Chapter 10 Symmetrical Faults

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Note that V 1 (F) denotes the voltage at bus 1 during the fault and V 1 (0) denotes the voltage at bus 1 before the fault i.e. the pre-fault voltage. Similarly V 2 (F) = V 2 (0) + V 2 = 1 – 0.32 = 0.68 pu V 3 (F) = V 3 (0) + V 3 = 1 – 0.68 = 0.32 pu (c) The line currents are calculated as follows: For the line between bus 1 and bus 2 I 12 (F) = = I 13 (F) = = -j0.1 pu = I 23 (F) = = -j1.1 pu = = -j0.9 pu <strong>Symmetrical</strong> Fault Analysis using the Bus Impedance Matrix Solving the faulted network using Thevenin’s method involves reducing the network and is not efficient and applicable to large networks. A more efficient method involves using 6
nodal analysis where the elements of the bus impedance matrix are used to calculate the fault currents and bus voltages during the fault. In chapter 7 the injected bus currents in terms of bus voltages for a n-bus network was calculated as I bus = Y bus V bus (1) I bus is the bus current vector entering the bus and Y bus is the bus admittance matrix. The diagonal element of the i th bus is the sum of the admittances connected to the i th bus: Y ii = with j i The off diagonal element is equal to the negative of the admittance between bus i and the other buses connected to it: Y ij = Y ji = -y ij where y ij is the admittance between bus i and bus j. For a fault at bus k, the current entering every bus except the faulted bus k is zero thus equation 1 becomes = Equation (2) can be written as (2) I bus (F) = Y bus V bus (3) Solving for the bus voltage changes in equation (3) gives V bus = Y bus -1 I bus (F) = Z bus I bus (F) (4) Z bus = Y bus -1 is the bus impedance matrix The bus voltages during the fault are obtained by adding (superposition) the pre-fault bus voltages and the bus voltage changes during the fault, as shown below V bus (F) = V bus (0) + V bus (5) Substituting (4) into equation (5) gives 7
Page 1 and 2: Chapter 10 Symmetrical Faults Intro
Page 3 and 4: Bus 1 X 12 =J0.8 X G1 =J0.2 X G2 =
Page 5: Z 33 = Z eq + Z 3s = j0.34 pu From
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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