WO2019229638A1

WO2019229638A1 - Fault location for parallel transmission lines with zero sequence currents estimated from faulted line measurements

Info

Publication number: WO2019229638A1
Application number: PCT/IB2019/054393
Authority: WO
Inventors: Neethu GEORGE; Obbalareddi DEMUDU NAIDU; Swaroop GAJARE; Sachin Srivastava; A.v.s.s.r. SAI
Original assignee: Abb Schweiz Ag
Priority date: 2018-05-31
Filing date: 2019-05-28
Publication date: 2019-12-05

Abstract

The invention provides a method for fault location in a power transmission system, with two terminals connected by parallel transmission lines. The fault is located in a first transmission line. The method comprises obtaining measurements of post-fault voltages and currents at one terminal, and measurements of post-fault currents at another terminal of the first transmission line. The post-fault measurements are used to calculate voltage and current phasors for various fault location values. For estimating the phasors for a fault location value, positive, negative and zero sequence voltage and current phasors are calculated for the fault location value. Here, the zero sequence phasors are calculated from the first line measurements, and zero sequence currents estimated for the second transmission line. The zero sequence currents for the second line are estimated with the zero sequence quantities of the first line measurements and line impedance parameters associated the two lines.

Description

FAULT LOCATION FOR PARALLEL TRANSMISSION LINES WITH ZERO SEQUENCE CURRENTS ESTIMATED FROM FAULTED LINE

MEASUREMENTS

FIELD OF THE INVENTION

[001] The present invention relates to fault location in power transmission systems. More specifically, the present invention relates to fault location in power transmission systems with parallel transmission lines.

BACKGROUND OF THE INVENTION

[002] Transmission lines are often subjected to electrical faults due to bad weather conditions, or failure of power system components. For example, there could be electrical faults due to storms, lightning, snow, freezing rain, insulation breakdown, short circuits because of birds, tree contact with a transmission line and other external objects and so forth. In many fault events, mechanical damages to line equipment need to be repaired before restoring the line into service. Service continuity is one of the most important concerns for utilities. Fast restoration of lines is very important to the utilities. Thus, accurate fault location in transmission lines is very important for maintenance crew to reach the fault point and undertake repair at earliest. Quick identification of fault location can assist in improving reliability, availability of supply and reducing revenue loss for the utilities.

[003] Fault location for parallel transmission lines (also referred as double circuit lines) may be influenced considerably by mutual coupling effect between the two lines (or circuits) especially for unbalanced faults. The fault location may be underestimated or overestimated, based on operation status of the healthy line (i.e. open / connected). In case both the lines are in service, fault location may be overestimated, because the fault current (i.e. current in faulted line) and residual current (i.e. current in healthy line) may flow in same direction. In case one of the two lines (i.e. the healthy line) is opened and grounded at both ends, the fault location may be underestimated, because the fault current and residual current may flow in opposite direction. Hence, to improve the accuracy in estimation of the fault location, compensation for the mutual coupling effect has to be done.

[004] Zero sequence current quantities from the healthy line is also required to achieve this mutual compensation. This can be a challenge, especially in cases where the healthy line is open and grounded, where healthy line current measurements are not available. For these cases the unavailable/unknown healthy line zero sequence current has to be estimated. The existing solutions for fault location in parallel transmission lines, which estimate zero sequence currents for the healthy line use source impedances. Such settings may not be available, and even if available, such values may not be accurate. Even in case the healthy line is connected, there is difficulty in accurately estimating the effect of mutual compensation because of the residual current. As the currents are not uniformly distributed over the line, there is difficulty in accurately obtaining the direction of the faulted current flow, which may not always be in the opposite direction of the healthy line current.

[005] There is accordingly a need for improved fault location based on estimation of zero sequence currents for the healthy line, wherein the estimation is independent of source impedance parameters, to enable mutual compensation. Further, two-ended fault location is preferred over single-ended fault location, due to technical and economic reasons.

SUMMARY OF THE INVENTION

[006] Various aspects of the invention relate to a method for fault location in a power transmission system. The power transmission system may be a two terminal system having two terminals, i.e. a first terminal and a second terminal. The two terminals are connected with parallel transmission lines (also referred as double circuit lines). The parallel transmission lines comprise at least a first transmission line and a second transmission line.

[007] There is an electrical fault (or disturbance) in the power transmission system, i.e. in one of the parallel transmission lines. In accordance with an embodiment, the first transmission line has the fault. Here, it is assumed that the first transmission line is the line having the fault, and the second transmission line is healthy (also referred as healthy circuit). The invention is applicable for fault in any of the parallel lines, and not limited to fault in the first line.

[008] The method for fault location is performed with a device associated with the power transmission system. The method comprises obtaining measurements of post- fault voltages and currents carried out at the first terminal of the first transmission line, and measurements of post-fault currents carried out at the second terminal of the first transmission line. Here, positive, negative and zero sequence quantities are obtained for the measurements. In other words positive sequence voltages / currents, negative sequence voltages / currents and zero sequence voltages / currents are obtained for one end of the faulted line (i.e. first line in accordance with the embodiment), and positive, negative and zero sequence currents for the other end of the faulted line.

[009] The method further comprises calculating voltage and current phasors for a plurality of fault location values based on the measurements. Here, the voltage and current phasors for a fault location value comprise positive, negative and zero sequence voltage and current phasors calculated for the fault location value. The positive sequence voltage and current phasors for a fault location value are calculated from the positive sequence quantities of the measurements and line impedance parameters associated with the first transmission line (faulted line). The negative sequence voltage and current phasors for a fault location value are calculated from the negative sequence quantities of the measurements. The zero sequence voltage and current phasors for a fault location value are calculated from the zero sequence quantities of the measurements, and zero sequence currents estimated for the second transmission line.

[0010] The zero sequence currents for the second transmission line are estimated for each end of the second transmission line, based on the zero sequence quantities of the measurements from first transmission line. The zero sequence currents for the second transmission line are estimated with the measurements of the zero sequence voltages and currents at the first terminal, the measurements of the zero sequence currents at the second terminal and line impedance parameters associated with the first and second transmission lines. Here, self-impedances of each of the two lines, and mutual- impedance between the two lines are considered.

[0011] In accordance with some embodiments, the line impedance parameters associated with the first transmission line comprises self-impedance of the first transmission line, and mutual-impedance between the first and second transmission lines. Similarly, for the second line, the self-impedance of the second line, and mutual- impedances between the lines is considered.

[0012] In accordance with an embodiment, the calculation of the positive, negative and zero sequence phasors for the fault location values, includes compensation for charging currents. The compensation is performed by considering line impedance parameters associated with charging currents. For example, the compensation can be provided by considering capacitance per unit length for a transmission line.

[0013] The voltage and current phasors calculated for the plurality of fault location values are used to estimate the fault location. The location of the fault (fault location) is estimated based on phase differences between the voltage and current phasors calculated for the plurality of fault location values. A phase difference between the voltage and current phasors for a fault location value can be estimated from angles of the voltage and current phasors. In one embodiment, the phase difference is the difference between the angles of the voltage and current phasors. In accordance with the embodiment, the fault location value for which the phase difference is zero is estimated as the location of the fault.

[0014] In accordance with various embodiments, the method is implemented with a device associated with the power transmission system. For example, the device can be an Intelligent Electronic Device (IED) associated with a terminal, or a point of the line. Taking another example, the device is a server connected with various power system devices associated with the parallel transmission lines. In such a case, the server can receive the measurements carried out at terminals of the first transmission line. Further, the IEDs may send measurements / processed information to the server for the purposes of fault location.

[0015] In an embodiment, the device is an IED associated with one of the two terminals. The IED can be associated with the first terminal, or second terminal of the first transmission line (i.e. the faulted line). The IED obtains one or more signals from one or more measurement equipment connected to the line. For example, the measurement equipment can include a current transformer, a potential transformer, a sensor-based measurement equipment (e.g. Rogowski coils, non-conventional instrument transformers etc.) and the like, which provides a signal corresponding to current, voltage or other information as sensed from the line. For example, a current transformer provides single/multiple phase current signal and a potential transformer can provide single/multiple phase voltage signal to the IED.

[0016] In an embodiment, the device is associated with one of the first terminal and the second terminal and receives data from other devices (that are associated with the other terminals). For example, the IED at the first terminal communicates with the IED at the second terminal of the first transmission line. Here, the IED at one terminal obtains the post-fault voltages and currents for the corresponding terminal (or bus), and receives post-fault currents measured at a remote terminal from another IED at the remote terminal. [0017] The device has one or more modules for performing the fault location and other functions of the device. Such modules may be implemented with a processor(s) of the corresponding device. In one embodiment, the device has an interface, a phasor calculator and a fault locator. The device can also have a memory with the line impedance parameters of the parallel transmission lines. The line impedance parameters are associated with self and mutual-impedances of the lines. The line impedance parameters can include parameters for compensating for charging currents (e.g. capacitance).

[0018] The interface obtains the measurements of the post-fault voltages and currents of the first terminal, and the measurements of the post-fault currents of the second terminal. That is the measurements of the post-fault voltages and currents at one end of the faulted line, and the measurements of the post-fault currents at the other end of the faulted line are obtained.

[0019] In case of the device being an IED, the local end measurements include the post-fault voltages and currents, while the remote end measurements include the post- fault currents. In case the device is the server, the measurements for the two terminals are communicated with the server. It is assumed that the various devices that are involved in the fault location are synchronized with each other. In other words, all the measurements required for the fault location estimation are synchronized.

[0020] The phasor calculator obtains positive, negative and zero sequence quantities from the measurements. Here, the calculator can calculate the values from the measurements, or receive the values obtained by another device (i.e. via communication). These quantities and the line impedance parameters associated with the parallel transmission lines are used to calculate the voltage and current phasors for the plurality of fault location values.

[0021] The phasor calculator calculates the positive sequence voltage and current phasors for the fault location values from the positive sequence quantities of the measurements at the first line, and the line impedance parameters associated with the first line (i.e. associated with self-impedances). Similarly, the phasor calculator calculates the negative sequence voltage and current phasors for the fault location values from the negative sequence quantities and the line impedance parameters.

[0022] The phasor calculator estimates zero sequence currents for the second line (healthy line) from the zero sequence quantities obtained from the measurements of the first line, the self-impedances of each of the two lines, and the mutual impedance of the two lines.

[0023] The phasor calculator calculates the zero sequence voltage and current phasors for the fault location values with the zero sequence quantities obtained for the faulted line, the zero sequence currents estimated for the healthy line, and the line impedance parameters of the two lines. Here, the line impedance parameters are associated with the self-impedances of the lines, and the mutual impedances between the lines.

[0024] The fault locator estimates the location of the fault in the first transmission line. The fault location is estimated based on phase differences between the fault point voltage and current phasors for the plurality of fault location values. The phase differences may be estimated by the phasor estimator or the fault locator.

BRIEF DESCRIPTION OF DRAWINGS

[0025] 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:

[0026] Fig. 1 shows a configuration of a power transmission system with parallel transmission lines, in which both lines are in operation; [0027] Fig. 2 shows another configuration of the power transmission system with parallel transmission lines, in which one of the two lines is open and grounded;

[0028] Fig. 3 shows an Intelligent Electronic Device (IED) connected with one or more measurement equipment associated with the power transmission system;

[0029] Fig. 4 is a block diagram of a device for fault location in the power transmission system;

[0030] Fig. 5 is a flowchart of a method for fault location in the power transmission system;

[0031] Fig. 6 shows equivalent positive sequence circuit diagrams for the two configurations of the power transmission system shown in Figs. 1 and 2;

[0032] Fig. 7 shows approximate pi model of zero sequence circuit when both lines of the power transmission system are in operation; and

[0033] Fig. 8 shows equivalent zero sequence circuit diagram when one of the parallel lines of the power transmission system is open and grounded.

DETAILED DESCRIPTION

[0034] Various embodiments of the present invention relate to fault location in a power transmission system. The power transmission system can be a two terminal system as shown in Fig. 1. Bus A (first terminal, or terminal A), and Bus B (second terminal, or terminal B) are the two terminals of the transmission system. The electrical bus A is connected to a source as shown, where the source can be a substation (or generating station). Likewise, the electrical bus B is connected to a source as shown.

[0035] The two terminals (or buses) are connected by parallel transmission lines as shown. In accordance with various embodiments, the transmission system comprises two parallel lines, with a first transmission line (A1B1), and a second transmission line (A2B2). Each of the parallel lines may comprise circuit breakers (not shown) to break the circuit when needed. In an embodiment, each of the two transmission lines may carry a three-phase current. The two transmission lines may be referred as double circuit lines, wherein one line or circuit is fault (faulted / faulty line or faulted / faulty circuit)), while the other is healthy (healthy line / healthy circuit).

[0036] There could be an electrical fault in one of the parallel transmission lines (e.g. first line A1B1, or second line A2B2). The fault location is estimated in response to the electrical fault (or disturbance) in the system (i.e. in one of the lines). The fault location is performed by a device associated with the power transmission system. The method is performed with one or more processors associated with the device. The device may be an Intelligent Electronic Device (IED) associated with a terminal of the faulted line. Alternately, the device may be a server or another device of the power system that receives voltage / current measurements at the ends (or terminals of the faulted line).

[0037] In an embodiment, the method is implemented by an JED associated with a terminal of the faulted line (e.g. terminal A of first transmission line). An example is illustrated in Fig. 3, wherein the JED (302) is associated with Bus A. The JED (302) receives one or more signals from one or more measurement equipment connected to the line. In the example of Fig. 3, a current transformer (CT) provides single/multiple phase current signal and a potential transformer (PT) provides single/multiple phase voltage signal to the IED.

[0038] 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 communication bus (e.g. process bus) or in a communication channel or through suitable interface (e.g., input/output modules), and the JED (e.g. subscribed to receive data from such bus/communication channel) receives the measurements over the communication bus. The IED also communicates with IEDs associated with other electrical buses (i.e. Bus B). 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 bus A.

[0039] In an embodiment, the device has a plurality of modules. 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 302). 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. interface for voltage / current measurements, phasor estimator etc.). Alternately, the method may be implemented at the server, and the fault location communicated to the IED. Here, the server has also information about the line that has the fault (e.g. communicated to the server from IED or other fault line detector), and line parameters of the two lines (including self and mutual impedances, parameters for charging currents etc.).

[0040] Fig. 4 is a simplified block diagram of the device (400). In accordance with the embodiment illustrated in Fig. 4, the plurality of modules includes an interface (402), a memory (404), a phasor calculator (406), and a fault locator (408).

[0041] The interface (402) obtains measurements of voltages and currents, that are measured at the two ends (or terminals) of the line with the fault. Here, the measurements are synchronized measurements. The post-fault voltages and currents at one end (e.g. bus A) of the faulted line, along with post-fault currents at another end (e.g. bus B) of the faulted line are used for the purposes of fault location.

[0042] Consider that the device (400) is the IED (302) at bus A. In this case, the IED receives the measurements obtained from the measurement equipment at Bus A. Alternately, the interface (402) can receive a signal(s) from the measurement equipment and obtain measurements therefrom. The interface also acts as a communication interface for receiving information from other devices (e.g. other IEDs or server). For instance, the measurements may be published over the process bus, and the IED subscribes to the same. Taking another example, the IED at bus A can receive information from IED at buses B or other modules (e.g. a phasor calculator (406)) of other devices (e.g. on the server or other power system devices).

[0043] The memory (404) (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. In one embodiment, the self and mutual impedances for the lines is available with the device. For example, information such as surge impedance of the first and / or second transmission lines, propagation constant of the first and / or second transmission lines, mutual impedances between the lines etc. can be stored. Such parameter information can be stored in the device beforehand (e.g. by an operating personnel). This may also be stored in the server or other power system device for fault location purposes.

[0044] The phasor calculator (406) obtains positive, negative and zero sequence quantities from the measurements. These may be calculated by the phasor calculator or received (communicated) from another device (e.g. IED at other end). The phasor calculator calculates voltage and current phasors for a plurality of fault location values from the positive, negative and zero sequence measurements. For example, voltage and current phasors can be estimated for different values of fault distances (e.g.‘O’,‘L’, ‘L/2’etc. where‘L’ is the line length of the two lines). There could be an optimization with regards to selection of the fault location values for which the phasors are calculated.

[0045] The phasor calculator calculates positive, negative and zero sequence phasors for the fault location values to estimate the voltage and current phasors for the fault location values. The device can calculate the different voltage and current phasors (e.g. using suitable phasor calculation such as Fourier calculations etc.), from the voltage / current measurements carried out at the associated terminals of the faulted line. Positive, negative and zero sequence quantities can be derived by using methods such as symmetrical component analysis etc.

[0046] In accordance with some embodiments, the calculation of the positive and negative sequence voltage and current phasors for the fault location values is performed using the positive and negative sequence quantities/ measurements from the faulted circuit alone. Further, in accordance with the embodiments, the calculation of the zero sequence voltage and current phasors for the fault location values is performed using the zero sequence quantities/ measurements from the faulted circuit (line), and estimate of zero sequence currents for the healthy circuit (line). The zero sequence currents for the healthy line are estimated for each end (i.e. bus A, or bus B) of the line. For an end, the estimation of the zero sequence current is based on the voltages and currents measured at the same (or local) end for the faulted line, the currents measured at the other (or remote) end of the faulted line, and self and mutual impedances of the two lines (described in further details below).

[0047] The fault locator (408) estimates the location of the fault (fault location) based on phase differences between the fault point voltage and current phasors. The phase differences may be estimated by the phasor estimator or the fault locator. A phase difference between the voltage and current phasors for a fault location value can be estimated from the angles of the voltage and current phasors. In one embodiment, the phase difference is the difference between the angles of the voltage and current phasors calculated for the fault location value. In accordance with the embodiment, the fault location value for which the phase difference is zero is estimated as the fault location.

[0048] The following describes the method of the invention, various steps of which are implemented using the device (or modules) (400) described hereinabove. [0049] The method will be described with references to the two terminal system illustrated in Figs. 1 and 2. Fig. 1 shows the case where both the lines (first line A1B1, and second line A2B2) are connected. Fig. 2 shows the case where one line (faulted line) is connected and the other (healthy line) is open and grounded.

[0050] The positive, negative and zero sequence equivalent networks during fault for both the cases of the two terminal double circuit system are analyzed for the fault location method. The positive and negative sequence equivalent networks for each of the cases (Figs. 1, 2) are similar and is presented in Fig. 6. However, while considering the zero sequence equivalent network of both the cases, it can be seen that both are different. For case 1 (Fig. 1), both the lines are mutually coupled and the zero sequence mutual impedance elements can be observed as shown in Fig. 7. For case 2 (Fig. 2), the equivalent circuit can be derived as presented in Fig. 8. Hence, the fault location method considers zero sequence mutual compensation for the two cases. This compensation depends on the cases of the parallel transmission line (double circuit line) as explained using Figs. 7 and 8 below.

[0051] Terminal A and B are the two terminals (or electrical buses) of the system. Line connecting Al to Bl is the first line (referred A1B1 above) and the line connecting A2 to B2 is the second line (referred A2B2 above). Here, both the lines are of length L km. Both the circuits (lines) are mutually coupled. VAI¹, VA2¹, VBI¹ and VB2¹ are the voltages measured at the terminals Al, A2, Bl and B2 respectively. The superscript‘i’ can be equal to 0, 1 or 2, denoting zero, positive and negative sequence quantities respectively. Similarly, IAI¹, , IBI¹ and are the currents measured at the terminals Al, A2, Bl and B2 respectively. The superscript‘i’ can be equal to 0, 1 or 2, denoting zero, positive and negative sequence quantities respectively. ABCD¹ parameters are used to represent the impedance parameters of the line. The superscript‘i’ can be equal to 0, 1 or 2, denoting zero, positive and negative sequence quantities respectively. The subscript ‘m’ wherever used denotes the mutual quantities between the two lines. [0052] At 502, these measurements are obtained for estimating the fault location. The measurements are obtained at the device (e.g. interface 402). As described above, the measurements may be obtained by the IEDs associated with the corresponding terminals, or communicated from IEDs to the server. For example, IED at Al of first line has voltage / current measurements at Al (e.g. from the corresponding measurement equipment), and receives current measurements at Bl from IED at Bl . Here, the IEDs communicate the current measurements (or phasors as estimated based on the measurements).

[0053] The fault is assumed to be located on line 1, connecting terminals Al and Bl, at a fractional distance, d, from the terminal Al . In order to calculate voltage and current phasors for different fault location values (different values for‘d’) at 512, positive, negative and zero sequence voltage and current phasors for fault location values are required. The various phasors may be calculated at the device (i.e. IED or server). Such calculation may be performed by the phasor calculator (406). Here, the phasor calculator can obtain the positive, negative and zero sequence quantities from the measurements to arrive at the voltage and current phasors for the fault location (or point) values.

[0054] At 504, the calculation of positive sequence voltage and current phasors is performed for fault location value(s) (i.e. taking values for fault distance (d)). Since the positive sequence networks of both the circuits of the double circuit line are not mutually coupled, the positive sequence voltage and current phasors for the fault location can be calculated using positive sequence quantities/ measurements from the faulted circuit alone.

[0055] With reference to Fig. 6, using the positive sequence post-fault voltage and positive sequence post-fault current at terminal Al of the faulted circuit, the fault point voltage, V_F ¹ can be calculated using equation (1). Further, the fault current contribution from terminal Al, I_FA ¹ can be calculated using equation (2).

[0056] In the above, A_d ¹, B_d ¹, C_d ¹ and D_d ¹ are ABCD parameters of the first line (A1B1) defined upto the fault location (i.e.‘d’).

A_d =—D_d = cosh

sinh

= VO¹ + jmZ¹)(jmc¹)

[0057] In the above r¹, l ¹ and c ¹ are positive sequence resistance, inductance and capacitance per unit length of the line.

[0058] Using measurements from terminal B 1 , we can calculate the fault point voltage, VF¹ and contribution to fault current from Bl, [J; , as below

(3) ; lF¹B = Cl_®V^_i + Dl__dl_B ¹ ₁ (4)

[0059] Where, AH¹, Bi-_d ¹, Ci-_d ¹ and Di-_d ¹ are ABCD parameters of the line defined from fault location to remote terminal.

A __d =—D __d = cosh(y¹(l— d)L ) ; Bl__d =— Z sinh(y¹(l— d)L ) ; C __d

[0060] In the above r¹, l¹ and c¹ are positive sequence resistance, inductance and capacitance per unit length.

[0061] Substituting

from (3) in (4),

[0062] Substituting V_p from (1) in (5),

[0063] The total fault current can be calculated as, l IF¹—— ^l IF¹A 4 ⁺- ' IF¹B (7)

[0064] Substituting (2) and (6) in (7),

[0066] At 506, the calculation of negative sequence voltage and current phasors for the fault location value(s) is performed. The negative sequence network is similar to positive sequence network and hence negative sequence fault point voltage and fault current can be calculated in the same way as explained in the previous step, just by replacing all positive sequence quantities by negative sequence quantities.

[0067] At 508, the estimation of zero sequence currents in the healthy circuit in terms of the fault location value(s) is performed. This is required to calculate the zero sequence voltage and current phasors for the fault location value(s). Such estimation of the zero sequence currents for the healthy line is performed with the device (e.g. phasor calculator).

[0068] The zero sequence currents are estimated using the zero sequence voltage and current quantities / measurements from local terminal of the faulted line, and the zero sequence current quantities / measurements from the remote terminal of the faulted line.

[0069] Zero sequence impedance parameters (ABCD) including the mutual components can be written as below,

n°

uάί ^udm

n° nO

udm ^uΊ d2^'

[0070] Where, the subscript‘dl’ denotes self-impedance of line 1 till the fault location, subscript‘d2’ denotes self-impedance of line 2 till the fault location, subscript‘dm’ denotes mutual-impedance between both the circuits till the fault location.

[0071] Similarly,

[0072] Where, the subscript‘(l-d)l’ denotes self-impedance of line 1 from fault location to terminal B, subscript‘(l-d)2’ denotes self-impedance of line 2 from fault location to terminal B, subscript‘(l-d)m’ denotes mutual-impedance between both the circuits from fault location to terminal B.

[0073] Now, we have four unknowns namely, VBI°, VB2°, IA2° and IB2°. [0074] For case 1, where both the lines are connected, VBI° = VB2°. For case 2, where healthy line is open and grounded, VB2° = 0.

[0075] Case 1 : Both lines are in service

[0076] Relation 1 :

4° 4° n O n O

dm V°

+ d ₁1 dm l 1 A D°1

4 ⁰

1° dm ^Ά 4°ά v M°2 ‘-'dm B_d°₂ 1 A2

(10)

4° 4 ° r 0

i⁴(l-d)l ^(1— ci)m I/⁰ oO

(l-d)l B ^1J (l-d)m 1°

+ B1

4° 4°

^(l- Om ^i¾(l-d)2 V n O nO

^VB° ^(l-d^m (1-ά)2 / B°2

[0077] Taking the first row in this corresponding to the faulted line, we get

[0078] Since both the lines are connected, substituting, _„o_

VBI° = VB2^U= VB¹

2

[0079] This is the first equation in three unknowns, VB°, IA2° and IB2°

[0080] Relation 2: Calculation of voltage at terminal B2 from terminal A2.

[0081] Voltage at terminal B2 can be calculated using voltage current from terminal A2. This can be written from the second row of equation (14)

B o

(l-d)2¹B2 = o [0082] Since both the lines are connected, substituting, VBA° = VBB _,o^u_= VB o

[0083] This is the second equation in three unknowns, VB°, IA2° and IB2^U.

[0084] Relation 3: Calculation of current at terminal B2 from terminal A2

[0085] From second row of equation (15) corresponding to the healthy line, the third equation can be derived.

rO T/0 . O T/0 . r_jO TO . r_jO TO _ O _T/0 _ /Ό T/0 _ r_jO rO

' '^ -‘d27 ^{n V}AA27 ' ^u ^,ddmm^l1AA -l[ ' ^u 'ήd27¹‘AA27, (11 -tdίϊ)tmh ^^vB7?1l ^{^ (L l-ήdL)27 ^nvB22 ^u '((Ll-ήdL^th ¹BBl

(16)

D 0

(l-d)2 1^IB2₇ = 0

[0086] Since both the lines are connected, substituting, _„o_

VBI° = VB2^U= VB¹

- J¾-d)2 = 0

[0087] Using the three equations described above, the three unknowns, zero sequence voltage at remote terminal, zero sequence current at local terminal and zero sequence current at remote terminal can be estimated.

[0088] Case 2: One line is open and grounded

[0089] In the case of case 2, where the healthy line is open and grounded, V_B2°= 0 [0090] Hence the three unknowns will be VBI°, IA2° and IB2°. The three equations to solve for these three unknowns can be obtained from equations (15), (17) and (20), by substituting VB2°= 0.

[0091] Relation 1 :

A°_diV_A°i + A°_drnV^ + B _n /° + B T/0 nO _jO _ nO J 0 — n

¹ dm ^VA2 dl‘Al ⁱdm l¹ 1A°2— ^Ά A? - d)l ^VBl ^{~ ΰ}(1- d)l½l ^ΰ(1- d)m¹B2 — ^u (18)

[0092] Relation 2:

[0094] Using the three equations described above, the three unknowns, zero sequence voltage at remote terminal of faulted line, zero sequence current at local terminal of healthy line and zero sequence current at remote terminal of healthy line can be estimated.

[0095] At 510, the calculation of zero sequence fault point voltage and fault current for the fault location value (zero sequence voltage and current phasors for the fault location value(s)) is performed. The fault point voltage is obtained using A-end data is calculated as,

[0096] Fault current contribution from terminal A is calculated as,

[0097] Similarly, using B-end data, the following relation can be written

[0098] Rearranging equation (27), we get fault current contribution from terminal B,

[0099] Fault current can be written as, r° -— ro 7° (25)

F41 'FFl

[00100] At 512, the voltage and current phasors for the fault location value(s) are calculated. The fault point voltage can be calculated as

[00101] Similarly, fault current can be calculated as

[00102] At 514, the estimation of the fault location is performed. This estimation is performed by the device (e.g. with the fault locator). In order to estimate the fault location, calculation of phase differences between fault point voltage and fault current is required. The phase differences may be calculated by the phasor estimator or fault locator. In accordance with an embodiment, the phase difference between fault point voltage and fault current, is calculated by

K(d) = angle(y )— angle (if) (28)

[00103] K is essentially zero (assumption: fault resistance is purely resistive in nature) when calculated for the correct fault location. That is, the angle of fault point voltage and fault current will be ideally equal (i.e. V and I are in phase), at the fault location. However for any other value of d, K is non-zero.

[00104] Hence, actual fault location can be identified by finding the value of fault location at which the following condition is satisfied:

K(d) = 0.

[00105] Thus, the method of the invention estimates unknown/unavailable zero- sequence currents of the healthy line using known/available limited measurements from the faulted line. The known/available limited measurements from the faulted line include voltage and current measurements from the local terminal, and current measurements from remote terminal. These are used to determine the unknown / unavailable zero sequence currents, which are used for zero sequence mutual compensation. The invention considers and accounts for capacitive charging on the transmission line which makes it more accurate. This is performed with consideration of line impedance parameters such as capacitance per unit length, thereby accounting for distribution of current in the line.

Claims

CLAIMS We Claim

1. A method for locating a fault in a power transmission system, wherein the power transmission system comprises two terminals connected by parallel transmission lines comprising at least a first transmission line and a second transmission line, wherein the fault is located in the first transmission line, wherein the method is performed with a device associated with the power transmission system, the method comprising:

obtaining measurements of post-fault voltages and currents carried out at a first terminal of the first transmission line, and measurements of post-fault currents carried out at a second terminal of the first transmission line;

calculating voltage and current phasors corresponding to a plurality of fault location values based on the measurements, wherein the voltage and current phasors for a fault location value comprise:

positive sequence voltage and current phasors for the fault location value, calculated from positive sequence quantities of the measurements and line impedance parameters of the first transmission line;

negative sequence voltage and current phasors for the fault location value, calculated from negative sequence quantities of the measurements and the line impedance parameters of the first transmission line; and

zero sequence voltage and current phasors for the fault location value, calculated from zero sequence quantities of the measurements, zero sequence currents estimated for the second transmission line and line impedance parameters associated with the first and the second transmission lines, wherein the zero sequence currents for the second transmission line are estimated with the zero sequence voltages and currents at the first terminal of the first transmission line, the zero sequence currents at the second terminal of the first transmission line and the line impedance parameters associated with the two transmission lines; and

estimating the location of the fault in the first transmission line, based on phase differences between the voltage and current phasors calculated for the plurality of fault location values.

2. The method of claim 1 , wherein the calculation of each of the positive, negative and zero sequence voltage and current phasors for the plurality of fault location values comprises compensation for charging currents.

3. The method of claim 1, wherein the line impedance parameters comprise one or more of:

parameters associated with self-impedance of the first transmission line;

parameters associated with self-impedance of the second transmission line; parameters associated with mutual-impedance between the first and second transmission lines; and

parameters associated with charging currents.

4. The method of claim 1 , wherein a phase difference between the voltage and current phasors for a fault location value is the difference between angles of the voltage and current phasors for the fault location value.

5. The method of claim 4, wherein the fault location value for which the phase difference is zero is estimated at the location of the fault.

6. The method of claim 1, wherein the zero sequence currents for the second transmission line are estimated for each end of the second transmission line, based on the zero sequence quantities of the measurements of the first transmission line and the line impedance parameters of the first and second transmission lines.

7. A device for locating a fault in a power transmission system, wherein the power transmission system comprises two terminals connected by parallel transmission lines comprising at least a first transmission line and a second transmission line, wherein the fault is located in the first transmission line of the power transmission system, the device comprising:

an interface for obtaining measurements of post-fault voltages and currents carried out at a first terminal of the first transmission line, and measurements of post- fault currents carried out at a second terminal of the first transmission line;

a phasor calculator for:

obtaining positive, negative and zero sequence quantities from the measurements of the post-fault voltages and currents at the first terminal and the measurements of the post-fault currents at the second terminal of the first transmission line;

estimating zero sequence currents for the second transmission line based on the zero sequence quantities obtained from the measurements and line impedance parameters associated with the first and second transmission lines;

calculating voltage and current phasors for a plurality of fault location values based on the calculated positive, negative and zero sequence quantities, wherein the voltage and current phasors for a fault location value comprise:

positive sequence voltage and current phasors for the fault location value, calculated from the positive sequence quantities obtained from the measurements;

negative sequence voltage and current phasors for the fault location value, calculated from the negative sequence quantities obtained from the measurements; and

zero sequence voltage and current phasors for the fault location value, calculated from the zero sequence quantities obtained from the measurements, and the zero sequence currents estimated for the second transmission line; and a fault locator for estimating the location of the fault in the first transmission line, based on phase differences between the fault point voltage and current phasors.

8. The device of claim 7, wherein the device is an intelligent electronic device associated with the first terminal, and communicates with an intelligent electronic device associated with the second terminal.

9. The device of claim 8, wherein the intelligent electronic device associated with the first terminal obtains the measurements of the post-fault voltages and currents carried out at the first terminal from one or more measurement equipment associated with the first terminal, and wherein the intelligent electronic device receives the measurements of the post-fault currents from the intelligent electronic device associated with the second terminal.

10. The device of claim 8, wherein the device comprises a memory with the line impedance parameters of the parallel transmission lines, wherein the line impedance parameters are associated with self-impedance and mutual-impedance of the first and second transmission lines.