A method of determining a measurement impedance

Abstract

The application provides a determination method of measurement impedance, which can efficiently and accurately determine the measurement impedance of a same-tower double-circuit parallel joint line through simplifying the same-tower double-circuit parallel joint line. The determination method of the measurement impedance is applied to the same-tower double-circuit parallel joint line and comprises the following steps: obtaining electrical parameters of the same-tower double-circuit parallel joint line; simplifying the same-tower double-circuit parallel joint line, wherein the simplification is to equivalently regard the joint areas of the same-tower double-circuit parallel joint line except the joint area where the fault point is located as single-circuit line circuits; obtaining a joint scheme of the same-tower double-circuit parallel joint line after the simplification; and calculating the measurement impedance of the same-tower double-circuit parallel joint line according to the electrical parameters and the joint scheme after the simplification.

Description

Technical Field

[0001] This application relates to the field of power system relay protection technology, and in particular to a method for determining impedance measurement. Background Technology

[0002] With the growth of national electricity demand and the expansion of urban areas, the outgoing corridors of transmission lines are becoming increasingly congested. In order to improve the utilization efficiency of power grid line assets and increase the transmission capacity of the lines, the A, B, and C phases of the first circuit of the early-built double-circuit line on the same tower are connected to the A, B, and C phases of the second circuit to form a parallel double-circuit line on the same tower (denoted by D), so as to increase the line current carrying capacity of this section of the line.

[0003] Due to the complex operation of double-circuit parallel-connected lines on the same tower and the existence of mutual inductance coupling between the lines, it is urgent to solve the problem of how to efficiently and accurately determine the measurement impedance of double-circuit parallel-connected lines on the same tower after a fault occurs. Summary of the Invention

[0004] This application provides a method for determining the measured impedance, which can efficiently and accurately determine the measured impedance of a double-circuit parallel-connected line on the same tower.

[0005] Firstly, a method for determining impedance measurement is provided, applicable to double-circuit parallel-connected lines on the same tower, including:

[0006] Obtain the electrical parameters of the parallel-connected double-circuit lines on the same tower;

[0007] The double-circuit parallel connection on the same tower is simplified by treating the connection area of ​​the double-circuit parallel connection on the same tower, except for the connection area where the fault point is located, as a single-circuit line.

[0008] Obtain the simplified connection scheme for the parallel connection of two-circuit lines on the same tower;

[0009] Based on the electrical parameters and the simplified connection scheme, calculate the measured impedance of the double-circuit parallel connection line on the same tower.

[0010] In a feasible design, when a double-circuit parallel connection line on the same tower is connected to a double-circuit line on the same pole, a simplified connection scheme for the double-circuit parallel connection line on the same tower is obtained, including:

[0011] An overlap point is set at a preset interval on the parallel double-loop line on the same pole;

[0012] Based on the double-circuit lines on the same pole after the lap joint point is set, obtain the lap joint scheme of the double-circuit parallel lap joint lines on the same tower.

[0013] In a feasible design, the method also includes:

[0014] The length of the target segment relative to the total length of the single-circuit line is determined based on the splicing plan. The target segment includes the first line segment, the second line segment, and the third line segment.

[0015] The first line segment is the first joint point near the first distance protection installation location closest to the fault point, and the line segment between the first distance protection installation location and the first distance protection installation location. The first distance protection installation location is located at one end of a double-circuit line on the same pole.

[0016] The second line segment is the line segment between the fault point and the first connection point;

[0017] The third line segment is the overlapping area where the fault point is located.

[0018] In a feasible design, the electrical parameters include one or more of the following parameters:

[0019] The data include the phase voltages at the first distance protection installation point, the phase currents at the first distance protection installation point, the zero-sequence current at the first distance protection installation point, the positive-sequence impedance of the entire single-circuit line, the positive-sequence unit impedance of the single-circuit line, the zero-sequence unit mutual impedance of the double-circuit line on the same pole, the phase currents at the second distance protection installation point located at the other end of the double-circuit line on the same pole, the zero-sequence current of the second distance protection installation point, the unit zero-sequence impedance of the double-circuit line on the same pole, the zero-sequence compensation coefficient of the double-circuit line on the same pole, and the total zero-sequence current of the double-circuit line on the same pole.

[0020] In a feasible design, the measured impedance of the double-circuit parallel-connected lines on the same tower is calculated based on electrical parameters and connection scheme, including:

[0021] Based on the electrical parameters and connection scheme, the measuring impedance Z of the grounding distance protection for a double-circuit parallel-connected line on the same tower is calculated using the following formula. m :

[0022]

[0023]

[0024]

[0025]

[0026] in, For the voltage at the first distance protection installation point, For the first distance protection installation point current, Let Z1 be the zero-sequence current at the first distance protection installation point, α1 be the percentage of the length of the first line segment to the length of the single-circuit line, β1 be the percentage of the length of the second line segment to the length of the single-circuit line, β be the percentage of the length of the third line segment to the length of the single-circuit line, Z1 be the positive-sequence impedance of the total length of the single-circuit line, and Z0 be the unit zero-sequence impedance of the line. m0 Z1 is the zero-sequence unit mutual impedance of a double-circuit line on the same pole, K1 is the positive-sequence unit impedance of a single-circuit line, K′ is the zero-sequence compensation coefficient, and C is the amplification coefficient. M0 C is the zero-sequence current distribution coefficient at the installation location of the first distance protection. N0 The zero-sequence current distribution coefficient at the installation location of the second distance protection. This represents the total zero-sequence current of the line. The zero-sequence current at the first distance protection installation point, The zero-sequence current at the installation location of the second distance protection is denoted as i, where i is A, B, or C, where A represents phase A, B represents phase B, and C represents phase C.

[0027] In a feasible design, the measured impedance of the double-circuit parallel-connected lines on the same tower is calculated based on electrical parameters and connection scheme, including:

[0028] Based on the electrical parameters and connection scheme, the measuring impedance Z of the phase-to-phase distance protection for a double-circuit parallel connection on the same tower is calculated using the following formula. m :

[0029]

[0030] The voltage of phase i at the installation location of the first distance protection is given, where i can be A, B, or C, where A represents phase A, B represents phase B, and C represents phase C. The voltage of phase j at the installation location of the first distance protection is given, where j is A, B, or C, and j ≠ i. The i-phase current at the first distance protection installation location. Let α1 be the j-phase current at the first distance protection installation point, β1 be the percentage of the length of the first line segment to the total length of the single-circuit line, β1 be the percentage of the length of the second line segment to the total length of the single-circuit line, β be the percentage of the length of the third line segment to the total length of the single-circuit line, and Z1 be the positive sequence impedance of the entire single-circuit line. This refers to the i-phase current at the installation location of the second distance protection.

[0031] Secondly, an impedance measurement and determination device is provided, applicable to double-circuit parallel-connected lines on the same tower, including:

[0032] The electrical parameter acquisition module is used to acquire the electrical parameters of the parallel-connected double-circuit lines on the same tower.

[0033] The line simplification module is used to simplify the parallel connection of double-circuit lines on the same tower. The simplification process is to treat the connection area of ​​the parallel connection of double-circuit lines on the same tower, except for the connection area where the fault point is located, as a single-circuit line.

[0034] The splicing scheme acquisition module is used to acquire the splicing scheme of the double-circuit parallel splicing line on the same tower after simplification.

[0035] The impedance measurement determination module is used to calculate the measured impedance of a double-circuit parallel connection line on the same tower based on electrical parameters and a simplified connection scheme.

[0036] In a feasible design, when a double-circuit parallel connection line on the same tower is connected to a double-circuit line on the same pole, a simplified connection scheme for the double-circuit parallel connection line on the same tower is obtained, including:

[0037] An overlap point is set at a preset interval on the parallel double-loop line on the same pole;

[0038] Based on the double-circuit lines on the same pole after the lap joint point is set, obtain the lap joint scheme of the double-circuit parallel lap joint lines on the same tower.

[0039] In one feasible design, the device also includes a target segmentation ratio determination module;

[0040] The target segment percentage determination module is used to determine the percentage of the target segment's length relative to the total length of a single-circuit line, based on the splicing scheme. The target segments include the first line segment, the second line segment, and the third line segment.

[0041] The first line segment is the first joint point near the first distance protection installation location closest to the fault point, and the line segment between the first distance protection installation location and the first distance protection installation location. The first distance protection installation location is located at one end of a double-circuit line on the same pole.

[0042] The second line segment is the line segment between the fault point and the first connection point;

[0043] The third line segment is the overlapping area where the fault point is located.

[0044] In a feasible design, the electrical parameters include one or more of the following parameters:

[0045] The data include the phase voltages at the first distance protection installation point, the phase currents at the first distance protection installation point, the zero-sequence current at the first distance protection installation point, the positive-sequence impedance of the entire single-circuit line, the positive-sequence unit impedance of the single-circuit line, the zero-sequence unit mutual impedance of the double-circuit line on the same pole, the phase currents at the second distance protection installation point located at the other end of the double-circuit line on the same pole, the zero-sequence current of the second distance protection installation point, the unit zero-sequence impedance of the double-circuit line on the same pole, the zero-sequence compensation coefficient of the double-circuit line on the same pole, and the total zero-sequence current of the double-circuit line on the same pole.

[0046] In the above embodiments of this application, by simplifying the double-circuit parallel connection on the same tower, the connection area of ​​the double-circuit parallel connection on the same tower, excluding the connection area where the fault point is located, is equivalent to a single-circuit line. This facilitates efficient and accurate calculation of the measured impedance of the double-circuit parallel connection on the same tower based on electrical parameters and connection scheme after a fault occurs. Attached Figure Description

[0047] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a schematic diagram of an exemplary embodiment of the present application applied to an IA-G fault composite sequence network of a double-circuit parallel-connected line on the same tower;

[0049] Figure 2 This is a schematic diagram of an exemplary embodiment of the present application applied to an IA-G fault composite sequence network of a double-circuit parallel-connected line on the same tower;

[0050] Figure 3 This is a schematic diagram illustrating an example of a single-circuit fault in a double-circuit parallel connection line on the same tower, provided by an exemplary embodiment of this application.

[0051] Figure 4 This is a schematic diagram of an exemplary embodiment of the present application applied to an IBC-G fault composite sequence network of a double-circuit parallel-connected line on the same tower;

[0052] Figure 5 This is a schematic flowchart illustrating an exemplary method for determining impedance measurement provided in an exemplary embodiment of this application;

[0053] Figure 6 This is a schematic diagram of a fault in section be of a double-circuit parallel-connected line on the same tower, provided by an exemplary embodiment of this application.

[0054] Figure 7This is an exemplary embodiment of the present application, providing a schematic diagram of the equivalent circuit for a fault in the be section of a double-circuit parallel-connected line on the same tower.

[0055] Figure 8 This is a schematic diagram of an exemplary embodiment of the present application applied to a double-circuit parallel connection on the same tower;

[0056] Figure 9 This is a schematic diagram of an exemplary method for calculating impedance measurement provided in an exemplary embodiment of this application;

[0057] Figure 10 This is a schematic diagram illustrating the actual protection range of an IA-G fault provided in an exemplary embodiment of this application;

[0058] Figure 11 This is a schematic diagram illustrating the actual protection range of an IBC fault provided in an exemplary embodiment of this application;

[0059] Figure 12 This is a schematic diagram illustrating the actual protection range of an IBIIC fault provided in an exemplary embodiment of this application;

[0060] Figure 13 This is yet another schematic diagram illustrating the actual protection range of an IA-G fault provided in an exemplary embodiment of this application;

[0061] Figure 14 This is another example of the actual protection range of an IBC fault provided by an exemplary embodiment of this application;

[0062] Figure 15 This is yet another example of the actual protection range of an IBIIC fault provided by an exemplary embodiment of this application;

[0063] Figure 16 This is a schematic diagram of an example impedance determination device provided in an exemplary embodiment of this application. Detailed Implementation

[0064] The embodiments of this application are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application. It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other.

[0065] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this application means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0066] To determine the measured impedance of a double-circuit parallel-connected line on the same tower, this application makes the following inference regarding the validity of "treating the connection area of ​​a double-circuit parallel-connected line on the same tower, excluding the connection area where the fault point is located, as equivalent to a single-circuit line":

[0067] Faults in double-circuit parallel-connected lines on the same tower are typically analyzed using the six-sequence fault component method. According to this method, the reverse vector current circulates in the double-circuit line, but in systems outside the double-circuit line, the reverse vector current is zero, and the reverse vector voltage on both busbars is zero. Compared to a single-circuit line, the zero-sequence same-vector impedance in the zero-sequence network is the zero-sequence impedance of a single-circuit line plus three times the inter-line mutual impedance; while the positive-sequence and negative-sequence equivalent networks are independent of inter-line mutual inductance and can be equivalent to a single-circuit line. The impedance parameters of the six-sequence component method are shown in Table 1.

[0068] This invention treats the I and II circuits as a whole to achieve protection. The distance protection measures the voltage and current at the protection installation point. After decomposition using the six-sequence component method, it can be seen that the measured current at the protection installation point is twice the same vector current.

[0069] Table 1

[0070] Six-sequence impedance symbol Impedance conversion Zero-sequence common impedance <![CDATA[Z T0 ]]> <![CDATA[Z s +2Z m +3Z m0 ]]> Zero-sequence reverse impedance <![CDATA[Z F0 ]]> <![CDATA[Z s +2Z m -3Z m0 ]]> Orthogonal impedance <![CDATA[ Z T1 ]]> <![CDATA[Z s -WITH m ]]> Forward and reverse impedance <![CDATA[Z F1 ]]> <![CDATA[Z s -WITH m ]]> negative common impedance <![CDATA[Z F2 ]]> <![CDATA[Z s -WITH m ]]> Negative reverse impedance <![CDATA[Z F2 ]]> <![CDATA[Z s -WITH m ]]>

[0071] Table 1 records the parameters corresponding to different six-sequence component impedances.

[0072] Referring to Table 1, taking the parallel double-circuit line on the same tower as an example, which uses the method of connecting and erecting parallel double-circuit lines on the same pole, this application further analyzes the measured impedance for different types of faults:

[0073] (1) Analysis of single-phase-to-ground short-circuit faults in a single-circuit line

[0074] According to the six-sequence fault component method, the composite sequence network of IA-G faults on parallel double-circuit lines on the same pole is as follows: Figure 1 As shown. Figure 1In the diagram, T1, T2, and T0 represent the positive, negative, and zero-sequence networks of the same vector, respectively; F1, F2, and F0 represent the positive, negative, and zero-sequence networks of the opposite vector, respectively; R represents the resistance; D represents one end of the parallel connection of the double-circuit line on the same tower; and k represents the other end of the parallel connection of the double-circuit line on the same tower.

[0075] Will Figure 1 The positive, negative, and zero-sequence networks of the inverse and reverse quantities are equivalent to the equivalent impedance Z. equ Then, according to Table 1 and Figure 1 The Ia-G composite sequence network can be simplified to Figure 2 Equivalent impedance Z equ As shown in formula (1):

[0076] Z equ =2(Z) 1m / / Z 1n )+(Z 0m -3Z′ mM ) / / (Z 0n -3Z n ′ M (1);

[0077] in, The electromotive forces of the power supply on the M and N sides are respectively, Z 1m Z 2m Z 0m +3Z m0 These are the positive, negative, and zero-sequence impedances of the same vector on the M side, respectively, Z 1n Z 2n Z 0n +3Z m0 These are the positive, negative, and zero-sequence impedances of the N-side, which are in the same vector. These are the positive, negative, and zero-sequence currents on the M side, respectively, in the same vector. These represent the positive, negative, and zero-sequence currents on the N-side, respectively, and 2Z 1sm 2Z 2sm 2Z 0sm Let be the system impedances at the corresponding locations on the M side, and 2Z. 1sn 2Z 2sn 2Z 0sn These are the system impedances at the corresponding locations on the N side, and Z is the Z-axis impedance. 0m Z′ is the zero-sequence impedance of the M-side single-circuit line. mM The mutual impedance between the M-side lines is shown; " / / " indicates parallel connection; Z 0n Z′ is the zero-sequence impedance of the N-side single-circuit line. nM Z is the mutual impedance between the N-side lines. m0 The zero-sequence unit mutual impedance of a double-circuit line on the same pole. This is the positive sequence current at the fault point. The negative sequence current at the fault point. R is the zero-sequence current at the fault point. g This is the transition resistor at the fault point.

[0078] according to Figure 2 The measured voltage at the distance protection installation point at the beginning of the double-circuit line can be obtained. As shown in formula (2):

[0079]

[0080] in, These are the same-vector positive, negative, and zero-sequence voltages on the M side, respectively. These represent the positive, negative, and zero-sequence voltages in the same vector at the fault point, respectively, and l is the distance from the fault point to side M. These are the positive, negative, and zero-sequence currents on the M side, respectively.

[0081] Due to the influence of the inverse vector network, in formula (2) Its value is related to Z equ The relevant details are shown in formula (3):

[0082]

[0083] The measured impedance Z at the M-side distance protection installation location m As shown in formula (4):

[0084]

[0085] Where, K = (Z0 + 3Z) m0 -Z1) / 3Z1, where K is the zero-sequence compensation coefficient for double-circuit lines on the same pole. Z0 is the current measured at the protection installation point on the M side, Z1 is the zero-sequence impedance of the line, and Z0 is the positive-sequence impedance of the line.

[0086] Substituting formula (2) into formula (4), the distance protection measurement impedance Z on the M side is... m It can be shown in the following formula (5):

[0087]

[0088] in, K' is the amplification factor. For the same vector current on the M side, For the zero-sequence current of the same vector on the M side, This represents the same vector voltage on side M. The voltage at the fault location is the same vector voltage. The current measured on side M. The current measured on the N side. The zero-sequence current is α, where α is the proportion of the fault to the total length of a single circuit (also known as a single-circuit line). Figure 3 (As shown), G represents ground, Z keq Z is the equivalent fault impedance. Δ1 To add impedance in parallel, Z Δ2 To increase the added impedance, The equivalent fault impedance Z keq This reflects the equivalent positive sequence impedance from the fault point to the distance protection installation location when the parallel double-circuit lines are considered as a whole to form a distance protection system, and the parallel additional impedance Z. Δ1 This indicates the additional impedance introduced due to the parallel operation of two circuits on the same pole; the additional impedance Z is increased. Δ2 This represents the additional impedance introduced by the N-side power supply.

[0089] It can be seen that the measured impedance Z at the M-side distance protection installation location m It can be viewed as being composed of the equivalent fault impedance Z keq Parallel additional impedance Z Δ1 and the additional impedance Z Δ2 It consists of three parts.

[0090] As can be seen from formula (5), due to the special structure of the double-circuit line on the same pole, the measured impedance Z of its grounding distance protection is... m It cannot accurately reflect the equivalent fault impedance Z from the fault point to the short circuit point. keq This will affect the sensitivity of protective actions.

[0091] Parallel additional impedance Z Δ1 The magnitude of the current on the opposite side is irrelevant; it is only affected by the location of the fault point. As can be seen from formula (5), the parallel additional impedance Z is only applied when α = 0 or α = 1, i.e., when the beginning or end of the overhead line is short-circuited. Δ1 =0, the impedance measuring element can accurately measure the distance from the fault point to the protection installation location. Faults at other points will cause an increase in the measured impedance amplitude, a reduction in the protection range, and a decrease in sensitivity. Z Δ1 The magnitude of the error is linearly related to the distance from the fault point to the protection installation location. The smaller the distance, the greater the relative measurement error caused by the parallel additional impedance.

[0092] Adding additional impedance Z Δ2 The main influence is on the amplification coefficient; the larger the amplification coefficient K', the greater Z. Δ2 The larger the value, the lower the protection sensitivity. The amplification factor K' is related to the ratio of the measured current, the zero-sequence current, the positive-sequence impedance, and the zero-sequence mutual impedance between circuits. The simplified amplification factor K' is shown in formula (6):

[0093]

[0094] in, This is the zero-sequence current on the N-side. For the zero-sequence current on the M side, C N0 C is the zero-sequence current distribution coefficient on the N-side. M0 The zero-sequence current distribution coefficient on the M side.

[0095] Command: Z Δ =Z Δ1 +Z Δ2 Then Z Δ As shown in the following formula (7):

[0096]

[0097] Among them, Z Δ This represents the total additional impedance.

[0098] The total additional impedance Z can be obtained according to formula (7). Δ The maximum value.

[0099] The actual performance of distance protection needs to comprehensively consider the effects of parallel additional impedance and auxiliary additional impedance. Let's assume that the setting value of the distance protection stage I is the line impedance α. set The actual protection range r of distance protection segment I can be calculated from equation (8) as shown in equation (8):

[0100]

[0101] It can be seen that r decreases monotonically as the boosting coefficient K′ increases. When K′ equals zero (i.e., single-sided power supply), r reaches its maximum value. But it is still less than α set This indicates that even under ideal conditions with no power supply boost on the opposite side, the maximum protection range of distance protection stage I cannot reach the expected protection range α. set .

[0102] (2) Analysis of two-phase-to-ground short-circuit faults in a single-circuit line

[0103] Taking a single-circuit BC two-phase-to-ground short-circuit fault as an example, according to the six-sequence fault component method, its composite sequence network is as follows: Figure 4 As shown.

[0104] Depend on Figure 4 It can be seen that when the reverse vector sequence network F1, F2, and F0 are connected in series with the corresponding loop of the same vector, the effect on the measured impedance is the same as that of the transition resistance, which will cause the measured impedance amplitude to increase and the sensitivity to decrease.

[0105] At this time, the measuring impedance Z at the distance protection installation point on the M side m As shown in formula (9):

[0106]

[0107] in, The voltage measured on side M.

[0108] The current measured on side M.

[0109] Based on the six-sequence fault component method, analyze the measured impedance Z at this time. m It can be characterized as:

[0110]

[0111] in, This is the phase-to-phase voltage value. This is the current in phase B. For the current in phase C, The voltage of phase B. The voltage of phase C, The voltage of phase B with the same vector at the fault location.

[0112] The voltage of phase C with the same vector at the fault location. For phase B currents with the same vector, These are C-phase currents in the same vector.

[0113] Similar to single-phase grounding faults, the measured impedance Z in formula (10) m It can also be viewed as being caused by the equivalent fault impedance Parallel additional impedance and increase additional impedance The system consists of three parts. The effect of the parallel additional impedance on the distance protection is explained in the relevant section on single-phase grounding faults, and will not be repeated here. The amplification coefficient K″ of the additional impedance is shown in formula (11).

[0114]

[0115] in, The current measured on the N side. The current measured on side M.

[0116] (3) Analysis of three-phase short-circuit faults on a single-circuit line

[0117] The method for calculating the measured impedance in a single-circuit three-phase short-circuit fault is the same as that for a single-circuit two-phase-to-ground short-circuit fault.

[0118] (4) Fault analysis of IAIIA-G, IBCIIBC-G, and IABCIIABC

[0119] The fault types IAIIA-G, IBCIIBC-G, and IABCIIABC are equivalent to a short circuit occurring after a bridging at the fault point. The current flowing through the two parallel double-circuit lines on both sides of the fault point is almost equal, which can be equivalent to a single-circuit line. Therefore, the calculation method for the measured impedance under these fault types is the same as that for the measured impedance under a single-circuit line fault.

[0120] Based on the above inferences regarding the measured impedance under different fault types, this application provides a method for determining the measured impedance, applicable to double-circuit parallel-connected lines on the same tower, such as... Figure 5 As shown, the method includes:

[0121] S110, obtain the electrical parameters of the double-circuit parallel connection on the same tower.

[0122] S120, the parallel connection of the double-circuit line on the same tower is simplified by treating the connection area of ​​the parallel connection of the double-circuit line on the same tower, except for the connection area where the fault point is located, as a single-circuit line.

[0123] like Figure 6 As shown, assuming points b, c, d, and e are the overlap points, the be section of the line is divided into three segments of equal length. Analyze the impact of the overlap scheme on the be section during a fault.

[0124] At the junction point, all phases of the double-circuit are at the same potential, i.e., at points b, c, d, and e. Since each circuit of the double-circuit has identical line parameters and length, the current flowing through each circuit in the non-faulty junction areas bc and de (excluding the faulty junction area (cd)) is the same. Therefore, the non-faulty junction areas bc and de can be considered equivalent to a single-circuit line. Figure 7 As shown.

[0125] In the above example, by treating the overlapping area of ​​the parallel double-circuit line on the same tower, excluding the overlapping area where the fault point is located, as a single-circuit line, the circuit can be simplified, which is conducive to efficiently and accurately determining the measurement impedance of the parallel double-circuit line on the same tower.

[0126] S130, Obtain the simplified connection scheme of the parallel connection of the double-circuit line on the same tower.

[0127] In a feasible design, when a double-circuit parallel connection line on the same tower is connected to a double-circuit line on the same pole, the connection scheme for the double-circuit parallel connection line on the same tower is obtained, including:

[0128] An overlap point is set at a preset interval on the parallel double-loop line on the same pole;

[0129] Based on the double-circuit lines on the same pole after the lap joint point is set, obtain the lap joint scheme of the double-circuit parallel lap joint lines on the same tower.

[0130] In such Figure 7 As shown, an overlap point is set every x km on the parallel double-loop line, generating a structure like this. Figure 8 The overlapping scheme is shown. In Figure 8 In the diagram, the first distance protection installation point closest to point a is located on side M, and the second distance protection installation point closest to point e is located on side N. QF represents the circuit breaker, and G represents the grounding. One side of the double-circuit line is called distance protection section I, and the other side is called distance protection section II.

[0131] In a feasible design, the method also includes:

[0132] The length of the target segment relative to the total length of the single-circuit line is determined based on the splicing plan. The target segment includes the first line segment, the second line segment, and the third line segment.

[0133] The first line segment is the first joint point near the first distance protection installation location closest to the fault point, and the line segment between the first distance protection installation location and the first distance protection installation location. The first distance protection installation location is located at one end of a double-circuit line on the same pole.

[0134] The second line segment is the line segment between the fault point and the first connection point;

[0135] The third line segment is the overlapping area where the fault point is located.

[0136] like Figure 9 As shown, α1 is the percentage of the length of the first line segment to the length of the single-circuit line, β1 is the percentage of the length of the second line segment to the length of the single-circuit line, and β is the percentage of the length of the third line segment to the length of the single-circuit line.

[0137] In a feasible design, the electrical parameters include one or more of the following parameters:

[0138] The target segment's length is the percentage of the single-circuit line's length, the phase voltages at the first distance protection installation point, the phase currents at the first distance protection installation point, the zero-sequence current at the first distance protection installation point, the positive-sequence impedance of the entire single-circuit line, the positive-sequence unit impedance of the single-circuit line, the zero-sequence unit mutual impedance of the double-circuit line on the same pole, the phase currents at the second distance protection installation point located at the other end of the double-circuit line on the same pole, the zero-sequence current at the second distance protection installation point, the unit zero-sequence impedance of the double-circuit line on the same pole, the zero-sequence compensation coefficient of the double-circuit line on the same pole, and the total zero-sequence current of the double-circuit line on the same pole.

[0139] For example, electrical parameters also include parameters such as line-to-line mutual inductance.

[0140] S140, based on electrical parameters and a simplified connection scheme, calculate the measured impedance of a double-circuit parallel connection line on the same tower.

[0141] In a feasible design, combining Figure 9 And the contents of formulas (1) to (11), based on electrical parameters and connection schemes, calculate the measured impedance of the double-circuit parallel connection line on the same tower, including:

[0142] Based on the electrical parameters and the connection scheme, the measured impedance Z of the grounding distance protection of the double-circuit parallel connection line on the same tower is calculated using the following formula (12). m :

[0143]

[0144] in, For the voltage at the first distance protection installation point, For the first distance protection installation point current, Let Z1 be the zero-sequence current at the first distance protection installation point, α1 be the percentage of the length of the first line segment to the length of the single-circuit line, β1 be the percentage of the length of the second line segment to the length of the single-circuit line, β be the percentage of the length of the third line segment to the length of the single-circuit line, Z1 be the positive-sequence impedance of the total length of the single-circuit line, and Z0 be the unit zero-sequence impedance of the line. m0 Z1 is the zero-sequence unit mutual impedance of a double-circuit line on the same pole, K1 is the positive-sequence unit impedance of a single-circuit line, K′ is the zero-sequence compensation coefficient, and C is the amplification coefficient. M0 C is the zero-sequence current distribution coefficient at the installation location of the first distance protection. N0 The zero-sequence current distribution coefficient at the installation location of the second distance protection. It is the zero-sequence current. The zero-sequence current at the first distance protection installation point, The zero-sequence current at the installation location of the second distance protection is denoted as i, where i is A, B, or C, where A represents phase A, B represents phase B, and C represents phase C.

[0145] The above example efficiently and accurately determines the measured impedance of the grounding distance protection when a grounding fault occurs in a double-circuit parallel-connected line on the same tower. Furthermore, the measured impedance can be calculated using the above method regardless of the type of fault.

[0146] In a feasible design, combining Figure 9 And the contents of formulas (1) to (11), based on electrical parameters and connection schemes, calculate the measured impedance of the double-circuit parallel connection line on the same tower, including:

[0147] Based on the electrical parameters and the connection scheme, the measured impedance Z of the phase-to-phase distance protection of the double-circuit parallel connection line on the same tower is calculated using the following formula (13). m :

[0148]

[0149] The voltage of phase i at the installation location of the first distance protection is given, where i can be A, B, or C, where A represents phase A, B represents phase B, and C represents phase C. The voltage of phase j at the installation location of the first distance protection is given, where j is A, B, or C, and j ≠ i. The i-phase current at the first distance protection installation location. Let α1 be the j-phase current at the first distance protection installation point, β1 be the percentage of the length of the first line segment to the total length of the single-circuit line, β1 be the percentage of the length of the second line segment to the total length of the single-circuit line, β be the percentage of the length of the third line segment to the total length of the single-circuit line, and Z1 be the positive sequence impedance of the entire single-circuit line. This refers to the i-phase current at the installation location of the second distance protection.

[0150] The above example efficiently and accurately determines the measured impedance of phase-to-phase distance protection when a phase-to-phase fault occurs in a double-circuit parallel-connected line on the same tower. Furthermore, the measured impedance can be calculated using the above method regardless of the fault type.

[0151] The impedance measurement verification will be performed below:

[0152] Combination Figure 9 Suppose that an overlap is used at the distance akm from the protection installation point, and the length of the overlap area is β, which is the proportion of the single circuit in the double-circuit line on the same tower. The proportion of akm to the total length of the single circuit in the double-circuit line on the same tower is α1. A fault occurs at the overlap point b in this overlap section. β1 is the percentage of the distance from the fault point to the nearest overlap point (which is close to the protection installation side) to the single circuit in the double-circuit line on the same tower.

[0153] A 330kV parallel double-circuit line model was built using PSCAD / EMTDC simulation software. The total line length is 40km, the simulation step size is 250μs, and the system parameters are: M-side positive sequence impedance Z. MS1 =0.1+j11.103Ω, Z MS0 = 1 + j28.061Ω; N-side system positive sequence impedance Z NS1 =0.1+j8.007Ω, Z NS0= 1 + j24.021Ω. Line parameters: Positive sequence impedance Z1 = 0.0478 + j0.2826Ω / km; Zero sequence impedance Z0 = 0.1903 + j0.628Ω / km; Inter-line impedance Z1 = 0.0422 + j0.2282Ω / km; Positive sequence capacitive reactance C1 = 0.2654MΩ*km; Zero sequence capacitive reactance C0 = 0.41306MΩ*km. The phase angle difference between the power supplies at both ends of the line is 10°. Considering the different fault types, splicing methods, and fault locations of double-circuit lines on the same pole, the effectiveness of the setting method proposed in this invention is analyzed and verified.

[0154] Using an overlap scheme with an 8km interval, the simulation results of the measured impedance of IA-G, IBC, and IBCIB at different locations are shown in Tables 2, 3, and 4, respectively:

[0155] Table 2

[0156] Fault distance (%) Measurement impedance Zm Measurement impedance |Zm| 5％ 0.0429+0.5389i 0.5406 15％ 0.1637+1.1235i 1.1353 25％ 0.2925+1.7078i 1.7327 35％ 0.4279+2.2918i 2.3314 45％ 0.5632+2.8761i 2.9308 55％ 0.7019+3.4618i 3.5322 65％ 0.8394+4.40486i 4.1347 75％ 1.2485+5.7895i 5.9226 85％ 1.1128+5.2284 5.3455 95％ 1.2499+5.8221i 5.9547 100％ 0.9560+5.652i 5.732

[0157] Table 2 shows the measured impedance values ​​at different locations during an I-G fault.

[0158] Table 3

[0159] Fault distance (%) Measurement impedance Zm Measurement impedance |Zm| 5％ 0.048+0.286i 0.290 15％ 0.0943+1.2254i 1.2290 25％ 0.2054+1.8125i 1.8241 35％ 0.2785+2.3767i 2.3930 45％ 0.455+2.445i 2.487 55％ 0.450+3.237i 3.268 65％ 0.628+4.016i 4.065 75％ 0.724+4.161i 4.223 85％ 0.817+4.976i 5.043 95％ 0.909+5.382i 5.458 100％ 0.9560+5.652i 5.732

[0160] Table 3 shows the measured impedance values ​​at different locations during IBC faults.

[0161] Table 4

[0162]

[0163]

[0164] Table 4 shows the measured impedance values ​​at different locations during an IBCIB fault.

[0165] After substituting the simulation parameters into formula (12) or formula (13), and comparing them with the measured impedance values ​​in Tables 2, 3 and 4, the correctness of the measured impedance formula provided in this application is verified.

[0166] Combining formula (8), for the overlapping scheme at 8km intervals, the actual protection ranges of IA-G, IBC, and IBIIC at different locations are as follows: Figure 10 , Figure 11 , Figure 12 As shown. Among them, in Figure 10 , Figure 11 and Figure 12 In the middle, the dashed line and Z m The actual protection range is defined by the α value corresponding to the intersection point and the segment from the α value to 0.

[0167] Using a 20km overlap scheme, the simulation results of the measured impedances of IA-G, IBC, and IBIIC at different locations are shown in Tables 5, 6, and 7, respectively:

[0168] Table 5

[0169] Fault distance (%) Measurement impedance Zm Measurement impedance |Zm| 5％ 0.0410+0.5901i 0.5915 15％ 0.1464+1.6061i 1.6127 25％ 0.2735+2.2609i 2.2774 35％ 0.4116+2.8154i 2.8454 45％ 0.5644+2.9431i 2.9968 55％ 0.6316+3.2375i 3.2985 65％ 0.8153+4.6680i 4.7387 75％ 0.9372+5.4918i 5.5712 85％ 1.0901+5.9343i 6.0336 95％ 1.1812+5.6100i 5.733 100％ 0.9560+5.652i 5.732

[0170] Table 5 shows the measured impedance values ​​at different locations during an I-G fault.

[0171] Table 6

[0172]

[0173]

[0174] Table 6 shows the measured impedance values ​​at different locations during an IBC fault.

[0175] Table 7

[0176] Fault distance (%) Measurement impedance Zm Measurement impedance |Zm| 5％ 0.0336+0.5488i 0.5498 15％ 0.4089+1.0527i 1.1294 25％ 0.1727+2.2350i 2.2416 35％ 0.2718+2.6656i 2.6794 45％ 3.2501+1.1677i 3.4535 55％ 0.1655+1.3085i 1.3189 65％ 0.5317+4.7880i 4.8174 75％ 0.5914+5.4042i 5.4364 85％ 0.6693+6.0099i 6.0471 95％ 0.8136+5.6060i 5.6648 100％ 0.9560+5.652i 5.732

[0177] Table 7 shows the measured impedance values ​​at different locations during an IBCIB fault.

[0178] For the overlapping scheme with intervals of 20km, the actual protection ranges of IA-G, IBC, and IBIIC at different locations are as follows: Figure 13 , Figure 14 and Figure 15 As shown. Where Z m For the calculated measured impedance value, Z set This is the setpoint value. Wherein, Figure 13 , Figure 14 and Figure 15 In the middle, the dashed line and Z m The actual protection range is defined by the α value corresponding to the intersection point and the segment from the α value to 0.

[0179] In the above embodiments of this application, by simplifying the double-circuit parallel connection on the same tower, the connection area of ​​the double-circuit parallel connection on the same tower, excluding the connection area where the fault point is located, is equivalent to a single-circuit line. This facilitates efficient and accurate calculation of the measured impedance of the double-circuit parallel connection on the same tower based on electrical parameters and connection scheme after a fault occurs.

[0180] Combining the above methods for measuring impedance, such as Figure 16 As shown, this application also provides a device for determining impedance measurement, applied to a double-circuit parallel-connected line on the same tower, comprising:

[0181] The electrical parameter acquisition module is used to acquire the electrical parameters of the parallel-connected double-circuit lines on the same tower.

[0182] The line simplification module is used to simplify the parallel connection of double-circuit lines on the same tower. The simplification process is to treat the connection area of ​​the parallel connection of double-circuit lines on the same tower, except for the connection area where the fault point is located, as a single-circuit line.

[0183] The splicing scheme acquisition module is used to acquire the splicing scheme of the double-circuit parallel splicing line on the same tower after simplification.

[0184] The impedance measurement determination module is used to calculate the impedance of a double-circuit parallel connection on the same tower based on electrical parameters and connection scheme.

[0185] In a feasible design, when a double-circuit parallel connection line on the same tower is connected to a double-circuit line on the same pole, the connection scheme acquisition module obtains the simplified connection scheme of the double-circuit parallel connection line on the same tower in the following ways:

[0186] An overlap point is set at a preset interval on the parallel double-loop line on the same pole;

[0187] Based on the double-circuit lines on the same pole after the lap joint point is set, obtain the lap joint scheme of the double-circuit parallel lap joint lines on the same tower.

[0188] In one feasible design, the device also includes a target segmentation ratio determination module;

[0189] The target segment percentage determination module is used to determine the percentage of the target segment's length relative to the total length of a single-circuit line, based on the splicing scheme. The target segments include the first line segment, the second line segment, and the third line segment.

[0190] The first line segment is the first joint point near the first distance protection installation location closest to the fault point, and the line segment between the first distance protection installation location and the first distance protection installation location. The first distance protection installation location is located at one end of a double-circuit line on the same pole.

[0191] The second line segment is the line segment between the fault point and the first connection point;

[0192] The third line segment is the overlapping area where the fault point is located.

[0193] In a feasible design, the electrical parameters include one or more of the following parameters:

[0194] The data include the phase voltages at the first distance protection installation point, the phase currents at the first distance protection installation point, the zero-sequence current at the first distance protection installation point, the positive-sequence impedance of the entire single-circuit line, the positive-sequence unit impedance of the single-circuit line, the zero-sequence unit mutual impedance of the double-circuit line on the same pole, the phase currents at the second distance protection installation point located at the other end of the double-circuit line on the same pole, the zero-sequence current of the second distance protection installation point, the unit zero-sequence impedance of the double-circuit line on the same pole, the zero-sequence compensation coefficient of the double-circuit line on the same pole, and the total zero-sequence current of the double-circuit line on the same pole.

[0195] In a feasible design, the impedance determination module calculates the impedance of a double-circuit parallel-connected line on the same tower based on electrical parameters and connection scheme, including:

[0196] Based on the electrical parameters and connection scheme, the measuring impedance Z of the grounding distance protection for a double-circuit parallel-connected line on the same tower is calculated using the following formula. m :

[0197]

[0198]

[0199]

[0200]

[0201] in, For the voltage at the first distance protection installation point, For the first distance protection installation point current, Let Z1 be the zero-sequence current at the first distance protection installation point, α1 be the percentage of the length of the first line segment to the length of the single-circuit line, β1 be the percentage of the length of the second line segment to the length of the single-circuit line, β be the percentage of the length of the third line segment to the length of the single-circuit line, Z1 be the positive-sequence impedance of the total length of the single-circuit line, and Z0 be the unit zero-sequence impedance of the line. m0 Z1 is the zero-sequence unit mutual impedance of a double-circuit line on the same pole, K1 is the positive-sequence unit impedance of a single-circuit line, K′ is the zero-sequence compensation coefficient, and C is the amplification coefficient. M0 C is the zero-sequence current distribution coefficient at the installation location of the first distance protection. N0 The zero-sequence current distribution coefficient at the installation location of the second distance protection. It is the zero-sequence current. The zero-sequence current at the first distance protection installation point, The zero-sequence current at the installation location of the second distance protection is denoted as i, where i is A, B, or C, where A represents phase A, B represents phase B, and C represents phase C.

[0202] In a feasible design, the impedance determination module is implemented by calculating the measured impedance of a double-circuit parallel-connected line on the same tower based on electrical parameters and connection scheme, including:

[0203] Based on the electrical parameters and connection scheme, the measuring impedance Z of the phase-to-phase distance protection for a double-circuit parallel connection on the same tower is calculated using the following formula. m :

[0204]

[0205] The voltage of phase i at the installation location of the first distance protection is given, where i can be A, B, or C, where A represents phase A, B represents phase B, and C represents phase C. The voltage of phase j at the installation location of the first distance protection is given, where j is A, B, or C, and j ≠ i. The i-phase current at the first distance protection installation location. Let α1 be the j-phase current at the first distance protection installation point, β1 be the percentage of the length of the first line segment to the total length of the single-circuit line, β1 be the percentage of the length of the second line segment to the total length of the single-circuit line, β be the percentage of the length of the third line segment to the total length of the single-circuit line, and Z1 be the positive sequence impedance of the entire single-circuit line. This refers to the i-phase current at the installation location of the second distance protection.

[0206] Other implementations and effects of this device are described in the embodiments of the method for determining the measurement impedance, and will not be repeated here.

[0207] The basic principles of this application have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this application are merely examples and not limitations, and should not be considered as essential features of each embodiment of this application. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the application to the necessity of employing the aforementioned specific details for implementation.

[0208] It should be understood that although the steps in the flowcharts of the accompanying figures are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the accompanying figures may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0209] The block diagrams of devices, apparatuses, devices, and systems involved in this application are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0210] It should also be noted that in the apparatus, equipment, and methods of this application, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered as equivalent solutions of this application.

[0211] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this application. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of this application. Therefore, this application is not intended to be limited to the aspects shown herein, but rather to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0212] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this application to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. A determination method for measuring impedance applied to a same-tower double-circuit parallel jointed line, characterized in that, The method comprises: obtaining electrical parameters of the same-tower double-circuit parallel joint line; simplifying the same-tower double-circuit parallel joint line, wherein the simplification is to equivalently regard the joint regions of the same-tower double-circuit parallel joint line except the joint region where the fault point is located as single-circuit line; obtaining a joint scheme of the same-tower double-circuit parallel joint line after simplification; calculating the measured impedance of the same-tower double-circuit parallel joint line according to the electrical parameters and the joint scheme after simplification.

2. The method of claim 1, wherein, In the case of jointing the same-tower double-circuit parallel joint line with the same-pole double-circuit line, the obtaining of the joint scheme of the same-tower double-circuit parallel joint line after simplification comprises: setting a joint point every preset distance on the same-pole double-circuit line; obtaining the joint scheme of the same-tower double-circuit parallel joint line according to the same-pole double-circuit line after setting the joint point.

3. The method of claim 2, wherein, The method further comprises: determining the percentage of the length of the target segment to the length of the single-circuit line according to the joint scheme, wherein the target segment comprises a first line segment, a second line segment and a third line segment, the first line segment is a line segment between a first joint point near the first distance protection installation and the first distance protection installation, wherein the first distance protection installation is located at one end of the same-pole double-circuit line, the second line segment is a line segment between the fault point and the first joint point; and the third line segment is the joint region where the fault point is located.

4. The method of claim 3, wherein, The electrical parameters comprise one or more of the following parameters: the phase voltage of the first distance protection installation, the phase current of the first distance protection installation, the zero sequence current of the first distance protection installation, the positive sequence impedance of the full length of the single-circuit line, the positive sequence unit impedance of the single-circuit line, the zero sequence unit mutual impedance of the same-pole double-circuit line, the phase current of a second distance protection installation located at the other end of the same-pole double-circuit line, the zero sequence current of the second distance protection installation, the line unit zero sequence impedance of the same-pole double-circuit line, the line zero sequence compensation coefficient of the same-pole double-circuit line and the total zero sequence current of the same-pole double-circuit line.

5. The method of claim 4, wherein, The calculation of the measured impedance of the same-tower double-circuit parallel joint line according to the electrical parameters and the joint scheme comprises: According to the electrical parameter and the parallel connection scheme, the measured impedance Z of the ground distance protection of the double-circuit parallel connection line on the same tower is calculated by the following formula m : wherein, is the voltage at the first distance protection installation, is the current at the first distance protection installation, is the zero sequence current at the first distance protection installation, is the percentage of the length of the first line section to the length of the single circuit line, is the percentage of the length of the second line section to the length of the single circuit line, is the percentage of the length of the third line section to the length of the single circuit line, is the positive sequence impedance of the full length of the single circuit line, is the line unit zero sequence impedance, is the zero sequence unit mutual impedance of the same pole double circuit line, is the positive sequence unit impedance of the single circuit line, is the line zero sequence compensation factor, is the auxiliary increase factor, is the zero sequence current distribution factor at the first distance protection installation, m0 is the zero sequence unit mutual impedance of the same pole double circuit line, is the positive sequence unit impedance of the single circuit line, is the line zero sequence compensation factor, is the auxiliary increase factor, is the zero sequence current distribution factor at the first distance protection installation, M0 is the zero sequence current distribution factor at the first distance protection installation, N0 is the zero sequence current distribution factor at the second distance protection installation, is the total zero sequence current of the line, is the zero sequence current at the first distance protection installation, is the zero sequence current at the second distance protection installation, i is A, B or C, A represents A phase power, B represents B phase power, and C represents C phase power.

6. The method of claim 4, wherein, The calculation of the measured impedance of the same-tower double-circuit parallel joint line according to the electrical parameters and the joint scheme comprises: According to the electrical parameter and the lap scheme, a measured impedance Z of the phase-to-phase distance protection of the double-circuit parallel lap line is calculated by the following formula m : the i-phase voltage at the installation of the first distance protection, i being A, B or C, A denoting A-phase current, B denoting B-phase current, C denoting C-phase current, the j-phase voltage at the installation of the first distance protection, j being A, B or C, j≠i, the i-phase current at the installation of the first distance protection, the j-phase current at the installation of the first distance protection, a1 being the percentage of the length of the first line section to the length of the single-circuit line, β1 being the percentage of the length of the second line section to the length of the single-circuit line, β being the percentage of the length of the third line section to the length of the single-circuit line, Z1 being the positive sequence impedance of the full length of the single-circuit line, the i-phase current at the installation of the second distance protection.

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