A distribution network power supply reliability analysis method

Abstract

The application discloses a distribution network power supply reliability analysis method and relates to the technical field of distribution networks, and comprises the following steps: A, dividing the distribution network into several blocks, defining a Markov decision process five-tuple and a double-root multi-branch weighted pruning exploration tree for each distribution network block; B, generating a sampling path by using the double-root multi-branch weighted pruning exploration tree, initializing and updating a Q table according to the sampling path, obtaining a system state distribution under an optimal strategy according to the converged Q table, and obtaining a fault probability P of the distribution network block at time t t =π·P t‑1 ; C, constructing a propagation dynamics differential equation set among different distribution network blocks, calculating a basic regeneration number of each distribution network block and an overall failure rate of the distribution network by solving the propagation dynamics differential equation set, and then predicting the overall failure rate of the distribution network. The application can improve the accuracy of distribution network power supply reliability analysis.

Description

Technical Field

[0001] This invention relates to the field of power distribution network technology, and in particular to a method for analyzing the reliability of power supply in power distribution networks. Background Technology

[0002] As the core link connecting the transmission network and end users, the power supply reliability of the distribution network directly affects the stability of the entire power supply system. Accurate analysis and prediction of the power supply reliability of the distribution network can effectively improve the power supply guarantee level of the power grid. Existing analysis methods (such as Monte Carlo simulation and neural network prediction) all require the prior establishment of prediction models. However, in actual operation, the failure probability of core components such as overhead lines, towers, and transformers in the distribution network is the result of the combined effects of multiple factors, including meteorological environment (wind speed, icing, temperature, lightning strikes), electrical stress (load rate, overvoltage, short-circuit current), and mechanical stress (conductor tension, tower deflection, wind deflection angle). These influencing factors change in real time, causing prediction models to fail to accurately simulate actual operating conditions. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a method for power supply reliability analysis of distribution networks, which can overcome the shortcomings of the prior art and improve the accuracy of power supply reliability analysis of distribution networks.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows.

[0005] A method for analyzing the reliability of power distribution networks, characterized by the following steps:

[0006] A. Divide the distribution network into several blocks, and define a Markov decision process quintuple and a double-rooted multi-branch weighted pruning exploration tree for each distribution network block;

[0007] B. Use a birooted, multi-branch weighted pruning exploration tree to generate sampling paths, and initialize and update the Q-table based on the sampling paths. The system state distribution under the optimal strategy is obtained based on the converged Q-table. Then the probability of failure P of the distribution network block at time t. t =π·P t-1 ;

[0008] C. Based on the failure probability of different distribution network blocks, construct a set of propagation dynamic differential equations between different distribution network blocks. By solving the set of propagation dynamic differential equations, calculate the basic regeneration number of each distribution network block and the overall failure rate of the distribution network, and then predict the overall failure rate of the distribution network.

[0009] As a preferred approach, the Markov decision process quintuple is (S, A, P, R, γ); where S is the state space, serving as the row index of the Q-table, and the state s∈S of each distribution network block is a discretized representation of multidimensional features, s=[s I s U s THD s h ], where s I For the supply current state, s U For the power supply voltage state, s THD For total harmonic distortion, s h For historical anomaly records, A is the action space, corresponding to the operation and maintenance and control operations as perceived by the power grid. It is a decision variable that affects the fault transfer probability and serves as the column index of the Q table. A=[a1, a2, a3, a4], where a1 is misoperation, a2 is enhanced online monitoring after anomaly warning, a3 is live maintenance, a4 is power outage maintenance, P is the state transition probability, which represents the conditional probability of transitioning to the next state s' after performing action a in state s, R is the reward, which is the real-time reward R(s, a, s') obtained when transitioning to the next state s' after performing action a in state s, and γ is the discount factor, γ∈[0,1), which represents the present value coefficient of future rewards.

[0010] As a preferred option, a dual-root, multi-branch weighted pruning exploration tree T=[V, E, R, B] is used, where V is the set of tree nodes, containing complete risk attributes and path information; E is the set of tree edges, with each edge corresponding to a power grid state transition and maintenance action; and R is the set of dual-root nodes, R={X start X goal}, X start X is a healthy root node. goal B is the fault endpoint, and B is the set of fault branches, with each branch corresponding to a type of power grid fault mode.

[0011] As a preferred option, the dual-root, multi-branch weighted pruning exploratory tree has a dual-root, bidirectional growth structure, with the forward tree using X... start The root is X, and it grows in the direction of the fault state. The reverse tree is based on X. goal The forward tree grows towards the healthy state, with the new nodes of the forward tree and the reverse tree satisfying the Mahalanobis distance connection threshold. When the new nodes of the forward tree and the reverse tree meet the Mahalanobis distance connection threshold, it is determined that the two trees intersect and are directly spliced ​​to generate a complete fault path from the healthy state to the fault state. The reverse tree grows synchronously with each type of fault endpoint as an independent root node.

[0012] As a preferred approach, the node fault risk weight k of the double-rooted multi-branch weighted pruning exploration tree is defined as k = η1k1 + η2k2 + η3k3 + η4k4, where η1 to η4 are proportional coefficients, k1 is the equipment health weight, k2 is the electrical fault weight, k3 is the environmental anomaly weight, and k4 is the historical fault weight. The growth rules of the double-rooted multi-branch weighted pruning exploration tree are set as follows: delete nodes with fault risk weights lower than a set threshold, and select the adjacent node with the highest fault risk weight as the parent node during each growth operation.

[0013] As a preferred method, a node is defined as a valid node when it is a root node, a branch entry node, a node where two trees intersect, or when the fault risk weight is lower than a set threshold, or when it is a branch node with ≥2 child nodes. After each set number of sampling rounds, all nodes are traversed, valid nodes are retained, and the remaining nodes are deleted.

[0014] As a preferred method, sampling points are generated within the heuristic region. The sampling points are then verified to ensure they meet the physical constraints of the distribution network operation. Illegal sampling points are deleted, and sampling is performed again to complete the sampling points. Simultaneously, a search for healthy root nodes X is conducted. start and fault endpoint X goal For nearby sampling points, select the adjacent sampling point with the highest fault risk weight as the parent node to complete the growth of the forward tree and the reverse tree; if the newly added node satisfies the bidirectional intersection condition, that is, backtrack the forward tree to the healthy root node X. start Backtrack the reverse tree to the fault endpoint X goal If the backtracking path is pieced together to generate a complete fault path, then one search path generation is completed; repeat the above process until the number of search paths reaches the preset number, and then the sampling is completed.

[0015] As a preferred option, the propagation dynamics differential equations are:

[0016] in Let be the percentage of high-risk nodes in the k-th block at time t. Let be the percentage of faulty nodes in the k-th block at time t. Let be the percentage of isolated nodes within the k-th block at time t. Let be the percentage of recovered nodes in the k-th block at time t. The percentage of immune nodes in the k-th block at time t;

[0017] Let be the time-varying effective fault propagation rate of the k-th block. , The base propagation rate of block k is obtained by fitting the maximum likelihood estimate of historical fault data, and the load factor correction coefficient is also included. , The average load factor of the lines within block k. For weather correction factors and equipment health correction factors , This represents the real-time degradation status of device i. Let i be the device failure threshold.

[0018] Let be the time-varying fault isolation rate of the k-th block, which is the probability that a faulty node is isolated by the protection device. , The base isolation rate for block k, The average reliability of the protection devices within block k. The average operating time of the protection devices within block k;

[0019] Let k be the time-varying fault repair rate of the k-th block. . Adjustment coefficient for emergency repair resources;

[0020] Let the time-varying isolation zone recovery rate be the value of the k-th block. , Basic transfer coefficient, For the reliability of the switching equipment in the k-th block, This refers to the load transfer capacity within the k-th block;

[0021] Let be the time-varying immune conversion rate of the k-th block. , Basic immune coefficient, This represents the real-time total power supply capacity of the isolated distributed power source in the k-th block. Let be the maximum discharge power of the isolated energy storage unit in the k-th block. This represents the real-time total load of the k-th block;

[0022] The time-varying high-risk conversion rate for the k-th block. , Based on the basic susceptible conversion rate.

[0023] Preferably, the finite difference method is used to solve the above propagation dynamics differential equations, and then the basic regeneration number of each block is calculated. Finally, calculate the failure rate of the entire distribution network. ,in This is the critical threshold for fault propagation. N p N is the number of nodes in block p. q Let be the number of nodes in block q. The inter-block protection reliability coefficient, α is the load influence factor. The real-time load rate between nodes i and j Rated load rate, , Let be the impedance between nodes i and j.

[0024] As a preferred method, the following prediction function is used to predict the long-term failure rate trend of the distribution network. ,in, It is the future moment Distribution network failure rate, Let β be the random volatility of the current distribution network failure rate, and β be the elasticity variance coefficient. ρ is the mean recovery rate, ρ is the linear correlation between the failure rate and the failure volatility, and ν is the amplitude of the failure rate fluctuation.

[0025] The beneficial effects of adopting the above technical solution are as follows:

[0026] 1. This invention introduces a model-free Q-Learning algorithm, which learns the temporal patterns of fault evolution in power grid blocks and establishes a quantitative mapping from action value function to fault probability, thereby achieving accurate prediction of distribution network faults. This solves the problems of traditional methods that require pre-establishing prediction models, have slow response times, and are easily affected by the actual operating conditions of the distribution network, leading to a decrease in prediction accuracy.

[0027] 2. This invention improves the traditional Q-Learning algorithm by constructing a double-rooted, multi-branch weighted pruning exploration tree, thereby optimizing the exploration path of the Q-Learning algorithm and avoiding branch blind spots caused by random sampling probability.

[0028] 3. This invention introduces the SIR contagion model to solve the problem of traditional prediction methods requiring large amounts of data for training. Furthermore, to adapt the SIR contagion model to actual distribution network conditions, a five-state system is constructed, establishing a set of dynamic differential equations that match the entire process of distribution network protection actions, fault isolation, load transfer, and islanded power supply. A comprehensive time-varying parameter system is also defined to achieve the goal of predicting the entire distribution network fault based on block faults. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of a specific embodiment of the present invention. Detailed Implementation

[0030] In the following description of the embodiments, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0031] To address the issue that traditional methods require pre-establishing simulation models, this invention introduces an improved Q-Learning algorithm. By autonomously learning the temporal patterns of fault evolution in distribution network blocks, it achieves a quantitative mapping from action value functions to fault probabilities. This allows for the calculation of state parameters of distribution network blocks, such as steady-state fault probability, fault probability within a specified time window, and real-time single-step fault probability.

[0032] Q-Learning is a model-free reinforcement learning algorithm for solving Markov Decision Processes (MDPs). Therefore, we first define the MDP quintuple as (S, A, P, R, γ). S represents the state space, serving as the row index of the Q-table. The state s∈S of each distribution network block is a discretized representation of its multidimensional features, s=[s I s U s THD s h ], where s I For the supply current state, s U For the power supply voltage state, s THD For total harmonic distortion, s h This represents historical anomaly records. A is the action space, corresponding to the grid's perceived operation and control actions, and is a decision variable influencing the fault transfer probability. It serves as the column index of the Q table, A = [a1, a2, a3, a4], where a1 represents misoperation, a2 represents enhanced online monitoring after an anomaly warning, a3 represents live-line maintenance, and a4 represents outage maintenance. P is the state transition probability, representing the conditional probability of transitioning to the next state s' after performing action a in state s. R is the reward, the real-time reward R(s, a, s') obtained when transitioning to the next state s' after performing action a in state s. γ is the discount factor, γ∈[0,1), representing the present value coefficient of future rewards.

[0033] Because the traditional Q-Learning algorithm involves random exploration during each iteration, it leads to severe undersampling of sparse fault paths in distribution network blocks, slow convergence of the Q-table, and low accuracy in long-term prediction. To address these shortcomings of the traditional Q-Learning algorithm, we pre-optimize the search path.

[0034] Construct a two-rooted, multi-branch, weighted pruning exploration tree T=[V, E, R, B], where V is the set of tree nodes containing complete risk attributes and path information, E is the set of tree edges, each edge corresponding to a power grid state transition and maintenance action, and R is the set of two-rooted nodes, R={X start X goal}, X start X is a healthy root node. goal B is the fault endpoint, and B is the set of fault branches, with each branch corresponding to a type of power grid fault mode.

[0035] Two-root, multi-branch weighted pruning exploration trees have a two-root, bidirectional growth structure, with the forward tree using X... start The root is X, and it grows in the direction of the fault state. The reverse tree is based on X. goal The forward tree grows towards the healthy state, with each new node in the forward tree as the root. When the newly added nodes in both the forward and reverse trees meet the Mahalanobis distance connection threshold, they are considered to have intersected, and are directly spliced ​​together to generate a complete fault path from the healthy state to the faulty state. The reverse tree grows synchronously with each type of fault endpoint as an independent root node, essentially tracing back from the "fault result" to the "fault cause," avoiding branch blind spots caused by random sampling probabilities. Regardless of the probability of a fault occurring, each fault endpoint has its own dedicated reverse growth link, directly covering the complete evolution path of that fault mode from the endpoint to the cause. The forward tree only needs to grow to the common entry node of the fault branch (such as the slightly deteriorated state), and the reverse tree has already grown from the fault endpoint to the branch's dedicated node. The two trees can intersect in the middle of the branch, splicing together to generate a complete path. The forward tree does not need to extend from the healthy state to the low-probability fault endpoint, reducing the sampling threshold for branch discovery from "random hits along the entire path" to "intersection of nodes in the middle," greatly improving the efficiency of low-probability branch discovery. Inverse trees allocate independent sampling and growth resources to each faulty branch, avoiding the Matthew effect where the main branch monopolizes the vast majority of sampling resources. Low-probability, high-impact branches can obtain sufficient sampling density, ensuring the accuracy of their transition probability estimation.

[0036] Based on the full path samples of the bidirectional tree, the constructed Markov transition matrix fully includes bidirectional transition terms. Finally, by incorporating the steady-state fault probability calculated from the Markov chain, the reduction effect of different maintenance strategies on the fault probability can be accurately reflected, perfectly aligning with the actual operation rules of the power grid. Bidirectional growth splits a long path of length L into two half-paths of length L / 2, significantly improving search efficiency. Simultaneously, the alternating expansion mechanism of the bidirectional tree avoids overgrowth of a single tree, reducing the average convergence time by more than 50% compared to a unidirectional tree, and significantly lowering sampling computation costs.

[0037] In actual distribution networks, the fault absorption state is not a single endpoint, but includes multiple fault endpoints such as main transformer faults, bus faults, line faults, and protection device faults. The root node of the reverse tree used in this invention is a set of all types of fault endpoints. All fault endpoints grow synchronously as the root node of the reverse tree at the same time. There is no need to run the algorithm separately for each fault endpoint. One algorithm run can cover all fault modes.

[0038] The node fault risk weight of a two-root, multi-branch weighted pruning exploration tree is defined as k = η1k1 + η2k2 + η3k3 + η4k4, where η1 to η4 are proportional coefficients, k1 is the equipment health weight, k2 is the electrical fault weight, k3 is the environmental anomaly weight, and k4 is the historical fault weight. The growth rules of the two-root, multi-branch weighted pruning exploration tree are set as follows: delete nodes with fault risk weights below a set threshold; and during each growth operation, select the adjacent node with the highest fault risk weight as the parent node.

[0039] We introduce the concept of "valid nodes" to perform effective pruning operations on a weighted pruning exploration tree with two roots and multiple branches. A node is defined as a valid node when it is the root node, a branch entry node, a node at the intersection of two trees, or a branch node with a fault risk weight lower than a set threshold, or a branch node with ≥2 child nodes. After each set number of sampling rounds, all nodes are traversed, valid nodes are retained, and the rest are deleted.

[0040] Sampling points are generated within the heuristic area. The sampling points are verified to ensure they meet the physical constraints of the distribution network operation. Illegal sampling points are deleted, and then sampling is performed again to complete the sampling points.

[0041] Synchronous search for healthy root node X start and fault endpoint X goal For nearby sampling points, select the adjacent sampling point with the highest fault risk weight as the parent node to complete the growth of the forward tree and the reverse tree. If the newly added node satisfies the bidirectional intersection condition, that is, backtrack the forward tree to the healthy root node X. start Backtrack the reverse tree to the fault endpoint X goal Then, the backtracking path is pieced together to generate a complete fault path, completing one search path generation. This process is repeated until a preset number of search paths are reached, completing the sampling process.

[0042] Based on the entire search path, complete the initialization and update of the Q table. α is the learning rate.

[0043] The system state distribution under the optimal strategy is obtained from the converged Q-table. Then the probability of failure P of the distribution network block at time t. t =π·P t-1 .

[0044] After obtaining the fault probability of each distribution network block, the next step is to use the fault rate of each block to predict the fault rate of the entire distribution network. Common machine learning prediction methods, such as neural networks, require large amounts of data for training and cannot respond promptly to dynamic changes in distribution network topology and operating modes. To address this problem, this invention introduces the SIR (Self-Improving Influence) model for distribution network fault rate prediction. However, the traditional SIR model assumes that all nodes are in uniform contact and that the fault propagation probability is the same. The propagation probability of a distribution network is strongly correlated with multiple factors such as electrical distance and line load rate, and the specific parameters of these influencing factors change in real time. Furthermore, the traditional SIR model lacks an immunity module; it assumes that individuals gain permanent immunity after recovery and will not be reinfected. However, in reality, distribution networks can effectively block fault propagation through multi-level control measures such as fault isolation and distribution network islanding.

[0045] To address the aforementioned issues, we improved the SIR propagation model by introducing electrical topology weights and adding isolation and immune states to establish a hierarchical propagation architecture with time-varying parameters, thus resolving the problem that the traditional model does not conform to the actual operating rules of distribution networks.

[0046] Define the electrical distance between distribution network nodes , Let i be the impedance between nodes i and j. Define the topological weights of adjacent blocks. α is the load influence factor. The real-time load rate between nodes i and j The rated load rate. Elements of the inter-block coupling matrix B. N p N is the number of nodes in block p. q Let be the number of nodes in block q. This represents the protection reliability coefficient between blocks.

[0047] Construct a set of differential equations for the propagation dynamics between different blocks.

[0048]

[0049] in Let be the percentage of high-risk nodes in the k-th block at time t. Let be the percentage of faulty nodes in the k-th block at time t. Let be the percentage of isolated nodes within the k-th block at time t. Let be the percentage of recovered nodes in the k-th block at time t. Let t be the percentage of immune nodes in the k-th block at time t.

[0050] Let be the time-varying effective fault propagation rate of the k-th block. . The base propagation rate of block k is obtained by fitting the maximum likelihood estimate of historical fault data, and the load factor correction coefficient is also included. , The average load factor of the lines within block k. For weather correction factors and equipment health correction factors , This represents the real-time degradation status of device i. Let be the device failure threshold for device i.

[0051] Let be the time-varying fault isolation rate of the k-th block, which is the probability that a faulty node is isolated by the protection device. . The base isolation rate for block k, The average reliability of the protection devices within block k. This represents the average operating time of the protection devices within block k.

[0052] Let k be the time-varying fault repair rate of the k-th block. . Adjustment coefficient for emergency repair resources.

[0053] Let the time-varying isolation zone recovery rate be the value of the k-th block. . Basic transfer coefficient, For the reliability of the switching equipment in the k-th block, This represents the load transfer capacity within the k-th block.

[0054] Let be the time-varying immune conversion rate of the k-th block. . Basic immune coefficient, This represents the real-time total power supply capacity of the isolated distributed power source in the k-th block. Let be the maximum discharge power of the isolated energy storage unit in the k-th block. This represents the real-time total load of the k-th block.

[0055] The time-varying high-risk conversion rate for the k-th block. , Based on the basic susceptible conversion rate.

[0056] The above propagation dynamics differential equations are solved using the finite difference method, and then the basic regeneration number for each block is calculated. Finally, calculate the failure rate of the entire distribution network. ,in This is the critical threshold for fault propagation.

[0057] Finally, the following prediction function is used to predict the long-term failure rate trend of the distribution network. ,in, It is the future moment Distribution network failure rate, Let β be the random volatility of the current distribution network failure rate, and β be the elasticity variance coefficient. ρ is the mean recovery rate, ρ is the linear correlation between the failure rate and the failure volatility, and ν is the amplitude of the failure rate fluctuation.

[0058] The IEEE 33-node system was used for simulation, incorporating historical fault datasets, equipment ledgers, meteorological data, and operation and maintenance records of the distribution network in a certain region from 2020 to 2024. The simulation platform employed MATLAB / Simulink 2024a and OpenDSS distribution network simulation software.

[0059] Simulations were performed using the prediction method provided in this invention and the traditional Monte Carlo simulation method, respectively. The results are as follows:

[0060] This invention 1575 5.2 97.6 Monte Carlo simulation 6892 113.5 81.3

[0061] It can be seen that, compared with traditional prediction methods, the present invention has significant improvements in response speed and prediction accuracy.

[0062] The present invention can implement all or part of the processes in the methods of the above embodiments, or it can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable medium can include: any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

[0063] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing the reliability of power distribution networks, characterized in that... Includes the following steps: A. Divide the distribution network into several blocks, and define a Markov decision process quintuple and a double-rooted multi-branch weighted pruning exploration tree for each distribution network block; B. Use a two-root, multi-branch weighted pruning exploration tree to generate sampling paths, and initialize and update the Q-table based on the sampling paths. The system state distribution under the optimal strategy is obtained based on the converged Q-table. Then the probability of failure P of the distribution network block at time t. t =π·P t-1 ; C. Based on the failure probability of different distribution network blocks, construct a set of propagation dynamic differential equations between different distribution network blocks. By solving the set of propagation dynamic differential equations, calculate the basic regeneration number of each distribution network block and the overall failure rate of the distribution network, and then predict the overall failure rate of the distribution network.

2. The power supply reliability analysis method for distribution networks according to claim 1, characterized in that: The Markov decision process quintuple is (S, A, P, R, γ); where S is the state space, serving as the row index of the Q-table, and the state s∈S of each distribution network block is a discretized representation of multidimensional features, s=[s I s U s THD s h ], where s I For the supply current state, s U For the power supply voltage state, s THD For total harmonic distortion, s h For historical anomaly records, A is the action space, corresponding to the operation and maintenance and control operations as perceived by the power grid. It is a decision variable that affects the fault transfer probability and serves as the column index of the Q table. A=[a1, a2, a3, a4], where a1 is misoperation, a2 is enhanced online monitoring after anomaly warning, a3 is live maintenance, a4 is power outage maintenance, P is the state transition probability, which represents the conditional probability of transitioning to the next state s' after performing action a in state s, R is the reward, which is the real-time reward R(s, a, s') obtained when transitioning to the next state s' after performing action a in state s, and γ is the discount factor, γ∈[0,1), which represents the present value coefficient of future rewards.

3. The power distribution network reliability analysis method according to claim 2, characterized in that: A two-rooted, multi-branch, weighted pruning exploration tree T=[V, E, R, B], where V is the set of tree nodes containing complete risk attributes and path information, E is the set of tree edges, each edge corresponding to a power grid state transition and maintenance action, and R is the set of two-rooted nodes, R={X start X goal }, X start X is a healthy root node. goal B is the fault endpoint, and B is the set of fault branches, with each branch corresponding to a type of power grid fault mode.

4. The power supply reliability analysis method for distribution networks according to claim 3, characterized in that: Two-root, multi-branch weighted pruning exploration trees have a two-root, bidirectional growth structure, with the forward tree using X... start The root is X, and it grows in the direction of the fault state. The reverse tree is based on X. goal The forward tree grows towards the healthy state, with the new nodes of the forward tree and the reverse tree satisfying the Mahalanobis distance connection threshold. When the new nodes of the forward tree and the reverse tree meet the Mahalanobis distance connection threshold, it is determined that the two trees intersect and are directly spliced ​​to generate a complete fault path from the healthy state to the fault state. The reverse tree grows synchronously with each type of fault endpoint as an independent root node.

5. The power supply reliability analysis method for distribution networks according to claim 4, characterized in that: Define the node fault risk weight k = η1k1 + η2k2 + η3k3 + η4k4 for the two-root multi-branch weighted pruning exploration tree, where η1 to η4 are proportional coefficients, k1 is the equipment health weight, k2 is the electrical fault weight, k3 is the environmental anomaly weight, and k4 is the historical fault weight. The growth rules of the two-root multi-branch weighted pruning exploration tree are set as follows: delete nodes with fault risk weights lower than a set threshold, and select the adjacent node with the highest fault risk weight as the parent node during each growth operation.

6. The power supply reliability analysis method for distribution networks according to claim 5, characterized in that: A node is defined as a valid node if it is the root node, a branch entry node, a node where two trees intersect, or if its fault risk weight is lower than a set threshold, or if it is a branch node with ≥2 child nodes. After each set number of sampling rounds, all nodes are traversed, valid nodes are retained, and the rest are deleted.

7. The power supply reliability analysis method for distribution networks according to claim 6, characterized in that: Within the heuristic area, sampling points are generated, and it is verified whether the sampling points meet the physical constraints of the distribution network operation. Illegal sampling points are deleted, and then sampling is performed again to complete the sampling points. Synchronous search for healthy root node X start and fault endpoint X goal For nearby sampling points, select the adjacent sampling point with the highest fault risk weight as the parent node to complete the growth of the forward tree and the reverse tree; if the newly added node satisfies the bidirectional intersection condition, that is, backtrack the forward tree to the healthy root node X. start Backtrack the reverse tree to the fault endpoint X goal If the backtracking path is pieced together to generate a complete fault path, then one search path generation is completed; repeat the above process until the number of search paths reaches the preset number, and then the sampling is completed.

8. The power supply reliability analysis method for distribution networks according to claim 1, characterized in that: The system of differential equations for propagation dynamics is as follows in Let be the percentage of high-risk nodes in the k-th block at time t. Let be the percentage of faulty nodes in the k-th block at time t. Let be the percentage of isolated nodes within the k-th block at time t. Let be the percentage of recovered nodes in the k-th block at time t. The percentage of immune nodes in the k-th block at time t; Let be the time-varying effective fault propagation rate of the k-th block. , The base propagation rate of block k is obtained by fitting the maximum likelihood estimate of historical fault data, and the load factor correction coefficient is also included. , The average load factor of the lines within block k. For weather correction factors and equipment health correction factors , This represents the real-time degradation status of device i. Let i be the device failure threshold. Let be the time-varying fault isolation rate of the k-th block, which is the probability that a faulty node is isolated by the protection device. , The base isolation rate for block k, The average reliability of the protection devices within block k. The average operating time of the protection devices within block k; Let k be the time-varying fault repair rate of the k-th block. , Adjustment coefficient for emergency repair resources; Let the time-varying isolation zone recovery rate be the value of the k-th block. , Basic transfer coefficient, For the reliability of the switching equipment in the k-th block, This refers to the load transfer capacity within the k-th block; Let be the time-varying immune conversion rate of the k-th block. , Basic immune coefficient, This represents the real-time total power supply capacity of the isolated distributed power source in the k-th block. Let be the maximum discharge power of the isolated energy storage unit in the k-th block. This represents the real-time total load of the k-th block; The time-varying high-risk conversion rate for the k-th block. , Based on the basic susceptible conversion rate.

9. The power supply reliability analysis method for distribution networks according to claim 8, characterized in that: The above propagation dynamics differential equations are solved using the finite difference method, and then the basic regeneration number for each block is calculated. Finally, calculate the failure rate of the entire distribution network. ,in This is the critical threshold for fault propagation. N p N is the number of nodes in block p. q Let be the number of nodes in block q. The inter-block protection reliability coefficient, α is the load influence factor. The real-time load rate between nodes i and j Rated load rate, , Let be the impedance between nodes i and j.

10. The power supply reliability analysis method for distribution networks according to claim 9, characterized in that: The following prediction function is used to predict the long-term failure rate trend of the distribution network. ,in, It is the future moment Distribution network failure rate, Let β be the random volatility of the current distribution network failure rate, and let β be the elasticity variance coefficient. ρ is the mean recovery rate, ρ is the linear correlation between the failure rate and the failure volatility, and ν is the amplitude of the failure rate fluctuation.

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