Power supply method for distribution network considering distributed photovoltaic cluster division and mobile energy storage coordination

Abstract

The application relates to the technical field of power systems, and particularly discloses a power supply guarantee method for a distribution network considering distributed photovoltaic cluster division and mobile energy storage coordination, which comprises the following steps: in the pre-disaster prevention stage, an improved Louvain algorithm is used for distributed photovoltaic cluster division, a pre-disaster coordinated scheduling model for minimizing load reduction and mobile energy storage configuration cost is established, and the optimal layout node of the mobile energy storage in each cluster is solved through multiple cyclic iterations; in the post-disaster recovery stage, according to the fault line isolation condition and the post-disaster source and load state, photovoltaic clusters are re-divided, a new post-disaster scheduling scheme is formulated for the mobile energy storage, and a post-disaster recovery stage model is constructed based on the re-division result of the photovoltaic clusters. The application has the advantages that through two-stage coordinated optimization of pre-disaster prevention and post-disaster recovery, the dimension reduction advantage of cluster division and the flexibility characteristics of mobile energy storage are utilized to jointly improve the ability of the distribution network to resist extreme disasters.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a distribution network supply guarantee method that considers the division of distributed photovoltaic clusters and the coordination of mobile energy storage. Background Technology

[0002] The large-scale integration of distributed photovoltaic (PV) power into the distribution network presents challenges due to its randomness and volatility, posing both absorption issues and new challenges to power supply assurance during extreme disasters. Recent extreme disasters have demonstrated that improving the resilience of the distribution network under extreme weather conditions is particularly important compared to the transmission network. Existing research typically divides the disaster process into prevention, mitigation, adaptation, and recovery phases, with different operational objectives for each phase. The prevention phase focuses on "reducing the risk of disaster impact," requiring advance deployment of emergency resources (such as mobile energy storage and repair equipment) and optimization of distribution network operation. The mitigation phase focuses on "maintaining core power supply during disasters," prioritizing continuous power supply to critical loads such as hospitals and emergency command centers. The adaptation phase requires "dynamically adjusting operational strategies," optimizing power output and load control schemes in real time based on the disaster's development. The recovery phase aims to "rapidly repair faults and restore power to the entire region," coordinating the pace of fault repair and power restoration. Therefore, how to adapt to the output characteristics of distributed photovoltaic power, break through the limitations of traditional distribution network disaster relief strategies, build a "source-grid-load-storage coordinated" supply guarantee system, and improve the supply guarantee capacity of large-scale distributed photovoltaic power grid access has become a core issue that urgently needs to be addressed in the current distribution network field, and is also a key direction for future energy transition and power security research.

[0003] Existing literature [1] uses the Monte Carlo method to simulate the scenario of power distribution line and traffic road failure interruption during the pre-disaster prevention stage, and constructs a pre-layout model including mobile emergency power charging stations and maintenance stations for maintenance personnel. Existing literature [2] considers the pre-layout of mobile energy storage before disasters in the context of the integration of power grid and transportation network, and carries out multi-dimensional collaborative recovery based on the dynamic scheduling and time-series output characteristics of mobile energy storage, electric vehicles and diesel generators after disasters. Existing literature [3] establishes an optimized configuration model of mobile energy storage from the aspects of economy, vulnerability and capacity after disasters, and realizes emergency power supply recovery under extreme disasters. The above studies show that mobile energy storage devices, due to their flexibility, rapid response and other characteristics, can provide power and energy support for the fault repair of power distribution networks, and have positive and negative regulation functions. They are an important measure to deal with disasters. However, mobile energy storage has high cost, small capacity and the location of the access node will directly affect its role.

[0004] In view of the characteristics of distributed photovoltaic points being numerous, widespread, poor observability, and difficult to operate and manage, the concept of clusters in the academic field can be extended and applied to manage the numerous and geographically dispersed distributed photovoltaics in a cluster manner. Existing literature [4] proposes an evaluation method based on cluster division to address the problems of increased network losses, power backflow, and voltage over-limit caused by the increased penetration rate of distributed photovoltaics in the distribution network. Existing literature [5] proposes a distributed photovoltaic cluster collaborative optimization voltage control strategy, using an improved community algorithm to divide reactive and active power clusters; existing literature [6] proposes a distribution network cluster division strategy that coordinates electric vehicles and distributed photovoltaics, realizing the full absorption of distributed photovoltaics by utilizing the charging flexibility of electric vehicles, and achieving the goal of coordinated operation with the distribution network. All the above studies show that distributed photovoltaic clusters have advantages such as high scalability, decentralized power production, reduced transmission losses, improved grid reliability and robustness. How to use the guidance of effective distributed photovoltaic clusters to improve the degree of fault recovery is an effective measure, but there is a lack of collaborative design with emergency energy storage resources. Existing studies have not established a collaborative mechanism between distributed photovoltaic clusters and emergency resources such as mobile energy storage. Secondly, the dynamic changes in the distribution network topology are not connected. After a fault, the distribution network topology will change significantly due to line isolation and fault clearing. However, the existing cluster division is mostly based on a fixed topology structure and lacks dynamic reorganization capability.

[0005] Related literature:

[0006] [1] Kong Huiwen, Ma Jing, Cheng Peng, et al. Two-stage fault recovery strategy for distribution system resilience based on disaster scenario prediction [J]. Power System Technology, 2024, 48(09):3812-3821

[0007] [2] Wang Yuehan, Liu Wenxia, ​​Yao Qi, et al. Pre-deployment and dynamic dispatch strategy of mobile energy storage for improving the resilience of distribution networks [J]. Automation of Electric Power Systems, 2022, 46(15):37-45.

[0008] [3] Liu Yongmei, Wu Ming, Li Ying, et al. Strategies for improving the disaster resistance of distribution networks considering mobile energy storage configuration and dispatch [J / OL]. China Electric Power, 1-13 [2025-10-03]

[0009] [4] Li Yan, Lü Nanjun, Liu Xuetao. A Method for Evaluating the Output of Distributed Photovoltaic Clusters Considering New Energy Consumption and Grid Loss [J]. Electric Power Construction, 2022, Vol. 43 No. 10

[0010] [5] Ge Jinming, Liu Yingru, Pang Dan, et al. Cluster partitioning voltage control strategy for photovoltaic distribution networks with high penetration rate [J], High Voltage Engineering, January 31, 2024, Vol. 50, No. 1: 74-82

[0011] [6] Chen Kai, Wang Jinggang, Wang Hui, et al. Considering the distribution network cluster division and operation scheduling strategy of electric vehicle and distributed photovoltaic coordination [J] Southern Power Grid Technology 2024(18):1-9. Summary of the Invention

[0012] The purpose of this invention is to overcome the shortcomings of the prior art and provide a distribution network supply guarantee method that considers the division of distributed photovoltaic clusters and the coordination of mobile energy storage.

[0013] The objective of this invention is achieved through the following technical solution: a distribution network supply guarantee method considering the division of distributed photovoltaic clusters and the coordination of mobile energy storage, the method comprising,

[0014] In the pre-disaster prevention phase, an improved Louvain algorithm is used to divide distributed photovoltaic clusters, so that the photovoltaic output within the cluster is highly matched with the load demand. Based on the cluster division, a pre-disaster collaborative scheduling model is established to minimize the load reduction and mobile energy storage configuration cost. Through multiple iterations, the optimal layout nodes of mobile energy storage within each cluster are solved.

[0015] During the post-disaster recovery phase, based on the isolation status of faulty lines and the post-disaster source-load status, the photovoltaic clusters are re-divided with the goal of minimizing the reduction in supply load, and a new post-disaster dispatch scheme is formulated for mobile energy storage. Based on the results of the photovoltaic cluster re-division, the spatiotemporal output allocation of mobile energy storage among the clusters is optimized. A post-disaster recovery phase model is constructed with the goal of minimizing load reduction, and the access location, charging and discharging power, and dispatch path of mobile energy storage in each time period are solved.

[0016] Specifically, the method of using the improved Louvain algorithm for distributed photovoltaic cluster partitioning includes:

[0017] According to the traditional Louvain algorithm, the modularity index is as follows:

[0018] (1)

[0019] In the formula, For nodes With nodes Connection weights; For nodes The sum of the weights of all connected edges; For nodes The sum of the weights of all connected edges; This represents the total network weight. For indicator functions, if node and If they belong to the same cluster, the value is 1; otherwise, it is 0.

[0020] The improved modularity metrics are as follows:

[0021] (2)

[0022] In the formula, For nodes With nodes Electrical distance parameters between them; This is a voltage sensitivity parameter used to characterize the magnitude of the voltage amplitude change at one node caused by a change in power injection at another node. and These are reactive power support and active power support, which together serve as indicators of flexibility support. These are the weighting coefficients for each indicator.

[0023] Specifically, the objective function of the pre-disaster collaborative scheduling model is:

[0024] (3)

[0025] In the formula, Assigned variables for mobile energy storage; For branch switching decision variables; Contribute to distributed photovoltaic power The set of uncertainties; To minimize the system operating cost given the worst-case distributed photovoltaic power output scenario and outer decision variables; Cost per unit of mobile energy storage configuration; For mobile energy storage pre-deployment decision variables; For nodes The weight of load reduction costs; This is the system's reference power. , , , , , , , They are nodes Active power reduction, reactive power reduction, active power output, reactive power output, branch Active current, reactive current, and nodes voltage, branch The current.

[0026] Specifically, the constraints of the pre-disaster collaborative scheduling model include:

[0027] Pre-deployment constraints of mobile energy storage within the cluster:

[0028] (4)

[0029] (5)

[0030] (6)

[0031] (7)

[0032] (8)

[0033] (9)

[0034] (10)

[0035] In the formula, For the first A set of branches within a cluster; For all cluster sets; branch road State variables; This represents the percentage of branches that are allowed to disconnect within the cluster, with a value between 0 and 1. For mobile energy storage at nodes Pre-layout decision variables; For clusters The set of all nodes contained therein; This is the sum of the number of mobile energy storage units pre-deployed for the entire system; The upper limit for the number of mobile energy storage units to be configured is predetermined; This is a charging indicator; For discharge identification; and These are the actual charging and discharging power of the mobile energy storage, respectively. For clusters exist The dynamic deployment of mobile energy storage is a key variable. and These are the upper limits for charging and discharging of mobile energy storage and the charging power; This is the system's reference power. The active power output of the photovoltaic system within cluster c at time t; For the active load within cluster c;

[0036] Uncertainty constraints in photovoltaics:

[0037] (11)

[0038] (12)

[0039] In the formula, It has made actual contributions to photovoltaic power generation; This results in actual reactive power output from photovoltaic systems. Forecast value of photovoltaic power output; The uncertainty is... The set of uncertainties for distributed photovoltaic power output; and These are the maximum and minimum power factors of the photovoltaic inverter, respectively.

[0040] Load reduction constraints:

[0041] (13)

[0042] In the formula, For nodes The reduction in active power load; For nodes Active load; For nodes The amount of reactive load reduction; For nodes Existing reactive load;

[0043] Radial topology constraints of distribution networks:

[0044] (14)

[0045] (15)

[0046] (16)

[0047] In the formula, For distribution network branch collection; The total number of nodes; branch road State variables; This refers to the number of isolated islands. Virtually inject power into the nodes; For the node The collection of the endpoints of the outflowing branch roads; For the node The set of originating branches of the inflow; It is a set of nodes containing distributed power sources; For branch virtual power flow; For nodes To the node Virtual power flow; For nodes; It is the root node; Used as a 0-1 variable flag for virtual power supply; It is a constant;

[0048] Power flow safety operation constraints:

[0049] (17)

[0050] (18)

[0051] (19)

[0052] (20)

[0053] (twenty one)

[0054] (twenty two)

[0055] (twenty three)

[0056] In the formula, and Branch roads The equivalent resistance and reactance; and Branch roads The active power and reactive power transmitted; For nodes The active power output of mobile energy storage; For nodes Reactive power output of mobile energy storage; node Original reactive load; For nodes The square of the voltage amplitude; For nodes The square of the voltage amplitude; branch road The square term of the steady-state current RMS value;

[0057] (twenty four)

[0058] In the formula, The relaxation coefficient;

[0059] Transform equation (23) into a second-order cone model:

[0060] (25).

[0061] Specifically, the objective function of the post-disaster recovery phase model is:

[0062] (26)

[0063] In the formula, This is a set of fault recovery periods; This represents the total number of clusters after dynamic repartitioning. and Clusters Cost reduction in critical / regular load units within the organization; and For clusters During the period Power reduction for critical / non-critical loads.

[0064] Specifically, the constraints of the post-disaster recovery phase model include:

[0065] Temporal and spatial constraints of mobile energy storage:

[0066] (27)

[0067] (28)

[0068] (29)

[0069] (30)

[0070] In the formula, A 0-1 variable representing mobile energy storage During the period Access Cluster ; For the isolated island The collection of clusters included; It is a collection of mobile energy storage devices, representing the scope of all mobile energy storage individuals participating in the dispatch; It is a time set that covers all time ranges involved in the scheduling; For nodes The other node is used to describe the movement of mobile energy storage between different nodes; The threshold for cross-island movement time; For the first Taiwan Mobile Energy Storage The actual energy storage capacity; For the charging and discharging efficiency of mobile energy storage; , These are the minimum and maximum allowable energy storage capacities for mobile energy storage, respectively. This is the system's reference power.

[0071] Photovoltaic output constraints:

[0072] (31)

[0073] In the formula, and They are nodes The active and reactive power outputs of distributed photovoltaic systems; and They are nodes The maximum active and reactive power capacity of the distributed photovoltaic system;

[0074] Power balance constraints:

[0075] (32)

[0076] (33)

[0077] In the formula, For the distributed photovoltaic active power output of cluster c at time t; Let m be the active power of the mobile energy storage device at time t. The active power of charging mobile energy storage m at time t; Net active power output for mobile energy storage across all clusters; Let be the active power of the electric vehicle during discharge at time t; The active power for charging the electric vehicle at time t; Let be the active load of cluster c at time t; The amount of active power reduction in cluster c at time t; The first one formed after the disaster An isolated island.

[0078] Specifically, the solution method for the pre-disaster collaborative scheduling model is to use the column constraint generation algorithm C&CG to decompose the original problem into a main problem and sub-problems, approximate the optimal solution through iterative solution, and introduce a dynamic cluster update mechanism to re-divide the photovoltaic clusters based on the current network topology after each iteration.

[0079] The compact form of the original problem is as follows:

[0080] (34)

[0081] In the formula, variables Including mobile energy storage deployment variables Branch switching decision variables ;variable Including photovoltaic power output variables ;variable include Inner layer control variables; Uncertain set of power output for photovoltaics The feasible region of the variable; Variables in the objective function The coefficient vector; Variables in the objective function The coefficient vector; This is the constraint matrix; To constrain the right-hand vector, it is usually the upper limit of the system state; For the i-th constraint, regarding The coefficient matrix is ​​used to construct " "Joint vector expression, For the target vector, This represents the maximum permissible deviation from the target state.

[0082] The main problem is the pre-deployment optimization of mobile energy storage under a given cluster partitioning:

[0083] (35)

[0084] In the formula, These are slack variables; This refers to the current iteration round; For the first The candidate solutions for the inner control variables generated in the next iteration; after solving the main problem, the optimal mobile energy storage layout for the current iteration is obtained. lower bound of the objective function ;

[0085] The subproblem is a given mobile energy storage layout. Search for the worst-case photovoltaic scenario:

[0086] (36)

[0087] In the formula, For nodes The weight of load reduction costs; node The amount of active power reduction; This is the system's reference power. The set of all nodes in the system;

[0088] Define Lagrange multipliers λ, μ, The dual form of the subproblem is:

[0089] (37)

[0090] In the formula, For the set of uncertainties in photovoltaic power output; Uncertainty set for photovoltaic power output; Lagrange multipliers Used for dual transformation, it introduces the constraints of the original problem into the objective function; This is a coefficient matrix that describes the relationship between mobile energy storage layout, photovoltaic output, and system status. This serves as a reference vector for system status, load, and other related parameters. Correspondence with The relevant constraint right-hand vector; Let be the coefficient matrix, and connect the Lagrange multipliers to the coefficients of the objective function of the original problem in the dual constraints. ; for The 2-norm of the Lagrange multiplier restricts the size of the Lagrange multiplier to ensure the boundedness of the dual problem; To constrain the quantity; these factors work together to achieve solvability of the problem and ensure optimal scheduling of the system under the scenario of "mobile energy storage deployment - photovoltaic output fluctuation".

[0091] Introducing binary variables Photovoltaic power output is expressed as:

[0092] (38)

[0093] Introducing auxiliary variables The bilinear terms are transformed into linear constraints through Big-M relaxation:

[0094] (39)

[0095] Description of the The degree of correlation between the photovoltaic system and other parts of the system; In order to be with the first The Lagrange multipliers associated with each photovoltaic unit reflect the marginal impact of the photovoltaic output on the system optimization objective;

[0096] After solving the subproblems, the worst-case photovoltaic scenario is obtained. optimal value of subproblems And update the upper bound of the objective function. ,like If the iteration converges, then the problem is solved; otherwise, a cut constraint needs to be added to the main problem to proceed to the next iteration.

[0097] Specifically, after each iteration of the column constraint generation algorithm C&CG, the improved Louvain algorithm is re-executed based on the current network topology to update the cluster structure. The specific steps are as follows:

[0098] From the optimal solution of the main problem Extracting branch switching status Construct the distribution network topology for the current iteration. ;

[0099] Based on topology Recalculate electrical distance index Voltage sensitivity index Reactive power support indicators Active support indicators ;

[0100] Adopting an improved modularity index Perform cluster repartitioning, if and If the algorithm converges, it will output the optimal cluster partition. With mobile energy storage deployment Otherwise, according to Update constraints (4)-(6).

[0101] The present invention has the following advantages:

[0102] 1. The pre-disaster collaborative scheduling model of the present invention takes into account both the electrical structure and supply balance capability within the distributed photovoltaic cluster, reduces the risk of supply operation caused by photovoltaic fluctuations, and makes more adequate and economical preparations for post-disaster supply.

[0103] 2. The coordinated optimization of cluster re-partitioning and cross-cluster rescheduling of mobile energy storage during the recovery phase enables optimal allocation of electrical energy in the spatiotemporal dimensions, significantly improving the load recovery effect and resource utilization efficiency of the distribution network. The constructed mechanism of maximizing supply within the cluster and optimizing supply support between clusters effectively solves the defects of "local priority and global imbalance" in node-level scheduling, and greatly improves the utilization efficiency of distributed photovoltaic power.

[0104] 3. The distributed photovoltaic cluster partitioning method based on the improved Louvain algorithm can effectively reduce the dimensionality of the solution and improve the solution efficiency. Furthermore, it maximizes the supply guarantee capacity within the cluster for the prevention and recovery phases, significantly reducing load shedding losses and improving the supply guarantee capacity for critical loads. Attached Figure Description

[0105] Fig. 1 This is a diagram illustrating the supply guarantee framework of the present invention, which integrates cluster partitioning and mobile energy storage coordination.

[0106] Fig. 2 This is a schematic diagram of the solution process for the pre-disaster collaborative scheduling model of the present invention. Detailed Implementation

[0107] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described embodiments are merely some embodiments of the invention, and not all embodiments. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0108] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0109] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0110] The present invention will be further described below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0111] like Figs. 1-2 As shown, a distribution network supply guarantee method considering the division of distributed photovoltaic clusters and the coordination of mobile energy storage is proposed. This method includes,

[0112] In the pre-disaster prevention phase, the core logic is "distributed photovoltaic cluster partitioning and mobile energy storage working together." This phase aims to improve the coordination and matching between photovoltaic power generation and load, and to address the impact of photovoltaic output uncertainty on supply stability. It maximizes the power grid's supply capacity before extreme disasters by optimizing the pre-deployment cost of mobile energy storage. Specifically, an improved Louvain algorithm is used for distributed photovoltaic cluster partitioning, ensuring a high degree of matching between photovoltaic output and load demand within the cluster. This balances the cluster's electrical structure and power supply capacity, improves the tightness of supply coupling within the cluster, and lays the foundation for the precise deployment of mobile energy storage within the cluster. To address the uncertainty of photovoltaic output, a robust optimization algorithm is used to optimize the pre-deployment of mobile energy storage based on cluster partitioning. A pre-disaster collaborative scheduling model is established to minimize load reduction and mobile energy storage configuration costs. Through multiple iterations, the optimal deployment nodes for mobile energy storage within each cluster are determined. This ensures that mobile energy storage efficiently supports the cluster load under the worst-case photovoltaic output conditions, achieving the collaborative supply guarantee goal of cluster partitioning and mobile energy storage deployment.

[0113] Distribution networks containing large-scale distributed photovoltaic (PV) power exhibit complex characteristics, evolving from dual-source power supply to multi-source power supply. The addition of mobile energy storage further increases the system's complexity and flexibility. To reduce computational complexity, this invention employs an improved Louvain algorithm for PV cluster partitioning, specifically including:

[0114] According to the traditional Louvain algorithm, the modularity metric is as follows:

[0115] (1)

[0116] In the formula, For nodes With nodes Connection weights; For nodes The sum of the weights of all connected edges; For nodes The sum of the weights of all connected edges; This represents the total network weight. For indicator functions, if node and If they belong to the same cluster, the value is 1; otherwise, it is 0.

[0117] To account for the impact of distributed photovoltaic (PV) grid connection on operational status, voltage sensitivity, reactive power support, and active power support indicators are further incorporated into the modularity calculation. Therefore, the improved modularity indicators are as follows:

[0118] (2)

[0119] In the formula, For nodes With nodes Electrical distance parameters between them; This is a voltage sensitivity parameter used to characterize the magnitude of the voltage amplitude change at one node caused by a change in power injection at another node. and These are reactive power support and active power support, which together serve as indicators of flexibility support. These are the weighting coefficients for each indicator. For the specific calculation of each indicator, please refer to "Multi-objective Clustering and Voltage Coordination Control of Distribution Network Based on Improved Louvain and BAAM-ADMM", High Voltage Engineering, Vol. 50, No. 1, January 31, 2024.

[0120] During the pre-disaster preparedness phase, the improved Louvain algorithm is used for cluster partitioning to enhance source-load matching within the clusters. Secondly, a pre-disaster collaborative scheduling model is established to minimize both mobile energy storage configuration costs and load reduction costs. This model solves for the optimal cluster partitioning scheme and the collaborative scheme of mobile energy storage pre-deployment, maximizing pre-disaster power supply capacity. The objective function of the pre-disaster collaborative scheduling model is:

[0121] (3)

[0122] In the formula, Assigned variables for mobile energy storage; For branch road switching decision variables; Contribute to distributed photovoltaic power The set of uncertainties; To minimize the system operating cost given the worst-case distributed photovoltaic power output scenario and outer decision variables; Cost per unit of mobile energy storage configuration; For mobile energy storage pre-deployment decision variables; For nodes The weight of load reduction costs; This is the system's reference power. , , , , , , , They are nodes Active power reduction, reactive power reduction, active power output, reactive power output, branch Active current, reactive current, and nodes voltage, branch Current; outer layer Optimize mobile energy storage attribution variables Branch road switching decision variables Minimize the decision-making level cost of the system; middle level For distributed photovoltaic power output Uncertainty set Select the photovoltaic output scenario most unfavorable to the system to ensure the robustness of the strategy under extreme conditions; inner layer To minimize the system operating cost under a given worst-case distributed photovoltaic power output scenario and outer decision variables.

[0123] The constraints of the pre-disaster collaborative scheduling model include:

[0124] Pre-deployment constraints of mobile energy storage within the cluster:

[0125] (4)

[0126] (5)

[0127] (6)

[0128] (7)

[0129] (8)

[0130] (9)

[0131] (10)

[0132] In the formula, For the first A set of branches within a cluster; For all cluster sets; branch road State variables; This represents the percentage of branches that are allowed to disconnect within the cluster, with a value between 0 and 1. For mobile energy storage at nodes Pre-layout decision variables; For clusters The set of all nodes contained therein; This is the sum of the number of mobile energy storage units pre-deployed for the entire system; The upper limit for the number of mobile energy storage units to be configured is predetermined; This is a charging indicator; For discharge identification; and These are the actual charging and discharging power of the mobile energy storage, respectively. For clusters exist The dynamic deployment of mobile energy storage is a key variable. and These are the upper limits for charging and discharging of mobile energy storage and the charging power; This is the system's baseline power. This constraint means that mobile energy storage can only be in a charging or discharging state at any given time, and the power should be less than its upper limit. The active power output of the photovoltaic system within cluster c at time t; For the active load within cluster c, For the mobile energy storage within cluster c, this constraint ensures that the mobile energy storage aims for self-balancing supply within the cluster during pre-disaster deployment, thus finding the optimal cluster; Equation (4) is the topological connectivity constraint within the cluster, which ensures that during the iteration of cluster partitioning and robust optimization, the cluster is prevented from becoming multiple isolated sub-networks due to excessive splitting, thereby improving the supply capacity within the cluster; Equations (5) and (6) are the pre-deployment constraints of mobile energy storage within the cluster, for any cluster The sum of the decision variables for mobile energy storage configuration across all nodes within the cluster does not exceed 1, meaning each cluster can be configured with at most one mobile energy storage unit, and the total number of mobile energy storage units configured is limited. It should be equal to the predetermined upper limit of quantity. Equations (7)-(9) are the charging and discharging constraints for mobile energy storage; Equation (10) is the power constraint within the cluster.

[0133] Photovoltaic uncertainty constraints: Photovoltaic output is affected by natural factors such as light intensity and ambient temperature, and there is significant uncertainty. Its fluctuations will directly affect the robustness of pre-disaster layout plans. The range of fluctuations is quantified by the box uncertainty set.

[0134] (11)

[0135] (12)

[0136] In the formula, It has made actual contributions to photovoltaic power generation; This results in actual reactive power output from photovoltaic systems. Forecast value of photovoltaic power output; The uncertainty is... It represents the set of uncertainties in distributed photovoltaic power output, covering the worst-case scenarios of power output fluctuations; and These are the maximum and minimum power factors of the photovoltaic inverter, respectively.

[0137] Load reduction constraints:

[0138] (13)

[0139] In the formula, For nodes The reduction in active power load; For nodes Active load; node Active load reduction It should not exceed the original active power load of the node. ; For nodes The amount of reactive load reduction; For nodes Existing reactive load;

[0140] The radial topology constraint of the distribution network is addressed by employing the Virtual Power Flow method to ensure that the reconstructed network meets the radial operation requirements, allowing for the formation of multiple islands, and relaxing nonlinear constraints using the Big-M method.

[0141] (14)

[0142] (15)

[0143] (16)

[0144] In the formula, For distribution network branch collection; The total number of nodes; branch road State variables; The constraint, which determines the number of isolated nodes, ensures that the total number of operational branches equals the total number of nodes minus the number of isolated nodes. Virtually inject power into the nodes; For the node The collection of the endpoints of the outflowing branch roads; For the node The set of originating branches of the inflow; It is a set of nodes containing distributed power sources; For branch virtual power flow; For nodes To the node Virtual power flow; For nodes; It is the root node; Used as a 0-1 variable flag for virtual power supply; As a sufficiently large constant, this constraint defines the virtual power flow and virtual power injection power at nodes, enabling power to flow from the root node or distributed power source to the load, thereby ensuring the power flow operation logic of the radial topology after the distribution network is reconfigured.

[0145] To address power flow safety constraints, considering the topology dynamics caused by feeder switch state changes during network reconfiguration, a large-M relaxation technique is introduced to linearize the nonlinear voltage constraints. The constraints are as follows:

[0146] (17)

[0147] (18)

[0148] (19)

[0149] (20)

[0150] (twenty one)

[0151] (twenty two)

[0152] (twenty three)

[0153] In the formula, and Branch roads The equivalent resistance and reactance; and Branch roads The active power and reactive power transmitted; For nodes The active power output of mobile energy storage; For nodes Reactive power output of mobile energy storage; node Original reactive load; For nodes The allowable fluctuation range of the squared voltage amplitude term is determined by... and Common definition; For nodes The square of the voltage amplitude; branch road The maximum permissible value of the square term of the steady-state current RMS value is controlled by... Equations (19) and (20) introduce relaxation coefficients. A linearized model of the nonlinear voltage drop constraint was achieved. Theoretically, this parameter must satisfy:

[0154] (twenty four)

[0155] In the formula, The relaxation coefficient;

[0156] Since the relationship between voltage, current and power in equation (23) is nonlinear, it is usually transformed into a second-order cone model through the second-order cone method for ease of solution:

[0157] (25).

[0158] During the post-disaster recovery phase, based on the isolation status of faulty lines and the post-disaster source-load status, the photovoltaic clusters are re-divided with the goal of minimizing the reduction in supply load, and a new post-disaster dispatch scheme is formulated for mobile energy storage. Based on the results of the photovoltaic cluster re-division, the spatiotemporal output allocation of mobile energy storage among the clusters is optimized. A post-disaster recovery phase model is constructed with the goal of minimizing load reduction, and the access location, charging and discharging power, and dispatch path of mobile energy storage in each time period are solved to achieve rapid load recovery.

[0159] The objective function of the post-disaster recovery phase model is:

[0160] (26)

[0161] In the formula, This is a set of fault recovery periods; This represents the total number of clusters after dynamic repartitioning. and Clusters Cost reduction in critical / regular load units within the organization; and For clusters During the period Power reduction for critical / non-critical loads.

[0162] The constraints of the post-disaster recovery phase model include:

[0163] Considering that each mobile energy storage device can only belong to one cluster in each time period, the temporal and spatial scheduling constraints of mobile energy storage are as follows:

[0164] (27)

[0165] (28)

[0166] The state of charge (SOC) of mobile energy storage should fluctuate within a safe range:

[0167] (29)

[0168] (30)

[0169] In the formula, A 0-1 variable representing mobile energy storage During the period Access Cluster ; For the isolated island The collection of clusters included; It is a collection of mobile energy storage devices, representing the scope of all mobile energy storage individuals participating in the dispatch; It is a time set that covers all time ranges involved in the scheduling; For nodes The other node is used to describe the movement of mobile energy storage between different nodes; As a threshold for cross-island movement time, this constraint ensures that mobile energy storage cannot appear in two different clusters simultaneously before the transfer cycle is completed; For the first Taiwan Mobile Energy Storage The actual energy storage capacity; For the charging and discharging efficiency of mobile energy storage; , These are the minimum and maximum allowable energy storage capacities for mobile energy storage, respectively. The system reference power is given by equation (29). Equation (29) indicates that the energy storage capacity of mobile energy storage at time t is determined by the capacity at the previous time, the energy gain during charging, and the energy loss during discharging. Equation (30) constrains the actual energy storage capacity of mobile energy storage within a safe range through normalization. Finally, the charging and discharging power constraints of mobile energy storage are detailed in the pre-disaster constraints section.

[0170] Photovoltaic output constraints:

[0171] (31)

[0172] In the formula, and They are nodes The active and reactive power outputs of distributed photovoltaic systems; and They are nodes The maximum active and reactive power capacity of distributed photovoltaic systems;

[0173] Power balance constraints exist in a fault state where the distribution network is divided into multiple islands, each of which must satisfy power balance constraints. Furthermore, to ensure source-load balance within each cluster of an island and reduce reliance on power support between clusters, the mathematical expression for the constraints is as follows:

[0174] (32)

[0175] (33)

[0176] In the formula, For the distributed photovoltaic active power output of cluster c at time t; Let m be the active power of the mobile energy storage device at time t. The active power of charging mobile energy storage m at time t; Net active power output for mobile energy storage across all clusters; Let be the active power of the electric vehicle during discharge at time t; The active power for charging the electric vehicle at time t; Let be the active load of cluster c at time t; The amount of active power reduction in cluster c at time t; The first one formed after the disaster An isolated island; the same applies to reactive power balance constraints.

[0177] The constraints of the post-disaster recovery phase model also include power flow constraints and load reduction constraints; the constraints of electric vehicle charging and discharging and capacity are the same as those of mobile energy storage, which are the same as those of pre-disaster constraints (17)-(23) and (13).

[0178] The pre-disaster collaborative scheduling model formulas (3)-(25) are pre-disaster collaborative scheduling models with a three-layer structure of “min–max–min”, and the decision variables include integer variables and continuous variables, making direct solution difficult. In addition, the division result of photovoltaic clusters will directly affect the pre-layout of mobile energy storage, and the network reconstruction in robust optimization may change the electrical boundary of the cluster, requiring dynamic adjustment of the cluster structure; the solution method of the pre-disaster collaborative scheduling model is to use the column constraint generation algorithm C&CG to decompose the original problem into a main problem and sub-problems, and to approach the optimal solution through iterative solution, and to introduce a dynamic cluster update mechanism to re-divide the photovoltaic clusters based on the current network topology after each iteration;

[0179] The compact form of the original problem is as follows:

[0180] (34)

[0181] In the formula, variables Including mobile energy storage deployment variables Branch switching decision variables ;variable Including photovoltaic power output variables ;variable include Inner layer control variables; Uncertain set of power output for photovoltaics The feasible region of the variable; Variables in the objective function The coefficient vector; Variables in the objective function The coefficient vector; This is the constraint matrix; To constrain the right-hand vector, it is usually the upper limit of the system state; matrix This includes the deployment range of mobile energy storage and the logical constraints on branch switching; vector Corresponding to the upper limit values ​​of various indicators of mobile energy storage; Corresponding to and The joint constraint matrix characterizes the mutual influence between the two; vector This mainly includes the coupling constraints of "mobile energy storage layout - inner layer control variables"; For the i-th constraint, regarding The coefficient matrix is ​​used to construct " "Joint vector expression, Characteristic variables The impact on the system Characteristic variables The impact on the system; For the target vector, This represents the maximum permissible deviation from the target state.

[0182] The main problem is the pre-layout optimization of mobile energy storage under a given cluster partition, which is essentially a mixed-integer second-order cone programming problem (MISOCP) that can be solved directly using commercial solvers. Its core is to fix the current cluster structure. In the scenario of photovoltaic output prediction, the goal is to minimize the configuration cost and load shedding cost of mobile energy storage while satisfying cluster, topology, and power flow constraints, as shown in the following equation:

[0183] (35)

[0184] In the formula, These are slack variables, representing the upper bound of the objective function; This refers to the current iteration round; For the first The candidate solutions for the inner control variables generated in the next iteration; after solving the main problem, the optimal mobile energy storage layout for the current iteration is obtained. lower bound of the objective function ;

[0185] The subproblem is a given mobile energy storage layout. The worst-case photovoltaic scenario search is as follows; the core is to verify the robustness of the solution to the main problem, that is, in the uncertain set of photovoltaic output. In the process, we will seek out the extreme scenarios that maximize the cost of ensuring system supply. ;

[0186] (36)

[0187] In the formula, For nodes The weight of load reduction costs; node The amount of active power reduction; This is the system's reference power. The set of all nodes in the system;

[0188] inner layer of the subproblem Applying Lagrange duality theory, the problem is transformed from a three-level nested problem into a two-level optimization problem, eliminating the inner-level minimization. Lagrange multipliers λ, μ, and μ are defined. The dual form of the subproblem is:

[0189] (37)

[0190] In the formula, For the set of uncertainties in photovoltaic output, satisfying equations (11) and (12); Lagrange multipliers Used for dual transformation, it introduces the constraints of the original problem into the objective function; The coefficient matrix, the matrix Describe the relationship between mobile energy storage deployment and system state, in a matrix. Describe the relationship between photovoltaic power output and system status; This serves as a reference vector for system status, load, and other related parameters. Correspondence with The relevant constraint right-hand vector; Let be the coefficient matrix, and connect the Lagrange multipliers to the coefficients of the objective function of the original problem in the dual constraints. ; for The 2-norm of the Lagrange multiplier restricts the size of the Lagrange multiplier to ensure the boundedness of the dual problem; To constrain the quantity;

[0191] The objective function of the subproblem includes photovoltaic output. Non-convex bilinear terms with Lagrange multiplier λ Linearization is achieved through binary variable indication and big-M relaxation; binary variables are introduced. Photovoltaic power output is expressed as:

[0192] (38)

[0193] Introducing auxiliary variables The bilinear terms are transformed into linear constraints through Big-M relaxation:

[0194] (39)

[0195] In the formula, Description of the The degree of correlation between the photovoltaic system and other parts of the system. In order to be with the first Lagrange multipliers associated with a photovoltaic unit;

[0196] After solving the subproblems, the worst-case photovoltaic scenario is obtained. optimal value of subproblems And update the upper bound of the objective function. ,like If the iteration converges, then the problem is solved; otherwise, a cut constraint needs to be added to the main problem to proceed to the next iteration.

[0197] After each iteration of the column constraint generation algorithm C&CG, the improved Louvain algorithm is re-executed based on the current network topology to update the cluster structure. The specific steps are as follows:

[0198] From the optimal solution of the main problem Extracting branch switching status Construct the distribution network topology for the current iteration. ;

[0199] Based on topology Recalculate electrical distance index Voltage sensitivity index Reactive power support indicators Active support indicators ;

[0200] Adopting an improved modularity index Perform cluster repartitioning, if and If the algorithm converges, it will output the optimal cluster partition. With mobile energy storage deployment Otherwise, according to Update constraints (4)-(6).

[0201] The post-disaster recovery phase model is a multi-period mixed integer linear programming (MILP) model. The objective is to minimize the load reduction across all time periods, with constraints covering factors such as the time-spacing of mobile energy storage, power balance between clusters and islands, and power flow security. During the solution process, the photovoltaic cluster is first re-partitioned based on the post-disaster fault topology and source / load states. Then, the model is transformed into a standard MILP form and solved directly using the CPLEX solver.

[0202] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any person skilled in the art can make many possible variations and modifications to the technical solution of the present invention, or modify it into equivalent embodiments, without departing from the scope of the present invention. Therefore, any modifications, equivalent changes, and alterations made to the above embodiments based on the technology of the present invention without departing from the scope of the present invention are within the protection scope of the present invention.

Claims

1. A distribution network supply guarantee method considering the division of distributed photovoltaic clusters and the coordination of mobile energy storage, characterized in that: The method includes, In the pre-disaster prevention phase, an improved Louvain algorithm is used to divide distributed photovoltaic clusters, so that the photovoltaic output within the cluster is highly matched with the load demand. Based on the cluster division, a pre-disaster collaborative scheduling model is established to minimize the load reduction and mobile energy storage configuration cost. Through multiple iterations, the optimal layout nodes of mobile energy storage within each cluster are solved. The method of using the improved Louvain algorithm for distributed photovoltaic cluster partitioning includes: According to the traditional Louvain algorithm, the modularity index is as follows: （1） In the formula, For nodes With nodes Connection weights; For nodes The sum of the weights of all connected edges; For nodes The sum of the weights of all connected edges; This represents the total network weight. For indicator functions, if node and If they belong to the same cluster, the value is 1; otherwise, it is 0. The improved modularity metrics are as follows: （2） In the formula, For nodes With nodes Electrical distance parameters between them; This is a voltage sensitivity parameter used to characterize the magnitude of the voltage amplitude change at one node caused by a change in power injection at another node. and These are reactive power support and active power support, which together serve as indicators of flexibility support. These are the weighting coefficients for each indicator; The objective function of the pre-disaster collaborative scheduling model is: （3） In the formula, Assigned variables for mobile energy storage; For branch road switching decision variables; Contribute to distributed photovoltaic power The set of uncertainties; To minimize the system operating cost given the worst-case distributed photovoltaic power output scenario and outer decision variables; Cost per unit of mobile energy storage configuration; For mobile energy storage pre-deployment decision variables; For nodes The weight of load reduction costs; This is the system's reference power. , , , , , , , They are nodes Active power reduction, reactive power reduction, active power output, reactive power output, branch Active current, reactive current, and nodes voltage, branch The current; During the post-disaster recovery phase, based on the isolation status of faulty lines and the post-disaster source-load status, the photovoltaic clusters are re-divided with the goal of minimizing the reduction in supply load, and a new post-disaster dispatch scheme is formulated for mobile energy storage. Based on the results of the photovoltaic cluster re-division, the spatiotemporal output allocation of mobile energy storage among the clusters is optimized. A post-disaster recovery phase model is constructed with the goal of minimizing load reduction, and the access location, charging and discharging power, and dispatch path of mobile energy storage in each time period are solved.

2. The distribution network supply guarantee method considering distributed photovoltaic cluster division and mobile energy storage coordination according to claim 1, characterized in that: The constraints of the pre-disaster collaborative scheduling model include: Pre-deployment constraints of mobile energy storage within the cluster: （4） （5） （6） （7） （8） （9） （10） In the formula, For the first A set of branches within a cluster; For all cluster sets; branch road State variables; This represents the percentage of branches that are allowed to disconnect within the cluster, with a value between 0 and 1. For mobile energy storage at nodes Pre-layout decision variables; For cluster The set of all nodes contained therein; This is the sum of the number of mobile energy storage units pre-deployed for the entire system; The upper limit of the number of mobile energy storage units to be configured is predetermined; This is a charging indicator; For discharge identification; and These are the actual charging and discharging power of the mobile energy storage, respectively. For cluster exist The dynamic deployment of mobile energy storage is a key variable. and These are the upper limits for charging and discharging of mobile energy storage and the charging power; This is the system's reference power. The active power output of the photovoltaic system within cluster c at time t; For the active load within cluster c; Uncertainty constraints in photovoltaics: （11） （12） In the formula, It has made actual contributions to photovoltaic power generation; This results in actual reactive power output from photovoltaic systems. Forecast value of photovoltaic power output; For uncertainty; The set of uncertainties for distributed photovoltaic power output; and These are the maximum and minimum power factors of the photovoltaic inverter, respectively. Load reduction constraints: （13） In the formula, For nodes The reduction in active power load; For nodes Active load; For nodes The amount of reactive load reduction; For nodes Existing reactive load; Radial topology constraints of distribution networks: （14） （15） （16） In the formula, For distribution network branch collection; The total number of nodes; branch road State variables; This refers to the number of isolated islands. Virtually inject power into the nodes; For the node The collection of the endpoints of the outflowing branch roads; For the node The set of originating branches of the inflow; It is a set of nodes containing distributed power sources; For nodes To the node Virtual power flow; For nodes To the node Virtual power flow; For nodes; It is the root node; Used as a 0-1 variable flag for virtual power supply; It is a constant; Power flow safety operation constraints: （17） （18） （19） （20） （21） （22） （23） In the formula, and Branch roads The equivalent resistance and reactance; and Branch roads The active power and reactive power transmitted; For nodes The active power output of mobile energy storage; For nodes Reactive power output of mobile energy storage; node Original reactive load; For nodes The square of the voltage amplitude; For nodes The square of the voltage amplitude; branch road The square term of the steady-state current RMS value; （24） In the formula, The relaxation coefficient; Transform equation (23) into a second-order cone model: （25）。 3. The distribution network supply guarantee method considering distributed photovoltaic cluster division and mobile energy storage coordination according to claim 1, characterized in that: The objective function of the post-disaster recovery phase model is: （26） In the formula, This is a set of fault recovery periods; This represents the total number of clusters after dynamic repartitioning. and Clusters Cost reduction in critical / regular load units within the organization; and For cluster During the period Power reduction for critical / non-critical loads.

4. The distribution network supply guarantee method considering distributed photovoltaic cluster division and mobile energy storage coordination according to claim 3, characterized in that: The constraints of the post-disaster recovery phase model include: Temporal and spatial constraints of mobile energy storage: （27） （28） （29） （30） In the formula, A 0-1 variable representing mobile energy storage During the period Access Cluster ; For the isolated island The collection of clusters included; It is a collection of mobile energy storage devices, representing the scope of all mobile energy storage individuals participating in the dispatch; It is a time set that covers all time ranges involved in the scheduling; For nodes The other node is used to describe the movement of mobile energy storage between different nodes; The threshold for cross-island movement time; For the first Taiwan Mobile Energy Storage The actual energy storage capacity; For the charging and discharging efficiency of mobile energy storage; , These are the minimum and maximum allowable energy storage capacities for mobile energy storage, respectively. This is the system's reference power. Photovoltaic output constraints: （31） In the formula, and They are nodes The active and reactive power outputs of distributed photovoltaic systems; and They are nodes The maximum active and reactive power capacity of the distributed photovoltaic system; Power balance constraints: （32） （33） In the formula, For the distributed photovoltaic active power output of cluster c at time t; Let m be the active power of the mobile energy storage device at time t. The active power of charging mobile energy storage m at time t; Net active power output for mobile energy storage across all clusters; Let be the active power of the electric vehicle during discharge at time t; The active power for charging the electric vehicle at time t; Let be the active load of cluster c at time t; The amount of active power reduction in cluster c at time t; The first one formed after the disaster An isolated island.

5. The distribution network supply guarantee method considering distributed photovoltaic cluster division and mobile energy storage coordination according to claim 2, characterized in that: The solution method for the pre-disaster collaborative scheduling model is to use the column constraint generation algorithm C&CG to decompose the original problem into a main problem and sub-problems, and to approximate the optimal solution through iterative solution. A dynamic cluster update mechanism is also introduced to re-divide the photovoltaic clusters based on the current network topology after each iteration. The compact form of the original problem is as follows: （34） In the formula, variables Including mobile energy storage layout variables Branch switching decision variables ;variable Including photovoltaic power output variables ;variable include Inner layer control variables; Uncertain set of power output for photovoltaics The feasible region of the variable; Variables in the objective function The coefficient vector; Variables in the objective function The coefficient vector; This is the constraint matrix; To constrain the right-hand vector; For the i-th constraint, regarding The coefficient matrix; For the target vector, This represents the maximum permissible deviation from the target state. The main problem is the pre-deployment optimization of mobile energy storage under a given cluster partitioning: （35） In the formula, These are slack variables; This refers to the current iteration round; For the first The candidate solutions for the inner control variables generated in the next iteration; after solving the main problem, the optimal mobile energy storage layout for the current iteration is obtained. lower bound of the objective function ; The subproblem is a given mobile energy storage layout. Search for the worst-case photovoltaic scenario: （36） In the formula, For nodes The weight of load reduction costs; node The amount of active power reduction; This is the system's reference power. The set of all nodes in the system; Define Lagrange multipliers λ, μ, The dual form of the subproblem is: （37） In the formula, Uncertainty set for photovoltaic power output; Lagrange multipliers Used for dual transformation, it introduces the constraints of the original problem into the objective function; It is a coefficient matrix; This serves as a reference vector for system status, load, and other related parameters. Correspondence with The relevant constraint right-hand vector; Let the coefficient matrix be the matrix in which the Lagrange multipliers are connected to the coefficients of the objective function of the original problem within the dual constraints. ; for The 2-norm of the Lagrange multiplier restricts the size of the Lagrange multiplier to ensure the boundedness of the dual problem; To constrain the quantity; Introducing binary variables Photovoltaic power output is expressed as: （38） Introducing auxiliary variables The bilinear terms are transformed into linear constraints through Big-M relaxation: （39） In the formula, Description of the The degree of correlation between the photovoltaic system and other parts of the system. In order to be with the first Lagrange multipliers associated with each photovoltaic unit; After solving the subproblems, the worst-case photovoltaic scenario is obtained. optimal value of subproblems And update the upper bound of the objective function. ,like If the iteration converges, then the problem is solved; otherwise, a cut constraint needs to be added to the main problem to proceed to the next iteration.

6. The distribution network supply guarantee method considering distributed photovoltaic cluster division and mobile energy storage coordination according to claim 5, characterized in that: After each iteration of the column constraint generation algorithm C&CG, the improved Louvain algorithm is re-executed based on the current network topology to update the cluster structure. The specific steps are as follows: From the optimal solution of the main problem Extracting branch switching status Construct the distribution network topology for the current iteration. ; Based on topology Recalculate electrical distance index Voltage sensitivity index Reactive power support indicators Active support indicators ; Adopting an improved modularity index Perform cluster repartitioning, if and If the algorithm converges, it will output the optimal cluster partition. With mobile energy storage deployment Otherwise, according to Update constraints (4)-(6).

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