Toughness power distribution network fault section positioning method suitable for complex multiple faults

Abstract

A tough power distribution network fault section positioning method suitable for complex multiple faults comprises the following steps: establishing a finite [mu] PMU stationing optimization configuration model, and solving the model to obtain the stationing position of a [mu] PMU in a power distribution network; determining the position of a fault branch according to the distribution position of the mu PMU in the power distribution network and a fault branch judgment method, and then obtaining a fault branch constraint according to the section where the fault branch is located and the section state of the section; establishing a power failure area constraint according to a three-section protection principle of the power distribution network; establishing a node expectation state constraint, a fault multiple number constraint and a section state constraint; constructing a power distribution network section positioning objective function, and establishing a power distribution network fault section positioning optimization model in combination with fault branch constraints, power failure area constraints, node expected state constraints, fault multiple number constraints and section state constraints; and solving the power distribution network fault section positioning optimization model, and outputting a positioning result. The method can reduce the economic cost of the power distribution network; and the power distribution network fault section positioning speed and accuracy are improved.

Description

Technical Field

[0001] The present invention relates to the field of fault section positioning in a distribution network, and in particular to a fault section positioning method for a resilient distribution network applicable to complex multiple faults. Background Art

[0002] In recent years, extreme disasters have occurred frequently, threatening the safe operation of distribution networks. The location of complex and multiple fault sections in distribution networks is a prerequisite for fault isolation and power supply restoration. For multi-source distribution networks containing DGs, the network topology changes, which increases the difficulty of fault handling.

[0003] When complex multiple faults occur in the distribution network under extreme disasters, the positioning accuracy and fault tolerance of the fault section positioning method of the distribution network in the existing technology are poor. The switching function used is difficult to fully describe the current direction characteristics under complex multiple faults, that is, the switching function cannot correctly calculate the expected state of the node where the main power supply fault current and the distributed fault current are reversed on the shared branch. Solving the accuracy and fault tolerance of the distribution network section positioning under complex multiple faults under extreme disasters and taking into account FTU missed reports and false reports is the primary task to improve the resilience of the distribution network.

[0004] With the continuous development of communication technology and wide-area measurement technology, μPMU measurement devices are more widely used. Because they can obtain high-precision and synchronous electrical data in the distribution network, the errors of amplitude and phase angle are only 0.5% and 0.01° respectively, which provides conditions for accurate positioning of the distribution network;

[0005] Therefore, the μPMU measurement device is introduced to process fault information in real time, limit the fault area, and improve the speed and accuracy of fault section location. According to the three-stage protection principle of the distribution network, the power outage area constraint is established. Therefore, it is of great significance to study the fault section location method of the resilient distribution network with complex multiple faults taking into account the μPMU information and the power outage area constraint. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a method for locating fault sections of a resilient distribution network suitable for complex multiple faults. The method takes the minimum configuration of μPMU measurement devices as the objective function, establishes a limited μPMU distribution optimization configuration model, and can reduce the economic cost of the distribution network; according to the three-stage protection principle of the distribution network, a power outage area constraint is established, which can improve the speed and accuracy of locating the fault section of the distribution network.

[0007] The technical solution adopted by the present invention is:

[0008] A fault section location method for a resilient distribution network applicable to complex multiple faults includes the following steps:

[0009] Step 1: Establish a limited μPMU point optimization configuration model, solve the model, and obtain the point locations of μPMU in the distribution network;

[0010] Step 2: Determine the location of the fault branch according to the location of the μPMU in the distribution network and the fault branch determination method, and then obtain the fault branch constraint according to the section where the fault branch is located and its section status;

[0011] Step 3: Establish power outage area constraints based on the three-stage protection principle of the distribution network;

[0012] Step 4: Establish node expected state constraints, fault multiplicity constraints and segment state constraints;

[0013] Step 5: According to the minimum set theory of fault diagnosis, with the goal of minimizing the deviation between the actual value of the fault current information transmitted by the FTU and the expected value, the distribution network section location objective function is constructed. Combined with the fault branch constraint in step 2, the power outage area constraint in step 3, and the node expected state constraint, fault multiplicity constraint and section state constraint in step 4, the distribution network fault section location optimization model is established;

[0014] Step 6: Solve the distribution network fault section location optimization model of step 5 and output the location result.

[0015] In step 1, the method for establishing a limited μPMU point optimization configuration model is as follows:

[0016] Set an n-dimensional vector x = [x 1 ,x 2 ,...,x n ] indicates the configuration of μPMU, x 1 ,x 2 ,...,x n They represent whether the corresponding nodes in the n-node distribution network are configured with μPMUs. The optimal configuration model for limited μPMU placement is as follows:

[0017]

[0018]

[0019] In the formula, I is the node set; c i is the weight coefficient, which represents the installation cost of μPMU at node i; A ij is the adjacency matrix; n b is the matrix A ij rank; x DG is the configuration of DG; f(x i ) is the μPMU configuration cost; x i is the configuration of μPMU; x jis the μPMU configuration at node j;

[0020] Solving the optimal configuration model for limited μPMU placement includes the following steps:

[0021] First, clarify the objective function and constraints of the model and define the decision variable x in the MATLAB platform. i , programming the objective function and constraints;

[0022] Secondly, input the topological information of the distribution network, network nodes, branches and adjacency matrix;

[0023] Then, use the CPLEX solver to solve the problem;

[0024] Finally, the location of μPMU in the distribution network is obtained.

[0025] The location of μPMU in the distribution network is as follows: Figure 1 As shown, μPMU measurement devices (a-g) are connected to the power outlet, the end of the topological node and the important nodes.

[0026] In step 2, according to the fault branch determination method, the method for establishing the fault branch constraint is as follows:

[0027] The node voltage equation of a general single-fault network is as follows:

[0028]

[0029] Where, △V i is the positive sequence voltage at node i; Z ii is the positive sequence self impedance of node i; Z ij is the positive sequence mutual impedance between nodes i and j; △I j is the positive sequence fault current at fault point j.

[0030] Based on the μPMU configuration in step 1, select M elements and their corresponding M rows of impedance matrix in the measured voltage vector of equation (2), M<<N, to form a new underdetermined node voltage equation:

[0031] ΔV=ZΔI (3);

[0032] Where ΔV is the node positive sequence voltage; Z is the positive sequence impedance; ΔI is the positive sequence fault current.

[0033] The fault current components of multiple faults can be expressed as the superposition of multiple single faults:

[0034]

[0035] Where K is the number of faults; ΔI vis the virtual injection current of the vth fault. Solving equation (2) to obtain ΔI, we can know the positions of all non-zero elements in the current vector, that is, the branch where the fault is located;

[0036] Since equation (3) is an underdetermined equation, we decouple equation (3) and obtain:

[0037]

[0038] Where, △V Re is the real part of ΔV; ΔV Im is the imaginary part of ΔV; Z Re is the real part of Z; Z Im is the imaginary part of Z; △I Re is the real part of ΔI; ΔI Im is the imaginary part of ΔI.

[0039] Assuming that vector X is sparse, use the observation matrix Φ to observe X and obtain the observation vector Y:

[0040] Y = ΦX (6);

[0041] For the distribution network fault location problem, the actual problem is to solve the minimum l with constraints. 0 Norm problem:

[0042] argmin||X|| 0 stY=ΦX (7);

[0043] In the formula, ||X|| 0 is the fault current vector X to be solved. 0 Norm.

[0044] Minimum l 0 The norm problem can be equivalent to the minimum l 1 Norm problem:

[0045] argmin||X|| 1 stY=ΦX (8);

[0046] In the formula, ||X|| 1 is the l of vector X 1 Norm.

[0047] Relax the constraints in equation (8):

[0048] argmin||X|| 1 ||Y-ΦX|| 2 ≤ε (9);

[0049] In the formula, ||Y-ΦX|| 2 is the residual Y-ΦX 2norm; ε is the threshold of allowable error.

[0050] Usually, formula (9) can be rewritten as:

[0051]

[0052] Where, the parameter λ>0 has the function of balancing the sparsity of the solution vector X and the approximation error.

[0053] Utilize l 1 Regularized least squares method is used to solve the fault current:

[0054]

[0055] In the formula, To solve the approximate fault current I a .

[0056] Assume that after a fault, the current vector I of the branch (i, j) measured by a node μPMU is f , compare it with the approximate fault current value, and determine the fault branch location when the error is the smallest. The fault branch determination method is as follows:

[0057]

[0058] Where ε(i,j) is the calculation error index of branch (i,j); K is the number of μPMUs configured in the branch where the fault area is located, and I a (i,j),θ a (i, j) are the magnitude and phase angle of the approximate fault current of branch (i, j) respectively; is the measured value I f ,θ f y is the average value of the calculation error of different branches, and the corresponding branch is the fault branch.

[0059] Determine all the sections and their status contained in the faulty branch and establish the faulty branch constraint:

[0060] x 1 ∪x 2 ∪...∪x j =1,j∈Ω LS,b (13);

[0061] In the formula, x i is the segment status; x 1 ∪x 2 ∪...∪x j is the logical OR relationship of all segment states; Ω LS,b It is the set of sections of the faulty branch determined by μPMU.

[0062] In step 3, according to the traditional three-stage protection principle, when a fault occurs within the third stage protection range, the circuit breaker of the third stage line protection device will trip to ensure the normal operation of the distribution network. The protection criterion for the circuit breaker tripping is:

[0063]

[0064] Where, I is the fault current; I D =KI cmax , is the fault identification current constant, K is the reliability coefficient; I cmax is the maximum value of the impact load current; U is the fault voltage; U D Voltage setting for short circuit fault identification.

[0065] The section fault must be within the protection range of the action protection device, so the power outage area constraints are established as follows:

[0066]

[0067] In the formula, To protect the device R k The set of LS segments within the protection range; x j is the segment state; Ω OR A collection of devices for protection.

[0068] In step 4, according to the topological structure of the distribution network, the node expected state constraint, fault multiplicity constraint and section state constraint are established as follows:

[0069] The topology of the distribution network is as follows: Figure 1 As shown in the figure, according to the location of each section, at its corresponding node, the distribution network is divided into two parts, the upstream network with substation and the downstream network without substation. According to the distribution characteristics of the fault current direction and the construction logic of the switch function, the node state expected value of the switch function in the fault section location problem of the distribution network is established. constraint:

[0070]

[0071] In the formula, I ju (x) is the switch function of the upstream part of the node; jd (x) is the switching function of the downstream part of the node; is the switching function of node j; For FTU j The number of power sources in the upstream network; For FTU j To upstream power supply S uk The set of segments on the path; S uk is the kth upstream power source; For FTU j To upstream power supply S uk The segment status on the path; For FTU j The set of all segments in the downstream network, ∩ represents logical "and", - represents logical "not"; x l For FTU j To downstream power supply S dk The segment status on the path; For FTU j The number of power sources in the downstream network; For FTU j To downstream power supply S dk The set of segments on the path of ; For FTU j The set of all segments in the upstream network;

[0072] Under extreme disasters, the probability of triple or more failures is very small. Therefore, the failure multiplicity constraint is established as follows:

[0073]

[0074] In the formula, Ω LS is the set of all sections of the distribution network; M 1 The maximum fault severity is 3.

[0075] For a distribution network with DG access, the section state constraints are established as follows:

[0076]

[0077] In the formula, I j The actual upload status value for node jFTU.

[0078] In step 5, the distribution network section positioning objective function established is as follows:

[0079]

[0080] Where, F(x) is the deviation between the actual fault current information value transmitted by FTU and the expected value; D is the total number of FTU switches; the value of M is taken as twice the number of FTU switches;

[0081] I j is the fault current information actually uploaded by the jth FTU; is the expected fault current information of the jth FTU calculated; ω is the weight coefficient set according to the minimum set theory of fault diagnosis, which is generally set to 0.5 to avoid misjudgment; It is the sum of the number of all faulty feeder sections.

[0082] Establishing the distribution network fault section location optimization model includes:

[0083] Objective function: formula (19); Constraints: formulas (13), (15) to (18).

[0084] The distribution network fault section location optimization model can be expressed as an optimization problem with 0-1 discrete constraints, as shown below:

[0085]

[0086] Where F(X) is the deviation between the actual fault current information value transmitted by FTU and the expected value; X is the set of all section states; x i is a 0-1 variable, indicating the state of the distribution network section; n is the number of distribution network nodes.

[0087] In step 6, BKA is used to solve the distribution network fault section location optimization model. The principle of the BKA algorithm is as follows:

[0088] Read the distribution network information and set the initial parameters. According to the number of distribution network feeder sections, determine the population size pop, population dimension Dim, and maximum number of iterations T.

[0089] Population initialization, calculate the fitness value of the individuals in the initialized population according to formula (19). The initialization mathematical formula for generating the position of the initialized population is as follows:

[0090] X i =BK lb +rand(BK ub -BK lb ) (twenty one);

[0091] Where, X i is the initial population position; i is an integer between 1-pop; BK ub , BK lb are the upper and lower limits of the ith individual in the jth dimension; rand(BK ub -BK lb ) is a randomly generated random number uniformly distributed between (0-1);

[0092] Start the iteration and select the individual with the best fitness in the current population as the leader of the population. The mathematical formula for determining the initial leader with the minimum fitness value is as follows:

[0093] f best =min(f(X i )) (twenty two);

[0094] In the formula, f best is the minimum fitness value; f(X i) is the fitness value of each individual;

[0095] X L =X(find(f best = = f(X i ))) (twenty three);

[0096] Where, X L is the location of the leader; find(f best = = f(X i )) is used to judge X i Whether the corresponding fitness value is the minimum fitness value; X(find(f best = = f(X i ))) is the individual position corresponding to the minimum fitness value.

[0097] According to the population attack behavior, update the individual position. Compare its fitness value with the historical optimal fitness value, and update the optimal individual position and optimal fitness value. The mathematical model of the attack behavior is as follows:

[0098]

[0099] In the formula, are the positions of the i-th individual in the j-th dimension in the t-th and t+1-th iteration steps respectively; r is a random number between 0 and 1; p is a constant of 0.9; T is the total number of iterations; t is the number of iterations completed so far; n is a dynamic convergence factor, which is used to control the balance between global search and local search during the optimization process.

[0100] According to the population migration behavior, the position of the random population is generated. The fitness value is compared with the historical optimal fitness value to obtain the updated individual position. The updated individual fitness value is compared with the historical value to update the optimal individual position and optimal fitness value. The mathematical model of migration behavior is as follows:

[0101]

[0102] m = 2 × sin (r + π / 2) (27);

[0103] In the formula, is the leader of the individual on the jth dimension at the tth iteration so far; are the individual positions of the jth dimension in the tth and t+1th iterations respectively; F i is the current position of individual i in the jth dimension in the tth iteration; F ri is the fitness value of the random position of the jth dimension of individual i in the tth iteration; C(0,1) is the Cauchy mutation; m is the migration step factor, which is used to control the migration step; r is a random number between 0 and 1.

[0104] The BKA is used to solve the distribution network fault section location optimization model, which includes the following steps: Figure 2 As shown:

[0105] Step 1: According to the number of feeder sections in the distribution network, determine the population size pop, population dimension Dim, and maximum number of iterations T.

[0106] step2: Randomly generate pop i A dim black-winged kite Each black kite is composed of 0 or 1. The fitness value XFit of the initialized population individuals is calculated according to formula (19).

[0107] Step 3: Start iteration, and select the individual with the best fitness in the current population as the leader XLeader_Pos in the population according to formula (23), whose fitness value is XLesder_Fit.

[0108] Step 4: Calculate the updated individual position XPosNew according to equations (24) and (25). Calculate the individual fitness value XFit_New after the updated position according to equation (18), compare the current individual fitness value with the historical optimal fitness value, and update the optimal individual position XPos and the optimal fitness value XFit.

[0109] Step 5: Randomly generate a population position s and obtain its corresponding fitness value r_XFitness. Compare it with the historical optimal fitness value, and calculate the updated individual position XPosNew by equations (26) and (27). Compare the updated individual fitness value XFit_New with the historical optimal fitness value, and update the optimal individual position XPos and the optimal fitness value XFit.

[0110] Step 6: Compare the current individual optimal fitness value XFit with the leader's optimal fitness value XLeader_Fit, and update the optimal black-winged kite individual Best_Pos_BKA and the optimal fitness value Best_Fitness_BKA until the iteration ends.

[0111] The present invention provides a method for locating a fault section of a resilient distribution network applicable to complex multiple faults, and the technical effects are as follows:

[0112] 1) The limited μPMU point optimization configuration model of step 1 of the present invention converts the state estimation problem of the complex distribution network into a solvable optimization problem through mathematical modeling, explicitly considers the distribution network topology, node importance and various factors of the whole network, realizes the smallest possible μPMU points, and balances the economic operation of the power grid and the system observation capability.

[0113] 2) Step 2 of the present invention uses high-precision μPMU data to quickly and accurately locate the faulty branch, and then combines the faulty branch section status to limit the fault area, so that the faulty section location is suitable for simple distribution networks, and is also suitable for distribution network section location in complex multi-branch and multi-fault situations.

[0114] 3) Step 3 of the present invention uses the action information of the three-stage protection circuit breaker to limit the power outage area to the minimum necessary area, minimize the impact of the power outage in the non-fault area, and form a double insurance of limiting the fault area with step 2, ensuring that the fault area can still be limited when one side fails, thereby improving the positioning speed.

[0115] 4) Step 4 of the present invention performs refined modeling of the operating status and fault characteristics of the distribution network from multiple dimensions, providing more comprehensive constraints and more accurate solution space description for optimization, and providing strong support for the reliability of the solution;

[0116] 5) The objective function in the distribution network fault section location optimization model of step 5 of the present invention is based on the minimum deviation principle, which reduces the error to a minimum, improves the positioning accuracy and model solution reliability, and also combines multi-dimensional constraints to improve the positioning speed and accuracy, providing a reliable basis for subsequent rapid fault isolation and recovery.

[0117] 6) The present invention proposes a method for locating a fault section based on the number and position of μPMUs deployed before a fault occurs. With the minimum configuration of μPMU measurement devices as the objective function, a limited μPMU point optimization configuration model is established, which can reduce the economic cost of the system. This method establishes power outage area constraints based on the three-stage protection principle of the distribution network, which can improve the speed and accuracy of locating the fault section of the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0118] The present invention will be further described below in conjunction with the accompanying drawings and examples;

[0119] Figure 1 This is the IEEE33-node distribution network system diagram.

[0120] Figure 2 A specific flow chart of solving the optimization model for fault section location in distribution network for BKA.

[0121] Figure 3 Dimensional state value diagram for locating single and multiple fault sections under different fault locations and information distortion conditions.

[0122] Figure 4 This is a flow chart of fault section location of the present invention. DETAILED DESCRIPTION

[0123] A fault section location method for a resilient distribution network applicable to complex multiple faults includes the following steps:

[0124] The first step is to establish a limited μPMU point optimization configuration model, solve the model, and obtain the location of μPMU in the distribution network;

[0125] The second step is to establish a fault branch location optimization model based on the location of the μPMU in the distribution network, and then collect the current phasors measured by the μPMU after the fault to obtain the fault branch constraints;

[0126] The third step is to establish power outage area constraints based on the three-stage protection principle of the distribution network;

[0127] The fourth step is to establish node expected state constraints, fault multiplicity constraints and section state constraints according to the topological structure of the distribution network;

[0128] The fifth step is to construct the distribution network section location objective function based on the fault diagnosis minimum set theory and take the minimum deviation between the actual fault current information value uploaded by FTU and the expected value as the goal. Combined with the fault branch constraint in step 2, the power outage area constraint in step 3, and the node expected state constraint, fault multiplicity constraint and section state constraint in step 4, the distribution network fault section location optimization model is established.

[0129] In the sixth step, BKA is used to solve the distribution network fault section location optimization model in step 5 and output the location results. This method can reasonably configure the number and location of μPMU devices, make full use of μPMU measurement information, and improve the speed and accuracy of fault section location by establishing power outage area constraints.

[0130] Example:

[0131] The IEEE 33-node distribution network system diagram containing 2 DGs is used as the research object to verify the effectiveness of this method. The IEEE 33-node distribution network system diagram is shown in Figure 1 shown.

[0132] Assume that the feeder has 33 FTUs with directional elements. One side of the transformer is the main power source. DGs are connected at nodes 18 and 33. The positive direction is from the main power source to the end of the feeder and the DG is defined. The numbering of the feeder sections is consistent with the switch adjacent to the upstream. A μPMU measuring device (a to g) is connected at the end of each branch.

[0133] Assuming that the FTU information is not distorted at the network nodes, the system has single ground faults and multiple ground faults at different fault locations, and all DGs are connected to the grid. The simulation results are shown in Table 1:

[0134] Table 1 Results of locating single and multiple fault sections at different fault locations

[0135]

[0136] It can be seen from Table 1 that the fault section locating method proposed in the present invention is applicable to section locating of single and multiple faults at different fault locations.

[0137] Assuming that FTU information distortion occurs at the network node, the system has single ground faults and multiple ground faults at different fault locations, and all DGs are connected to the grid. The simulation results are shown in Table 2:

[0138] Table 2 Single and multiple fault section location results under different fault locations and distortion conditions

[0139]

[0140] As can be seen from Table 2, the fault section location method proposed in the present invention is applicable to the section location results of single and multiple faults under different positions and information distortion conditions. The corresponding dimension state value of each section is as follows: Figure 3 shown.

[0141] Depend on Figure 3 It can be seen that, corresponding to the six fault scenarios in Table 2, the fault section location method proposed in the present invention can accurately reflect the dimensional state of the 33 sections under each fault, and is consistent with its corresponding fault section, reflecting the effectiveness and fault tolerance of the fault section location method proposed in the present invention.

Claims

1. A fault section location method for a resilient distribution network with complex multiple faults, characterized by: The following steps are involved: Step 1: Establish a limited μPMU point optimization configuration model, solve the model, and obtain the point locations of μPMU in the distribution network; Step 2: Determine the location of the fault branch according to the location of the μPMU in the distribution network and the fault branch determination method, and then obtain the fault branch constraint according to the section where the fault branch is located and its section status; Step 3: Establish power outage area constraints based on the three-stage protection principle of the distribution network; Step 4: Establish node expected state constraints, fault multiplicity constraints and segment state constraints; Step 5: According to the minimum set theory of fault diagnosis, with the goal of minimizing the deviation between the actual value of the fault current information transmitted by the FTU and the expected value, the distribution network section location objective function is constructed. Combined with the fault branch constraint in step 2, the power outage area constraint in step 3, and the node expected state constraint, fault multiplicity constraint and section state constraint in step 4, the distribution network fault section location optimization model is established; Step 6: Solve the distribution network fault section location optimization model of step 5 and output the location result.

2. The method for locating fault sections in a resilient distribution network applicable to complex multiple faults according to claim 1 is characterized in that: In step 1, the method for establishing a limited μPMU point optimization configuration model is as follows: Set an n-dimensional vector x = [x1, x2, ..., x n ] represents the configuration of μPMU, x1, x2, ..., x n They represent whether the corresponding nodes in the n-node distribution network are configured with μPMUs. The optimal configuration model for limited μPMU placement is as follows: Where I is the node set; c i is the weight coefficient, which represents the installation cost of μPMU at node i; A ij is the adjacency matrix; n b is the matrix A ij rank; x DG is the configuration of DG; f(x i ) is the μPMU configuration cost; x i is the configuration of μPMU; x j is the μPMU configuration at node j.

3. The method for locating fault sections in a resilient distribution network applicable to complex multiple faults according to claim 2 is characterized in that: Solving the optimal configuration model for limited μPMU placement includes the following steps: First, clarify the objective function and constraints of the model and define the decision variable x in the MATLAB platform. i , programming the objective function and constraints; Secondly, input the topological information of the distribution network, network nodes, branches and adjacency matrix; Then, use the CPLEX solver to solve the problem; Finally, the location of μPMU in the distribution network is obtained.

4. The method for locating fault sections in a resilient distribution network applicable to complex multiple faults according to claim 1 is characterized in that: In step 2, according to the fault branch determination method, the method for establishing the fault branch constraint is as follows: The node voltage equation of a general single-fault network is as follows: Where, △V i is the positive sequence voltage at node i; Z ii is the positive sequence self impedance of node i; Z ij is the positive sequence mutual impedance between nodes i and j; △I j is the positive sequence fault current at fault point j; Based on the μPMU configuration in step 1, select M elements and their corresponding M rows of impedance matrix in the measured voltage vector of equation (2), M<<N, to form a new underdetermined node voltage equation: ΔV=ZΔI (3); Where, ΔV is the node positive sequence voltage; Z is the positive sequence impedance; ΔI is the positive sequence fault current; The fault current components of multiple faults are written as the superposition of multiple single faults: Where K is the number of faults; ΔI v is the virtual injection current of the vth fault; Solving equation (2) to obtain ΔI, we can know the positions of all non-zero elements in the current vector, that is, the branch where the fault is located; Since equation (3) is an underdetermined equation, we decouple equation (3) and obtain: Where, △V Re is the real part of ΔV; ΔV Im is the imaginary part of ΔV; Z Re is the real part of Z; Z Im is the imaginary part of Z; △I Re is the real part of ΔI; ΔI Im is the imaginary part of ΔI; Assume that vector X is sparse, use the observation matrix Φ to observe X and obtain the observation vector Y: Y = ΦX (6); For the distribution network fault location problem, it is actually to solve the minimum l0 norm problem with constraints: argmin||X||0 stY=ΦX (7); Where, ||X||0 is the l0 norm of the fault current vector X to be solved; The minimum l0 norm problem can be equivalent to the minimum l1 norm problem: argmin||X||1s.t. Y=ΦX (8); Where ||X||1 is the l1 norm of vector X; Relax the constraints in equation (8): argmin||X||1 ||Y-ΦX||2≤ε (9); Where, ||Y-ΦX||2 is the l2 norm of the residual Y-ΦX; ε is the threshold of the allowable error; Formula (9) can be rewritten as: In the formula, the parameter λ>0 has the function of balancing the sparsity of the solution vector X and the approximation error; The fault current is solved using the l1 regularized least squares method: In the formula, To solve the approximate fault current I a ; Assume that the current vector I of the branch (i, j) measured by a node μPMU after the fault is f , compare it with the approximate fault current value, and determine the fault branch location when the error is the smallest; then the fault branch determination method is as follows: Where ε(i,j) is the calculation error index of branch (i,j); K is the number of μPMUs configured in the branch where the fault area is located, and I a (i,j),θ a (i, j) are the magnitude and phase angle of the approximate fault current of branch (i, j) respectively; is the measured value I f ,θ f The average value of y is the minimum value of the calculation error of different branches, and the corresponding branch is the fault branch; Determine all the sections and their status contained in the faulty branch and establish the faulty branch constraint: x1∪x2∪...∪x j =1,j∈Ω LS,b (13); In the formula, x i is the segment state; x1∪x2∪...∪x j is the logical OR relationship of all segment states; Ω LS,b It is the set of sections of the faulty branch determined by μPMU.

5. The method for locating fault sections in a resilient distribution network applicable to complex multiple faults according to claim 1 is characterized in that: In step 3, according to the traditional three-stage protection principle, when a fault occurs within the third stage protection range, the circuit breaker of the third stage line protection device will trip to ensure the normal operation of the distribution network; the protection criterion for the circuit breaker tripping is: Where, I is the fault current; I D =KI cmax , is the fault identification current constant, K is the reliability coefficient; I cmax is the maximum value of the impact load current; U is the fault voltage; U D Voltage setting for short circuit fault identification; The section fault must be within the protection range of the action protection device, so the power outage area constraints are established as follows: In the formula, Ω LS-Rk To protect the device R k The set of LS segments within the protection range; x j is the segment state; Ω OR A collection of devices for protection.

6. The method for locating fault sections in a resilient distribution network applicable to complex multiple faults according to claim 1 is characterized in that: In step 4, according to the topological structure of the distribution network, the node expected state constraint, fault multiplicity constraint and section state constraint are established as follows: Establishing the node state expected value of the switch function in the distribution network fault section location problem constraint: In the formula, I ju (x) is the switch function of the upstream part of the node; jd (x) is the switching function of the downstream part of the node; is the switching function of node j; For FTU j The number of power sources in the upstream network; For FTU j To upstream power supply S uk The set of segments on the path; S uk is the kth upstream power source; For FTU j To upstream power supply S uk The segment status on the path; For FTU j The set of all segments in the downstream network, ∩ represents logical "and", Indicates logical "not"; x l For FTU j To downstream power supply S dk The segment status on the path; N Sd For FTU j The number of power sources in the downstream network; For FTU j To downstream power supply S dk The set of segments on the path of ; For FTU j The set of all segments in the upstream network; The fault multiplicity constraint is established as follows: In the formula, Ω LS is the set of all sections of the distribution network; M1 is the maximum fault severity; For a distribution network with DG access, the section status constraints are established as follows: In the formula, I j The actual upload status value for node jFTU.

7. The method for locating fault sections in a resilient distribution network applicable to complex multiple faults according to claim 1 is characterized in that: In step 5, the distribution network section positioning objective function established is as follows: Where, F(x) is the deviation between the actual fault current information value transmitted by FTU and the expected value; D is the total number of FTU switches; the value of M is taken as twice the number of FTU switches; I j is the fault current information actually uploaded by the jth FTU; is the expected fault current information of the jth FTU calculated; ω is the weight coefficient set according to the minimum set theory of fault diagnosis; It is the sum of the number of all faulty feeder sections.

8. The method for locating fault sections in a resilient distribution network applicable to complex multiple faults according to claim 7 is characterized in that: The distribution network fault section location optimization model can be expressed as an optimization problem with 0-1 discrete constraints, as shown below: Where F(X) is the deviation between the actual fault current information value transmitted by FTU and the expected value; X is the set of all section states; x i is a 0-1 variable, indicating the state of the distribution network section; n is the number of distribution network nodes.

9. The method for locating fault sections in a resilient distribution network applicable to complex multiple faults according to claim 8, characterized in that: In step 6, BKA is used to solve the distribution network fault section location optimization model. The principle of the BKA algorithm is as follows: Read the distribution network information and set the initial parameters; determine the population size pop, population dimension Dim, and maximum number of iterations T according to the number of distribution network feeder sections; Population initialization: The fitness value of the individuals in the initialized population is calculated according to formula (19); the initialization mathematical formula for generating the position of the initialized population is as follows: X i =BK lb +rand(UK ub -BK lb ) (21); Where, X i is the initial population position; i is an integer between 1-pop; BK ub , BK lb are the upper and lower limits of the ith individual in the jth dimension; rand(BK ub -BK lb ) is a randomly generated random number uniformly distributed between (0-1); Start the iteration and select the individual with the best fitness in the current population as the leader of the population; the mathematical formula for determining the initial leader with the minimum fitness value is as follows: f best =min(f(X i )) (22); In the formula, f best is the minimum fitness value; f(X i ) is the fitness value of each individual; X L =X(find(f best ==f(X i ))) (23); Where, X L is the location of the leader; find(f best = = f(X i )) is used to judge X i Whether the corresponding fitness value is the minimum fitness value; X(find(f best = = f(X i ))) is the individual position corresponding to the minimum fitness value; According to the population attack behavior, update the individual position; compare its fitness value with the historical optimal fitness value, update the optimal individual position and optimal fitness value; the mathematical model of the attack behavior is as follows: In the formula, are the positions of the i-th individual in the j-th dimension at the t-th and t+1-th iteration steps respectively; r is a random number between 0 and 1; p is a constant of 0.9; T is the total number of iterations; t is the number of iterations completed so far; n is a dynamic convergence factor, which is used to control the balance between global search and local search during the optimization process; According to the population migration behavior, the position of the random population is generated; its fitness value is compared with the historical optimal fitness value to obtain the updated individual position; the updated individual fitness value is compared with the historical value to update the optimal individual position and the optimal fitness value; the mathematical model of migration behavior is as follows: m = 2 × sin (r + π / 2) (27); Where, L t j is the leader of the individual on the jth dimension at the tth iteration so far; are the individual positions of the jth dimension in the tth and t+1th iterations respectively; F i is the current position of individual i in the jth dimension at the tth iteration; F ri is the fitness value of the random position of the jth dimension of individual i in the tth iteration; C(0,1) is the Cauchy mutation; m is the migration step factor, which is used to control the migration step; r is a random number between 0 and 1.

10. The method for locating fault sections in a resilient distribution network applicable to complex multiple faults according to claim 9, characterized in that: The BKA is used to solve the distribution network fault section location optimization model, which includes the following steps: Step 1: According to the number of feeder sections in the distribution network, determine the size of the population pop, the population dimension Dim, and the maximum number of iterations T; step2: Randomly generate pop i A dim black-winged kite Each black-winged kite is composed of 0 or 1; the fitness value XFit of the initialized population individual is calculated according to formula (19); Step 3: Start iteration, and select the individual with the best fitness in the current population as the seed according to formula (23); the leader of the population is XLeader_Pos, and its fitness value is XLesder_Fit; Step 4: Calculate the updated individual position XPosNew according to equations (24) and (25); calculate the individual fitness value XFit_New after the updated position according to equation (18), compare the current individual fitness value with the historical optimal fitness value, and update the optimal individual position XPos and the optimal fitness value XFit; Step 5: Randomly generate a population position s and obtain its corresponding fitness value r_XFitness; compare it with the historical optimal fitness value, and calculate the updated individual position XPosNew by equations (26) and (27); compare the updated individual fitness value XFit_New with the historical optimal fitness value, and update the optimal individual position XPos and the optimal fitness value XFit; Step 6: Compare the current individual optimal fitness value XFit with the leader's optimal fitness value XLeader_Fit, and update the optimal black-winged kite individual Best_Pos_BKA and the optimal fitness value Best_Fitness_BKA until the iteration ends.

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