Transmission Line Fault Analysis using Bus Impedance Matrix Method

Transcription

1 Transmission Line Fault Analysis using Bus mpedance Matrix Method Prajakta. Dhole 1 First Year Engineering Department, JSPM's mperial College of Engg. & Research, Wagholi, Pune Savitribai Phule Pune University, Pune, ndia Farina S. Khan 1 First Year Engineering Department, JSPM's mperial College of Engg. & Research, Wagholi, Pune Savitribai Phule Pune University, Pune, ndia Abstract -- The ult analysis is done for the three phase symmetrical ult and the unsymmetrical ults. The unsymmetrical ults include single line to ground, line to line and double line to ground ult. The method employed is bus impedance matrix which has certain advantages over thevenin s equivalent method. The advantage of this approach over conventional method is to make the analysis of three typical un-symmetrical ults, namely single-line-to-ground ult, line-to-line ult and double-line-to-ground ult more unified. So it is unnecessary to cumbersomely connect three sequence networks when calculating the ult voltages at each bus and ult currents flowing from one bus to its neighboring bus. Keywords- Bus impedance matrix; ult analysis; ult impedance; thevenin s equivalent.. NTRODUCTON The steady state operating mode of a power system is balanced 3-phase ac. However due to sudden external or internal changes in the system, this condition is disrupted. When the insulation of the system ils at one or more points or a conducting object comes in contact with a live point, a short circuit or ult occurs. A ult involving all the three phases is known as symmetrical (balanced) ult while one involving only one or two phases is known as unsymmetrical ult. Majority of the ults are unsymmetrical. Fault calculations involve finding the voltage and current distribution throughout the system during the ult. t is important to determine the values of system voltages and currents during ult conditions so that the protective devices may be set to detect the ult and isolate the ulty portion of the system.. FAULTS N A THREE PHASE SYSTEM 1. Symmetrical three-phase ult. Single line-to-ground ult (SLG) 3. Line-to-line ult (LL) 4. Double line-to-ground ult (DLG) The most common type of ults by r is the SLG ult, followed in frequency of occurrence by the LL ult, DLG ult, and three-phase ult. Out of the above four ults, two are of the line-toground ults. Most of these occur as a result of insulator flashover during electrical storms. The balanced threephase ult is the rarest in occurrence and the least complex in so r as the ult current calculations are concerned. The other three unsymmetrical ults will require the knowledge and use of symmetrical components. Unsymmetrical ults cause unbalanced currents to flow in the system. The method of symmetrical components is a very powerful tool which makes the calculations of unsymmetrical ults almost as easy as the calculations of a three-phase ult. To analyze un-symmetrical ults, one needs to develop positive-, negative-, and zero-sequence networks of the power system under study, based on which one further need to work out the impedance of three thevenin equivalent circuits as viewed from ulty point. Then the positive-, negative- and zero-sequence components of phase-a ulty-point-to-ground current can be calculated. To calculate three-phase currents flowing from one bus to its neighboring bus and three-phase voltages at each bus, one needs to connect three sequence networks uniquely for each type of ult. This may make circuit drawing very cumbersome. Furthermore by using the network with three sequence networks connected, it is impossible to appreciate the impedance matrix approach to calculate the sequence voltage at each bus when ult occurs. To overcome these two drawbacks, paper [1] introduces a new approach to unify the analysis of three typical unsymmetrical ults, namely single-line-to-ground ult, line-to-line ult and double-line-to-ground ult. This new method allows the analysis of three typical un-symmetrical ults to share all steps except one. The only different step is how to calculate the positive-, negative-, and zerosequence components of phase-a-to-ground ult current at ulty point. t also makes impedance matrix approach more understandable when used to calculate the sequence voltages at each bus. 948

2 All the above four ults (1,, 3, 4) are being solved using the bus impedance matrix. Fig. 3. Double line to ground ult Fig. 1. Single line to ground ult. BUS MPEDANCE MATRX METHOD We can work out a universal representation of all three typical un-symmetrical ults. This representation is valid with the imposition of different ult conditions for each typical un-symmetrical ult, such as for the single-line-toground ult, such as for the single-line-to-ground ult, the ult conditions being kaz f, fb fc. Fig.. Line to line ult n the following formulation, per-unit system is adopted. Zero-sequence voltage at each bus contributed by equivalent current source is determined by Y11 Y 1 1k 1n Y1 Y k n Yk1 Y k kn - Y n1 Y n nk nn where Y Y Y Y Y Y Y Y Y k1 k kn 949

3 is the admittance matrix for the sub-transient or transient zero-sequence network. Then Y11 Y 1 1k 1n Y1 Y k n Yk1 Y k - kn Yn1 Y n nk nn Where, Z - Z Z.. Z.. Z Z Z.. Z.. Z Z Z Z.. Z.. Z Z Z.. Z.. Z k1 k kn Z Z.. Z.. Z Z Z.. Z.. Z Z Z.. Z.. Z Z Z.. Z.. Z k1 k kn So -Z1k -Zk -Z -Znk n a similar way, positive-sequence voltage at each bus contributed by equivalent current source as is determined by Y Y Y Y Y Y Y Y k1 k kn This gives Z Z.. Z.. Z Z Z.. Z.. Z Z Z.. Z.. Z Z Z.. Z.. Z k1 k kn Z1k -Zk -Z -Znk f pre-ult current is ignored, then the pre-ult voltage at each bus is the same and equal to that at ult bus k before ult occurs, which is assumed to be f. So the positive sequence voltage at each bus when ult occurs can be written as follows. 95

4 k 1 1 n f -Z1k f -Zk + f -Z f -Znk tem Base MA oltage Rating X 1 X X G1 1 k G 1 k T1 1 / k T 1 / k TL1 1 k TL 1 k TL3 1 k f -Z1k 1 1 f -Zk 1 1 f -Z 1 1 f -Znk n a similar way, the negative-sequence voltage at each bus can be computed by -Z1k -Zk -Z -Znk Z Z.. Z.. Z Z Z.. Z.. Z Z Z Z.. Z.. Z Z Z.. Z.. Z k1 k kn Fig. 4. Single line diagram 1. MATHEMATCAL ANALYSS A. Sequence impedance networks Firstly let us obtain the sequence impedance networks. From the data given in table 4.1 the following positive, negative and zero sequence impedance networks are obtained in fig.4.6, 4.7 and 4.8 respectively. TABLE. POWER SYSTEM NETWORK PARAMETERS Fig. 5. Positive Sequence impedance network 951

5 Fig. 6. Negative Sequence impedance network Fig. 9. Positive Sequence admittance network -j j8 j Ybus Y bus j8 -j16 j4 j6.667 j4 -j1.667 Fig. 7. Zero Sequence impedance network Fig. 1. Zero Sequence admittance network -j8.69 j j.8571 Y bus j j j1.435 j.8571 j j4.66 B. MPEDANCE MATRCES The impedance matrices are obtained from the admittance matrices. Fig. 8. Positive Sequence admittance network Z 1 bus Z bus j.145 j.15 j.13 j.15 j.145 j.1 j.13 j.1 j. j.18 j.545 j.14 Z bus j.545 j.864 j.65 j.14 j.65 j.35 95

6 C. Single Line To Ground Fault At Bus 3 Through A Fault mpedance Of J.1 When single line to ground ult occurs, the sequence components of ult current at bus three are given by 1 The ult current is () Z +Z +Z +3Z k 1 f () 3 1 Z 33+Z 33+Z 33+3Zf 1 j.+j.+j.35+3(j.1) 1 j1.9 -j.9174 p.u. a b c 3 3(-j.9174) -j At bus 1 -Z ()-Z13 -j.14(-j.9174) 3 1-j.13(-j.9174) Z13 3 -j.13(-j.9174).1193 At bus -Z3 3 -j.65(-j.9174) ()-Z3 3 1-j.1(-j.9174) Z3 3 -j.1(-j.9174).111 At bus3 -Z j.35(-j.9174) ()-Z333 1-j.(-j.9174).798 -Z33 3 -j.(-j.9174).18 The voltages during ult are At bus 1 a b 1 c At bus a b 1 c At bus 3 a b 1 c The symmetrical components of voltages during ult at buses 1, and 3 953

7 CONCLUSON This paper presents a method to tackle typical unsymmetrical ults. t is found that the bus impedance matrix method involves comparatively less computations than the thevenin s equivalent method. The proposed approach has another advantage over traditional method that it is more intuitive when matrix approach is adopted to tackle a ult problem.. REFERENCES [1] Daming Zhang, An alternative approach to analyze unsymmetrical ults in power system. TENCON 9, from ieeexplore. [] B. R. Gupta, Power System Analysis and Design, published by S. Chand and Company Ltd., p