Fault location in multi-terminal tapped lines

Abstract

A device can be used with a power transmission system that includes three section that are connected at a junction, each section being from a corresponding. An input interface receives measurements of voltages and currents carried out at one or more of the first terminal, the second terminal and the third terminal or positive sequence voltage and current phasors obtained from the measurements of voltages and currents carried out at one or more of the first terminal, the second terminal and the third terminal. A phasor calculation module calculates positive sequence voltage and current phasors from the measurements of voltages and currents carried out at a terminal of the power transmission system. A fault locator obtains the fault location based on the section with the fault, the positive sequence voltage and current phasors obtained for each terminal, and the positive sequence line impedance parameters of each section.

Claims

1. A device for use in a power transmission system comprising a multiterminal tapped line, wherein the power transmission system comprises a first section, a second section and a third section that are connected at a junction, the first section being from a first terminal to the junction, the second section being from a second terminal to the junction, and the third section being from a third terminal to the junction, wherein the device is configured to determine a fault located in the first section, the second section or the third section, the device comprising: an input interface for receiving one or more of: measurements of voltages and currents carried out at one or more of the first terminal, the second terminal and the third terminal; and positive sequence voltage and current phasors obtained from the measurements of voltages and currents carried out at one or more of the first terminal, the second terminal and the third terminal; a phasor calculation module for calculating positive sequence voltage and current phasors from the measurements of voltages and currents carried out at a terminal of the power transmission system; a storage with positive sequence line impedance parameters of each section of the power transmission system; and a fault locator for obtaining the fault location based on the section with the fault, the positive sequence voltage and current phasors obtained for each terminal, and the positive sequence line impedance parameters of each section.

2. The device of claim 1, wherein the fault locator is configured to obtain the fault location by calculating an inverse hyperbolic tangent of K1/K2, wherein K1 and K2 are calculated from one or more of the positive sequence voltage and current phasors of each terminal and from the positive sequence line impedance parameters of each section.

3. The device of claim 2, wherein the positive sequence line impedance parameters comprises parameters associated with charging currents.

4. The device of claim 1, wherein K1 and K2 are obtained by equating the current flowing at the junction end in the first, second and third sections; wherein, for the two sections that are the sections other than the section with the fault, the current flowing into the junction is calculated with at least the positive sequence voltage and current phasors obtained from measurements carried out at the corresponding terminals and the positive sequence line impedance parameters of the corresponding sections; and wherein in the section with the fault, the current at the junction end is calculated as a function of the unknown fault location with at least the positive sequence voltage and current phasors obtained from measurements carried out at the corresponding terminal and the positive sequence line impedance parameters of the corresponding section.

5. The device of claim 4, wherein the current at the junction end of the section with the fault is calculated by: calculating the voltage at the fault location from a two port network between the corresponding terminal and the fault location; and calculating the current at the junction end from a two port network between the fault location and the junction, using the voltage at the fault location.

6. The device of claim 1, wherein the device is an Intelligent Electronic Device associated with one of the first terminal, the second terminal, and the third terminal, wherein the Intelligent Electronic Device is configured to: obtain measurements of voltages and currents carried out at the corresponding terminal; obtain positive sequence voltage and current phasors from the measurements of voltages and currents carried out at the corresponding terminal; and receive positive sequence voltage and current phasors obtained from the voltage and current measurements carried out at the other terminals, from Intelligent Electronic Devices associated with the corresponding terminals.

7. The device of claim 1, further comprising a fault section identification module for determining the section having the fault, from the positive sequence voltage and current phasors obtained from the measurements of voltages and currents carried out at each terminal of the power transmission system after the fault has occurred in the power transmission system, wherein the section with the fault is determined by: calculating a voltage phasor for each terminal of the power transmission system, wherein the calculation of the voltage phasor for a terminal is performed using the current phasor of the corresponding terminal and at least the voltage and current phasors obtained for at least one other terminal of the power transmission system; and determining the section having the fault, based on a comparison of the calculated and obtained voltage phasors for each terminal.

8. The device of claim 7, wherein the section with the fault is determined by comparing the difference between the calculated and obtained voltage phasors for each terminal.

9. A device for use in a power transmission system comprising a multiterminal tapped line, wherein the power transmission system comprises a first section, a second section and a third section that are connected at a junction, the first section being from a first terminal to the junction, the second section being from a second terminal to the junction, and the third section being from a third terminal to the junction, wherein the device is configured to determine a fault located in the first section, the second section or the third section, the device comprising: an input interface configured to receive measurements of voltages and currents carried out at one or more of the first terminal, the second terminal and the third terminal, or positive sequence voltage and current phasors obtained from the measurements of voltages and currents carried out at one or more of the first terminal, the second terminal and the third terminal; a storage with positive sequence line impedance parameters of each section of the power transmission system; a processing unit coupled to the input interface, the processing unit comprising one or more processors; a non-transitory storage medium storing a program that, when executed by the processing unit causes the processing unit to: calculate positive sequence voltage and current phasors from the measurements of voltages and currents carried out at a terminal of the power transmission system; and obtain the fault location based on the section with the fault, the positive sequence voltage and current phasors obtained for each terminal, and the positive sequence line impedance parameters of each section, wherein the fault location is obtained by calculating an inverse hyperbolic tangent of K1/K2, wherein K1 and K2 are calculated from one or more of the positive sequence voltage and current phasors of each terminal and from the positive sequence line impedance parameters of each section.

10. The device of claim 9, wherein K1 and K2 are obtained by equating the current flowing at the junction end in the first, second and third sections; wherein, for the two sections that are the sections other than the section with the fault, the current flowing into the junction is calculated with at least the positive sequence voltage and current phasors obtained from measurements carried out at the corresponding terminals and the positive sequence line impedance parameters of the corresponding sections; wherein in the section with the fault, the current at the junction end is calculated as a function of the unknown fault location with at least the positive sequence voltage and current phasors obtained from measurements carried out at the corresponding terminal and the positive sequence line impedance parameters of the corresponding section; and wherein the current at the junction end of the section with the fault is calculated by calculating the voltage at the fault location from a two port network between the corresponding terminal and the fault location and calculating the current at the junction end from a two port network between the fault location and the junction, using the voltage at the fault location.

11. The device of claim 9, wherein the device is an Intelligent Electronic Device associated with one of the first terminal, the second terminal, and the third terminal, wherein the Intelligent Electronic Device is configured to: obtain measurements of voltages and currents carried out at the corresponding terminal; obtain positive sequence voltage and current phasors from the measurements of voltages and currents carried out at the corresponding terminal; and receive positive sequence voltage and current phasors obtained from the voltage and current measurements carried out at the other terminals, from Intelligent Electronic Devices associated with the corresponding terminals.

12. The device of claim 9, further comprising a fault section identification module for determining the section having the fault, from the positive sequence voltage and current phasors obtained from the measurements of voltages and currents carried out at each terminal of the power transmission system after the fault has occurred in the power transmission system, wherein the section with the fault is determined by: calculating a voltage phasor for each terminal of the power transmission system, wherein the calculation of the voltage phasor for a terminal is performed using the current phasor of the corresponding terminal and at least the voltage and current phasors obtained for at least one other terminal of the power transmission system; and determining the section having the fault, based on a comparison of the calculated and obtained voltage phasors for each terminal.

13. The device of claim 12, wherein the section with the fault is determined by comparing the difference between the calculated and obtained voltage phasors for each terminal.

14. A method for determining a fault in a power transmission system comprising a multiterminal tapped line, wherein the power transmission system comprises a first section, a second section and a third section that are connected at a junction, the first section being from a first terminal to the junction, the second section being from a second terminal to the junction, and the third section being from a third terminal to the junction, the method comprising: receiving measurements of voltages and currents carried out at one or more of the first terminal, the second terminal and the third terminal or positive sequence voltage and current phasors obtained from the measurements of voltages and currents carried out at one or more of the first terminal, the second terminal and the third terminal; calculating positive sequence voltage and current phasors from the measurements of voltages and currents carried out at a terminal of the power transmission system; storing positive sequence line impedance parameters of each section of the power transmission system; and obtaining a fault location in the first section, the second section or the third section based on the positive sequence voltage and current phasors obtained for each terminal and the positive sequence line impedance parameters of each section.

15. The method of claim 14, wherein obtaining the fault location comprises calculating an inverse hyperbolic tangent of K1/K2, wherein K1 and K2 are calculated from one or more of the positive sequence voltage and current phasors of each terminal and from the positive sequence line impedance parameters of each section.

16. The method of claim 15, wherein the positive sequence line impedance parameters comprises parameters associated with charging currents.

17. The method of claim 14, wherein K1 and K2 are obtained by equating the current flowing at the junction end in the first, second and third sections; wherein, for the two sections that are the sections other than the section with the fault, the current flowing into the junction is calculated with at least the positive sequence voltage and current phasors obtained from measurements carried out at the corresponding terminals and the positive sequence line impedance parameters of the corresponding sections; and wherein in the section with the fault, the current at the junction end is calculated as a function of the unknown fault location with at least the positive sequence voltage and current phasors obtained from measurements carried out at the corresponding terminal and the positive sequence line impedance parameters of the corresponding section.

18. The method of claim 17, wherein the current at the junction end of the section with the fault is calculated by: calculating the voltage at the fault location from a two port network between the corresponding terminal and the fault location; and calculating the current at the junction end from a two port network between the fault location and the junction, using the voltage at the fault location.

19. The method of claim 14, wherein method is performed by an Intelligent Electronic Device associated with one of the first terminal, the second terminal, and the third terminal, wherein the Intelligent Electronic Device performs the steps of: obtaining measurements of voltages and currents carried out at the corresponding terminal; obtaining positive sequence voltage and current phasors from the measurements of voltages and currents carried out at the corresponding terminal; and receiving positive sequence voltage and current phasors obtained from the voltage and current measurements carried out at the other terminals, from Intelligent Electronic Devices associated with the corresponding terminals.

20. The method of claim 14, further comprising determining the section having the fault, from the positive sequence voltage and current phasors obtained from the measurements of voltages and currents carried out at each terminal of the power transmission system after the fault has occurred in the power transmission system, wherein the section with the fault is determined by: calculating a voltage phasor for each terminal of the power transmission system, wherein the calculation of the voltage phasor for a terminal is performed using the current phasor of the corresponding terminal and at least the voltage and current phasors obtained for at least one other terminal of the power transmission system; and determining the section having the fault, based on a comparison of the calculated and obtained voltage phasors for each terminal.

21. The method of claim 20, wherein the section with the fault is determined by comparing the difference between the calculated and obtained voltage phasors for each terminal.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) The subject matter of the invention will be explained in more detail in the following text with reference to exemplary embodiments which are illustrated in attached drawings in which:

(2) FIG. 1 is a simplified representation of a power transmission system, in accordance with an embodiment of the invention;

(3) FIG. 2 is a simplified representation of a connection of an intelligent electronic device for obtaining measurements from a line, in accordance with an embodiment of the invention;

(4) FIG. 3 is a simplified block diagram of a device for fault location, in accordance with an embodiment of the invention;

(5) FIG. 4 is a flowchart of a method for fault location, in accordance with an embodiment of the invention; and

(6) FIG. 5 is a simplified representation of a fault on section AJ of the power transmission system, in accordance with an embodiment of the invention.

DETAILED DESCRIPTION

(7) Various aspects of the present invention relate to fault location in a power transmission system. The power transmission system comprises a multi-terminal tapped line (multi-terminal line), which has three or more terminals.

(8) Referring to FIG. 1, which illustrates a multi-terminal tapped line (also referred as tapped line) connecting three terminals in accordance with an embodiment of the invention. The transmission system shown in FIG. 1 is a three terminal system. Bus A (first terminal), Bus B (second terminal) and Bus C (third terminal) are the three terminals and J is the junction. There could also be more than one junction (e.g. two or more) in case of multiple line sections between the terminals (not shown in FIG. 1). There are three sections in the system shown in FIG. 1. The first section (AJ) is from bus A and the junction, the second section is from bus B to the junction, and the third section is from bus C to the junction.

(9) The invention provides a device and method for fault location in such a power transmission system. The fault location is performed in response to a fault in the system. The method is performed with one or more processors associated with the device. For example, the method can be implemented by an Intelligent Electronic Device (IED) with a processor. This may be an IED associated with one of a line section, a junction, a terminal etc. An example is illustrated in FIG. 2, wherein the IED (202) is associated with Bus A. The IED receives one or more signals from one or more measurement equipment connected to the line. In the example of FIG. 2, a current transformer (CT) provides single/multiple phase current signal and a potential transformer (PT) provides single/multiple phase voltage signal to the IED.

(10) In an embodiment, the IED receives a signal(s) from the measurement equipment, and obtain measurements therefrom. In another embodiment, the measurement equipment publishes the measurements over a bus (e.g. process bus), and the IED (e.g. subscribed to receive data from such bus) receives the measurements over the bus.

(11) The IED also communicates with IEDs associated with other buses (i.e. Bus B, C). Here, the IED at bus A may receive measurements, or phasors obtained at other IEDs. Similarly, the IED at bus B would receive information from IED at buses A and/or C, and IED at bus C would receive information from IED at buses A and/or B.

(12) In an embodiment, the device has a plurality of modules. FIG. 3 is a simplified block diagram of the device. In accordance with the embodiment illustrated in FIG. 3, the plurality of modules include an input interface (302), a phasor calculation module (304), a fault locator (306), a fault section identification module (308) and a memory (310). The plurality of modules may be implemented using one or more processors. For instance, the one or more processors may be a processor of an IED (e.g. IED 202).

(13) The method may also be implemented with communication between a device associated with the line, and a server. Here, some of the modules may be implemented with one or more processors of the server (e.g. calculations or use of models using measurements from various measurement equipment at various terminals of the line), while the others are performed with one or more processors of the device (e.g. input interface, fault locator etc.). Alternately, the method may be implemented at the server, and the fault location communicated to the IED or other power system device.

(14) The input interface receives one or more of measurements of voltages and currents. Consider that the device is the IED at bus A. In this case, the IED receives the measurements obtained from the measurement equipment at Bus A. Alternately, the input interface can receive a signal(s) from the measurement equipment and obtain measurements therefrom. The input interface also acts as a communication interface for receiving information from other devices. For instance, the measurements may be published over the bus, and the IED subscribes to the same. Taking another example, the IED at bus A can receive information from IED at buses B and C, or other modules (e.g. a phasor calculation module) of other devices (e.g. on the server or other power system devices).

(15) The phasor calculation module calculates positive sequence voltage and current phasors from the measurements of voltages and currents. The phasor calculation module can calculate different phasors from measured data. For example, the phasor calculation module can calculate positive sequence voltage and current phasors from measurements at one terminal (or bus). Such phasors may be obtained using a suitable phasor calculation such as, but not limited to, Fourier calculations. For example, from the calculated voltage phasors, positive sequence quantities are computed using following transformation matrix:

(16) $\left[\begin{array}{c}{V}_{a0}\\ V_{a1}\\ V_{a2}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& a& a^2\\ 1& a^2& a\end{array}\right]\left[\begin{array}{c}{V}_a\\ V_b\\ V_c\end{array}\right]\mathrm{where},a=e^{j120°}=-\frac{1}{2}+j\frac{\sqrt{3}}{2}.$

(17) The calculation of the voltage phasor for a terminal may also be performed for fault section identification, using voltage and current phasors obtained for another terminal, and the current phasor obtained for the same terminal. This is another/second voltage phasor (different from the first phasor that can be calculated from the voltage phasor from the measurement at the same terminal). For example, in case of the three terminal system with, the voltage phasor for the first terminal can be calculated using the voltage and current phasors obtained for the second terminal, and the current phasor obtained the first terminal. Here, in place of using the voltage and current phasors obtained for the second terminal, voltage and current phasors obtained for the third terminal may be used. Alternately, two voltage phasors can be calculated using the second and third terminal measurements along with the first terminal measurements, and one of the two selected.

(18) The storage (of the device or on server) can be any suitable storage for storing different information such as, but not limited to, disturbance records, line parameters etc. Positive sequence line impedance parameters of each section of the power transmission system, is available in the storage. Such parameter information can be stored in the device beforehand (e.g. by operating personnel). This may also be stored in the server or other device, and communicated to the IED for fault location purposes.

(19) The fault locator obtains the fault location based on the section with the fault, the positive sequence voltage and current phasors obtained for each terminal, and the positive sequence line impedance parameters of each section. The fault section identification may optionally be performed with the fault section identification module.

(20) In an embodiment, the section with the fault is determined by calculating a value for a voltage phasor (second phasor mentioned above) for each terminal, and comparing that calculated value with the voltage phasor value (i.e. first phasor obtained from the voltage measurements carried at the terminal). Here, the voltage phasor is calculated for each terminal of the power transmission system. The calculation of the voltage phasor for a terminal is performed using the current phasor of the corresponding terminal and at least the voltage and current phasors obtained for at least one other terminal of the power transmission system.

(21) The fault section information is used for fault location calculations. In an embodiment, the fault locator obtains the fault location by calculating an inverse hyperbolic tangent of K1/K2. Here, K1 and K2 are calculated from one or more of the positive sequence voltage and current phasors of each terminal, and the positive sequence line impedance parameters of each section.

(22) The following describes the method of the invention, various steps of which are implemented using the device (or modules) described hereinabove.

(23) The three-terminal system as shown in FIG. 1 is used for describing the fault location solution explained below. As shown, terminals A, B and C are the first, second and third terminals; sections AJ, BJ and CJ are the first, second and third sections and J is the junction common to all three sections. The respective line lengths of the sections AJ, BJ and CJ are denoted by L.sub.a, L.sub.b and L.sub.c (not shown in FIG. 1).

(24) Positive sequence line impedance parameters of the three sections AJ, BJ and CJ are represented using ABCD parameters. Here, A.sub.AJ.sup.1, B.sub.AJ.sup.1, C.sub.AJ.sup.1 and D.sub.AJ.sup.1 are respectively A, B, C and D parameters of section AJ. Similarly, A.sub.BJ.sup.1, B.sub.BJ.sup.1, C.sub.BJ.sup.1 and D.sub.BJ.sup.1 are respectively A, B, C and D parameters of section BJ, and, A.sub.CJ.sup.1, B.sub.CJ.sup.1, C.sub.CJ.sup.1 and D.sub.CJ.sup.1 are respectively A, B, C and D parameters of section CJ. The line parameters may be obtained and stored beforehand, at 402.

(25) Voltage and current measurements are available from the disturbance recorders (IEDs) at all the three terminals. Voltage and current measurements are recorded at terminal A and post fault positive sequence voltage and current phasors are calculated from these measurements. These are denoted by V.sub.A.sup.1 and I.sub.A.sup.1 respectively (i.e. phasors obtained from measurements at terminal A). Pre-fault positive sequence voltage and current phasors may also be calculated and are denoted by V.sub.Apre.sup.1 and I.sub.Apre.sup.1 respectively. Similarly, post-fault positive sequence voltage and current phasors calculated from measurements at terminal B and C are denoted by V.sub.B.sup.1, I.sub.B.sup.1 and V.sub.c.sup.1, I.sub.c.sup.1 respectively. Pre-fault positive sequence voltage and current phasors may be calculated from measurements at terminal B and C, and are denoted by V.sub.Bpre.sup.1,I.sub.Bpf.sup.1 and V.sub.cpre.sup.1, I.sub.cpre.sup.1 respectively. The phasors can be calculated using the phasor calculation module.

(26) At 404, the section with the fault may be determined. In order to obtain the fault location, it is required to determine which section has the fault. Such determination may be performed using the steps described below, or using other fault section identification methods. These steps are performed with the fault section identification module. It is assumed that the measurements at the three terminals are synchronized.

(27) Step I in Fault Section Identification: Calculate the Voltages at all Three Terminals Using Measurements from the Other Terminals:

(28) The post-fault positive sequence voltage at terminal C is calculated using voltage and current measured at terminal B, and current measured at terminal C, using equation (1)

(29) $\begin{array}{cc}{V}_{\mathrm{C\_calculated}}^1=\frac{D_{BJ}^1*V_B^1-B_{BJ}^1*I_B^1+B_{CJ}^1*I_C^1}{D_{CJ}^1}& \left(1\right)\end{array}$

(30) Similarly, the post-fault voltage at terminal A is calculated using voltage and current measured at terminal C, and current measured at terminal A, using equation (2)

(31) $\begin{array}{cc}{V}_{\mathrm{A\_calculated}}^1=\frac{D_{\mathrm{CJ}}^1*V_C^1-B_{\mathrm{CJ}}^1*I_C^1+B_{\mathrm{AJ}}^1*I_A^1}{D_{AJ}^1}& \left(2\right)\end{array}$

(32) In a similar manner, the post-fault voltage at terminal B is calculated using voltage and current measured at terminal A, and current measured at terminal B, using equation (3)

(33) $\begin{array}{cc}{V}_{\mathrm{B\_calculated}}^1=\frac{D_{AJ}^1*V_A^1-B_{AJ}^1*I_A^1+B_{BJ}^1*I_B^1}{D_{BJ}^1}& \left(3\right)\end{array}$

(34) For calculating post-fault voltage of terminal C, measurements at terminal A may be used in place of measurements of terminal B. Alternately, two phasors can be calculated for comparison purposes (described below). Similar calculations can be performed for other terminals.

(35) Step II in Fault Section Identification: Compare the Calculated Voltage at Each Terminal to the Measured Voltage at the Respective Terminals:

(36) The comparison between the measured and calculated voltages for each terminal can be done using equations (4), (5) and (6):
[ΔV.sub.B2A]=|V.sub.B_calculated.sup.1−V.sub.B.sup.1|  (4)
[ΔV.sub.C2B]=|V.sub.C_calculated.sup.1−V.sub.C.sup.1|  (5)
[ΔV.sub.A2C]=|V.sub.A_calculated.sup.1−V.sub.A.sup.1|  (6)

(37) Step III: Identification of Faulted Section:

(38) Case I: Fault at the Junction

(39) If the fault is at the junction, ideally, the calculated voltages at all three terminals should be equal to the respective measured voltages. That is, ΔV.sub.B2A, ΔV.sub.A2C and ΔV.sub.C2B should be ideally equal to zero. Hence, if ΔV.sub.B2A, ΔV.sub.A2C and ΔV.sub.C2B are less than a small threshold value, c, the fault is identified to be at the junction.

(40) Case II: Fault in Section AJ

(41) If the fault is in section AJ, V.sub.C_calculated.sup.1 calculated from Bus B measurements will be ideally equal to the measured value, V.sub.C.sup.1. That is, ΔV.sub.C2B will be ideally zero.

(42) Case III: Fault in Section BJ

(43) Similarly, if fault is in section BJ, V.sub.A_calculated.sup.1 calculated from Bus C measurements will be ideally equal to the measured value, V.sub.C.sup.1. That is, ΔV.sub.A2C will be ideally zero.

(44) Case IV: Fault in Section CJ

(45) Similarly, if fault is in section CJ, V.sub.B_calculated.sup.1 calculated from Bus A measurements will be ideally equal to the measured value, V.sub.B.sup.1. That is, ΔV.sub.B2A will be ideally zero.

(46) Based on the above, we can conclude the following conditions: If ΔV.sub.B2A, ΔV.sub.A2C and ΔV.sub.C2B<ϵ.fwdarw.Fault at junction If ΔV.sub.C2B is minimum, section AJ has the fault.fwdarw.Fault in section AJ If ΔV.sub.A2C is minimum, section BJ has the fault.fwdarw.Fault in section BJ If ΔV.sub.B2A is minimum, section CJ has the fault.fwdarw.Fault in section CJ

(47) After faulted section is identified, the fault location can be calculated using the appropriate one among the following sub-routines.

(48) Case I: Fault is at the Junction

(49) If fault is at junction, IED A will display length of the section AJ as fault location IED B will display length of the section BJ as fault location IED C will display length of the section CJ as fault location

(50) Case II: Fault in Section AJ

(51) For fault in section AJ, the unknown fault location from terminal A is denoted by d.sub.A. For calculating the fault location, the current flowing into the junction from the terminals corresponding to the healthy sections (406), and at the junction end in the section with the fault (408) needs to be calculated.

(52) Calculate the current flowing into the junction from one of the two terminals corresponding to one of the two healthy sections: Let us take terminal B here. From the two port network between terminal B and the junction J, the current flowing into the junction, I.sub.fB, is calculated as,
I.sub.f.sub.B=C.sub.BJ.sup.1V.sub.B.sup.1+D.sub.BJ.sup.1I.sub.B.sup.1  (7)

(53) Where, C.sub.BJ.sup.1, D.sub.BJ.sup.1—positive sequence ABCD parameters of section BJ

(54) $C_{BJ}^1=-\cosh \left({\gamma }_{BJ}{L}_B\right);D_{BJ}^1=\frac{1}{Z_{CBJ}^1}\sinh \left({\gamma }_{BJ}{L}_B\right)$ Z.sub.CBJ.sup.1—characteristic impedance of section BJ γ.sub.BJ.sup.1—propagation constant of section BJ I.sub.f.sub.B—current flowing into the junction from terminal B

(55) Here, the positive sequence ABCB parameters comprises parameters associated with charging currents (i.e. γ.sub.BJ.sup.1 propagation constant).

(56) Calculate the current flowing into the junction from second of the two terminals corresponding to second of the two healthy sections: Let us take terminal C here. From the two port network between terminal C and the junction J, the current flowing into the junction, I.sub.fC, is calculated as,
I.sub.f.sub.C=C.sub.CJ.sup.1V.sub.C.sup.1+D.sub.CJ.sup.1I.sub.C.sup.1  (8)

(57) Where, C.sub.CJ.sup.1, D.sub.CJ.sup.1—positive sequence ABCD parameters of section CJ

(58) $C_{CJ}^1=-\cosh \left({\gamma }_{CJ}{L}_C\right);D_{\mathrm{CJ}}^1=\frac{1}{Z_{\mathrm{CCJ}}^1}\sinh \left({\gamma }_{\mathrm{CJ}}{L}_C\right)$ Z.sub.CCJ.sup.1—characteristic impedance of section CJ γ.sub.CJ.sup.1—propagation constant of section CJ I.sub.f.sub.C—current flowing into the junction from terminal C

(59) With the knowledge that fault is on section AJ, calculate the current flowing at the junction end on section AJ, namely, I.sub.fA. From the two port network between terminal A and the fault point F (see FIG. 5), calculate the voltage at receiving end F using voltage and current at terminal A. This will be a function of the unknown fault distance.
V.sub.F=A.sub.d.sub.A.sup.1V.sub.A.sup.1+B.sub.d.sub.A.sup.1I.sub.A.sup.1  (9)

(60) Where, A.sub.dA.sup.1=cos h(γ.sub.AJ.sup.1d.sub.A) B.sub.dA.sup.1=−Z.sub.CAJ.sup.1 sin h(γ.sub.AJ.sup.1d.sub.A) d.sub.A—distance to the fault measured from terminal A A.sub.dA.sup.1, B.sub.dA.sup.1—positive sequence ABCD parameters defined for the line up to fault point Z.sub.CAJ.sup.1— characteristic impedance of section AJ γ.sub.AJ.sup.1— propagation constant of section AJ VF—Voltage at F calculated from terminal A

(61) From two-port networks between F and J; and J and B, and using the voltage VF calculated in equation (9), the current I.sub.fA can be calculated as in (10). This will be a function of the unknown fault distance.

(62) $\begin{array}{cc}{I}_{f_A}=\frac{V_F-A_{L_A-d_A}^1\left(A_{BJ}^1{V}_B^1+B_{BJ}^1{I}_B^1\right)}{B_{L_A-d_A}^1}& \left(10\right)\end{array}$

(63) Substituting (9) in (10), we get,

(64) $\begin{array}{cc}{I}_{f_A}=\frac{A_{d_A}^1{V}_A^1+B_{d_A}^1{I}_A^1-A_{L_A-d_A}^1\left(A_{BJ}^1{V}_B^1+B_{BJ}^1{I}_B^1\right)}{B_{L_A-d_A}^1}& \left(11\right)\end{array}$

(65) Where, A.sub.L.sub.A.sub.−d.sub.A.sup.1=cos h(γ.sub.AJ(L.sub.A−d.sub.A)); B.sub.L.sub.A.sub.−d.sub.A.sup.1=−Z.sub.CAJ.sup.1 sin h(γ.sub.AJ(L.sub.A−d.sub.A)) d.sub.A—distance to the fault measured from terminal A A.sub.L.sub.A.sub.−d.sub.A.sup.1B.sub.L.sub.A.sub.−d.sub.A.sup.1—positive sequence ABCD parameters defined for the line upto fault point Z.sub.CAJ.sup.1— characteristic impedance of section AJ γ.sub.AJ.sup.1— propagation constant of section AJ

(66) The sum of all the three currents at the junction is equated to zero to obtain the fault location at 410. Accordingly, equate the sum of all three currents, I.sub.fA, I.sub.fB and I.sub.fC to zero, since the sum of currents at any node is equal to zero. Using this relation, solve for the unknown fault location.
I.sub.f.sub.A+I.sub.f.sub.B+I.sub.f.sub.C  (12)

(67) Substituting (7), (8) and (11) in (12), we get,

(68) 0$\begin{array}{cc}\frac{\begin{array}{c}{A}_{d_A}^1{V}_A^1+B_{d_A}^1{I}_A^1-\\ A_{L_A-d_A}^1\left(\begin{array}{c}{A}_{BJ}^1{V}_B^1+\\ B_{BJ}^1{I}_B^1\end{array}\right)\end{array}}{B_{L_A-d_A}^1}+C_{BJ}^1{V}_B^1+D_{BJ}^1{I}_B^1+C_{CJ}^1{V}_C^1+D_{CJ}^1{I}_C^1=0& \left(13\right)\end{array}$

(69) Simplifying equation (13) further gives,
A.sub.d.sub.A.sup.1V.sub.A.sup.1+B.sub.d.sub.A.sup.1I.sub.A.sup.1−A.sub.L.sub.A.sub.−d.sub.A.sup.1(A.sub.BJ.sup.1V.sub.B.sup.1+B.sub.BJ.sup.1I.sub.B.sup.1)+B.sub.L.sub.A.sub.−d.sub.A.sup.1(C.sub.BJ.sup.1V.sub.B.sup.1+D.sub.BJ.sup.1I.sub.B.sup.1+C.sub.CJ.sup.1V.sub.C.sup.1+D.sub.CJ.sup.1I.sub.C.sup.1)=0  (14)

(70) Substituting for A.sub.L.sub.A.sub.−d.sub.A.sup.1, B.sub.L.sub.A.sub.−d.sub.A.sup.1, A.sub.d.sub.A.sup.1, B.sub.d.sub.A.sup.1 in equation (14), gives equation (15) as below,

(71) $\begin{array}{cc}{V}_A^1\cosh \left({\gamma }_{AJ}{d}_A\right)-Z_{CAJ}^1\sinh \left({\gamma }_{AJ}{d}_A\right)*I_A^1=\cosh \left({\gamma }_{AJ}\left(L_A-d_A\right)\right)*\left(A_{BJ}^1{V}_B^1+B_{BJ}^1{I}_B^1\right)+Z_{CAJ}^1\sinh \left({\gamma }_{AJ}\left(L_A-d_A\right)\right)\left(C_{BJ}^1{V}_B^1+D_{BJ}^1{I}_B^1+C_{\mathrm{CJ}}^1{V}_C^1+D_{\mathrm{CJ}}^1{I}_C^1\right)& \left(15\right)\end{array}$

(72) The cosine and sine hyperbolic terms can be expanded such as,
Sin h(γ.sub.AJ(L.sub.A−d.sub.A))=sin h(γ.sub.AJL.sub.A)cos h(γ.sub.AJL.sub.Ad.sub.A)−cos h(γ.sub.AJL.sub.A)sin h(γ.sub.AJL.sub.Ad.sub.A)

(73) Expanding, the cosine and sine hyperbolic terms in equation (15) and simplifying, we get equation (16),
(C.sub.AJ.sup.1V.sub.A.sup.1−I.sub.A.sup.1A.sub.AJ.sup.1+C.sub.BJ.sup.1V.sub.B.sup.1+D.sub.BJ.sup.1I.sub.B.sup.1+C.sub.CJ.sup.1V.sub.C.sup.1+D.sub.CJ.sup.1I.sub.C.sup.1*sin h(γ.sub.AJ.sup.1d.sub.A)=cos h(γ.sub.AJ.sup.1d.sub.A)*(V.sub.A.sup.1A.sub.AJ.sup.1+I.sub.A.sup.1B.sub.AJ.sup.1−V.sub.B.sup.1A.sub.BJ.sup.1−I.sub.B.sup.1B.sub.BJ.sup.1)  (16)

(74) Simplifying further,

(75) $\frac{\sinh \left({\gamma }_{AJ}^1{d}_A\right)}{\cosh \left({\gamma }_{AJ}^1{d}_A\right)}=\frac{\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}{V}_A^1-V_B^1{A}_{AJ}^1{A}_{BJ}^1-\\ I_B^1{A}_{AJ}^1{B}_{BJ}^1+B_{AJ}^1{C}_{BJ}^1{V}_B^1+\end{array}\\ B_{AJ}^1{D}_{BJ}^1{I}_B^1+B_{AJ}^1{C}_{CJ}^1{V}_C^1+\end{array}\\ B_{AJ}^1{D}_{CJ}^1{I}_C^1\end{array}\right)}{(Z{c}_{AJ}^1*\left(\begin{array}{c}\begin{array}{c}{I}_A^1-C_{AJ}^1{A}_{BJ}^1{V}_B^1-\\ C_{AJ}^1{B}_{BJ}^1{I}_B^1+A_{AJ}^1{C}_{BJ}^1{V}_B^1+\end{array}\\ \begin{array}{c}{A}_{AJ}^1{D}_{BJ}^1{I}_B^1+A_{AJ}^1{C}_{CJ}^1{V}_C^1+\\ A_{AJ}^1{D}_{CJ}^1{I}_C^1\end{array}\end{array}\right)}$

(76) The unknown fault location d.sub.A can be derived from the above equation as,

(77) $\begin{array}{cc}{d}_A=\frac{1}{{\gamma }_{AJ}^1}{\tanh }^{-1}\left(\frac{K1}{K2}\right)& \left(17\right)\end{array}$

(78) Where,
K1=(V.sub.A.sup.1−V.sub.B.sup.1A.sub.AJ.sup.1A.sub.BJ.sup.1−I.sub.B.sup.1A.sub.AJ.sup.1B.sub.BJ.sup.1+B.sub.AJ.sup.1C.sub.BJ.sup.1V.sub.B.sup.1+B.sub.AJ.sup.1D.sub.BJ.sup.1I.sub.B.sup.1+B.sub.AJ.sup.1C.sub.CJ.sup.1V.sub.C.sup.1+B.sub.AJ.sup.1D.sub.CJ.sup.1I.sub.C.sup.1)
K2=(Zc.sub.AJ.sup.1*(I.sub.A.sup.1−C.sub.AJ.sup.1A.sub.BJ.sup.1V.sub.B.sup.1−C.sub.AJ.sup.1B.sub.BJ.sup.1I.sub.B.sup.1−A.sub.AJ.sup.1C.sub.BJ.sup.1V.sub.B.sup.1−A.sub.AJ.sup.1D.sub.BJ.sup.1I.sub.B.sup.1−A.sub.AJ.sup.1C.sub.CJ.sup.1V.sub.C.sup.1−A.sub.AJ.sup.1D.sub.CJ.sup.1I.sub.C.sup.1)

(79) The fault locator can obtain the fault location by calculating the inverse hyperbolic tangent. This may be calculated by making certain assumptions or taking only a limited number of terms in the expansion series for the hyperbolic.

(80) Case III: Fault in Section BJ

(81) For fault in section BJ, the unknown fault location from terminal B is denoted by d.sub.B. Like in case of section AJ, calculate currents at the junctions on all three sections. Equate the sum of all three currents to zero and solve for unknown fault distance as in equation (18)

(82) $\begin{array}{cc}{d}_B=\frac{1}{{\gamma }_{BJ}^1}{\tanh }^{-1}\left(\frac{K1}{K2}\right)& \left(18\right)\end{array}$

(83) Where,
K1=(V.sub.B.sup.1−V.sub.A.sup.1A.sub.AJ.sup.1A.sub.BJ.sup.1−I.sub.A.sup.1A.sub.BJ.sup.1B.sub.AJ.sup.1+B.sub.BJ.sup.1C.sub.AJ.sup.1V.sub.A.sup.1+B.sub.BJ.sup.1D.sub.AJ.sup.1I.sub.A.sup.1+B.sub.BJ.sup.1C.sub.CJ.sup.1V.sub.C.sup.1+B.sub.BJ.sup.1D.sub.CJ.sup.1I.sub.C.sup.1)
K2=(Zc.sub.BJ.sup.1*(I.sub.B.sup.1−C.sub.BJ.sup.1A.sub.AJ.sup.1V.sub.A.sup.1−C.sub.BJ.sup.1B.sub.AJ.sup.1I.sub.A.sup.1−A.sub.BJ.sup.1C.sub.AJ.sup.1V.sub.A.sup.1−A.sub.BJ.sup.1D.sub.AJ.sup.1I.sub.A.sup.1−A.sub.BJ.sup.1C.sub.CJ.sup.1V.sub.C.sup.1−A.sub.BJ.sup.1D.sub.CJ.sup.1I.sub.C.sup.1)

(84) Case IV: Fault in Section CJ

(85) For fault in section CJ, the unknown fault location from terminal C is denoted by dC. Like the above, equate the sum of all three currents at the junction to zero and solve for unknown fault distance as in equation (19)

(86) $\begin{array}{cc}{d}_{C1}=\frac{1}{{\gamma }_{CJ}^1}{\tanh }^{-1}\left(\frac{K1}{K2}\right)& \left(19\right)\end{array}$

(87) Where,
K1=(V.sub.C.sup.1−V.sub.A.sup.1A.sub.AJ.sup.1A.sub.CJ.sup.1−I.sub.A.sup.1A.sub.CJ.sup.1B.sub.AJ.sup.1+B.sub.CJ.sup.1C.sub.AJ.sup.1V.sub.A.sup.1+B.sub.CJ.sup.1D.sub.AJ.sup.1I.sub.A.sup.1+B.sub.CJ.sup.1C.sub.BJ.sup.1V.sub.B.sup.1+B.sub.CJ.sup.1D.sub.BJ.sup.1I.sub.B.sup.1)
K2=(Zc.sub.CJ.sup.1*(I.sub.C.sup.1−C.sub.CJ.sup.1A.sub.AJ.sup.1V.sub.A.sup.1−C.sub.CJ.sup.1B.sub.AJ.sup.1I.sub.A.sup.1−A.sub.CJ.sup.1C.sub.BJ.sup.1V.sub.B.sup.1−A.sub.CJ.sup.1D.sub.BJ.sup.1I.sub.B.sup.1−A.sub.CJ.sup.1C.sub.AJ.sup.1V.sub.A.sup.1−A.sub.CJ.sup.1D.sub.AJ.sup.1I.sub.A.sup.1)

(88) The invention provides an accurate fault location device and method for multi-terminal/tapped lines using synchronized data from all terminals. The solution identifies the faulted section first, and then points the fault location on the identified section. This invention requires post fault positive sequence voltage and current measurements and positive sequence line parameters only. This invention is independent of source impedances, fault resistance, loading information, phase unbalance, zero sequence parameters, mutual compensation, fault loop information etc.