6.14. The 26-bus power system network of an electric utility company is shown in Figure 61. Obtain the power flow solution by the following methods: (a) Gauss-Seidel power flow (see Example 6.9). (b) Newton-Raphson power flow (see Example 6.11). (c) Fast decoupled power flow (see Example 6.13). 1 The load data is as follows. LOAD DATA Bus Load Bus No. MW Mvar No. 51.0 41.0 14 2 22.0 15.0 15 3 64.0 50.0 16 4 25.0 10.0 17 5 50.0 30.0 18 6 76.0 29.0 19 7 0.0 0.0 20 8 0.0 0.0 21 9 89.0 50.0 22 10 0.0 0.0 23 11 25.0 15.0 24 89.0 48.0 25 13 31.0 15.0 26 Load MW Mvar 24.0 12.0 70.0 31.0 55.0 27.0 78.0 38.0 153.0 67.0 75.0 15.0 48.0 27.0 46.0 23.0 45.0 22.0 25.0 12.0 54.0 27.0 28.0 13.0 40.0 20.0 12 R, 1 1 LINE AND TRANSFORMER DATA Bus Bus R X, Bus Bus X, No. No. pu pu pu No. No. pu pu pu 2 0.0005 0.0048 0.0300 10 22 0.0069 0.0298 0.005 18 0.0013 0.0110 0.0600 | 11 25 0.0960 0.2700 0.010 2 3 0.0014 0.0513 0.060011 26 0.0165 0.0970 0,004 2 7 0.0103 0.0586 0.018012 14 0.0327 0.0802 0.000 2 8 0.0074 0.0321 0.0390 12 15 0.0180 0.0598 0.000 2 13 0.0035 0.0967 0.0250 13 14 0.0016 0.0271 0.001 2 26 0.0323 0.1967 0.000013 15 0.0116 0.0610 0.000 3 13 0.0007 0.0051 0.0005 13 16 0.0179 0.0888 0.001 4 8 0.0008 0.0240 0.0001 14 15 0.0069 0.0382 0.000 4 12 0.0016 0.0207 0.0150 15 16 0.0209 0.0512 0.000 5 6 0.0069 0.0300 0.0900 16 17 0.0990 0.0600 0.000 6 7 0.0053 0.0306 0.0010 16 20 0.0239 0.0585 0.000 11 0.0097 0.0570 0.0001 18 0.0032 0.0600 0.038 6 18 0.0037 0.0222 0.0012 17 21 0.2290 0.44500,000 6 19 0.0035 0.0660 0.045019 23 0.0300 0.1310 0.000 6 21 0.0050 0.0900 0.0226 19 24 0.0300 0.1250 0.002 7 8 0.0012 0.0069 0.0001 19 25 0.1190 0.2249 0.004 7 9 0.0009 0.0429 0.025020 21 0.0657 0.15700.000 8 12 0.0020 0.0180 0.020020 22 0.0150 0.0366 0.000 9 10 0.0010 0.0493 0.001021 24 0.0476 0.1510 0.000 10 12 0.0024 0.0132 0.0100 22 23 0.0290 0.0990 0.000 10 19 0.0547 0.2360 0.000022 24 0.0310 0.0880 0.000 10 20 0.0066 0.0100 0.001023 25 0.0987 0.1168 0.000 17 1 Voltage magnitude, generation schedule, and the reactive power limits for the regu- lated buses are tabulated below. Bus 1, whose voltage is specified as Vi = 1,02570", is taken as the slack bus. CENERATION DATA Bus Voltage Generation Mvar Limits No. Mag. MW Min Max. 1.025 2 1.020 79.0 40.0 250.0 3 1.025 20.0 40.0 150.0 4 1.050 100.0 40.0 80.0 5 1.045 300.0 40.0 160.0 26 1.015 60.0 15.0 50.0 The Mvar of the shunt capacitors installed at substations and the transformer tap settings are given below. SHUNT CAPACITORS TRANSFORMER TAP Bus No. Mvar 4.0 Designation Tap Setting 2-3 4 2.0 0.960 5.0 2-13 5 0.960 3- 13 6 2.0 1.017 4 - 8 11 1.5 1.050 4 - 12 12 2.0 1.050 6 - 19 15 0.5 0.950 19 5.0 0.950 The line and transformer data containing the series resistance and reactance in per unit and one-half the total capacitance in per unit susceptance on a 100-MVA base are tabulated below. Slack G G 2 3 126 13 18 6 7 4 9 12 16 25 19 11 10 23 24 15 22 20 21 17 FIGURE 61 One-line diagram for Problem 6.14. 6.14. The 26-bus power system network of an electric utility company is shown in Figure 61. Obtain the power flow solution by the following methods: (a) Gauss-Seidel power flow (see Example 6.9). (b) Newton-Raphson power flow (see Example 6.11). (c) Fast decoupled power flow (see Example 6.13). 1 The load data is as follows. LOAD DATA Bus Load Bus No. MW Mvar No. 51.0 41.0 14 2 22.0 15.0 15 3 64.0 50.0 16 4 25.0 10.0 17 5 50.0 30.0 18 6 76.0 29.0 19 7 0.0 0.0 20 8 0.0 0.0 21 9 89.0 50.0 22 10 0.0 0.0 23 11 25.0 15.0 24 89.0 48.0 25 13 31.0 15.0 26 Load MW Mvar 24.0 12.0 70.0 31.0 55.0 27.0 78.0 38.0 153.0 67.0 75.0 15.0 48.0 27.0 46.0 23.0 45.0 22.0 25.0 12.0 54.0 27.0 28.0 13.0 40.0 20.0 12 R, 1 1 LINE AND TRANSFORMER DATA Bus Bus R X, Bus Bus X, No. No. pu pu pu No. No. pu pu pu 2 0.0005 0.0048 0.0300 10 22 0.0069 0.0298 0.005 18 0.0013 0.0110 0.0600 | 11 25 0.0960 0.2700 0.010 2 3 0.0014 0.0513 0.060011 26 0.0165 0.0970 0,004 2 7 0.0103 0.0586 0.018012 14 0.0327 0.0802 0.000 2 8 0.0074 0.0321 0.0390 12 15 0.0180 0.0598 0.000 2 13 0.0035 0.0967 0.0250 13 14 0.0016 0.0271 0.001 2 26 0.0323 0.1967 0.000013 15 0.0116 0.0610 0.000 3 13 0.0007 0.0051 0.0005 13 16 0.0179 0.0888 0.001 4 8 0.0008 0.0240 0.0001 14 15 0.0069 0.0382 0.000 4 12 0.0016 0.0207 0.0150 15 16 0.0209 0.0512 0.000 5 6 0.0069 0.0300 0.0900 16 17 0.0990 0.0600 0.000 6 7 0.0053 0.0306 0.0010 16 20 0.0239 0.0585 0.000 11 0.0097 0.0570 0.0001 18 0.0032 0.0600 0.038 6 18 0.0037 0.0222 0.0012 17 21 0.2290 0.44500,000 6 19 0.0035 0.0660 0.045019 23 0.0300 0.1310 0.000 6 21 0.0050 0.0900 0.0226 19 24 0.0300 0.1250 0.002 7 8 0.0012 0.0069 0.0001 19 25 0.1190 0.2249 0.004 7 9 0.0009 0.0429 0.025020 21 0.0657 0.15700.000 8 12 0.0020 0.0180 0.020020 22 0.0150 0.0366 0.000 9 10 0.0010 0.0493 0.001021 24 0.0476 0.1510 0.000 10 12 0.0024 0.0132 0.0100 22 23 0.0290 0.0990 0.000 10 19 0.0547 0.2360 0.000022 24 0.0310 0.0880 0.000 10 20 0.0066 0.0100 0.001023 25 0.0987 0.1168 0.000 17 1 Voltage magnitude, generation schedule, and the reactive power limits for the regu- lated buses are tabulated below. Bus 1, whose voltage is specified as Vi = 1,02570", is taken as the slack bus. CENERATION DATA Bus Voltage Generation Mvar Limits No. Mag. MW Min Max. 1.025 2 1.020 79.0 40.0 250.0 3 1.025 20.0 40.0 150.0 4 1.050 100.0 40.0 80.0 5 1.045 300.0 40.0 160.0 26 1.015 60.0 15.0 50.0 The Mvar of the shunt capacitors installed at substations and the transformer tap settings are given below. SHUNT CAPACITORS TRANSFORMER TAP Bus No. Mvar 4.0 Designation Tap Setting 2-3 4 2.0 0.960 5.0 2-13 5 0.960 3- 13 6 2.0 1.017 4 - 8 11 1.5 1.050 4 - 12 12 2.0 1.050 6 - 19 15 0.5 0.950 19 5.0 0.950 The line and transformer data containing the series resistance and reactance in per unit and one-half the total capacitance in per unit susceptance on a 100-MVA base are tabulated below. Slack G G 2 3 126 13 18 6 7 4 9 12 16 25 19 11 10 23 24 15 22 20 21 17 FIGURE 61 One-line diagram for Problem 6.14