Power distribution network voltage sag monitoring point multi-target selection method considering low voltage ride through characteristic of distributed power supply

Abstract

The invention discloses a power distribution network voltage sag monitoring point multi-target selection method considering a distributed power supply low voltage ride through characteristic. The method comprises the following steps: providing a distributed power supply low voltage ride through strategy; deriving a voltage sag amplitude analytical expression under various short circuit fault types considering the low voltage ride through characteristic of the distributed power supply; introducing a position variable to construct a function relation between a voltage sag amplitude and a fault position; solving a voltage sag domain critical point by using a differential evolution algorithm; based on the sag domain critical point, establishing a monitoring point multi-target selection model taking economical efficiency, redundancy and construction urgency minimization as a target function; solving the established monitoring point multi-target selection model by adopting a multi-target particle swarm algorithm to obtain a Pareto optimal solution set; and according to the obtained Pareto optimal solution set, adopting an ideal point method to screen out an optimal point distribution scheme. According to the method, the voltage sag domain can be accurately divided, and multi-objective optimization of economical efficiency, low redundancy and low construction urgency of monitoring point layout is realized on the premise of satisfying panoramic observability.

Description

Technical Field

[0001] This invention relates to the field of novel distribution network voltage sag monitoring technology, specifically to a multi-objective selection method for distribution network voltage sag monitoring points that takes into account the low-voltage ride-through characteristics of distributed generation sources. Background Technology

[0002] Voltage sags, as the most frequent power quality disturbances in power systems, have a significant impact on sensitive loads such as industrial control equipment and information electronic loads, and have become a core focus of power grid operation monitoring. However, with the continuous increase in the penetration rate of inverter-interfaced distributed generators (IIDGs) in distribution networks, the system fault characteristics are fundamentally different from those of traditional distribution networks centered on synchronous generators. Directly applying existing voltage sag monitoring schemes can easily lead to significant deviations in monitoring results in active distribution networks.

[0003] The existing research still has the following problems: it focuses on the optimization of monitoring points in traditional distribution networks, and the models are mostly based on the severity of substation voltage sags or the observability of loads, but the impact of high proportion of IIDG access and its low voltage ride through (LVRT) characteristics on voltage sag propagation has not been considered, which leads to a decrease in the applicability of the method in active distribution networks, as recorded in the literature [1]: Wang Ying, Liu Huizi, Hu Wenxi. Distribution network voltage sag assessment method based on key control parameters of distributed power source [J]. Power System Technology, 2025, 49(02): 727-737.

[0004] Most existing methods adopt a single-objective optimization framework, or take the minimum number of monitoring points as the objective, or only focus on the observability of voltage sag, failing to incorporate the need to take into account multiple influencing factors in engineering practice, thus making it difficult for the generated monitoring scheme to meet the comprehensive needs of complex power grid operation scenarios. For example, reference [2]: Xiao Xianyong, Tan Yaou, Hu Wenxi, et al. Selection and evaluation method of monitoring node number of voltage sag system index [J]. Electric Power Automation Equipment, 2020, 40(10): 8-14. It mainly focuses on the optimization of the single dimension of voltage sag observable area or fault location, and has not yet combined the fault characteristics of IIDG and LVRT function to establish a voltage sag propagation model adapted to active distribution network, and cannot accurately characterize the impact of the dynamic changes of voltage sag amplitude and range on the selection of monitoring points, as recorded in reference [3]: Francisco LADK, Maria JG, Lessa FT, et al. Fast and accurate voltage sag detection algorithm [J]. International Journal of Electrical Power and Energy Systems, 2022, 135.

[0005] Therefore, there is an urgent need for a voltage sag monitoring point selection method that can adapt to scenarios with a high proportion of distributed power supply access and comprehensively consider multiple objectives. Summary of the Invention

[0006] This invention proposes a multi-objective selection method for voltage sag monitoring points in distribution networks that takes into account the low voltage ride-through characteristics of distributed power sources. This method can accurately delineate voltage dip regions and, under the premise of ensuring panoramic observability, achieve multi-objective optimization of the economy, low redundancy, and low construction urgency of monitoring point deployment. This significantly improves the accuracy of voltage sag monitoring in distribution networks under distributed power source access scenarios and the economy of monitoring device deployment.

[0007] The technical solution adopted in this invention is as follows: A multi-objective selection method for voltage sag monitoring points in distribution networks, taking into account the low-voltage ride-through characteristics of distributed generation, includes the following steps: Step 1: Propose a low-voltage ride-through strategy for distributed power sources; Step 2: Based on Step 1, using the symmetrical component method and iterative method, analytical expressions for voltage sag amplitude under various short-circuit fault types that take into account the low voltage ride-through characteristics of distributed power sources are derived. Step 3: Introduce location variables and construct a functional relationship between voltage sag magnitude and fault location; Step 4: Use the differential evolution algorithm to solve for the critical point of the voltage dip region, so as to achieve accurate division of the voltage dip region in the distribution network; Step 5: Based on the critical point of the temporary descent region, establish a multi-objective selection model for monitoring points with the objective functions of minimizing economy, redundancy, and construction urgency; Step 6: Based on the MATLAB platform, the multi-objective particle swarm optimization algorithm is used to solve the multi-objective selection model of monitoring points established in Step 5, and the Pare is obtained. t o Optimal solution set; Step 7: Obtain Pare based on Step 6 t The optimal solution set is selected using the ideal point method to find the optimal point layout scheme.

[0008] In step 1, a low-voltage ride-through strategy for distributed power sources is proposed as follows: Grid-connection regulations for photovoltaic power plants require them to output a certain amount of reactive power after a grid voltage dip to support grid-side voltage recovery. This includes the dynamic reactive current injected into the grid connection point. The voltage changes at the grid connection point should be tracked in real time, and the specific requirements are as shown in equation (1) below: (1); In formula (1): Indicates reactive current; and This is the reactive power compensation coefficient; This represents the per-unit value of the positive sequence component of the voltage at the grid connection point of the photovoltaic power station.

[0009] Photovoltaic grid-connected inverters typically employ a dual closed-loop control strategy, namely a power-voltage outer loop and a current inner loop inverter control strategy. When the positive sequence voltage at the grid connection point is detected to drop below 0.9 pu, in order to meet the LVRT requirement, reactive power priority control is adopted, the power-voltage outer loop is disconnected, and active and reactive current reference values ​​are directly given in the current inner loop. The fault equivalent model is as follows: 1) Reactive current Given by equation (1); 2) When the positive sequence voltage per unit value at the grid connection point , = , This is the reference value for active current when the DG is operating normally; This refers to the active component of the DG output current.

[0010] At this time, IID G It has not entered the low voltage ride-through operation state, but is in the normal operation state; 3) When the positive sequence voltage per unit value at the grid connection point In order to maintain the system's active power balance as much as possible without overcurrent in the inverter, IID should be set to... G The maximum permissible active power output is: (2); In formula (2): This is the maximum allowable output current of the distributed power inverter.

[0011] 4) When the positive sequence voltage at the grid connection point hour, =0. At this time, IID = 0. G It does not generate active power.

[0012] In step 2, the analytical expressions for voltage sag amplitude under various short-circuit fault types are established as follows: (1) Three-phase short circuit fault: When the fault point K When a three-phase short-circuit fault occurs, since it is a symmetrical and balanced fault, only the positive sequence is considered, and the monitoring node... m The three-phase voltage sag values ​​are the same at point A, and the voltage sag value of one phase is: (3); (4); (5); In the above formula: for m Voltage sag at point; for m Voltage before the fault at the point; for K Voltage before the fault at the point; These are positive sequence mutual impedances; It is a positive-sequence self-impedance; This is the fault current; When the fault occurs, IID G Injected current; This is the reactive component of the DG output current, which is usually 0 during normal operation.

[0013] From equation (3), we know that m Voltage sag at point It is related to the system's structural parameters and its operating state before the failure. When the fault point... K When an asymmetrical short-circuit fault occurs with phase A as the special phase, the symmetrical component method must be used for analysis. The relationship between phase voltage and sequence voltage is shown in equation (6): (6); In formula (6): , , They represent a , b,c Three-phase voltage; , , These represent zero-sequence, positive-sequence, and negative-sequence voltages, respectively. ; .

[0014] (2) Single-phase ground fault: When the fault point K When a single-phase ground fault occurs with phase A as the special phase, the sequence currents are calculated as follows: (7); In equation (7): It is the zero-sequence current; It is a positive sequence current; It is a positive sequence current; These are the positive and negative zero-sequence mutual impedances. These are the positive and negative zero-sequence self-impedances. i =0,1,2.

[0015] Therefore, zero order, positive order, and negative order are in m The voltage at point is: (8); In equation (8): for m Zero-sequence voltage at the point; for m Positive sequence voltage at the point; for m Negative sequence voltage at the point; for m Points and points K Zero-sequence mutual impedance between them; for m Points and points K Positive-sequence mutual impedance between them; for m Points and points K Negative sequence mutual impedance between them; for m The positive sequence reference voltage of the point.

[0016] By combining equations (5) to (8), we can obtain the result when the fault point... m When a single-phase-to-ground short-circuit fault occurs at a location with phase A as the special phase, m Three-phase voltage sag at point: (9); In equation (9): for m The voltage of phase A when a three-phase short circuit occurs; for m The voltage of phase B when a three-phase short circuit occurs at point B; for m The voltage of phase C when a three-phase short circuit occurs; form The reference voltage of phase A at point A is normally equal to... m The reference voltage of the point; For point m and K Zero-sequence, positive-sequence, and negative-sequence mutual impedances between them; for m Points and points K Zero-sequence mutual impedance between them; for m Points and points K Positive-sequence mutual impedance between them; for m Points and points K Negative sequence mutual impedance between them; For point m Zero-sequence, positive-sequence, and negative-sequence self-impedance; for K The reference voltage of the point; For distributed power sources K Fault current injected at the point; For rotation factor, .

[0017] (3) Two-phase short circuit fault: When a two-phase short-circuit fault occurs in phases B and C, the positive-sequence and negative-sequence currents are connected in series, and the zero-sequence current is 0. The positive and negative-sequence currents are calculated as follows: (10); In formula (10): for K The positive-sequence self-impedance of the point; for K Point negative sequence self-impedance.

[0018] Therefore, when a two-phase short-circuit fault occurs in phases B and C, m The three-phase voltage sag values ​​at point A are as follows: (11); (4) Two ground faults: When a two-phase-to-ground short-circuit fault occurs in phases B and C, the three-sequence networks are connected in parallel, and the currents of each sequence are calculated as follows: (12); In equation (12): for K Zero-sequence self-impedance.

[0019] Therefore, when a two-phase-to-ground short-circuit fault occurs in phases B and C, m The three-phase voltage sag values ​​at point A are as follows: (13); in: for K The positive-sequence self-impedance, negative-sequence self-impedance, and zero-sequence self-impedance of a point are multiplied in pairs and then added together. .

[0020] Due to the integration of distributed power sources, the system becomes nonlinear, and the superposition theorem cannot be used to calculate the amplitude. Therefore, an iterative solution is employed. The specific process is as follows: ① Calculate the sag amplitude according to the above amplitude calculation method; ② Modify IID according to equations (1), (2), and (5) G The output short-circuit current; ③ Repeat steps ① to ② until the voltage deviation at the grid connection point in the two calculations meets the following requirements: (14); In equation (13): For the first K Distributed power grid connection point after +1 iteration m The voltage; For the first K The voltage at the grid connection point of the distributed power source after the next iteration; For convergence accuracy; Since the low-voltage ride-through of distributed power sources is a dynamic process, step ① yields the first voltage sag value. At this point, the short-circuit current is corrected through step ②. Then, this current is used to calculate step ①. The voltage obtained in step ① is then used in the short-circuit current calculation in step ②. This process is repeated until step ③ is satisfied.

[0021] ④ The voltage of each node at this time is obtained from the power flow calculation.

[0022] In step 3, the functional relationship between the voltage sag magnitude and the fault location is constructed as follows: When a short-circuit fault occurs on the system bus, its self-impedance and mutual impedance can be directly retrieved from the node impedance matrix; however, when a short-circuit fault occurs at a point on the line, the calculation of its self-impedance and mutual impedance requires the introduction of location variables. p The impedance matrix of the nodes is then used to obtain the solution. For example... Figure 1 As shown, transmission line FT superior K When a short circuit fault occurs at a point, use position variables. p (0≤p≤1) Locate the fault point. m The point is the bus node where the load is located. For the line FT The sequence impedance. When the fault point... K On the line FT When moving upwards, its three-sequence self-impedance and fault pointK and M Three-order mutual impedance between points All can be derived from the target network impedance matrix Z and position variables p express: (15); (16); In the formula: , These are the system bus nodes. F , T The sequence self-impedance; , , These are the system bus nodes. F and T sequence mutual impedances, busbars F and load nodes m The sequence mutual impedances and busbars between them T and load nodes m The mutual impedances between each sequence can be retrieved from the system node impedance matrix; For nodes FT Inter-line sequence impedance; for m Point and K Zero-sequence, positive-sequence, and negative-sequence mutual impedances between points.

[0023] In addition, the fault point m Voltage before the fault occurred Fault location variables can also be used. p To indicate: (17); In equation (17): , busbars F and T The voltage before the fault can be obtained through power flow calculation.

[0024] therefore m The voltage sag at a point can be represented by the pre-fault voltage and the sequence impedances. Substituting equations (15) to (17) into the above four fault conditions... m The expression for the three-phase voltage sag at a fault point can be used to calculate the voltage drop when any short-circuit fault occurs at any fault point. m Point voltage sag amplitude with respect to location variable p Functional expression The purpose of this step is to establish m Point voltage sag amplitude with respect to location variable p Functional expression Then, in step 4, the position variables are solved. p The value of .

[0025] In step 4, the goal of solving the voltage sag region problem is to find the critical point on the line. p Solve based on step 3 =0, making the voltage sag amplitude equal to threshold : (18); Includes the following steps: S4.1: Define NP individuals, each representing a fault location. , i =1,2,…,NP , Then, an initial population is randomly generated and evenly distributed within the interval [0,1].

[0026] S4.2: Define the fitness function as the deviation between the voltage sag and the threshold: (19); In equation (19): The fitness function is defined as the deviation between the voltage sag and the threshold.

[0027] S4.3: Determine if the maximum number of iterations is satisfied. Or it meets the convergence condition. ,This article Take 0.0.1; if satisfied, jump to S4.8. S4.4: For the first g For each experimental individual Select three distinct individuals from the population. , , Generate mutated individuals: (20); In equation (20): For the first g The generation i One mutated individual; For a first g The experimental individual is defined as r1; For a first g The experimental individual is defined as r2; For a first g The experimental individual is defined as r3; for F and The product of; where , is the scaling factor, which controls the magnitude of variation; in this paper, it is set to 0.7.

[0028] S4.5: Cross the mutation vector with the current individual to obtain the experimental individual: (twenty one); In equation (21): For the first g The generation i One experimental individual; For the first g The generation i One experimental individual; To generate random numbers between 0 and 1; , where is the crossover probability, which is set to 0.6 in this paper.

[0029] S4.6: Compare the fitness of the experimental individuals with that of their parents, and select the better individuals to enter the next generation: (twenty two); In equation (22): For the first g +1st generation i One experimental individual; No. g The generation i The fitness of each experimental individual; No. g The generation i The fitness of each experimental individual.

[0030] S4.7: Determine whether all individuals in the current generation have been traversed. If so, jump to S4.3; otherwise, jump to S4.4. S4.8: Output results.

[0031] In step 5, the multi-target selection model for monitoring points is constructed as follows: 5.1 Economic Objectives: The deployment scheme for voltage sag monitoring must consider economic efficiency. This paper uses the purchase cost, installation cost, and annual operating cost of the monitoring equipment to represent the economic efficiency of the scheme. The objective function is as follows: (twenty three); In equation (22): The costs incurred by this plan; For nodes i The cost of purchasing monitoring equipment; For nodes i Installation costs; For nodes i Annual operating expenses; For 0-1 variables, if the node i As a monitoring point, =1; otherwise, =0; This represents the number of system nodes.

[0032] 5.2 Redundancy Target: The basic requirement for selecting monitoring points is to ensure the comprehensive observability of the system voltage dips. Since step 4 has already solved the dip region and obtained the critical points of the dip region for each node under different fault types, this boundary information can be directly used in the constraints to characterize the monitoring range. Assume the nodes... i of t The type of depression region is: (twenty four); In equation (24): t =1, 2, 3, 4, representing the four fault types: single-phase short circuit, two-phase short circuit, phase-to-phase short circuit, and three-phase short circuit, respectively. For nodes i of t In the concave region; Line 1 belongs to node i of t Part of a concave region; For the line 1 Belongs to node i of t Part of a concave region; For the line j Belongs to node i of t A portion within a concave region.

[0033] In step 4, the critical points of the concave regions of each node have been obtained using the differential evolution algorithm; let the node... i line l of t The number of boundary points of the concave region is Its corresponding boundary is: (25); In equation (25): For nodes i exist t Line under type of fault l The set of critical points; For nodes i exist t Line under type of fault l The first critical point; For nodes i exist t The second critical point of line l under type-3 fault; For nodes i exist tLine under type of fault l The set of two critical points.

[0034] Therefore, the depression region of the line is: (26); In equation (26): For nodes i exist t Line under type of fault l The line section formed by the critical point and the endpoint; For nodes i exist t Line under type of fault l The line section formed by the two critical points.

[0035] Taking all four fault scenarios into account, the resulting depression area after considering all fault types is... for: (27); In equation (27): For nodes i The depression region after considering all fault types; For the occurrence t The probability of a type of failure; For the line j Belongs to node i of t A portion within a concave region.

[0036] set up n The selection of monitoring points for each node is as follows: (28); In equation (28): This is a vector indicating whether all nodes are monitoring nodes; For variables of 0-1, if node 1 is a monitoring point, =1; otherwise, =0; For 0-1 variables, if the node i As a monitoring point, =1; otherwise, =0; For variables of 0-1, if node n is a monitoring point, =1; otherwise, =0; This is the transpose of the matrix.

[0037] (29); Based on the selection of monitoring points, the matrix H The union of the elements in the middle column is used to obtain the configuration scheme for the line.j The monitoring scope is as follows: (30); In equation (30): For the deployment plan, the route j The monitoring coverage area; The deployment plan for the line j One endpoint of the monitoring coverage area; The deployment plan for the line j The other endpoint of the monitoring coverage; For the deployment plan, the route j The monitoring coverage area; This represents the number of system nodes.

[0038] The monitoring range of each line in the system is represented by a matrix. W Represented as: (31); In equation (31): The monitoring coverage area of ​​Line 1 is determined by the deployment plan; For the deployment plan, the route j The monitoring coverage area; For the deployment plan, the route l The monitoring coverage area.

[0039] line j Line length within the monitoring range The calculation formula is: (32); In equation (32): For the line j The actual length of the line within the monitoring scope.

[0040] In engineering practice, achieving full-network fault observability in a large regional power grid requires the installation of numerous monitoring devices, which places a heavy economic burden on power grid companies. This paper takes power grid fault observability as the optimization objective, and the objective function for minimizing the observability loss rate is shown below: (33); In equation (33): The observable loss rate; Indicates the probability of a fault type; For nodes i exist t Line under type of fault j The actual length of the line within the monitoring scope; In order to be in t Line under type of fault j The actual length of the line within the monitoring scope.

[0041] This represents the total number of lines.

[0042] 5.3. Urgent Objectives for Construction: Compared to traditional optimization models that aim to minimize the number of monitoring devices, this paper considers the urgency of constructing monitoring devices at each node in practice, and uses minimizing the construction urgency coefficient as the objective function: (34); In equation (34): To assess the urgency of construction; For 0-1 variables, if the node i As a monitoring point, =1; otherwise, =0; For the occurrence t Nodes during fault types i The voltage sag.

[0043] 1) Panoramic view constraint: When the monitoring range of the deployed monitoring devices can cover all lines, the deployment scheme can satisfy the requirement of panoramic observability, thus establishing observability constraints: (35); In equation (35): For the line j Length; L Total number of all lines; For the line j The actual length of the line within the monitoring scope; 2) Constraints on the number of monitoring points: (36); In equation (36): The maximum number of monitoring points planned; For 0-1 variables, if the node i As a monitoring point, =1; otherwise, =0.

[0044] 3) Cost constraints: (37); In equation (37): For nodes i The cost of purchasing monitoring equipment; For nodes i Installation costs; For nodes i Annual operating expenses; For 0-1 variables, if the nodei As a monitoring point, =1; otherwise, =0; The maximum cost in the plan.

[0045] Step 6 includes the following steps: S6.1: Initialize the particle swarm: a) Setting parameters: Set the number of particles N and the size of the archive set. Maximum number of iterations Inertia weight Learning factors , Each particle represents a monitoring device deployment scheme, encoded using a 0-1 vector of length N.

[0046] b) Under the premise of satisfying the constraints, randomly generate the initial population and initialize the position vector of each particle. and velocity vector

[0047] S6.2: For each particle, calculate the values ​​of equations (23), (33), and (34), perform multi-objective fitness evaluation, and monitor feasibility. If the full constraint conditions are violated, the fitness value is corrected through a penalty function.

[0048] S6.3: Construct an external archive A to store the non-dominated solution set of the current iteration; in each iteration, use fast non-dominated sorting and crowding distance calculation to select the Pare. t The frontier solution is then updated, and the external archive is updated. To handle constraints, a penalty function is applied to particles that violate the panoramic observability condition, adjusting their fitness values ​​to a maximum value, thereby guiding the search for feasible solutions.

[0049] S6.4: For each particle, if the current fitness dominates its historical best position, then update the individual optimal solution. Select the globally optimal solution from external archives using congestion distance. This is to ensure the diversity of solutions.

[0050] S6.5: Update the particle velocity and position according to equations (38) and (39), and apply S to the position vector. igm o i The d function is mapped to the [0,1] interval and discretized according to the threshold rule to obtain a new monitoring point layout scheme.

[0051] (38); In equation (39): For the first i The first particle K +1 iteration speed; Inertial weights; For the first i The first particle K The speed of each iteration; For the first i The first particle K The position of the next iteration; This represents the individual optimal solution for each particle. This is the globally optimal solution; The weights for a particle to learn from its own historical best solution; The weights for particles to learn towards the global optimal solution; and These are two random numbers that are uniformly distributed between 0 and 1.

[0052] (39); In equation (39): For the first i The first particle K Position vector of +1 iterations.

[0053] S6.6: Correct individuals that do not meet the panoramic viewability constraints of the concave region, such as by forcibly adding key nodes, until the constraints are met.

[0054] S6.7: If the maximum number of iterations is reached If the external archive is no longer updated within a certain number of generations, the algorithm converges and outputs the non-dominated solution set in the external archive.

[0055] S6.8: Output results.

[0056] In step 7, the optimal point layout scheme is selected using the ideal point method, as follows: The optimal ideal solution method is used to screen the objectives, and the solution set is evaluated using the value of the objective function to find the optimal solution that comprehensively considers economy, risk, and urgency under different scenarios. After calculating the value of the evaluation index, it is normalized, and the formula is as follows: (40); In equation (40): For Pare t o Solution set i After normalization, the solution of the i-th solution is... m The values ​​of each evaluation indicator; for The solution m One objective function; For the first m The minimum value of an objective function; For the first m The maximum value of each objective function.

[0057] To find the optimal solution that simultaneously considers multiple objectives, the convergence degree to the ideal point is calculated for all optimized solutions, and all Pare... t o The squared Euclidean distance from the optimal solution to the target ideal point for: (41); In equation (41): This represents the ideal solution value for the evaluation index; m The number of objective functions.

[0058] This article is based on all Pare t The optimal decision scheme is objectively determined based on the principle of minimizing the sum of the squared Euclidean distances between the optimal solution and the ideal point on each objective, as shown in equation (42): (42); In equation (42): This is the optimal solution selected for this scenario.

[0059] This invention provides a multi-target selection method for voltage sag monitoring points in distribution networks that takes into account the low-voltage ride-through characteristics of distributed generation sources. The beneficial effects are as follows: 1) This invention considers the impact of the low voltage ride-through characteristics of distributed power sources on voltage sag propagation. Through accurate voltage sag calculation and dip domain division, the monitoring point deployment scheme is more adaptable to modern distribution networks with a high proportion of new energy access.

[0060] 2) This invention establishes a multi-objective optimization model that comprehensively considers economy, redundancy and construction urgency, overcoming the limitations of single-objective optimization and making the site layout scheme more applicable and economical in engineering practice.

[0061] 3) This invention employs a strategy that combines differential evolution algorithm with multi-objective particle swarm optimization algorithm to ensure the computational accuracy and efficiency of depression domain division and monitoring point optimization.

[0062] 4) Through calculation examples, the method of the present invention can effectively reduce the number of monitoring points and improve the coverage while ensuring panoramic visibility. It avoids the monitoring blind spots and redundant point layout problems caused by the traditional method due to the failure to consider the low voltage ride-through characteristics. Attached Figure Description

[0063] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a schematic diagram for calculating the voltage sag.

[0064] Figure 2 This is a flowchart of the concave region solution based on the differential evolution algorithm.

[0065] Figure 3Wiring diagram for the IEEE 33-node power distribution system.

[0066] Figure 4 A comparison chart showing the results of monitoring range critical points calculated using different methods.

[0067] Figure 5 Pareto front plot for monitoring points with a temporary threshold of 0.8 pu.

[0068] Figure 6 This is a two-dimensional projection of the Pareto front.

[0069] Figure 7 This is a distribution chart of transient drop values ​​under different scenarios.

[0070] Figure 8 This is a statistical chart showing the temporary decrease value below the threshold.

[0071] Figure 9 A comparison chart showing the voltage sag monitoring range under different short-circuit conditions.

[0072] Figure 10 A comparison chart of indicators for different deployment schemes under different temporary descent thresholds. Detailed Implementation

[0073] A multi-objective selection method for voltage sag monitoring points in distribution networks, considering the low-voltage ride-through characteristics of distributed generation (DVR), is proposed. This method includes: proposing a DVR low-voltage ride-through strategy; establishing a voltage sag amplitude calculation model based on LVRT; decomposing the ordinal network using the symmetric component method for four typical fault types, and iteratively deriving the post-fault voltage of each node by combining the IIDG fault injection current, thus determining the sag amplitude under different faults; then, establishing a concave region model based on the differential evolution algorithm: defining the concave region as the line area where a fault causes a node sag, setting 0.8 pu rated voltage as the threshold, searching for critical positions to divide the interval, and clarifying the concave region range of each node. Next, considering factors such as economy, redundancy, and construction urgency, a multi-objective selection method for monitoring points considering ride-through characteristics is proposed, and a multi-objective particle swarm optimization algorithm is used for solution. Finally, the constructed framework is verified through a numerical example using the IEEE 33-node system in the MATPOWER software package within the MATLAB environment. The results show that, with a threshold of 0.8 pu, this method reduces the number of monitoring points by 16.7% while maintaining panoramic observability, significantly outperforming traditional methods and improving the economic efficiency of monitoring point deployment. This provides a reference for voltage sag monitoring in renewable energy-dominated distribution networks. The method was validated using MATLAB with MATPOWER's IEEE 33-bus system, connecting two 1MW IIDGs. Three comparative scenarios were set up, and the effectiveness of the method was verified by analyzing indicators such as the number of monitoring points, coverage efficiency, and cost.

[0074] A multi-objective selection method for voltage sag monitoring points in distribution networks, taking into account the low-voltage ride-through characteristics of distributed generation, includes the following steps: Step 1: Distributed power source low-voltage ride-through strategy; Step 2: Based on Step 1, using the symmetrical component method and iterative method, analytical expressions for voltage sag amplitude under various short-circuit fault types that take into account the low voltage ride-through characteristics of distributed power sources are derived. Step 3: Based on Step 2, introduce a location variable to construct a functional relationship between the voltage sag amplitude and the fault location; Step 4: Based on Step 3, use the differential evolution algorithm to solve for the critical point of the voltage trough region, so as to achieve accurate division of the voltage trough region in the distribution network. Step 5: Based on the critical point of the voltage sag region in Step 4, a multi-objective selection method for monitoring points is proposed, with the objectives of minimizing economy, redundancy, and construction urgency. Step 6: Based on the MATLAB platform, the multi-objective particle swarm optimization algorithm is used to solve the multi-objective selection model of monitoring points proposed in Step 4, and the Pare algorithm is obtained. t o Optimal solution set; Step 7: Based on the Pareto optimal solution set obtained in Step 5, the optimal point placement scheme is selected using the ideal point method.

[0075] The simulation process is as follows: Based on the multi-target selection method for monitoring points obtained from the above steps, program and input parameters in the MATLAB environment to solve the problem.

[0076] s t ep1: A multi-target selection method for monitoring points based on multi-target particle swarm optimization algorithm, and a deterministic calculation program is written in MATLAB; s t ep2: Set simulation input conditions, including key parameters such as access node location and temporary descent threshold; s t ep3: By changing different sag thresholds, the calculation program is run to obtain the corresponding voltage sag placement schemes, and the differences in placement results with and without considering the LVRT characteristics of DG are compared, thereby analyzing the impact of LVRT on the placement scheme.

[0077] Figure 1 This diagram illustrates the calculation of voltage sag amplitude considering low-voltage ride-through of distributed generation (DVR). The right side derives analytical expressions for voltage sag amplitude based on different short-circuit fault types. The left side considers the DVR characteristics of DVR and uses an iterative solution method to calculate the corrected voltage sag amplitude, ultimately outputting the voltage sag amplitude. This diagram visually demonstrates how DVR characteristics affect the calculation of voltage sag in distribution networks and provides a theoretical basis for the deployment of monitoring points. Figure 2This is a flowchart of the voltage dip domain solution based on the differential evolution algorithm, which describes in detail how to solve the critical point of the voltage dip domain using the differential evolution algorithm. Figure 3 This is a wiring diagram of the IEEE 33-node power distribution system, showing the connection of photovoltaic power sources to each node.

[0078] Figure 4 It can be seen that the curve obtained by the differential evolution method proposed in this paper is basically consistent with the actual amplitude curve, while the amplitude curves obtained by the BA algorithm, bisection method, and golden section method deviate significantly from the actual amplitude curves. The actual values ​​of the critical points of the two concave regions of line 26-27 are 0.0294 and 0.6391, respectively. The critical points obtained by the bisection method are 0.0923 and 0.6109, the critical points obtained by the golden section method are 0.0804 and 0.6493, and the transient boundary positions obtained by the BA algorithm are 0.0273 and 0.6391. Therefore, it is evident that the differential evolution algorithm improves the accuracy of solving the transient boundary points compared to the bisection method and the golden section method, and can effectively avoid monitoring blind spots.

[0079] Figure 5 The Pareto front plot for monitoring points with a temporary threshold reduction of 0.8 pu presents a non-dominated solution set, reflecting the trade-off between economic efficiency, redundancy, and construction urgency. Figure 6 This is a two-dimensional projection of the Pareto front, visually displaying the distribution of solutions across two objective dimensions. It clearly identifies the merits of solutions under different objective combinations, aiding in selection. For example, in cost and redundancy projection, it can quickly locate solutions with moderate cost and reasonable redundancy. Figure 5 The selection of the optimal solution provides a more intuitive two-dimensional perspective, which together enhances the scientific nature of the selection of monitoring points.

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[0081] Table 1 compares typical solutions with a threshold of 0.8 pu, including the optimal solution, the lowest cost solution, the lowest redundancy solution, and the lowest construction urgency solution. The results show that the lowest cost solution requires an investment of only 253,000 yuan, saving approximately 12.7% of the cost compared to the optimal solution. However, both redundancy and construction urgency increase, with the urgency index rising by 19.8%, indicating a significant increase in system construction pressure and risk while reducing investment. The lowest redundancy solution reduces redundancy by 23.9% by minimizing redundant coverage, demonstrating a more streamlined monitoring point configuration. However, the total cost rises to 428,000 yuan, 33.4% higher than the optimal solution, and the construction urgency also decreases. The lowest construction urgency solution performs best in terms of urgency index, at only 8.8, a 36.2% reduction compared to the optimal solution. However, this comes at the cost of a total cost increase to 362,000 yuan, 27.0% higher, and relatively higher redundancy. Comprehensive comparison shows that the optimal solution achieves a construction urgency index of 13.8 and a moderate level of redundancy at a moderate cost of 285,000 yuan. It achieves a good balance between economy, redundancy control and construction urgency, verifying the effectiveness of the proposed model in multi-objective trade-offs.

[0082] To analyze D in detail G The LVRT characteristic continues to provide voltage support during voltage sags. I A case study analysis of the EEE33-node system is conducted, taking a three-phase short circuit at node 12 as an example. The voltage sag threshold is set to 0.8 pu, and the following three scenarios are constructed: Scenario 1, no distributed generation (DG) is connected to the distribution network; Scenario 2, DG is connected to nodes 10 and 20, with only PQ nodes participating in short-circuit settlement, and low-voltage ride-through characteristics are not considered; Scenario 3, DG is connected to nodes 10 and 20, and low-voltage ride-through characteristics are considered. The distribution of voltage sag amplitude in the three scenarios is analyzed, such as... Figure 7 As shown.

[0083] Depend on Figure 7 It can be seen that due to the short-circuit fault at node 12, the voltage amplitude of node 12 is significantly reduced in all three scenarios, which also leads to a reduction in the voltage of its adjacent nodes. However, the voltage of nodes with DG access is not considered... L VR T The sag is more severe, with the maximum sag value decreasing from 0.42 pu to 0.38 pu. This is because, without considering LVRT, the DG fault leads to rapid disconnection from the grid, which not only results in the loss of voltage support but may also cause sudden power flow changes, leading to uneven sag distribution.

[0084] consider L VR T At that time, D GThe transient rate of the grid connection point and surrounding nodes has significantly improved. The transient rate of nodes 10 and 20 has increased to 0.82 pu and 0.88 pu, respectively, a 45% improvement compared to scenario 1; the maximum transient rate has increased to 0.51 pu, a 26% reduction compared to scenario 1. This indicates that D G During a fault, reactive current was injected to support the grid connection voltage, suppressing sag propagation. Furthermore, in scenario 3, the sag amplitude distribution became more gradual, with standard deviations reduced by 31% and 42% compared to scenarios 1 and 2, respectively. This indicates that LVRT can effectively improve the spatial variability of sags, providing a more stable voltage environment for monitoring point optimization.

[0085] Figure 8 The number of nodes with sag values ​​below the threshold of 0.8 pu in different scenarios was quantified, further revealing the impact of LVRT on monitoring requirements. Under three-phase short-circuit faults, 18 nodes in scenario 1 were below the sag threshold, accounting for 54.5% of the total nodes; in scenario 2, this increased to 21 nodes, accounting for 63.6%, indicating that not considering LVRT would amplify the sag's impact range and increase the risk of monitoring blind spots. In scenario 3, the number of nodes below the sag threshold decreased to 13 nodes, accounting for 39.4%, a decrease of 38.3% compared to scenario 2, validating the... L VR T The effect of suppressing the temporary drop range.

[0086] Assuming a voltage sag monitoring device is connected to node 9, the monitoring range of the voltage sag at node 10 in the above three scenarios is as follows: Figure 9 As shown. Analysis Figure 9 The voltage sag monitoring range under the four short-circuit conditions shows that the voltage sag monitoring range in scenario 1 is larger than that in scenario 2. This is because the IIDG in scenario 2 does not consider LVRT, which can lead to voltage sag during the voltage sag period. II D G Disconnection from the grid exacerbates the voltage drop at the grid connection point, resulting in even lower voltage drops at nearby nodes and ultimately a smaller monitoring range. However, the voltage sag monitoring range in Scenario 3 is larger than that in Scenario 2. This is because, when considering LVRT, the IIDG provides reactive power support during faults, which improves the voltage sag amplitude at the grid connection point, effectively reducing the dip amplitude. This improves the edge areas that previously required additional monitoring, thus reducing redundant monitoring points.

[0087] Table 2 shows the monitoring range of four typical faults under three scenarios. It can be seen that, under all fault types, Scenario 3 has a superior monitoring coverage compared to the other two scenarios, especially in the cases of single-phase short circuit and two-phase ground fault. Scenario 3's coverage rates are 50% and 65% respectively, significantly higher than Scenario 1's 42% and 58%, and Scenario 2's 39% and 55%. This further demonstrates that during voltage sags, the LVRT characteristic of distributed generation can effectively reduce the depth of voltage sags, thereby improving the monitoring system's coverage.

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[0089] Table 3 shows the optimal monitoring point deployment schemes for the three scenarios. In Scenario 2, compared to Scenario 1, the monitoring range decreases due to the impact of DG on the voltage sag propagation path, requiring an increase in the number of monitoring points to ensure coverage. For example, at thresholds of 0.9 pu and 0.7 pu, Scenario 1 requires 8 and 6 monitoring points respectively, while Scenario 2 requires 9 and 7. In Scenario 3, considering the low voltage ride-through characteristics, the DG provides reactive power support during short-circuit faults, weakening the voltage sag amplitude in some areas and expanding the monitoring range. As a result, the number of monitoring points is reduced compared to Scenario 1, decreasing by 2 at both 0.9 pu and 0.7 pu thresholds, and by 1 at both 0.8 pu and 0.6 pu thresholds. This indicates that the introduction of LVRT improves the system's voltage support capability to some extent, thereby reducing the required number of monitoring points.

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[0091] Figure 10 The study demonstrates the differences in performance indicators for different monitoring point selection schemes under varying sag thresholds. The results show that considering distributed generation (DG) and its LVRT characteristics significantly impacts monitoring point selection. The difference between Scenario 1 and Scenario 2 indicates that simply connecting DG may actually increase deployment requirements, while Scenario 3 shows that considering LVRT reduces the need for DG deployment. G It can effectively improve voltage sag characteristics and reduce the number of redundant monitoring points. This indicates that in modern distribution networks with distributed generation (DG), LVRT characteristics must be incorporated into the monitoring point optimization model to ensure the scientific validity and engineering applicability of the results.

Claims

1. A method for multi-objective selection of voltage sag monitoring points in a distribution network considering low voltage ride through (LVRT) characteristics of distributed generation (DG), characterized in that The method comprises the following steps: Step 1: a low-voltage ride-through strategy of a distributed power supply is proposed; Step 2: based on step 1, a symmetric component method and an iteration method are adopted to deduce analytical expressions of voltage sag amplitudes under multiple short-circuit fault types considering low-voltage ride-through characteristics of the distributed power supply; Step 3: a position variable is introduced to construct a functional relationship between the voltage sag amplitude and the fault position; Step 4: a differential evolution algorithm is used to solve critical points of a voltage sag domain, and accurate division of the voltage sag domain in the distribution network is realized; Step 5: based on the critical points of the voltage sag domain, a multi-objective selection model of monitoring points is established, and minimization of economy, redundancy and construction urgency is taken as an objective function; Step 6: The multi-objective particle swarm optimization algorithm is used to solve the multi-objective selection model of monitoring points established in Step 5, and the Pareto optimal solution set is obtained. t o Step 7: Pare obtained according to step 6 t o Optimal solution set, the ideal point method is used to screen out the optimal distribution scheme.

2. The method of claim 1, wherein the method further comprises: In step 1, the low-voltage ride-through strategy of the distributed power supply is proposed as follows: The photovoltaic power station is required to output certain reactive power after grid voltage drop occurs, support the recovery of grid voltage; the dynamic reactive current injected into the grid connection point The voltage change of the grid connection point should be tracked in real time, and the specific requirements are shown in the following formula (1): （1）； In formula (1): represents the reactive current; and is the reactive compensation coefficient; is the positive sequence component of the voltage at the grid connection point of the photovoltaic power station. A photovoltaic grid-connected inverter adopts an inverter control strategy of a power-voltage outer loop and a current inner loop; when it is monitored that a positive sequence voltage at a grid-connected point drops to below 0.9pu, in order to meet the LVRT requirement, reactive power priority control is adopted, the power-voltage outer loop is disconnected, and active and reactive current reference values are directly given in the current inner loop; and a fault equivalent model is as follows: 1) reactive current given by equation (1); 2) when the grid-connected point positive sequence voltage norm , = , is the active current reference value when the DG is in normal operation; is the active component of the DG output current; At this time the IID G does not enter a low voltage ride through operating state, but is in a normal operating state; 3) When the grid point positive sequence voltage norm to maintain the system active balance as much as possible without overcurrent of the inverter, the IID G emits the maximum allowed active power, that is: （2）； In formula (2): is the maximum allowed output current of the distributed power inverter; 4) When the positive sequence voltage at the grid connection point hour, =0; at this time, IID G It does not generate active power.

3. The method of claim 1, wherein the method further comprises: determining the voltage of the power distribution network at the monitoring point; and determining whether the voltage of the power distribution network at the monitoring point is less than the low voltage threshold. In step 2, the analytical expressions of the voltage sag amplitudes under the multiple short-circuit fault types are established as follows: (1) three-phase short-circuit fault: When a three-phase short-circuit fault occurs at the fault point K Since it belongs to a symmetrical balanced fault, only the positive sequence is considered, and the three-phase voltage sag amplitude at the monitoring node m The voltage sag amplitude of a certain phase is: （3）； （4）； （5）； In the above formulae: is the voltage at the point of common coupling (PCC) after the fault; m is the voltage at the point of common coupling (PCC) before the fault; is the voltage at the point of common coupling (PCC) after the fault; m is the voltage at the point of common coupling (PCC) before the fault; is the voltage at the point of common coupling (PCC) before the fault; K is the voltage at the point of common coupling (PCC) before the fault; is the positive sequence mutual impedance; is the positive sequence self-impedance; is the fault current; is the IID at the point of common coupling (PCC) during the fault; G is the current injected by the DG; is the reactive component of the DG output current; From equation (3), m Voltage sag amplitude at point Related to system structure parameters and system operating state before fault; when fault point K When asymmetric short-circuit fault occurs at point with A phase as special phase, symmetric component method is used for analysis; relationship between phase voltage and sequence voltage is shown in equation (6): （6）； In formula (6): , , respectively represent a , b,c three-phase voltages; , , respectively represent zero-sequence, positive-sequence, and negative-sequence voltages; ; ; (2) single-phase grounding short-circuit fault: When a single-phase ground fault occurs at the fault point K The sequence currents are calculated as follows: （7）； In formula (7): is a zero sequence current; is a positive sequence current; is a positive sequence current; is a positive and zero sequence mutual impedance, is a positive and zero sequence self impedance, i =0, 1, 2; Therefore, the voltage of zero sequence, positive sequence and negative sequence at the point is: m V = V0+ V1+ V2 （8）； in formula (8): is the zero sequence voltage of point m ; is the positive sequence voltage of point m ; is the negative sequence voltage of point m ; is the zero sequence mutual impedance between point m and point K ; is the positive sequence mutual impedance between point m and point K ; is the negative sequence mutual impedance between point m and point K ; is the positive sequence reference voltage of point m ; By combining equations (5)~(8), the single-phase ground fault with A-phase as the special phase is obtained when the fault point m occurs, m the three-phase voltage sag amplitude at the point: （9）； In formula (9), is m A-phase voltage at the point of three-phase short circuit; is m B-phase voltage at the point of three-phase short circuit; is m C-phase voltage at the point of three-phase short circuit; is m A-phase reference voltage at the point, normally equal to m reference voltage at the point; is the zero-sequence, positive-sequence, negative-sequence mutual impedance between the points m and K is m the zero-sequence mutual impedance between the points K and m is K the positive-sequence mutual impedance between the points and m K is the negative-sequence mutual impedance between the points m and K is the reference voltage at the point K ; is the fault current injected by the distributed power source into the point is the rotation factor, ;​​​​ (3) two-phase short-circuit fault: When two-phase short-circuit faults occur in the B phase and the C phase, the positive sequence and the negative sequence are in series, the zero sequence current is 0, and the positive and negative sequence currents are calculated as follows: （10）； In formula (10): is K positive sequence self-impedance of the point; is K negative sequence self-impedance of the point; Therefore, when two-phase short circuit faults occur in phase B and phase C, m The three-phase voltage sag amplitudes at the point are as follows: （11）； (4) two-phase grounding short-circuit fault: When two-phase grounding short-circuit faults occur in the B phase and the C phase, three sequence networks are in parallel, and each sequence current is calculated as follows: （12）； In formula (12): is K point zero sequence self-impedance; Therefore, when two-phase ground fault occurs in phase B and phase C, m The three-phase voltage sag amplitudes at the point are as follows: （13）； wherein: is K the positive, negative and zero sequence self-impedances of the point are multiplied two by two and added; .

4. The method of claim 3, wherein the method further comprises: Due to the access of the distributed power supply, the system at this time is nonlinear, and an iteration solution is adopted, and the specific process is as follows: ① voltage sag amplitude calculation is performed according to the above amplitude calculation method; (ii) correct the IID according to formula (1), formula (2), formula (5) to output short circuit current G ; ③ steps 1 and 2 are repeated until the voltage deviation at the grid-connected point in the previous and next two times meets the following requirements: （14）； In formula (13): is the voltage of the point of common coupling (PCC) after the first iteration; K is the voltage of the point of common coupling (PCC) after the first iteration; m is the voltage of the point of common coupling (PCC) after the first iteration; is the voltage of the point of common coupling (PCC) after the first iteration; K is the voltage of the point of common coupling (PCC) after the first iteration; is the voltage of the point of common coupling (PCC) after the first iteration; ④ the voltage at each node at this time is obtained through power flow calculation.

5. The method of claim 4, wherein the method further comprises: In step 3, the functional relationship between the voltage sag amplitude and the fault position is constructed as follows: When the fault point K on the line F-T its three-sequence self-impedance and the fault point K with M the three-sequence mutual impedance between the points can be represented by the target network impedance matrix Z and the location variable p : （15）； （16）； In the formula: , are the self-impedances of the system bus nodes F , T respectively; , , are the mutual impedances of the system bus nodes F and T , the mutual impedances between the bus F and the load nodes m , the mutual impedances between the bus T and the load nodes m , all of which can be called from the system node impedance matrix; is the line sequence impedance between the nodes F-T ; is the zero sequence, positive sequence, and negative sequence mutual impedance between the points m and K ; Furthermore, the fault point m the voltage before the fault may also be expressed by the fault location variable p : （17）； In formula (17), , are the pre-fault voltages on the bus F and T , respectively, which can be obtained by power flow calculation. Thus m The voltage sag magnitude at the point can be expressed in terms of the pre-fault voltage and the respective sequence impedances; Substituting the equations (15) to (17) into the above expression of the three-phase voltage sag amplitude at the point m , the function expression of the voltage sag amplitude at the point with respect to the position variable m p at the point of any short-circuit fault can be obtained .​ 6. The method of claim 5, wherein the method further comprises: In step 4, the goal of the voltage sag dip domain solution is to find the critical point on the line p , based on the solution of step 3 =0, so that the voltage sag magnitude is equal to the threshold : （18）。 7. The method of claim 6, wherein the method further comprises: The method comprises the following steps: S4.1: Set NP individuals, each individual represents a fault location , i = 1,2,..., NP, , Then an initial population is randomly generated and uniformly distributed in the interval [0, 1]; S4.2: the fitness function is defined as the deviation between the voltage sag amplitude and the threshold value: （19）； In formula (19): The fitness function is defined as the deviation of the voltage sag magnitude from the threshold value. S4.3: Determine whether the maximum number of iterations is met or the convergence condition is met If so, go to S4.8; S4.4: For each experimental individual g From the population, select three different individuals , , , Generate a mutated individual: （20）； In equation (20): For the first g The generation i One mutated individual; For a first g The experimental individual is defined as r1; For a first g The experimental individual is defined as r2; For a first g The experimental individual is defined as r3; for F and The product of; where , which is the scaling factor, controls the magnitude of variation; S4.5: the mutation vector is crossed with the current individual to obtain a test individual: （21）； In formula (21): is the first g generation the i th test individual; is the first g generation the i th experimental individual; is a random number generated between 0 and 1; is the crossover probability; S4.6: the fitness of the test individual and the parent individual is compared, and the better one is selected into the next generation: （22）； In formula (22): Generation 1 g Generation 1 i experimental individuals; Generation 1 g Generation 1 i fitness of the experimental individuals; Generation 1 g Generation 1 i fitness of the experimental individuals; S4.7: whether all individuals in the current generation are traversed is judged, if yes, the step S4.3 is jumped to, otherwise, the step S4.4 is jumped to; S4.8: the result is output.

8. The method of claim 7, wherein the method further comprises: In step 5, the multi-objective selection model of the monitoring points is constructed as follows: 5.1, economy target: The economy of the scheme is represented by monitoring equipment procurement cost, installation cost and annual operation cost, and the target function is as follows: （23）； In formula (22): the cost of the solution; the cost of the monitoring equipment for the node i ; the installation cost for the node i ; the annual operating cost for the node i ; is a 0-1 variable, if the node i is a monitoring point, = 1; otherwise, = 0; is the number of system nodes; 5.2, redundancy target: Since the concave region of each node has been solved in Step 4, and the critical points of the concave region of each node under different fault types have been obtained, the boundary information is directly called in the constraint condition to depict the monitoring range; assuming that the concave region of node i is i and the concave region of node j is t ​ （24）； In formula (24): t =1, 2, 3, 4, respectively represent single-phase short circuit, two-phase short circuit, inter-phase short circuit, three-phase short circuit 4 fault types; is a node i in the t class recessive domain; is a part of line 1 belonging to the i class recessive domain of node t ; is a part of line 1 belonging to the i class recessive domain of node t ; is a part of line j belonging to the i class recessive domain of node t ; In step 4, the critical points of the concave domain of each node are obtained by the differential evolution algorithm; let the node i line l of t the number of concave domain boundary points is , and the corresponding boundary is: （25）； In formula (25): is a node i In t the first critical point of the line l under the class fault; l is a node In i the second critical point of the line l under the class fault; t is a node l In the first critical point of the line l under the class fault; i is a node t In the second critical point of the line l under the class fault; i is a node t In l the first critical point of the line l under the class fault; Therefore, the sag domain interval of the line is: （26）； In equation (26): For nodes i exist t Line under type of fault l The line section formed by the critical point and the endpoint; For nodes i exist t Line under type of fault l The line section formed by the two critical points; Taking into account the four fault conditions, the recessed area after considering all fault types is is: （27）； In formula (27): is a node i concave domain after integrating all fault types; is a fault t probability of the same type of fault; is a line j part of the i same concave domain of the node t ; Set n The monitoring point selection of the nodes is as follows: （28）； In formula (28): is a vector of 0-1 variables, where is a 0-1 variable, where if node 1 is a monitor, = 1; otherwise, = 0; is a 0-1 variable, where if node i is a monitor, = 1; otherwise, = 0; is a 0-1 variable, where if node n is a monitor, = 1; otherwise, = 0; is the transpose of matrix （29）； According to the selection of monitoring points, the matrix H The union of the column elements in the matrix is obtained, and the monitoring range of the configuration scheme on the line j is as follows: （30）； In formula (30): monitoring coverage of the line by the placement scheme; j one end of the monitoring coverage of the line by the placement scheme; the other end of the monitoring coverage of the line by the placement scheme; j the other end of the monitoring coverage of the line by the placement scheme; the other end of the monitoring coverage of the line by the placement scheme; j the other end of the monitoring coverage of the line by the placement scheme; the other end of the monitoring coverage of the line by the placement scheme; j the other end of the monitoring coverage of the line by the placement scheme; the number of system nodes; The monitoring range of each line of the system is represented by a matrix W is represented as: （31）； In formula (31): monitoring coverage of the line 1 by the placement scheme; monitoring coverage of the line j by the placement scheme; monitoring coverage of the line l by the placement scheme; Line j Line length belonging to the monitoring range The calculation formula is: （32）； In formula (32): the line j actual length of the line within the monitoring range; The grid fault observability is taken as an optimization target, and the target function of minimizing the observability loss rate is as follows: （33）； In equation (33): The observable loss rate; Indicates the probability of a fault type; For nodes i exist t Line under type of fault j The actual length of the line within the monitoring scope; In order to be in t Line under type of fault j The actual length of the line within the monitoring scope; N is the total number of bus lines; 5.3, construction urgency target: The construction urgency of the monitoring device of each node in the actual process is considered, and the minimization of the construction urgency coefficient is taken as the target function: （34）； In formula (34): is the construction urgency coefficient; is a 0-1 variable, if the node i is a monitoring point, = 1; otherwise, = 0; is the voltage sag amplitude of the node t when a i similar fault occurs. 1) Panoramic observability constraint: When the monitoring device arranged can cover all the lines, the layout scheme can meet the panoramic observability, and a constructability constraint condition is established: （35）； In equation (35): For the line j Length; L Total number of all lines; For the line j The actual length of the line within the monitoring scope; 2) Monitoring point number constraint: （36）； In formula (36): is the number of planned monitoring points; is a 0-1 variable, if node i is a monitoring point, = 1 ; otherwise, = 0. 3) Cost constraint: （37）； In formula (37): is the cost of the monitoring device for node i ; is the installation cost for node i ; is the annual operating cost for node i ; is a 0-1 variable, if node i is a monitoring point, = 1; otherwise, = 0; is the planned maximum cost.

9. The method of claim 8, wherein the method further comprises: The step 6 comprises the following steps: S6.1: initialize the particle swarm: a) Set parameters: set number of particles N, archive set size , maximum number of iterations , inertia weight , learning factor , Each particle represents a monitoring device placement scheme, encoded as a 0-1 vector of length N; b) initializing the position vector of each particle and the velocity vector of each particle under the premise of meeting the constraint condition S6.2: calculate the values of formula (23), formula (33) and formula (34) for each particle, perform multi-objective fitness evaluation, and monitor the feasibility; if the overall constraint condition is violated, the fitness value is corrected by a penalty function; S6.3: Construct external archive A to save the non-dominated solution set of the current iteration; in each generation iteration, use fast non-dominated sorting and crowding distance calculation to select Pareto t o front solution and update the external archive; for processing constraints, impose a penalty function on particles that violate the panoramic observability condition, adjust their fitness value to a maximum value, and guide the search for feasible solutions; S6.4: For each particle, if the current fitness dominates its historical best position, update the individual best solution Select the global best solution from the external archive using crowding distance To ensure the diversity of solutions; S6.5: Update particle velocity and position according to formula (38), formula (39), and adopt S igm o i The d function is mapped to the interval [0, 1], discretized according to the threshold rule, and a new monitoring point distribution scheme is obtained. （38）； In equation (39), is the velocity of the i-th particle at the j-th iteration; i is the position of the i-th particle at the j-th iteration; K is the velocity of the i-th particle at the j-th iteration; is the inertia weight; is the velocity of the i-th particle at the j-th iteration; i is the position of the i-th particle at the j-th iteration; K is the velocity of the i-th particle at the j-th iteration; is the position of the i-th particle at the j-th iteration; i is the velocity of the i-th particle at the j-th iteration; K is the position of the i-th particle at the j-th iteration; is the individual best solution of the particle; is the global best solution; is the weight of the particle learning from its own historical best solution; is the weight of the particle learning from the global best solution; and are two random numbers uniformly distributed between 0 and 1. （39）； In formula (39): is the first i is the first K is the position vector of the first particle after the first iteration. S6.6: correct the individual that does not meet the panoramic observability constraint of the concave domain, such as forcibly adding a key node, until the constraint is met; S6.7: If the maximum number of iterations is reached or the external archive is not updated for a number of consecutive generations, then the algorithm converges and outputs the non-dominated solution set in the external archive. S6.8: output the result.

10. The method of claim 9, wherein the method further comprises: In the step 7, the ideal point method is used to screen the optimal layout scheme as follows: The optimal ideal solution method is used to screen the target, the value of the objective function is used to evaluate the solution set, and the optimal solution under different scenes is found out by comprehensively considering the economy, risk and urgency. After the value of the evaluation index is calculated, it is normalized, and the formula is as follows: （40）； In formula (40): is Pare t o solution in the set i normalized value of the m evaluation index; is the m objective function of the solution; is the minimum value of the m objective function; is the maximum value of the m objective function; In order to find the optimal solution that takes into account multiple objectives, ideal point closeness calculation is carried out on all optimization solutions, and all Pareto t optimal solutions to the Euclidean distance square of the ideal point of the target is: （41）； In formula (41): is the value of the ideal solution of the evaluation index; m is the number of objective functions; In this paper, all Pare t The best decision scheme is determined objectively by the principle that the sum of the square of the Euclidean distance between the optimal solution and the ideal point on each objective is minimum, as shown in equation (42). （42）； In formula (42): is the optimal solution selected for this scenario.

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