Chapter 10 Symmetrical Faults

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Bus 1 X G1 =J0.2 X G2 = J0.4 Bus 2 Z 1s =J0.2 S Z 3s =J0.1 Z 2s =J0.2 Bus 3 V th Z f =J0.16 Figure 2: We also observe from the above figure that the branch from star point S to bus 1 to ground and the branch from star point S to bus 2 to ground form a parallel network. The equivalent impedance of the parallel network is Z eq = = = j0.24 pu Combining the parallel branches results in the following network as shown below: Z eq = J0.24 Z 3s =J0.1 Bus 3 V th Z f =J0.16 The Thevenin impedance as viewed from the faulted bus 3 is 4
Z 33 = Z eq + Z 3s = j0.34 pu From the above figure the fault current is I 3 (F) = = = -j2 pu Note that I 3 (F) denotes the current resulting from the fault at bus 3. (b) Before we calculate the bus voltages during the fault, we first calculate the voltage changes at each of the buses during the fault. Considering Figure 2, the fault current is split between the two parallel branches containing bus 1 and bus 2 as follows: I Bus1 = I Bus2 = I 3 (F) = -j1.2 pu I 3 (F) = -j0.8 pu Voltage changes at the three buses due to the fault are then calculated as follows: At bus 1: The direction of fault current opposes to the generator current, so there will be a decrease in the voltage which is indicated with a minus below V 1 = -I bus1 X G1 = -(-j1.2)(j0.2) = -0.24 pu At bus 2: The direction of fault current opposes to the generator current, so there will be a decrease in the voltage which is indicated with a minus below V 2 = -I bus2 X G2 = -(-j0.8)(j0.4) = -0.32 pu At bus 3: The change in voltage is the sum of V th and the volt drop across Z f due to I 3 (f), therefore V 3 = -V th + I 3 (F)Z f = -1 + (-j2)(j0.16) = -0.68 pu The bus voltages during the fault are calculated as follows: V 1 (F) = V 1 (0) + V 1 = 1 – 0.24 = 0.76 pu 5
Page 1 and 2: Chapter 10 Symmetrical Faults Intro
Page 3: Bus 1 X 12 =J0.8 X G1 =J0.2 X G2 =
Page 7 and 8: nodal analysis where the elements o
Page 9 and 10: V i (F) = V i (0) - Z ik I k (F) (9
Page 11 and 12: Y bus = The inverse of the above ma
Page 13 and 14: V 1 (F) = 0.76 and V 3 (F) = 0.32 a
Page 15: = 0.0825 + j0.3163 = 0.327ㄥ75.36

Chapter 10 Symmetrical Faults

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