Apparatus, system, and method for dual loop transmission system

Abstract

An apparatus (20) is provided for use in a double circuit power transmission system having a first line (11) and a second line (12). The apparatus (20) includes an interface for receiving current measurements of the second line (12). The apparatus includes at least one processing module operable to estimate a first zero sequence current in the first line (11) based on a second zero sequence current and determine an apparent impedance based on the estimated first zero sequence current.

Description

Technical Field

[0001] The present invention relates to power transmission systems and apparatus and methods for protecting power transmission systems. The present invention particularly relates to methods and apparatus operable to take into account mutual coupling between parallel lines of a double-circuit transmission system when performing protection functions. Background Art

[0002] Double-circuit transmission line systems are widely used to facilitate power transmission in narrow physical corridors. These systems can include double-circuit towers with transmission lines sharing the right-of-way, or single-circuit towers.

[0003] A dual-circuit transmission line is essentially a pair of current-carrying conductors placed close together (e.g., in parallel). Consequently, the magnetic flux from one line links to the other. This flux linkage is proportional to the total current flowing through the line. The sum of the positive- and negative-sequence currents flowing through the line is zero, and therefore the flux linkage is zero. Consequently, there is no positive- and negative-sequence mutual impedance in a transposed parallel transmission line.

[0004] However, the zero-sequence currents in all three phases of the transmission line are in phase with each other and their sum is not equal to zero. This creates an interconnection link between the two lines and is called zero-sequence mutual coupling. The zero-sequence mutual coupling effect can be effectively represented by the zero-sequence mutual impedance in the equivalent circuit.

[0005] Distance protection operating based on the calculated apparent impedance seen by the relay is widely used for transmission line protection.

[0006] The apparent impedance can be calculated using the voltage and current measurements at the terminals where the protection relay is placed. Traditionally, the apparent impedance Z is calculated for the phase-to-ground element of the distance relay. app , as shown in the following equation (1).

[0007]

[0008] U ph is the local phase-to-ground voltage in the fault phase, and I ph is the short-circuit current in the fault phase.

[0009] I0 is the zero sequence current. K0 is The compensation factor obtained.

[0010] Z0 is the zero-sequence line impedance of the line protected by the protection relay. Z1 is the positive-sequence line impedance of the line protected by the protection relay.

[0011] However, equation (1) is not accurate for dual circuits / parallel lines because it does not take into account the zero-sequence mutual coupling effect. Mutual coupling effects, if not properly compensated, can cause the distance element to over-range or under-range, depending on the direction of the current in the parallel line.

[0012] Yi Hu et al., "An adaptive scheme for parallel-line distance protection," IEEE Transactions on Power Delivery, Vol. 17, No. 1, pp. 105–110, January 2002, doi:10.1109 / 61.974195, and WO 1999 / 040662 A1, disclose an adaptive scheme for parallel-line protection. The scheme uses line operating states prepared based on field data to adjust its zone limits in a manner that achieves maximum coverage and error-free operation. Worst-case zone characteristics are used when a status signal is unavailable.

[0013] An adaptive scheme for parallel line protection is disclosed in M. Sharifzadeh and M. Sanaye-Pasand, "An adaptive distance scheme for double circuit line protection," 2007 42nd International Universities Power Engineering Conference, Brighton, 2007, pp. 310-315. The techniques disclosed in this document may not perform well in all system conditions.

[0014] B. R. B. Halja and R. P. Maheshwari, “High-Resistance Faults on Two-Terminal Parallel Transmission Line: Analysis, Simulation Studies, and an Adaptive Distance Relaying Scheme,” IEEE Transactions on Power Transmission, Vol. 22, No. 2, pp. 801-812, April 2007, provide an analysis of the apparent impedance seen from the relay point that considers the effects of transmission line parameter uncertainty, the interaction of parallel lines in simple and more complex configurations, the effects of parallel capacitance, and variations in the system external to the protected line. An adaptive digital distance relaying scheme is proposed using a radial basis function neural network. The large data and training requirements of the neural network scheme may be undesirable for various protection applications.

[0015] The zero-sequence mutual coupling effect in dual-loop / parallel lines makes the traditional apparent impedance calculation according to equation (1) inaccurate.

[0016] To improve the accuracy of the determined apparent impedance, a term proportional to the current in a good parallel line can be included in the calculation of the apparent impedance in a dual circuit / parallel line. Zero-sequence mutual coupling compensation can be achieved by modifying the relay current to include a term proportional to the current flowing through the good parallel line. This traditionally requires measuring the current in the parallel line as input.

[0017] However, obtaining current measurements from parallel lines can be challenging in dual-circuit lines for a number of reasons. First, when the parallel line is disconnected and grounded (perhaps for maintenance), the unavailability of the current transformers on the beaker line side can render such current measurements impossible. Second, even if both lines are in service, transmitting current measurements from one line to the protection relays of the other line is undesirable for safety reasons.

[0018] Another approach to mutual coupling compensation is to use a configuration group that uses domain expertise and research to modify the K0 factor. However, this approach can be challenging to adapt to different types of systems, especially as the grid evolves with increasing penetration of renewable energy. Summary of the Invention

[0019] There is a need for improved techniques for accounting for mutual coupling between lines of a double-circuit transmission system, such as parallel conductors of a double-circuit transmission system. There is a need for apparatus, systems, and methods that allow for zero-sequence mutual coupling compensation in a double-circuit transmission system without requiring current measurements from good lines. There is a need for apparatus, systems, and methods that allow for zero-sequence mutual coupling compensation in a double-circuit transmission system, the apparatus, systems, and methods being suitable for use with protection functions (such as distance protection functions) in various system configurations (such as different transformer configurations).

[0020] Embodiments of the present invention provide devices, systems, and methods operable to perform zero-sequence mutual coupling compensation in a dual-circuit transmission system, which can estimate the current in a line (referred to herein as the "first line") extending parallel to a line protected by the device (referred to herein as the "second line"). The estimated current in the first line can be used to calculate a more accurate value of the apparent impedance as seen by a device (e.g., a protection relay) and take appropriate protective action (e.g., distance protection).

[0021] The estimated current in the first line can be the estimated zero-sequence current in the first line extending parallel to the protected line. The estimated zero-sequence current can be estimated using the measured current in the protected line, thereby avoiding the need to obtain current measurements of the first line for determining the apparent impedance. The apparatus and method eliminate the need for current measurements or the need to transmit current measurements from the first line (i.e., the good line) to the apparatus protecting the second line (i.e., the faulted line). The apparent impedance can be determined so that it adapts to the mutual coupling, thereby performing mutual coupling compensation.

[0022] Additional information may be used to estimate the zero sequence current in the first line.For example, voltage measurements are obtained at local terminals (ie terminals closer to the location of the device).

[0023] The apparatus, system and method provide adaptive mutual coupling compensation for distance protection of dual-circuit lines without requiring current measurements from a good first line. The current in the parallel first line is estimated using available local measurements obtained at the line protected by the apparatus.

[0024] The apparatus, system, and method are operable to perform an iterative technique in which an initial estimate of a fault location, a zero-sequence current in a first line, and an apparent impedance is calculated, and subsequently refined estimates of the fault location, the zero-sequence current in the first line, and the apparent impedance are calculated. The initial estimate and the refined estimate may be calculated using only (a) system parameters (such as (i) line impedance, (ii) mutual coupling impedance, and at least one of (iii) transformer impedance and (iv) source impedance) and (b) measurements obtained at a second line protected by the apparatus.

[0025] The measurement results obtained at the second line may be measurements obtained at a local terminal close to the device. For example, for a protection relay, the initial estimate and the refined estimate may be calculated using only (a) system parameters (such as (i) line impedance, (ii) mutual coupling impedance, and at least one of (iii) transformer impedance and (iv) source impedance) and (b) measurements obtained at the local terminal of the second line protected by the device, without using measurements from a remote terminal of the second line.

[0026] The apparatus, system, and method are operable to estimate mutual inductance current (eg, current induced by mutual coupling) by taking into account the fault location and parallel loop current direction. Thus, the apparatus and method provide a more accurate technique for determining apparent impedance.

[0027] The apparatus, system and method are operable such that the same procedure can be invoked to estimate current in a line parallel to the line on which the protection device is provided, regardless of the transformer configuration and / or line status.

[0028] The apparatus, system and method are operable to use digital substation data to determine line configuration. The apparatus and method are operable to determine, based on the line configuration (and optionally based on the transformer configuration), which program to invoke to estimate the current in a line parallel to the line on which the protection device is provided.

[0029] The apparatus, system, and method allow for estimating zero-sequence current in a line parallel to a line protected by the apparatus using status signals from digital substation data, local measurements, and system impedance parameters. The system impedance parameters may include line impedance and, depending on the line configuration, at least one of transformer impedance and source impedance.

[0030] An apparatus according to an embodiment is operable for use with a double-circuit power transmission system having a first line and a second line, the first line being parallel to the second line. The apparatus comprises an interface for receiving current measurements of the second line; and at least one processing module operable to calculate a second zero-sequence current in the second line from the current measurements, estimate a first zero-sequence current in the first line based on the second zero-sequence current, and determine an apparent impedance based on the estimated first zero-sequence current.

[0031] The device may be a protection relay.

[0032] The device is operable to perform a protection function based on the apparent impedance.

[0033] The apparatus is operable to perform a distance protection function based on the apparent impedance.

[0034] The apparatus is operable to estimate the first zero-sequence current without using current measurements of the first line.

[0035] The device is operable to estimate the first zero-sequence current using voltage measurements at local terminals of the second line (ie terminals closer to the device).

[0036] The apparatus is operable to estimate the first zero-sequence current without using a voltage measurement of the first line.

[0037] The apparatus is operable to determine an estimate of a fault location of a fault in the second line.

[0038] The apparatus is operable to estimate the first zero-sequence current based on the estimate of the fault location.

[0039] The apparatus is operable to determine estimates of the fault location, the first zero-sequence current, and the apparent impedance in an iterative procedure.

[0040] The interface is operable to receive voltage measurements indicative of a zero-sequence voltage at terminals of the second line.

[0041] The apparatus is operable to determine the first zero-sequence current based on the zero-sequence voltage.

[0042] The apparatus is operable to multiply the second zero-sequence current by a multiplication factor to estimate the first zero-sequence current.

[0043] The apparatus is operable to determine the multiplication factor.

[0044] The multiplication factor may be independent of the state of the first line and / or the transformer configuration of transformers at opposite terminals of both the first line and the second line.

[0045] The apparatus is operable such that the multiplication factor depends on a state of the first line.

[0046] The apparatus is operable such that the multiplication factor depends on whether the first line is (i) in use or (ii) disconnected and connected to ground.

[0047] The apparatus is operable such that the multiplication factor depends on a transformer configuration at the two terminals of the first line and the second line.

[0048] The apparatus is operable such that the multiplication factor depends on whether the configuration of the transformer is (i) delta-wye grounded or (ii) wye-wye grounded.

[0049] The apparatus is operable such that the multiplication factor depends on at least one transformer impedance of the transformer of the delta-wye grounding transformer configuration.

[0050] The apparatus is operable such that the multiplication factor depends on at least one source impedance of a source behind the transformer of the wye-wye transformer configuration.

[0051] The apparatus is operable to determine a configuration of the first line and / or a configuration of the transformer using digital substation data.

[0052] The apparatus is operable to use digital substation data to determine which of several calculation routines to invoke to estimate a first zero-sequence current of the first line.

[0053] The apparatus is operable to perform mutual coupling compensation using the estimated first zero-sequence current in the first line to determine the apparent impedance.

[0054] The apparatus is operable to determine the apparent impedance including mutual coupling compensation, the mutual coupling compensation being dependent on an estimated first zero-sequence current in the first line.

[0055] The apparatus is operable to perform the mutual coupling compensation for distance protection of the double-circuit transmission system.

[0056] The apparatus is operable to perform the mutual coupling compensation including determining the apparent impedance by calculating a sum of: a short circuit current in a faulted phase of the second line, a product of a first factor and an estimated first zero sequence current, and a product of a second factor and the second zero sequence current.

[0057] The apparatus is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 independently of whether the first line is in use and / or independently of whether the transformer is in the wye-wye configuration or in the delta-wye configuration, such that the first zero-sequence current satisfies

[0058]

[0059] in,

[0060] in:

[0061] V A0 is the zero-sequence voltage at a local terminal (i.e., a terminal of the second line closer to the device);

[0062] I0 is the second zero-sequence current in the second circuit;

[0063] d is the estimated fractional fault location from the local terminal;

[0064] Z 0L is the positive sequence impedance of the second line;

[0065] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0066] Z S2 is the source impedance behind the remote terminals.

[0067] The apparatus is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 independently of whether the first line is in use and / or independently of whether the transformer is in the wye-wye configuration or in the delta-wye configuration, such that the first zero-sequence current satisfies

[0068]

[0069] in,

[0070] in:

[0071] I0 is the second zero-sequence current in the second circuit;

[0072] d is the estimated fractional fault location from the local terminal;

[0073] Z 0L is the positive sequence impedance of the second line;

[0074] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0075] Z S1 , Z S2 are the source impedance behind the local and remote terminals respectively.

[0076] The apparatus is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is in service and the transformer is in the delta-wye grounding configuration, such that the first zero-sequence current satisfies

[0077]

[0078] in,

[0079] in:

[0080] V A0 is the zero-sequence voltage at a local terminal (i.e., a terminal of the second line closer to the device);

[0081] I0 is the second zero-sequence current in the second circuit;

[0082] d is the estimated fractional fault location from the local terminal;

[0083] Z 0L is the positive sequence impedance of the second line;

[0084] Z 0Mis the zero-sequence mutual impedance of the first line and the second line;

[0085] Z T2 is the transformer impedance of the remote transformer.

[0086] The apparatus is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is in use and the transformer is in the Y-grounded-Y-grounded configuration, such that the first zero-sequence current satisfies

[0087]

[0088] in,

[0089] in:

[0090] V A0 is the zero-sequence voltage at a local terminal (i.e., a terminal of the second line closer to the device);

[0091] I0 is the second zero-sequence current in the second circuit;

[0092] d is the estimated fractional fault location from the local terminal;

[0093] Z 0L is the positive sequence impedance of the second line;

[0094] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0095] Z S2 is the source impedance behind the remote terminals.

[0096] The apparatus is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is disconnected and grounded and the transformer is in the delta-wye grounded configuration, such that the first zero-sequence current satisfies

[0097]

[0098] in,

[0099] in:

[0100] V A0 is the zero-sequence voltage at a local terminal (i.e., a terminal of the second line closer to the device);

[0101] I0 is the second zero-sequence current in the second circuit;

[0102] d is the estimated fractional fault location from the local terminal;

[0103] Z 0L is the positive sequence impedance of the second line;

[0104] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0105] Z T2 is the transformer impedance of the remote transformer.

[0106] The apparatus is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is disconnected and grounded and the transformer is in the Y-grounded-Y-grounded configuration, such that the first zero-sequence current satisfies

[0107]

[0108] in,

[0109] in:

[0110] V A0 is the zero-sequence voltage at a local terminal (i.e., a terminal of the second line closer to the device);

[0111] I0 is the second zero-sequence current in the second circuit;

[0112] d is the estimated fractional fault location from the local terminal;

[0113] Z 0L is the positive sequence impedance of the second line;

[0114] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0115] Z S2 is the source impedance behind the remote terminals.

[0116] The apparatus is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is in service and the transformer is in the delta-wye grounding configuration, such that the first zero-sequence current satisfies

[0117]

[0118] in,

[0119] in:

[0120] I0 is the second zero-sequence current in the second circuit;

[0121] d is the estimated fractional fault location from the local terminal;

[0122] Z 0L is the positive sequence impedance of the second line;

[0123] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0124] Z T1 , Z T2 are the transformer impedances of the local transformer and the remote transformer respectively.

[0125] The apparatus is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is in use and the transformer is in the Y-grounded-Y-grounded configuration, such that the first zero-sequence current satisfies

[0126]

[0127] in,

[0128] in:

[0129] I0 is the second zero-sequence current in the second circuit;

[0130] d is the estimated fractional fault location from the local terminal;

[0131] Z 0L is the positive sequence impedance of the second line;

[0132] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0133] Z S1 , Z S2 are the source impedance behind the local and remote terminals respectively.

[0134] The apparatus is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is disconnected and grounded and the transformer is in the delta-wye grounded configuration, such that the first zero-sequence current satisfies

[0135]

[0136] in,

[0137] in:

[0138] I0 is the second zero-sequence current in the second circuit;

[0139] d is the estimated fractional fault location from the local terminal;

[0140] Z 0L is the positive sequence impedance of the second line;

[0141] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0142] Z T1 , Z T2 are the transformer impedances of the local transformer and the remote transformer respectively.

[0143] The apparatus is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is disconnected and grounded and the transformer is in the Y-grounded-Y-grounded configuration, such that the first zero-sequence current satisfies

[0144]

[0145] in,

[0146] in:

[0147] I0 is the second zero-sequence current in the second circuit;

[0148] d is the estimated fractional fault location from the local terminal;

[0149] Z 0L is the positive sequence impedance of the second line;

[0150] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0151] Z S1 , Z S2 are the source impedance behind the local and remote terminals respectively.

[0152] The arrangement may be operable such that the multiplication factor may depend on an estimated fault location of a fault in the second line.

[0153] The apparatus is operable to determine an estimated fault location based on: a phase-to-earth voltage U in the second line; ph , the short-circuit current I in the second circuit ph , the zero-sequence line impedance Z of the second line 0L, the positive-sequence line impedance Z1 of the second line, and the second zero-sequence current I0.

[0154] The apparatus is operable to determine the estimated fault location, the first zero-sequence current and the apparent impedance in an iterative procedure.

[0155] The apparatus is operable such that in a first iteration of the iterative procedure an initial fractional fault location estimate may be determined such that the initial fractional fault location estimate satisfies

[0156]

[0157] The apparatus is operable such that in a first iteration of the iterative procedure an initial estimate of the apparent impedance is determined such that the initial estimate of the apparent impedance satisfies

[0158]

[0159] in,

[0160] in:

[0161] I0′(d in ) is the initial fractional fault location estimate d in Obtaining an initial estimate of the first zero-sequence current,

[0162] U ph is the phase-to-ground voltage in the phase associated with the second line,

[0163] I ph is the short-circuit current in the phase associated with the second line,

[0164] Z 0L is the zero-sequence line impedance of the second line,

[0165] Z1 is the positive sequence line impedance of the second line, and

[0166] Z 0M is the zero-sequence mutual impedance of the first line and the second line in a fault-free state.

[0167] The apparatus is operable such that in a second iteration of the iterative procedure the fault location may be determined as a refined fractional fault location estimate

[0168]

[0169] The apparatus is operable such that in a second iteration of the iterative procedure a refined estimate of the apparent impedance is determined such that the refined estimate of the apparent impedance satisfies

[0170]

[0171] in,

[0172] in:

[0173] I0′(d) is a refined estimate of the first zero-sequence current obtained for the refined fractional fault location estimate.

[0174] The apparatus is operable such that after a k-th iteration (where k≧2) of the iterative procedure the refined estimate of the apparent impedance is used for performing a protection function, in particular a distance protection function.

[0175] The apparatus is operable to receive current measurements in the second line from a current transformer and to process the current measurements to estimate the first zero-sequence impedance.

[0176] An electric power system according to an embodiment includes a double-circuit transmission system, the double-circuit transmission system including a first line; a second line parallel to the first line; and an apparatus according to any embodiment disclosed herein, the apparatus operably coupled to the second line to perform a protection function on the second line.

[0177] The first line and the second line may form a three-phase double-circuit transmission system.

[0178] The first line and the second line may have equal line impedance.

[0179] The first line and the second line may have the same length and the same diameter.

[0180] First terminals of the first line and the second line may be coupled to the first bus and second ends of the first line and the second line may be coupled to the second bus.

[0181] The power system may be a power generation, distribution or transmission system having a first source coupled to a first line and a second line via a first transformer and having a second source coupled to the first line and the second line via a second transformer.

[0182] The device may be a protection relay.

[0183] The power system may include a current transformer to perform current measurement in the second line.

[0184] The power system may include a voltage sensing device that senses a voltage at a local terminal and provides the sensed voltage to a device for estimating the first zero-sequence current.

[0185] The power system may include relays, circuit breakers, or switches that trip in response to apparent impedance.

[0186] The method according to an embodiment includes estimating, by a device, a first zero-sequence current in a first line of a double-circuit transmission system, the first line being parallel to a second line having a fault, the first zero-sequence current being estimated based on a second zero-sequence current in the second line, and determining, by the device, an apparent impedance based on the estimated first zero-sequence current.

[0187] The method may further comprise calculating the second zero sequence current in the second line from current measurements.

[0188] The method may further include performing a protection function based on the apparent impedance.

[0189] The protection function may be a distance protection function.

[0190] The first zero-sequence current may be estimated without using current measurements of the first line.

[0191] The first zero-sequence current may be estimated using voltage measurements at local terminals of the second line (ie terminals closer to the device).

[0192] The first zero-sequence current may be estimated without using voltage measurements of the first line.

[0193] The method may comprise determining an estimate of a fault location of a fault in the second line.

[0194] The first zero-sequence current may be estimated based on the estimation of the fault location.

[0195] The method may include an iterative process for determining estimates of the fault location, the first zero-sequence current, and the apparent impedance.

[0196] The method may comprise receiving a voltage measurement indicative of a zero sequence voltage at a terminal of the second line.

[0197] The first zero-sequence current may be determined based on the zero-sequence voltage.

[0198] Estimating the first zero-sequence current may include multiplying the second zero-sequence current by a multiplication factor.

[0199] The multiplication factor may be independent of the state of the first line and / or the transformer configuration of transformers at opposite terminals of both the first line and the second line.

[0200] The multiplication factor may depend on the state of the first line.

[0201] The multiplication factor may depend on whether the first line is (i) in use or (ii) disconnected and connected to ground.

[0202] The multiplication factor may depend on a transformer configuration at the two terminals of the first line and the second line.

[0203] The multiplication factor may depend on whether the transformer configuration is (i) delta-wye grounded or (ii) wye-wye grounded.

[0204] The multiplication factor may depend on at least one transformer impedance of the transformer of the delta-wye grounded transformer configuration.

[0205] The multiplication factor may depend on at least one source impedance of a source behind the transformer of the wye-wye transformer configuration.

[0206] The method may further comprise determining a configuration of the first line and / or a configuration of the transformer using digital substation data.

[0207] The method may further include using digital substation data to determine which calculation process of several calculation procedures to invoke to estimate a first zero-sequence current of the first line.

[0208] The method may include performing mutual coupling compensation based on the estimated first zero-sequence current in the first line to determine the apparent impedance.

[0209] The method may comprise determining the apparent impedance including mutual coupling compensation, the mutual coupling compensation being dependent on an estimated first zero sequence current in the first line.

[0210] The method may include performing the mutual coupling compensation for distance protection of the dual-circuit transmission system.

[0211] Performing the mutual coupling compensation includes calculating a sum of the following to determine the apparent impedance: a short-circuit current in the faulted phase of the second line, a product of a first factor and the estimated first zero-sequence current, and a product of a second factor and the second zero-sequence current.

[0212] Estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 independently of whether the first line is in use and / or independently of whether the transformer is in the Y-grounded-Ye grounded configuration or in the delta-Ye grounded configuration, such that the first zero-sequence current satisfies

[0213]

[0214] in,

[0215] in:

[0216] V A0 is the zero-sequence voltage at a local terminal (i.e., a terminal of the second line closer to the device);

[0217] I0 is the second zero-sequence current in the second circuit;

[0218] d is the estimated fractional fault location from the local terminal;

[0219] Z 0L is the positive sequence impedance of the second line;

[0220] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0221] Z S2 is the source impedance behind the remote terminals.

[0222] Estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 independently of whether the first line is in use and / or independently of whether the transformer is in the Y-grounded-Ye grounded configuration or in the delta-Ye grounded configuration, such that the first zero-sequence current satisfies

[0223]

[0224] in,

[0225] in:

[0226] I0 is the second zero-sequence current in the second circuit;

[0227] d is the estimated fractional fault location from the local terminal;

[0228] Z 0L is the positive sequence impedance of the second line;

[0229] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0230] Z S1 , Z S2 are the source impedance behind the local and remote terminals respectively.

[0231] Estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is in use and the transformer is in the delta-wye grounding configuration, such that the first zero-sequence current satisfies

[0232]

[0233] in,

[0234] in:

[0235] V A0 is the zero-sequence voltage at a local terminal (i.e., a terminal of the second line closer to the device);

[0236] I0 is the second zero-sequence current in the second circuit;

[0237] d is the estimated fractional fault location from the local terminal;

[0238] Z 0L is the positive sequence impedance of the second line;

[0239] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0240] Z T2 is the transformer impedance of the remote transformer.

[0241] Estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is in use and the transformer is in the Y-grounded-Y-grounded configuration, such that the first zero-sequence current satisfies

[0242]

[0243] in,

[0244] in:

[0245] V A0 is the zero-sequence voltage at a local terminal (i.e., a terminal of the second line closer to the device);

[0246] I0 is the second zero-sequence current in the second circuit;

[0247] d is the estimated fractional fault location from the local terminal;

[0248] Z 0L is the positive sequence impedance of the second line;

[0249] Z 0Mis the zero-sequence mutual impedance of the first line and the second line;

[0250] Z S2 is the source impedance behind the remote terminals.

[0251] Estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is disconnected and grounded and the transformer is in the delta-wye grounding configuration, such that the first zero-sequence current satisfies

[0252]

[0253] in,

[0254] in:

[0255] V A0 is the zero-sequence voltage at a local terminal (i.e., a terminal of the second line closer to the device);

[0256] I0 is the second zero-sequence current in the second circuit;

[0257] d is the estimated fractional fault location from the local terminal;

[0258] Z 0L is the positive sequence impedance of the second line;

[0259] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0260] Z T2 is the transformer impedance of the remote transformer.

[0261] Estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is disconnected and grounded and the transformer is in the Y-grounded-Y-grounded configuration, such that the first zero-sequence current satisfies

[0262]

[0263] in,

[0264] in:

[0265] V A0 is the zero-sequence voltage at a local terminal (i.e., a terminal of the second line closer to the device);

[0266] I0 is the second zero-sequence current in the second circuit;

[0267] d is the estimated fractional fault location from the local terminal;

[0268] Z 0L is the positive sequence impedance of the second line;

[0269] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0270] Z S2 is the source impedance behind the remote terminals.

[0271] Estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is in use and the transformer is in the delta-wye grounding configuration, such that the first zero-sequence current satisfies

[0272]

[0273] in,

[0274] in:

[0275] I0 is the second zero-sequence current in the second circuit;

[0276] d is the estimated fractional fault location from the local terminal;

[0277] Z 0L is the positive sequence impedance of the second line;

[0278] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0279] Z T1 , Z T2 are the transformer impedances of the local transformer and the remote transformer respectively.

[0280] Estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is in use and the transformer is in the Y-grounded-Y-grounded configuration, such that the first zero-sequence current satisfies

[0281]

[0282] in,

[0283] in:

[0284] I0 is the second zero-sequence current in the second circuit;

[0285] d is the estimated fractional fault location from the local terminal;

[0286] Z 0Lis the positive sequence impedance of the second line;

[0287] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0288] Z S1 , Z S2 are the source impedance behind the local and remote terminals respectively.

[0289] Estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is disconnected and grounded and the transformer is in the delta-wye grounding configuration, such that the first zero-sequence current satisfies

[0290]

[0291] in,

[0292] in:

[0293] I0 is the second zero-sequence current in the second circuit;

[0294] d is the estimated fractional fault location from the local terminal;

[0295] Z 0L is the positive sequence impedance of the second line;

[0296] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0297] Z T1 , Z T2 are the transformer impedances of the local transformer and the remote transformer respectively.

[0298] Estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 when the first line is disconnected and grounded and the transformer is in the Y-grounded-Y-grounded configuration, such that the first zero-sequence current satisfies

[0299]

[0300] in,

[0301] in:

[0302] I0 is the second zero-sequence current in the second circuit;

[0303] d is the estimated fractional fault location from the local terminal;

[0304] Z 0L is the positive sequence impedance of the second line;

[0305] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0306] Z S1 , Z S2 are the source impedance behind the local and remote terminals respectively.

[0307] The multiplication factor may depend on an estimated fault location of a fault in the second line.

[0308] The method may further comprise determining the estimated fault location based on: the phase-to-ground voltage U in the second line ph , the short-circuit current I in the second circuit ph , the zero-sequence line impedance Z of the second line 0L , the positive-sequence line impedance Z1 of the second line, and the second zero-sequence current I0.

[0309] The estimated fault location, the first zero-sequence current and the apparent impedance may be determined in an iterative procedure.

[0310] In the first iteration of the iterative procedure, an initial fractional fault location estimate may be determined such that the initial fractional fault location estimate satisfies

[0311]

[0312] In a first iteration of the iterative procedure, an initial estimate of the apparent impedance may be determined such that the initial estimate of the apparent impedance satisfies

[0313]

[0314] in,

[0315] in:

[0316] I0′(d in ) is the initial fractional fault location estimate d in Obtaining an initial estimate of the first zero-sequence current,

[0317] U ph is the phase-to-ground voltage in the phase associated with the second line,

[0318] I ph is the short-circuit current in the phase associated with the second line,

[0319] Z0 is the zero-sequence line impedance of the second line,

[0320] Z1 is the positive sequence line impedance of the second line, and

[0321] Z 0M is the zero-sequence mutual impedance of the first line and the second line in a fault-free state.

[0322] In a second iteration of the iterative procedure the fault location may be determined as a refined fractional fault location estimate

[0323]

[0324] In a second iteration of the iterative procedure, a refined estimate of the apparent impedance is determined such that the refined estimate of the apparent impedance satisfies

[0325]

[0326] in,

[0327] in:

[0328] I0′(d) is a refined estimate of the first zero-sequence current obtained for the refined fractional fault location estimate.

[0329] The refined estimate of the apparent impedance after the k-th iteration (where k≧2) of the iterative procedure is used for performing a protection function, in particular a distance protection function.

[0330] The method may further include receiving current measurements in the second line from a current transformer and processing the current measurements to estimate the first zero-sequence impedance.

[0331] The first line and the second line may form a three-phase transmission system.

[0332] The first line and the second line may have approximately equal line impedances.

[0333] The first line and the second line may have the same length and the same diameter.

[0334] First terminals of the first line and the second line may be coupled to the first bus and second ends of the first line and the second line may be coupled to the second bus.

[0335] The first and second lines may consist of an electric power system, in particular an electric power generation, distribution or transmission system, having a first source coupled to the first and second lines via a first transformer and having a second source coupled to the first and second lines via a second transformer.

[0336] The method is performed by a protection relay.

[0337] The method may further comprise measuring the current in the second line by a current transformer.

[0338] The method may further include tripping a relay, a circuit breaker, or a switch based on the apparent impedance.

[0339] By means of the apparatus, system and method according to the embodiments, various effects and advantages are obtained.

[0340] Adaptive mutual coupling compensation for distance protection of a dual-circuit transmission system line is obtained without requiring current measurements from a first line extending parallel to a line protected by a device that determines an apparent impedance. Adaptive mutual coupling compensation does not require transmitting current measurements from the first line to a device (e.g., a relay) on the protected line (i.e., the second line), which may be undesirable due to unavailability of measurements or safety concerns.

[0341] The apparatus, system and method are operable without requiring a set of settings derived from domain expertise, standards and research. The apparatus, system and method are suitable for modern developing grids with increasing penetration of renewable energy sources.

[0342] The apparatus, system, and method account for changes in direction of current in parallel circuits and are therefore more accurate than conventional techniques.

[0343] The apparatus, method and system according to the embodiments may be used in conjunction with a three-phase transmission system having parallel lines. These apparatus, methods and systems may be used to improve the distance protection function performed by a protection relay, but are not limited thereto. BRIEF DESCRIPTION OF THE DRAWINGS

[0344] The subject matter of the invention will be explained in more detail with reference to preferred exemplary embodiments illustrated in the accompanying drawings, in which:

[0345] Figure 1 It is a partial schematic diagram of a system including double-circuit lines and protection equipment.

[0346] Figure 2 It is a schematic diagram of a dual-circuit transmission system.

[0347] Figure 3 It is a block diagram of the protection device.

[0348] Figure 4 is a flow chart of the method.

[0349] Figure 5 is a block diagram of the processing performed by a protection device.

[0350] Figure 6 is a schematic diagram of a system including a dual-circuit line with a delta-wye grounded transformer configuration and a first line that is disconnected and grounded.

[0351] Figure 7 yes Figure 6 The system status and the equivalent zero-sequence network of the configured double-circuit line.

[0352] Figure 8 is a schematic representation of a system including a dual-circuit line with a wye-grounded-wye-grounded transformer configuration and a disconnected and grounded first line.

[0353] Figure 9 yes Figure 8 The system status and the equivalent zero-sequence network of the configured double-circuit line.

[0354] Figure 10 is a schematic representation of a system comprising a double circuit line with a delta-wye grounding transformer configuration and a first line in use.

[0355] Figure 11 yes Figure 10 The system status and the equivalent zero-sequence network of the configured double-circuit line.

[0356] Figure 12 is a schematic representation of a system comprising a dual-circuit line with a wye-wye transformer configuration and a first line in use.

[0357] Figure 13 yes Figure 12 The system status and the equivalent zero-sequence network of the configured double-circuit line.

[0358] Figure 14 is a flow chart of the method.

[0359] Figure 15 is a schematic representation of a system comprising a double-circuit transmission system line and protection equipment, for which Figures 16 to 19 data.

[0360] Figure 16 is a graph showing the actual impedance for a delta-wye grounded transformer configuration with the first line disconnected and grounded, the apparent impedance obtained when using current measurements at the first line, and the apparent impedance obtained when using the techniques of the present invention to estimate the zero sequence current in the first line.

[0361] Figure 17 is a graph showing the actual impedance for a wye-grounded-wye-grounded transformer configuration with the first line disconnected and grounded, the apparent impedance obtained when using current measurements at the first line, and the apparent impedance obtained when using the techniques of the present invention to estimate the zero-sequence current in the first line.

[0362] Figure 18is a diagram showing the actual impedance of a first line in use, the apparent impedance obtained when using current measurements at the first line, and the apparent impedance obtained when using the technique of the present invention to estimate the zero sequence current in the first line, for a delta-wye grounding transformer configuration.

[0363] Figure 19 is a diagram showing the actual impedance of a first line in use, the apparent impedance obtained when using current measurements at the first line, and the apparent impedance obtained when using the technique of the present invention to estimate the zero sequence current in the first line, for a wye-grounded-wye transformer configuration.

[0364] Figure 20 is a graph showing the actual impedance obtained when the technique of the present invention is used to estimate the zero sequence current in the first line for a delta-wye grounded transformer configuration with the first line disconnected and grounded and for an actual remote source impedance with the remote source impedance varying around its actual value. DETAILED DESCRIPTION

[0365] Exemplary embodiments of the present invention will be described with reference to the accompanying drawings, wherein the same or similar reference numerals represent the same or similar elements. Although some embodiments will be described in the context of the present invention, the methods and apparatus described in detail below can be used in a variety of systems.

[0366] Unless specifically stated otherwise, the features of the embodiments can be combined with each other.

[0367] According to an embodiment of the present invention, an apparatus and method are provided that are operable to perform protection functions, particularly distance protection functions, of an electric power system. More specifically, the apparatus and method are operable to provide mutual coupling compensation for distance protection functions in a double-circuit transmission system. As used herein, the term "double-circuit transmission system" (also often referred to in the art as a "double-circuit transmission line") carries conductors of two loops. For a two-phase double-circuit transmission system, each tower supports four conductors and insulates the four conductors. For a three-phase double-circuit transmission system, each tower supports six conductors and insulates the six conductors. Typically, a double-circuit transmission system is a transmission system in which the conductors of the two loops share the same right-of-way and / or are suspended from the same tower.

[0368] The protection device may be implemented as a protection relay.The protection device may be operatively associated with a second line of a double-circuit transmission system, wherein the double-circuit transmission system has a first line extending parallel to the second line.

[0369] The protection device is operable to: receive a current measurement obtained for the second line (e.g., from a current transformer at the second line); estimate a first zero-sequence current in the first line based on a second zero-sequence current in the second line; and determine an apparent impedance based on the estimated first zero-sequence current.

[0370] The apparent impedance may be determined based on current and voltage measurements obtained on the second line associated with the protection device, and does not require any current measurements obtained on the first line.

[0371] Determining the apparent impedance may include determining the apparent impedance based on a weighted sum of the first zero-sequence current and the second zero-sequence current. The weighted sum may be determined as K0I0+K 0m I0′, where I0 is the second zero-sequence current obtained by processing the measurement results and I′0 is the estimated first zero-sequence current. 0m It may depend on the system impedance (particularly the line impedance). In this way, mutual coupling may be taken into account (thereby providing mutual coupling compensation).

[0372] The protection device is operable to perform a protection function of the second line based on the apparent impedance. The protection function may include tripping a protection element such as a circuit breaker or switch. The protection function may include performing a controlled disconnection and / or reconnection.

[0373] Alternatively or additionally, the protection device may be operable to generate an output such as an alarm, warning or other information based on the apparent impedance.The output may be provided to an operator via a user interface.

[0374] When estimating the first zero-sequence current and / or determining the apparent impedance and / or performing mutual coupling compensation, the protection device can use various parameters, such as one or more source impedances and / or one or more transformer impedances. The techniques disclosed herein are robust to inaccuracies in the values ​​of the source and / or transformer impedances. Therefore, the terms "source impedance" and "transformer impedance" as used herein encompass estimates of the source impedance or transformer impedance or other values ​​that accommodate some variation from the actual values.

[0375] Figure 1 1 is a partial schematic diagram of an electric power system 10. The electric power system has a first line 11 and a second line 12 extending in parallel. The first line 11 and the second line 12 may each be a conductor of a double-circuit transmission system.

[0376] The first line 11 and the second line 12 may be transmission lines of a double-circuit transmission system as current-carrying conductors placed close to each other.The first line 11 and the second line 12 may be transmission lines and the transmission lines may be operated such that the sum of their currents is not equal to zero.

[0377] First terminals of the first and second lines 11, 12 may be coupled to a first transformer 16. A first source 15 may be coupled to the first transformer 16, located after the first transformer 16 (as viewed from the protection device 20, 20'), i.e., at first ends of the first and second lines 11, 12.

[0378] Although Figure 1 Not shown in FIG, but opposite second terminals of the first line 11 and the second line 22 may be coupled to a second transformer. A second source may be coupled to the second transformer, ie at second ends of the first line 11 and the second line 12.

[0379] The protection device 20 is arranged to protect the second line 12. The protection device 20 is operable to provide distance protection or another protection function for the second line 22. The protection device 22 may be a protection relay.

[0380] The protection device 20 is provided at or near a first terminal of the second line 22. Therefore, the first terminal is also referred to as a "local terminal." Hereinafter, the transformer provided at the end of the second line 12 where the protection device 20 is provided will be referred to as a "local transformer," and the source at the end of the second line 12 where the protection device 20 is provided will be referred to as a "local source." The transformer at the opposite end of the second line 12 will be referred to as a "remote transformer," and the source at the opposite end of the second line 12 will be referred to as a "remote source."

[0381] It should be understood that another protection device ( Figure 1 The protection device 15 is typically located at an opposite end of the second line 12, for which the source 15 is a "remote source" (because it is located at an end of the second line 12 opposite to the end at which the other protection device is located) and the transformer 16 is a "remote transformer" (because it is located at an end of the second line 12 opposite to the end at which the other protection device is located).

[0382] The protection device 20 is coupled to the current transformer 30 at the first end of the second line 12. The protection device 20 is operable to receive current measurements of the second line 12. The current measurements allow the zero-sequence current of the second line 12 to be derived. For simplicity, the zero-sequence current of the second line 12 is referred to as the "second zero-sequence current." For simplicity, the zero-sequence current of the first line 11 is referred to as the "first zero-sequence current."

[0383] The protection device 20 is operable to provide an enhanced technique that takes into account the interconnection link between the two lines 11, 12 and is referred to as zero-sequence mutual coupling. The zero-sequence mutual coupling effect can be effectively represented by the zero-sequence mutual impedance in the equivalent circuit. As viewed from the protection device 20, the protection device 20 is operable to determine an apparent impedance that takes into account the mutual coupling and includes a term that is proportional to an estimate of the first zero-sequence current in the first line 11. The protection device 20 is operable to determine the apparent impedance in the dual circuit / parallel line as

[0384]

[0385] in,

[0386] I′0 is an estimate of the first zero-sequence current in the first parallel line 11,

[0387] K 0m and K0 are coefficients that depend on the line impedance, as will be explained in more detail below, where K 0m It is proportional to the mutual impedance between the first line 11 and the second line 12 .

[0388] The protection device 20 is operable to determine an estimate of the first zero-sequence current I′0 based on the measured current in the second line 12 and using a known system impedance (the line impedance and at least one of the transformer impedance or the source impedance). The procedure by which the estimate of the first zero-sequence current I′0 is determined depends on the transformer configuration of the transformers at both the local and remote ends of the second line 12 and the state of the first line 11. The protection device 20 can retrieve information about the transformer configuration and the state of the first line 11 from the digital substation status and configuration data 19. For example, the digital substation status and configuration data 19 may include a substation configuration description and / or a dynamic substation topology, which the protection device 20 uses to determine which of several procedures to invoke to estimate the apparent impedance.

[0389] While the operation of the device according to the present invention will be described with reference to the protection device 20, the protection device 20′ associated with the first line 11 can have similar operation. Specifically, the protection device 20′ can be operable to receive current measurements of the first line 11 from the current transformer 30′ on the first line 11, can estimate a second zero-sequence current based thereon and based on the system impedance using the substation status and configuration data, and can determine the apparent impedance using the first zero-sequence current obtained from the measurements of the first line and the second zero-sequence current obtained by the estimation, without requiring any current measurements to be transmitted between the protection devices 20, 20′ or any current measurements to be transmitted from the current transformer 30 to the protection device 20′.

[0390] Figure 2Schematic diagram showing a tower of a double circuit transmission system, wherein the conductors of the two circuits share the same right-of-way and / or are supported on the same tower. The first line 11 and the second line 12 may be conductors of different circuits of the double circuit transmission system. Figure 2 As shown, a three-phase, dual-loop transmission line has a total of six conductors a', b', c', a, b, c, arranged to form two different transmission loops, a first line 11 and a second line 12. First line 11 includes three conductors a', b', c' corresponding to the three phases, and second line 12 includes another three conductors a, b, c corresponding to the three phases. Running first line 11 and second line 12 close to each other would involve inductive coupling between the conductors, for example if they were arranged in parallel.

[0391] Figure 3 is a block diagram of a protection device 20 according to an embodiment. The protection device 20 has a first interface 28 operable to receive current measurements of a line protected by the protection device 20. The first interface 20 is operable to couple to a current transformer.

[0392] The protection device 20 has one or more integrated circuits (ICs) 21 that perform processing functions. The one or more ICs 21 may include one or more processors, microprocessors, controllers, microcontrollers, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), or any combination thereof.

[0393] The one or more ICs 21 are operable to implement an apparent impedance determination element 22. The apparent impedance determination element 22 may receive current and voltage measurements of the protected line as input, may estimate a zero-sequence current in another line running parallel to the protected line, and may use the estimated zero-sequence current in the first line 11 running parallel to the line on which the protection device 20 is provided, in combination with the zero-sequence current in the protected line, to estimate the apparent impedance, which takes into account mutual coupling in the dual-line loop.

[0394] One or more ICs 21 are operable to implement a distance element 23. The distance element 23 is operable to perform a protection function, specifically a distance protection function. The distance element 23 is operable to use apparent impedance to determine required corrective measures. The distance element 23 is operable to determine areas requiring protection. By using apparent impedance that accounts for mutual coupling, the risk of over-range or under-range operation of the distance element 23 is mitigated.

[0395] The one or more ICs 21 are operable to issue a signal or command via the at least one second interface 29 to cause a determined protective action to be taken.

[0396] One or more ICs 21 are operable to implement an output generation element 24. The output generation element 24 may cause an output (alarm, warning, notification, or other information) to be output to an operator at, for example, a control center.

[0397] Figure 4 is a flow chart of the method 40. The method 40 may be automatically performed by the protection device 20.

[0398] At step 41, a current measurement of a line protected by a protection device is obtained. A voltage measurement of the protected line (particularly a relative ground voltage) may be received.

[0399] Step 41 may optionally comprise receiving a voltage measurement indicative of a zero sequence voltage at a local terminal of the second line.

[0400] At step 42, system status and configuration data is optionally retrieved. The system status and configuration data may include information about whether another line running parallel to the protected line is in operation or disconnected and grounded (as might be the case for maintenance). The system status and configuration data may include information about the transformer configuration of the transformers at both ends of the protected line. Step 42 is optional. Methods and apparatus according to embodiments may be operable without requiring information about the status of the line running parallel to the protected line and / or without requiring information about the transformer configuration.

[0401] At step 43, a zero-sequence current in the line parallel to the protected line is estimated. The estimate of the zero-sequence current in the line parallel to the protected line may be determined from the zero-sequence current in the protected line using data processing that depends on the state of the first line (in use or disconnected and grounded) and / or the transformer configuration. The estimate of the zero-sequence current in the line parallel to the protected line may be determined without requiring (and in particular without using) any current measurements in the line parallel to the protected line.

[0402] At step 44, an apparent impedance is determined using an estimate of the zero sequence current in the line parallel to the protected line. The apparent impedance may be determined such that it depends on a weighted sum of the first zero sequence current and the second zero sequence current. The weighted sum may be determined as K0I0+K 0mI0 ', where I0 is the zero sequence current obtained from the measurement results on the protected line and I'0 is the estimated zero sequence current in the first line. 0m It may depend on the system impedance (particularly the line impedance and at least one transformer impedance or source impedance).

[0403] Steps 43 and 44 may be implemented in an iterative procedure. The iterative procedure may involve initializing an estimate of the fault location and apparent impedance of the fault in the protected line. The fault location, the estimate of the zero-sequence current in the first line, and the apparent impedance may be iteratively refined in at least one iteration after initialization.

[0404] The apparent impedance may be used to perform a protection function, in particular a distance protection function.

[0405] Figure 5 50 is a diagram illustrating the overall operation of the protection device 20 and method according to an embodiment. The inputs 51 used are voltage and current measurements from the protected line, the line impedance, and at least one of transformer impedance parameters and source impedance parameters from two terminals. Digital substation data 52, including circuit breaker status at the local and remote ends of the two lines, is also acquired to determine the line configuration. Additionally, transformer configuration information is also retrieved. Line current estimation and a two-step apparent impedance calculation 53 can be performed on the first line 11 to obtain an accurate estimate 54 of the apparent impedance (after mutual coupling compensation) that can be used as an output.

[0406] Techniques that may be employed in the protection device 20 and method according to embodiments are described in two parts: (A) estimation of the zero-sequence current in the first line, and (B) mutual coupling compensation using the estimated first zero-sequence current of the first line 11 .

[0407] (A) Estimation of zero-sequence current in parallel lines

[0408] Independent estimation of parallel line status and transformer configuration

[0409] Estimation of the zero-sequence current in the first line 11 (i.e. the line in parallel with the protected second line 12) can be performed without requiring information about whether the first line 11 is in operation or disconnected and grounded and without requiring information about the transformer configuration at the local terminals and remote terminals.

[0410] The device 20 is operable to estimate a first zero-sequence current in the first line 11 as a function of at least a second zero-sequence current in the second line, an estimated fractional fault location from a local terminal, a positive-sequence impedance of the second line, a zero-sequence mutual impedance of the first line and the second line, and a source impedance behind the remote terminal. The device 20 may additionally use at least one of (i) a zero-sequence voltage at the local terminal and (ii) a source impedance behind the local terminal to determine the estimate of the first zero-sequence current in the first line 11.

[0411] The apparatus 20 is operable such that estimating the first zero-sequence current may include estimating the first zero-sequence current I′0 independently of whether the first line is in use and / or independently of whether the transformer is in a wye-wye configuration or a delta-wye configuration, such that the first zero-sequence current satisfies

[0412]

[0413] in,

[0414] in:

[0415] V A0 is the zero-sequence voltage at the local terminal (ie the terminal of the second line closer to the device):

[0416] I0 is the second zero-sequence current in the second circuit;

[0417] d is the estimated fractional fault location from the local terminal;

[0418] Z 0L is the positive sequence impedance of the second line;

[0419] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0420] Z S2 is the source impedance behind the remote terminals.

[0421] Alternatively or additionally, the apparatus can be operable such that estimating the first zero-sequence current may comprise estimating the first zero-sequence current I′0 independently of whether the first line is in use and / or independently of whether the transformer is in a wye-wye configuration or in a delta-wye configuration, such that said first zero-sequence current satisfies

[0422]

[0423] in,

[0424] in:

[0425] I0 is the second zero-sequence current in the second circuit;

[0426] d is the estimated fractional fault location from the local terminal;

[0427] Z 0L is the positive sequence impedance of the second line;

[0428] Z 0M is the zero-sequence mutual impedance of the first line and the second line;

[0429] Z S1 , Z S2 are the source impedance behind the local and remote terminals respectively.

[0430] The estimated fractional fault location may be obtained as described in more detail below and may be iteratively improved in an iterative process comprising an initial step and at least one further iteration, as will be described below.

[0431] Equations (3), (4) or equations (5), (6) can be derived for specific parallel line states and transformer configurations, but surprisingly, provide a robust estimation and a robust distance protection function that uses mutual coupling compensation independently of whether the first line 11 (i.e., the line 11 parallel to the line 12 protected by the device 20) is disconnected and grounded or in operation and independently of the transformer configuration at the local terminal and the remote terminal. The implementation using equations (3), (4) or equations (5), (6) provides the effect of implementing reliable mutual coupling compensation without requiring information about whether the first line 11 (i.e., the line 11 parallel to the line 12 protected by the device 20) is disconnected and grounded or in operation and without requiring information about the transformer configuration at the local terminal and the remote terminal.

[0432] Estimation considering parallel line status and transformer configuration

[0433] During a fault on the protected line, an estimation of the zero-sequence current in the good first line can be achieved using the zero-sequence equivalent circuit of the double-circuit transmission line system.

[0434] The zero-sequence equivalent circuit depends on (1) the transformer configuration at both terminals of the dual-circuit line and (2) the circuit breaker status at the local and remote ends of the two lines. This information can be obtained as input from the digital substation data and can be used to determine how (i.e., which expressions or data processing routines to use) to determine the zero-sequence current in the first line (also called the "first zero-sequence impedance").

[0435] The most common transformer configuration when connecting power stations is delta-wye grounding. Similarly, the most common transformer configuration when connecting substations is wye-wye grounding. Furthermore, two common configurations for dual-circuit lines are: both lines in operation, and one line in operation with the other disconnected and grounded. The following explains the formation of the equivalent circuit and current estimation for the first line of each of these configurations.

[0436] The following notation is used below:

[0437] I′0: zero-sequence current in the line parallel to the protected line (also called “first zero-sequence current”);

[0438] I0: zero-sequence current in the protected line (also known as "second zero-sequence current");

[0439] V A0 : zero-sequence voltage at the local terminal of the protected line (also called local zero-sequence voltage);

[0440] I F : Fault current flowing into the fault resistor;

[0441] d: fractional fault location from the local terminal (“fractional” fault location means the fraction of the zero-sequence impedance of the line after which the fault occurs);

[0442] Z1, Z 0L : positive sequence impedance and zero sequence impedance of the line;

[0443] Z 0m : mutual impedance between the first line and the second line;

[0444] Z T1 , Z T2 : transformer impedance of the transformer at the local terminals and remote terminals, respectively (index 1 represents the transformer at the local terminals (i.e., the terminals close to the protection device performing the protection function), while index 2 represents the transformer at the remote terminals);

[0445] Z S1 , Z S2 : Source impedance behind the local terminals and remote terminals respectively (index 1 indicates the source at the local terminals (i.e., the terminals close to the protection device performing the protection function), while index 2 indicates the source at the remote terminals).

[0446] The following will discuss the correlation between the zero-sequence current in the line parallel to the protected line (also referred to as the "first zero-sequence current") and the measured zero-sequence current in the protected line (also referred to as the "second zero-sequence current") for different states of the first line 11 and for different transformer configurations, respectively.

[0447] The first line is disconnected and grounded

[0448] Transformer configuration: Delta-Wye grounded

[0449] The good first line 11 is disconnected and grounded ( Figure 6 The equivalent zero sequence network of the double-circuit line is as follows Figure 7 The transformer configuration at both terminals is delta-wye grounded. A fault occurs at a distance d from terminal A on line 12, which is in operation and protected by protective relay R1.

[0450] exist Figure 7In the diagram, the upper branch A1-B1 represents the good first line 11 that is disconnected and grounded. I'0 is the zero sequence current in the first line. I0×d×Z 0m is the voltage induced by the current I0 in the section before the fault point F. (I0-I F )×(1-d)×Z 0m The current (I0-I F )induced voltage.

[0451] The lower branch A2-B2 represents the protected line 12 in operation. I0 is the zero sequence current in the protected line. I′0×Z 0m is the voltage induced in line 12 by the current I′ 0 in the first line 11 .

[0452] Apply Kirchhoff's laws to loop 1 and loop 2 (e.g. Figure 7 As shown), the following equations (7) and (8) are obtained.

[0453] Z 0L I′0-Z 0M I0+(1-d)Z 0M I F =0 (7)

[0454] (Z T1 +Z 0L +Z T2 )I0-((1-d)Z0+Z T2 )I F -Z 0M I′0=0 (8)

[0455] These expressions are obtained for parallel lines with substantially the same line impedance, i.e., Z 0L ≈Z′ 0L This is a good approximation for lines of the same material and diameter running in parallel, such as in a power transmission network.

[0456] Unknown fault current I F It can be obtained from equation (7), as shown in the following equation (9),

[0457]

[0458] The fault current I from equation (9) F Substituting into equation (8), the first zero-sequence current in the first line 11 parallel to the protected line 12 can be expressed as

[0459]

[0460] in,

[0461]

[0462] Therefore, the zero sequence current in the first line 11 is expressed as a function of the fault location, the system impedance (more specifically: the transformer impedance) and the line impedance (zero sequence impedance Z 0L and zero-sequence mutual impedance Z 0M ) and the zero-sequence current I0 obtained from the current measured at the protected line 12.

[0463] When V A0 When the zero-sequence voltage at the local terminal of the line 12 protected by the device 20 is obtained through the measurement result, the first zero-sequence current in the first line 11 parallel to the protected line 12 can be expressed as

[0464]

[0465] in,

[0466]

[0467] Using equations (12) and (13), the zero sequence current in the first line 11 is determined as a function of the fault location, the system impedance (more specifically: the remote transformer impedance), the line impedance (zero sequence impedance Z 0L and zero-sequence mutual impedance Z 0M ), the zero-sequence current I0 obtained from the current measured at the protected line 12, and the zero-sequence voltage at the local terminal of the line 12.

[0468] Transformer configuration: Y-grounded-Y-grounded

[0469] The good first line 11 is disconnected and grounded ( Figure 8 The equivalent zero sequence network of the double-circuit line is as follows Figure 9 The transformer configuration at both terminals is Y-grounded-Y-grounded. A fault occurs at a distance d from terminal A on line 12 in operation.

[0470] The correlation of the zero sequence current in the first line 11 with the zero sequence current in the protected line 12 can be estimated using similar techniques as described above. The expression is given in equation (14).

[0471]

[0472] in,

[0473]

[0474] Therefore, the zero sequence current in the first line 11 is represented as a function of the fault location, the system impedance (specifically the source impedance) and the line impedance and the zero sequence current derived from the current measured at the protected line 12 .

[0475] When V A0 When the zero-sequence voltage at the local terminal of the line 12 protected by the device 20 is obtained through the measurement result, the first zero-sequence current in the first line 11 parallel to the protected line 12 can be expressed as

[0476]

[0477] in,

[0478]

[0479] Using equations (16) and (17), the zero sequence current in the first line 11 is determined as a function of the fault location, the system impedance (more specifically: the remote source impedance), the line impedance (zero sequence impedance Z 0L and zero-sequence mutual impedance Z 0M ), the zero-sequence current I0 obtained from the current measured at the protected line 12, and the zero-sequence voltage at the local terminal of the line 12.

[0480] Two lines 11 and 12 in operation

[0481] Transformer configuration: Delta-Wye grounded

[0482] The first line 11 without fault is in use ( Figure 10 The equivalent zero sequence network of the double-circuit line is as follows Figure 11 The transformer configuration at both terminals is delta-wye grounded. A fault F occurs at a distance d from a terminal A on the line 12 in operation protected by a protected device (eg, relay R1).

[0483] The correlation of the zero sequence current in the first line 11 with the zero sequence current in the protected line 12 can be estimated using similar techniques as described above. The expression is given in equation (18).

[0484]

[0485] in,

[0486]

[0487] Therefore, the zero sequence current in the first line 11 is expressed as a function of the fault location, the system impedance (more specifically: the transformer impedance) and the line impedance (zero sequence impedance Z 0L and zero-sequence mutual impedance Z 0M) and the zero-sequence current I0 obtained from the current measured at the protected line 12.

[0488] When V A0 When the zero-sequence voltage at the local terminal of the line 12 protected by the device 20 is obtained through the measurement result, the first zero-sequence current in the first line 11 parallel to the protected line 12 can be expressed as

[0489]

[0490] in,

[0491]

[0492] Using equations (20) and (21), the zero sequence current in the first line 11 is determined as a function of the fault location, the system impedance (more specifically: the remote transformer impedance), the line impedance (zero sequence impedance Z 0L and zero-sequence mutual impedance Z 0M ), the zero-sequence current I0 obtained from the current measured at the protected line 12, and the zero-sequence voltage at the local terminal of the line 12.

[0493] Transformer configuration: Y-grounded-Y-grounded

[0494] The good first line 11 is in use ( Figure 12 The equivalent zero sequence network of the double-circuit line is as follows Figure 13 The transformer configuration at both terminals is Y-grounded-Y-grounded. A fault F occurs at a distance d from a terminal A on the line 12 in operation protected by a protected device (eg, relay R1).

[0495] The correlation of the zero sequence current in the first line 11 with the zero sequence current in the protected line 12 can be estimated using similar techniques as described above. The expression is given in equation (22).

[0496]

[0497] in,

[0498]

[0499] Therefore, the zero-sequence current in the first line 11 is represented as a function of the fault location, the system impedance (specifically the source impedance) and the line impedance, and the zero-sequence current I0 derived from the current measured at the protected line 12 .

[0500] When V A0When the zero-sequence voltage at the local terminal of the line 12 protected by the device 20 is obtained through the measurement result, the first zero-sequence current in the first line 11 parallel to the protected line 12 can be expressed as

[0501]

[0502] in,

[0503]

[0504] Using equations (24) and (25), the zero sequence current in the first line 11 is determined as a function of the fault location, the system impedance (more specifically: the remote source impedance), the line impedance (zero sequence impedance Z 0L and zero-sequence mutual impedance Z 0M ), the zero-sequence current I0 obtained from the current measured at the protected line 12, and the zero-sequence voltage at the local terminal of the line 12.

[0505] (B) Mutual coupling compensation using the estimated first zero-sequence current

[0506] As explained above, zero-sequence mutual coupling compensation is achieved by adding a term to the relay measured current that is proportional to the zero-sequence current of the first line 11. The above describes how the first zero-sequence current can be estimated using local measurements of the protected line and impedance parameters. This section describes how this estimated current can be used to achieve adaptive zero-sequence mutual coupling compensation.

[0507] The expression for the first zero-sequence current is a function of the unknown fault location d, as shown in equations (3)-(6) and (10)-(25). Therefore, mutual coupling compensation can be performed in an iterative procedure. Mutual coupling compensation can be performed as a two-step procedure.

[0508] As a first step, an initial estimate of the unknown fault location can be obtained using the conventional apparent impedance calculated using the following equation (26), which does not take mutual coupling into account.

[0509] An initial estimate of the apparent impedance Z app，in Divide by the total positive sequence line impedance Z1 to obtain an initial estimate of the fractional fault location (Equation (27)).

[0510]

[0511]

[0512] As a next step, using the calculated initial estimate d of the fault location in To estimate the zero-sequence current I′0 in the first line 11 .

[0513] For example, using any one of equations (3), (4) or (5), (6), the estimation of the zero-sequence current I′0 in the first line 11 can be performed independently of the line configuration and the transformer configuration.

[0514] Alternatively, the estimation of the zero-sequence current I'0 in the first line 11 can be performed by selecting an appropriate procedure based on the line and transformer configuration. For each configuration explained above, possible expressions for the zero-sequence current in the first line 11 (i.e., the "first zero-sequence current") are summarized in the following two tables.

[0515] The expression may be selected from the following table, which relates to the case where the zero sequence voltage at the local terminals is used.

[0516]

[0517] The expression may be selected from the following table, which relates to the case where the zero sequence voltage at the local terminals is not used.

[0518]

[0519] The corresponding equations (regardless of whether the line state and transformer configuration are taken into account) are initially evaluated using the fault location estimates obtained according to equations (26) and (27).

[0520] When estimating the zero-sequence current in the first line 11, the apparent impedance is updated using the following equation (28). In this step, the zero-sequence current in the first line 11 is used as I0′ in the following expression (28):

[0521]

[0522] in,

[0523] Then, by using Z according to equation (28) app Replace Z in equation (27) in To update the fault location estimate. The updated estimate of the fault location can be determined as

[0524]

[0525] Using the updated fault location estimate for equation (29), an updated estimate of the first line current can be obtained using one of the expressions given in the table above (where the appropriate expression is selected based on the line state and transformer configuration). An updated value of the apparent impedance is determined using equation (28) (using the updated estimated zero-sequence current for I0′).

[0526] This updated apparent impedance may be output as a final apparent impedance and / or may be used to implement a protection function.

[0527] Although an iterative procedure has been described which involves an initialization step and then only one further iteration, an iterative procedure with two, three or more than three iterations may be implemented. Figures 15 to 19 More detailed description, as described above and Figure 14 The iterative procedure in provides very good results.

[0528] Figure 14 is a flow chart of the method 60. The method 60 may be performed by the protection device 20.

[0529] At step 61, a measurement result of the protected line is received. The measurement result may include U ph , I ph The measurement result may comprise the value of the zero sequence voltage at the local terminals or may allow the protection device to derive said value.

[0530] The protection device can also obtain the positive sequence impedance Z1 of the protected line and the zero sequence impedance Z 0L , and the mutual impedance Z of lines 11 and 12 (in the fault-free state) 0m These system impedance parameters (as well as source and / or transformer impedances) may be stored locally in the protection device 20 or may be retrieved by the protection device from a separate storage system.

[0531] At step 62, the status of the line 11 extending parallel to the line 12 protected by the device 20 may optionally be determined. The determination may include obtaining a status signal or status information. This information may be obtained from digital substation data.

[0532] The transformer configuration may optionally be obtained at step 62. The transformer configuration may be obtained from a substation configuration description, may be specified by an operator, or may be provided in other ways.

[0533] As explained above, step 62 is optional.The apparatus 20 is operable to determine an estimate of the first zero sequence current, determine an estimate of the apparent impedance and / or perform mutual coupling compensation independently of the state of the line 11 extending parallel to the protected line 12 and / or independent of the transformer configuration.

[0534] At step 63, an estimate of the apparent impedance may be initialized. The apparent impedance estimate may be initialized according to equation (27) (ie, without considering mutual coupling).

[0535] An estimate of the fault location in the protected line may be initialized at step 64. The initial value of the fault location may be determined according to equation (28).

[0536] At step 65, an initial estimate of the zero-sequence current in the first line may be determined using the zero-sequence current in the protected line obtained from the measurements, the previously obtained fault location estimate, and the system impedance parameter. The manner in which the initial estimate of the zero-sequence current depends on the zero-sequence current obtained from the current measurements in the protected line, the previously obtained fault location estimate, and the system impedance parameter may be independent or may depend on (i) the state of the first line (in service or disconnected and grounded) and (ii) the transformer configuration, as explained above.

[0537] At step 66, the estimate of the apparent impedance is updated using the previously obtained estimate of the zero sequence current in the first line. This can be done using equation (28).

[0538] At step 67, a refined estimate of the fault location may be determined (using equation (29) and the previously determined estimate of the apparent impedance) and the zero sequence current in line 11 parallel to the protected line may be determined. This may be done again using equations (3) and (4) (independent of (i) the state of the first line (in service or disconnected and grounded) and (ii) the transformer configuration), equations (5) and (6) (independent of (i) the state of the first line (in service or disconnected and grounded) and (ii) the transformer configuration), or using an appropriate one of equations (10) to (24) selected based on (i) the state of the first line (in service or disconnected and grounded) and (ii) the transformer configuration (it will be understood that the definition of A is associated with the expression for the zero sequence current, respectively).

[0539] While one iteration generally provides very good results, as will be explained below, multiple iterations may be performed by repeating step 67 .

[0540] At step 68, the final estimate of the apparent impedance may be used as the apparent impedance. The apparent impedance may be output and / or may be used to perform a protection function. Mutual coupling compensation may be performed by taking into account the mutual coupling according to, for example, equation (28).

[0541] Example

[0542] This section presents the results obtained using the protection devices and methods according to the embodiments. Figure 15 The 50 Hz, 400 kV double circuit transmission line system 69 with a length of 200 km is modeled. The impedance parameters are given below.

[0543] Impedance parameters value Positive sequence impedance 0.36<84.9°ohm / km Zero-sequence impedance 1.41<82.8°ohm / km Zero-sequence mutual impedance 0.95<80.6ohm / km Transformer positive sequence impedance 42.35<59ohm

[0544] Line A1-B1 is the line protected by relay R1. Voltage and current measurements from terminal A1 of line A1-B1, along with line and system impedance parameters, are used as inputs. Additionally, status signals from the digital substation data are used to determine the line configuration. The transformer configurations at both terminals are also acquired.

[0545] Different combinations of line and transformer configurations were tested and the results are discussed below.

[0546] The first line is disconnected and grounded

[0547] Transformer configuration: Delta-Wye grounded

[0548] Figure 16 Shown for Figure 15 Figure 1 shows the values ​​and plots of apparent impedance calculated for faults at different locations on the second line 12. The fault location is determined as a fractional fault location (i.e. the portion of the line impedance before the fault relative to the total line impedance, as measured from the terminals where the protection device is arranged).

[0549] Figure 16 The actual impedance 71 as seen by the protection device R1 is shown.

[0550] Figure 16 The apparent impedance 73 (shown by a solid line and solid diamond symbols) obtained using a protection device or method according to an embodiment is shown. More specifically, using Figure 13 The apparent impedance 73 is obtained by a method wherein only one iteration is performed at step 67. The apparent impedance 73 is obtained without requiring any current measurement of the first line 11.

[0551] Figure 16 An apparent impedance 72 (shown by a solid line and open circles) obtained using a method in which the first zero-sequence current in the first line 11 is derivable from measurements is shown.

[0552] As from Figure 16 As can be seen, the apparent impedance 73 obtained using a protection device or method according to an embodiment is very consistent with the apparent impedance 72 using actual current measurements from the first line 11. Thus, the protection device and method of the embodiment provide results comparable to those obtained when using actual current measurements from the first line 11, while avoiding the need to transmit such current measurements from the current transformer on the first line 11 to the protection device R1 providing the protection function of the line 12.

[0553] The apparent impedance 73 also provides a good approximation of the actual impedance obtained by PSCAD. The apparent impedance calculated using the estimated current is very close to the impedance calculated using the measured current and deviates no more from the actual impedance 71 than the apparent impedance 73 calculated using the current measured from the other line. This demonstrates the accuracy of the proposed algorithm.

[0554] Transformer configuration: Y-grounded-Y-grounded

[0555] Similarly, Figure 17 The figure shows the apparent impedances calculated for a fault at different locations on the second line 12 when the first line 11 is disconnected and grounded and the transformer is configured in a wye-wye grounded configuration. Shown are the actual impedance 71, the apparent impedance 72 calculated using the current measured from the first line, and the apparent impedance 73 calculated using the first line current estimated in the proposed solution, as obtained by the protection device and method according to an embodiment. The apparent impedance 73 calculated using the estimated current is very close to the apparent impedance 72 calculated using the measured current, while avoiding the need to obtain current measurements from lines parallel to the line protected by the protection device performing mutual coupling compensation.

[0556] The two lines in operation are omitted

[0557] Transformer configuration: Delta-Wye grounded

[0558] Figure 18 The figure shows the apparent impedances calculated for faults at different locations on the second line 12 when both lines 11, 12 are in operation and the transformer is configured for delta-wye grounding. Shown are the actual impedance 71, the apparent impedance 72 calculated using the current measured from the first line, and the apparent impedance 73 calculated using the first line current estimated in the proposed solution, as obtained by the protection device and method according to an embodiment. The apparent impedance 73 calculated using the estimated current is very close to the apparent impedance 72 calculated using the measured current, while avoiding the need to obtain current measurements from lines parallel to the line protected by the protection device performing mutual coupling compensation.

[0559] Transformer configuration: Y-grounded-Y-grounded

[0560] Figure 19The figure shows the apparent impedances calculated for faults at different locations on the second line 12 when both lines 11, 12 are in operation and the transformer is configured for delta-wye grounding. Shown are the actual impedance 71, the apparent impedance 72 calculated using the current measured from the first line, and the apparent impedance 73 calculated using the first line current estimated in the proposed solution, as obtained by the protection device and method according to an embodiment. The apparent impedance 73 calculated using the estimated current is very close to the apparent impedance 72 calculated using the measured current, while avoiding the need to obtain current measurements from lines parallel to the line protected by the protection device performing mutual coupling compensation.

[0561] Robustness to system impedance variations

[0562] The techniques disclosed herein are shown to be robust against variations in system impedances, such as one or more source impedances and / or one or more transformer impedances. Thus, the estimates are sufficient to approximate the one or more source impedances and / or one or more transformer impedances in the techniques disclosed above. In the absence of more specific information, the estimates can even be default values ​​or can be received as system configuration information.

[0563] Figure 20 The actual impedance 71 of the first line in use for a Y-grounded-Ye-grounded transformer configuration and the apparent impedances 73-77 obtained when the technique of the present invention is used to estimate the zero sequence current in the first line are shown. Curve 73 shows the actual remote source impedance Z when used. S2 Curve 74 shows the apparent impedance obtained when using a Z that exceeds the actual remote source impedance by 10%. S2 Curve 75 shows the apparent impedance obtained when using a Z value that exceeds the actual remote source impedance by 20%. S2 Curve 76 shows the apparent impedance obtained when using a Z value that is 10% smaller than the actual remote source impedance. S2 Curve 77 shows the apparent impedance obtained when using a Z value that is 20% smaller than the actual remote source impedance. S2 The apparent impedance obtained when the value

[0564] As from Figure 20 It can be clearly seen that the results are robust to deviations of the value of one or more source impedances from their actual values. This applies similarly when using one or more equations that depend on both the local source impedance and the remote source impedance and / or when using one or more equations that depend on one or more transformer impedances.

[0565] Protection devices, methods, and systems according to embodiments provide zero-sequence mutual coupling compensation for distance protection of dual-circuit transmission lines. The devices, methods, and systems according to embodiments eliminate the need to obtain current measurements from a line parallel to the line on which the protection device is located to implement mutual coupling compensation. Instead, a first zero-sequence current in a first line current is estimated using available digital substation data, local measurements on the protected line, and impedance parameters.

[0566] Apparatus, methods and systems according to embodiments provide results that are both accurate and robust.

[0567] The devices, methods and systems according to embodiments may be used to provide distance protection for transmission networks, wherein the lengths of the lines may be at least 50 km, at least 100 km, at least 150 km, at least 200 km, but are not limited thereto.

[0568] The apparatus, method and system according to the embodiments may be used to provide distance protection for a transmission network in a power grid including renewable energy sources.

[0569] Although the invention has been described in detail in the drawings and foregoing description, such description should be considered illustrative or exemplary rather than restrictive. Variations of the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention based on a study of the drawings, the present disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the indefinite article "a" or "an" does not exclude a plurality. The mere fact that certain elements or steps are recited in different claims does not indicate that a combination of these elements or steps cannot be used to advantage, and in particular, apart from actual claim dependencies, any other meaningful claim combination should be considered disclosed.

Claims

1. A device for a double-circuit power transmission system having a first line and a second line, wherein: The device is a protection device operable to perform a protection function based on an apparent impedance, and wherein the protection function is a distance protection function, the device comprising: an interface for receiving a current measurement result of the second line; and at least one processing module operable to: calculating a second zero-sequence current in the second line based on the current measurement result, estimating a first zero-sequence current in the first line based on the second zero-sequence current, wherein the apparatus is operable to multiply the second zero-sequence current by a multiplication factor to estimate the first zero-sequence current, and wherein the multiplication factor depends on a state of the first line and a transformer configuration of transformers at opposite terminals of both the first line and the second line, and The apparent impedance is determined based on the second zero-sequence current, the estimated first zero-sequence current, and a coefficient associated with system impedance.

2. The device according to claim 1, wherein The apparatus is operable to estimate the first zero-sequence current without using current measurements of the first line.

3. The apparatus of claim 1, wherein: The apparatus is operable to determine an estimate of a fault location of a fault in the second line based on the apparent impedance and a positive sequence line impedance of the second line.

4. The apparatus of claim 3, wherein: The apparatus is operable to estimate the first zero-sequence current based on: An estimate of the fault location, The second zero-sequence current, the positive sequence line impedance of the second line, the zero-sequence mutual impedance of the first line and the second line, and a source impedance at a side of a local terminal of the second line opposite to the device, and / or a source impedance at a side of a remote terminal of the second line opposite to the device.

5. The apparatus according to claim 3 or 4, wherein: The apparatus is operable to determine an estimate of the fault location, the first zero sequence current and the apparent impedance in an iterative procedure.

6. The apparatus according to claim 3 or 4, wherein: The interface is operable to receive a zero-sequence voltage at a terminal of the second line, and the device is operable to determine the first zero-sequence current based on at least one of: the zero-sequence voltage, and a source impedance at a side of a local terminal of the second line opposite the device.

7. The apparatus of claim 1, wherein: The multiplication factor depends on: whether the first line is (i) in use or (ii) disconnected and grounded, and The transformer configuration of the transformers at opposite terminals of both the first line and the second line is (i) delta-wye grounded or (ii) wye grounded-wye grounded.

8. The apparatus of claim 1, wherein: The multiplication factor: depends on the transformer impedance of at least one of the transformers and is independent of the source impedance for a delta-wye grounded transformer configuration, and A source impedance is dependent on at least one of the sources of a grounded wye-grounded wye transformer configuration coupled to a side of the transformer opposite the device.

9. The apparatus of claim 1, wherein: The apparatus is operable to determine the apparent impedance including mutual coupling compensation, wherein determining the apparent impedance including the mutual coupling compensation comprises calculating a sum of the following items to determine the apparent impedance: a short-circuit current in the faulted phase of the second line, a product of a first factor and an estimated first zero-sequence current, and a product of a second factor and the second zero-sequence current.

10. A power system, comprising: A dual-circuit transmission system, comprising: First line and Second line; and A device as claimed in any preceding claim, operatively coupled to the second line.

11. A method for estimating a first zero-sequence current of a first line in a double-circuit power transmission system using the apparatus according to any one of claims 1 to 9, the method comprising: estimating, by the device, a first zero-sequence current in a first line of a double-circuit transmission system, the first zero-sequence current being estimated based on a second zero-sequence current in a faulty second line of the double-circuit transmission system; as well as An apparent impedance is determined by the apparatus based on the estimated first zero-sequence current.

12. The method of claim 11, wherein: Determining the apparent impedance includes: Determine the apparent impedance including mutual coupling compensation, wherein determining the apparent impedance including the mutual coupling compensation includes calculating the sum of the following items to determine the apparent impedance: the short-circuit current in the faulted phase of the second line, the product of a first factor and the estimated first zero-sequence current, and the product of a second factor and the second zero-sequence current.

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