Distributed generation siting planning method considering line fault and grid resilience

Abstract

A method for distributed generation siting planning considering line fault and grid resilience is proposed, including the following steps: considering the line fault model under the influence of typhoon load, analyzing the influence of typhoon on line meteorological load; combining with the actual load capacity of line, the line fault probability is calculated; the fault scene is selected by using system information entropy, the fault scale and its probability caused by typhoon are determined, and the distributed generation siting model is established based on the calculated line fault probability; the multi-objective particle swarm optimization algorithm is used to solve the distributed generation siting planning model considering line fault rate and grid resilience. The method can get the distributed generation siting position that meets the constraints and maximizes the grid resilience for different typical scenarios.

Description

Technical Field

[0001] This invention relates to the field of distribution network site selection optimization technology, specifically to a distributed power source site selection planning method that considers line faults and grid resilience. Background Technology

[0002] Extreme events (natural disasters, cyberattacks, etc.) have consistently led to severe power system failures. Especially in recent years, with increasingly severe global climate change, natural disasters have resulted in widespread power outages with significant social and economic impacts. As the power system network that directly distributes electricity to users, the distribution network is characterized by its complex structure, wide distribution, and poor security environment, making it one of the most vulnerable parts of the power system. Therefore, the distribution network's ability to cope with disasters has received increasing attention. Based on this, the term "resilience" has been introduced to assess the distribution network's ability to withstand disasters and quickly recover to expected levels under extreme disaster conditions.

[0003] Traditional recovery strategies for distribution networks mainly include pre-disaster reinforcement of line components, post-disaster reconfiguration of the distribution network, and allocation and dispatching of dispatchable power sources and maintenance personnel. With the deepening research on distributed generation, microgrids, and electric vehicle technologies both domestically and internationally, more and more scholars are beginning to utilize distributed generation, electric vehicles, and microgrids to restore lost power loads. Because faults caused by extreme disasters generally involve disconnection from the upstream power grid, a large impact area, and numerous lost power loads, resilient distribution networks place higher demands on disaster models, assessment indicators, and recovery strategies.

[0004] Existing research on improving grid resilience mainly includes:

[0005] Chinese patent "A Collaborative Planning Modeling Method for Transmission Lines and Energy Storage Planning Systems Considering the Enhancement of Resilient Power Grid Resilience" (application number: 202210398654.9) proposes a three-layer robust collaborative planning model to improve the resilience of resilient power systems. The first-layer model is a mathematical model for selecting power system operators to determine the expansion scheme and construction cost of transmission networks and energy storage systems, as well as the operating cost of the power system. The second-layer model is a mathematical model for predicting the number of damaged transmission lines and generators under extreme natural disasters. The third-layer model is a mathematical model for selecting the operating cost and load shedding cost of power system operators to cope with the worst-case scenario of extreme natural disasters by optimizing scheduling and load shedding. By optimizing the model, a system operation scheme that meets the requirements is obtained, minimizing the system operating cost.

[0006] Chinese patent "A Highly Resilient Power Grid Source-Grid-Load-Storage Multi-Party Coordinated Optimization Control Method" (application number: 202111001591.0) discloses a highly resilient power grid source-grid-load-storage multi-party coordinated optimization control method. First, a multi-party coordinated optimization control model is established. Then, the characteristics of demand-side response are analyzed, and a demand-side response scheduling model is established to achieve coordinated scheduling and effective interaction between power grid supply and demand. Next, the characteristics of energy storage units are analyzed, and a model is established to analyze grid-side constraints. Based on the above control model, a MOPSO-based coordinated optimization control method is established, along with an objective function and a multi-objective optimization model. The source-grid-load-storage coordinated optimization scheduling problem is solved efficiently using MOPSO. By setting an update strategy for the non-dominated solution set, the feasibility of multi-objective optimization scheduling is well guaranteed, thereby rationally scheduling various resources (source, grid, load, and storage) and improving the economic efficiency of power grid operation.

[0007] Chinese patent “A Comprehensive Assessment Method and System for the Resilience of Distribution Networks” (application number: 202111059384.0) discloses a comprehensive assessment method and system for distribution networks. It focuses on three functions: distribution network situation awareness, disturbance response, and self-improvement capability, targeting six categories of key characteristics of resilient power grids. It can establish a more comprehensive and refined comprehensive assessment system under the requirements of resilience, and improve the accuracy and reliability of assessment results.

[0008] The aforementioned patents take into account methods for improving the resilience of the power grid under natural disasters and multi-source collaborative optimization control of power generation, grid, load and storage. However, they do not take into account the complexity of scenarios where natural disasters cause large-scale failures, nor do they consider the impact of line failure rates on distributed power source location models and changes in the distribution network topology. Therefore, the establishment of their models inevitably differs from the actual situation after high-risk, low-probability events have a huge impact on the distribution network.

[0009] Existing research on failure rate assessment models mainly relies on historical data statistical models. These models require historical data detailed enough to support the joint probability distribution of multidimensional random variables, but they cannot reflect the disaster-causing mechanisms and details. The macroscopic requirements of resilient power grids for long-term data, the large-scale impact of natural disasters on the power grid, and the short-term evolution of disaster situations are all difficult to statistically analyze.

[0010] Existing literature on distributed generation (DG) location and capacity grading models largely focuses on algorithm improvements and the uncertainties in DG generation and load. However, these studies rarely consider large-scale failures caused by natural disasters, the impact of line failure rates on DG location models, or changes in distribution network topology. Summary of the Invention

[0011] To address the problem of distributed generation location optimization in distribution network planning, this invention analyzes the impact of system component failure rate on distributed generation location under typhoon conditions during the planning stage. It provides a distributed generation location planning method that considers line faults and grid resilience. This method can obtain distributed generation location locations that meet various constraints and maximize grid resilience for different typical scenarios.

[0012] The technical solution adopted in this invention is as follows:

[0013] A distributed generation location planning method considering line faults and grid resilience includes the following steps:

[0014] Step 1: Consider the line fault model under the influence of typhoon load, and analyze the impact of typhoon on the meteorological load of the line;

[0015] Step 2: Calculate the line fault probability based on the actual load capacity that the line can withstand;

[0016] Step 3: Propose using system information entropy to select fault scenarios, determine the possible fault scale and probability of occurrence caused by typhoons, and establish a distributed power source location model based on the line fault probability calculated in Step 2.

[0017] Step 4: Use the multi-objective particle swarm optimization algorithm to solve the distributed power source location planning model that takes into account both line failure rate and grid resilience.

[0018] In step 1, the wind speed and direction at a point within the influence area are determined based on the Batts wind field model, expressed as:

[0019]

[0020] In equation (1): V represents the wind speed at that point, and its wind direction is the clockwise tangent of the circle with the typhoon center as the center point; R m The distance between the point of maximum wind speed and the center of the typhoon is represented by V. Rm The value of x is: r is the distance between the line and the center of the typhoon, and x is an empirical coefficient with a value range of [0.5, 0.7].

[0021] The line loads, wind load N1, and gravity load N2 are respectively expressed as:

[0022]

[0023] In equation (2): D is the outer diameter of the conductor; θ is the angle between the wind direction and the line;

[0024] N2=m l g (3)

[0025] In equation (3): m ldenoted as , where is the weight of the conductor; g is the acceleration due to gravity.

[0026] The tension at the highest suspension point of the conductor, its force expression is:

[0027]

[0028] In equation (4), T represents the horizontal force at the lowest point of the conductor's sag; β represents the angle between the line connecting the suspension points at both ends of the conductor and the horizontal plane; l gv The horizontal distance between the lowest point of the sag and the highest point of the conductor suspension; N is the total load on the conductor;

[0029] The stress on the conductor cross-section at the suspension point is:

[0030]

[0031] In equation (5), S l T represents the cross-sectional area of ​​the conductor; g This indicates the tension at the suspension point of the conductor.

[0032] In step 2, whether a line fracture fault occurs depends on the stress on the line cross-section and the strength of the conductor material itself. Therefore, a component function can be defined to describe the line fault rate based on the load effect and material strength of the line components. When the component function is greater than 0, it indicates that the component is in a reliable operating state. Its expression is:

[0033] p r =P{(RS)>0} (6)

[0034] In equation (6), S is the magnitude of the stress on the component; R is the ultimate strength of the component material.

[0035] In step 3, the ultimate strength of the conductor material is a random variable. According to the "Unified Standard for Reliability Design of Building Structures," the probability distribution of the ultimate strength of the conductor material can be represented by a normal distribution function, thus yielding the probability of unreliable operation of the line:

[0036]

[0037] In equation (7), μ and δ are the mean and standard deviation of the tensile strength of the conductor, respectively; σ represents the magnitude of the stress on the conductor.

[0038] Based on the probability of unreliable line operation, the system entropy value in this scenario is calculated:

[0039]

[0040] In equation (8), Ω B Indicates a distribution line set; p i，t Let z be the failure rate of component i at time t;i，t Indicates whether component i fails at time t; ω i This represents the value weight of the components. Scenarios where the system entropy value is within a suitable range are selected as typical scenarios for the distributed power source addressing model for optimization.

[0041] In step 3, since the typical scenarios selected for system entropy value selection have characteristics such as large impact and high probability of occurrence, it is necessary to determine the scale of the potential faults caused by the typhoon and their probability of occurrence, and to screen out typical scenarios with these characteristics. Statistical analysis of typical scenarios uses the number of faulty lines in the system to represent the number of system fault duplications, and uses the proportion of the number of identical system fault duplications to the total number of scenarios as the basis for selecting typical fault scenarios.

[0042] In step 3, a distributed power source location model considering line failure rate is established, as follows:

[0043] The objective function of the distributed power supply addressing model considering component failure rate is expressed as:

[0044]

[0045] In equation (9), y i Let y be a 0-1 decision variable, representing whether node i should build a distributed power source. If a distributed power source is built at node i, then y i Set the value to 1, otherwise set it to 0; S and L are the scene set and node set, respectively; ω i The weighting coefficient for load i; For node i to restore its state in scenario s, the load is powered. Otherwise, it is 0.

[0046]

[0047] In equation (10), P DG C represents the total active power supplied by the distributed power source; DG Indicates the total cost of installing distributed power sources; η i C represents the average annual cost factor for the i-th distributed power source; IC Indicates the unit capacity cost of distributed power sources; C MT This represents the unit capacity maintenance cost of distributed power sources.

[0048] The two objective functions are normalized, where the baseline value of N is the function value when all loads are in a powered state, and C... DG The benchmark value is the absolute value of the difference between the maximum and minimum expected investment, expressed as:

[0049]

[0050] In equation (11), N′ represents the baseline value of the objective function N; S is the set of fault scenarios; L is the set of system nodes; ω i is the weighting coefficient for load i.

[0051]

[0052] In equation (12), C′ DG Represent the objective function C DG The baseline value; C DGmax and C DGmin These represent the upper and lower limits of the planned total cost of investing in distributed power sources.

[0053] Constraints of the distributed power source location model include:

[0054] Constraint 1: Constraint on the number of distributed power sources, the formula of which is:

[0055]

[0056] In the formula, L represents the set of all candidate nodes for distributed power sources; P represents the maximum number of distributed power sources that can be constructed.

[0057] Constraint 2: Power flow constraint, its formula is:

[0058]

[0059]

[0060] In equations (14) and (15), P i Q i V represents the active and reactive power injected into node i, respectively; i V j G represents the node voltages at nodes i and j, respectively; ij B ij These are the real and imaginary parts of the nodal admittance matrix, respectively.

[0061] Constraint 3: Constraints on active and reactive power output of distributed power sources, the formula of which is:

[0062] P DGmin ≤P DGi(t) ≤P DGmax (16)

[0063] Q DGmin ≤Q DGi(t) ≤Q DGmax (17)

[0064] In equations (16) and (17), P DGi(t) Let P be the active power of the distributed power source at node i at time t. DGmax PDGmin These represent the upper and lower limits of the active power output of the distributed power source, respectively; Q DGmax Q DGmin These are the upper and lower limits of the active power output of the distributed power source, respectively.

[0065] Constraint 4: Node voltage constraint, the formula of which is:

[0066] V imin ≤V i(t) ≤V imax (18)

[0067] In equation (18), the node voltage constraint represents the voltage V of all nodes. i(t) It must be maintained within a specific range, with the node voltage amplitude between [0.9, 1.1].

[0068] Constraint 5: Line transmission limit constraint, the formula of which is:

[0069] S i ≤S imax (19)

[0070] In equation (19), S i Indicates the power transmitted through the line; S imax This indicates the limit of the line's transmission power.

[0071] In step 4, a multi-objective particle swarm optimization algorithm based on an improved population update and fitness strategy is used to optimize and solve the distributed power source location model. This specifically includes the following steps:

[0072] S4.1: Using the distributed power supply installation node as the particle position, randomly generate the initial position x of the particle with a dimension of 90×4 and an element value range of [0, 33] and a velocity v with a dimension of 90×4 and each element value of 0 or 1 within the constraint range. Set the particle population size pop = 90 and the maximum number of iterations gen = 100.

[0073] S4.2: Calculate network loss using the forward-backward power flow calculation method and calculate the current particle fitness value.

[0074] The iterative formula for the (n+1)th step of the forward-backward power flow algorithm for distribution networks is as follows:

[0075] The formula for calculating the forward propagation of node i is:

[0076]

[0077]

[0078] In the formula: n is the number of iterations; r ki For branch k iimpedance; and For branch k i Power loss; and For the branch k i The power. P Di and Q Di Let i be the load of node i, neglecting the load voltage characteristics.

[0079] The formula for calculating the voltage at node i is as follows:

[0080]

[0081]

[0082] In the formula For branch k i Current; The conjugate of the complex voltage at node k; (r ki +jx ki ) is branch k i The impedance.

[0083] Based on node hierarchies, the iterative process of the forward-backward power flow algorithm for distribution networks is as follows:

[0084] (1) Initialization: Given the voltage V at the root node of the distribution feeder r And assign V to the voltage of other nodes. (0) n = 0;

[0085] (2) Forward calculation: Starting from the last layer, based on the given sub-node voltage and power, calculate the voltage drop towards the parent node, and then use formulas (1) and (2) to calculate the power distribution of each branch.

[0086] (3) Back-substitution calculation: Starting from the root node, calculate the node voltage distribution V by back-substituting back to the child nodes layer by layer based on the load power of the parent node using formulas (3) and (4). (n+1) ;

[0087] Network loss S i =U i *I i

[0088] In the formula, U i and I i These are the node voltage phasors U. i and node injection current phasor I i conjugate

[0089] The total construction and operation cost C of a typical scenario DG The weighted load power supply N (objective function) is the current particle fitness value.

[0090] S4.3: Perform iterative optimization: Update the particle velocity v and position x according to the calculated pbest and gbest values ​​based on the improved iterative formula.

[0091] pbest represents the historical best of an individual. Each individual is constantly changing during the evolutionary process. If a better individual emerges during this process, then pbest should be updated; otherwise, it remains unchanged. pbest = N' - C' DG .

[0092] After each evolution of all individuals, the best individual, gbest, needs to be selected. In multi-objective scenarios, the non-dominant individual—that is, the individual not dominated by any other individual—is necessarily the best in the current group, and there is usually more than one non-dominant individual. Therefore, all non-dominant individuals are first selected and placed into a set gbest.

[0093] Improved iterative formula:

[0094]

[0095]

[0096] ω(t) is the inertia weight; c 1t c 2t It is the learning factor; r1 and r2 are random numbers between [0, 1]. ki and x ki Let i represent the particle velocity and the particle's current position at the k-th iteration, respectively. and Let represent the individual optimal position and the global optimal position of particle i in the (k-1)th iteration, respectively.

[0097] S4.4: Recalculate the fitness value and remove inferior solutions with low fitness from the new population to ensure that the number of individuals in the new population does not exceed its maximum capacity; based on the results, obtain the current global optimal solution gbest; check whether the maximum number of iterations has been reached, and if not, return to S4.3 to continue the calculation.

[0098] According to S4.3, gbest is the set of historical optimal solutions pbest, where the global optimal solution can be represented by gbest = N'-C'. DG To obtain.

[0099] This invention provides a distributed generation location planning method that considers line faults and grid resilience, with the following technical advantages:

[0100] 1) This invention first establishes a failure rate model for the disaster-causing mechanism of typhoons, which can clearly reflect the causal inertia of power grid failures caused by typhoons and can also realize various sensitivity analyses; then, it identifies its parameters based on effective historical data; and then, it evaluates the line failure rate in real time based on the actual evolution information of the external environment.

[0101] 2) To study the line failure rate under typhoon disasters, a failure rate mechanism model based on the characteristics of typhoon disasters and the material properties of line components is proposed. Due to the wide impact and long duration of typhoon disasters, this invention proposes using the Batts wind field model to simulate wind force and direction during typhoon passage, considering the impact of system component failure rate on distributed power source location under typhoon conditions.

[0102] 3) This invention proposes to select fault scenarios by calculating the line fault probability, determine the possible fault scale and probability of occurrence caused by typhoons, and propose a distributed power source location planning strategy based on the line fault rate.

[0103] 4) This invention utilizes the multi-objective particle swarm optimization algorithm, which has the following advantages: it does not depend on problem information, uses real numbers for solving, has strong versatility, is simple in principle, easy to implement, requires few parameters to be adjusted, has a fast convergence speed, does not require much computer memory, and the leapfrog nature of the particle swarm optimization algorithm makes it easier to find the global optimum rather than being trapped in a local optimum. Attached Figure Description

[0104] Figure 1 Schematic diagram of conductor suspension point

[0105] Figure 2 This is a structural diagram of the IEEE-33 node system described in this invention.

[0106] Figure 3 This is a time-varying fault rate diagram for Line 1 and Line 16 as described in this invention.

[0107] Figure 4 This is the entropy probability distribution diagram described in this invention.

[0108] Figure 5 This is the non-fragmented set graph of the distributed power source addressing model described in this invention.

[0109] Figure 6 These are system performance diagrams for the various scenarios described in this invention.

[0110] Figure 7(a) is a diagram of the distribution network division structure of the location scheme in scenario 2 described in this invention;

[0111] Figure 7(b) is a diagram of the power distribution network division structure of the location scheme for scenario 3 described in this invention;

[0112] In Figures 7(a) and 7(b), the meanings of each label are as follows:

[0113] • Level 3 load; Secondary load; Level 1 load;

[0114] Faulty circuit; Distributed power supply area; Detailed Implementation

[0115] To address the shortcomings of existing technologies described in the background section, and considering the reality that power grids in some coastal areas of my country are frequently affected by typhoons, this invention provides a distributed generation (DG) location planning method that considers both line faults and grid resilience. First, a line fault model considering typhoon loads is studied. Then, the impact of typhoons on meteorological loads on lines is analyzed, and the probability of line faults is calculated based on the actual load capacity of the lines. On this basis, a fault scenario selection method is proposed using system information entropy to determine the potential fault scale and probability of occurrence caused by typhoons. A DG location planning strategy is then proposed based on the line fault rate. A multi-objective particle swarm optimization algorithm is used to solve the established DG location planning model that considers both line fault rate and grid resilience. Finally, to demonstrate the effectiveness of the DG capacity-based location planning method based on line component fault rates, a suitable resilience assessment index is proposed by combining load recovery and load weight, and a comparative analysis is conducted with traditional grid resilience improvement methods.

[0116] Figure 1 This is a schematic diagram of the conductor suspension point. By calculating the wind and gravity loads on the conductor, the stress at the highest suspension point is obtained. By comparing the stress on the line cross-section with the strength of the line material itself, it can be determined whether the line has broken. Step 1: This invention uses a calculation example of an improved IEEE-33 node system, such as... Figure 2 As shown, the geographical routes of each feeder are consistent with those shown in the diagram. The total load requirement of the node system is 3715kW.

[0117] Step Two: Taking Line 1 and Line 16 as examples, the relationship curve between failure rate and wind speed during a typhoon is as follows: Figure 3 As shown, the start time is the time of typhoon landfall. The system information entropy value is distributed between [4, 18], as... Figure 4 As shown, the selection of typical failure scenarios will also be set within this range.

[0118] Step 3: Taking the scenario selected in Step 2 as the basic example, model and solve the example using the distributed power source location model proposed in this paper, obtaining the non-dominated solution set of the distributed power source location model, such as... Figure 5 As shown in the figure, the maximum value of the normalized objective function is the optimal solution.

[0119] Step Four: Figure 6 The fault recovery process is described in four scenarios:

[0120] Scenario 1: The operation of a distribution network without distributed power sources, and line fault repair cannot be carried out under typhoon conditions. After the typhoon passes, the faults are repaired in the order of component failure.

[0121] Scenario 2: The restoration process of a distribution network with distributed power sources under the consideration of line failure rate. The access nodes of the distributed power sources are 6, 13, 18, 19, and 33 to ensure the power supply to the load.

[0122] Scenario 3: The restoration process of a distribution network containing distributed power sources, with the distributed power sources connected at nodes 6, 16, 20, 24, and 30.

[0123] Scenario 4: Fault recovery process of a distribution network without distributed power sources. The recovery process of the faulty component is selected based on minimizing load loss, that is, repairing the faulty lines in the order of line 9, line 19, line 30, line 14, and line 16.

[0124] Among them, system performance SP represents the ratio of the total power of the system after being affected by a disaster to the total power during normal operation.

[0125] By analyzing the load loss area under various failure scenarios, the corresponding resilience assessment results can be obtained, as shown in Table 1:

[0126] Table 1. Resilience assessment results under different scenarios

[0127]

[0128] When the location of the distributed power source takes into account the failure rate of the line components, the access node of the distributed power source is shown in Figure 7(a). Compared with scenario 3, the distributed power source can supply power to nodes 10, 11, 12, 13, and 14 after the S9 failure at 7h.

[0129] If distributed generation (DG) is connected to the grid without considering line component failure rates, and a fault occurs at S19 at 9.25h, the DG supplies power to nodes 19, 20, 21, and 22, thus improving the resilience of the distribution network compared to when no DG is connected. The distribution network structure is shown in Figure 7(b). This demonstrates that the DG location strategy, considering line failure rates, can more effectively improve grid resilience.

[0130] When a faulty component repair strategy that minimizes the load loss area is adopted, the load loss situation is improved compared to Scenario 1. After the first component is repaired, the system provides an additional 15% power compared to the system in Scenario 1. This shows that optimizing the faulty component repair strategy can improve grid resilience to a certain extent.

[0131] As shown in Table 1, for the original distribution network, the load power supply was only 75.9% of the normal level after being affected by the typhoon. After improving the post-disaster repair strategy, the grid resilience improved slightly to 82.4%. Adding distributed power sources can effectively improve the grid resilience to 87.0%. The site selection optimization strategy considering the line failure rate can further improve the grid resilience to 91.9%.

Claims

1. A distributed generation location planning method considering line faults and grid resilience, characterized in that... Includes the following steps: Step 1: Consider the line fault model under the influence of typhoon load, and analyze the impact of typhoon on the meteorological load of the line; Step 2: Calculate the line fault probability based on the actual load capacity that the line can withstand; Step 3: Propose using system information entropy to select fault scenarios, determine the possible fault scale and probability of occurrence caused by typhoons, and establish a distributed power source location model based on the line fault probability calculated in Step 2. Step 4: Solve the distributed power source location planning model that takes into account both line failure rate and grid resilience using the multi-objective particle swarm optimization algorithm. In step 3, a distributed power source location model considering line failure rate is established, as follows: The objective function of the distributed power supply addressing model considering component failure rate is expressed as: （9）； In equation (9), y i 0-1 decision variables, representing nodes i Whether to build distributed power sources, if so i Nodes build distributed power sources y i Select 1, otherwise select 0; S , L These are respectively a set of scenes and a set of nodes; For nodes i Weighting coefficients; For nodes i In the scene s In the recovery state, the load is powered. Otherwise, it is 0; （10）； In equation (10), P DG This represents the total active power supplied by the distributed power source. C DG This indicates the total cost of installing a distributed power source; Indicates the first i The average annual cost factor of a distributed power source; C IC This indicates the cost per unit capacity of distributed power sources; C MT This represents the unit capacity maintenance cost of distributed power sources. The two objective functions are normalized, where N The baseline value is the function value when all loads are in a powered state. C DG The benchmark value is the absolute value of the difference between the maximum and minimum expected investment, expressed as: (11) ； In equation (11), Describe the objective function N The baseline value; S A set of fault scenarios; L For the system node set; For load i Weighting coefficients; (12)； In equation (12), Describe the objective function The baseline value; and These represent the upper and lower limits of the planned total cost of investing in distributed power sources.

2. The distributed generation location planning method considering line faults and grid resilience according to claim 1, characterized in that: In step 1, the wind speed and direction at a point within the influence area are determined based on the Batts wind field model, expressed as: (1)； In formula (1): V This indicates the wind speed at that point, and its wind direction is the clockwise tangent to the circle with the center of the typhoon as the center point. The distance between the point of maximum wind speed and the center of the typhoon is represented by the wind speed at that point. express; The distance between the power line and the typhoon center is denoted by x; x is an empirical coefficient. Determine line load and wind load. N 1. Gravity load N 2 is represented as: (2) ； In formula (2): D The outer diameter of the conductor; The angle between the wind direction and the line; （3）； In formula (3): m l The weight of the conductor; g It is the acceleration due to gravity; The tension at the highest suspension point of the conductor, its force expression is: (4) ； In equation (4), T This indicates that the lowest point of the conductor's sag is subjected to horizontal force. β This indicates the angle between the line connecting the two suspension points of the conductor and the horizontal plane; l gv The horizontal distance between the lowest point of the sag and the highest point of the conductor suspension; N This refers to the combined load on the conductor; The stress on the conductor cross-section at the suspension point is: （5）； In equation (5), S l Represents the cross-sectional area of ​​the conductor; T g This indicates the tension at the suspension point of the conductor.

3. The distributed generation location planning method considering line faults and grid resilience according to claim 1, characterized in that: In step 2, a component function is defined to describe the line failure rate based on the load effect and material strength of the line components. When the component function is greater than 0, it indicates that the component is in a reliable operating state. Its expression is: （6）； In equation (6), S The magnitude of the stress on the component; R This represents the ultimate strength of the component material.

4. The distributed power generation location planning method considering line faults and grid resilience according to claim 2, characterized in that... In step 3, the ultimate strength of the conductor material is a random variable, and its probability distribution can be represented by a normal distribution function. Therefore, the probability of unreliable line operation can be obtained. (7)； In equation (7), , These are the mean and standard deviation of the conductor's tensile strength, respectively. This indicates the magnitude of the stress on the conductor; Based on the probability of unreliable line operation, the system entropy value in this scenario is calculated: （8）； In equation (8), Ω B Indicates a distribution line set; For components exist t Failure rate at any given time; Indicator element exist t Whether a malfunction occurs at any given time; Indicator element Value weight.

5. The distributed power generation location planning method considering line faults and grid resilience according to claim 4, characterized in that... Constraints of the distributed power source location model include: Constraint 1: Constraint on the number of distributed power sources, the formula of which is: (13) ； In the formula L Represents the set of all candidate nodes for distributed power sources; P This represents the maximum number of distributed power sources that can be built. Constraint 2: Power flow constraint, its formula is: （14）； （15）； In equations (14) and (15), P i , Q i These represent injections into the nodes. i Active and reactive power; V i , V j Representing nodes respectively i , j The node voltage; G ij , B ij These are the real and imaginary parts of the nodal admittance matrix, respectively. Constraint 3: Constraints on active and reactive power output of distributed power sources, the formula of which is: （16）； （17）； In equations (16) and (17), P DGi(t) For distributed power sources t Time Node i active power, P DGmax , P DGmin These are the upper and lower limits of the active power output of the distributed power source, respectively. Q DGmax , Q DGmin These are the upper and lower limits of the active power output of the distributed power source, respectively. Constraint 4: Node voltage constraint, the formula of which is: (18) ； In equation (18), the node voltage constraint represents the voltage of all nodes. V i(t) It must be maintained within a specific range, with the node voltage amplitude between [0.9, 1.1]. Constraint 5: Line transmission limit constraint, the formula of which is: (19) ； In equation (19), S i Indicates the amount of power transmitted through the line; S imax This indicates the limit of the line's transmission power.

6. The distributed generation location planning method considering line faults and grid resilience according to claim 1, characterized in that... In step 4, a multi-objective particle swarm optimization algorithm based on an improved population update and fitness strategy is used to optimize and solve the distributed power source location model. This specifically includes the following steps: S4.1: Using the distributed power supply installation nodes as the positions of the particles, randomly generate the initial positions and velocities of the particle swarm within the constraints, and set the particle swarm size and the maximum number of iterations. S4.2: Calculate network loss and current particle fitness using the forward-backward power flow calculation method; S4.3: Perform iterative optimization: for the calculated pbest , gbest The particle velocity is updated according to the improved iterative formula. v and location x ; S4.4: Recalculate the fitness value and remove inferior solutions with low fitness from the new population to ensure that the number of individuals in the new population does not exceed its maximum capacity; based on the results, obtain the current global optimum. gbest Check if the maximum number of iterations has been reached. If not, return to S4.3 to continue the calculation.

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