Same-tower double-circuit AC-to-DC system fault positioning method based on multi-phase-mode transformation

Abstract

The multi-phase-mode transformation-based fault positioning method for the same-tower double-circuit alternating current-direct current system comprises the following steps of: constructing an impedance matrix of the same-tower double-circuit alternating current-direct current system, and obtaining a fault circuit discrimination matrix; a decoupling matrix is introduced to decouple an impedance matrix of the same-tower double-circuit alternating current-to-direct current system, and moduli obtained through decoupling are extracted to form a modulus matrix; the voltage modulus obtained by decoupling is judged, and a fault pole is determined according to the polarity combination of the voltage modulus; and calculating the approximate entropy of the voltage moduli at the two ends of the fault pole, and positioning the wave head of the fault traveling wave. According to the method, a self-adaptive decoupling method based on multi-phase-mode transformation is provided, and the method has the functions of accurately identifying a fault loop and effectively decoupling each line; meanwhile, a fault pole identification scheme based on voltage modulus polarity combination and a fault positioning scheme based on approximate entropy are provided, and accurate fault positioning of the same-tower double-circuit alternating current-to-direct current system is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of DC power transmission system fault location, and particularly relates to a fault location method for a same-tower double-circuit AC-to-DC conversion system based on multiple phase-mode transformations. Background Art

[0002] At present, large-scale new energy sources represented by wind power and photovoltaic power are continuously connected to regional power grids. The volatility of the active power output of new energy and the increasing demand for power supply pose challenges to the power transmission and consumption capabilities of regional power grids. Compared with AC systems, DC systems have both a larger transmission capacity and fast and flexible power control. By adding a DC system or converting some AC lines to DC, an embedded DC system with both the sending and receiving ends within the same regional power grid is an effective solution to improve the power transmission and consumption capabilities of regional power grids. Currently, the Yangzhou-Zhenjiang AC-to-DC conversion project in Jiangsu is the first embedded DC power transmission project in China. This project plans to convert 6 conductors in the 220 kV Wufengshan crossing line into a 3-circuit bipolar DC power transmission system, forming a same-tower three-circuit DC power transmission system. Compared with traditional single-circuit DC power transmission systems, its fault types are more diverse, and its coupling characteristics are more complex. Moreover, no effective fault pole identification scheme has been proposed yet.

[0003] There are strong coupling characteristics between the lines of the same-tower double-circuit AC-to-DC conversion system. Any fault on one line will generate induced components on other non-fault lines, which may cause misoperation of protection devices. Therefore, decoupling each line is a prerequisite for fault identification. Currently, DC systems usually introduce phase-mode transformations such as Clarke transformation, Karenbauer transformation, and Wedpohl transformation in AC systems to achieve decoupling. For same-tower multi-circuit DC power transmission systems, loop decoupling needs to be performed first, and then phase decoupling. Typical schemes include the six-sequence component method for same-tower double-circuit transmission systems and the twelve-sequence component method for same-tower four-circuit transmission lines. However, such methods cannot achieve complete decoupling of same-tower three-circuit transmission systems. In addition, theoretically, there are more than a hundred fault types in the same-tower double-circuit AC-to-DC conversion system. Effectively identifying the fault pole and selectively tripping the fault pole is a prerequisite for ensuring maximum power transmission under fault conditions. However, no effective identification scheme has been proposed yet. It can be seen that there is currently a lack of quantitative analysis of the coupling characteristics of same-tower three-circuit DC power transmission systems, as well as corresponding decoupling methods and fault location schemes. Summary of the Invention

[0004] Aiming at the problems of complex coupling characteristics and difficult fault location in the same-tower double-circuit alternating-to-direct conversion system, the present invention provides a fault location method for the same-tower double-circuit alternating-to-direct conversion system based on multiple phase-mode transformations. This method proposes an adaptive decoupling method based on multiple phase-mode transformations, which combines accurate identification of the fault loop and effective decoupling of each line; at the same time, a fault pole identification scheme based on the polarity combination of voltage moduli and a fault location scheme based on approximate entropy are proposed to achieve precise fault location in the same-tower double-circuit alternating-to-direct conversion system.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A fault location method for the same-tower double-circuit alternating-to-direct conversion system based on multiple phase-mode transformations includes the following steps:

[0007] Step 1: Construct the impedance matrix of the same-tower double-circuit alternating-to-direct conversion system and obtain the fault loop discrimination matrix;

[0008] Step 2: Introduce a decoupling matrix to decouple the impedance matrix of the same-tower double-circuit alternating-to-direct conversion system, and extract the moduli obtained by decoupling to form a modulus matrix;

[0009] Step 3: Judge the voltage moduli obtained by each decoupling, and determine the fault pole according to the polarity combination of the voltage moduli;

[0010] Step 4: Calculate the approximate entropy of the voltage moduli at both ends of the fault pole and locate the wavefront of the fault traveling wave.

[0011] In the above step 1, in the same-tower double-circuit alternating-to-direct conversion system, assuming that the mutual impedance between each circuit remains unchanged, considering the influence of the layer height and the symmetrical arrangement of the pole lines, the impedance matrix is constructed as:

[0012]

[0013] In formula (1): z s1 is the self-impedance of each pole line of circuit I and circuit II; z s2 is the self-impedance of each pole line of circuit III; z n1 is the mutual impedance between two pole lines in circuit I or circuit II; z n2 is the mutual impedance between two pole lines in circuit III; z p1 is the mutual impedance between each pole line between circuit I, circuit III and circuit II, circuit III; z p2 is the mutual impedance between each pole line between circuit I and circuit II;

[0014] In step 1, a loop decoupling matrix P1 is proposed to decouple the impedance matrix Z, as shown in formula (2):

[0015]

[0016] Introduce the Clarke phase-mode transformation matrix P cDecouple the matrix P1Z obtained from Equation (2) between poles to obtain the fault loop discrimination matrix P circuit It is:

[0017]

[0018] where O is the zero matrix.

[0019]

[0020] In Equation (3), P c is the Clarke phase-mode transformation matrix, and there is In the said Step 1, take the voltage mutation amount as the fault feature quantity, and after transformation by the fault loop discrimination matrix P circuit it is obtained:

[0021]

[0022] In Equation (4): u x (t) is the voltage mutation amount before and after the fault at the beginning or end of the pole line. The subscripts 1P, 1N, 2P, 2N, 3P, 3N are the positive and negative poles of the first, second, and third circuits respectively; u1(t), u3(t), u5(t) are the moduli reflecting whether there are faults in the first, second, and third circuits respectively.

[0023] According to the mutation characteristics of u1(t), u3(t), u5(t), construct a fault startup criterion as shown in Equation (5).

[0024]

[0025] In Equation (5): Δu act is the voltage mutation amount startup value; u1(t) is the fault loop discrimination modulus corresponding to the first circuit; u3(t) is the fault loop discrimination modulus corresponding to the second circuit; u5(t) is the fault loop discrimination modulus corresponding to the third circuit. By collecting voltage quantities in real time and calculating u1(t), u3(t), u5(t), the criteria in Equation (5) respectively indicate that faults occur in the first, second, and third circuits.

[0026] In the said Step 2, introduce the decoupling matrix P3:

[0027]

[0028] Take the inter-pole decoupling matrix P5 = P3 to decouple the impedance matrix Z to obtain a decoupling matrix. The obtained decoupling matrix is completely decoupled in odd rows (or columns) and even rows (or columns) respectively, as shown in the following formula:

[0029]

[0030] Therefore, decoupling is performed using P4 and P5 respectively, specifically as follows:

[0031] Taking the decoupling of the voltage mutation as an example, as shown in Equations (7) and (8).

[0032] And extract the moduli obtained from the complete decoupling to form a modulus matrix. Taking the decoupling of the voltage mutation as an example, as shown in Equation (9).

[0033] After determining the number of fault loops, select a decoupling matrix of the same scale for decoupling, specifically as follows:

[0034] When a single-line fault occurs, take P3 = P c ; when a two-line fault occurs, take When a three-line fault occurs, P3 is as shown in Equation (6).

[0035] In step 2, the voltage mutation is used as the fault feature quantity for decoupling, and the decoupled modulus matrix is as shown in Equation (9):

[0036] [u′1(t) u′2(t) u′3(t) u′4(t) u′5(t) u′6(t)] T = P4[u 1P (t) u 1N (t) u 2P (t) u 2N (t) u 3P (t) u 3N (t)] T (7);

[0037] [u″1(t) u″2(t) u″3(t) u″4(t) u″5(t) u″6(t)] T = P5[u 1P (t) u 1N (t) u 2P (t) u 2N (t) u 3P (t) u 3N (t)] T (8);

[0038] u = [u″1(t) u′2(t) u″3(t) u′4(t) u″5(t) u′6(t)] (9);

[0039] In the above formula: u x (t) is the voltage mutation before and after the fault at the beginning or end of the line, and the subscripts 1P, 1N, 2P, 2N, 3P, 3N are the positive and negative poles of the first, second, and third lines respectively; u′ x(t) is the voltage modulus obtained after decoupling by P4, and the subscripts 1, 2, 3, 4, 5, and 6 are the modulus labels respectively; u″ x (t) is the voltage modulus obtained after decoupling by P5, and the subscripts 1, 2, 3, 4, 5, and 6 are the modulus labels respectively.

[0040] In step 3, the polarities of the voltage moduli obtained by decoupling under different fault types are different. The fault pole is identified according to the combination of the polarities of the 6 voltage moduli, and the polarity discrimination is shown in equations (10) and (11):

[0041]

[0042] In equation (10): f(x) is the operation of the five-point cubic smoothing method; N f is the calculation window length; K act is the polarity discrimination starting value. If equation (10) is satisfied, the positive and negative polarities of the voltage modulus can be further judged; otherwise, the voltage modulus has a zero polarity.

[0043]

[0044] Use the multiple characteristics of u1(t), u3(t), and u5(t) to preliminarily classify the faults, divide the fault types with overlapping polarity combinations into different groups, and construct the following criterion:

[0045]

[0046] In equation (12): u i (t), u j (t) are the fault loop discrimination moduli; i and j are the labels of the loop discrimination moduli respectively. For three-circuit line faults, i = 1, 3, 5, j = 1, 3, 5, and i ≠ j; for two-circuit line faults, i and j take the labels of the fault loops, and i ≠ j; K set_1 is the proportionality coefficient.

[0047]

[0048] In equation (13): K set_2 is the proportionality coefficient.

[0049] In step 3, the preliminary fault classification includes:

[0050] ①. If it is a single-circuit line fault, use equation (11) to judge the polarities of each modulus, and identify the fault pole line based on the polarity combination.

[0051] ②. If it is a two-circuit line fault, use criterion (12) and criterion (13) for preliminary classification:

[0052] Traverse i and j. If both satisfy the criterion formula (12), it is determined that the fault is a two-pole fault or a four-pole fault. Since the polarity combinations of the four-pole fault and the two-pole fault do not overlap, the faulty pole lines can be identified according to the polarity combination. If the criterion formula (12) is not satisfied, it can be determined that the fault is a three-pole short-circuit fault or a three-pole grounding fault.

[0053] Further classify using the criterion formula (13). If there are i and j that satisfy the criterion formula (13), it can be determined that the fault is a three-pole short-circuit fault; otherwise, it is a three-pole grounding fault. The faulty pole lines are identified according to the polarity combination.

[0054] For the specific fault types in the three-pole short-circuit fault, there is a problem of overlapping polarity combinations. Further classify them into two categories using the criterion formula (14), and identify the faulty pole lines according to the polarity combination.

[0055] |u l (t)| > |u k (t)| (14);

[0056] In formula (14): l and k are the subscripts reflecting the fault modal values of the loop, where l = 1, 3, 5, k = 1, 3, 5, and l ≠ k.

[0057] ③. If it is a three-circuit line fault, classify using the criterion formula (12) and the criterion formula (13):

[0058] Traverse i and j. If both satisfy the criterion (12), it can be determined that the fault is a three-pole grounding fault or a six-pole fault. Since the polarity combinations of these two types of faults do not overlap, the faulty pole lines can be identified according to the polarity combination. If there are i and j that satisfy the criterion formula (13), it can be determined that the fault is a four-pole short-circuit fault or a five-pole short-circuit fault; otherwise, it is a three-pole short-circuit fault, a four-pole short-circuit fault, a four-pole grounding fault, or a five-pole grounding fault. Since the polarity combinations of these four types of faults do not overlap, the faulty pole lines can be identified according to the polarity combination.

[0059] For the four-pole short-circuit fault and the five-pole short-circuit fault, there is a problem of overlapping polarity combinations. First, arrange |u1(t)|, |u3(t)|, |u5(t)| from largest to smallest as {u1, u2, u3}, where u1, u2, u3 correspond to the results of arranging |u1(t)|, |u3(t)|, |u5(t)| from largest to smallest in turn;

[0060] Substitute into the criterion formula (15):

[0061]

[0062] If both criteria in formula (15) are satisfied, it is a four-pole short-circuit fault; otherwise, it is a five-pole short-circuit fault. Then, identify the faulty pole lines according to the polarity combination.

[0063] In step 4, after determining the specific faulty pole, calculate the approximate entropy of the voltage modulus at both ends of the faulty pole, as follows:

[0064] Taking the voltage modulus u1″(t) as an example, illustrate the calculation method of approximate entropy:

[0065] The calculated voltage modulus u1″(t) = [u1, u2,..., u N , where N represents N data, and u1, u2,..., u N respectively represent the data constituting u1″(t);

[0066] Reconstruct the m-dimensional vector [U(1), U(2),..., U(N - m + 1)], where m represents the dimension of the constructed vector;

[0067] U(1) = [u1, u2], U(2) = [u2, u3],..., U(N - m + 1) = [u N-1 , u N ; U(1), U(2),..., U(N - m + 1) are all constructed two-dimensional vectors.

[0068] For i, j ∈ [1, N - m + 1], count the number of vectors that satisfy the following conditions:

[0069]

[0070] In formula (16): d[U(i), U(j)] is the distance between two two-dimensional vectors; d[U(i), U(j)] = max|U(i) - U(j)|; r is the similarity tolerance; is the number of two-dimensional vectors similar to U(i); U(i) and U(j) are the i-th and j-th two-dimensional vectors respectively, with i, j ∈ [1, N - m + 1].

[0071] Let Then the approximate entropy can be expressed as

[0072] where h ApEn is the calculation result of the approximate entropy; is the intermediate value calculated using two-dimensional vectors; is the intermediate value calculated using three-dimensional vectors.

[0073] According to the approximate entropy mutation point, determine the arrival times t M , t N of the traveling wave at both end measuring points, and substitute them into the double-ended ranging formula (17) to calculate the distance x M from the fault point to the M end as:

[0074]

[0075] In formula (17): L is the line length; v is the traveling wave propagation speed.

[0076] The fault location method for the same-tower double-circuit AC-to-DC conversion and straightening system based on multiple phase-mode transformations according to the present invention has the following technical effects:

[0077] 1) The present invention proposes an effective decoupling scheme for the same-tower double-circuit AC-to-DC conversion and straightening system, eliminating the coupling characteristics between lines and laying a theoretical foundation for subsequent fault feature analysis.

[0078] 2) The present invention utilizes the polarity characteristics of the sudden change in fault voltage to propose a fault pole identification scheme applicable to the same-tower double-circuit AC-to-DC conversion and straightening system, which has the advantages of simple principle, strong anti-interference ability, and low requirement for sampling rate.

[0079] 3) The present invention uses approximate entropy to locate the fault traveling wave head, with advantages such as high fault location accuracy, strong ability to withstand transition resistance, and low requirement for sampling rate.

[0080] 4) The method of the present invention has the advantages of high sensitivity, strong anti-interference ability, and low requirement for sampling rate, and has significant application value. Description of the Drawings

[0081] The present invention will be further described below in conjunction with the drawings and examples;

[0082] Figure 1 Schematic diagram of the pole line layout of the same-tower double-circuit AC-to-DC conversion and straightening system.

[0083] Figure 2 Flow chart of fault location for the same-tower double-circuit AC-to-DC conversion and straightening system.

[0084] Figure 3 Model diagram of the same-tower double-circuit AC-to-DC conversion and straightening system. Detailed Embodiment

[0085] The fault location method for the same-tower double-circuit AC-to-DC conversion and straightening system based on multiple phase-mode transformations specifically includes: real-time acquisition of voltage quantities, and using the fault loop discrimination matrix P circuit for decoupling to obtain the mode quantities reflecting the loop fault, and identifying the occurrence of the fault by detecting its mutation; selecting a decoupling matrix of the same scale according to the number of fault loops to decouple the voltage sudden change quantities of each line; judging the polarity of each mode quantity, and determining the fault pole according to the mode quantity polarity combination; calculating the approximate entropy of the mode quantities at both ends of the fault pole, determining the wave arrival time according to the mutation of the approximate entropy, and substituting it into the double-end ranging formula to calculate the fault location. Specifically, it includes the following steps:

[0086] Step S1: The same-tower double-circuit AC-to-DC conversion and straightening system transforms the 6 AC conductors in the original same-tower double-circuit line into 3 bipolar DC systems, and each bipolar system uses 2 conductors. Its pole line layout is as Figure 1As shown in the figure. Regarding each loop as a whole and assuming that the mutual impedance between loops remains unchanged, considering the influence of floor height and symmetrical arrangement of pole lines, the impedance matrix is constructed as follows:

[0087]

[0088] In Equation (1): z s1 is the self-impedance of each pole line of Loop I and Loop II; z s2 is the self-impedance of each pole line of Loop III; z n1 is the mutual impedance between two pole lines in Loop I or Loop II; z n2 is the mutual impedance between two pole lines in Loop III; z p1 is the mutual impedance between each pole line of Loop I and Loop III, and between Loop II and Loop III; z p2 is the mutual impedance between each pole line of Loop I and Loop II.

[0089] A loop decoupling matrix P1 is proposed, and its effect is as shown in Equation (2).

[0090]

[0091] Further introduce the Clarke phase-mode transformation matrix P c to perform pole decoupling. After decoupling by this matrix, one of the moduli corresponding to each loop will be constantly zero, as shown in Equation (2). However, the remaining moduli can reflect the fault conditions of each loop. Therefore, the fault loop discrimination matrix is taken as where O is the zero matrix.

[0092]

[0093] In the present invention, the voltage mutation amount is taken as the fault characteristic quantity. After transformation by the fault loop discrimination matrix, we can obtain:

[0094]

[0095] In Equation (4): u x (t) is the voltage mutation amount before and after the fault at the beginning or end of the pole line. The subscripts 1P, 1N, 2P, 2N, 3P, 3N are the positive and negative poles of Loop I, Loop II, and Loop III respectively; u1(t), u3(t), u5(t) are the moduli reflecting whether there are faults in Loop I, Loop II, and Loop III respectively.

[0096] According to the characteristics of u1(t), u3(t), u5(t), a fault startup criterion is constructed, as shown in Equation (5).

[0097]

[0098] In the formula: Δu act is the voltage mutation amount startup value.

[0099] By collecting voltage values in real time and calculating u1(t), u3(t), and u5(t), the criteria in Equation (5) indicate that a fault has occurred in Circuit I, Circuit II, and Circuit III, respectively.

[0100] Step S2: Introduce the decoupling matrix P3:

[0101]

[0102] Take the inter-pole decoupling matrix P5 = P3 decouples Z. The resulting decoupling matrices are completely decoupled in the odd rows (or columns) and even rows (or columns). Therefore, use P4 and P5 for decoupling respectively, and extract the moduli obtained from the complete decoupling to form the modulus matrix. After determining the number of fault loops, select a decoupling matrix of the same scale for decoupling. For example, when a fault occurs in one circuit, take P3 = P c ; when a fault occurs in two circuits, take When a fault occurs in three circuits, P3 is as shown in Equation (6).

[0103] Step S3: Use the voltage mutation as the fault characteristic quantity for decoupling. The decoupled modulus matrix is as shown in Equation (9).

[0104] [u′1(t) u′2(t) u′3(t) u′4(t) u′5(t) u′6(t)] T = P4[u 1P (t) u 1N (t) u 2P (t) u 2N (t) u 3P (t) u 3N (t)] T (7);

[0105] [u″1(t) u″2(t) u″3(t) u″4(t) u″5(t) u″6(t)] T = P5[u 1P (t) u 1N (t) u 2P (t) u 2N (t) u 3P (t) u 3N (t)] T (8);

[0106] u = [u″1(t) u2′(t) u″3(t) u4(t) u″5(t) u′6(t)] (9);

[0107] Where: u x(t) is the voltage mutation before and after the fault at the beginning or end of the line. The subscripts 1P, 1N, 2P, 2N, 3P, and 3N are the positive and negative poles of the first, second, and third lines respectively; u′ x (t) is the voltage modulus obtained after decoupling by P4. The subscripts 1, 2, 3, 4, 5, and 6 are the modulus labels respectively; u″ x (t) is the voltage modulus obtained after decoupling by P5. The subscripts 1, 2, 3, 4, 5, and 6 are the modulus labels respectively.

[0108] The polarities of the voltage moduli obtained by decoupling under different fault types are different. The fault poles can be identified according to the combinations of the polarities of the 6 moduli. The polarity discrimination is shown in Equations (10) and (11).

[0109]

[0110] In Equation (10): f(x) is the operation of the five-point cubic smoothing method; N f is the calculation window length; K act is the polarity discrimination starting value.

[0111] If Equation (10) is satisfied, the positive and negative polarities can be further judged, otherwise it is the zero polarity.

[0112]

[0113] Obviously, the combinations of the polarities of the 6 moduli proposed in the present invention are difficult to cover all the fault types of the same-tower double-circuit AC-to-DC conversion system, and there will inevitably be cases of overlapping polarity combinations. Therefore, the multiples characteristics of u1(t), u3(t), and u5(t) are used to preliminarily classify the faults, and the fault types with overlapping polarity combinations are divided into different groups, and the following criterion is constructed:

[0114]

[0115] In the formula: i and j are the labels of the loop discrimination moduli respectively. For the faults of the three lines, i = 1, 3, 5, j = 1, 3, 5, and i≠j (there are 6 combinations of i and j in total). For the faults of the two lines, i and j take the labels of the fault loops, and i≠j (there are 2 combinations of i and j in total); K set_1 is the proportionality coefficient.

[0116]

[0117] In the formula: K set_2 is the proportionality coefficient.

[0118] The steps of the preliminary fault classification are as follows, and the flow chart is as Figure 2 shown:

[0119] 1) Identify the number of faulty circuits using the criterion formula (5), and perform decoupling using a phase-mode transformation matrix of the same scale.

[0120] 2) For a single-circuit line fault, judge the polarities of each modulus using formula (11), and identify the faulty pole line based on the polarity combination.

[0121] 3) For a two-circuit line fault, perform a preliminary classification using criterion formula (12) and criterion formula (13). Traverse i and j. If both satisfy criterion formula (12), it can be determined that the fault is a two-pole fault or a four-pole fault. The polarity combinations of the four-pole fault and the two-pole fault do not overlap, and the faulty pole line can be identified according to the polarity combination. If formula (12) is not satisfied, it can be determined that the fault is a three-pole short-circuit fault or a three-pole ground fault. Further classify it using criterion (13). If there are i and j that satisfy criterion formula (13), it can be determined that the fault is a three-pole short-circuit fault; otherwise, it is a three-pole ground fault. Identify the faulty pole line according to the polarity combination.

[0122] For the specific fault types under a three-pole short-circuit fault, there is a problem of overlapping polarity combinations. Use criterion formula (14) to further divide it into two categories, and identify the faulty pole line according to the polarity combination.

[0123] |Δu l (t)| > |Δu k (t)| (14);

[0124] In the formula: l and k are the subscripts reflecting the faulty modulus of the circuit, where l = 1, 3, 5, k = 1, 3, 5, and l ≠ k.

[0125] 4) For a three-circuit line fault, classify it using criterion formula (12) and criterion formula (13). Traverse i and j. If both satisfy criterion (12), it can be determined that the fault is a three-pole ground fault or a six-pole fault. The polarity combinations of the two types of faults do not overlap, and the faulty pole line can be identified according to the polarity combination. If there are i and j that satisfy criterion formula (13), it can be determined that the fault is a four-pole short-circuit fault (asymmetrical) or a five-pole short-circuit fault; otherwise, it is a three-pole short-circuit fault, a four-pole short-circuit fault (symmetrical), a four-pole ground fault (asymmetrical), or a five-pole ground fault. The polarity combinations of these four types of faults do not overlap, and the faulty pole line can be identified according to the polarity combination. "Symmetrical" and "asymmetrical" respectively refer to the cases where the number of positive and negative faulty poles is equal and not equal.

[0126] For the four-pole short-circuit fault (asymmetrical) and the five-pole short-circuit fault, there is a problem of overlapping polarity combinations. First, arrange |Δu1(t)|, |Δu3(t)|, |Δu5(t)| from largest to smallest as {u1, u2, u3}, and substitute them into criterion formula (15).

[0127]

[0128] If both criteria in Equation (15) are satisfied, it is a four-pole short-circuit fault (asymmetrical); otherwise, it is a five-pole short-circuit fault. Then, the faulty pole line is identified according to the polarity combination.

[0129] Step S4: After determining the specific faulty pole, calculate the approximate entropy of the voltage modulus at both ends of the faulty pole. Determine the arrival times t M and t N of the traveling wave at both measuring points according to the approximate entropy mutation point, and substitute them into the double-ended ranging formula to calculate the distance x of the fault point from the M end M as follows:

[0130]

[0131] where: L is the line length; v is the traveling wave propagation speed.

[0132] Verification example:

[0133] Verify the fault location scheme of the same-tower double-circuit cross-to-straight system. Build the same-tower double-circuit cross-to-straight system model shown in Figure 3 in the power system simulation software. The voltage levels of the three DC systems are all 200 kV, and the transmission capacity is 1.2 million kilowatts.

[0134] 1. Verification of faulty pole identification:

[0135] Set specific faults under different fault types for verification. The fault occurrence time is 1.5 s. Take K set_1 = 1.4, K set_2 = 2.7. Substitute the peak values of the first wave crests of u1(t), u3(t), and u5(t) into the criterion formulas (12), (13), (14), and (15) for discrimination. The discrimination results are shown in Tables 1 and 2.

[0136] Table 1 Fault classification effect of the same-tower double-circuit cross-to-straight system

[0137]

[0138] Table 2 Modulus polarity discrimination for different fault types

[0139]

[0140]

[0141] As can be seen from Tables 1 and 2, for faults in more than two circuits, the criteria proposed in this paper can initially classify the faults and avoid the influence of overlapping polarity combinations. For example, for faults in two circuits, the modulus amplitude ratios of two-pole faults and four-pole faults do not exceed K set_1 , that is, they satisfy the criterion formula (12). For three-pole short-circuit faults and three-pole grounding faults, there are combinations of i and j that exceed Kset_1 , it does not satisfy the criterion formula (12). Based on this, the two-pole short-circuit fault and the three-pole short-circuit can be divided into different groups to avoid repeated polarity combinations. For the three-pole short-circuit fault, there are combinations of i and j that exceed K set_2 , which satisfies the criterion formula (13), while for the three-pole ground fault, there are no combinations of i and j that exceed K set_2 , it does not satisfy the criterion formula (13). Therefore, the three-pole short-circuit fault can be further separated. In the three-pole short-circuit fault, the polarity combinations of 1P-1N-2P and 2P-2N-1N, 1P-1N-2N and 2P-2N-1P are repeated, and for 1P-1N-2P and 1P-1N-2N, Δu1(t) / Δu3(t) > K set_2 , that is, Δu1(t) > Δu3(t); for 2P-2N-1N and 2P-2N-1P, Δu3(t) / Δu1(t) > K set_2 , that is, Δu3(t) > Δu1(t). Based on this, they can be further divided to avoid overlapping polarity combinations, as shown in criterion formula (14).

[0142] For the three-line fault, the modulus amplitude ratios of the three-pole ground fault and the six-pole fault do not exceed K set_1 , that is, it satisfies the criterion formula (12). For the four-pole short-circuit fault (asymmetrical) and the five-pole ground fault, there are combinations of i and j that exceed K set_2 , which satisfies the criterion formula (12). Based on this, they are divided into three groups, and there is no problem of overlapping polarity combinations between the groups. To further distinguish the four-pole short-circuit fault (asymmetrical) and the five-pole short-circuit fault, criterion formula (15) is proposed. Taking the 1P-1N-2P-3P short-circuit fault and the 1P-1N-2P-2N-3P short-circuit fault in Table 1 as examples, arranging |Δu1(t)|, |Δu3(t)|, |Δu5(t)| from large to small and comparing the maximum value with the other two values respectively, we can get [3.73, 3.73], [2.90, 0.98]. It can be seen that the 1P-1N-2P-3P short-circuit fault satisfies the criterion formula (15) and is a four-pole short-circuit fault (asymmetrical), while the 1P-1N-2P-2N-3P short-circuit fault does not satisfy the criterion formula (15) and is a five-pole short-circuit fault.

[0143] After the preliminary fault classification, there is no problem of overlapping polarity combinations among the faults in different groups. Therefore, the fault poles can be further identified.

[0144] 2. Fault location verification:

[0145] Taking the sampling rate as 200 kHz and the fault occurrence time as 1.5 s, considering the metallic fault and the high-resistance fault (500 Ω), the influence of different fault locations and different fault types on the proposed scheme is verified, as shown in Table 3.

[0146] Table 3 Effect of Fault Location Scheme

[0147]

[0148]

[0149] As can be seen from Table 3, the location scheme based on approximate entropy has a high location accuracy when the sampling rate is low, and the maximum error does not exceed 3% of the full length of the line, and the error is within a reasonable range. In practical applications, with the improvement of the performance of the sampling device, the ranging error will gradually decrease.

Claims

1. A fault location method for a double-crossover system on the same tower based on multiple phase mode transformation, characterized in that The following steps are involved: Step 1: Construct the impedance matrix of the double-circuit crossover system on the same tower and obtain the fault circuit discrimination matrix; Step 2: Introduce a decoupling matrix to decouple the impedance matrix of the double-circuit crossover system on the same tower, and extract the modulus obtained by decoupling to form a modulus matrix; Step 3: Determine the voltage modulus obtained by decoupling each section, and determine the fault pole according to the voltage modulus polarity combination; Step 4: Calculate the approximate entropy of the voltage modulus at both ends of the fault pole and locate the head of the fault traveling wave.

2. According to the method for locating faults in a double-crossover system on the same tower based on multiple phase mode transformations in claim 1, it is characterized by: In step 1, in the double-circuit alternating direct current system on the same tower, assuming that the mutual impedance between each loop remains unchanged, the influence of the floor height and the symmetrical arrangement of the polar lines is considered, and the impedance matrix is ​​constructed as follows: In formula (1): z s1 is the self-impedance of each pole line of circuit Ⅰ and circuit Ⅱ; s2 is the self-impedance of each pole line of the III circuit; n1 is the mutual impedance of the two poles in the Ⅰ or Ⅱ circuit; n2 is the mutual impedance of the two poles in the III circuit; p1 is the mutual impedance of each pole line between the Ⅰ-loop and Ⅲ-loop lines and between the Ⅱ-loop and Ⅲ-loop lines; p2 is the mutual impedance of each pole line between circuits Ⅰ and Ⅱ; The loop decoupling matrix P1 is proposed to decouple the impedance matrix Z, as shown in formula (2): Introducing Clarke phase transformation matrix P c Perform inter-pole decoupling on the matrix P1Z obtained by equation (2) to obtain the fault circuit discrimination matrix P circuit for: Where O is a zero matrix; In formula (3), P c is the Clarke phase transformation matrix, 3. According to claim 2, the fault location method for the same-tower double-circuit crossover system based on multiple phase mode transformation is characterized by: The voltage mutation is taken as the fault characteristic quantity, and the fault circuit discrimination matrix P circuit Transform to get: In formula (4): u x (t) is the voltage mutation before and after the fault at the beginning or end of the pole line. The subscripts 1P, 1N, 2P, 2N, 3P, and 3N are the positive and negative poles of the Ⅰ, Ⅱ, and Ⅲ lines respectively. u1(t), u3(t), and u5(t) are the moduli reflecting whether there are faults in the Ⅰ, Ⅱ, and Ⅲ lines respectively.

4. According to claim 3, the fault location method for the same-tower double-circuit crossover system based on multiple phase mode transformation is characterized by: According to the mutation characteristics of u1(t), u3(t), and u5(t), the fault initiation criterion is constructed, as shown in formula (5); In formula (5): △u act is the starting value of the voltage mutation; u1(t) is the fault circuit discrimination modulus corresponding to the Ⅰ-loop line; u3(t) is the fault circuit discrimination modulus corresponding to the Ⅱ-loop line; u5(t) is the fault circuit discrimination modulus corresponding to the Ⅲ-loop line.

5. The fault location method for the same-tower double-crossover direct current conversion system based on multiple phase mode transformation according to claim 4 is characterized in that: In step 2, the decoupling matrix P3 is introduced: Take the inter-pole decoupling matrix P5=P3 decouples the impedance matrix Z to obtain a decoupling matrix. The obtained decoupling matrix is ​​completely decoupled in odd rows or columns and even rows or columns, as shown in the following formula: After determining the number of fault loops, select decoupling matrices of the same size for decoupling, as follows: When one circuit fails, P3=P c ; When two circuits fail, When the three-circuit line fails, P3 is as shown in formula (6).

6. The fault location method for the same-tower double-crossover direct current conversion system based on multiple phase mode transformation according to claim 5 is characterized by: In step 2, the voltage mutation is used as the fault characteristic quantity for decoupling, and the modulus matrix after decoupling is shown in formula (9): [u′1(t) u′2(t) u′3(t) u′4(t) u′5(t) u′6(t)] T =P4[u 1P (t) u 1N (t) u 2P (t) u 2N (t)u 3P (t) u 3N (t)] T (7); [u″1(t) u″2(t) u″3(t) u″4(t) u″5(t) u″6(t)] T =P5[u 1P (t) u 1N (t) u 2P (t) u 2N (t)u 3P (t) u 3N (t)] T (8); u=[u″1(t) u′2(t) u″3(t) u′4(t) u″5(t) u′6(t)] (9); In the above formula: u x (t) is the voltage mutation before and after the fault at the beginning or end of the line. The subscripts 1P, 1N, 2P, 2N, 3P, and 3N are the positive and negative poles of the I, II, and III lines respectively; u′ x (t) is the voltage modulus obtained after P4 decoupling, and the subscripts 1, 2, 3, 4, 5, and 6 are the modulus numbers respectively; u″ x (t) is the voltage modulus obtained after decoupling by P5, and the subscripts 1, 2, 3, 4, 5, and 6 are the modulus numbers respectively.

7. The fault location method for the same-tower double-crossover direct current conversion system based on multiple phase mode transformation according to claim 1 is characterized by: In step 3, the polarity of the voltage modulus obtained by decoupling under different fault types is different. The fault pole is identified according to the combination of 6 voltage modulus polarities. The polarity discrimination is shown in equations (10) and (11): In formula (10): f(x) is the five-point cubic smoothing operation; N f is the calculation window length; K act It is the polarity discrimination start value; If equation (10) is satisfied, the positive and negative polarity of the voltage modulus can be further determined; Otherwise the voltage modulus is zero polarity; 8. The fault location method for the same-tower double-crossover direct current conversion system based on multiple phase mode transformation according to claim 7 is characterized by: The faults are preliminarily classified using the multiple features of u1(t), u3(t), and u5(t). The fault types with overlapping polarity combinations are divided into different groups, and the following criteria are constructed: In formula (12): u i (t),u j (t) is the fault circuit identification modulus; i and j are the numbers of the circuit identification modulus. For a three-circuit line fault, i = 1, 3, 5, j = 1, 3, 5, and i ≠ j; for a two-circuit line fault, i and j are the numbers of the fault circuit, and i ≠ j; K set_1 is the proportionality coefficient; In formula (13): K set_2 is the proportionality coefficient.

9. The fault location method for the same-tower double-circuit crossover system based on multiple phase mode transformation according to claim 8 is characterized by: The initial classification of faults includes: ①. If it is a single-circuit line fault, use formula (11) to determine the polarity of each modulus, and identify the fault polar line based on the polarity combination; ②. If there are two circuit faults, use the criterion formula (12) and criterion formula (13) for preliminary classification: Traversing i and j, if both satisfy the criterion formula (12), the fault is determined to be a two-pole fault or a four-pole fault, and the polarity combination of the four-pole fault and the two-pole fault is not repeated, and the fault pole line can be identified according to the polarity combination; if the criterion formula (12) is not satisfied, the fault can be determined to be a three-pole short circuit fault or a three-pole grounding fault. Further classification is performed using criterion formula (13). If i and j satisfy criterion formula (13), the fault can be determined to be a three-pole short circuit fault, otherwise it is a three-pole grounding fault. The faulty pole line is identified according to the polarity combination. The specific fault types under the three-pole short-circuit fault have the problem of overlapping polarity combinations. The criterion formula (14) is used to further divide them into two categories, and the fault pole line is identified according to the polarity combination; |u l (t)|>|u k (t)|(14); In formula (14), l and k are the subscripts reflecting the fault modulus of the circuit, respectively, l = 1, 3, 5, k = 1, 3, 5, and l ≠ k; ③. If it is a three-circuit line fault, use the judgment formula (12) and judgment formula (13) to classify: Traversing i and j, if both satisfy criterion (12), it can be determined that the fault is a three-pole grounding fault or a six-pole fault. The polarity combinations of the two types of faults are not repeated, and the fault pole line can be identified according to the polarity combination; if i and j satisfy criterion (13), it can be determined that the fault is a four-pole short circuit fault or a five-pole short circuit fault, otherwise it is a three-pole short circuit fault, a four-pole short circuit fault, a four-pole grounding fault or a five-pole grounding fault. The polarity combinations of these four types of faults are not overlapping, and the fault pole line can be identified according to the polarity combination; There is a problem of overlapping polarity combinations in the four-pole short-circuit fault and the five-pole short-circuit fault. First, |u1(t)|, |u3(t)|, |u5(t)| are arranged from large to small as {u1,u2,u3}, and u1,u2,u3 correspond to the results of |u1(t)|, |u3(t)|, |u5(t)| arranged from large to small. Substitute into the criterion (15): If both criteria in equation (15) are satisfied, it is a four-pole short circuit fault, otherwise it is a five-pole short circuit fault. Then the faulty pole line is identified according to the polarity combination.

10. The fault location method for the same-tower double-circuit crossover system based on multiple phase mode transformation according to claim 9 is characterized in that: In step 4, after determining the specific fault pole, the approximate entropy of the voltage modulus at both ends of the fault pole is calculated. For the voltage modulus u″1(t), the calculation method of the approximate entropy is as follows: The calculated voltage modulus u″1(t)=[u1,u2,…,u N ], N represents N data, u1,u2,…,u N They represent the data constituting u″1(t); Reconstruct an m-dimensional vector [U(1), U(2), ..., U(N-m+1)], where m represents the dimension of the constructed vector; U(1) = [u1, u2], U(2) = [u2, u3], ..., U(N-m+1) = [u N-1 ,u N ]; U(1), U(2),…, U(N-m+1) are all constructed two-dimensional vectors; For i,j∈[1,N-m+1], count the number of vectors that satisfy the following conditions: In formula (16), d[U(i),U(j)] is the distance between two two-dimensional vectors; d[U(i),U(j)]=max|U(i)-U(j)|; r is the similarity tolerance; is the number of two-dimensional vectors similar to U(i); U(i) and U(j) are the i-th and j-th two-dimensional vectors respectively, with i,j∈[1,N-m+1]; make Then the approximate entropy can be expressed as Among them, h ApEn is the result of approximate entropy calculation; is the intermediate value calculated using the two-dimensional vector; is the intermediate value calculated using the three-dimensional vector; Determine the time t when the traveling wave reaches the two end measurement points based on the approximate entropy mutation point M ,t N , substituting into the two-terminal distance measurement formula (17), the distance x from the fault point to the M end can be calculated M for: In formula (17), L is the line length; v is the traveling wave propagation velocity.

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