | 4( 1)| 8.77 100.49 -171.02 2018.18 76.79 859.69 | 4( 1)| 15.74 126.88 -82.47 2497.08 87.19 1288.87 55- 56 | 4( 1)| 5.02 82.97 -101.43 1731.39 75.94 538.79 | 4( 1)| 8.25 99.04 -175.28 1990.01 68.25 838.43 | 4( 1)| 15.38 125.11 -85.75 2461.73 79.55 1263.96 56- 57 | 4( 1)| 4.69 81.75 -108.43 1702.10 67.90 517.79 | 4( 1)| 7.74 97.60 -179.79 1954.69 59.64 811.60 | 4( 1)| 15.02 123.34 -89.67 2414.95 71.38 1229.67 57- 58 | 4( 1)| 4.16 80.45 -115.69 1675.15 58.49 497.09 | 4( 1)| 7.17 96.06 -184.30 1922.95 49.61 785.29 | 4( 1)| 14.62 121.45 -93.30 2374.26 62.24 1197.92 58- 59 | 4( 1)| 3.65 79.15 -122.94 1650.04 49.08 477.95 | 4( 1)| 6.60 94.52 -188.73 1893.82 39.60 761.02 | 4( 1)| 14.21 119.55 -96.70 2337.76 53.29 1169.60 59- 60 | 4( 1)| 2.04 74.07 -151.93 1552.73 15.80 411.31 | 4( 1)| 4.45 88.49 -206.29 1781.77 4.20 676.21 | 4( 1)| 12.84 112.13 -109.92 2198.85 21.88 1072.65 60- 61 | 4( 1)| 1.74 72.78 -159.19 1527.14 6.39 391.77 | 4( 1)| 3.88 86.96 -210.75 1751.96 -6.11 651.45 | 4( 1)| 12.48 110.23 -113.40 2161.24 12.69 1043.47 61- 62 | 3( 1)| 15.81 36.72 -519.85 331.01 -723.58 -331.93 | 3( 1)| 5.50 35.82 -462.97 379.46 -775.99 294.15 | 3( 1)| 4.35 40.05 -409.92 524.91 -830.74 281.62 62- 63 | 3( 1)| 16.47 38.02 -529.45 300.15 -743.19 -342.88 | 3( 1)| 5.94 36.84 -470.61 344.13 -797.38 285.15 | 3( 1)| 3.12 40.51 -441.41 524.36 -854.08 274.76 63- 64 | 3( 1)| 17.04 39.11 -537.69 275.36 -760.65 -352.66 | 3( 1)| 6.32 37.77 -477.04 316.09 -816.75 277.11 | 3( 1)| 2.11 41.89 -466.76 523.32 -875.26 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.87 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.72 2.02 10.46 35.08 11.86 26.22 | 1( 1)| 0.53 2.35 5.59 41.79 10.16 30.00 | 1( 1)| 0.35 2.87 -0.19 52.10 7.67 34.18 66- 67 | 1( 1)| 0.36 1.01 5.23 17.54 5.93 13.11 | 1( 1)| 0.27 1.18 2.80 20.89 5.08 15.00 | 1( 1)| 0.17 1.43 -0.10 26.05 3.84 17.09 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.53 22.01 -485.96 2.51 -117.61 17.71 | 1( 1)| 0.49 26.70 -593.20 4.30 -132.03 112.32 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.28 22.53 -496.77 -27.09 -127.91 -4.88 | 1( 1)| 1.49 27.14 -603.08 -31.32 -147.87 105.94 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 57.798s Elapsed Solve time : 800.062s Elapsed CPU time: 857.860s Sumatorio de erros e2 0.00016 Sumatorio de erros pq 0.11186 Sumatorio de erros vi 0.14215 Factor de erro e2 10.00 Factor de erro pq 1.00 Factor de erro vi 1.00 Maximum Psae error 1136.11506 Maximo erro superior 0.0888 Maximo erro inferior -8.8369 TRANSITION 17 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 48960 nonlinear variables 83598 linear variables 211995 constraints, all linear; 886938 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: optimal solution; objective 17072.0157 41 separable QP barrier iterations No basis. Funcao Ojetivo($)/ Investment/ O&M: 17071.95 3712.36 13359.59 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2676.04/ 2623.94/ 1327.11 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 342.92 0.00 0.00 176.84 965.83 0.00 51 0.00 0.00 0.00 204.43 0.00 0.00 64 0.00 0.00 0.00 809.98 89.73 107.19 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 800.00 0.00 0.00 67.00 0.00 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 721.39 403.61 0.00 50.00 0.00 0.00 0.00 69.00 0.00 920.31 185.27 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 374.34 995.05 67.00 0.00 0.00 0.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 0.85 0.85 0.85 1.71 Switchable CBs 4.00 7.55 7.91 11.74 PV systems 495.41 495.41 495.41 994.03 Wind systems 597.45 1525.31 1635.07 2174.93 EES systems 0.00 227.95 773.93 439.92 Total invesment cost 1142.59 2301.95 2958.05 3712.38 Purchased energy cost 5623.45 6021.94 7115.15 12105.80 Carbon tax payment 194.92 342.19 720.49 685.18 O&M PV cost 48.48 38.88 36.69 86.77 O&M wind cost 102.28 285.35 306.94 397.80 O&M EES cost 0.00 43.54 147.87 84.05 Total O&M cost 5969.13 6731.90 8327.14 13359.59 Total cost 7111.73 9033.85 11285.19 17071.97 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 7981.93 7705.88 130306.45 873.58 0.00 2 112692.49 7981.81 21848.58 141404.09 894.96 223.99 3 131989.20 7981.87 23827.23 161754.72 1217.58 826.71 CO2 Emissions (Ton): Period Distribution EV 1 9738.13 4980.53 2 9837.02 4906.75 3 9889.39 4780.66 4 9916.36 4659.94 5 9991.74 4476.17 6 8525.37 4266.91 7 8604.63 4025.47 8 8668.70 3733.05 9 8710.46 3403.07 10 8849.27 2999.31 11 8861.97 2539.22 12 9017.27 2025.48 13 9140.68 1443.32 14 9220.39 753.85 15 9464.24 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 579.24 4404.71 280.54 1942.55 0.90 0.97 Infinity -Infinity 2 0.00 5008.81 -0.00 2168.15 0.90 0.99 1.00 1.00 3 0.00 6301.03 -0.00 2571.91 0.90 0.98 1.00 1.00 Reactive Power by DG Period PV Wind min max min max 1 0.00 224.33 0.00 152.11 2 -197.29 160.44 -99.51 197.19 3 -207.91 136.30 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 299.47 299.47 1497.37 1095.51 1095.51 5477.55 67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 253.82 374.34 767.94 1247.24 67 0.00 0.00 0.00 0.00 0.00 0.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 4( 2)| 29.35 218.26 579.23 4403.88 280.53 1941.84 | 4( 2)| 0.00 248.55 0.00 5007.73 -0.00 2167.28 | 4( 2)| 0.00 310.37 0.00 6299.35 -0.00 2570.43 2- 3 | 4( 2)| 28.87 216.90 571.88 4377.61 271.22 1919.93 | 4( 2)| 0.31 246.94 -7.06 4976.14 -8.65 2144.04 | 4( 2)| 0.27 308.41 -4.92 6259.13 -7.47 2541.31 3- 4 | 4( 2)| 19.63 189.22 421.04 3875.36 89.67 1520.07 | 4( 2)| 7.05 214.09 -153.14 4374.76 -177.98 1725.44 | 4( 2)| 5.64 268.27 -107.14 5508.49 -153.70 2035.02 4- 5 | 4( 1)| 11.84 142.44 158.04 3002.72 -207.20 867.08 | 4( 1)| 12.43 158.54 -406.97 3343.96 -453.43 1047.06 | 4( 1)| 11.93 200.12 -362.41 4209.29 -396.54 1218.90 5- 6 | 4( 1)| 11.98 141.14 150.68 2972.42 -216.64 841.94 | 4( 1)| 12.79 156.99 -414.27 3308.04 -462.29 1020.40 | 4( 1)| 12.00 198.21 -371.20 4161.25 -405.51 1192.02 6- 7 | 4( 1)| 12.15 139.84 143.32 2942.06 -226.08 816.76 | 4( 1)| 13.16 155.44 -421.59 3272.06 -471.17 993.68 | 4( 1)| 12.10 196.31 -380.01 4113.10 -414.50 1165.08 7- 8 | 4( 1)| 12.41 137.77 131.53 2901.56 -239.96 785.29 | 4( 1)| 12.85 152.97 -433.03 3224.38 -483.99 961.27 | 4( 1)| 12.27 193.27 -394.09 4052.07 -427.69 1133.18 8- 9 | 4( 1)| 5.51 131.74 87.09 2753.71 -86.06 848.78 | 4( 1)| 6.75 145.33 -475.95 3050.52 -487.01 885.97 | 4( 1)| 5.65 183.86 -446.39 3831.50 -458.16 1153.83 9- 10 | 1( 1)| 4.96 45.92 23.35 969.15 -212.78 223.72 | 1( 1)| 1.27 58.31 -729.37 1055.95 -1228.22 2.55 | 1( 1)| 0.60 64.73 -907.70 1351.15 -1119.88 42.87 10- 11 | 3( 1)| 9.97 53.53 13.38 941.41 212.20 675.48 | 3( 1)| 8.19 58.16 -737.66 1022.91 110.26 731.93 | 3( 1)| 9.23 71.30 -913.79 1309.08 134.83 841.78 11- 12 | 1( 1)| 6.89 43.39 -51.55 761.57 143.91 543.12 | 1( 1)| 5.16 46.36 -804.72 812.23 46.42 580.51 | 1( 1)| 5.83 56.94 -953.79 1041.07 72.86 668.90 12- 13 | 1( 1)| 3.68 32.11 -123.47 563.61 67.70 396.82 | 1( 1)| 3.86 36.43 -384.89 642.51 61.54 443.75 | 1( 1)| 3.96 45.25 -436.55 828.53 59.50 513.35 13- 14 | 1( 1)| 3.80 29.96 -137.90 522.10 54.66 370.97 | 1( 1)| 3.22 33.93 -397.57 593.23 49.44 414.08 | 1( 1)| 3.83 42.17 -446.45 765.49 48.70 479.25 14- 15 | 1( 1)| 3.04 27.74 -152.34 480.96 40.22 342.84 | 1( 1)| 2.54 31.34 -410.29 544.76 36.02 381.83 | 1( 1)| 2.73 38.98 -456.37 703.20 36.74 441.81 15- 16 | 1( 1)| 2.46 26.26 -162.41 456.27 29.48 322.58 | 1( 1)| 2.07 29.62 -417.97 515.78 26.08 358.64 | 1( 1)| 1.95 36.89 -461.66 666.34 27.89 415.34 16- 17 | 1( 1)| 2.00 23.75 -181.26 411.56 13.63 292.18 | 1( 1)| 1.86 26.68 -435.59 463.31 11.40 323.84 | 1( 1)| 1.22 33.28 -471.30 599.64 13.91 375.62 17- 18 | 1( 1)| 1.76 20.56 -206.16 353.00 -4.67 257.19 | 1( 1)| 1.90 22.95 -458.47 394.66 -5.85 283.81 | 1( 1)| 1.25 28.65 -483.29 512.63 -2.30 330.00 18- 19 | 1( 1)| 1.87 17.36 -231.16 294.23 -22.99 222.16 | 1( 1)| 1.67 21.96 -481.72 325.76 -26.62 243.73 | 1( 1)| 1.17 25.39 -497.28 425.23 -24.15 284.30 19- 20 | 1( 1)| 1.88 16.18 -241.58 269.78 -28.11 212.38 | 1( 1)| 1.94 22.20 -491.49 297.09 -32.68 232.53 | 1( 1)| 1.42 25.51 -506.21 388.85 -30.54 274.47 20- 21 | 1( 1)| 1.90 14.57 -254.16 240.33 -37.45 194.17 | 1( 1)| 1.79 22.51 -503.41 262.56 -43.76 211.70 | 1( 1)| 1.52 25.61 -517.12 345.03 -42.65 267.83 21- 22 | 1( 1)| 1.19 13.76 -301.45 129.23 -80.22 113.44 | 1( 1)| 1.39 24.47 -546.74 132.87 -96.56 152.74 | 1( 1)| 1.03 25.92 -556.35 180.71 -99.22 238.07 22- 23 | 1( 1)| 1.13 14.78 -322.23 80.65 -98.72 78.56 | 1( 1)| 1.18 25.36 -565.99 75.92 -121.71 139.05 | 1( 1)| 1.04 26.10 -573.88 110.85 -123.68 225.13 23- 24 | 1( 1)| 0.86 15.31 -332.81 56.35 -109.50 58.62 | 1( 1)| 1.19 25.81 -576.14 47.44 -136.95 131.06 | 1( 1)| 0.78 26.18 -583.18 76.38 -137.94 217.50 24- 25 | 1( 1)| 0.82 15.89 -344.87 30.37 -120.18 38.69 | 1( 1)| 0.85 26.33 -588.39 16.11 -152.03 123.14 | 1( 1)| 0.71 26.40 -594.47 37.45 -152.05 209.80 25- 26 | 1( 1)| 0.51 16.44 -355.46 7.42 -130.96 18.76 | 1( 1)| 0.73 26.79 -598.54 -10.10 -167.28 115.16 | 1( 1)| 0.49 26.79 -603.75 3.01 -166.32 202.18 26- 27 | 1( 1)| 0.85 17.03 -367.10 -18.07 -141.55 -1.17 | 1( 1)| 1.94 27.31 -609.63 -39.70 -182.26 107.32 | 1( 1)| 1.58 27.24 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.18 13.15 30.27 226.37 62.25 182.76 | 1( 1)| 2.15 15.83 -1.03 282.29 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.80 11.49 26.26 196.35 54.95 161.22 | 1( 1)| 1.89 13.81 -0.89 244.85 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.42 9.82 22.24 166.23 47.66 139.65 | 1( 1)| 1.64 11.79 -0.75 207.28 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.01 8.15 18.36 137.29 39.72 116.57 | 1( 1)| 1.36 9.77 -0.62 171.19 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.61 6.48 14.49 108.32 31.77 93.49 | 1( 1)| 1.08 7.76 -0.49 135.06 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.20 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.81 5.57 -0.34 94.24 18.10 79.77 33- 34 | 1( 1)| 0.99 2.49 10.73 35.98 18.70 41.02 | 1( 1)| 0.79 2.90 5.74 42.86 16.15 47.31 | 1( 1)| 0.53 3.40 -0.20 53.44 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.00 1.37 -0.10 26.05 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 4( 1)| 17.51 48.40 253.23 850.56 285.96 632.45 | 4( 1)| 12.87 56.23 135.36 1012.21 244.96 723.65 | 4( 1)| 8.45 68.26 -4.59 1262.27 184.93 824.68 47- 48 | 4( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 4( 1)| 12.47 54.56 131.48 983.13 237.01 700.43 | 4( 1)| 8.17 66.25 -4.46 1225.98 178.93 798.19 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.30 49.47 119.16 890.51 214.86 634.65 | 3( 1)| 7.41 60.07 -4.07 1110.27 162.30 723.14 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.65 24.74 59.58 445.19 107.43 317.31 | 1( 1)| 3.71 30.04 -2.04 555.03 81.15 361.55 8- 51 | 1( 1)| 1.95 8.25 22.27 74.66 -179.20 38.33 | 1( 1)| 1.14 8.34 11.90 88.94 -182.58 58.34 | 1( 1)| 0.75 8.32 -0.41 110.88 -181.22 55.24 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 4( 1)| 5.74 87.79 -74.18 1824.87 108.96 603.77 | 4( 1)| 10.30 104.69 -158.31 2098.19 103.96 921.30 | 4( 1)| 16.79 132.05 -68.98 2596.85 110.83 1361.27 53- 54 | 4( 1)| 5.29 85.51 -86.80 1782.17 92.63 570.83 | 4( 1)| 9.30 102.01 -165.96 2048.93 86.68 879.54 | 4( 1)| 16.04 128.76 -74.77 2535.62 95.39 1313.15 54- 55 | 4( 1)| 5.13 84.17 -94.45 1755.65 83.85 552.53 | 4( 1)| 8.74 100.43 -170.63 2018.16 77.37 856.31 | 4( 1)| 15.64 126.83 -78.36 2497.06 87.02 1285.99 55- 56 | 4( 1)| 5.02 82.94 -101.43 1731.38 75.83 535.78 | 4( 1)| 8.23 98.99 -174.90 1989.99 68.87 835.04 | 4( 1)| 15.28 125.06 -81.64 2461.71 79.37 1261.07 56- 57 | 4( 1)| 4.66 81.71 -108.43 1702.10 67.79 514.78 | 4( 1)| 7.71 97.54 -179.40 1954.68 60.25 808.22 | 4( 1)| 14.93 123.29 -85.57 2414.94 71.20 1226.80 57- 58 | 4( 1)| 4.14 80.41 -115.69 1675.16 58.38 494.09 | 4( 1)| 7.14 96.01 -183.91 1922.95 50.25 781.92 | 4( 1)| 14.52 121.40 -89.20 2374.25 62.06 1195.06 58- 59 | 4( 1)| 3.62 79.11 -122.94 1650.05 48.98 474.95 | 4( 1)| 6.57 94.46 -188.34 1893.82 40.29 757.65 | 4( 1)| 14.11 119.50 -92.61 2337.75 53.11 1166.74 59- 60 | 4( 1)| 2.01 74.03 -151.93 1552.74 15.69 408.31 | 4( 1)| 4.43 88.44 -205.90 1781.77 4.12 672.85 | 4( 1)| 12.74 112.08 -105.83 2198.85 21.70 1069.79 60- 61 | 4( 1)| 1.72 72.75 -159.19 1527.15 6.28 388.77 | 4( 1)| 3.85 86.90 -210.35 1751.97 -6.20 648.09 | 4( 1)| 12.38 110.18 -109.31 2161.25 12.37 1040.61 61- 62 | 3( 1)| 15.86 36.72 -519.85 331.02 -726.17 -332.98 | 3( 1)| 5.58 35.81 -463.00 379.46 -775.95 294.15 | 3( 1)| 4.22 40.06 -411.59 526.60 -830.99 281.63 62- 63 | 3( 1)| 16.52 38.02 -529.45 300.16 -745.78 -343.93 | 3( 1)| 6.03 36.84 -470.63 344.13 -797.34 285.15 | 3( 1)| 2.98 40.56 -443.08 526.06 -854.34 274.76 63- 64 | 3( 1)| 17.08 39.10 -537.69 275.36 -763.25 -353.71 | 3( 1)| 6.42 37.77 -477.08 316.09 -816.71 277.11 | 3( 1)| 1.96 41.94 -468.43 525.01 -875.51 268.50 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.87 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.72 2.02 10.46 35.08 11.86 26.22 | 1( 1)| 0.53 2.35 5.59 41.79 10.16 30.00 | 1( 1)| 0.35 2.87 -0.19 52.10 7.67 34.18 66- 67 | 1( 1)| 0.36 1.01 5.23 17.54 5.93 13.11 | 1( 1)| 0.27 1.18 2.80 20.89 5.08 15.00 | 1( 1)| 0.17 1.43 -0.10 26.05 3.84 17.09 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.53 22.01 -485.96 2.51 -116.93 17.71 | 1( 1)| 0.49 26.70 -593.22 4.30 -131.76 112.34 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.28 22.53 -496.77 -27.09 -127.91 -4.88 | 1( 1)| 1.49 27.14 -603.11 -31.33 -147.59 105.95 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 61.579s Elapsed Solve time : 851.265s Elapsed CPU time: 912.844s Sumatorio de erros e2 0.00001 Sumatorio de erros pq 0.06161 Sumatorio de erros vi 0.14519 Factor de erro e2 10.00 Factor de erro pq 1.00 Factor de erro vi 1.00 Maximum Psae error 1136.18081 Maximo erro superior 0.0836 Maximo erro inferior -3.8184 TRANSITION 18 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 1392 binary variables 1122 integer variables 48960 nonlinear variables 81084 linear variables 211995 constraints, all linear; 886938 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: mipgap=3e-2 mipdisplay=2 rinsheur=100 nodes=1500 return_mipgap=7 qtolin=0 Retaining values of one MIP start for possible repair. MIQP Presolve eliminated 79898 rows and 4862 columns. MIQP Presolve modified 27 coefficients. Reduced MIQP has 130036 rows, 125635 columns, and 784437 nonzeros. Reduced MIQP has 984 binaries, 1122 generals, 0 SOSs, and 0 indicators. Reduced MIQP objective Q matrix has 47052 nonzeros. Probing fixed 0 vars, tightened 226315 bounds. Probing time = 5.61 sec. (2983.98 ticks) MIQP Presolve eliminated 6 rows and 6 columns. MIQP Presolve modified 6 coefficients. Reduced MIQP has 130030 rows, 125629 columns, and 784395 nonzeros. Reduced MIQP has 984 binaries, 1122 generals, 0 SOSs, and 0 indicators. Reduced MIQP objective Q matrix has 47052 nonzeros. Probing fixed 0 vars, tightened 112949 bounds. Probing time = 4.75 sec. (1168.24 ticks) Clique table members: 2393. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: deterministic, using up to 12 threads. Root relaxation solution time = 65.11 sec. (86415.74 ticks) Nodes Cuts/ Node Left Objective IInf Best Integer Best Bound ItCnt Gap 0 0 17072.0434 985 17072.0434 2134 0 0 17131.1494 914 Cuts: 2104 8206 0 0 17134.0351 914 Cuts: 701 8430 Heuristic still looking. * 0+ 0 22431.9370 17134.0351 23.62% Repair heuristic found nothing. 0 2 17134.0351 914 22431.9370 17134.0351 8430 23.62% Elapsed time = 1062.09 sec. (855129.34 ticks, tree = 0.02 MB) 1 3 17144.4207 910 22431.9370 17134.0351 11804 23.62% 2 3 17152.3176 908 22431.9370 17134.0351 11471 23.62% 3 5 17207.1263 905 22431.9370 17144.4207 15384 23.57% 4 4 17148.9214 913 22431.9370 17144.4207 14622 23.57% 5 4 17289.4721 906 22431.9370 17144.4207 14781 23.57% 6 7 17191.0224 901 22431.9370 17144.4233 18530 23.57% 7 8 17307.5115 909 22431.9370 17148.9219 21876 23.55% 8 7 17154.3058 918 22431.9370 17148.9219 18740 23.55% 9 10 17310.2415 907 22431.9370 17148.9219 22825 23.55% 11 6 17218.7442 903 22431.9370 17148.9219 17130 23.55% Elapsed time = 1212.64 sec. (913777.64 ticks, tree = 0.06 MB) 12 12 17366.3644 906 22431.9370 17152.3183 24279 23.54% 15 9 17220.6608 906 22431.9370 17152.3183 23834 23.54% 20 14 17221.9385 904 22431.9370 17152.3183 27579 23.54% 21 8 17316.9098 900 22431.9370 17152.3183 23539 23.54% 22 19 17324.9341 904 22431.9370 17152.3183 34638 23.54% 24 17 17286.1576 903 22431.9370 17152.3183 31355 23.54% 25 23 17225.0130 898 22431.9370 17152.3183 40188 23.54% 28 20 17415.6446 913 22431.9370 17152.3183 35871 23.54% 29 26 17296.4992 905 22431.9370 17152.3183 44786 23.54% 30 24 17229.6917 1017 22431.9370 17152.3183 41299 23.54% Elapsed time = 1349.84 sec. (936881.99 ticks, tree = 0.15 MB) 31 27 17297.2431 903 22431.9370 17152.3183 45232 23.54% 33 31 17432.8901 909 22431.9370 17152.3183 50135 23.54% 36 25 17340.6395 908 22431.9370 17152.3183 44686 23.54% 40 27 17281.9174 906 22431.9370 17152.3183 47173 23.54% 43 32 17451.1546 910 22431.9370 17152.3183 50986 23.54% 46 39 17303.5556 1019 22431.9370 17152.3183 60639 23.54% 47 35 17254.1514 903 22431.9370 17152.3183 56557 23.54% 48 42 17325.1003 903 22431.9370 17154.3058 66903 23.53% 49 40 17301.5757 903 22431.9370 17154.3058 61267 23.53% 52 41 17302.9899 898 22431.9370 17154.3058 61799 23.53% Elapsed time = 1474.84 sec. (956142.24 ticks, tree = 0.80 MB) 55 36 17261.0486 901 22431.9370 17154.3058 57797 23.53% 56 51 17305.7035 727 22431.9370 17154.3058 73188 23.53% 57 55 17263.8352 730 22431.9370 17154.3058 77244 23.53% 60 52 17307.8553 794 22431.9370 17154.3058 73739 23.53% 61 56 17265.9419 795 22431.9370 17154.3058 77788 23.53% 62 57 17223.7594 918 22431.9370 17158.0887 81702 23.51% 63 56 17235.9003 909 22431.9370 17158.0887 79659 23.51% 64 37 17382.1097 901 22431.9370 17158.0887 62629 23.51% 65 53 17342.8206 911 22431.9370 17158.0887 77064 23.51% 67 60 17356.0760 907 22431.9370 17158.0887 89325 23.51% Elapsed time = 1660.09 sec. (981942.86 ticks, tree = 0.98 MB) 68 53 17351.3757 695 22431.9370 17158.0887 76738 23.51% 71 68 17313.0491 648 22431.9370 17158.0887 99911 23.51% 72 66 17361.6706 615 22431.9370 17158.0887 95776 23.51% 79 73 17364.3450 605 22431.9370 17158.0887 95862 23.51% 89 83 17365.8449 594 22431.9370 17158.0887 95912 23.51% 93 87 17366.5647 593 22431.9370 17158.0887 95947 23.51% 94 59 17398.5467 905 22431.9370 17158.0887 89012 23.51% 95 88 17395.0064 591 22431.9370 17158.0887 96520 23.51% 100 93 17367.1929 585 22431.9370 17158.0887 96580 23.51% 106 103 17368.4098 583 22431.9370 17158.0887 107179 23.51% Elapsed time = 1729.86 sec. (998437.49 ticks, tree = 2.81 MB) 114 110 17369.4491 577 22431.9370 17158.0887 107206 23.51% 127 119 17370.2479 571 22431.9370 17158.0887 107232 23.51% 135 125 17375.0145 553 22431.9370 17158.0887 107348 23.51% 139 129 17376.0209 550 22431.9370 17158.0887 107408 23.51% 145 104 17288.4689 605 22431.9370 17158.0887 111217 23.51% 154 108 17289.0797 602 22431.9370 17158.0887 111320 23.51% 159 105 17512.3090 904 22431.9370 17158.0887 119657 23.51% 163 145 17380.1461 538 22431.9370 17158.0887 107577 23.51% 171 152 17381.5551 532 22431.9370 17158.0887 107635 23.51% 177 158 17382.4037 528 22431.9370 17158.0887 107683 23.51% Elapsed time = 1792.55 sec. (1009072.34 ticks, tree = 5.44 MB) 180 61 17383.3628 912 22431.9370 17158.0887 93502 23.51% 184 71 17251.5907 895 22431.9370 17158.0887 107985 23.51% 185 168 17387.4690 526 22431.9370 17158.0887 126433 23.51% 198 179 17387.3275 514 22431.9370 17158.0887 126468 23.51% 207 188 17388.5884 507 22431.9370 17158.0887 126559 23.51% 215 196 17389.6380 502 22431.9370 17158.0887 126630 23.51% 222 203 17390.5738 494 22431.9370 17158.0887 126728 23.51% * 225+ 67 18067.0883 17158.0887 5.03% 226 104 17376.4261 906 18067.0883 17158.0887 114187 5.03% 228 180 17274.2257 893 18067.0883 17158.0887 135867 5.03% 229 169 17360.2224 914 18067.0883 17158.0887 132026 5.03% Elapsed time = 1887.06 sec. (1025893.76 ticks, tree = 4.92 MB) 231 206 17424.1045 491 18067.0883 17158.0887 127915 5.03% 243 234 17391.7080 488 18067.0883 17158.0887 146434 5.03% 250 239 17396.5196 504 18067.0883 17158.0887 146527 5.03% 259 106 17512.3850 903 18067.0883 17158.0887 119673 5.03% 261 233 17517.0585 904 18067.0883 17158.0887 147306 5.03% 262 186 17282.4055 899 18067.0883 17158.0887 142219 5.03% 264 16 17902.6229 918 18067.0883 17158.0887 38444 5.03% 265 180 17274.0909 919 18067.0883 17158.0887 138315 5.03% 266 189 17450.4448 903 18067.0883 17158.0887 146307 5.03% 267 233 17933.9419 914 18067.0883 17158.0887 157800 5.03% Elapsed time = 1984.53 sec. (1043050.99 ticks, tree = 5.77 MB) 271 247 17394.0637 474 18067.0883 17158.0887 146569 5.03% 274 259 17394.2841 473 18067.0883 17158.0887 166741 5.03% 282 266 17400.3294 485 18067.0883 17158.0887 166863 5.03% 291 272 17401.5726 479 18067.0883 17158.0887 166946 5.03% 298 34 18648.7406 918 18067.0883 17158.0887 66130 5.03% 301 274 17246.1546 909 18067.0883 17158.0887 191032 5.03% 303 178 17289.3921 601 18067.0883 17158.0887 131865 5.03% 305 238 17288.4588 895 18067.0883 17158.0887 166510 5.03% 310 275 17328.3140 591 18067.0883 17158.0887 176136 5.03% 316 281 17329.0023 587 18067.0883 17158.0887 176206 5.03% Elapsed time = 2076.02 sec. (1059834.59 ticks, tree = 7.31 MB) 324 289 17329.8330 578 18067.0883 17158.0887 176238 5.03% 335 281 17402.1507 474 18067.0883 17158.0887 168321 5.03% 351 289 17404.3084 466 18067.0883 17158.0887 168395 5.03% 371 308 17333.4396 558 18067.0883 17158.0887 176441 5.03% 383 282 17249.2854 845 18067.0883 17158.0887 192481 5.03% 400 337 17406.9789 436 18067.0883 17158.0887 199801 5.03% 411 348 17407.8487 424 18067.0883 17158.0887 199858 5.03% 428 363 17408.6344 409 18067.0883 17158.0887 199922 5.03% 438 280 17295.4136 596 18067.0883 17158.0887 192869 5.03% 467 277 17750.0695 639 18067.0883 17158.0887 195446 5.03% Elapsed time = 2148.08 sec. (1073363.38 ticks, tree = 6.51 MB) 490 343 17636.6509 639 18067.0883 17158.0887 214709 5.03% 511 379 17302.7626 561 18067.0883 17158.0887 216677 5.03% * 519+ 367 17438.6675 17158.0887 1.61% 544 405 17310.0907 549 17438.6675 17158.0887 216876 1.61% 559 291 17751.1156 630 17438.6675 17158.0887 195556 1.61% 563 358 17300.1163 809 17438.6675 17158.0887 210966 1.61% 565 332 18061.6113 935 17438.6675 17158.0887 213341 1.61% 566 345 17636.9484 637 17438.6675 17158.0887 214732 1.61% Flow cuts applied: 240 Mixed integer rounding cuts applied: 1988 Root node processing (before b&c): Real time = 1059.63 sec. (853053.29 ticks) Parallel b&c, 12 threads: Real time = 1246.23 sec. (285212.80 ticks) Sync time (average) = 211.32 sec. Wait time (average) = 0.00 sec. ------------ Total (root+branch&cut) = 2305.86 sec. (1138266.09 ticks) CPLEX 20.1.0.0: optimal (non-)integer solution within mipgap or absmipgap; objective 17438.66753 258741 MIP simplex iterations 568 branch-and-bound nodes No basis. 2 integer variables rounded (maxerr = 8.53459e-07). Assigning integrality = 4e-07 might help. Currently integrality = 1e-05. suffix absmipgap OUT; Funcao Ojetivo($)/ Investment/ O&M: 17286.64 3917.93 13368.71 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2795.85/ 2863.15/ 1343.37 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 600.00 0.00 0.00 0.00 900.00 0.00 51 0.00 0.00 0.00 300.00 0.00 0.00 64 0.00 0.00 0.00 600.00 300.00 0.00 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 612.61 0.00 179.74 67.00 0.00 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 900.00 225.00 0.00 50.00 0.00 225.00 0.00 69.00 0.00 900.00 0.00 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 300.00 1000.00 67.00 0.00 0.00 100.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.30 26.30 26.30 52.77 Structures 18.01 18.01 18.01 36.14 Fixed CBs 2.55 2.55 2.55 5.11 Switchable CBs 7.05 14.52 14.52 21.66 PV systems 379.37 379.37 448.17 787.71 Wind systems 760.89 1825.30 1825.30 2597.99 EES systems 0.00 182.68 786.25 416.56 Total invesment cost 1194.16 2448.73 3121.09 3917.94 Purchased energy cost 5616.57 6014.74 7110.09 12092.50 Carbon tax payment 194.92 341.74 720.11 684.75 O&M PV cost 37.13 29.78 36.34 69.63 O&M wind cost 127.60 313.91 309.61 441.88 O&M EES cost 0.00 34.90 151.18 79.95 Total O&M cost 5976.21 6735.07 8327.33 13368.71 Total cost 7170.37 9183.79 11448.43 17286.65 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 6112.22 9613.73 130306.45 868.24 0.00 2 112550.11 6112.13 24035.09 141404.09 934.97 249.94 3 131920.43 7905.53 24034.63 161754.72 1235.79 836.91 CO2 Emissions (Ton): Period Distribution EV 1 9735.18 4980.53 2 9836.13 4906.75 3 9889.77 4780.66 4 9917.38 4659.94 5 9994.18 4476.17 6 8511.51 4266.91 7 8592.41 4025.47 8 8657.79 3733.05 9 8700.37 3403.07 10 8841.58 2999.31 11 8856.76 2539.22 12 9012.30 2025.48 13 9135.92 1443.32 14 9215.77 753.85 15 9459.99 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 671.50 4413.24 187.89 1983.74 0.90 0.98 Infinity -Infinity 2 0.00 5036.58 -0.64 2186.70 0.90 0.98 0.95 0.95 3 0.00 6307.71 -30.15 2506.44 0.90 1.00 0.95 0.95 Reactive Power by DG Period PV Wind min max min max 1 -43.53 222.94 -22.59 142.81 2 -151.08 218.46 -130.22 180.95 3 -205.92 284.71 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.00 0.00 64 0.00 0.00 0.00 268.16 240.00 1200.00 1040.00 1040.00 5200.00 67 0.00 0.00 0.00 0.00 0.00 0.00 100.00 80.00 400.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 216.03 299.42 730.56 1196.22 67 0.00 0.00 0.00 0.00 48.91 100.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 5( 2)| 33.07 220.60 671.48 4412.38 187.87 1982.99 | 5( 2)| 0.00 249.88 0.00 5035.49 -0.64 2185.79 | 5( 2)| 0.00 309.52 0.00 6306.04 -30.15 2504.98 2- 3 | 5( 2)| 32.61 219.23 664.12 4386.05 178.56 1961.88 | 5( 2)| 0.00 248.27 -7.06 5003.85 -8.84 2162.77 | 5( 2)| 0.00 307.57 -4.92 6265.86 -37.39 2475.88 3- 4 | 5( 2)| 23.59 191.37 513.26 3883.74 -2.82 1579.66 | 5( 2)| 2.49 215.41 -153.14 4407.81 -177.98 1750.33 | 5( 2)| 5.64 267.53 -107.14 5515.25 -179.09 1969.60 4- 5 | 5( 2)| 13.38 144.16 250.22 3010.79 -298.07 955.66 | 5( 2)| 10.03 160.71 -292.97 3397.83 -468.81 1089.43 | 5( 2)| 13.14 200.25 -267.41 4232.71 -428.91 1161.56 5- 6 | 5( 2)| 13.37 142.82 242.84 2980.12 -307.42 930.91 | 5( 2)| 10.41 159.14 -300.15 3361.48 -477.63 1062.10 | 5( 2)| 13.41 198.36 -276.12 4184.60 -436.49 1130.66 6- 7 | 5( 2)| 13.38 141.48 235.45 2949.40 -316.79 906.11 | 5( 2)| 10.79 157.57 -307.33 3325.06 -486.46 1034.71 | 5( 2)| 13.68 196.47 -284.84 4136.37 -444.08 1099.69 7- 8 | 5( 2)| 13.39 139.38 223.65 2908.81 -330.49 875.86 | 5( 2)| 11.37 155.09 -318.74 3277.26 -499.26 1001.95 | 5( 2)| 14.09 193.44 -298.89 4075.31 -455.26 1064.25 8- 9 | 5( 2)| 4.65 131.63 179.20 2760.97 -140.43 867.89 | 5( 2)| 0.00 148.23 -361.62 3103.25 -506.88 887.62 | 5( 2)| 8.39 185.71 -351.17 3854.62 -495.57 1234.48 9- 10 | 1( 1)| 9.50 44.50 -61.39 957.80 -373.83 138.85 | 1( 1)| 2.71 57.06 -719.20 1057.94 -1201.38 35.09 | 1( 1)| 0.00 63.28 -771.81 1367.71 -1158.24 114.47 10- 11 | 3( 1)| 9.74 54.28 -71.37 930.02 217.49 719.38 | 3( 1)| 7.64 59.78 -727.47 1024.80 164.94 790.05 | 3( 1)| 7.24 72.97 -777.60 1325.51 182.45 882.12 11- 12 | 1( 1)| 6.33 44.13 -136.38 750.05 154.71 587.00 | 1( 1)| 6.03 47.96 -793.57 813.80 108.87 638.56 | 1( 1)| 4.89 58.59 -850.15 1057.09 124.05 715.84 12- 13 | 1( 1)| 4.21 32.84 -210.95 551.93 78.14 440.67 | 1( 1)| 4.75 36.62 -384.88 642.58 74.83 450.70 | 1( 1)| 4.55 45.56 -436.55 828.78 77.67 514.43 13- 14 | 1( 1)| 3.99 30.69 -227.82 510.29 65.03 414.78 | 1( 1)| 4.09 34.12 -397.56 593.31 62.24 421.02 | 1( 1)| 4.34 42.48 -446.45 765.66 67.30 481.76 14- 15 | 1( 1)| 3.23 28.47 -244.71 469.02 50.50 386.63 | 1( 1)| 3.26 31.53 -410.29 544.80 48.30 388.76 | 1( 1)| 3.04 39.29 -456.37 703.29 55.82 445.85 15- 16 | 1( 1)| 2.50 26.98 -255.13 444.31 39.71 366.36 | 1( 1)| 2.73 29.80 -417.98 515.81 37.99 365.57 | 1( 1)| 2.28 37.19 -461.66 666.42 47.31 420.39 16- 17 | 1( 1)| 0.00 24.47 -274.07 399.56 23.79 335.95 | 1( 1)| 2.34 26.87 -435.59 463.34 22.77 330.77 | 1( 1)| 1.60 33.59 -471.30 599.69 30.24 382.21 17- 18 | 1( 1)| 0.00 21.30 -299.00 340.99 5.40 300.96 | 1( 1)| 2.05 23.14 -458.48 394.68 5.39 290.74 | 1( 1)| 1.25 28.96 -483.29 512.68 7.30 338.31 18- 19 | 1( 1)| 1.32 18.14 -324.09 282.20 -13.01 265.92 | 1( 1)| 1.82 21.98 -481.73 325.78 -12.03 250.65 | 1( 1)| 1.41 25.39 -497.28 425.26 -15.66 294.34 19- 20 | 1( 1)| 0.51 16.99 -334.56 257.73 -18.16 256.13 | 1( 1)| 2.04 22.22 -491.50 297.10 -16.79 239.45 | 1( 1)| 1.53 25.51 -506.21 388.87 -22.17 282.05 20- 21 | 1( 1)| 0.00 15.40 -347.25 228.25 -27.56 237.92 | 1( 1)| 1.95 22.52 -503.42 262.57 -25.79 218.62 | 1( 1)| 1.69 25.61 -517.12 345.04 -34.93 267.83 21- 22 | 1( 1)| 0.00 17.35 -394.54 117.15 -70.51 156.23 | 1( 1)| 1.48 24.46 -546.74 132.87 -78.43 152.74 | 1( 1)| 0.00 25.92 -556.35 180.73 -93.35 238.07 22- 23 | 1( 1)| 0.00 18.30 -415.38 68.56 -89.10 120.92 | 1( 1)| 1.22 25.34 -565.99 75.92 -103.94 139.05 | 1( 1)| 1.18 26.10 -573.88 110.85 -118.61 225.13 23- 24 | 1( 1)| 0.00 18.79 -426.09 45.10 -99.95 100.75 | 1( 1)| 1.19 25.79 -576.15 47.44 -119.17 131.06 | 1( 1)| 0.89 26.18 -583.18 76.38 -133.48 217.50 24- 25 | 1( 1)| 0.00 19.34 -438.41 19.59 -110.70 80.57 | 1( 1)| 0.85 26.30 -588.40 16.11 -134.43 123.14 | 1( 1)| 0.71 26.41 -594.47 37.45 -149.57 209.80 25- 26 | 1( 1)| 0.33 19.85 -449.12 -3.36 -121.55 60.40 | 1( 1)| 0.73 26.76 -598.54 -10.10 -150.13 115.16 | 1( 1)| 0.79 26.80 -603.75 3.01 -165.85 202.18 26- 27 | 1( 1)| 1.21 20.42 -460.83 -28.86 -132.20 40.23 | 1( 1)| 1.93 27.28 -609.63 -39.70 -165.56 107.32 | 1( 1)| 1.38 27.25 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.18 13.15 30.27 226.37 62.25 182.76 | 1( 1)| 2.15 15.83 -1.03 282.29 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.80 11.49 26.26 196.35 54.95 161.22 | 1( 1)| 1.90 13.81 -0.89 244.85 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.42 9.82 22.24 166.23 47.66 139.65 | 1( 1)| 1.64 11.79 -0.75 207.28 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.01 8.15 18.36 137.29 39.72 116.57 | 1( 1)| 1.37 9.78 -0.62 171.19 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.61 6.48 14.49 108.32 31.77 93.49 | 1( 1)| 1.10 7.76 -0.49 135.06 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.20 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.83 5.58 -0.34 94.24 18.10 79.77 33- 34 | 1( 1)| 0.99 58.65 10.73 35.98 18.70 41.02 | 1( 1)| 0.79 2.90 5.74 42.86 16.15 47.31 | 1( 1)| 0.56 3.41 -0.20 53.44 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.16 1.38 -0.10 26.05 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 3( 1)| 17.51 48.41 253.26 850.74 285.96 632.46 | 3( 1)| 12.32 55.80 82.75 994.68 255.08 728.75 | 3( 1)| 7.18 67.74 -49.60 1245.37 162.54 821.05 47- 48 | 3( 1)| 16.97 46.96 245.98 826.16 276.67 612.18 | 3( 1)| 11.90 54.12 78.63 965.39 246.32 705.52 | 3( 1)| 6.90 65.72 -49.91 1208.75 156.54 794.55 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 10.73 49.04 65.61 872.84 221.93 639.75 | 3( 1)| 6.13 59.54 -50.87 1093.09 139.91 719.50 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 2.54 24.30 -7.30 427.53 98.51 322.41 | 1( 1)| 0.00 29.51 -55.49 537.86 58.76 357.91 8- 51 | 1( 1)| 0.00 11.80 22.27 74.66 -274.77 53.32 | 1( 1)| 0.00 11.91 11.90 88.94 -278.15 61.15 | 1( 1)| 0.00 11.88 -0.41 110.88 -276.86 66.23 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 5( 2)| 7.46 89.47 69.22 1827.14 164.05 754.02 | 5( 2)| 13.40 104.89 -135.36 2128.94 145.23 1016.92 | 5( 2)| 18.21 134.70 -74.67 2602.81 39.10 1418.10 53- 54 | 5( 2)| 6.00 87.13 56.60 1784.26 141.85 725.55 | 5( 2)| 12.38 102.23 -143.03 2079.65 117.79 978.00 | 5( 2)| 17.46 131.37 -80.45 2541.14 14.46 1369.92 54- 55 | 5( 2)| 5.09 85.74 48.96 1757.50 129.88 709.80 | 5( 2)| 11.79 100.66 -147.73 2048.83 102.61 956.53 | 5( 2)| 17.06 129.40 -84.04 2502.01 0.84 1342.69 55- 56 | 5( 2)| 4.15 84.47 41.99 1733.01 118.96 695.40 | 5( 2)| 11.25 99.22 -152.02 2020.62 88.71 936.90 | 5( 2)| 16.70 127.60 -87.32 2466.11 -11.63 1317.71 56- 57 | 5( 2)| 3.00 83.16 35.10 1702.56 107.77 677.84 | 5( 2)| 10.70 97.78 -156.63 1985.04 71.69 913.46 | 5( 2)| 16.34 125.70 -91.24 2416.43 -26.78 1283.08 57- 58 | 5( 2)| 0.00 81.80 27.93 1675.08 94.88 660.22 | 5( 2)| 10.09 96.26 -161.20 1953.17 54.40 889.62 | 5( 2)| 15.92 123.73 -94.87 2374.39 -42.27 1251.18 58- 59 | 5( 2)| 0.00 80.46 20.71 1649.78 82.08 643.74 | 5( 2)| 9.49 94.73 -165.65 1924.00 38.24 867.17 | 5( 2)| 15.51 121.79 -98.28 2337.39 -56.76 1222.80 59- 60 | 5( 2)| 0.00 75.24 -8.22 1552.25 36.91 586.11 | 5( 2)| 7.15 88.75 -183.22 1811.87 -17.34 788.00 | 5( 2)| 14.12 114.29 -111.50 2197.89 -106.70 1125.78 60- 61 | 5( 2)| 0.00 73.90 -15.40 1526.40 24.11 569.35 | 5( 2)| 6.51 87.23 -187.70 1781.97 -33.81 765.24 | 5( 2)| 13.74 112.34 -114.97 2159.54 -121.48 1096.51 61- 62 | 3( 1)| 3.02 28.38 -375.91 330.34 -605.74 -106.77 | 3( 1)| 0.00 36.18 -405.48 409.43 -785.10 247.88 | 3( 1)| 0.00 36.86 -372.59 499.56 -796.79 279.58 62- 63 | 3( 1)| 1.59 29.65 -385.26 299.60 -625.90 -117.27 | 3( 1)| 0.00 37.09 -411.14 374.04 -806.48 238.89 | 3( 1)| 2.76 37.90 -404.08 499.04 -820.12 272.72 63- 64 | 3( 1)| 0.36 30.69 -392.29 275.36 -643.71 -126.53 | 3( 1)| 1.83 37.93 -415.83 348.25 -825.86 230.90 | 3( 1)| 2.44 38.86 -429.40 498.13 -841.23 266.51 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.87 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.72 2.02 10.46 35.08 11.86 26.22 | 1( 1)| 0.53 2.35 5.59 41.79 10.16 30.00 | 1( 1)| 0.00 3.06 -12.58 104.71 7.67 34.18 66- 67 | 1( 1)| 0.36 1.01 5.23 17.54 5.93 13.11 | 1( 1)| 0.27 1.18 2.80 20.89 5.08 15.00 | 1( 1)| 0.00 1.65 -30.75 102.36 3.84 17.09 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.68 21.33 -474.77 3.76 -125.86 154.30 | 1( 1)| 0.00 20.96 -479.33 17.97 -88.12 133.43 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 0.61 21.82 -485.57 -25.84 -134.39 142.25 | 1( 1)| 0.00 21.43 -489.15 -19.07 -104.08 123.31 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 65.391s Elapsed Solve time : 3157.406s Elapsed CPU time: 3222.797s Sumatorio de erros e2 3.14311 Sumatorio de erros pq 120.59957 Sumatorio de erros vi 1.33849 Factor de erro e2 10 Factor de erro pq 1 Factor de erro vi 10 Maximum Psae error 1077.74053 Maximo erro superior 1258.0928 Maximo erro inferior -315.7049 Relative GAP 0.0161 TRANSITION 19 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 1392 binary variables 1122 integer variables 48960 nonlinear variables 81084 linear variables 211995 constraints, all linear; 886940 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: mipgap=3e-2 mipdisplay=2 rinsheur=100 nodes=1500 return_mipgap=7 qtolin=0 Retaining values of one MIP start for possible repair. MIQP Presolve eliminated 79899 rows and 4863 columns. MIQP Presolve modified 28 coefficients. Reduced MIQP has 130036 rows, 125635 columns, and 784438 nonzeros. Reduced MIQP has 984 binaries, 1122 generals, 0 SOSs, and 0 indicators. Reduced MIQP objective Q matrix has 47052 nonzeros. Probing fixed 0 vars, tightened 226798 bounds. Probing time = 5.63 sec. (3039.45 ticks) MIQP Presolve eliminated 4 rows and 4 columns. MIQP Presolve modified 4 coefficients. Reduced MIQP has 130032 rows, 125631 columns, and 784410 nonzeros. Reduced MIQP has 984 binaries, 1122 generals, 0 SOSs, and 0 indicators. Reduced MIQP objective Q matrix has 47052 nonzeros. Probing fixed 0 vars, tightened 118972 bounds. Probing time = 4.76 sec. (1195.26 ticks) Clique table members: 2388. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: deterministic, using up to 12 threads. Root relaxation solution time = 77.83 sec. (112262.64 ticks) Nodes Cuts/ Node Left Objective IInf Best Integer Best Bound ItCnt Gap 0 0 17093.6055 994 17093.6055 2593 0 0 17147.4380 872 Cuts: 2347 5199 0 0 17149.3902 983 Cuts: 145 5439 * 0+ 0 17302.8031 17149.3902 0.89% Flow cuts applied: 256 Mixed integer rounding cuts applied: 1881 Root node processing (before b&c): Real time = 312.38 sec. (261150.99 ticks) Parallel b&c, 12 threads: Real time = 0.00 sec. (0.00 ticks) Sync time (average) = 0.00 sec. Wait time (average) = 0.00 sec. ------------ Total (root+branch&cut) = 312.38 sec. (261150.99 ticks) CPLEX 20.1.0.0: optimal (non-)integer solution within mipgap or absmipgap; objective 17302.80308 5439 MIP simplex iterations 0 branch-and-bound nodes No basis. 2 integer variables rounded (maxerr = 8.71638e-07). Assigning integrality = 4e-07 might help. Currently integrality = 1e-05. Funcao Ojetivo($)/ Investment/ O&M: 17279.22 3914.09 13365.13 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2794.47/ 2855.90/ 1347.54 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 600.00 0.00 0.00 0.00 900.00 0.00 51 0.00 0.00 0.00 300.00 0.00 0.00 64 0.00 0.00 0.00 900.00 0.00 0.00 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 610.02 0.00 184.41 67.00 0.00 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 900.00 225.00 0.00 50.00 0.00 225.00 0.00 69.00 0.00 900.00 0.00 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 300.00 1000.00 67.00 0.00 0.00 100.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 2.55 2.55 2.55 5.11 Switchable CBs 7.48 11.65 11.65 19.21 PV systems 377.76 377.76 448.35 785.18 Wind systems 760.89 1825.30 1825.30 2597.99 EES systems 0.00 182.68 786.25 416.56 Total invesment cost 1193.56 2444.82 3118.98 3914.11 Purchased energy cost 5616.57 6011.67 7106.76 12089.31 Carbon tax payment 194.92 341.59 719.86 684.56 O&M PV cost 36.97 29.65 36.44 69.43 O&M wind cost 127.60 313.91 309.61 441.88 O&M EES cost 0.00 34.90 151.18 79.95 Total O&M cost 5976.06 6731.71 8323.85 13365.13 Total cost 7169.62 9176.53 11442.83 17279.23 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 6086.38 9613.73 130306.45 884.33 0.00 2 112498.17 6086.29 24035.09 141404.09 944.70 270.46 3 131875.48 7926.23 24034.63 161754.72 1243.10 840.00 CO2 Emissions (Ton): Period Distribution EV 1 9735.44 4980.53 2 9836.20 4906.75 3 9889.74 4780.66 4 9917.30 4659.94 5 9993.96 4476.17 6 8507.41 4266.91 7 8588.36 4025.47 8 8653.83 3733.05 9 8696.46 3403.07 10 8837.62 2999.31 11 8853.99 2539.22 12 9009.39 2025.48 13 9132.80 1443.32 14 9212.46 753.85 15 9456.54 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 675.19 4409.26 187.85 1983.66 0.90 0.98 Infinity -Infinity 2 0.07 5032.58 -0.63 2186.63 0.90 1.00 0.97 0.99 3 0.00 6304.36 -29.61 2506.23 0.90 1.00 0.95 0.95 Reactive Power by DG Period PV Wind min max min max 1 -43.35 229.24 -22.36 142.89 2 -150.44 217.54 -130.12 180.94 3 -206.46 285.45 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 46 0.00 -0.00 0.00 0.00 -0.00 0.00 0.00 -0.00 0.00 64 0.00 0.00 0.00 269.58 240.00 1200.00 1040.00 1040.00 5200.00 67 0.00 -0.00 0.00 0.00 0.00 0.00 84.55 80.00 400.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 215.83 298.19 730.34 1196.55 67 0.00 0.00 0.00 0.00 51.88 100.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 5( 2)| 33.82 220.49 675.17 4408.41 187.83 1982.91 | 5( 2)| 0.00 249.71 0.07 5031.49 -0.63 2185.72 | 5( 2)| 0.00 309.39 0.00 6302.69 -29.61 2504.77 2- 3 | 5( 2)| 33.35 219.13 667.81 4382.10 178.52 1961.80 | 5( 2)| 0.39 248.10 -6.99 4999.88 -8.83 2162.71 | 5( 2)| 0.27 307.43 -4.92 6262.50 -36.85 2475.67 3- 4 | 5( 2)| 24.17 191.28 516.96 3879.82 -2.86 1579.59 | 5( 2)| 5.20 215.25 -153.08 4404.59 -177.95 1750.27 | 5( 2)| 5.64 267.39 -107.14 5511.88 -178.55 1969.40 4- 5 | 5( 2)| 14.17 144.10 253.96 3007.17 -298.11 955.62 | 5( 2)| 12.23 160.57 -292.97 3394.99 -468.57 1089.33 | 5( 2)| 13.60 200.15 -266.86 4229.88 -428.92 1161.41 5- 6 | 5( 2)| 14.10 142.78 246.58 2976.75 -307.47 930.88 | 5( 2)| 12.54 159.02 -300.23 3358.92 -477.39 1062.03 | 5( 2)| 13.87 198.26 -275.62 4181.83 -436.51 1130.54 6- 7 | 5( 2)| 14.05 141.47 239.20 2946.26 -316.84 906.10 | 5( 2)| 12.87 157.48 -307.50 3322.79 -486.23 1034.67 | 5( 2)| 14.14 196.37 -284.40 4133.67 -444.12 1099.60 7- 8 | 5( 2)| 13.97 139.37 227.41 2905.73 -330.55 875.85 | 5( 2)| 13.35 155.01 -318.93 3275.06 -499.04 1001.93 | 5( 2)| 14.55 193.35 -298.47 4072.63 -455.29 1064.17 8- 9 | 5( 2)| 8.53 131.53 182.94 2757.89 -140.46 867.71 | 5( 2)| 1.80 148.21 -361.86 3101.15 -507.04 887.60 | 5( 2)| 9.36 185.62 -350.79 3852.01 -495.61 1234.39 9- 10 | 1( 1)| 14.16 44.68 -61.06 957.86 -374.30 138.62 | 1( 1)| 5.72 57.08 -719.18 1057.94 -1201.04 35.16 | 1( 1)| 6.81 63.36 -771.79 1365.48 -1158.23 114.43 10- 11 | 3( 1)| 10.34 54.31 -71.04 930.11 217.02 719.16 | 3( 1)| 7.67 59.85 -727.46 1024.84 164.94 790.11 | 3( 1)| 10.70 72.94 -777.75 1323.35 181.72 882.14 11- 12 | 1( 1)| 7.21 44.17 -136.08 750.13 154.68 586.77 | 1( 1)| 6.06 48.06 -793.56 813.83 108.87 638.62 | 1( 1)| 5.91 58.65 -850.05 1057.12 124.09 715.86 12- 13 | 1( 1)| 4.68 32.89 -210.63 552.00 78.10 440.44 | 1( 1)| 4.80 36.64 -384.87 642.58 74.79 450.75 | 1( 1)| 4.60 45.58 -436.52 828.80 77.90 514.44 13- 14 | 1( 1)| 4.11 30.75 -227.56 510.34 64.98 414.55 | 1( 1)| 4.21 34.13 -397.55 593.32 62.21 421.07 | 1( 1)| 4.39 42.50 -446.42 765.67 67.54 481.77 14- 15 | 1( 1)| 3.48 28.54 -244.52 469.07 50.45 386.39 | 1( 1)| 3.37 31.54 -410.28 544.80 48.26 388.81 | 1( 1)| 3.06 39.31 -456.35 703.30 56.06 445.86 15- 16 | 1( 1)| 3.04 27.05 -254.95 444.35 39.65 366.12 | 1( 1)| 2.85 29.82 -417.98 515.82 37.96 365.61 | 1( 1)| 2.31 37.21 -461.64 666.42 47.54 420.41 16- 17 | 1( 1)| 2.52 24.55 -273.91 399.60 23.72 335.71 | 1( 1)| 2.44 26.88 -435.59 463.34 22.73 330.81 | 1( 1)| 1.61 33.61 -471.28 599.70 30.24 382.22 17- 18 | 1( 1)| 2.32 21.39 -298.84 341.03 5.34 300.72 | 1( 1)| 2.07 23.16 -458.48 394.68 5.36 290.79 | 1( 1)| 1.25 28.98 -483.27 512.68 7.30 338.32 18- 19 | 1( 1)| 2.56 18.25 -323.95 282.23 -13.08 265.69 | 1( 1)| 1.83 21.99 -481.73 325.78 -12.06 250.70 | 1( 1)| 1.42 25.43 -497.27 425.27 -15.66 294.35 19- 20 | 1( 1)| 2.56 17.11 -334.44 257.76 -18.22 255.90 | 1( 1)| 2.05 22.23 -491.50 297.10 -16.82 239.50 | 1( 1)| 1.51 25.55 -506.20 388.88 -22.23 282.06 20- 21 | 1( 1)| 2.31 15.95 -347.15 228.27 -27.63 237.68 | 1( 1)| 1.95 22.53 -503.42 262.57 -25.83 218.67 | 1( 1)| 1.67 25.65 -517.11 345.04 -34.98 267.83 21- 22 | 1( 1)| 1.54 17.90 -394.45 117.18 -70.58 155.99 | 1( 1)| 1.46 24.47 -546.74 132.88 -78.43 152.74 | 1( 1)| 1.09 25.96 -556.34 180.73 -93.40 238.07 22- 23 | 1( 1)| 1.11 18.81 -415.30 68.58 -89.17 120.69 | 1( 1)| 1.20 25.35 -565.99 75.92 -103.97 139.05 | 1( 1)| 1.18 26.14 -573.87 110.85 -118.67 225.13 23- 24 | 1( 1)| 0.93 19.28 -426.02 45.11 -100.02 100.51 | 1( 1)| 1.19 25.80 -576.15 47.44 -119.21 131.06 | 1( 1)| 0.89 26.22 -583.17 76.38 -133.48 217.50 24- 25 | 1( 1)| 0.73 19.82 -438.39 19.59 -110.78 80.33 | 1( 1)| 0.85 26.31 -588.39 16.11 -134.42 123.14 | 1( 1)| 0.71 26.44 -594.46 37.45 -149.57 209.80 25- 26 | 1( 1)| 0.73 20.31 -449.11 -3.36 -121.63 60.16 | 1( 1)| 0.73 26.77 -598.54 -10.10 -150.12 115.16 | 1( 1)| 0.79 26.84 -603.75 3.01 -165.85 202.18 26- 27 | 1( 1)| 1.60 20.85 -460.83 -28.86 -132.28 39.98 | 1( 1)| 1.94 27.29 -609.63 -39.70 -165.55 107.32 | 1( 1)| 1.63 27.29 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.18 13.15 30.27 226.37 62.25 182.76 | 1( 1)| 2.15 15.83 -1.03 282.29 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.80 11.49 26.26 196.35 54.95 161.22 | 1( 1)| 1.90 13.81 -0.89 244.85 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.42 9.82 22.24 166.23 47.66 139.65 | 1( 1)| 1.64 11.79 -0.75 207.28 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.01 8.15 18.36 137.29 39.72 116.57 | 1( 1)| 1.37 9.78 -0.62 171.19 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.61 6.48 14.49 108.32 31.77 93.49 | 1( 1)| 1.10 7.76 -0.49 135.06 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.20 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.83 5.58 -0.34 94.24 18.10 79.77 33- 34 | 1( 1)| 0.99 60.46 10.73 35.98 18.70 41.02 | 1( 1)| 0.79 2.90 5.74 42.86 16.15 47.31 | 1( 1)| 0.56 3.41 -0.20 53.44 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.16 1.38 -0.10 26.05 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 5( 2)| 17.51 48.41 253.23 850.56 285.96 632.45 | 5( 2)| 12.65 55.81 82.75 994.50 255.08 728.73 | 5( 2)| 7.89 67.75 -49.59 1245.07 165.82 821.08 47- 48 | 5( 2)| 16.97 46.97 245.98 826.16 276.67 612.18 | 5( 2)| 12.25 54.14 78.65 965.42 246.32 705.52 | 5( 2)| 7.63 65.74 -49.89 1208.78 159.81 794.59 48- 49 | 3( 1)| 15.39 42.60 222.94 748.50 250.79 554.73 | 3( 1)| 11.11 49.05 65.61 872.84 221.93 639.75 | 3( 1)| 6.93 59.57 -50.87 1093.09 143.18 719.55 49- 50 | 1( 1)| 7.69 21.30 111.46 374.20 125.40 277.36 | 1( 1)| 5.47 24.32 -7.30 427.53 98.37 322.41 | 1( 1)| 3.33 29.53 -55.49 537.86 62.03 357.96 8- 51 | 1( 1)| 1.72 12.58 22.27 74.66 -274.77 53.32 | 1( 1)| 1.14 12.69 11.90 88.94 -278.15 61.15 | 1( 1)| 0.75 12.65 -0.41 110.88 -276.86 66.23 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 5( 2)| 13.55 89.54 73.79 1825.23 164.77 754.11 | 5( 2)| 13.92 104.92 -134.88 2128.19 145.12 1017.35 | 5( 2)| 18.26 134.67 -76.54 2598.42 39.27 1417.83 53- 54 | 5( 2)| 12.58 87.21 61.07 1782.49 142.58 725.65 | 5( 2)| 12.93 102.26 -142.55 2078.92 117.69 978.45 | 5( 2)| 17.51 131.37 -82.33 2537.12 14.61 1369.67 54- 55 | 5( 2)| 12.04 85.84 53.29 1755.93 130.61 709.92 | 5( 2)| 12.37 100.69 -147.23 2048.14 102.52 957.02 | 5( 2)| 17.11 129.43 -85.93 2498.47 0.98 1342.45 55- 56 | 5( 2)| 11.54 84.59 46.18 1731.62 119.68 695.53 | 5( 2)| 11.85 99.26 -151.50 2019.96 88.63 937.42 | 5( 2)| 16.75 127.65 -89.21 2463.03 -11.50 1317.49 56- 57 | 5( 2)| 11.05 83.35 38.49 1702.08 108.50 678.03 | 5( 2)| 11.35 97.85 -156.05 1984.56 71.64 914.11 | 5( 2)| 16.39 125.89 -93.15 2415.64 -26.72 1282.94 57- 58 | 5( 2)| 10.50 82.02 30.92 1675.00 95.61 660.42 | 5( 2)| 10.78 96.34 -160.58 1952.79 54.36 890.33 | 5( 2)| 15.98 123.99 -96.79 2374.64 -42.24 1251.07 58- 59 | 5( 2)| 9.95 80.69 23.55 1649.85 82.82 643.95 | 5( 2)| 10.22 94.81 -165.02 1923.65 38.21 867.89 | 5( 2)| 15.58 122.07 -100.20 2338.02 -56.75 1222.70 59- 60 | 5( 2)| 7.87 75.49 -5.54 1552.48 37.65 586.33 | 5( 2)| 8.08 88.84 -182.58 1811.57 -17.36 788.75 | 5( 2)| 14.20 114.61 -113.42 2198.97 -106.70 1125.69 60- 61 | 5( 2)| 7.31 74.17 -12.94 1526.82 24.84 569.57 | 5( 2)| 7.52 87.33 -187.05 1781.74 -33.83 766.01 | 5( 2)| 13.82 112.69 -116.91 2161.17 -121.49 1096.44 61- 62 | 3( 1)| 10.69 29.60 -373.50 330.72 -604.70 -105.67 | 3( 1)| 3.12 36.42 -404.83 409.21 -784.60 247.26 | 3( 1)| 4.71 36.92 -372.53 498.73 -797.04 280.12 62- 63 | 3( 1)| 10.81 30.84 -382.91 299.91 -624.89 -116.19 | 3( 1)| 3.64 37.33 -410.50 373.85 -805.99 238.26 | 3( 1)| 3.49 37.96 -404.02 498.20 -820.37 273.27 63- 64 | 3( 1)| 10.89 31.90 -390.28 275.36 -642.77 -125.60 | 3( 1)| 4.08 38.17 -415.25 347.36 -825.38 230.26 | 3( 1)| 2.51 38.93 -429.36 497.23 -841.50 267.05 64- 65 | 1( 1)| 1.19 3.33 17.17 57.57 19.15 42.36 | 1( 1)| 0.87 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.72 2.02 10.46 35.08 11.86 26.22 | 1( 1)| 0.53 2.35 5.59 41.79 10.16 30.00 | 1( 1)| 0.50 4.79 -15.55 104.72 7.67 34.18 66- 67 | 1( 1)| 0.36 1.01 5.23 17.54 5.93 13.11 | 1( 1)| 0.27 1.18 2.80 20.89 5.08 15.00 | 1( 1)| 0.30 4.67 -33.71 102.36 3.84 17.09 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.68 21.43 -474.77 3.76 -126.19 154.20 | 1( 1)| 0.57 21.65 -479.32 17.97 -87.93 133.00 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.21 21.92 -485.57 -25.84 -134.72 142.15 | 1( 1)| 0.98 22.11 -489.15 -19.07 -103.97 123.39 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 69.235s Elapsed Solve time : 3470.062s Elapsed CPU time: 3539.297s Sumatorio de erros e2 1.93641 Sumatorio de erros pq 0.42216 Sumatorio de erros vi 0.01514 Factor de erro e2 10 Factor de erro pq 10 Factor de erro vi 10 Maximum Psae error 1078.24791 Maximo erro superior 1297.7153 Maximo erro inferior -39.7254 Relative GAP 0.0089 TRANSITION 20 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 1392 binary variables 1122 integer variables 48960 nonlinear variables 81084 linear variables 211995 constraints, all linear; 886957 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: mipgap=3e-2 mipdisplay=2 rinsheur=100 nodes=1500 return_mipgap=7 qtolin=0 1 of 1 MIP starts provided solutions. MIP start 'm1' defined initial solution with objective 17298.5474. MIQP Presolve eliminated 79894 rows and 4858 columns. MIQP Presolve modified 34 coefficients. Reduced MIQP has 130040 rows, 125639 columns, and 784457 nonzeros. Reduced MIQP has 984 binaries, 1122 generals, 0 SOSs, and 0 indicators. Reduced MIQP objective Q matrix has 47052 nonzeros. Probing fixed 0 vars, tightened 235297 bounds. Probing time = 5.59 sec. (2805.72 ticks) MIQP Presolve eliminated 4 rows and 4 columns. MIQP Presolve modified 4 coefficients. Reduced MIQP has 130036 rows, 125635 columns, and 784429 nonzeros. Reduced MIQP has 984 binaries, 1122 generals, 0 SOSs, and 0 indicators. Reduced MIQP objective Q matrix has 47052 nonzeros. Probing fixed 0 vars, tightened 117436 bounds. Probing time = 4.88 sec. (1235.80 ticks) Clique table members: 2425. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: deterministic, using up to 12 threads. Root relaxation solution time = 574.06 sec. (859512.74 ticks) Nodes Cuts/ Node Left Objective IInf Best Integer Best Bound ItCnt Gap * 0+ 0 17298.5474 -3645040.8303 --- 0 0 infeasible 17298.5474 17683 0.00% Root node processing (before b&c): Real time = 660.63 sec. (958556.45 ticks) Parallel b&c, 12 threads: Real time = 0.00 sec. (0.00 ticks) Sync time (average) = 0.00 sec. Wait time (average) = 0.00 sec. ------------ Total (root+branch&cut) = 660.63 sec. (958556.45 ticks) CPLEX 20.1.0.0: optimal integer solution; objective 17298.54739 17683 MIP simplex iterations 0 branch-and-bound nodes No basis. Funcao Ojetivo($)/ Investment/ O&M: 17279.01 3913.93 13365.08 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2794.25/ 2855.90/ 1347.70 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 600.00 0.00 0.00 0.00 900.00 0.00 51 0.00 0.00 0.00 300.00 0.00 0.00 64 0.00 0.00 0.00 900.00 0.00 0.00 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 609.87 0.00 184.58 67.00 0.00 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 900.00 225.00 0.00 50.00 0.00 225.00 0.00 69.00 0.00 900.00 0.00 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 300.00 1000.00 67.00 0.00 0.00 100.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 2.55 2.55 2.55 5.11 Switchable CBs 7.48 11.65 11.65 19.21 PV systems 377.67 377.67 448.32 785.02 Wind systems 760.89 1825.30 1825.30 2597.99 EES systems 0.00 182.68 786.25 416.56 Total invesment cost 1193.47 2444.73 3118.95 3913.94 Purchased energy cost 5616.57 6011.73 7106.58 12089.27 Carbon tax payment 194.92 341.59 719.87 684.56 O&M PV cost 36.96 29.64 36.44 69.42 O&M wind cost 127.60 313.91 309.61 441.88 O&M EES cost 0.00 34.90 151.18 79.95 Total O&M cost 5976.04 6731.77 8323.68 13365.08 Total cost 7169.52 9176.50 11442.63 17279.03 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 6084.89 9613.73 130306.45 883.75 0.00 2 112499.48 6084.80 24035.09 141404.09 943.89 271.53 3 131877.08 7926.44 24034.63 161754.72 1242.26 841.38 CO2 Emissions (Ton): Period Distribution EV 1 9735.44 4980.53 2 9836.20 4906.75 3 9889.74 4780.66 4 9917.30 4659.94 5 9993.96 4476.17 6 8507.50 4266.91 7 8588.46 4025.47 8 8653.93 3733.05 9 8696.57 3403.07 10 8837.71 2999.31 11 8854.07 2539.22 12 9009.49 2025.48 13 9132.91 1443.32 14 9212.58 753.85 15 9456.68 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 675.27 4409.37 187.74 1983.66 0.90 0.98 Infinity -Infinity 2 0.05 5031.43 -0.64 2186.57 0.90 0.99 0.98 0.98 3 0.00 6303.98 -29.61 2506.00 0.90 1.00 0.95 0.95 Reactive Power by DG Period PV Wind min max min max 1 -43.31 229.18 -22.16 142.71 2 -150.40 217.48 -130.12 180.94 3 -206.47 285.46 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 269.43 240.00 1200.00 1040.00 1040.00 5200.00 67 0.00 0.00 0.00 0.00 0.00 0.00 81.01 80.00 400.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 215.83 297.93 730.09 1196.76 67 0.00 0.00 0.00 0.00 53.09 100.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 5( 2)| 33.83 220.50 675.25 4408.52 187.72 1982.91 | 5( 2)| 0.00 249.66 0.05 5030.34 -0.64 2185.66 | 5( 2)| 0.00 309.37 0.00 6302.31 -29.61 2504.53 2- 3 | 5( 2)| 33.35 219.13 667.89 4382.21 178.41 1961.80 | 5( 2)| 0.39 248.05 -7.01 4998.73 -8.84 2162.65 | 5( 2)| 0.27 307.41 -4.92 6262.12 -36.85 2475.44 3- 4 | 5( 2)| 24.17 191.28 517.03 3879.93 -2.97 1579.59 | 5( 2)| 5.22 215.20 -153.09 4404.33 -177.96 1750.21 | 5( 2)| 5.64 267.37 -107.14 5511.50 -178.55 1969.16 4- 5 | 5( 2)| 14.18 144.10 254.03 3007.28 -298.22 955.62 | 5( 2)| 12.23 160.51 -292.99 3394.73 -468.54 1089.27 | 5( 2)| 13.78 200.13 -265.04 4229.51 -428.92 1161.33 5- 6 | 5( 2)| 14.17 142.78 246.66 2976.83 -307.59 930.88 | 5( 2)| 12.54 158.96 -300.24 3358.65 -477.37 1061.98 | 5( 2)| 14.05 198.24 -273.80 4181.44 -436.51 1130.46 6- 7 | 5( 2)| 14.17 141.46 239.28 2946.33 -316.96 906.10 | 5( 2)| 12.86 157.41 -307.52 3322.50 -486.21 1034.63 | 5( 2)| 14.32 196.34 -282.58 4133.26 -444.12 1099.52 7- 8 | 5( 2)| 14.18 139.36 227.49 2905.79 -330.66 875.85 | 5( 2)| 13.35 154.94 -318.95 3274.77 -499.02 1001.88 | 5( 2)| 14.72 193.32 -296.65 4072.21 -455.29 1064.09 8- 9 | 5( 2)| 8.53 131.53 183.02 2757.94 -140.55 867.41 | 5( 2)| 1.81 148.18 -361.88 3100.86 -506.79 887.56 | 5( 2)| 9.41 185.59 -348.97 3851.59 -495.61 1234.28 9- 10 | 1( 1)| 14.19 44.67 -61.06 957.85 -374.29 138.32 | 1( 1)| 5.72 57.05 -719.18 1057.93 -1200.74 35.17 | 1( 1)| 6.76 63.34 -772.12 1365.09 -1158.23 114.32 10- 11 | 3( 1)| 10.34 54.29 -71.04 930.09 217.02 718.86 | 3( 1)| 7.67 59.84 -727.46 1024.84 164.94 790.11 | 3( 1)| 10.71 72.92 -778.07 1322.95 181.12 882.11 11- 12 | 1( 1)| 7.21 44.15 -136.08 750.12 154.85 586.47 | 1( 1)| 6.06 48.05 -793.56 813.82 108.87 638.61 | 1( 1)| 5.92 58.65 -850.06 1057.12 124.38 715.83 12- 13 | 1( 1)| 4.68 32.88 -210.63 551.99 78.28 440.14 | 1( 1)| 4.80 36.63 -384.87 642.58 74.81 450.74 | 1( 1)| 4.60 45.57 -436.53 828.79 78.04 514.41 13- 14 | 1( 1)| 4.52 30.74 -227.56 510.34 65.16 414.25 | 1( 1)| 4.21 34.13 -397.56 593.32 62.22 421.06 | 1( 1)| 4.39 42.49 -446.42 765.67 67.67 481.74 14- 15 | 1( 1)| 3.94 28.52 -244.52 469.06 50.62 386.09 | 1( 1)| 3.37 31.53 -410.28 544.80 48.28 388.80 | 1( 1)| 3.06 39.30 -456.36 703.30 56.19 445.83 15- 16 | 1( 1)| 3.54 27.04 -254.95 444.35 39.83 365.82 | 1( 1)| 2.85 29.81 -417.98 515.82 37.97 365.61 | 1( 1)| 2.31 37.21 -461.64 666.42 47.68 420.38 16- 17 | 1( 1)| 2.90 24.54 -273.91 399.59 23.90 335.41 | 1( 1)| 2.44 26.88 -435.59 463.34 22.75 330.81 | 1( 1)| 1.60 33.60 -471.28 599.70 30.26 382.19 17- 18 | 1( 1)| 2.56 21.38 -298.84 341.02 5.51 300.43 | 1( 1)| 2.07 23.15 -458.48 394.68 5.37 290.78 | 1( 1)| 1.25 28.97 -483.27 512.68 7.31 338.29 18- 19 | 1( 1)| 2.56 18.24 -323.95 282.23 -12.90 265.39 | 1( 1)| 1.83 21.98 -481.73 325.78 -12.05 250.70 | 1( 1)| 1.40 25.42 -497.27 425.27 -15.65 294.32 19- 20 | 1( 1)| 2.56 17.10 -334.44 257.75 -18.05 255.60 | 1( 1)| 2.05 22.23 -491.50 297.10 -16.81 239.50 | 1( 1)| 1.48 25.54 -506.20 388.88 -22.28 282.03 20- 21 | 1( 1)| 2.28 15.95 -347.15 228.27 -27.45 237.39 | 1( 1)| 1.95 22.52 -503.42 262.57 -25.81 218.67 | 1( 1)| 1.65 25.64 -517.11 345.04 -35.03 267.83 21- 22 | 1( 1)| 1.54 17.90 -394.45 117.18 -70.41 155.69 | 1( 1)| 1.44 24.46 -546.74 132.88 -78.43 152.74 | 1( 1)| 1.09 25.96 -556.34 180.73 -93.45 238.07 22- 23 | 1( 1)| 1.11 18.82 -415.29 68.58 -89.00 120.39 | 1( 1)| 1.18 25.35 -565.99 75.92 -103.96 139.05 | 1( 1)| 1.18 26.13 -573.87 110.85 -118.72 225.13 23- 24 | 1( 1)| 0.93 19.29 -426.02 45.11 -99.85 100.21 | 1( 1)| 1.19 25.80 -576.15 47.44 -119.19 131.06 | 1( 1)| 0.89 26.21 -583.17 76.38 -133.48 217.50 24- 25 | 1( 1)| 0.73 19.82 -438.39 19.59 -110.61 80.03 | 1( 1)| 0.85 26.31 -588.39 16.11 -134.42 123.14 | 1( 1)| 0.71 26.43 -594.46 37.45 -149.57 209.80 25- 26 | 1( 1)| 0.73 20.31 -449.11 -3.36 -121.46 59.86 | 1( 1)| 0.73 26.77 -598.54 -10.10 -150.13 115.16 | 1( 1)| 0.79 26.83 -603.75 3.01 -165.85 202.18 26- 27 | 1( 1)| 1.59 20.86 -460.83 -28.86 -132.11 39.69 | 1( 1)| 1.94 27.29 -609.63 -39.70 -165.56 107.32 | 1( 1)| 1.63 27.28 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.18 13.15 30.27 226.37 62.25 182.76 | 1( 1)| 2.15 15.83 -1.03 282.29 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.80 11.49 26.26 196.35 54.95 161.22 | 1( 1)| 1.90 13.81 -0.89 244.85 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.42 9.82 22.24 166.23 47.66 139.65 | 1( 1)| 1.64 11.79 -0.75 207.28 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.01 8.15 18.36 137.29 39.72 116.57 | 1( 1)| 1.37 9.78 -0.62 171.19 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.61 6.48 14.49 108.32 31.77 93.49 | 1( 1)| 1.10 7.76 -0.49 135.06 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.20 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.83 5.58 -0.34 94.24 18.10 79.77 33- 34 | 1( 1)| 0.99 60.55 10.73 35.98 18.70 41.02 | 1( 1)| 0.79 2.90 5.74 42.86 16.15 47.31 | 1( 1)| 0.56 3.41 -0.20 53.44 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.16 1.38 -0.10 26.05 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 5( 2)| 17.51 48.40 253.23 850.56 285.96 632.45 | 5( 2)| 12.65 55.80 82.75 994.50 255.08 728.71 | 5( 2)| 8.07 67.74 -49.59 1245.07 169.81 821.09 47- 48 | 5( 2)| 16.97 46.96 245.98 826.16 276.67 612.18 | 5( 2)| 12.25 54.13 78.65 965.42 246.32 705.50 | 5( 2)| 7.81 65.72 -49.89 1208.78 163.80 794.61 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.11 49.04 65.61 872.84 221.93 639.73 | 3( 1)| 7.10 59.55 -50.87 1093.09 147.17 719.56 49- 50 | 1( 1)| 7.69 21.29 111.46 374.20 125.40 277.36 | 1( 1)| 5.47 24.31 -7.30 427.53 98.35 322.39 | 1( 1)| 3.36 29.52 -55.49 537.86 66.02 357.97 8- 51 | 1( 1)| 1.72 12.58 22.27 74.66 -274.77 53.32 | 1( 1)| 1.14 12.68 11.90 88.94 -278.15 61.15 | 1( 1)| 0.75 12.65 -0.41 110.88 -276.86 66.23 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 5( 2)| 13.54 89.55 73.05 1825.26 165.51 754.11 | 5( 2)| 13.96 104.89 -134.44 2127.91 145.09 1017.35 | 5( 2)| 18.25 134.65 -76.54 2598.45 39.27 1417.64 53- 54 | 5( 2)| 12.58 87.22 60.40 1782.52 143.31 725.65 | 5( 2)| 12.97 102.23 -142.10 2078.64 117.67 978.45 | 5( 2)| 17.50 131.35 -82.33 2537.13 14.61 1369.48 54- 55 | 5( 2)| 12.03 85.85 52.71 1755.94 131.34 709.92 | 5( 2)| 12.41 100.66 -146.79 2047.86 102.49 957.02 | 5( 2)| 17.10 129.40 -85.92 2498.45 0.98 1342.26 55- 56 | 5( 2)| 11.53 84.59 45.68 1731.62 120.42 695.52 | 5( 2)| 11.90 99.23 -151.06 2019.68 88.60 937.42 | 5( 2)| 16.74 127.62 -89.20 2462.99 -11.50 1317.30 56- 57 | 5( 2)| 11.03 83.34 38.46 1702.07 109.24 678.03 | 5( 2)| 11.38 97.80 -155.61 1984.29 71.63 914.13 | 5( 2)| 16.38 125.84 -93.13 2415.58 -26.72 1282.75 57- 58 | 5( 2)| 10.48 82.01 31.10 1675.00 96.35 660.43 | 5( 2)| 10.82 96.27 -160.14 1952.51 54.35 890.35 | 5( 2)| 15.97 123.94 -96.77 2374.60 -42.24 1250.88 58- 59 | 5( 2)| 9.92 80.68 23.81 1649.84 83.56 643.96 | 5( 2)| 10.25 94.74 -164.57 1923.38 38.20 867.92 | 5( 2)| 15.57 122.02 -100.18 2337.98 -56.75 1222.52 59- 60 | 5( 2)| 7.85 75.48 -5.21 1552.48 38.38 586.33 | 5( 2)| 8.12 88.77 -182.14 1811.30 -17.37 788.78 | 5( 2)| 14.19 114.56 -113.40 2198.94 -106.70 1125.51 60- 61 | 5( 2)| 7.29 74.16 -12.50 1526.82 25.58 569.58 | 5( 2)| 7.55 87.25 -186.61 1781.47 -33.83 766.05 | 5( 2)| 13.81 112.64 -116.88 2161.16 -121.49 1096.26 61- 62 | 3( 1)| 10.68 29.49 -373.09 330.72 -604.65 -105.62 | 3( 1)| 3.12 36.36 -404.39 408.95 -784.58 247.22 | 3( 1)| 4.70 36.92 -372.38 499.14 -797.17 280.13 62- 63 | 3( 1)| 10.80 30.71 -382.56 299.91 -624.83 -116.14 | 3( 1)| 3.63 37.26 -410.06 373.59 -805.97 238.22 | 3( 1)| 3.48 37.96 -403.87 498.61 -820.50 273.27 63- 64 | 3( 1)| 10.88 31.76 -390.16 275.36 -642.72 -125.55 | 3( 1)| 4.07 38.09 -414.80 347.08 -825.35 230.22 | 3( 1)| 2.50 38.92 -429.20 497.62 -841.62 267.06 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.72 2.02 10.46 35.08 11.86 26.22 | 1( 1)| 0.53 2.35 5.59 41.79 10.16 30.00 | 1( 1)| 0.51 4.78 -16.76 104.72 7.67 34.18 66- 67 | 1( 1)| 0.36 1.01 5.23 17.54 5.93 13.11 | 1( 1)| 0.27 1.18 2.80 20.89 5.08 15.00 | 1( 1)| 0.26 4.66 -34.93 102.36 3.84 17.09 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.68 21.43 -474.77 3.76 -126.17 154.21 | 1( 1)| 0.57 21.64 -479.32 17.97 -87.70 133.02 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.21 21.91 -485.57 -25.84 -134.70 142.16 | 1( 1)| 0.98 22.11 -489.15 -19.07 -103.97 123.57 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 73.000s Elapsed Solve time : 4130.922s Elapsed CPU time: 4203.922s Sumatorio de erros e2 1.94600 Sumatorio de erros pq 0.00747 Sumatorio de erros vi 0.00008 Factor de erro e2 10 Factor de erro pq 10 Factor de erro vi 10 Maximum Psae error 1078.20191 Maximo erro superior 1299.5775 Maximo erro inferior -0.5059 Relative GAP 0.0000 TRANSITION 21 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 1392 binary variables 1122 integer variables 48960 nonlinear variables 81084 linear variables 211995 constraints, all linear; 886952 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: mipgap=3e-2 mipdisplay=2 rinsheur=100 nodes=1500 return_mipgap=7 qtolin=0 1 of 1 MIP starts provided solutions. MIP start 'm1' defined initial solution with objective 17473.6013. MIQP Presolve eliminated 79895 rows and 4859 columns. MIQP Presolve modified 33 coefficients. Reduced MIQP has 130039 rows, 125638 columns, and 784451 nonzeros. Reduced MIQP has 984 binaries, 1122 generals, 0 SOSs, and 0 indicators. Reduced MIQP objective Q matrix has 47052 nonzeros. Probing fixed 0 vars, tightened 244130 bounds. Probing time = 5.72 sec. (3273.44 ticks) MIQP Presolve eliminated 4 rows and 4 columns. MIQP Presolve modified 4 coefficients. Reduced MIQP has 130035 rows, 125634 columns, and 784423 nonzeros. Reduced MIQP has 984 binaries, 1122 generals, 0 SOSs, and 0 indicators. Reduced MIQP objective Q matrix has 47052 nonzeros. Probing fixed 0 vars, tightened 120550 bounds. Probing time = 4.75 sec. (1218.17 ticks) Clique table members: 2358. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: deterministic, using up to 12 threads. Root relaxation solution time = 317.31 sec. (425325.18 ticks) Nodes Cuts/ Node Left Objective IInf Best Integer Best Bound ItCnt Gap * 0+ 0 17473.6013 -3645065.7020 --- Root node processing (before b&c): Real time = 403.50 sec. (524572.12 ticks) Parallel b&c, 12 threads: Real time = 0.00 sec. (0.00 ticks) Sync time (average) = 0.00 sec. Wait time (average) = 0.00 sec. ------------ Total (root+branch&cut) = 403.50 sec. (524572.12 ticks) CPLEX 20.1.0.0: unrecoverable failure: singular basis 0 MIP simplex iterations 0 branch-and-bound nodes No basis. Funcao Ojetivo($)/ Investment/ O&M: 17279.01 3913.93 13365.08 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2794.25/ 2855.90/ 1347.70 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 600.00 0.00 0.00 0.00 900.00 0.00 51 0.00 0.00 0.00 300.00 0.00 0.00 64 0.00 0.00 0.00 900.00 0.00 0.00 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 609.87 0.00 184.58 67.00 0.00 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 900.00 225.00 0.00 50.00 0.00 225.00 0.00 69.00 0.00 900.00 0.00 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 300.00 1000.00 67.00 0.00 0.00 100.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 2.55 2.55 2.55 5.11 Switchable CBs 7.48 11.65 11.65 19.21 PV systems 377.67 377.67 448.32 785.02 Wind systems 760.89 1825.30 1825.30 2597.99 EES systems 0.00 182.68 786.25 416.56 Total invesment cost 1193.47 2444.73 3118.95 3913.94 Purchased energy cost 5616.57 6011.73 7106.58 12089.27 Carbon tax payment 194.92 341.59 719.87 684.56 O&M PV cost 36.96 29.64 36.44 69.42 O&M wind cost 127.60 313.91 309.61 441.88 O&M EES cost 0.00 34.90 151.18 79.95 Total O&M cost 5976.04 6731.77 8323.68 13365.08 Total cost 7169.52 9176.50 11442.63 17279.03 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 6084.89 9613.73 130306.45 883.75 0.00 2 112499.48 6084.80 24035.09 141404.09 943.89 271.53 3 131877.08 7926.44 24034.63 161754.72 1242.26 841.38 CO2 Emissions (Ton): Period Distribution EV 1 9735.44 4980.53 2 9836.20 4906.75 3 9889.74 4780.66 4 9917.30 4659.94 5 9993.96 4476.17 6 8507.50 4266.91 7 8588.46 4025.47 8 8653.93 3733.05 9 8696.57 3403.07 10 8837.71 2999.31 11 8854.07 2539.22 12 9009.49 2025.48 13 9132.91 1443.32 14 9212.58 753.85 15 9456.68 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 675.27 4409.37 187.74 1983.66 0.90 0.98 Infinity -Infinity 2 0.05 5031.43 -0.64 2186.57 0.90 0.99 0.98 0.98 3 0.00 6303.98 -29.61 2506.00 0.90 1.00 0.95 0.95 Reactive Power by DG Period PV Wind min max min max 1 -43.31 229.18 -22.16 142.71 2 -150.40 217.48 -130.12 180.94 3 -206.47 285.46 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 269.43 240.00 1200.00 1040.00 1040.00 5200.00 67 0.00 0.00 0.00 0.00 0.00 0.00 81.01 80.00 400.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 215.83 297.93 730.09 1196.76 67 0.00 0.00 0.00 0.00 53.09 100.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 5( 2)| 33.83 220.50 675.25 4408.52 187.72 1982.91 | 5( 2)| 0.00 249.66 0.05 5030.34 -0.64 2185.66 | 5( 2)| 0.00 309.37 0.00 6302.31 -29.61 2504.53 2- 3 | 5( 2)| 33.35 219.13 667.89 4382.21 178.41 1961.80 | 5( 2)| 0.39 248.05 -7.01 4998.73 -8.84 2162.65 | 5( 2)| 0.27 307.41 -4.92 6262.12 -36.85 2475.44 3- 4 | 5( 2)| 24.17 191.28 517.03 3879.93 -2.97 1579.59 | 5( 2)| 5.22 215.20 -153.09 4404.33 -177.96 1750.21 | 5( 2)| 5.64 267.37 -107.14 5511.50 -178.55 1969.16 4- 5 | 5( 2)| 14.18 144.10 254.03 3007.28 -298.22 955.62 | 5( 2)| 12.23 160.51 -292.99 3394.73 -468.54 1089.27 | 5( 2)| 13.78 200.13 -265.04 4229.51 -428.92 1161.33 5- 6 | 5( 2)| 14.17 142.78 246.66 2976.83 -307.59 930.88 | 5( 2)| 12.54 158.96 -300.24 3358.65 -477.37 1061.98 | 5( 2)| 14.05 198.24 -273.80 4181.44 -436.51 1130.46 6- 7 | 5( 2)| 14.17 141.46 239.28 2946.33 -316.96 906.10 | 5( 2)| 12.86 157.41 -307.52 3322.50 -486.21 1034.63 | 5( 2)| 14.32 196.34 -282.58 4133.26 -444.12 1099.52 7- 8 | 5( 2)| 14.18 139.36 227.49 2905.79 -330.66 875.85 | 5( 2)| 13.35 154.94 -318.95 3274.77 -499.02 1001.88 | 5( 2)| 14.72 193.32 -296.65 4072.21 -455.29 1064.09 8- 9 | 5( 2)| 8.53 131.53 183.02 2757.94 -140.55 867.41 | 5( 2)| 1.81 148.18 -361.88 3100.86 -506.79 887.56 | 5( 2)| 9.41 185.59 -348.97 3851.59 -495.61 1234.28 9- 10 | 1( 1)| 14.19 44.67 -61.06 957.85 -374.29 138.32 | 1( 1)| 5.72 57.05 -719.18 1057.93 -1200.74 35.17 | 1( 1)| 6.76 63.34 -772.12 1365.09 -1158.23 114.32 10- 11 | 3( 1)| 10.34 54.29 -71.04 930.09 217.02 718.86 | 3( 1)| 7.67 59.84 -727.46 1024.84 164.94 790.11 | 3( 1)| 10.71 72.92 -778.07 1322.95 181.12 882.11 11- 12 | 1( 1)| 7.21 44.15 -136.08 750.12 154.85 586.47 | 1( 1)| 6.06 48.05 -793.56 813.82 108.87 638.61 | 1( 1)| 5.92 58.65 -850.06 1057.12 124.38 715.83 12- 13 | 1( 1)| 4.68 32.88 -210.63 551.99 78.28 440.14 | 1( 1)| 4.80 36.63 -384.87 642.58 74.81 450.74 | 1( 1)| 4.60 45.57 -436.53 828.79 78.04 514.41 13- 14 | 1( 1)| 4.52 30.74 -227.56 510.34 65.16 414.25 | 1( 1)| 4.21 34.13 -397.56 593.32 62.22 421.06 | 1( 1)| 4.39 42.49 -446.42 765.67 67.67 481.74 14- 15 | 1( 1)| 3.94 28.52 -244.52 469.06 50.62 386.09 | 1( 1)| 3.37 31.53 -410.28 544.80 48.28 388.80 | 1( 1)| 3.06 39.30 -456.36 703.30 56.19 445.83 15- 16 | 1( 1)| 3.54 27.04 -254.95 444.35 39.83 365.82 | 1( 1)| 2.85 29.81 -417.98 515.82 37.97 365.61 | 1( 1)| 2.31 37.21 -461.64 666.42 47.68 420.38 16- 17 | 1( 1)| 2.90 24.54 -273.91 399.59 23.90 335.41 | 1( 1)| 2.44 26.88 -435.59 463.34 22.75 330.81 | 1( 1)| 1.60 33.60 -471.28 599.70 30.26 382.19 17- 18 | 1( 1)| 2.56 21.38 -298.84 341.02 5.51 300.43 | 1( 1)| 2.07 23.15 -458.48 394.68 5.37 290.78 | 1( 1)| 1.25 28.97 -483.27 512.68 7.31 338.29 18- 19 | 1( 1)| 2.56 18.24 -323.95 282.23 -12.90 265.39 | 1( 1)| 1.83 21.98 -481.73 325.78 -12.05 250.70 | 1( 1)| 1.40 25.42 -497.27 425.27 -15.65 294.32 19- 20 | 1( 1)| 2.56 17.10 -334.44 257.75 -18.05 255.60 | 1( 1)| 2.05 22.23 -491.50 297.10 -16.81 239.50 | 1( 1)| 1.48 25.54 -506.20 388.88 -22.28 282.03 20- 21 | 1( 1)| 2.28 15.95 -347.15 228.27 -27.45 237.39 | 1( 1)| 1.95 22.52 -503.42 262.57 -25.81 218.67 | 1( 1)| 1.65 25.64 -517.11 345.04 -35.03 267.83 21- 22 | 1( 1)| 1.54 17.90 -394.45 117.18 -70.41 155.69 | 1( 1)| 1.44 24.46 -546.74 132.88 -78.43 152.74 | 1( 1)| 1.09 25.96 -556.34 180.73 -93.45 238.07 22- 23 | 1( 1)| 1.11 18.82 -415.29 68.58 -89.00 120.39 | 1( 1)| 1.18 25.35 -565.99 75.92 -103.96 139.05 | 1( 1)| 1.18 26.13 -573.87 110.85 -118.72 225.13 23- 24 | 1( 1)| 0.93 19.29 -426.02 45.11 -99.85 100.21 | 1( 1)| 1.19 25.80 -576.15 47.44 -119.19 131.06 | 1( 1)| 0.89 26.21 -583.17 76.38 -133.48 217.50 24- 25 | 1( 1)| 0.73 19.82 -438.39 19.59 -110.61 80.03 | 1( 1)| 0.85 26.31 -588.39 16.11 -134.42 123.14 | 1( 1)| 0.71 26.43 -594.46 37.45 -149.57 209.80 25- 26 | 1( 1)| 0.73 20.31 -449.11 -3.36 -121.46 59.86 | 1( 1)| 0.73 26.77 -598.54 -10.10 -150.13 115.16 | 1( 1)| 0.79 26.83 -603.75 3.01 -165.85 202.18 26- 27 | 1( 1)| 1.59 20.86 -460.83 -28.86 -132.11 39.69 | 1( 1)| 1.94 27.29 -609.63 -39.70 -165.56 107.32 | 1( 1)| 1.63 27.28 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.18 13.15 30.27 226.37 62.25 182.76 | 1( 1)| 2.15 15.83 -1.03 282.29 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.80 11.49 26.26 196.35 54.95 161.22 | 1( 1)| 1.90 13.81 -0.89 244.85 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.42 9.82 22.24 166.23 47.66 139.65 | 1( 1)| 1.64 11.79 -0.75 207.28 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.01 8.15 18.36 137.29 39.72 116.57 | 1( 1)| 1.37 9.78 -0.62 171.19 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.61 6.48 14.49 108.32 31.77 93.49 | 1( 1)| 1.10 7.76 -0.49 135.06 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.20 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.83 5.58 -0.34 94.24 18.10 79.77 33- 34 | 1( 1)| 0.99 60.55 10.73 35.98 18.70 41.02 | 1( 1)| 0.79 2.90 5.74 42.86 16.15 47.31 | 1( 1)| 0.56 3.41 -0.20 53.44 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.16 1.38 -0.10 26.05 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 5( 2)| 17.51 48.40 253.23 850.56 285.96 632.45 | 5( 2)| 12.65 55.80 82.75 994.50 255.08 728.71 | 5( 2)| 8.07 67.74 -49.59 1245.07 169.81 821.09 47- 48 | 5( 2)| 16.97 46.96 245.98 826.16 276.67 612.18 | 5( 2)| 12.25 54.13 78.65 965.42 246.32 705.50 | 5( 2)| 7.81 65.72 -49.89 1208.78 163.80 794.61 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.11 49.04 65.61 872.84 221.93 639.73 | 3( 1)| 7.10 59.55 -50.87 1093.09 147.17 719.56 49- 50 | 1( 1)| 7.69 21.29 111.46 374.20 125.40 277.36 | 1( 1)| 5.47 24.31 -7.30 427.53 98.35 322.39 | 1( 1)| 3.36 29.52 -55.49 537.86 66.02 357.97 8- 51 | 1( 1)| 1.72 12.58 22.27 74.66 -274.77 53.32 | 1( 1)| 1.14 12.68 11.90 88.94 -278.15 61.15 | 1( 1)| 0.75 12.65 -0.41 110.88 -276.86 66.23 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 5( 2)| 13.54 89.55 73.05 1825.26 165.51 754.11 | 5( 2)| 13.96 104.89 -134.44 2127.91 145.09 1017.35 | 5( 2)| 18.25 134.65 -76.54 2598.45 39.27 1417.64 53- 54 | 5( 2)| 12.58 87.22 60.40 1782.52 143.31 725.65 | 5( 2)| 12.97 102.23 -142.10 2078.64 117.67 978.45 | 5( 2)| 17.50 131.35 -82.33 2537.13 14.61 1369.48 54- 55 | 5( 2)| 12.03 85.85 52.71 1755.94 131.34 709.92 | 5( 2)| 12.41 100.66 -146.79 2047.86 102.49 957.02 | 5( 2)| 17.10 129.40 -85.92 2498.45 0.98 1342.26 55- 56 | 5( 2)| 11.53 84.59 45.68 1731.62 120.42 695.52 | 5( 2)| 11.90 99.23 -151.06 2019.68 88.60 937.42 | 5( 2)| 16.74 127.62 -89.20 2462.99 -11.50 1317.30 56- 57 | 5( 2)| 11.03 83.34 38.46 1702.07 109.24 678.03 | 5( 2)| 11.38 97.80 -155.61 1984.29 71.63 914.13 | 5( 2)| 16.38 125.84 -93.13 2415.58 -26.72 1282.75 57- 58 | 5( 2)| 10.48 82.01 31.10 1675.00 96.35 660.43 | 5( 2)| 10.82 96.27 -160.14 1952.51 54.35 890.35 | 5( 2)| 15.97 123.94 -96.77 2374.60 -42.24 1250.88 58- 59 | 5( 2)| 9.92 80.68 23.81 1649.84 83.56 643.96 | 5( 2)| 10.25 94.74 -164.57 1923.38 38.20 867.92 | 5( 2)| 15.57 122.02 -100.18 2337.98 -56.75 1222.52 59- 60 | 5( 2)| 7.85 75.48 -5.21 1552.48 38.38 586.33 | 5( 2)| 8.12 88.77 -182.14 1811.30 -17.37 788.78 | 5( 2)| 14.19 114.56 -113.40 2198.94 -106.70 1125.51 60- 61 | 5( 2)| 7.29 74.16 -12.50 1526.82 25.58 569.58 | 5( 2)| 7.55 87.25 -186.61 1781.47 -33.83 766.05 | 5( 2)| 13.81 112.64 -116.88 2161.16 -121.49 1096.26 61- 62 | 3( 1)| 10.68 29.49 -373.09 330.72 -604.65 -105.62 | 3( 1)| 3.12 36.36 -404.39 408.95 -784.58 247.22 | 3( 1)| 4.70 36.92 -372.38 499.14 -797.17 280.13 62- 63 | 3( 1)| 10.80 30.71 -382.56 299.91 -624.83 -116.14 | 3( 1)| 3.63 37.26 -410.06 373.59 -805.97 238.22 | 3( 1)| 3.48 37.96 -403.87 498.61 -820.50 273.27 63- 64 | 3( 1)| 10.88 31.76 -390.16 275.36 -642.72 -125.55 | 3( 1)| 4.07 38.09 -414.80 347.08 -825.35 230.22 | 3( 1)| 2.50 38.92 -429.20 497.62 -841.62 267.06 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.72 2.02 10.46 35.08 11.86 26.22 | 1( 1)| 0.53 2.35 5.59 41.79 10.16 30.00 | 1( 1)| 0.51 4.78 -16.76 104.72 7.67 34.18 66- 67 | 1( 1)| 0.36 1.01 5.23 17.54 5.93 13.11 | 1( 1)| 0.27 1.18 2.80 20.89 5.08 15.00 | 1( 1)| 0.26 4.66 -34.93 102.36 3.84 17.09 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.68 21.43 -474.77 3.76 -126.17 154.21 | 1( 1)| 0.57 21.64 -479.32 17.97 -87.70 133.02 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.21 21.91 -485.57 -25.84 -134.70 142.16 | 1( 1)| 0.98 22.11 -489.15 -19.07 -103.97 123.57 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 76.829s Elapsed Solve time : 4534.687s Elapsed CPU time: 4611.516s Sumatorio de erros e2 1.94600 Sumatorio de erros pq 0.00004 Sumatorio de erros vi 0.00000 Factor de erro e2 100 Factor de erro pq 10 Factor de erro vi 10 Maximum Psae error 1078.20191 Maximo erro superior 1299.5775 Maximo erro inferior -0.5059 Relative GAP Infinity TRANSITION 22 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 1392 binary variables 1122 integer variables 48960 nonlinear variables 81084 linear variables 211995 constraints, all linear; 886952 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: mipgap=3e-2 mipdisplay=2 rinsheur=100 nodes=1500 return_mipgap=7 mipstartalg=2 qtolin=0 1 of 1 MIP starts provided solutions. MIP start 'm1' defined initial solution with objective 17473.6013. MIQP Presolve eliminated 79895 rows and 4859 columns. MIQP Presolve modified 33 coefficients. Reduced MIQP has 130039 rows, 125638 columns, and 784451 nonzeros. Reduced MIQP has 984 binaries, 1122 generals, 0 SOSs, and 0 indicators. Reduced MIQP objective Q matrix has 47052 nonzeros. Probing fixed 0 vars, tightened 244130 bounds. Probing time = 5.75 sec. (3273.44 ticks) MIQP Presolve eliminated 4 rows and 4 columns. MIQP Presolve modified 4 coefficients. Reduced MIQP has 130035 rows, 125634 columns, and 784423 nonzeros. Reduced MIQP has 984 binaries, 1122 generals, 0 SOSs, and 0 indicators. Reduced MIQP objective Q matrix has 47052 nonzeros. Probing fixed 0 vars, tightened 120550 bounds. Probing time = 4.77 sec. (1218.17 ticks) Clique table members: 2358. MIP emphasis: balance optimality and feasibility. MIP search method: dynamic search. Parallel mode: deterministic, using up to 12 threads. Root relaxation solution time = 723.70 sec. (873313.07 ticks) Nodes Cuts/ Node Left Objective IInf Best Integer Best Bound ItCnt Gap * 0+ 0 17473.6013 -3645065.7020 --- 0 0 unbounded 17473.6013 -3645065.7020 191849 --- Root node processing (before b&c): Real time = 809.41 sec. (972570.76 ticks) Parallel b&c, 12 threads: Real time = 0.00 sec. (0.00 ticks) Sync time (average) = 0.00 sec. Wait time (average) = 0.00 sec. ------------ Total (root+branch&cut) = 809.41 sec. (972570.76 ticks) CPLEX 20.1.0.0: integer unbounded ray. 191849 MIP simplex iterations 0 branch-and-bound nodes No basis. Funcao Ojetivo($)/ Investment/ O&M: 17279.01 3913.93 13365.08 Required investment at the beginning of T1/T2/T3/Total (10^3$) 2794.25/ 2855.90/ 1347.70 Investment plan: Power transformers (kVA): Node T1 T2 T3 1 0.00 0.00 0.00 Conductor replacement at the beginning of T1/T2/T3: See Conductor type, current and power flow Structure replacement at the beginning of T1/T2/T3: known through conductor replacement Fixed/Switchable capacitor banks (kVAr): Node Fixed CB Switchable CB T1 T2 T3 T1 T2 T3 10 600.00 0.00 0.00 0.00 900.00 0.00 51 0.00 0.00 0.00 300.00 0.00 0.00 64 0.00 0.00 0.00 900.00 0.00 0.00 PV systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 609.87 0.00 184.58 67.00 0.00 0.00 0.00 Wind systems (kW): Node T1 T2 T3 27.00 900.00 225.00 0.00 50.00 0.00 225.00 0.00 69.00 0.00 900.00 0.00 ESS systems (kW): Node T1 T2 T3 35.00 0.00 0.00 0.00 46.00 0.00 0.00 0.00 64.00 0.00 300.00 1000.00 67.00 0.00 0.00 100.00 Overview Distribution System Total Cost: Description T1 T2 T3 Total ------------------------------------------------------------------------ Substation reinforcement 0.00 0.00 0.00 0.00 Conductors 26.41 26.41 26.41 52.99 Structures 18.47 18.47 18.47 37.06 Fixed CBs 2.55 2.55 2.55 5.11 Switchable CBs 7.48 11.65 11.65 19.21 PV systems 377.67 377.67 448.32 785.02 Wind systems 760.89 1825.30 1825.30 2597.99 EES systems 0.00 182.68 786.25 416.56 Total invesment cost 1193.47 2444.73 3118.95 3913.94 Purchased energy cost 5616.57 6011.73 7106.58 12089.27 Carbon tax payment 194.92 341.59 719.87 684.56 O&M PV cost 36.96 29.64 36.44 69.42 O&M wind cost 127.60 313.91 309.61 441.88 O&M EES cost 0.00 34.90 151.18 79.95 Total O&M cost 5976.04 6731.77 8323.68 13365.08 Total cost 7169.52 9176.50 11442.63 17279.03 Energy Balance (MWh): Period Subst. PV Wind | Demand Line_Loss EES_Loss 1 115491.56 6084.89 9613.73 130306.45 883.75 0.00 2 112499.48 6084.80 24035.09 141404.09 943.89 271.53 3 131877.08 7926.44 24034.63 161754.72 1242.26 841.38 CO2 Emissions (Ton): Period Distribution EV 1 9735.44 4980.53 2 9836.20 4906.75 3 9889.74 4780.66 4 9917.30 4659.94 5 9993.96 4476.17 6 8507.50 4266.91 7 8588.46 4025.47 8 8653.93 3733.05 9 8696.57 3403.07 10 8837.71 2999.31 11 8854.07 2539.22 12 9009.49 2025.48 13 9132.91 1443.32 14 9212.58 753.85 15 9456.68 0.00 Substation Operation Period Act. Power (kW) React. Power (kVAr) Ind. PF Cap. PF min max min max min max min max 1 675.27 4409.37 187.74 1983.66 0.90 0.98 Infinity -Infinity 2 0.05 5031.43 -0.64 2186.57 0.90 0.99 0.98 0.98 3 0.00 6303.98 -29.61 2506.00 0.90 1.00 0.95 0.95 Reactive Power by DG Period PV Wind min max min max 1 -43.31 229.18 -22.16 142.71 2 -150.40 217.48 -130.12 180.94 3 -206.47 285.46 -187.40 197.79 EES energy storaged: Node T1 T2 T3 initial min max initial min max initial min max 35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 0.00 269.43 240.00 1200.00 1040.00 1040.00 5200.00 67 0.00 0.00 0.00 0.00 0.00 0.00 81.01 80.00 400.00 EES maximum power exchange: Node T1 T2 T3 dis ch dis ch dis ch 35 0.00 0.00 0.00 0.00 0.00 0.00 46 0.00 0.00 0.00 0.00 0.00 0.00 64 0.00 0.00 215.83 297.93 730.09 1196.76 67 0.00 0.00 0.00 0.00 53.09 100.00 Conductor type, current and power flow: T1 T2 T3 Linha | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax | Tipo)| Imin Imax Pmin Pmax Qmin Qmax 1- 2 | 5( 2)| 33.83 220.50 675.25 4408.52 187.72 1982.91 | 5( 2)| 0.00 249.66 0.05 5030.34 -0.64 2185.66 | 5( 2)| 0.00 309.37 0.00 6302.31 -29.61 2504.53 2- 3 | 5( 2)| 33.35 219.13 667.89 4382.21 178.41 1961.80 | 5( 2)| 0.39 248.05 -7.01 4998.73 -8.84 2162.65 | 5( 2)| 0.27 307.41 -4.92 6262.12 -36.85 2475.44 3- 4 | 5( 2)| 24.17 191.28 517.03 3879.93 -2.97 1579.59 | 5( 2)| 5.22 215.20 -153.09 4404.33 -177.96 1750.21 | 5( 2)| 5.64 267.37 -107.14 5511.50 -178.55 1969.16 4- 5 | 5( 2)| 14.18 144.10 254.03 3007.28 -298.22 955.62 | 5( 2)| 12.23 160.51 -292.99 3394.73 -468.54 1089.27 | 5( 2)| 13.78 200.13 -265.04 4229.51 -428.92 1161.33 5- 6 | 5( 2)| 14.17 142.78 246.66 2976.83 -307.59 930.88 | 5( 2)| 12.54 158.96 -300.24 3358.65 -477.37 1061.98 | 5( 2)| 14.05 198.24 -273.80 4181.44 -436.51 1130.46 6- 7 | 5( 2)| 14.17 141.46 239.28 2946.33 -316.96 906.10 | 5( 2)| 12.86 157.41 -307.52 3322.50 -486.21 1034.63 | 5( 2)| 14.32 196.34 -282.58 4133.26 -444.12 1099.52 7- 8 | 5( 2)| 14.18 139.36 227.49 2905.79 -330.66 875.85 | 5( 2)| 13.35 154.94 -318.95 3274.77 -499.02 1001.88 | 5( 2)| 14.72 193.32 -296.65 4072.21 -455.29 1064.09 8- 9 | 5( 2)| 8.53 131.53 183.02 2757.94 -140.55 867.41 | 5( 2)| 1.81 148.18 -361.88 3100.86 -506.79 887.56 | 5( 2)| 9.41 185.59 -348.97 3851.59 -495.61 1234.28 9- 10 | 1( 1)| 14.19 44.67 -61.06 957.85 -374.29 138.32 | 1( 1)| 5.72 57.05 -719.18 1057.93 -1200.74 35.17 | 1( 1)| 6.76 63.34 -772.12 1365.09 -1158.23 114.32 10- 11 | 3( 1)| 10.34 54.29 -71.04 930.09 217.02 718.86 | 3( 1)| 7.67 59.84 -727.46 1024.84 164.94 790.11 | 3( 1)| 10.71 72.92 -778.07 1322.95 181.12 882.11 11- 12 | 1( 1)| 7.21 44.15 -136.08 750.12 154.85 586.47 | 1( 1)| 6.06 48.05 -793.56 813.82 108.87 638.61 | 1( 1)| 5.92 58.65 -850.06 1057.12 124.38 715.83 12- 13 | 1( 1)| 4.68 32.88 -210.63 551.99 78.28 440.14 | 1( 1)| 4.80 36.63 -384.87 642.58 74.81 450.74 | 1( 1)| 4.60 45.57 -436.53 828.79 78.04 514.41 13- 14 | 1( 1)| 4.52 30.74 -227.56 510.34 65.16 414.25 | 1( 1)| 4.21 34.13 -397.56 593.32 62.22 421.06 | 1( 1)| 4.39 42.49 -446.42 765.67 67.67 481.74 14- 15 | 1( 1)| 3.94 28.52 -244.52 469.06 50.62 386.09 | 1( 1)| 3.37 31.53 -410.28 544.80 48.28 388.80 | 1( 1)| 3.06 39.30 -456.36 703.30 56.19 445.83 15- 16 | 1( 1)| 3.54 27.04 -254.95 444.35 39.83 365.82 | 1( 1)| 2.85 29.81 -417.98 515.82 37.97 365.61 | 1( 1)| 2.31 37.21 -461.64 666.42 47.68 420.38 16- 17 | 1( 1)| 2.90 24.54 -273.91 399.59 23.90 335.41 | 1( 1)| 2.44 26.88 -435.59 463.34 22.75 330.81 | 1( 1)| 1.60 33.60 -471.28 599.70 30.26 382.19 17- 18 | 1( 1)| 2.56 21.38 -298.84 341.02 5.51 300.43 | 1( 1)| 2.07 23.15 -458.48 394.68 5.37 290.78 | 1( 1)| 1.25 28.97 -483.27 512.68 7.31 338.29 18- 19 | 1( 1)| 2.56 18.24 -323.95 282.23 -12.90 265.39 | 1( 1)| 1.83 21.98 -481.73 325.78 -12.05 250.70 | 1( 1)| 1.40 25.42 -497.27 425.27 -15.65 294.32 19- 20 | 1( 1)| 2.56 17.10 -334.44 257.75 -18.05 255.60 | 1( 1)| 2.05 22.23 -491.50 297.10 -16.81 239.50 | 1( 1)| 1.48 25.54 -506.20 388.88 -22.28 282.03 20- 21 | 1( 1)| 2.28 15.95 -347.15 228.27 -27.45 237.39 | 1( 1)| 1.95 22.52 -503.42 262.57 -25.81 218.67 | 1( 1)| 1.65 25.64 -517.11 345.04 -35.03 267.83 21- 22 | 1( 1)| 1.54 17.90 -394.45 117.18 -70.41 155.69 | 1( 1)| 1.44 24.46 -546.74 132.88 -78.43 152.74 | 1( 1)| 1.09 25.96 -556.34 180.73 -93.45 238.07 22- 23 | 1( 1)| 1.11 18.82 -415.29 68.58 -89.00 120.39 | 1( 1)| 1.18 25.35 -565.99 75.92 -103.96 139.05 | 1( 1)| 1.18 26.13 -573.87 110.85 -118.72 225.13 23- 24 | 1( 1)| 0.93 19.29 -426.02 45.11 -99.85 100.21 | 1( 1)| 1.19 25.80 -576.15 47.44 -119.19 131.06 | 1( 1)| 0.89 26.21 -583.17 76.38 -133.48 217.50 24- 25 | 1( 1)| 0.73 19.82 -438.39 19.59 -110.61 80.03 | 1( 1)| 0.85 26.31 -588.39 16.11 -134.42 123.14 | 1( 1)| 0.71 26.43 -594.46 37.45 -149.57 209.80 25- 26 | 1( 1)| 0.73 20.31 -449.11 -3.36 -121.46 59.86 | 1( 1)| 0.73 26.77 -598.54 -10.10 -150.13 115.16 | 1( 1)| 0.79 26.83 -603.75 3.01 -165.85 202.18 26- 27 | 1( 1)| 1.59 20.86 -460.83 -28.86 -132.11 39.69 | 1( 1)| 1.94 27.29 -609.63 -39.70 -165.56 107.32 | 1( 1)| 1.63 27.28 -613.87 -32.48 -181.84 194.75 3- 28 | 1( 1)| 4.21 11.29 56.37 189.12 72.51 159.40 | 1( 1)| 3.18 13.15 30.27 226.37 62.25 182.76 | 1( 1)| 2.15 15.83 -1.03 282.29 47.02 207.82 28- 29 | 1( 1)| 3.69 9.86 48.85 163.92 64.00 140.57 | 1( 1)| 2.80 11.49 26.26 196.35 54.95 161.22 | 1( 1)| 1.90 13.81 -0.89 244.85 41.51 183.27 29- 30 | 1( 1)| 3.17 8.43 41.33 138.64 55.48 121.73 | 1( 1)| 2.42 9.82 22.24 166.23 47.66 139.65 | 1( 1)| 1.64 11.79 -0.75 207.28 36.00 158.69 30- 31 | 1( 1)| 2.63 6.98 34.09 114.35 46.21 101.55 | 1( 1)| 2.01 8.15 18.36 137.29 39.72 116.57 | 1( 1)| 1.37 9.78 -0.62 171.19 30.00 132.39 31- 32 | 1( 1)| 2.09 5.54 26.84 90.03 36.94 81.38 | 1( 1)| 1.61 6.48 14.49 108.32 31.77 93.49 | 1( 1)| 1.10 7.76 -0.49 135.06 24.00 106.09 32- 33 | 1( 1)| 1.54 4.01 18.78 63.00 27.82 61.19 | 1( 1)| 1.20 4.68 10.11 75.58 23.96 70.40 | 1( 1)| 0.83 5.58 -0.34 94.24 18.10 79.77 33- 34 | 1( 1)| 0.99 60.55 10.73 35.98 18.70 41.02 | 1( 1)| 0.79 2.90 5.74 42.86 16.15 47.31 | 1( 1)| 0.56 3.41 -0.20 53.44 12.20 53.47 34- 35 | 1( 1)| 0.35 0.97 5.23 17.54 5.47 12.10 | 1( 1)| 0.25 1.13 2.80 20.89 4.69 13.85 | 1( 1)| 0.16 1.38 -0.10 26.05 3.54 15.78 3- 36 | 1( 1)| 6.02 16.54 85.77 288.71 99.57 218.95 | 1( 1)| 4.46 19.22 45.99 343.96 85.30 250.52 | 1( 1)| 2.94 23.31 -1.56 428.96 64.43 285.47 36- 37 | 1( 1)| 5.50 15.10 78.25 263.49 91.06 200.12 | 1( 1)| 4.07 17.56 41.97 313.91 78.00 228.96 | 1( 1)| 2.69 21.28 -1.42 391.48 58.92 260.91 37- 38 | 1( 1)| 4.98 13.67 70.73 238.24 82.54 181.28 | 1( 1)| 3.69 15.89 37.95 283.83 70.71 207.41 | 1( 1)| 2.44 19.26 -1.29 353.96 53.41 236.35 38- 39 | 1( 1)| 4.44 12.23 63.49 213.94 73.27 161.10 | 1( 1)| 3.29 14.22 34.08 254.88 62.77 184.33 | 1( 1)| 2.17 17.24 -1.15 317.86 47.41 210.05 39- 40 | 1( 1)| 3.97 10.90 56.51 190.53 65.52 143.95 | 1( 1)| 2.93 12.68 30.35 226.99 56.13 164.70 | 1( 1)| 1.94 15.37 -1.03 283.08 42.40 187.69 40- 41 | 1( 1)| 3.49 9.58 49.50 166.94 57.76 126.76 | 1( 1)| 2.58 11.14 26.60 198.86 49.48 145.03 | 1( 1)| 1.71 13.50 -0.91 247.95 37.38 165.25 41- 42 | 1( 1)| 2.95 8.14 42.25 142.59 48.49 106.58 | 1( 1)| 2.18 9.46 22.73 169.84 41.54 121.93 | 1( 1)| 1.43 11.49 -0.78 211.76 31.38 138.93 42- 43 | 1( 1)| 2.41 6.70 35.01 118.29 39.21 86.40 | 1( 1)| 1.77 7.79 18.86 140.91 33.60 98.85 | 1( 1)| 1.16 9.47 -0.64 175.68 25.38 112.63 43- 44 | 1( 1)| 2.05 5.70 29.78 100.75 33.29 73.29 | 1( 1)| 1.51 6.63 16.06 120.01 28.52 83.85 | 1( 1)| 0.98 8.05 -0.55 149.62 21.54 95.54 44- 45 | 1( 1)| 1.51 4.26 22.53 76.46 24.02 53.12 | 1( 1)| 1.10 4.95 12.19 91.07 20.57 60.77 | 1( 1)| 0.71 6.04 -0.42 113.55 15.54 69.24 45- 46 | 1( 1)| 0.76 2.13 11.27 38.23 12.01 26.56 | 1( 1)| 0.55 2.48 6.09 45.54 10.29 30.38 | 1( 1)| 0.36 3.02 -0.21 56.77 7.77 34.62 4- 47 | 5( 2)| 17.51 48.40 253.23 850.56 285.96 632.45 | 5( 2)| 12.65 55.80 82.75 994.50 255.08 728.71 | 5( 2)| 8.07 67.74 -49.59 1245.07 169.81 821.09 47- 48 | 5( 2)| 16.97 46.96 245.98 826.16 276.67 612.18 | 5( 2)| 12.25 54.13 78.65 965.42 246.32 705.50 | 5( 2)| 7.81 65.72 -49.89 1208.78 163.80 794.61 48- 49 | 3( 1)| 15.38 42.59 222.94 748.50 250.79 554.73 | 3( 1)| 11.11 49.04 65.61 872.84 221.93 639.73 | 3( 1)| 7.10 59.55 -50.87 1093.09 147.17 719.56 49- 50 | 1( 1)| 7.69 21.29 111.46 374.20 125.40 277.36 | 1( 1)| 5.47 24.31 -7.30 427.53 98.35 322.39 | 1( 1)| 3.36 29.52 -55.49 537.86 66.02 357.97 8- 51 | 1( 1)| 1.72 12.58 22.27 74.66 -274.77 53.32 | 1( 1)| 1.14 12.68 11.90 88.94 -278.15 61.15 | 1( 1)| 0.75 12.65 -0.41 110.88 -276.86 66.23 51- 52 | 1( 1)| 0.74 2.04 10.46 35.08 12.31 27.23 | 1( 1)| 0.55 2.37 5.59 41.79 10.55 31.15 | 1( 1)| 0.37 2.87 -0.19 52.10 8.07 35.50 9- 53 | 5( 2)| 13.54 89.55 73.05 1825.26 165.51 754.11 | 5( 2)| 13.96 104.89 -134.44 2127.91 145.09 1017.35 | 5( 2)| 18.25 134.65 -76.54 2598.45 39.27 1417.64 53- 54 | 5( 2)| 12.58 87.22 60.40 1782.52 143.31 725.65 | 5( 2)| 12.97 102.23 -142.10 2078.64 117.67 978.45 | 5( 2)| 17.50 131.35 -82.33 2537.13 14.61 1369.48 54- 55 | 5( 2)| 12.03 85.85 52.71 1755.94 131.34 709.92 | 5( 2)| 12.41 100.66 -146.79 2047.86 102.49 957.02 | 5( 2)| 17.10 129.40 -85.92 2498.45 0.98 1342.26 55- 56 | 5( 2)| 11.53 84.59 45.68 1731.62 120.42 695.52 | 5( 2)| 11.90 99.23 -151.06 2019.68 88.60 937.42 | 5( 2)| 16.74 127.62 -89.20 2462.99 -11.50 1317.30 56- 57 | 5( 2)| 11.03 83.34 38.46 1702.07 109.24 678.03 | 5( 2)| 11.38 97.80 -155.61 1984.29 71.63 914.13 | 5( 2)| 16.38 125.84 -93.13 2415.58 -26.72 1282.75 57- 58 | 5( 2)| 10.48 82.01 31.10 1675.00 96.35 660.43 | 5( 2)| 10.82 96.27 -160.14 1952.51 54.35 890.35 | 5( 2)| 15.97 123.94 -96.77 2374.60 -42.24 1250.88 58- 59 | 5( 2)| 9.92 80.68 23.81 1649.84 83.56 643.96 | 5( 2)| 10.25 94.74 -164.57 1923.38 38.20 867.92 | 5( 2)| 15.57 122.02 -100.18 2337.98 -56.75 1222.52 59- 60 | 5( 2)| 7.85 75.48 -5.21 1552.48 38.38 586.33 | 5( 2)| 8.12 88.77 -182.14 1811.30 -17.37 788.78 | 5( 2)| 14.19 114.56 -113.40 2198.94 -106.70 1125.51 60- 61 | 5( 2)| 7.29 74.16 -12.50 1526.82 25.58 569.58 | 5( 2)| 7.55 87.25 -186.61 1781.47 -33.83 766.05 | 5( 2)| 13.81 112.64 -116.88 2161.16 -121.49 1096.26 61- 62 | 3( 1)| 10.68 29.49 -373.09 330.72 -604.65 -105.62 | 3( 1)| 3.12 36.36 -404.39 408.95 -784.58 247.22 | 3( 1)| 4.70 36.92 -372.38 499.14 -797.17 280.13 62- 63 | 3( 1)| 10.80 30.71 -382.56 299.91 -624.83 -116.14 | 3( 1)| 3.63 37.26 -410.06 373.59 -805.97 238.22 | 3( 1)| 3.48 37.96 -403.87 498.61 -820.50 273.27 63- 64 | 3( 1)| 10.88 31.76 -390.16 275.36 -642.72 -125.55 | 3( 1)| 4.07 38.09 -414.80 347.08 -825.35 230.22 | 3( 1)| 2.50 38.92 -429.20 497.62 -841.62 267.06 64- 65 | 1( 1)| 1.18 3.32 17.17 57.57 19.15 42.36 | 1( 1)| 0.86 3.88 9.18 68.57 16.41 48.46 | 1( 1)| 0.57 4.73 -0.31 85.49 12.39 55.22 11- 66 | 1( 1)| 0.72 2.02 10.46 35.08 11.86 26.22 | 1( 1)| 0.53 2.35 5.59 41.79 10.16 30.00 | 1( 1)| 0.51 4.78 -16.76 104.72 7.67 34.18 66- 67 | 1( 1)| 0.36 1.01 5.23 17.54 5.93 13.11 | 1( 1)| 0.27 1.18 2.80 20.89 5.08 15.00 | 1( 1)| 0.26 4.66 -34.93 102.36 3.84 17.09 12- 68 | 1( 1)| 1.12 3.13 16.10 53.97 18.24 40.34 | 1( 1)| 0.68 21.43 -474.77 3.76 -126.17 154.21 | 1( 1)| 0.57 21.64 -479.32 17.97 -87.70 133.02 68- 69 | 1( 1)| 0.56 1.56 8.05 26.99 9.12 20.17 | 1( 1)| 1.21 21.91 -485.57 -25.84 -134.70 142.16 | 1( 1)| 0.98 22.11 -489.15 -19.07 -103.97 123.57 Voltage p.u. min max 1 0.97 1.01 2 0.96 1.03 3 0.95 1.03 Elapsed AMPL time : 80.126s Elapsed Solve time : 5344.343s Elapsed CPU time: 5424.469s Sumatorio de erros e2 1.94600 Sumatorio de erros pq 0.00004 Sumatorio de erros vi 0.00000 Factor de erro e2 100 Factor de erro pq 10 Factor de erro vi 10 Maximum Psae error 1078.20191 Maximo erro superior 1299.5775 Maximo erro inferior -0.5059 Relative GAP Infinity TRANSITION 23 Presolve eliminates 0 constraints and 168368 variables. Adjusted problem: 132558 variables: 1392 binary variables 1122 integer variables 48960 nonlinear variables 81084 linear variables 211995 constraints, all linear; 886952 nonzeros 100200 equality constraints 111795 inequality constraints 1 nonlinear objective; 74838 nonzeros. CPLEX 20.1.0.0: mipgap=3e-2 mipdisplay=2 rinsheur=100 nodes=1500 return_mipgap=7 mipstartalg=2 qtolin=0 1 of 1 MIP starts provided solutions. MIP start 'm1' defined initial solution with objective 17473.6013. MIQP Presolve eliminated 79895 rows and 4859 columns. MIQP Presolve modified 33 coefficients