A power distribution network prevention-correction coordinated control method and device

Abstract

The application provides a power distribution network prevention-correction coordinated control method and device, and relates to the technical field of power distribution network control for extreme events. Based on the complex dynamic network theory, the application establishes a toughness index representing the mathematical sense synchronization stability of the power distribution network under extreme conditions, and extracts key edges having an important influence on the toughness of the power distribution network. Taking the maximum toughness index and the minimum overall control cost as the objective function, and taking the operation control related constraints of the power distribution network including the key edge constraints as the constraint conditions, the application constructs a power distribution network prevention-correction coordinated control optimization model, so as to maximize the toughness index while reducing the overall control cost. The application proposes an inner-outer layer nested solution algorithm for solving, and iteratively optimizes until the output meets the convergence condition of the power distribution network prevention-correction coordinated control strategy. The application can promote the full coordination and complementation of the prevention control and the correction control, and measure and improve the toughness of the power distribution network from the topological level.

Description

Technical Field

[0001] This invention relates to the field of distribution network control technology for extreme events, and specifically to a distribution network prevention-correction coordinated control method and device based on the resilience index of complex dynamic networks. Background Technology

[0002] In recent years, global climate change has led to a significant increase in the frequency and intensity of extreme events, such as typhoons, floods, earthquakes, and heat waves. These disasters have a profound impact on infrastructure, particularly on power systems, directly threatening socio-economic stability and the safety of residents' lives. Considering the destructive and sudden nature of extreme events, there is an urgent need to study preventive-corrective coordinated control methods for distribution networks to enhance their resilience under extreme events.

[0003] While some research has focused on improving the resilience of distribution networks during extreme events, quantitative assessments of resilience still primarily rely on traditional indicators such as outage duration and the amount of power lost. However, these indicators typically remain at the service level. In actual operation, extreme weather events first impact the physical components and network topology of the power system, and topology-level structural degradation is the direct cause of decreased service performance. Although service-level indicators can reflect the ultimate impact of extreme events on power supply, they cannot fundamentally characterize the disaster resilience of the power system at the topology level.

[0004] Regarding control mechanisms, existing methods often separate preventive control before extreme events from corrective control after extreme events, failing to fully capture the complementary relationship between the two. However, it should be noted that insufficient implementation of preventive control may increase the burden on corrective control, further increasing the control costs of the corrective control phase; while excessive preventive control may produce ineffective control actions, leading to additional preventive control costs. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for coordinated prevention-correction control of distribution networks based on resilience indices of complex dynamic networks. This invention addresses the problems that service-level resilience indices cannot reveal the resilience of distribution networks related to mathematical synchronous stability at the topological level, and the lack of coordination between preventive and corrective control. By establishing a resilience index that can characterize the mathematical synchronous stability of distribution networks, extracting critical edges that have a significant impact on distribution network resilience, constructing an optimization model for coordinated prevention-correction control of distribution networks oriented towards extreme events, and proposing a nested solution algorithm for solving the model and outputting the optimal preventive and corrective control strategies, thereby improving the resilience of distribution networks oriented towards extreme events.

[0006] To achieve the above objectives, in a first aspect, the present invention provides a distribution network prevention-correction coordinated control method, comprising: Establish a resilience index characterizing the mathematical synchronization stability of the distribution network under extreme events, and extract the critical edges that have a significant impact on the resilience of the distribution network; Define preventive control variables and corrective control variables. Preventive control variables are used to characterize preventive control measures before extreme events occur, and corrective control variables are used to characterize emergency corrective measures after extreme events occur. Based on the anticipated failure scenarios caused by extreme events, construct an objective function that maximizes the resilience index and minimizes the overall control cost. The overall control cost includes preventive control cost and expected corrective control cost. Construct constraints including critical edge constraints. Obtain the preventive-corrective coordinated control optimization model. Based on the nested solution algorithm, the prevention-correction coordinated control optimization model is solved iteratively through inner and outer layers, and the optimal coordinated control strategy is output, thereby enabling prevention-correction coordinated control of the distribution network.

[0007] According to the distribution network prevention-correction coordinated control method provided by the present invention, a resilience index characterizing the mathematical synchronization stability of the distribution network under extreme events is established, and key edges that have a significant impact on the resilience of the distribution network are extracted, including: Based on complex dynamic network theory, the distribution network topology is modeled as a network topology structure consisting of nodes, edges, and cycles. The adjacency matrix, degree matrix, and Laplace matrix of the distribution network are generated according to the network topology structure. The eigenvalues ​​and corresponding eigenvectors of the Laplace matrix are solved, and the smallest non-zero eigenvalue is selected as a resilience index characterizing the mathematical synchronous stability of the distribution network, denoted as the Fiedler value. The eigenvector corresponding to the Fiedler value is denoted as the Fiedler vector. Based on the component differences represented by each adjacent node in the Fiedler vector, the contribution of each edge in the distribution network to the Fiedler value is calculated. Based on the contribution ranking, several key edges with the greatest impact on the resilience of the distribution network are extracted. According to the distribution network prevention-correction coordinated control method provided by the present invention, the network topology is described as an undirected graph. , is represented as: (1) in, N ={1,2,..., N G} represents a set of nodes, which in turn represents a bus in a distribution network; V×V represents the edge set, which represents the lines in the distribution network; The formulas for calculating the adjacency matrix A and the degree matrix D are: (2) (3) (4) (5) in, Indicates all N × N The set of real matrices a ij Represents a node i With nodes j The connection relationship, d i Indicates connection to node i The number of sides; The Laplacian matrix L is defined based on the adjacency matrix A and the degree matrix D, and its expression is: (6) The eigenvalues ​​of the Laplace matrix L are arranged in the following order: (7) in, λ 2 represents the smallest non-zero eigenvalue of the Laplace matrix L, i.e., the Fiedler value; According to the theory of complex dynamical networks, the Fiedler value and its corresponding eigenvector satisfy the following: (8) in, Represents the Federer vector. i and j These represent the first and second digits of the Fiedler vector. i row and number j The value of the row; calculate the contribution of the corresponding edge to the Fiedler value based on the differences of each component in the Fiedler vector, and extract the key edges that contribute the most to the Fiedler value, represented as: (9) (10) in, k ij Used for quantizing edges i - j Contribution to Federer's value, E crit Represents the set of key edges. K The number of critical edges. k (K) This represents the 1st position of all candidate edge contributions sorted in descending order. K Large value. According to the present invention, a distribution network prevention-correction coordinated control method is provided, which is based on an inner and outer nested solution algorithm. The method iteratively solves the prevention-correction coordinated control optimization model through inner and outer layers, and outputs the optimal coordinated control strategy, including: A hierarchical solution is adopted for the prevention-correction coordinated control optimization model. The outer layer uses a swarm intelligence optimization algorithm to search for topology adjustment schemes of the distribution network and passes the generated topology adjustment schemes to the inner layer. Based on the topology adjustment schemes given by the outer layer, the inner layer uses a mathematical programming solver to optimize the remaining prevention control variables and correction control variables, and feeds back the obtained objective function values ​​to the outer layer to update the topology adjustment schemes and iterate until the optimal prevention control strategy and the optimal correction control strategy that meet the convergence conditions are obtained.

[0008] According to the present invention, a distribution network prevention-correction coordinated control method includes prevention control variables such as power purchase, wind curtailment, solar curtailment, energy storage charging and discharging, and tie switch operation before the occurrence of an extreme event; and correction control variables such as power purchase, wind curtailment, solar curtailment, energy storage charging and discharging, tie switch operation, and load shedding after the occurrence of an extreme event. According to the distribution network prevention-correction coordinated control method provided by the present invention, the objective function is expressed as follows: (11) (12) (13) in, C pre and C cor Let represent the costs of the prevention and control phase and the correction and control phase, respectively, and let S represent the set of all failure scenarios. π s Indicates the fault scenario s The probability of occurrence x Indicates prevention and control variables. y s Indicates the control variable for correction. Represents the set of all correction control variables. Let K represent the mathematical expectation. pre and K cor These represent the action indices in the prevention and control phase and the corrective control phase, respectively. α k and β k These represent the unit control cost coefficients for the prevention and control phase and the correction and control phase, respectively. x k This indicates the control actions during the prevention and control phase. y s,k Indicates the fault scenario s Control actions during the next correction control phase Denotes the 1-norm. x k,ecoThis represents a reference value at the economically optimal operating point. and These represent the unit network loss cost during the prevention and control phase and the correction and control phase, respectively. and These represent the allocation coefficients for the prevention and control phase and the correction and control phase, respectively. and These represent the Fiedler value and the fault scenario during the prevention and control phase, respectively. s Fiedler value in the lower correction control phase and These represent the excitation coefficients of the Fiedler value during the preventive control phase and the corrective control phase, respectively. and These represent the network loss and fault scenarios during the prevention and control phase, respectively. s Network loss during the lower correction control phase. According to the distribution network prevention-correction coordinated control method provided by the present invention, the critical edge constraint is constructed based on the theory of complex dynamic networks, and is expressed as follows: (14) (15) in, To characterize the prevention phase circuit i - j Whether it is a key edge is a binary variable. To characterize the fault scenario s Lower calibration stage line i - j Whether it is a key edge is a binary variable. u ij,s To characterize the fault scenario s Downline i - j A binary variable indicating whether a fault exists. According to the distribution network prevention-correction coordinated control method provided by the present invention, the outer layer uses a swarm intelligence optimization algorithm to search for topology adjustment schemes of the distribution network, and transmits the generated distribution network topology for the prevention control stage and the correction control stage to the inner layer, as shown below: (16) in, and These are the distribution network topologies for the prevention and control phase and the correction and control phase, respectively. This represents the initial solution generated by the swarm intelligence optimization algorithm; Based on the given distribution network topology from the outer layer, the inner layer uses a mathematical programming solver to optimize the remaining preventive control variables and corrective control variables, as follows: (17) Where Eqs.(11)-(13) represent the objective functions represented by equations (11) to (13). Indicates the fault scenario s The following is a collection of faulty lines. x i Indicates the first i Prevention and control variables for the next iteration. y s,i Indicates the first i The correction control variable for the next iteration.

[0009] According to the distribution network prevention-correction coordinated control method provided by the present invention, the constraints also include load shedding constraints, wind curtailment constraints, solar curtailment constraints, power flow constraints, and power balance constraints.

[0010] In a second aspect, the present invention provides a distribution network prevention-correction coordination control device, comprising: The preprocessing unit is used to establish a resilience index for the mathematical synchronous stability of the distribution network under extreme events and to extract the critical edges that have a significant impact on the resilience of the distribution network. A modeling unit is used to define preventive control variables and corrective control variables. The preventive control variables are used to characterize preventive control measures before extreme events occur, and the corrective control variables are used to characterize emergency corrective measures after extreme events occur. Based on the anticipated failure scenarios caused by extreme events, an objective function is constructed to maximize the resilience index and minimize the overall control cost. The overall control cost includes the preventive control cost and the expected corrective control cost. Constraints including key edge constraints are constructed. The preventive-corrective coordinated control optimization model is obtained. The solver unit is used to solve the prevention-correction coordinated control optimization model through inner and outer nested solver algorithms, and output the optimal coordinated control strategy to perform prevention-correction coordinated control on the distribution network.

[0011] Compared with the prior art, the present invention has at least the following technical effects: This invention proposes a distribution network prevention-correction coordinated control method and device based on a resilience index of complex dynamic networks, which improves the resilience of distribution networks to extreme events from a topological perspective through control. First, based on complex dynamic network theory, the distribution network topology is modeled as a network topology structure composed of nodes, edges, and cycles. A resilience index characterizing the mathematical synchronization stability of the distribution network under extreme conditions is established, and key edges that have a significant impact on distribution network resilience are extracted. Further, with the objective functions of maximizing the resilience index and minimizing the overall control cost, and with distribution network operation control-related constraints including key edge constraints as constraints, a distribution network prevention-correction coordinated control optimization model is constructed to maximize the resilience index while minimizing the overall control cost. Finally, a nested solution algorithm is proposed. The outer layer uses a swarm intelligence optimization algorithm to search for topology adjustment schemes for the distribution network, while the inner layer optimizes the remaining prevention and correction control variables based on the given topology adjustment scheme from the outer layer. The optimization is iteratively performed until a distribution network prevention-correction coordinated control strategy that meets the convergence condition is output. This promotes full coordination and complementarity between prevention and correction control, measuring and improving distribution network resilience at the topological level. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0013] In the attached diagram: Figure 1 This is a flowchart of the distribution network prevention-correction coordinated control method of the present invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0015] The following detailed description of some embodiments of the present invention will be provided in conjunction with the accompanying drawings. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0016] The core idea of ​​this invention is as follows: Based on complex dynamic network theory, the distribution network topology is modeled as a network topology structure composed of nodes, edges, and cycles. A resilience index is established to characterize the mathematical synchronous stability of the distribution network under extreme events, and critical edges that have a significant impact on the resilience of the distribution network are extracted. On this basis, a distribution network prevention-correction coordinated control optimization model is constructed with the objective functions of maximizing the resilience index and minimizing the overall control cost. The established resilience index is embedded as an excitation term in its objective function, and critical edge constraints of lines that have a significant impact on the resilience of the distribution network are constructed. Finally, a nested solution algorithm is proposed, which outputs the optimal coordinated control strategy, namely the optimal prevention control strategy and the optimal correction control strategy, through iterative solution of the inner and outer layers. This enables prevention-correction coordinated control of the distribution network, thereby improving the resilience of the distribution network in the face of extreme events.

[0017] Please see Figure 1 This invention provides a distribution network prevention-correction coordinated control method based on the resilience index of complex dynamic networks, comprising the following steps: Step 1: Establish a resilience index that can characterize the mathematical synchronous stability of the distribution network under extreme events, and extract the critical edges that have an important impact on the resilience of the distribution network.

[0018] Specifically, based on the theory of complex dynamic networks, the distribution network topology is modeled as a network topology structure composed of nodes, edges, and cycles. Based on this, the adjacency matrix, degree matrix, and Laplace matrix of the distribution network are generated according to this network topology. Then, the eigenvalues ​​and corresponding eigenvectors of the Laplace matrix are solved, and the smallest non-zero eigenvalue is selected as a resilience index characterizing the mathematical synchronous stability of the distribution network, denoted as the Fiedler value. The eigenvector corresponding to this smallest non-zero eigenvalue is denoted as the Fiedler vector. Further, based on the component differences represented by each adjacent node in the Fiedler vector, the contribution of each edge in the distribution network to the Fiedler value is calculated, and several key edges with the greatest impact on the resilience of the distribution network are extracted based on the contribution ranking.

[0019] As a preferred embodiment, the resilience index established by this invention, which characterizes the mathematical synchronization stability of a distribution network under extreme events, and the specific calculation process for the critical edge that has a significant impact on the resilience of the distribution network, are as follows: To guide the construction of the objective function and constraints for the subsequent prevention-correction coordinated control optimization model, it is first necessary to quantitatively evaluate the mathematical synchronization stability of the distribution network under extreme events at the topology level, revealing the critical edges in the distribution network that have a significant impact on mathematical synchronization stability.

[0020] The network topology of a distribution network can be described as an undirected graph. Specifically, it can be modeled as follows: (1) In the formula: N ={1,2,..., N G} represents a set of nodes, which in turn represents a bus in a distribution network; V×V represents the edge set, which represents the lines in the distribution network.

[0021] The adjacency matrix A and the degree matrix D are calculated as follows: (2) (3) (4) (5) In the formula: Indicates all N × N The set of real matrices a ij Represents a node i With nodes j The connection between them d i Represents connection to node i The number of edges a node has reflects its strength in the network.

[0022] The Laplacian matrix L can be defined based on the adjacency matrix A and the degree matrix D, and its eigenvalues ​​can be arranged in the following order: (6) (7) In the formula: λ 2 represents the smallest non-zero eigenvalue of matrix L, denoted as the Fiedler value.

[0023] According to the theory of complex dynamical networks, the Fiedler value and its corresponding eigenvector satisfy the following: (8) In the formula: Represents the Federer vector. i and j Representing the first digit of the Fiedler vector respectively i row and number j The value of the row. Calculate the contribution of each edge to the network's Fiedler value based on the differences in each component of the Fiedler vector, and extract the key edges with the highest contribution to the Fiedler value. Specifically, this can be written as... (9) (10) In the formula: kij Used for quantizing edges i - j E's contribution to the network Fiedler value crit Represents the set of key edges. K The number of critical edges. k (K) Represents the number of candidate edges whose contributions are sorted in descending order. K Large value.

[0024] Based on the above modeling process, we obtained the distribution network resilience index and critical edge information. We need to further use this information to guide the coordinated optimization of prevention and correction, and promote resilience improvement.

[0025] Step 2: Construct an optimization model for the prevention-correction coordinated control of the distribution network.

[0026] Specifically, based on the resilience index established in step 1, which characterizes the mathematical synchronization stability of the distribution network under extreme events, and the extracted critical edges that have a significant impact on the resilience of the distribution network, preventive control variables and corrective control variables are defined. The preventive control variables are used to characterize preventive control measures before the occurrence of extreme events, and the corrective control variables are used to characterize emergency correction measures after the occurrence of extreme events. Based on the anticipated fault scenarios caused by extreme events, an objective function is constructed with the goal of maximizing the resilience index and minimizing the overall control cost. The overall control cost includes the preventive control cost and the expected corrective control cost. The established resilience index is embedded in the objective function as an incentive term. Furthermore, constraints related to the operation and control of the distribution network are constructed, including critical edge constraints, load shedding constraints, wind curtailment constraints, solar curtailment constraints, power flow constraints, and power balance constraints. Among them, the critical edge constraints are constructed based on the theory of complex dynamic networks. The distribution network topology is adjusted through the critical edge constraints to avoid anticipated faults occurring on lines that have a significant impact on the resilience of the distribution network.

[0027] Step 3: Propose an inner and outer nested solution algorithm for solving the prevention-correction coordinated control optimization model. Solve the prevention-correction coordinated control optimization model through inner and outer layer iterations, output the optimal coordinated control strategy, and thus perform prevention-correction coordinated control on the distribution network.

[0028] Specifically, the prevention-correction coordinated control optimization model constructed in step 2 is solved in layers. The outer layer uses a swarm intelligence optimization algorithm to search for topology adjustment schemes of the distribution network and passes the generated topology adjustment schemes to the inner layer. Based on the topology adjustment schemes given by the outer layer, the inner layer uses a mathematical programming solver to optimize and solve the remaining prevention control variables and correction control variables, and feeds back the obtained objective function values ​​to the outer layer to update the topology adjustment schemes and iterate until the optimal prevention control strategy and the optimal correction control strategy that meet the convergence conditions are obtained.

[0029] The distribution network prevention and correction control strategies output through the above methods not only enhance the resilience of the distribution network before and after extreme events, but also effectively reduce the overall control cost of the distribution network during the control process.

[0030] As a preferred embodiment, the distribution network prevention-correction coordinated control optimization model of the present invention is as follows: Based on the distribution network resilience index and critical edge information obtained in step 1, this invention further embeds the resilience index into the objective function of the optimization model as an incentive term to promote resilience improvement; and constructs critical edge constraints to avoid failures occurring on critical lines that have a significant impact on distribution network resilience.

[0031] (1) Optimize variables The defined optimization variables include preventive control variables and corrective control variables. Preventive control variables characterize preventative control measures implemented before extreme events occur, while corrective control variables characterize emergency corrective measures implemented after extreme events occur. Preventive control variables include purchased electricity, wind curtailment, solar curtailment, energy storage charging and discharging, and tie-down switch operation before extreme events occur; corrective control variables include purchased electricity, wind curtailment, solar curtailment, energy storage charging and discharging, tie-down switch operation, and load shedding after extreme events occur.

[0032] (2) Objective function The objective of preventative-corrective coordinated control is to maximize resilience while minimizing the sum of preventative control costs and expected corrective control costs. Preventative control costs refer to the control costs incurred by preventative measures implemented before an extreme event occurs, while expected corrective control costs represent the weighted control costs of corrective measures taken after an extreme event occurs, addressing various anticipated failure scenarios. The objective function can be specifically written as follows: (11) (12) (13) in, C pre and C cor Let represent the costs of the prevention and control phase and the correction and control phase, respectively, and let S represent the set of all failure scenarios. π s Indicates the fault scenario s The probability of occurrence x Indicates prevention and control variables. y s Indicates the control variable for correction. Represents the set of all correction control variables. Let K represent the mathematical expectation. pre and Kcor These represent the action indices in the prevention and control phase and the corrective control phase, respectively. α k and β k These represent the unit control cost coefficients for the prevention and control phase and the correction and control phase, respectively. x k This indicates the control actions during the prevention and control phase. y s,k Indicates the fault scenario s Control actions during the next correction control phase Denotes the 1-norm. x k,eco This represents a reference value at the economically optimal operating point. and These represent the unit network loss cost during the prevention and control phase and the correction and control phase, respectively. and These represent the allocation coefficients for the prevention and control phase and the correction and control phase, respectively. and These represent the Fiedler value and the fault scenario during the prevention and control phase, respectively. s Fiedler value in the lower correction control phase and These represent the excitation coefficients of the Fiedler value during the preventive control phase and the corrective control phase, respectively. and These represent the network loss and fault scenarios during the prevention and control phase, respectively. s Network loss during the lower correction control phase.

[0033] (3) Constraints Constraints include critical edge constraints, load shedding constraints, wind curtailment constraints, solar curtailment constraints, power flow constraints, and power balance constraints. Among these, critical edge constraints are constructed based on complex dynamic network theory, adjusting the distribution network topology to prevent anticipated faults from occurring on lines that significantly impact the resilience of the distribution network. Specifically, this can be written as... (14) (15) In the formula: To characterize the prevention phase circuit i - j Whether it is a key edge is a binary variable. To characterize the scene s Lower calibration stage line i - j Whether it is a key edge is a binary variable. u ij,s To characterize the scene s Downline i -j A binary variable indicating whether a fault exists.

[0034] Through the above modeling process, a preventive-corrective coordinated control optimization model for distribution networks under extreme events was obtained. This model achieves coordinated complementarity between preventive and corrective control, explicitly embeds resilience indicators, and constructs critical edge constraints for important lines, which contributes to improving the resilience of the distribution network.

[0035] As a preferred embodiment, the implementation flow of the nested solution algorithm for solving the prevention-correction coordinated control optimization model proposed in this invention is as follows: (1) The outer layer uses a swarm intelligence optimization algorithm to search for the topology adjustment scheme of the distribution network and transmits the generated distribution network topology of the prevention control stage and correction control stage to the inner layer.

[0036] (16) In the formula: and These are the distribution network topologies for the prevention and control phase and the correction and control phase, respectively. This represents the initial solution generated by the swarm intelligence optimization algorithm.

[0037] (2) The inner layer uses a mathematical programming solver to optimize the remaining prevention control variables and correction control variables based on the given distribution network topology of the outer layer.

[0038] (17) In the formula: Eqs.(11)-(13) represents the objective function shown in formulas (11)-(13). Indicates the fault scenario s The following is a collection of faulty lines. x i Indicates the first i Prevention and control variables for the next iteration. y s,i Indicates the first i The correction control variable for the next iteration.

[0039] (3) The inner layer feeds back the objective function value obtained by solving to the outer layer. The outer layer further updates the topology adjustment scheme and iteratively seeks optimization until the optimal coordination control strategy that satisfies the convergence condition is obtained.

[0040] Therefore, this invention forms a complete solution process for prevention and control strategies and correction control strategies under extreme events. It can effectively output prevention and control strategies applicable before extreme events occur and correction control strategies applicable after extreme events occur based on the anticipated fault scenarios, thereby improving the resilience of the distribution network in the face of extreme events.

[0041] Based on the same inventive concept, another embodiment of the present invention provides a distribution network prevention-correction coordination control device for implementing the distribution network prevention-correction coordination control method of the aforementioned embodiment. The device includes: The preprocessing unit is used to establish a resilience index characterizing the mathematical synchronous stability of the distribution network under extreme events and to extract the key edges that have an important impact on the resilience of the distribution network. A modeling unit is used to define preventive control variables and corrective control variables. The preventive control variables are used to characterize preventive control measures before extreme events occur, and the corrective control variables are used to characterize emergency corrective measures after extreme events occur. Based on the anticipated failure scenarios caused by extreme events, an objective function is constructed to maximize the resilience index and minimize the overall control cost. The overall control cost includes the preventive control cost and the expected corrective control cost. Constraints including key edge constraints are constructed. The preventive-corrective coordinated control optimization model is obtained. The solver unit is used to solve the prevention-correction coordinated control optimization model through inner and outer nested solver algorithms, and output the optimal coordinated control strategy to perform prevention-correction coordinated control on the distribution network.

[0042] In summary, the present invention has the following advantages: On the one hand, this invention establishes a resilience index based on complex dynamic network theory to characterize the mathematical synchronization stability of a distribution network under extreme events, and extracts critical edges that have a significant impact on the resilience of the distribution network. Compared with methods that assess resilience based on traditional service-level resilience indices, this invention can quantify the mathematical synchronization stability of the distribution network at the topology level, revealing critical edges that have a significant impact on it, thereby guiding the optimization of preventive-corrective coordinated control strategies.

[0043] On the other hand, this invention further constructs a distribution network prevention-correction coordinated control optimization model, explicitly embedding the aforementioned resilience indicators and constructing critical edge constraints to prevent anticipated faults from occurring on lines that have a significant impact on distribution network resilience. This model effectively achieves coordinated complementarity between prevention control and correction control, promoting the improvement of distribution network resilience.

[0044] Based on this, this invention proposes a nested inner and outer layer solution algorithm for solving the preventive-corrective coordinated control optimization model. The outer layer uses a swarm intelligence optimization algorithm to search for topology adjustment schemes for the distribution network, while the inner layer, based on the topology adjustment scheme given by the outer layer, uses a mathematical programming solver to optimize the remaining preventive and corrective control variables. Compared with the traditional mathematical programmable solution method, the algorithm proposed in this invention reduces the solution complexity, improves the solution efficiency, and effectively solves resilience indices that are difficult to characterize linearly.

[0045] Furthermore, this invention assesses the resilience of distribution networks at the topology level, promotes coordination and complementarity between preventive control and corrective control, and can effectively output preventive control strategies and corrective control strategies for extreme events. It measures and improves the resilience of distribution networks at the topology level and has good engineering applicability and promotion value.

[0046] The following are specific embodiments of the present invention.

[0047] To verify the feasibility and superiority of the present invention, a specific embodiment of the present invention selects a power distribution network model as the research object. The power distribution network includes multiple wind turbine units, photovoltaic and energy storage nodes, and has typical characteristics of high penetration rate of new energy.

[0048] Under this distribution network model, a set of anticipated fault scenarios was generated based on the typhoon wind field model and the component vulnerability model, as shown in Table 1. In this table, the two numbers for a faulty line represent lines connecting two distribution network nodes. For example, 14-15 represents the line connecting node 14 and node 15.

[0049] Table 1. Set of anticipated failure scenarios

[0050] For this set of anticipated failure scenarios, the method proposed in this invention is used to output corresponding preventive and corrective control strategies to verify the feasibility of the invention. Furthermore, the method proposed in this invention is compared with a method that only uses corrective control (Comparison Method 1) and a method that does not embed Fiedler values ​​and does not construct critical edge constraints (Comparison Method 2) to verify the superiority of the invention. Table 2 shows the comparison results between the method proposed in this invention and Comparison Method 1. Table 3 shows the comparison results between the method proposed in this invention and Comparison Method 2.

[0051] Table 2. Comparison of control costs between the method proposed in this invention and comparative method 1

[0052] Table 3. Comparison between the method proposed in this invention and comparative method 2

[0053] As can be seen from Table 2, the control cost of the method proposed in this invention is RMB 1643.85, which is RMB 108.49 less than the control cost of comparative method 1 (RMB 1752.34), a reduction of 6.60%, thus verifying the advantage of the method proposed in this invention in reducing the overall control cost.

[0054] As shown in Table 3, the weighted Fiedler values ​​of the proposed method in the prevention and correction phases are 0.0312 and 0.0536, respectively, representing increases of 60.0% and 24.1% compared to the weighted Fiedler values ​​of Comparative Method 2. This indicates that the proposed method effectively improves the resilience of the distribution network in both the prevention and correction phases. Furthermore, the proposed method reduces the service-level resilience index, i.e., the weighted load shedding, by 10.05 kW, demonstrating that improving topology-level resilience can indirectly mitigate load shedding and enhance service-level resilience. These results verify the feasibility and superiority of the proposed method in enhancing distribution network resilience from both topology and service perspectives.

[0055] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the embodiments disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. It should be understood that the invention is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A method for coordinated prevention and correction control of a power distribution network, characterized in that, include: Establish a resilience index characterizing the mathematical synchronization stability of the distribution network under extreme events, and extract the critical edges that have a significant impact on the resilience of the distribution network; Define preventive control variables and corrective control variables. The preventive control variables are used to characterize preventive control measures before the occurrence of extreme events, and the corrective control variables are used to characterize emergency corrective measures after the occurrence of extreme events. Based on the anticipated failure scenarios caused by extreme events, construct an objective function that maximizes the resilience index and minimizes the overall control cost. The overall control cost includes the preventive control cost and the expected corrective control cost. Construct constraints including critical edge constraints. Obtain the preventive-corrective coordinated control optimization model. Based on the nested solution algorithm, the prevention-correction coordinated control optimization model is solved iteratively through inner and outer layers to output the optimal coordinated control strategy, thereby enabling prevention-correction coordinated control of the distribution network.

2. The distribution network prevention-correction coordinated control method according to claim 1, characterized in that, The establishment of a resilience index characterizing the mathematical synchronization stability of the distribution network under extreme events, and the extraction of key edges that have a significant impact on the resilience of the distribution network, include: Based on complex dynamic network theory, the distribution network topology is modeled as a network topology structure consisting of nodes, edges, and cycles. Adjacency matrix, degree matrix, and Laplace matrix of the distribution network are generated according to this network topology. The eigenvalues ​​and corresponding eigenvectors of the Laplace matrix are solved, and the smallest non-zero eigenvalue is selected as a resilience index characterizing the mathematical synchronous stability of the distribution network, denoted as the Fiedler value. The eigenvector corresponding to the Fiedler value is denoted as the Fiedler vector. Based on the component differences represented by each adjacent node in the Fiedler vector, the contribution of each edge in the distribution network to the Fiedler value is calculated. Based on the contribution ranking, several key edges with the greatest impact on the resilience of the distribution network are extracted.

3. The distribution network prevention-correction coordinated control method according to claim 2, characterized in that, The network topology is described as an undirected graph. , represented as: (1) in, N ={1,2,..., N G } represents a set of nodes, which in turn represents a bus in a distribution network; V×V represents the edge set, which represents the lines in the distribution network; The formulas for calculating the adjacency matrix A and the degree matrix D are: (2) (3) (4) (5) in, Indicates all N × N The set of real matrices a ij Represents a node i With nodes j The connection relationship, d i Indicates connection to node i The number of sides; The Laplacian matrix L is defined based on the adjacency matrix A and the degree matrix D, and its expression is: (6) The eigenvalues ​​of the Laplace matrix L are arranged in the following order: (7) in, λ 2 represents the smallest non-zero eigenvalue of the Laplace matrix L, i.e., the Fiedler value; According to the theory of complex dynamical networks, the Fiedler value and its corresponding eigenvector satisfy the following: (8) in, Represents the Federer vector. i and j These represent the first and second digits of the Fiedler vector. i row and number j The value of the row; calculate the contribution of the corresponding edge to the Fiedler value based on the differences of each component in the Fiedler vector, and extract the key edges that contribute the most to the Fiedler value, represented as: (9) (10) in, k ij Used for quantizing edges i - j Contribution to Federer's value, E crit Represents the set of key edges. K The number of critical edges. k (K) This represents the 1st position of all candidate edge contributions sorted in descending order. K Large value.

4. The distribution network prevention-correction coordinated control method according to claim 1, characterized in that, The nested solution algorithm, which iteratively solves the prevention-correction coordinated control optimization model through inner and outer layers, outputs the optimal coordinated control strategy, including: The prevention-correction coordinated control optimization model is solved hierarchically. The outer layer uses a swarm intelligence optimization algorithm to search for topology adjustment schemes of the distribution network and passes the generated topology adjustment schemes to the inner layer. Based on the topology adjustment schemes given by the outer layer, the inner layer uses a mathematical programming solver to optimize the remaining prevention control variables and correction control variables, and feeds back the obtained objective function values ​​to the outer layer to update the topology adjustment schemes and iterate until the optimal prevention control strategy and the optimal correction control strategy that meet the convergence conditions are obtained.

5. The distribution network prevention-correction coordinated control method according to claim 4, characterized in that, The prevention and control variables include the purchased electricity volume, curtailed wind and solar power volume, energy storage charging and discharging volume, and the operation of the tie switch before the occurrence of the extreme event; the correction and control variables include the purchased electricity volume, curtailed wind and solar power volume, energy storage charging and discharging volume, the operation of the tie switch, and the load shedding volume after the occurrence of the extreme event.

6. The distribution network prevention-correction coordinated control method according to claim 5, characterized in that, The expression for the objective function is: (11) (12) (13) in, C pre and C cor Let represent the costs of the prevention and control phase and the correction and control phase, respectively, and let S represent the set of all failure scenarios. π s Indicates the fault scenario s The probability of occurrence x Indicates prevention and control variables. y s Indicates the control variable for correction. Represents the set of all correction control variables. Let K represent the mathematical expectation. pre and K cor These represent the action indices in the prevention and control phase and the corrective control phase, respectively. α k and β k These represent the unit control cost coefficients for the prevention and control phase and the correction and control phase, respectively. x k This indicates the control actions during the prevention and control phase. y s,k Indicates the fault scenario s Control actions during the next correction control phase, Denotes the 1-norm. x k,eco This represents a reference value at the economically optimal operating point. and These represent the unit network loss cost during the prevention and control phase and the correction and control phase, respectively. and These represent the allocation coefficients for the prevention and control phase and the correction and control phase, respectively. and These represent the Fiedler value and the fault scenario during the prevention and control phase, respectively. s Fiedler value in the lower correction control phase and These represent the excitation coefficients of the Fiedler value during the preventive control phase and the corrective control phase, respectively. and These represent the network loss and fault scenarios during the prevention and control phase, respectively. s Network loss during the lower correction control phase.

7. The distribution network prevention-correction coordinated control method according to claim 6, characterized in that, The key edge constraint is constructed based on complex dynamic network theory and is expressed as follows: (14) (15) in, To characterize the prevention phase circuit i - j Whether it is a key edge is a binary variable. To characterize the fault scenario s Lower calibration stage line i - j Whether it is a key edge is a binary variable. u ij,s To characterize the fault scenario s Downline i - j A binary variable indicating whether a fault exists.

8. The distribution network prevention-correction coordinated control method according to claim 6, characterized in that, The outer layer uses a swarm intelligence optimization algorithm to search for topology adjustment schemes for the distribution network, and then passes the generated distribution network topology for the prevention control phase and the correction control phase to the inner layer, represented as: (16) in, and These are the distribution network topologies for the prevention and control phase and the correction and control phase, respectively. This represents the initial solution generated by the swarm intelligence optimization algorithm; Based on the given distribution network topology from the outer layer, the inner layer uses a mathematical programming solver to optimize the remaining preventive control variables and corrective control variables, as follows: (17) Where Eqs.(11)-(13) represent the objective functions represented by equations (11) to (13). Indicates the fault scenario s The following is a collection of faulty lines. x i Indicates the first i Prevention and control variables for the next iteration. y s,i Indicates the first i The correction control variable for the next iteration.

9. The distribution network prevention-correction coordinated control method according to claim 1, characterized in that, The constraints also include load shedding constraints, wind curtailment constraints, solar curtailment constraints, power flow constraints, and power balance constraints.

10. A distribution network prevention-correction coordinated control device, characterized in that, include: The preprocessing unit is used to establish a resilience index for the mathematical synchronous stability of the distribution network under extreme events and to extract the critical edges that have a significant impact on the resilience of the distribution network. A modeling unit is used to define preventive control variables and corrective control variables. The preventive control variables characterize preventive control measures before extreme events occur, and the corrective control variables characterize emergency corrective measures after extreme events occur. Based on the anticipated failure scenarios caused by extreme events, an objective function is constructed that maximizes the resilience index and minimizes the overall control cost, where the overall control cost includes preventive control cost and expected corrective control cost. Constraints including key edge constraints are constructed, resulting in a preventive-corrective coordinated control optimization model. The solution unit is used to solve the prevention-correction coordinated control optimization model through inner and outer layer nested solution algorithms, and output the optimal coordinated control strategy to perform prevention-correction coordinated control on the distribution network.

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