MatrixRankWarning: Matrix is exactly singular #91
Description
I performed a cascading failure analysis on the IEEE 118-bus system. I set 13 initial fault branches (branch 7, 47, 183, 170, 35, 25, 31, 36, 40, 94, 96, 125, 126) and increased all loads by 2x, which caused the power grid to split into four subgrids.
（1）When performing DC power flow calculation on the largest subnetwork, the program prompted “Matrix is exactly singular“. How can I solve this problem?
Slack bus: bus 69.
B matrix dimension: (116, 116).
B_reduced dimension: (115, 115), Matrix rank: 115, Condition number: 2.83e+03.
（2）In addition, when performing DC power flow calculation on the IEEE 118-bus system (increase all loads by 2x) , the generation power of the slack bus exceeds its upper limit. How can I avoid this?
slack bus: bus 69, Pg = 2499.75, Pmax = 805.2.
PS: the data of the largest subgrid of IEEE 118-bus system is:
def case():
ppc = {"version": '2'}
##----- Power Flow Data -----##
## system MVA base
ppc["baseMVA"] = 100.0
ppc["work"] = True
ppc["bus"] = np.array([
[1.0, 2.0, 76.5, 27.0, 0.0, 0.0, 1.0, 0.955, 10.67, 138.0, 1.0, 1.06, 0.94],
[2.0, 1.0, 30.0, 9.0, 0.0, 0.0, 1.0, 0.971, 11.22, 138.0, 1.0, 1.06, 0.94],
[3.0, 1.0, 58.5, 10.0, 0.0, 0.0, 1.0, 0.968, 11.56, 138.0, 1.0, 1.06, 0.94],
[4.0, 2.0, 58.5, 12.0, 0.0, 0.0, 1.0, 0.998, 15.28, 138.0, 1.0, 1.06, 0.94],
[5.0, 1.0, 0.0, 0.0, 0.0, -40.0, 1.0, 1.002, 15.73, 138.0, 1.0, 1.06, 0.94],
[6.0, 2.0, 78.0, 22.0, 0.0, 0.0, 1.0, 0.99, 13.0, 138.0, 1.0, 1.06, 0.94],
[7.0, 1.0, 28.5, 2.0, 0.0, 0.0, 1.0, 0.989, 12.56, 138.0, 1.0, 1.06, 0.94],
[8.0, 2.0, 42.0, 0.0, 0.0, 0.0, 1.0, 1.015, 20.77, 345.0, 1.0, 1.06, 0.94],
[9.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.043, 28.02, 345.0, 1.0, 1.06, 0.94],
[10.0, 2.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.05, 35.61, 345.0, 1.0, 1.06, 0.94],
[11.0, 1.0, 105.0, 23.0, 0.0, 0.0, 1.0, 0.985, 12.72, 138.0, 1.0, 1.06, 0.94],
[12.0, 2.0, 70.5, 10.0, 0.0, 0.0, 1.0, 0.99, 12.2, 138.0, 1.0, 1.06, 0.94],
[13.0, 1.0, 51.0, 16.0, 0.0, 0.0, 1.0, 0.968, 11.35, 138.0, 1.0, 1.06, 0.94],
[14.0, 1.0, 21.0, 1.0, 0.0, 0.0, 1.0, 0.984, 11.5, 138.0, 1.0, 1.06, 0.94],
[15.0, 2.0, 135.0, 30.0, 0.0, 0.0, 1.0, 0.97, 11.23, 138.0, 1.0, 1.06, 0.94],
[16.0, 1.0, 37.5, 10.0, 0.0, 0.0, 1.0, 0.984, 11.91, 138.0, 1.0, 1.06, 0.94],
[17.0, 1.0, 16.5, 3.0, 0.0, 0.0, 1.0, 0.995, 13.74, 138.0, 1.0, 1.06, 0.94],
[18.0, 2.0, 90.0, 34.0, 0.0, 0.0, 1.0, 0.973, 11.53, 138.0, 1.0, 1.06, 0.94],
[19.0, 2.0, 67.5, 25.0, 0.0, 0.0, 1.0, 0.963, 11.05, 138.0, 1.0, 1.06, 0.94],
[20.0, 1.0, 27.0, 3.0, 0.0, 0.0, 1.0, 0.958, 11.93, 138.0, 1.0, 1.06, 0.94],
[21.0, 1.0, 21.0, 8.0, 0.0, 0.0, 1.0, 0.959, 13.52, 138.0, 1.0, 1.06, 0.94],
[22.0, 1.0, 15.0, 5.0, 0.0, 0.0, 1.0, 0.97, 16.08, 138.0, 1.0, 1.06, 0.94],
[23.0, 1.0, 10.5, 3.0, 0.0, 0.0, 1.0, 1.0, 21.0, 138.0, 1.0, 1.06, 0.94],
[24.0, 2.0, 19.5, 0.0, 0.0, 0.0, 2.0, 0.992, 20.89, 138.0, 1.0, 1.06, 0.94],
[25.0, 2.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.05, 27.93, 138.0, 1.0, 1.06, 0.94],
[26.0, 2.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.015, 29.71, 345.0, 1.0, 1.06, 0.94],
[27.0, 2.0, 106.5, 13.0, 0.0, 0.0, 1.0, 0.968, 15.35, 138.0, 1.0, 1.06, 0.94],
[28.0, 1.0, 25.5, 7.0, 0.0, 0.0, 1.0, 0.962, 13.62, 138.0, 1.0, 1.06, 0.94],
[29.0, 1.0, 36.0, 4.0, 0.0, 0.0, 1.0, 0.963, 12.63, 138.0, 1.0, 1.06, 0.94],
[30.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.968, 18.79, 345.0, 1.0, 1.06, 0.94],
[31.0, 2.0, 64.5, 27.0, 0.0, 0.0, 1.0, 0.967, 12.75, 138.0, 1.0, 1.06, 0.94],
[32.0, 2.0, 88.5, 23.0, 0.0, 0.0, 1.0, 0.964, 14.8, 138.0, 1.0, 1.06, 0.94],
[33.0, 1.0, 34.5, 9.0, 0.0, 0.0, 2.0, 0.972, 10.63, 138.0, 1.0, 1.06, 0.94],
[34.0, 2.0, 88.5, 26.0, 0.0, 14.0, 2.0, 0.986, 11.3, 138.0, 1.0, 1.06, 0.94],
[35.0, 1.0, 49.5, 9.0, 0.0, 0.0, 2.0, 0.981, 10.87, 138.0, 1.0, 1.06, 0.94],
[36.0, 2.0, 46.5, 17.0, 0.0, 0.0, 2.0, 0.98, 10.87, 138.0, 1.0, 1.06, 0.94],
[37.0, 1.0, 0.0, 0.0, 0.0, -25.0, 2.0, 0.992, 11.77, 138.0, 1.0, 1.06, 0.94],
[38.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.962, 16.91, 345.0, 1.0, 1.06, 0.94],
[39.0, 1.0, 40.5, 11.0, 0.0, 0.0, 2.0, 0.97, 8.41, 138.0, 1.0, 1.06, 0.94],
[40.0, 2.0, 99.0, 23.0, 0.0, 0.0, 2.0, 0.97, 7.35, 138.0, 1.0, 1.06, 0.94],
[41.0, 1.0, 55.5, 10.0, 0.0, 0.0, 2.0, 0.967, 6.92, 138.0, 1.0, 1.06, 0.94],
[42.0, 2.0, 144.0, 23.0, 0.0, 0.0, 2.0, 0.985, 8.53, 138.0, 1.0, 1.06, 0.94],
[43.0, 1.0, 27.0, 7.0, 0.0, 0.0, 2.0, 0.978, 11.28, 138.0, 1.0, 1.06, 0.94],
[44.0, 1.0, 24.0, 8.0, 0.0, 10.0, 2.0, 0.985, 13.82, 138.0, 1.0, 1.06, 0.94],
[45.0, 1.0, 79.5, 22.0, 0.0, 10.0, 2.0, 0.987, 15.67, 138.0, 1.0, 1.06, 0.94],
[46.0, 2.0, 42.0, 10.0, 0.0, 10.0, 2.0, 1.005, 18.49, 138.0, 1.0, 1.06, 0.94],
[47.0, 1.0, 51.0, 0.0, 0.0, 0.0, 2.0, 1.017, 20.73, 138.0, 1.0, 1.06, 0.94],
[48.0, 1.0, 30.0, 11.0, 0.0, 15.0, 2.0, 1.021, 19.93, 138.0, 1.0, 1.06, 0.94],
[49.0, 2.0, 130.5, 30.0, 0.0, 0.0, 2.0, 1.025, 20.94, 138.0, 1.0, 1.06, 0.94],
[50.0, 1.0, 25.5, 4.0, 0.0, 0.0, 2.0, 1.001, 18.9, 138.0, 1.0, 1.06, 0.94],
[51.0, 1.0, 25.5, 8.0, 0.0, 0.0, 2.0, 0.967, 16.28, 138.0, 1.0, 1.06, 0.94],
[52.0, 1.0, 27.0, 5.0, 0.0, 0.0, 2.0, 0.957, 15.32, 138.0, 1.0, 1.06, 0.94],
[53.0, 1.0, 34.5, 11.0, 0.0, 0.0, 2.0, 0.946, 14.35, 138.0, 1.0, 1.06, 0.94],
[54.0, 2.0, 169.5, 32.0, 0.0, 0.0, 2.0, 0.955, 15.26, 138.0, 1.0, 1.06, 0.94],
[55.0, 2.0, 94.5, 22.0, 0.0, 0.0, 2.0, 0.952, 14.97, 138.0, 1.0, 1.06, 0.94],
[56.0, 2.0, 126.0, 18.0, 0.0, 0.0, 2.0, 0.954, 15.16, 138.0, 1.0, 1.06, 0.94],
[57.0, 1.0, 18.0, 3.0, 0.0, 0.0, 2.0, 0.971, 16.36, 138.0, 1.0, 1.06, 0.94],
[58.0, 1.0, 18.0, 3.0, 0.0, 0.0, 2.0, 0.959, 15.51, 138.0, 1.0, 1.06, 0.94],
[59.0, 2.0, 415.5, 113.0, 0.0, 0.0, 2.0, 0.985, 19.37, 138.0, 1.0, 1.06, 0.94],
[60.0, 1.0, 117.0, 3.0, 0.0, 0.0, 2.0, 0.993, 23.15, 138.0, 1.0, 1.06, 0.94],
[61.0, 2.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.995, 24.04, 138.0, 1.0, 1.06, 0.94],
[62.0, 2.0, 115.5, 14.0, 0.0, 0.0, 2.0, 0.998, 23.43, 138.0, 1.0, 1.06, 0.94],
[63.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.969, 22.75, 345.0, 1.0, 1.06, 0.94],
[64.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.984, 24.52, 345.0, 1.0, 1.06, 0.94],
[65.0, 2.0, 0.0, 0.0, 0.0, 0.0, 2.0, 1.005, 27.65, 345.0, 1.0, 1.06, 0.94],
[66.0, 2.0, 58.5, 18.0, 0.0, 0.0, 2.0, 1.05, 27.48, 138.0, 1.0, 1.06, 0.94],
[67.0, 1.0, 42.0, 7.0, 0.0, 0.0, 2.0, 1.02, 24.84, 138.0, 1.0, 1.06, 0.94],
[68.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 1.003, 27.55, 345.0, 1.0, 1.06, 0.94],
[69.0, 3.0, 0.0, 0.0, 0.0, 0.0, 2.0, 1.035, 30.0, 138.0, 1.0, 1.06, 0.94],
[70.0, 2.0, 99.0, 20.0, 0.0, 0.0, 2.0, 0.984, 22.58, 138.0, 1.0, 1.06, 0.94],
[71.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.987, 22.15, 138.0, 1.0, 1.06, 0.94],
[72.0, 2.0, 18.0, 0.0, 0.0, 0.0, 2.0, 0.98, 20.98, 138.0, 1.0, 1.06, 0.94],
[73.0, 2.0, 9.0, 0.0, 0.0, 0.0, 2.0, 0.991, 21.94, 138.0, 1.0, 1.06, 0.94],
[74.0, 2.0, 102.0, 27.0, 0.0, 12.0, 3.0, 0.958, 21.64, 138.0, 1.0, 1.06, 0.94],
[75.0, 1.0, 70.5, 11.0, 0.0, 0.0, 3.0, 0.967, 22.91, 138.0, 1.0, 1.06, 0.94],
[76.0, 2.0, 102.0, 36.0, 0.0, 0.0, 3.0, 0.943, 21.77, 138.0, 1.0, 1.06, 0.94],
[77.0, 2.0, 91.5, 28.0, 0.0, 0.0, 3.0, 1.006, 26.72, 138.0, 1.0, 1.06, 0.94],
[78.0, 1.0, 106.5, 26.0, 0.0, 0.0, 3.0, 1.003, 26.42, 138.0, 1.0, 1.06, 0.94],
[79.0, 1.0, 58.5, 32.0, 0.0, 20.0, 3.0, 1.009, 26.72, 138.0, 1.0, 1.06, 0.94],
[80.0, 2.0, 195.0, 26.0, 0.0, 0.0, 3.0, 1.04, 28.96, 138.0, 1.0, 1.06, 0.94],
[81.0, 1.0, 0.0, 0.0, 0.0, 0.0, 3.0, 0.997, 28.1, 345.0, 1.0, 1.06, 0.94],
[82.0, 1.0, 81.0, 27.0, 0.0, 20.0, 3.0, 0.989, 27.24, 138.0, 1.0, 1.06, 0.94],
[83.0, 1.0, 30.0, 10.0, 0.0, 10.0, 3.0, 0.985, 28.42, 138.0, 1.0, 1.06, 0.94],
[84.0, 1.0, 16.5, 7.0, 0.0, 0.0, 3.0, 0.98, 30.95, 138.0, 1.0, 1.06, 0.94],
[85.0, 2.0, 36.0, 15.0, 0.0, 0.0, 3.0, 0.985, 32.51, 138.0, 1.0, 1.06, 0.94],
[88.0, 1.0, 72.0, 10.0, 0.0, 0.0, 3.0, 0.987, 35.64, 138.0, 1.0, 1.06, 0.94],
[89.0, 2.0, 0.0, 0.0, 0.0, 0.0, 3.0, 1.005, 39.69, 138.0, 1.0, 1.06, 0.94],
[90.0, 2.0, 244.5, 42.0, 0.0, 0.0, 3.0, 0.985, 33.29, 138.0, 1.0, 1.06, 0.94],
[91.0, 2.0, 15.0, 0.0, 0.0, 0.0, 3.0, 0.98, 33.31, 138.0, 1.0, 1.06, 0.94],
[92.0, 2.0, 97.5, 10.0, 0.0, 0.0, 3.0, 0.993, 33.8, 138.0, 1.0, 1.06, 0.94],
[93.0, 1.0, 18.0, 7.0, 0.0, 0.0, 3.0, 0.987, 30.79, 138.0, 1.0, 1.06, 0.94],
[94.0, 1.0, 45.0, 16.0, 0.0, 0.0, 3.0, 0.991, 28.64, 138.0, 1.0, 1.06, 0.94],
[95.0, 1.0, 63.0, 31.0, 0.0, 0.0, 3.0, 0.981, 27.67, 138.0, 1.0, 1.06, 0.94],
[96.0, 1.0, 57.0, 15.0, 0.0, 0.0, 3.0, 0.993, 27.51, 138.0, 1.0, 1.06, 0.94],
[97.0, 1.0, 22.5, 9.0, 0.0, 0.0, 3.0, 1.011, 27.88, 138.0, 1.0, 1.06, 0.94],
[98.0, 1.0, 51.0, 8.0, 0.0, 0.0, 3.0, 1.024, 27.4, 138.0, 1.0, 1.06, 0.94],
[99.0, 2.0, 63.0, 0.0, 0.0, 0.0, 3.0, 1.01, 27.04, 138.0, 1.0, 1.06, 0.94],
[100.0, 2.0, 55.5, 18.0, 0.0, 0.0, 3.0, 1.017, 28.03, 138.0, 1.0, 1.06, 0.94],
[101.0, 1.0, 33.0, 15.0, 0.0, 0.0, 3.0, 0.993, 29.61, 138.0, 1.0, 1.06, 0.94],
[102.0, 1.0, 7.5, 3.0, 0.0, 0.0, 3.0, 0.991, 32.3, 138.0, 1.0, 1.06, 0.94],
[103.0, 2.0, 34.5, 16.0, 0.0, 0.0, 3.0, 1.001, 24.44, 138.0, 1.0, 1.06, 0.94],
[104.0, 2.0, 57.0, 25.0, 0.0, 0.0, 3.0, 0.971, 21.69, 138.0, 1.0, 1.06, 0.94],
[105.0, 2.0, 46.5, 26.0, 0.0, 20.0, 3.0, 0.965, 20.57, 138.0, 1.0, 1.06, 0.94],
[106.0, 1.0, 64.5, 16.0, 0.0, 0.0, 3.0, 0.962, 20.32, 138.0, 1.0, 1.06, 0.94],
[107.0, 2.0, 75.0, 12.0, 0.0, 6.0, 3.0, 0.952, 17.53, 138.0, 1.0, 1.06, 0.94],
[108.0, 1.0, 3.0, 1.0, 0.0, 0.0, 3.0, 0.967, 19.38, 138.0, 1.0, 1.06, 0.94],
[109.0, 1.0, 12.0, 3.0, 0.0, 0.0, 3.0, 0.967, 18.93, 138.0, 1.0, 1.06, 0.94],
[110.0, 2.0, 58.5, 30.0, 0.0, 6.0, 3.0, 0.973, 18.09, 138.0, 1.0, 1.06, 0.94],
[111.0, 2.0, 0.0, 0.0, 0.0, 0.0, 3.0, 0.98, 19.74, 138.0, 1.0, 1.06, 0.94],
[112.0, 2.0, 102.0, 13.0, 0.0, 0.0, 3.0, 0.975, 14.99, 138.0, 1.0, 1.06, 0.94],
[113.0, 2.0, 9.0, 0.0, 0.0, 0.0, 1.0, 0.993, 13.74, 138.0, 1.0, 1.06, 0.94],
[114.0, 1.0, 12.0, 3.0, 0.0, 0.0, 1.0, 0.96, 14.46, 138.0, 1.0, 1.06, 0.94],
[115.0, 1.0, 33.0, 7.0, 0.0, 0.0, 1.0, 0.96, 14.46, 138.0, 1.0, 1.06, 0.94],
[116.0, 2.0, 276.0, 0.0, 0.0, 0.0, 2.0, 1.005, 27.12, 138.0, 1.0, 1.06, 0.94],
[117.0, 1.0, 30.0, 8.0, 0.0, 0.0, 1.0, 0.974, 10.67, 138.0, 1.0, 1.06, 0.94],
[118.0, 1.0, 49.5, 15.0, 0.0, 0.0, 3.0, 0.949, 21.92, 138.0, 1.0, 1.06, 0.94]])
ppc["gen"] = np.array([
[1.0, 0.0, 0.0, 15.0, -5.0, 0.955, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[4.0, 0.0, 0.0, 300.0, -300.0, 0.998, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[6.0, 0.0, 0.0, 50.0, -13.0, 0.99, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[8.0, 0.0, 0.0, 300.0, -300.0, 1.015, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[10.0, 448.4663665307945, 0.0, 200.0, -147.0, 1.05, 100.0, 1.0, 550.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[12.0, 84.48414146944906, 0.0, 120.0, -35.0, 0.99, 100.0, 1.0, 185.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[15.0, 0.0, 0.0, 30.0, -10.0, 0.97, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[18.0, 0.0, 0.0, 50.0, -16.0, 0.973, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[19.0, 0.0, 0.0, 24.0, -8.0, 0.962, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[24.0, 0.0, 0.0, 300.0, -300.0, 0.992, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[25.0, 219.10770416337135, 0.0, 140.0, -47.0, 1.05, 100.0, 1.0, 320.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[26.0, 312.8455922613617, 0.0, 1000.0, -1000.0, 1.015, 100.0, 1.0, 414.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[27.0, 0.0, 0.0, 300.0, -300.0, 0.968, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[31.0, 6.701638579627294, 0.0, 300.0, -300.0, 0.967, 100.0, 1.0, 107.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[32.0, 0.0, 0.0, 42.0, -14.0, 0.963, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[34.0, 0.0, 0.0, 24.0, -8.0, 0.984, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[36.0, 0.0, 0.0, 24.0, -8.0, 0.98, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[40.0, 0.0, 0.0, 300.0, -300.0, 0.97, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[42.0, 0.0, 0.0, 300.0, -300.0, 0.985, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[46.0, 18.66817748575372, 0.0, 100.0, -100.0, 1.005, 100.0, 1.0, 119.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[49.0, 203.1523189552028, 0.0, 210.0, -85.0, 1.025, 100.0, 1.0, 304.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[54.0, 47.587313175559245, 0.0, 300.0, -300.0, 0.955, 100.0, 1.0, 148.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[55.0, 0.0, 0.0, 23.0, -8.0, 0.952, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[56.0, 0.0, 0.0, 15.0, -8.0, 0.954, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[59.0, 154.28895175518653, 0.0, 180.0, -60.0, 0.985, 100.0, 1.0, 255.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[61.0, 159.27500963273923, 0.0, 300.0, -100.0, 0.995, 100.0, 1.0, 260.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[62.0, 0.0, 0.0, 20.0, -20.0, 0.998, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[65.0, 389.6308835756729, 0.0, 200.0, -67.0, 1.005, 100.0, 1.0, 491.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[66.0, 390.62809515118346, 0.0, 200.0, -67.0, 1.05, 100.0, 1.0, 492.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[69.0, 2499.7547606010803, 0.0, 300.0, -300.0, 1.035, 100.0, 1.0, 805.2, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[70.0, 0.0, 0.0, 32.0, -10.0, 0.984, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[72.0, 0.0, 0.0, 100.0, -100.0, 0.98, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[73.0, 0.0, 0.0, 100.0, -100.0, 0.991, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[74.0, 0.0, 0.0, 9.0, -6.0, 0.958, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[76.0, 0.0, 0.0, 23.0, -8.0, 0.943, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[77.0, 0.0, 0.0, 70.0, -20.0, 1.006, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[80.0, 475.39107906957895, 0.0, 280.0, -165.0, 1.04, 100.0, 1.0, 577.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[85.0, 0.0, 0.0, 23.0, -8.0, 0.985, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[89.0, 605.0285838859486, 0.0, 300.0, -210.0, 1.005, 100.0, 1.0, 707.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[90.0, 0.0, 0.0, 300.0, -300.0, 0.985, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[91.0, 0.0, 0.0, 100.0, -100.0, 0.98, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[92.0, 0.0, 0.0, 9.0, -3.0, 0.99, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[99.0, 0.0, 0.0, 100.0, -100.0, 1.01, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[100.0, 251.01847457970848, 0.0, 155.0, -50.0, 1.017, 100.0, 1.0, 352.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[103.0, 39.60962057147496, 0.0, 40.0, -15.0, 1.01, 100.0, 1.0, 140.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[104.0, 0.0, 0.0, 23.0, -8.0, 0.971, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[105.0, 0.0, 0.0, 23.0, -8.0, 0.965, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[107.0, 0.0, 0.0, 200.0, -200.0, 0.952, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[110.0, 0.0, 0.0, 23.0, -8.0, 0.973, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[111.0, 35.62077426943282, 0.0, 1000.0, -100.0, 0.98, 100.0, 1.0, 136.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[112.0, 0.0, 0.0, 1000.0, -100.0, 0.975, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[113.0, 0.0, 0.0, 200.0, -100.0, 0.993, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
[116.0, 0.0, 0.0, 1000.0, -1000.0, 1.005, 100.0, 1.0, 100.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]])
ppc["gencost"] = np.array([
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0222222, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.117647, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0454545, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0318471, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 1.42857, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.526316, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0490196, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.208333, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0645161, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0625, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0255754, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0255102, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0193648, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0209644, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0164745, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.0396825, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.25, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.277778, 20.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0],
[2.0, 0.0, 0.0, 3.0, 0.01, 40.0, 0.0]])
ppc["branch"] = np.array([
[1.0, 2.0, 0.0303, 0.0999, 0.0254, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[1.0, 3.0, 0.0129, 0.0424, 0.01082, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[4.0, 5.0, 0.00176, 0.00798, 0.0021, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[3.0, 5.0, 0.0241, 0.108, 0.0284, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[5.0, 6.0, 0.0119, 0.054, 0.01426, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[6.0, 7.0, 0.00459, 0.0208, 0.0055, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[8.0, 9.0, 0.00244, 0.0305, 1.162, 1100.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[8.0, 5.0, 0.0, 0.0267, 0.0, 880.0, 0.0, 0.0, 0.985, 0.0, 1.0, -360.0, 360.0],
[9.0, 10.0, 0.00258, 0.0322, 1.23, 1100.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[4.0, 11.0, 0.0209, 0.0688, 0.01748, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[5.0, 11.0, 0.0203, 0.0682, 0.01738, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[11.0, 12.0, 0.00595, 0.0196, 0.00502, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[2.0, 12.0, 0.0187, 0.0616, 0.01572, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[3.0, 12.0, 0.0484, 0.16, 0.0406, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[7.0, 12.0, 0.00862, 0.034, 0.00874, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[11.0, 13.0, 0.02225, 0.0731, 0.01876, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[12.0, 14.0, 0.0215, 0.0707, 0.01816, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[13.0, 15.0, 0.0744, 0.2444, 0.06268, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[14.0, 15.0, 0.0595, 0.195, 0.0502, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[12.0, 16.0, 0.0212, 0.0834, 0.0214, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[15.0, 17.0, 0.0132, 0.0437, 0.0444, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[16.0, 17.0, 0.0454, 0.1801, 0.0466, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[17.0, 18.0, 0.0123, 0.0505, 0.01298, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[18.0, 19.0, 0.01119, 0.0493, 0.01142, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[19.0, 20.0, 0.0252, 0.117, 0.0298, 220.0, 0.0, 0.0, 0.0, 0.0, 0.0, -360.0, 360.0],
[15.0, 19.0, 0.012, 0.0394, 0.0101, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[20.0, 21.0, 0.0183, 0.0849, 0.0216, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[21.0, 22.0, 0.0209, 0.097, 0.0246, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[22.0, 23.0, 0.0342, 0.159, 0.0404, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[23.0, 24.0, 0.0135, 0.0492, 0.0498, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[23.0, 25.0, 0.0156, 0.08, 0.0864, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[26.0, 25.0, 0.0, 0.0382, 0.0, 220.0, 0.0, 0.0, 0.96, 0.0, 1.0, -360.0, 360.0],
[25.0, 27.0, 0.0318, 0.163, 0.1764, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[27.0, 28.0, 0.01913, 0.0855, 0.0216, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[28.0, 29.0, 0.0237, 0.0943, 0.0238, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[30.0, 17.0, 0.0, 0.0388, 0.0, 660.0, 0.0, 0.0, 0.96, 0.0, 1.0, -360.0, 360.0],
[8.0, 30.0, 0.00431, 0.0504, 0.514, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[26.0, 30.0, 0.00799, 0.086, 0.908, 660.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[17.0, 31.0, 0.0474, 0.1563, 0.0399, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[29.0, 31.0, 0.0108, 0.0331, 0.0083, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[23.0, 32.0, 0.0317, 0.1153, 0.1173, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[31.0, 32.0, 0.0298, 0.0985, 0.0251, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[27.0, 32.0, 0.0229, 0.0755, 0.01926, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[15.0, 33.0, 0.038, 0.1244, 0.03194, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[19.0, 34.0, 0.0752, 0.247, 0.0632, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[35.0, 36.0, 0.00224, 0.0102, 0.00268, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[35.0, 37.0, 0.011, 0.0497, 0.01318, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[33.0, 37.0, 0.0415, 0.142, 0.0366, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[34.0, 36.0, 0.00871, 0.0268, 0.00568, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[34.0, 37.0, 0.00256, 0.0094, 0.00984, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[38.0, 37.0, 0.0, 0.0375, 0.0, 660.0, 0.0, 0.0, 0.935, 0.0, 1.0, -360.0, 360.0],
[37.0, 39.0, 0.0321, 0.106, 0.027, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[37.0, 40.0, 0.0593, 0.168, 0.042, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[30.0, 38.0, 0.00464, 0.054, 0.422, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[39.0, 40.0, 0.0184, 0.0605, 0.01552, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[40.0, 41.0, 0.0145, 0.0487, 0.01222, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[40.0, 42.0, 0.0555, 0.183, 0.0466, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[41.0, 42.0, 0.041, 0.135, 0.0344, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[43.0, 44.0, 0.0608, 0.2454, 0.06068, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[34.0, 43.0, 0.0413, 0.1681, 0.04226, 220.0, 0.0, 0.0, 0.0, 0.0, 0.0, -360.0, 360.0],
[44.0, 45.0, 0.0224, 0.0901, 0.0224, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[45.0, 46.0, 0.04, 0.1356, 0.0332, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[46.0, 47.0, 0.038, 0.127, 0.0316, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[46.0, 48.0, 0.0601, 0.189, 0.0472, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[47.0, 49.0, 0.0191, 0.0625, 0.01604, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[42.0, 49.0, 0.0715, 0.323, 0.086, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], ######
[42.0, 49.0, 0.0715, 0.323, 0.086, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], ######
[45.0, 49.0, 0.0684, 0.186, 0.0444, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[48.0, 49.0, 0.0179, 0.0505, 0.01258, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[49.0, 50.0, 0.0267, 0.0752, 0.01874, 220.0, 0.0, 0.0, 0.0, 0.0, 0.0, -360.0, 360.0],
[49.0, 51.0, 0.0486, 0.137, 0.0342, 220.0, 0.0, 0.0, 0.0, 0.0, 0.0, -360.0, 360.0],
[51.0, 52.0, 0.0203, 0.0588, 0.01396, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[52.0, 53.0, 0.0405, 0.1635, 0.04058, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[53.0, 54.0, 0.0263, 0.122, 0.031, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[49.0, 54.0, 0.073, 0.289, 0.0738, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], #####
[49.0, 54.0, 0.0869, 0.291, 0.073, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], #####
[54.0, 55.0, 0.0169, 0.0707, 0.0202, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[54.0, 56.0, 0.00275, 0.00955, 0.00732, 220.0, 0.0, 0.0, 0.0, 0.0, 0.0, -360.0, 360.0],
[55.0, 56.0, 0.00488, 0.0151, 0.00374, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[56.0, 57.0, 0.0343, 0.0966, 0.0242, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[50.0, 57.0, 0.0474, 0.134, 0.0332, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[56.0, 58.0, 0.0343, 0.0966, 0.0242, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[51.0, 58.0, 0.0255, 0.0719, 0.01788, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[54.0, 59.0, 0.0503, 0.2293, 0.0598, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[56.0, 59.0, 0.0825, 0.251, 0.0569, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], #####
[56.0, 59.0, 0.0803, 0.239, 0.0536, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], #####
[55.0, 59.0, 0.04739, 0.2158, 0.05646, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[59.0, 60.0, 0.0317, 0.145, 0.0376, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[59.0, 61.0, 0.0328, 0.15, 0.0388, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[60.0, 61.0, 0.00264, 0.0135, 0.01456, 440.0, 0.0, 0.0, 0.0, 0.0, 0.0, -360.0, 360.0],
[60.0, 62.0, 0.0123, 0.0561, 0.01468, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[61.0, 62.0, 0.00824, 0.0376, 0.0098, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[63.0, 59.0, 0.0, 0.0386, 0.0, 440.0, 0.0, 0.0, 0.96, 0.0, 1.0, -360.0, 360.0],
[63.0, 64.0, 0.00172, 0.02, 0.216, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[64.0, 61.0, 0.0, 0.0268, 0.0, 220.0, 0.0, 0.0, 0.985, 0.0, 1.0, -360.0, 360.0],
[38.0, 65.0, 0.00901, 0.0986, 1.046, 440.0, 0.0, 0.0, 0.0, 0.0, 101.0978133911194, -360.0, 360.0],
[64.0, 65.0, 0.00269, 0.0302, 0.38, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[49.0, 66.0, 0.018, 0.0919, 0.0248, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], #####
[49.0, 66.0, 0.018, 0.0919, 0.0248, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], #####
[62.0, 66.0, 0.0482, 0.218, 0.0578, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[62.0, 67.0, 0.0258, 0.117, 0.031, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[65.0, 66.0, 0.0, 0.037, 0.0, 220.0, 0.0, 0.0, 0.935, 0.0, 1.0, -360.0, 360.0],
[66.0, 67.0, 0.0224, 0.1015, 0.02682, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[65.0, 68.0, 0.00138, 0.016, 0.638, 220.0, 0.0, 0.0, 0.0, 0.0, 102.89357539388203, -360.0, 360.0],
[47.0, 69.0, 0.0844, 0.2778, 0.07092, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[49.0, 69.0, 0.0985, 0.324, 0.0828, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[68.0, 69.0, 0.0, 0.037, 0.0, 440.0, 0.0, 0.0, 0.935, 0.0, 102.35573291073936, -360.0, 360.0],
[69.0, 70.0, 0.03, 0.127, 0.122, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[24.0, 70.0, 0.00221, 0.4115, 0.10198, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[70.0, 71.0, 0.00882, 0.0355, 0.00878, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[24.0, 72.0, 0.0488, 0.196, 0.0488, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[71.0, 72.0, 0.0446, 0.18, 0.04444, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[71.0, 73.0, 0.00866, 0.0454, 0.01178, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[70.0, 74.0, 0.0401, 0.1323, 0.03368, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[70.0, 75.0, 0.0428, 0.141, 0.036, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[69.0, 75.0, 0.0405, 0.122, 0.124, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[74.0, 75.0, 0.0123, 0.0406, 0.01034, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[76.0, 77.0, 0.0444, 0.148, 0.0368, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[69.0, 77.0, 0.0309, 0.101, 0.1038, 220.0, 0.0, 0.0, 0.0, 0.0, 101.89879179220881, -360.0, 360.0],
[75.0, 77.0, 0.0601, 0.1999, 0.04978, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[77.0, 78.0, 0.00376, 0.0124, 0.01264, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[78.0, 79.0, 0.00546, 0.0244, 0.00648, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[77.0, 80.0, 0.017, 0.0485, 0.0472, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], #####
[77.0, 80.0, 0.0294, 0.105, 0.0228, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], #####
[79.0, 80.0, 0.0156, 0.0704, 0.0187, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[68.0, 81.0, 0.00175, 0.0202, 0.808, 220.0, 0.0, 0.0, 0.0, 0.0, 0.0, -360.0, 360.0],
[81.0, 80.0, 0.0, 0.037, 0.0, 220.0, 0.0, 0.0, 0.935, 0.0, 1.0, -360.0, 360.0],
[77.0, 82.0, 0.0298, 0.0853, 0.08174, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[82.0, 83.0, 0.0112, 0.03665, 0.03796, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[83.0, 84.0, 0.0625, 0.132, 0.0258, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[83.0, 85.0, 0.043, 0.148, 0.0348, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[84.0, 85.0, 0.0302, 0.0641, 0.01234, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[85.0, 88.0, 0.02, 0.102, 0.0276, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[85.0, 89.0, 0.0239, 0.173, 0.047, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[88.0, 89.0, 0.0139, 0.0712, 0.01934, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[89.0, 90.0, 0.0518, 0.188, 0.0528, 660.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], ######
[89.0, 90.0, 0.0238, 0.0997, 0.106, 660.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], ######
[90.0, 91.0, 0.0254, 0.0836, 0.0214, 660.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[89.0, 92.0, 0.0099, 0.0505, 0.0548, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], #####
[89.0, 92.0, 0.0393, 0.1581, 0.0414, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0], #####
[91.0, 92.0, 0.0387, 0.1272, 0.03268, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[92.0, 93.0, 0.0258, 0.0848, 0.0218, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[92.0, 94.0, 0.0481, 0.158, 0.0406, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[93.0, 94.0, 0.0223, 0.0732, 0.01876, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[94.0, 95.0, 0.0132, 0.0434, 0.0111, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[80.0, 96.0, 0.0356, 0.182, 0.0494, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[82.0, 96.0, 0.0162, 0.053, 0.0544, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[94.0, 96.0, 0.0269, 0.0869, 0.023, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[80.0, 97.0, 0.0183, 0.0934, 0.0254, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[80.0, 98.0, 0.0238, 0.108, 0.0286, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[80.0, 99.0, 0.0454, 0.206, 0.0546, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[92.0, 100.0, 0.0648, 0.295, 0.0472, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[94.0, 100.0, 0.0178, 0.058, 0.0604, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[95.0, 96.0, 0.0171, 0.0547, 0.01474, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[96.0, 97.0, 0.0173, 0.0885, 0.024, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[98.0, 100.0, 0.0397, 0.179, 0.0476, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[99.0, 100.0, 0.018, 0.0813, 0.0216, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[100.0, 101.0, 0.0277, 0.1262, 0.0328, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[92.0, 102.0, 0.0123, 0.0559, 0.01464, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[101.0, 102.0, 0.0246, 0.112, 0.0294, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[100.0, 103.0, 0.016, 0.0525, 0.0536, 440.0, 0.0, 0.0, 0.0, 0.0, 0.0, -360.0, 360.0],
[100.0, 104.0, 0.0451, 0.204, 0.0541, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[103.0, 104.0, 0.0466, 0.1584, 0.0407, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[103.0, 105.0, 0.0535, 0.1625, 0.0408, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[100.0, 106.0, 0.0605, 0.229, 0.062, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[104.0, 105.0, 0.00994, 0.0378, 0.00986, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[105.0, 106.0, 0.014, 0.0547, 0.01434, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[105.0, 107.0, 0.053, 0.183, 0.0472, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[105.0, 108.0, 0.0261, 0.0703, 0.01844, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[106.0, 107.0, 0.053, 0.183, 0.0472, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[108.0, 109.0, 0.0105, 0.0288, 0.0076, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[103.0, 110.0, 0.03906, 0.1813, 0.0461, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[109.0, 110.0, 0.0278, 0.0762, 0.0202, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[110.0, 111.0, 0.022, 0.0755, 0.02, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[110.0, 112.0, 0.0247, 0.064, 0.062, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[17.0, 113.0, 0.00913, 0.0301, 0.00768, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[32.0, 113.0, 0.0615, 0.203, 0.0518, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[32.0, 114.0, 0.0135, 0.0612, 0.01628, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[27.0, 115.0, 0.0164, 0.0741, 0.01972, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[114.0, 115.0, 0.0023, 0.0104, 0.00276, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[68.0, 116.0, 0.00034, 0.00405, 0.164, 440.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[12.0, 117.0, 0.0329, 0.14, 0.0358, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[75.0, 118.0, 0.0145, 0.0481, 0.01198, 220.0, 0.0, 0.0, 0.0, 0.0, 1.0, -360.0, 360.0],
[76.0, 118.0, 0.0164, 0.0544, 0.01356, 220.0, 0.0, 0.0, 0.0, 0.0, 0.0, -360.0, 360.0]])
return ppc