Power distribution network collaborative operation and restoration method based on island mutual aid

Abstract

The application provides a power distribution network collaborative operation and recovery method based on island mutual aid, comprising: establishing a power distribution network island division optimization model, solving the power distribution network island division optimization model, obtaining a switch opening and closing state matrix of the power distribution network, an island division scheme and an island-to-island energy mutual aid scheme; defining each island as an agent, determining an agent state space and an agent action space; training the agent by using a reinforcement learning algorithm based on a proximal policy optimization, obtaining an optimized island-to-island energy mutual aid scheme; constructing a mobile equipment optimization configuration model, taking maximizing the recovery of important load power supply as an optimization objective; solving the mobile equipment optimization configuration model, obtaining a mobile equipment scheduling scheme and a service scheme coordinated with the island-to-island energy mutual aid scheme; and the application provides a comprehensive solution for the power distribution network to cope with extreme weather events.

Description

Technical Field

[0001] This invention relates to the field of power distribution network post-disaster operation technology, and more specifically, to a method for collaborative operation and recovery of power distribution networks based on islanded mutual assistance. Background Technology

[0002] With the increasing frequency of extreme weather events, power distribution networks face severe challenges to power supply reliability. Under the influence of natural disasters such as typhoons, towers or lines in the distribution network may be damaged, leading to partial line disconnections, disrupting the transmission structure, and causing large-scale power outages. Traditional distribution network reconfiguration transfers lost loads via tie lines, but this has significant limitations under extreme weather conditions: non-faulty power loss areas may lack available tie lines or have tie lines fully loaded, resulting in insufficient power supply capacity and difficulty in coping with the continuous evolution of faults caused by the dynamic destructive characteristics of typhoons. With the widespread integration of distributed generation (DG), islanded operation has become an important emergency measure. DG can support local load power supply, compensating for the shortcomings of traditional reconfiguration. However, existing islanding operation technologies still face multiple bottlenecks: the lack of energy sharing mechanisms between islands means that islands with insufficient capacity cannot improve their overall power supply capacity through collaborative optimization; the randomness and intermittency of DG output exacerbate the instability of individual island operation; existing methods do not fully consider the impact of the spatiotemporal dynamic characteristics of typhoons on the probability of line failures, and static planning is difficult to adapt to the dynamic changes in disaster scenarios; and the lack of collaborative scheduling strategies for resources such as mobile energy storage and mobile generators during the post-disaster recovery phase limits the continuous power supply capacity of critical loads.

[0003] To address the aforementioned issues, existing research primarily focuses on static island partitioning and optimization across single time segments, failing to incorporate the wind field evolution patterns after typhoon landfall. This leads to a disconnect between simulated fault scenarios and the dynamic characteristics of actual disasters. Furthermore, traditional optimization methods rely on centralized decision-making, making rapid dynamic adjustments difficult in disaster environments with limited communication. Post-disaster recovery phases often depend on fixed resources, and a systematic approach to the spatiotemporal coordinated configuration of mobile equipment has not yet been developed, resulting in low recovery efficiency.

[0004] Therefore, there is an urgent need for a comprehensive solution that integrates typhoon dynamic modeling, accurate fault probability assessment, island collaborative support and mutual assistance, and mobile equipment scheduling. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, this invention provides a method and apparatus for the coordinated operation and recovery of distribution networks based on island mutual assistance. By constructing a dynamic energy exchange mechanism between islands and a coordinated scheduling strategy for mobile energy storage and generator vehicles, the invention achieves global optimization of distribution network resources, thereby improving the power supply reliability, operational resilience, and post-disaster recovery efficiency of the system under extreme weather conditions.

[0006] This invention establishes a dynamic wind field model based on historical typhoon data, combines Monte Carlo simulation and conditional probability model to quantify line fault risks, and constructs a two-stage island collaborative operation framework of "static planning plus dynamic adjustment": in the early stage, mixed integer programming is used to optimize island division and energy mutual assistance schemes, and in the later stage, reinforcement learning agents are introduced to realize distributed dynamic decision-making. Furthermore, it innovatively integrates multi-time-period scheduling strategies for mobile energy storage devices and generator vehicles. This method not only improves the resilience of the distribution network under typhoon disasters, but also significantly enhances the continuous power supply capacity of important loads through the optimized configuration of mobile equipment after the disaster, providing full-cycle technical support for the defense and recovery of the distribution network under extreme weather conditions.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] The method for coordinated operation and restoration of distribution networks based on islanded mutual assistance includes the following steps:

[0009] S1. Simulate power distribution network fault scenarios based on real typhoon information, establish a power distribution network islanding optimization model with minimizing load loss as the objective function, and determine the constraints of the power distribution network islanding optimization model.

[0010] S2. Solve the islanding optimization model of the distribution network to obtain the switching state matrix of each switch in the distribution network, the islanding scheme, and the energy mutual assistance scheme between islands.

[0011] S3. Based on the obtained island division scheme, each island is defined as an intelligent agent, and the state space and action space of the intelligent agent are determined. The state space of the intelligent agent includes the total output of the distributed power source, the total load demand, the charging / discharging power of the energy storage device, the remaining power of the energy storage device, and the connection status with the adjacent islands. The action space of the intelligent agent includes the load shedding action, the output setting of the distributed power source, the charging / discharging power setting of the energy storage device, and the request for mutual power from the adjacent islands.

[0012] S4. The agent is trained using a reinforcement learning algorithm based on near-end policy optimization. A distributed coordination mechanism based on consensus algorithm is implemented under the consideration of reward function. The load shedding and distributed energy output within each island are dynamically adjusted according to the real-time operating status of each island to obtain an optimized energy mutual assistance scheme between islands.

[0013] S5. Based on the optimized inter-island energy mutual assistance scheme, determine the supply and demand gap of each island, and construct an optimized configuration model for mobile equipment with the optimization goal of maximizing the restoration of power supply to critical loads.

[0014] S6. Solve the mobile equipment optimization configuration model to obtain a mobile equipment scheduling scheme and service scheme that is coordinated with the inter-island energy mutual assistance scheme, so as to realize the coordinated operation and restoration of the power distribution network.

[0015] Furthermore, the method for constructing the mobile equipment optimization configuration model in step S5, with the optimization objective of maximizing the restoration of power supply to critical loads, is as follows:

[0016]

[0017] Where T represents the set of planning time periods; For the gathering of isolated islands; ω is the set of generatrices in the isolated island d; i The importance weight of bus i; δ represents the power demand of bus i at time t; Δt is the time interval; δ i (t) represents the load reduction decision variable for bus i at time t.

[0018] Furthermore, in step S4, a reinforcement learning algorithm based on proximal policy optimization is used to train the agent. Considering the reward function, a distributed coordination mechanism based on a consensus algorithm is implemented. The method for dynamically adjusting load shedding and distributed energy output within each island according to its real-time operating status, thus obtaining the optimized inter-island energy mutual aid scheme, is as follows:

[0019] When training an agent using a reinforcement learning algorithm based on proximal policy optimization, the policy function is:

[0020] π θ (a d |s d )

[0021] The policy function represents the state s. d Take action a d The probability, θ is the policy network parameter;

[0022] The training objective function J(θ) for training the agent is:

[0023]

[0024] in, γ is the reward that agent d receives at time t. t a is the discount factor; d ~π θ This indicates action sampling, action a d From the current strategy π θ Obtained from sampling in the middle; This indicates the calculation of strategy π. θ The expectation of all possible action sequences and state transition paths; T J This represents the total number of time steps in a decision-making cycle.

[0025]

[0026] in, It is the mutual power transferred from agent d to agent e. It is the load requirement of agent d. For the load shedding action of agent d, The unbalanced power is used as a penalty; w1, w2, and w3 represent the importance weights of the three dimensions of load supply rate, power balance, and energy reconciliation cost, respectively.

[0027] Considering that communication is often limited under disaster conditions, a distributed coordination mechanism based on consensus algorithms is designed:

[0028]

[0029] in, N represents the mutual aid power transferred from agent d to e in the k-th iteration. d Let d be the set of the communicating neighbors of agent d. For step size parameters, This represents the energy exchange request from agent w to island e at the k-th iteration.

[0030] Through reinforcement learning, the agent can continuously improve energy sharing schemes from experience, dynamically adjust load shedding and distributed energy output to adapt to various changes during typhoon disasters.

[0031] Furthermore, the decision variables of the mobile equipment optimization configuration model constructed in step S5 include location decision variables, movement trajectory decision variables, and service decision variables; the constraint variables of the mobile equipment optimization configuration model include mobile equipment constraints, island power balance constraints, mobile equipment location constraints, trajectory constraints, service constraints, and road movement constraints.

[0032] Furthermore, when solving the mobile equipment optimization configuration model, the Benders decomposition algorithm is used to divide the solution process into a main problem of mobile path planning and a service scheduling subproblem. First, the position and movement variables of the mobile equipment are solved, and then the service variables are solved given the position. Through iterative solving between the main problem and the subproblem, a Benders cutting plane is generated, gradually approaching the global optimal solution, and the scheduling and service scheme of the mobile equipment is obtained.

[0033] Furthermore, in step S6, when obtaining the mobile equipment scheduling and service schemes coordinated with the inter-island energy sharing scheme, a mobile equipment allocation strategy based on the importance of the islands is designed, according to the island importance evaluation index I. d The supply and demand gap ΔP between isolated islands d The product of the numbers is used to sort the islands, prioritizing the allocation of mobile equipment to the islands ranked higher.

[0034] Furthermore, the island importance evaluation index I d for:

[0035]

[0036] The supply and demand gap ΔP of the isolated island d for:

[0037]

[0038] in, For the gathering of isolated islands; ω is the set of generatrices in the isolated island d; i The importance weight of bus i; Let i be the power demand of bus i at time t; The generating capacity of the units and distributed power sources within the isolated island (d); The energy storage output power of island d.

[0039] Furthermore, the method for establishing an optimization model for islanding in the distribution network, using the minimization of load loss as the objective function, is as follows:

[0040] The objective function is determined as follows:

[0041]

[0042] in, For the distribution network busbar set, δ i Let ω be the load reduction decision variable for bus i. i The importance weight of bus i, The required power for bus i.

[0043] Furthermore, the method for solving the aforementioned distribution network islanding optimization model is as follows:

[0044] In the islanding optimization model of the distribution network, the Distflow power flow constraints, power balance constraints, node voltage constraints, and network radial constraints are piecewise linearized. First, the mixed integer nonlinear programming problem is transformed into a mixed integer linear programming problem. The Big-M method is used to handle the coupling relationship between switch states and power flow constraints. A genetic algorithm is introduced to generate initial solutions. Finally, an optimization solver is used to solve the linearized problem. The solution results include the switching state matrix of each switch in the distribution network, the islanding scheme, and the energy mutual assistance scheme between islands.

[0045] Furthermore, the mobile equipment includes a mobile energy storage device and a mobile power generation vehicle.

[0046] This invention relates to a method and apparatus for coordinated operation and restoration of distribution networks based on islanded mutual assistance, which has the following beneficial effects:

[0047] This invention addresses the problem of significant load loss in distribution networks during extreme weather events by proposing a collaborative operation and recovery method for distribution networks based on islanding mutual assistance. It proposes a two-stage islanding partitioning and optimization method combining static planning and dynamic adjustment, and introduces an optimized configuration strategy for post-disaster energy mutual assistance channels using mobile equipment. Compared to traditional single-island operation, this method significantly improves the power supply reliability and resilience of the distribution network system, optimizes load supply during disasters, reduces critical load recovery time, minimizes load loss, and achieves rapid post-disaster recovery through the rational scheduling of mobile equipment, providing a comprehensive solution for distribution networks to cope with extreme weather events. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the distribution network collaborative operation and recovery method based on islanded mutual assistance provided in Embodiment 1 of the present invention. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] like Figure 1 As shown, the method for coordinated operation and restoration of distribution networks based on islanded mutual assistance includes the following steps:

[0051] S1. Simulate power distribution network fault scenarios based on real typhoon information, establish a power distribution network islanding optimization model with minimizing load loss as the objective function, and determine the constraints of the power distribution network islanding optimization model.

[0052] S2. Solve the islanding optimization model of the distribution network to obtain the switching state matrix of each switch in the distribution network, the islanding scheme, and the energy mutual assistance scheme between islands.

[0053] S3. Based on the obtained island division scheme, each island is defined as an intelligent agent, and the state space and action space of the intelligent agent are determined. The state space of the intelligent agent includes the total output of the distributed power source, the total load demand, the charging / discharging power of the energy storage device, the remaining power of the energy storage device, and the connection status with the adjacent islands. The action space of the intelligent agent includes the load shedding action, the output setting of the distributed power source, the charging / discharging power setting of the energy storage device, and the request for mutual power from the adjacent islands.

[0054] S4. The agent is trained using a reinforcement learning algorithm based on near-end policy optimization. A decision-making mechanism is constructed through a policy network and a value network. A distributed coordination mechanism based on a consensus algorithm is implemented under the consideration of the reward function. The load shedding and distributed energy output within each island are dynamically adjusted according to the real-time operating status of each island to obtain an optimized energy mutual assistance scheme between islands.

[0055] S5. Based on the optimized inter-island energy mutual assistance scheme, determine the supply and demand gap of each island, and construct an optimized configuration model for mobile equipment with the optimization goal of maximizing the restoration of power supply to critical loads.

[0056] S6. Solve the mobile equipment optimization configuration model to obtain a mobile equipment scheduling scheme and service scheme that is coordinated with the inter-island energy mutual assistance scheme, so as to realize the coordinated operation and recovery of the power distribution network.

[0057] Specifically, when establishing the optimization model for islanding in the distribution network, minimizing load loss is used as the objective function:

[0058]

[0059] in, For the distribution network busbar set, δ i Let δ be the load reduction decision variable for bus i. i =0 indicates that the load on this busbar was disconnected during the emergency response process, ω i The importance weight of bus i, Power required for bus i;

[0060] The constraints of the distribution network islanding optimization model include:

[0061] The power balance constraint is:

[0062]

[0063] in, Let (i,j) be the set of branches of the distribution network, where (i,j) represents branch j connected to bus i. and These represent the active power and reactive power of the outflowing branch ij, respectively. and These represent the active power and reactive power flowing into branch ij, respectively; j:(i,j) indicates the flow from i to j in branch j connected to bus i; j:(j,i) indicates the flow from j to i in branch j connected to bus i. and These are the active and reactive power outputs of the distributed power source connected to bus i, respectively. For the active power demand of bus i load, The reactive power demand of bus i load.

[0064] Node voltage constraints:

[0065]

[0066] Among them, V i,min With V i,max These represent the minimum and maximum allowable voltages, respectively; V represents the node voltage of bus i.

[0067] Line capacity constraints:

[0068]

[0069] in, and These are the upper and lower limits of the branch ij flow rate, respectively.

[0070] Distflow constraints:

[0071]

[0072] Where, r ij and x ij These are the branch resistance and reactance values ​​(ij), respectively, and the branch power flow constraints are linked to the line switch state variable (c) based on Big-M. ij To couple, where M is a sufficiently large positive number; u i The square of the voltage at bus i; u j Let be the square of the voltage of branch j connected to bus i.

[0073] Distributed power generation output constraints:

[0074]

[0075] in, For substation collection, A collection of distributed power sources; This represents the upper limit of the active power output of distributed power sources. This represents the upper limit of reactive power output of distributed power sources. and These refer to the active and reactive power outputs of the distributed power source connected to bus i, respectively.

[0076] Line fault state constraints:

[0077]

[0078] Among them, set This is a set of disconnected branches in a power distribution network fault scenario generated based on real typhoon information.

[0079] Bus energization constraints:

[0080]

[0081] Where, ε i The energizing variable of bus i; c is the number of branches connected to bus i; ji Indicates c ij Switch state variables with opposite directions; ε j This represents the energized variable of branch j connected to bus i.

[0082] Network radial constraints:

[0083]

[0084] in, and These are the non-negative continuous auxiliary variables that ensure the radial constraints of the distribution network, λ max In this embodiment, the maximum density of the radial network is achieved. This represents the set of branches originating from bus i. Represents the set of branches entering bus i; u ij It is a binary variable indicating whether the branch (i,j) is closed;

[0085] Energy mutual restraint:

[0086]

[0087] in, The generating capacity of the units and distributed power sources within the isolated island (d); The energy storage output power of island d; It is the mutual power transferred from island d to e; It is the mutual power transferred from island e to d; For the collection of isolated islands; Ω d Let be the set of isolated islands adjacent to isolated island d; For the load demand of island d; For the line loss or other forms of loss of the isolated island d; α represents the maximum transmission capacity of the mutual aid channel. de d represents the channel availability coefficient. n Let ξ be the set of busbars for the nth isolated island; ξ is the load recovery ratio.

[0088] The method for solving the aforementioned distribution network islanding optimization model is as follows:

[0089] The nonlinear constraints in the distribution network islanding optimization model, such as Distflow power flow constraints, power balance constraints, node voltage constraints, and network radial constraints, are piecewise linearized. First, the mixed-integer nonlinear programming problem is transformed into a mixed-integer linear programming problem. The Big-M method is used to handle the coupling relationship between switch states and power flow constraints. A genetic algorithm is introduced to generate initial solutions. Finally, an optimization solver is used to solve the linearized problem. The solution results include the switching state matrix of each switch in the distribution network, islanding schemes, and energy exchange schemes between islands. Specifically, the network reconfiguration scheme is analyzed based on the switching state matrix, the islanding scheme is determined based on the network partitioning results, and the energy exchange channels are determined based on the power exchange matrix.

[0090] After obtaining the on / off state matrix of each switch in the distribution network and the initial islanding scheme, each island obtained in the islanding scheme is defined as an agent, and a distributed cooperative control architecture is constructed. The agent's state space includes the total output of distributed power sources, total load demand, charging / discharging power of energy storage devices, remaining power of energy storage devices, and connection status with adjacent islands. The agent's action space includes load shedding actions, distributed power source output settings, energy storage device charging / discharging power settings, and requesting mutual power assistance from adjacent islands. The agent is trained using the Proximal Policy Optimization (PPO) algorithm, through the policy function π. θ (a d |s d ) indicates that in state s d Take action a d The probability is calculated, with the objective function being to maximize the expected cumulative reward. The reward function includes three dimensions: load supply rate, power balance, and energy mutual aid cost. Simultaneously, a distributed coordination mechanism based on a consensus algorithm is constructed, enabling agents to reach mutual aid decisions with minimal information exchange, dynamically adjusting load shedding and distributed energy output to adapt to changes during typhoon disasters. Specifically:

[0091] The initial solution is based on static optimization. While it can obtain the theoretically optimal solution, it is insufficient to handle dynamic changes during a disaster. Therefore, an adaptive agent mechanism is needed for dynamic adjustment. Based on the initial island partitioning, each island obtained from the partitioning scheme is defined as an agent, and a distributed cooperative control architecture is constructed. The agent's state space is as follows:

[0092]

[0093] in, It is the total output of all distributed power sources within the intelligent agent d; This is the load requirement of agent d; It is the charging / discharging power of the energy storage device within the intelligent agent d; It is the remaining power of the energy storage device within the intelligent agent d; This represents the connection state between agent d and its neighboring agents.

[0094] Action space of an agent:

[0095]

[0096] in, For the load shedding action of agent d; Set the output value of the distributed energy source DG for agent d; Set the charging / discharging power value for the energy storage device; The mutual aid power requested from the neighboring agent e.

[0097] Each agent makes real-time decisions to optimize its local objective based on its own state and available neighbor information, while coordinating energy sharing. The decision-making process is constrained by the initial island partitioning scheme, but can be dynamically adjusted within a certain range. To enable the agents to autonomously learn optimization strategies, a reinforcement learning algorithm based on Proximal Policy Optimization (PPO) is adopted; its policy function is:

[0098] π θ (a d |s d )(twenty one)

[0099] The policy function represents the state s. d Take action a d The probability, θ is the policy network parameter;

[0100] The objective function for optimizing the model is:

[0101]

[0102] in, γ is the reward that agent d receives at time t. t a is the discount factor; d ~π θ This indicates action sampling, action a d From the current strategy π θ Obtained from sampling in the middle; This indicates the calculation of strategy π. θ The expectation of all possible action sequences and state transition paths; T J This represents the total number of time steps in a decision-making cycle.

[0103] Specifically,

[0104]

[0105] in, The unbalanced power is used as a penalty; w1, w2, and w3 represent the importance weights of the three dimensions of load supply rate, power balance, and energy reconciliation cost, respectively.

[0106] Considering that communication is often limited under disaster conditions, a distributed coordination mechanism based on consensus algorithms is designed:

[0107]

[0108] in, N represents the mutual aid power transferred from agent d to e in the k-th iteration. d Let d be the set of the communicating neighbors of agent d. For step size parameters, This represents the energy exchange request from agent w to agent e at the k-th iteration step; this protocol enables agents to reach mutual assistance decisions with minimal information exchange, improving the system's resilience under communication-constrained conditions.

[0109] This protocol enables agents to make mutual aid decisions with minimal information exchange, improving the system's resilience under communication constraints. Through reinforcement learning, agents can continuously improve energy mutual aid schemes from experience, dynamically adjusting load shedding and distributed energy output under the constraints of the initial scheme to adapt to various changes during typhoon disasters.

[0110] In the later stages of a typhoon disaster, although islanding and energy sharing schemes can alleviate some power supply pressure, some critical loads may still face power outages. This invention, based on energy sharing between islands, innovatively introduces an optimized configuration strategy for post-disaster energy sharing channels based on mobile equipment, further enhancing the resilience of the distribution network.

[0111] This invention considers two types of mobile equipment: mobile energy storage devices and mobile generators.

[0112] Mobile energy storage device collection: M S ={1,2,...,N S It has the maximum charging power. Maximum discharge power Maximum energy storage capacity Minimum energy storage capacity (safety boundary) Charge / discharge efficiency η ch and η dis and movement speed Parameters such as these.

[0113] Mobile generator set: M G ={1,2,...,N G} has the largest power generation capacity Total energy available Fuel consumption rate Maximum fuel capacity movement speed Parameters such as these.

[0114] Construct an optimized configuration model for mobile equipment, with the optimization objective of maximizing the restoration of power supply to critical loads:

[0115]

[0116] Where T represents the set of planning time periods; For the gathering of isolated islands; ω is the set of generatrices in the isolated island d; i The importance weight of bus i; δ represents the power demand of bus i at time t; Δt is the time interval; δ i (t) represents the load reduction decision variable of bus i at time t; the optimization objective takes into account the load importance, load size and power supply duration, forming a comprehensive power supply capacity evaluation index.

[0117] The optimization objective considers load importance, load size, and power supply duration, forming a comprehensive power supply capacity evaluation index; the decision variables involve binary variables for location decisions. Represent whether the mobile energy storage device k and the mobile generator m are located on the island d at time t; binary variables for determining the movement trajectory. These represent the decision variables related to the service: whether the mobile energy storage device k and the mobile generator m move from island d to island e at time t. This represents the charging power of the mobile energy storage device k located on island d at time t. This represents the discharge power of the mobile energy storage device k located on island d at time t. This represents the power generation capacity of the mobile generator m located on island d at time t.

[0118] The constraint variables of the mobile equipment optimization configuration model include mobile equipment constraints, island power balance constraints, mobile equipment location constraints, trajectory constraints, service constraints, and road movement constraints. Specifically, mobile equipment constraints include charging and discharging power constraints, energy state constraints, energy dynamic balance constraints, charging and discharging mutual exclusion constraints of mobile energy storage devices, and power generation constraints, fuel consumption constraints, and total energy constraints of mobile generators. Mobile equipment location constraints include each mobile piece of equipment being located in at most one island at any given time (Equations (39) and (40)) and mobile equipment coordination constraints. Trajectory constraints include mobile equipment location and movement association constraints and movement time constraints. Service constraints include service and location association constraints and load recovery constraints. Road movement constraints are road traffic constraints. The specific formulas are as follows:

[0119] Charge and discharge power constraints of mobile energy storage devices:

[0120]

[0121] in, Let be the charging power of the mobile energy storage device k at time t; Let be the discharge power of the mobile energy storage device k at time t; This is the maximum charging power; This represents the maximum discharge power.

[0122] Energy state constraints for mobile energy storage devices:

[0123]

[0124] in, This represents the energy storage capacity of the mobile energy storage device k at time t; and These represent the minimum and maximum energy storage capacities, respectively.

[0125] Energy dynamic balance constraints of mobile energy storage devices:

[0126]

[0127] Where, η ch and η dis These represent the charge and discharge efficiencies, respectively.

[0128] Power generation constraints of mobile generator vehicles;

[0129]

[0130] in, This represents the power generation capacity of the moving generator m at time t; This indicates the maximum power output of the generator vehicle.

[0131] Fuel consumption constraints for mobile generators:

[0132]

[0133] in, This represents the fuel capacity of the moving generator m at time t; This represents the fuel consumption rate of the mobile generator m; This indicates the maximum fuel capacity.

[0134] Total energy constraint of mobile generator:

[0135]

[0136] Island power balance constraints:

[0137]

[0138] This constraint ensures a balance between power generation and load on each island, taking into account distributed power sources, mobile energy storage, mobile generators, and power sharing between islands.

[0139] Each piece of equipment can be located on at most one island at any given time:

[0140]

[0141] in, and Let represent whether the mobile energy storage device k and the mobile generator m are located on an island d at time t, respectively.

[0142] Mobile equipment location and movement association constraints:

[0143]

[0144] in, and These represent whether the mobile energy storage device k and the mobile generator m have moved from island d to island e at time t; and Indicate whether the mobile energy storage device k and the mobile generator m are located on the island e at time t; and These represent whether the mobile energy storage device k and the mobile generator m have moved from island e to island d at time t.

[0145] Road traffic restrictions: Mobile equipment can only travel through passable roads.

[0146]

[0147] Among them, R d,e (t) is the road state matrix, where a value of 1 indicates that the road between islands d and e is passable at time t, and a value of 0 indicates that it is not passable.

[0148] Shift time constraints:

[0149]

[0150] in, and The travel times for mobile energy storage device k and mobile generator m from island d to island e are respectively:

[0151]

[0152] Among them, D d,e The distance between island d and e is the distance between island d and e. This indicates rounding up to the nearest integer.

[0153] Service and location association constraints mean that mobile equipment can only provide services in its current location:

[0154]

[0155] in, and Let represent the charging power and discharging power of the mobile energy storage device k at time t when it is located on island d; Let represent the power generation capacity of the mobile generator m located on island d at time t.

[0156] Charging and discharging mutual exclusion constraint for mobile energy storage devices: Mobile energy storage devices cannot be charged and discharged simultaneously.

[0157]

[0158] Load restoration constraints: During post-disaster reconstruction, once power supply is restored, continuous power supply should be maintained as much as possible.

[0159]

[0160] This constraint prevents repeated load switching and improves power supply quality.

[0161] Mobile equipment coordination constraints:

[0162]

[0163] in, The maximum number of mobile equipment that an isolated island d can accommodate at the same time is determined by considering site limitations.

[0164] To improve solution efficiency, an initial allocation strategy for mobile equipment based on island importance was designed, considering the island importance evaluation index I. d :

[0165]

[0166] At the same time, it is necessary to calculate the supply and demand gap ΔP for each isolated island. d :

[0167]

[0168] According to importance index I d and gap ΔP d The product of the islands is sorted from largest to smallest, and mobile equipment is preferentially allocated to the islands with the highest ranking. This pre-allocation strategy provides a high-quality initial solution for global optimization and significantly improves the solution efficiency.

[0169] Post-disaster recovery is a multi-stage process that requires coordinated consideration of both short-term and long-term benefits. This invention employs a rolling time-domain optimization method, first dividing the planning period T into multiple sub-periods {T1, T2, ..., T...}. n For each sub-cycle, the optimization model is solved to obtain a detailed scheduling scheme. Then, the current sub-cycle scheme is executed, the system state is updated, and finally, based on the latest state, the next sub-cycle is planned forward.

[0170] When solving the mobile equipment optimization configuration model, the Benders decomposition algorithm is used to divide the solution process into a main problem of mobile path planning and a service scheduling subproblem. First, the position and movement variables of the mobile equipment are solved, and then the service variables are solved given the position. Through iterative solutions between the main problem and the subproblem, a Benders cutting plane is generated, which gradually approaches the global optimal solution to obtain the scheduling and service scheme of the mobile equipment.

[0171] It should be noted that in the line fault state constraints of the distribution network islanding optimization model, it is necessary to generate a set of distribution network disconnected branches based on real typhoon scenarios. In step S1, when simulating distribution network fault scenarios based on real typhoon information, the construction of distribution network fault scenarios is a key step in the resilience analysis of distribution networks under typhoon disasters. In this embodiment, by integrating the dynamic model of real typhoon wind fields with line vulnerability assessment, a causal relationship between meteorological parameters and line faults is established, realizing the prediction of the spatiotemporal evolution of faults. This method overcomes the limitations of traditional static models, captures the effects of typhoon movement, wind speed attenuation, and fault accumulation, and compensates for the lack of historical data on extreme weather through conditional probability and Monte Carlo simulation. The purpose of fault scenario construction is to provide a foundation for islanding optimization, improve the reliability of emergency decision-making, create an environment for agent learning, and support the scheduling of mobile equipment, ultimately achieving a closed-loop optimization of "static planning + dynamic adjustment" for distribution network disaster response, significantly improving the system's power supply reliability and recovery efficiency. The specific process is as follows:

[0172] When establishing a dynamic wind field model that considers the spatiotemporal dynamic characteristics of a real typhoon, a static wind field model of the typhoon at different time sections is first established based on the key parameters of the real typhoon. The wind speed and direction of the typhoon within each power distribution network in the typhoon-affected area are calculated, and the maximum wind speed and center position of the typhoon are continuously varied over time to simulate the impact of the typhoon's passage. Specifically, as shown below:

[0173] (1) Based on the best track dataset of tropical cyclones in the Northwest Pacific from 1949 to 2018 released by the Tropical Cyclone Data Center of China Meteorological Administration, key typhoon parameters such as typhoon landfall point, typhoon direction of movement at landfall, changes in typhoon direction of movement, typhoon speed, maximum wind speed radius, and typhoon center pressure difference at landfall were obtained.

[0174] (2) A typhoon wind field model is established based on real typhoon parameters. As a typhoon moves inland from its landfall point, the wind speed along its path changes. The typhoon wind field model can be defined by three key variables: maximum sustained wind speed (v...). max (in units of knots); the distance from the eye of the typhoon to the point of maximum sustained winds. The units are nautical miles (nm); and the typhoon radius (R) centered on the eye of the typhoon. S (Also measured in nautical miles);

[0175]

[0176] Where x is the distance from the eye of the typhoon; the Ψ parameter describes the rate of change of wind speed near the radius of maximum wind speed; K is a constant that depends on the nature of the typhoon; and the Λ parameter describes the distance from the radius of maximum wind speed (i.e., from the eye of the typhoon to the point of maximum sustained wind speed). ) to the typhoon boundary (R S The wind speed attenuation characteristics between ); β is the factor that reduces the maximum sustained wind speed at the typhoon boundary, assuming that the typhoon has no effect outside its boundary;

[0177] After establishing the typhoon wind field model, it is necessary to consider the dynamic behavior of typhoon movement and establish a typhoon disaster evolution model that considers the spatiotemporal dynamic characteristics of real typhoons. Combining parameters such as the land attenuation coefficient of typhoons after landfall obtained from the national typhoon database, a static wind field model under multiple time sections is formed. The dynamic behavior of typhoons can be captured by simulating the static model in several discrete time intervals. This dynamic wind field model allows us to track the severity of typhoons along their path after landfall. At the eye of the typhoon, the wind speed is the lowest and the air pressure is the highest. This phenomenon is described by formula (4):

[0178]

[0179] Where, φ 0，ζ It is the latitude of the landing location of trajectory ζ. Let ζ be the eye pressure of typhoon h at time step t = 0; here, it is assumed that for each ζ, landfall always occurs at time step t = 0. Let represent the maximum wind speed radius of typhoon h at the time of landfall (t=0) under its trajectory ζ. Therefore, for each typhoon h, the pressure at the eye of the wind at each time step t and trajectory ζ can be calculated as follows:

[0180]

[0181] Where α is the land attenuation parameter of the typhoon;

[0182] Using the above equations, we can update the parameter set for each typhoon scenario h at each time point t, based on the values ​​from the previous time step and known data. These parameters are used to generate the coordinates of each predicted typhoon path ζ. Using these updated values, we generate a static wind field for each t and ζ, thus forming a dynamic wind field model.

[0183] The method of using a conditional probability model to obtain the probability of power line breakage based on the local maximum wind speed, and then using a line failure rate model to construct power distribution network fault scenarios is as follows:

[0184] The conditional probability model is used to evaluate the fault condition p of the feeder. f :

[0185]

[0186] The critical wind speed for power line collapse is u. p The minimum wind speed threshold that affects transmission lines is u. c Failure probability P f (u) represents the probability of component failure at wind speed u; if the wind speed exceeds the collapse threshold, the probability of equipment survival is almost zero, and it can be considered a complete failure.

[0187] Extreme weather events are rare, and historical data is limited. To comprehensively evaluate the performance of the distribution network under different typhoon conditions, it is necessary to use a line failure rate model to construct failure scenarios and simulate the disaster evolution process.

[0188] Failure rate is usually defined as the proportion of a component that fails during its entire service life. The maximum load test cycle of a component usually covers its entire lifespan or a long period of time, which is far longer than the duration of a single typhoon impact. In stochastic simulation, if a line is judged to be operating normally under a certain condition, it is assumed that the line will not fail under the same or better conditions.

[0189] Monte Carlo stochastic simulation is used to analyze the probability distribution characteristics of line faults in order to evaluate the actual reliability level of equipment in the distribution network system. The randomness and uncertainty of faults can be simulated by the fault probability threshold criterion: a random number r is generated, and when r > p, it represents that the line is working normally, and when r ≤ p, it represents that the line is faulty. In addition, since there are often no conditions for repair during the occurrence of a disaster, this process satisfies the constraint that if a fault occurs at one moment, it will not be restored at the next moment.

[0190]

[0191] s (i,j),t ≥s (i,j),t+1 (61)

[0192] Among them, s (i,j),t This indicates the on / off state of branch j connected to bus i at time t. A value of 1 indicates the line is normal, and a value of 0 indicates the line is open. j,t p is a random number f (j,t) represents the fault status of branch j at time t.

[0193] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for coordinated operation and restoration of distribution networks based on islanded mutual assistance, characterized in that, Includes the following steps: S1. Simulate power distribution network fault scenarios based on real typhoon information, establish a power distribution network islanding optimization model with minimizing load loss as the objective function, and determine the constraints of the power distribution network islanding optimization model. S2. Solve the islanding optimization model of the distribution network to obtain the switching state matrix of each switch in the distribution network, the islanding scheme, and the energy mutual assistance scheme between islands. S3. Based on the obtained island division scheme, each island is defined as an intelligent agent, and the state space and action space of the intelligent agent are determined. The state space of the intelligent agent includes the total output of the distributed power source, the total load demand, the charging / discharging power of the energy storage device, the remaining power of the energy storage device, and the connection status with the adjacent islands. The action space of the intelligent agent includes the load shedding action, the output setting of the distributed power source, the charging / discharging power setting of the energy storage device, and the request for mutual power from the adjacent islands. S4. The agent is trained using a reinforcement learning algorithm based on near-end policy optimization. A distributed coordination mechanism based on consensus algorithm is implemented under the consideration of reward function. The load shedding and distributed energy output within each island are dynamically adjusted according to the real-time operating status of each island to obtain an optimized energy mutual assistance scheme between islands. S5. Based on the optimized inter-island energy mutual assistance scheme, determine the supply and demand gap of each island, and construct an optimized configuration model for mobile equipment with the optimization goal of maximizing the restoration of power supply to critical loads. S6. Solve the mobile equipment optimization configuration model to obtain a mobile equipment scheduling scheme and service scheme that is coordinated with the inter-island energy mutual assistance scheme, so as to realize the coordinated operation and recovery of the power distribution network. In step S4, a reinforcement learning algorithm based on proximal policy optimization is used to train the agent. Considering the reward function, a distributed coordination mechanism based on a consensus algorithm is implemented. The optimized inter-island energy sharing scheme is obtained by dynamically adjusting load shedding and distributed energy output within each island based on its real-time operating status. When training an agent using a reinforcement learning algorithm based on proximal policy optimization, the policy function is: The policy function represents the state s. d Take action a d The probability of is given by , where is the policy network parameter; Training objective function when training an agent for: in, Let be the reward that agent d receives at time t. Discount factor; This indicates action sampling, action a d From the current strategy Obtained from sampling in the middle; Indicates the computation of policy pairs The expectation of all possible action sequences and state transition paths; This represents the total number of time steps in a decision-making cycle. in, It is the mutual power transferred from agent d to agent e. It is the load requirement of agent d. For the load shedding action of agent d, The unbalanced power is used as a penalty; w1, w2, and w3 represent the importance weights of the three dimensions of load supply rate, power balance, and energy reconciliation cost, respectively. Considering communication limitations under disaster conditions, a distributed coordination mechanism based on consensus algorithms is designed: in, N represents the mutual aid power transferred from agent d to e in the k-th iteration. d Let d be the set of the communicating neighbors of agent d. For step size parameters, This represents the energy exchange request from agent w to island e at the k-th iteration. Through reinforcement learning, the agent can continuously improve energy sharing schemes from experience, dynamically adjust load shedding and distributed energy output to adapt to various changes during typhoon disasters.

2. The method for coordinated operation and restoration of distribution networks based on islanded mutual assistance according to claim 1, characterized in that, The method for constructing the mobile equipment optimization configuration model in step S5, with the optimization objective of maximizing the restoration of power supply to critical loads, is as follows: Where T represents the set of planning time periods; For the gathering of isolated islands; ω is the set of generatrices in the isolated island d; i The importance weight of bus i; Let Δt be the power demand of bus i at time t; Δt is the time interval. Let represent the load reduction decision variable for bus i at time t.

3. The method for coordinated operation and restoration of distribution networks based on islanded mutual assistance according to claim 2, characterized in that, The decision variables of the mobile equipment optimization configuration model constructed in step S5 include location decision variables, movement trajectory decision variables, and service decision variables; the constraint variables of the mobile equipment optimization configuration model include mobile equipment constraints, island power balance constraints, mobile equipment location constraints, trajectory constraints, service constraints, and road movement constraints.

4. The method for coordinated operation and restoration of distribution networks based on islanded mutual assistance according to claim 3, characterized in that, When solving the mobile equipment optimization configuration model, the Benders decomposition algorithm is used to divide the solution process into a main problem of mobile path planning and a service scheduling subproblem. First, the position and movement variables of the mobile equipment are solved, and then the service variables are solved given the position. Through iterative solving between the main problem and the subproblem, a Benders cutting plane is generated, which gradually approaches the global optimal solution to obtain the scheduling and service scheme of the mobile equipment.

5. The method for coordinated operation and restoration of distribution networks based on islanded mutual assistance according to claim 1, characterized in that, When obtaining the mobile equipment scheduling and service schemes coordinated with the inter-island energy sharing scheme in step S6, a mobile equipment allocation strategy based on the importance of the islands is designed, according to the island importance evaluation index I. d The supply and demand gap ΔP between isolated islands d The product of the products is used to sort the islands, and the islands are sorted from largest to smallest according to the product. Mobile equipment is then allocated to the islands ranked higher.

6. The method for coordinated operation and restoration of distribution networks based on islanded mutual assistance according to claim 5, characterized in that, The importance evaluation index of the island for: Supply and demand gap in isolated islands for: in, For the gathering of isolated islands; ω is the set of generatrices in the isolated island d; i The importance weight of bus i; Let i be the power demand of bus i at time t; The generating capacity of the units and distributed power sources within the isolated island (d); The energy storage output power of island d.

7. The method for coordinated operation and restoration of distribution networks based on islanded mutual assistance according to claim 1, characterized in that, The method for establishing an optimization model for islanding in a distribution network, using the minimization of load loss as the objective function, is as follows: The objective function is determined as follows: in, For distribution network busbar collection, busbar The load reduction decision variable, ω i The importance weight of bus i, busbar Power required.

8. The method for coordinated operation and restoration of distribution networks based on islanded mutual assistance according to claim 2, characterized in that, The method for solving the aforementioned distribution network islanding optimization model is as follows: In the islanding optimization model of the distribution network, the Distflow power flow constraints, power balance constraints, node voltage constraints, and network radial constraints are processed by piecewise linearization. First, the mixed integer nonlinear programming problem is transformed into a mixed integer linear programming problem. The Big-M method is used to handle the coupling relationship between switch states and power flow constraints. Finally, a genetic algorithm is introduced to generate the initial solution. Finally, an optimization solver is used to solve the linearized problem. The solution results include the switching state matrix of each switch in the distribution network, the islanding scheme, and the energy mutual assistance scheme between islands.

9. The method for coordinated operation and restoration of distribution networks based on islanded mutual assistance according to claim 1, characterized in that, The mobile equipment includes mobile energy storage devices and mobile power generation vehicles.

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