Distribution-micro cooperative fault recovery method considering network dynamic reconstruction

Abstract

The invention discloses a power distribution-micro cooperative fault recovery method considering network dynamic reconstruction, belongs to the technical field of power distribution networks, and completes power distribution-micro cooperative fault recovery through a power distribution-micro cooperative fault recovery model. The method has the following beneficial effects: the optimization model taking the electricity purchase cost, the voltage deviation, the network loss, the load reduction and the microgrid operation cost as the target is constructed, and the power flow constraint, the safe operation constraint and the network reconstruction constraint of the power distribution network are comprehensively considered. For privacy protection requirements of distributed energy in the micro-grid, a k-order approximation method is adopted to establish a micro-grid operation feasible region model, and operation characteristics of the micro-grid are represented through power and energy boundary constraints. In order to further realize distribution-microgrid collaborative optimization, a non-iterative solution method based on equivalent projection is provided, an original problem is decomposed into distribution network layer optimization and microgrid layer sub-problems, internal variables are eliminated through an equivalent projection technology, and collaborative optimization is realized on the premise of protecting microgrid privacy.

Description

Technical Field

[0001] This invention belongs to the field of power distribution network technology, and in particular relates to a distribution-micro cooperative fault recovery method that takes into account dynamic network reconfiguration. Background Technology

[0002] With the increasing penetration rate of renewable energy, distribution network fault recovery faces new challenges such as difficulties in coordinating distributed energy resources and high operational complexity. Traditional fault recovery methods struggle to simultaneously achieve both economic efficiency and reliability, and also suffer from insufficient privacy protection and low computational efficiency. Especially in fault scenarios such as extreme weather, achieving coordinated optimization between the distribution network and microgrids while ensuring secure information sharing has become a critical issue that urgently needs to be addressed. Regarding distribution-microgrid coordinated operation strategies, existing technologies have proposed distributed coordination methods that consider the uncertainties of new energy sources and the characteristics of discrete regulating equipment to achieve safe and economical system operation. Some literature has constructed a residential multi-microgrid coordinated operation method based on two-stage adaptive robust optimization, while other literature has built an interactive energy dispatch model between the distribution system and residential microgrids based on this. Distribution-microgrid coordinated operation modes have been extensively studied.

[0003] However, the aforementioned literature has not yet considered the application potential of microgrids in distribution network fault recovery and their collaborative control mechanisms. Existing literature has proposed various distributed methods for distribution-microgrid collaborative models, with the Alternating Direction Method of Multipliers (ADMM) being widely applied to optimal power flow problems and multi-timescale energy management problems in multi-microgrid distribution systems. An autonomous optimization model for distribution networks containing multiple microgrids, based on Analytical Target Cascading (ATC), achieves decoupling of optimal scheduling between the distribution network and microgrids.

[0004] However, the aforementioned coordination and solution methods often require repeated iterations to achieve consistency in the optimal strategies of multiple agents, resulting in heavy communication burdens and poor convergence. Therefore, it is necessary to propose a privacy-preserving and efficient collaborative fault recovery method for distribution-microgrid systems. Summary of the Invention

[0005] To address the shortcomings of existing research, which has not effectively integrated the collaborative control mechanism of microgrids in distribution network fault recovery and relies on iterative algorithms with high communication burdens, making it difficult to balance privacy protection and efficient solution requirements, this invention conducts research on a distribution-microgrid collaborative fault recovery method considering dynamic network reconfiguration. It proposes a two-layer collaborative optimization framework based on equivalent projection to achieve collaborative optimization of distribution network reconfiguration strategy and microgrid distributed resource scheduling, ultimately forming a fault recovery scheme that balances economy and security.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for fault recovery of distribution-micro cooperative systems considering network dynamic reconfiguration, comprising establishing a fault recovery model of distribution-micro cooperative systems considering network dynamic reconfiguration, and completing fault recovery of distribution-micro cooperative systems through the distribution-micro cooperative system model, including the following steps: Step S1: The distribution-microgrid collaborative fault recovery model aims to minimize the sum of distribution network power purchase cost, voltage deviation cost, network loss cost, load reduction cost and microgrid operating cost. It establishes an objective function by comprehensively considering distribution network constraints and microgrid constraints, and sets a limit on the maximum number of switching operations for network reconfiguration. Step S2: Aggregate the active and reactive power feasible regions (FRs) of the distributed energy resources (DERs) of the microgrid, and establish the microgrid operating feasible region (OFR). k An approximate model is used to calculate the upper and lower limits of microgrid output and upload them to the distribution network for coordinated and optimized operation. Step S3: In establishing the k In the approximate model, the decision variables in the distribution network and microgrid are divided into coordination variables. x and internal variables y Without altering the system's optimality, the microgrid's... y Build a microgrid-only system x With cost variables C The dimensionality reduction model is used, and each microgrid submits its dimensionality-reduced equivalent projection model to participate in the collaborative optimization operation of the distribution network layer, forming a decomposition framework of the distribution network layer optimization problem and the microgrid layer sub-problems; that is, when the distribution network and microgrid are coupled, the internal variables of the microgrid are... y It only appears in the microgrid constraints and no longer in the microgrid layer objective function, thus protecting the privacy information of the microgrid layer; Step S4: The distribution network layer solves for the optimal coordination variables based on the OFR feasible region uploaded by the microgrid. and optimal cost variables Simultaneously satisfying network reconfiguration constraints and power flow security constraints, a new power grid structure that meets the constraints is sought in each time period, and a switching operation scheme is generated. Step S5: Microgrid layer with and Calculate the internal variables of the microgrid as boundary conditions. The optimal solution, i.e. the optimal operating point of the microgrid, is to decompose the total output of the microgrid to each DER, so that the microgrid can also operate optimally. Step S6: Verify whether the reconfigured distribution-microgrid system meets all constraints, and check... k Check if the decomposition error of the approximate model meets the requirements. If decomposition error exists, adjust accordingly.k If the order of the approximate model is recalculated, the network topology is updated, switching operations are performed, and the scheduling plan for each microgrid DER is output. Step S7: Based on the scheduling plan generated in step S6, evaluate the fault recovery effect, calculate performance parameters such as comprehensive cost index, output the optimal collaborative recovery strategy of distribution-microgrid, and the process ends.

[0007] Furthermore, the distribution network constraints include distribution network power flow constraints, node power balance constraints, safe operation constraints, distributed photovoltaic inverter control constraints, and distribution network reconfiguration constraints.

[0008] Furthermore, the microgrid constraints include wind turbine output constraints, photovoltaic active and reactive power output constraints, micro gas turbine active and reactive power output constraints, energy storage system output constraints, and microgrid power balance constraints.

[0009] Furthermore, the basic quantities required for modeling the active and reactive power output (FR) of a microgrid's DER are the maximum and minimum output power and the energy demand over time. A power and energy boundary model is used to model the FR of a single DER cell: ; In the formula, express t The active power output of the microgrid at any given time. , They are respectively t The lower and upper limits of microgrid output at all times. , They are respectively t The lower and upper limits of the energy boundary of a microgrid at any given time. This is the minimum running time within the scheduling cycle; Based on the characteristics of DERs, DERs in microgrids are divided into two categories. DERs with no constraints on input and output energy and no restrictions on the duration of power output are classified as generator-like flexibility resources. DERs with constraints on both input and output energy and restrictions on the duration of power output are classified as energy storage-like flexibility resources. The power and energy boundary model for generator-like flexibility resources takes the following form: ; In the formula, , They are respectively Lower and upper limits for the output of time-based generator flexibility resources. , They are respectively t The lower and upper limits of the energy aggregation of flexible resources for time-based generators; For energy storage-like flexible resources, in time t The derivation of the upper and lower bounds of the shifted energy is as follows: ; In the formula, It is the initial charge state of a type of energy storage flexibility resource. , They are respectively t The upper limit of active power for charging and discharging of time-sensitive energy storage resources; the specified upper and lower energy limits are respectively the maximum energy capacity of the energy storage resources. 90% and 10%, variables and These represent the upper and lower limits of energy for flexible energy storage resources, respectively. The scheduling period; The precise feasible region is used for trajectory filtering using a binary structure, which is transformed into matrix inequality form, as follows: ; In the formula, This represents the feasible domain vector arranged in descending order of time. for The set of all trajectories of a complete binary structure; Representing the trajectory The data of all nodes, excluding the root node. 3D column vector; , Representing trajectories The corresponding upper and lower limits of the feasible operating domain; This is the matrix transpose operation.

[0010] Furthermore, the k-order approximation involves selecting paths with no more than k non-zero nodes to construct constraints; the OFR model under the k-order approximation is: ; In the formula, the definition is... And establish the trajectory and feasible region vector. The correspondence is obtained in the equivalent form Then the matrix inequality is equivalent to: This serves as the precise operational feasible region model for the microgrid; among which, For trajectory exist The value at time; For 1- t Time Track Summation of values; t To accumulate to the specified time; Take 1- t time; The feasible domain power vectors are arranged in descending order of time.

[0011] Furthermore, the total power decomposition model of the microgrid is as follows: ; In the formula: For decomposition error, Indicates the constraints of the microgrid layer. Indicates the microgrid n The Middle k The specific contributions of each DER K Indicates the number of DERs in the microgrid. N Represents a collection of microgrids. This is the index of the last non-zero element in the binary tree path.

[0012] Through the above design scheme, the present invention can bring the following beneficial effects: This invention proposes a distribution-microgrid collaborative fault recovery method considering dynamic network reconfiguration. An optimization model is constructed with the objectives of minimizing electricity purchase cost, voltage deviation, network loss, load reduction, and microgrid operating cost, comprehensively considering distribution network power flow constraints, safe operation constraints, and network reconfiguration constraints. To address the privacy protection requirements of distributed energy resources in microgrids, a k-order approximation method is used to establish a feasible region model of microgrid operation, characterizing its operating characteristics through power and energy boundary constraints. To further achieve distribution-microgrid collaborative optimization, a non-iterative solution method based on equivalent projection is proposed. This method decomposes the original problem into distribution network layer optimization and microgrid layer sub-problems, eliminating internal variables through equivalent projection technology, and achieving collaborative optimization while protecting microgrid privacy. Starting from the distribution-microgrid collaborative fault recovery model considering dynamic network reconfiguration and the non-iterative solution method based on equivalent projection, the economic efficiency and reliability of the fault recovery process are improved. Attached Figure Description

[0013] The present invention will be further described below with reference to the accompanying drawings and specific embodiments: Figure 1 This is a diagram illustrating the islanded operation mode of the power distribution network under scenario 1 of this invention; Figure 2 This refers to the load reduction amount under scenario 1 of the present invention; Figure 3 This is a diagram showing the power output of the microgrid under scenario 3 of the present invention; Figure 4 This is a diagram showing the power output of the microgrid under scenario 3 of the present invention; Figure 5 This is a diagram showing the power output of the microgrid under scenario 3 of the present invention; Figure 6 This is a diagram showing the power output of the microgrid under scenario 3 of the present invention. Detailed Implementation

[0014] The present invention will be further illustrated below with reference to specific embodiments, but the embodiments do not limit the present invention in any way.

[0015] The present invention provides a method for fault recovery based on network dynamic reconfiguration and micro-coordination, comprising the following steps: Establishing a fault recovery model based on network dynamic reconfiguration and performing fault recovery based on the model. Step S1: The distribution-microgrid collaborative fault recovery model aims to minimize the sum of distribution network power purchase cost, voltage deviation cost, network loss cost, load reduction cost and microgrid operating cost. It establishes an objective function by comprehensively considering distribution network constraints and microgrid constraints, and sets a limit on the maximum number of switching operations for network reconfiguration. The objective function of the aforementioned micro-cooperative fault recovery model can be expressed as:

[0016] In the formula: Describe the objective function. This indicates the cost of purchasing electricity for the power distribution network. This represents the cost of voltage deviation in the distribution network. This represents the cost of distribution network losses. This indicates the cost of load reduction. This represents the operating cost of a microgrid.

[0017] Distribution network electricity purchase cost :

[0018] In the formula: The time-of-use electricity price is the price set by the higher-level power grid. For distribution network nodes j Electricity purchased from the superior power grid.

[0019] Distribution network voltage deviation cost :

[0020] In the formula: Voltage deviation cost factor For the set of all nodes in the distribution network, for t Time Node j The voltage amplitude; Rated voltage, i.e. .; Distribution network loss cost :

[0021] In the formula: For i The set of all end nodes of the initial node; This is the network loss cost coefficient; For the branch road The square of the current amplitude; branch road The resistance value.

[0022] Load reduction costs :

[0023] In the formula: This refers to the load cost coefficient of the distribution network. for t Time Node i The reduction in active power load.

[0024] Microgrid operating costs :

[0025] In the formula: For time-of-use pricing in the power distribution network; For nodes j The amount of electricity purchased by the microgrid from the distribution network; N Number of microgrids; The cost of generating electricity from a gas turbine; For access nodes j The active power output of gas turbines in microgrids; Operating costs for charging and discharging ESS; For access nodes j The charging and discharging power of the ESS in the microgrid.

[0026] The distribution network constraints include distribution network power flow constraints, node power balance constraints, safe operation constraints, distributed photovoltaic inverter control constraints, and distribution network reconfiguration constraints.

[0027] The power flow model of the distribution network in this invention adopts the widely used branch power flow model of the distribution network. The current constraints and voltage drop constraints related to this branch model are shown in the following equations:

[0028] In the formula: M For an infinite number, express t Time Branch The connectivity status is indicated by 1 for connectivity and 0 for disconnection. For the branch road The square of the current amplitude; branch road The resistance value. , They are respectively t Time Node i and nodes j The square of the voltage amplitude, branch road The reactance value.

[0029] Node power balance constraints:

[0030] In the formula: u ( j ) as j The set of all initial nodes of the terminal node; , They are respectively t Time Branch The active and reactive power flowing through; , They are respectively t The photovoltaic inverter in the distribution network supplies power to the distribution network nodes at all times. j Injected active power and reactive power; , They are respectively t Injecting nodes at all times j The net active and reactive loads; for t The distribution network is constantly sending data to the access nodes. j Reactive power injected into the microgrid; for t Time Node j The amount of reactive load reduction.

[0031] Safe operation constraints: The distribution network must also ensure that the node voltage is within a safe range, and it must also meet the branch current constraints, as shown in the following formulas:

[0032] In the formula: express t Time Node i The square of the voltage amplitude, , They are nodes i The square of the maximum voltage amplitude and the square of the minimum voltage amplitude. Indicates the flow through a branch road The square of the current amplitude, To allow flow through the branch The square of the maximum current amplitude.

[0033] Control constraints for distributed photovoltaic inverters: This invention employs an optimal control model for PV inverters, which can regulate the active and reactive power outputs of the photovoltaic inverter. The resulting operating constraints are as follows:

[0034] In the formula: 、 They are respectively t Photovoltaic injection node j The active and reactive power; for t Photovoltaic injection node j The upper limit of active power at that location; For nodes j The rated capacity of the photovoltaic inverter; This is the minimum power factor of the PV inverter, which is usually a given constant.

[0035] Distribution network reconfiguration constraints:

[0036] In the formula: For 0-1 variables, if the node j For nodes i The parent node, then It is 1 if it is true, otherwise it is 0. For the collection of all branches of the distribution network, R The set of root nodes; ε This represents the maximum number of switching operations allowed during the network reconfiguration process within the scheduling cycle.

[0037] The microgrid constraints include wind turbine output constraints, photovoltaic active and reactive power output constraints, micro gas turbine active and reactive power output constraints, energy storage system output constraints, and microgrid power balance constraints.

[0038] Wind turbine output constraints:

[0039] In the formula: 、 They are respectively t Wind turbine injection node j The active and reactive power; for t Wind turbine injection node j The upper limit of active power at that location; 、 They are respectively t Wind turbine injection node j The upper and lower limits of reactive power at the location.

[0040] Constraints on active and reactive power output of photovoltaic power: consistent with the constraints on distributed photovoltaic power in the distribution network.

[0041]

[0042] Active and reactive power output constraints of micro gas turbines:

[0043] In the formula: 、 They are respectively t The micro gas turbine transmits power to the node via an inverter. j Injected active and reactive power; , They are respectively t Timing of micro gas turbine injection node j The upper and lower limits of active power at the location; For nodes j The rated capacity of the inverter for the micro gas turbine.

[0044] Energy storage system output constraints:

[0045] In the formula: , They are respectively t Real-time energy storage system at nodes j The upper limit of active power for charging and discharging; , They are respectively t Real-time energy storage system to nodes j Injected active power and reactive power; for t Time Node j The maximum apparent power of the energy storage system; for t Time Node j The amount of electricity stored in an energy storage system; for t Time Node j The upper limit of the amount of electricity that an energy storage system can store is generally set. In The level should be between 10% and 90% to protect the battery; , They are nodes jThe initial and final values ​​of the stored energy in the energy storage system during the scheduling cycle are equal, which is determined by the state of charge of the energy storage system.

[0046] Microgrid power balance constraints:

[0047] In the formula: , , , Access nodes j Active power output from wind power, photovoltaic power, gas turbines, and energy storage in a microgrid; , , , Access nodes j Reactive power output from wind power, photovoltaic power, gas turbines, and energy storage in a microgrid; , They are respectively t Always access node j Net active and reactive loads in a microgrid.

[0048] Step S2: Aggregate the active and reactive power feasible regions (FRs) of the distributed energy resources (DERs) of the microgrid, and establish the microgrid operating feasible region (OFR). k An approximate model is used to calculate the upper and lower limits of microgrid output and upload them to the distribution network for coordinated and optimized operation. The basic quantities required for modeling the active and reactive power output (FR) of a microgrid's DER are the maximum and minimum output power and the energy demand over time. A power and energy boundary model is used to model the FR of a single DER cell.

[0049]

[0050] In the formula: express t The active power output of the microgrid at any given time. , They are respectively t The lower and upper limits of microgrid output at all times. , They are respectively t The lower and upper limits of the energy boundary of a microgrid at any given time. This represents the minimum running time within the scheduling cycle.

[0051] Based on the characteristics of DERs, DERs in microgrids are divided into two categories. DERs with no constraints on input and output energy and no restrictions on the duration of power output are classified as generator-like flexibility resources. DERs with constraints on both input and output energy and restrictions on the duration of power output are classified as energy storage-like flexibility resources. The power and energy boundary model for generator-like flexibility resources takes the following form:

[0052] In the formula, , They are respectively τ Lower and upper limits for the output of time-based generator flexibility resources. , They are respectively t The lower and upper limits of the energy aggregation of flexible resources for time-based generators.

[0053] For energy storage-like flexible resources, in time t The derivation of the upper and lower bounds of the shifted energy is as follows:

[0054] In the formula, It is the initial charge state of a type of energy storage flexibility resource. , These represent the upper limits of active power for charging and discharging of the energy storage flexibility resource at time t; the specified upper and lower energy limits represent the maximum energy capacity of the energy storage resource. 90% and 10%. The derivation of the lower limit energy is similar to that of the upper limit energy. Variables and These represent the upper and lower limits of energy for flexible energy storage resources, respectively.

[0055] The precise feasible region is used for trajectory filtering using a binary structure, which is transformed into matrix inequality form, as follows:

[0056] In the formula, This represents the feasible domain vector arranged in descending order of time. for The set of all trajectories of a complete binary structure; Representing the trajectory The data of all nodes, excluding the root node. 3D column vector; , These represent the upper and lower limits of the feasible domain corresponding to trajectory l, respectively; This is a matrix transpose operation; Thek The order approximation is to choose those non-zero nodes with no more than [number missing]. k Use the path to construct constraints; k The OFR model under the first-order approximation is:

[0057] In the formula, the definition is... And establish the trajectory and feasible region vector. The correspondence is obtained in the equivalent form Then the matrix inequality is equivalent to: This serves as the precise operational feasible region model for the microgrid; among which, For trajectory exist The value at time; For 1- t Time Track Summation of values; t To accumulate to the specified time; Take 1- t time; The feasible domain power vectors are arranged in descending order of time. Since the microgrid aggregates the active and reactive power (FR) of the DER (Distribution Grid), calculates the upper and lower limits of the microgrid output, and uploads them to the distribution network for coordinated optimization operation, the distribution network no longer collects the specific parameters of the DER within the microgrid. Therefore, the distribution-microgrid coordinated optimization operation model is rewritten as follows:

[0058] In the formula, For the cost of purchasing electricity for the distribution network, Cost of voltage deviation in distribution network For distribution network loss costs, This indicates the cost of load reduction. This represents the operating cost of a microgrid.

[0059] Based on the different properties of variables in the system, the decision variables in the distribution network and microgrid are divided into coordination variables and internal variables. The distribution-microgrid collaborative optimization model can be expressed in the following form:

[0060] In the formula: Indicates the constraints of the distribution network layer; Indicates the constraints of the microgrid layer; n Indicating the index of the microgrid, N A collection of microgrids; x This represents the coordination variables between the distribution network and the microgrid, such as the interaction power between the two. y This represents the internal variables of the power grid, specifically the DER output in a microgrid. Represents variables within the distribution network layer. microgrid n The internal variables.

[0061] For the above model, due to the coordination variables x The existence of this prevents the distribution network layer and the microgrid layer from independently optimizing. If it were possible to fix... x By determining the value of , the joint optimization model can be solved hierarchically.

[0062] Step S3: Based on the equivalent projection theory, this invention eliminates internal variables in the microgrid optimization model without changing the system's optimality. y Only through a set of coordinating variables x The inequality constraints characterize the operating characteristics of the microgrid. Simultaneously, the operating cost of the microgrid is transformed into an inequality form using a superordinate diagram. The operating cost of a microgrid is represented by variables. limit The possible values ​​of , where It can be larger than the microgrid. n Operating costs For any value of the supremum, the model can be modified as follows:

[0063] In the above model, ( As a microgrid n The augmented coordination variables, the distribution network and the microgrid are only connected through ( Coupling, internal variables It only appears in the microgrid constraints and no longer in the microgrid layer objective function, effectively protecting privacy information such as microgrid layer cost.

[0064] Eliminating internal variables in the original model through equivalent projection. y Construct a system that only considers the coordinating variables. x With cost variables C The dimensionality reduction model uses the equivalent projected feasible region to replace the original subsystem model in the distribution network optimization decision-making, while ensuring that the result is equivalent to the original model.

[0065] Step S4: The distribution network layer solves for the optimal coordination variables based on the OFR feasible region uploaded by the microgrid. and optimal cost variables Simultaneously satisfying network reconfiguration constraints and power flow security constraints, a new power grid structure that meets the constraints is sought in each time period, and a switching operation scheme is generated. In the above process, each microgrid submits its reduced-dimensional equivalent projection model to replace the original model to participate in the collaborative optimization operation of the distribution network layer. The collaborative optimization operation model can be equivalently decomposed into the distribution network layer optimization model and the microgrid layer optimization model.

[0066] The distribution network layer optimization model is expressed as follows:

[0067] The microgrid layer optimization model is expressed as follows:

[0068] In the formula: and The optimal solution is obtained from the optimization model of the distribution network layer.

[0069] Step S5: Microgrid layer with and Calculate the internal variables of the microgrid as boundary conditions. The optimal solution, i.e. the optimal operating point of the microgrid, is to decompose the total output of the microgrid into each DER, so that the microgrid can also operate optimally.

[0070] Therefore, the total power decomposition model of the microgrid is as follows:

[0071] In the formula: For decomposition error, microgrid n The Middle k The specific contributions of each DER K Indicates the number of DERs in the microgrid. It is the index of the last non-zero element in the binary tree path.

[0072] Step S6: Verify whether the reconfigured distribution-microgrid system meets all constraints, and check... k Check if the decomposition error of the approximate model meets the requirements; if decomposition error exists, adjust accordingly. k If the order of the approximate model is recalculated, the network topology is updated, switching operations are performed, and the scheduling plan for each microgrid DER is output. Step S7: Based on the detailed scheduling plan generated in Step S6, evaluate the fault recovery effect, calculate performance parameters such as comprehensive cost index, output the optimal collaborative recovery strategy of distribution-microgrid, and the process ends.

[0073] Example: Comparative analysis of optimization results in different scenarios Considering the simultaneous occurrence of permanent line failures on two lines between nodes 5-6 and 13-14 of the distribution network under extreme weather conditions, the effectiveness of the proposed strategy is verified by setting up the following three scenarios: Scenario 1: The distribution network does not consider network reconfiguration, and the distribution network islands are supported by microgrids; Scenario 2: Close some tie switches in the distribution network to form a fault recovery topology that ensures the radial operation constraints of the distribution network; Scenario 3: Based on Scenario 2, dynamically adjust the state combination of the distribution network interconnection switch.

[0074] In Scenario 1, the power distribution network is divided into three independent islands due to a permanent line fault, such as... Figure 1 As shown in the diagram. Due to the change in grid topology after fault isolation, the upstream grid can only provide continuous power support to island 1, while islands 2 and 3 lose their connection to the main grid and can only rely on the autonomous operation of their internal distributed photovoltaic power generation systems and microgrids to maintain power supply. This operating mode makes the electricity purchase cost from the upstream grid for the distribution network significantly lower than in scenarios 2 and 3. However, during periods of insufficient photovoltaic output, the power generation capacity within islands 2 and 3 cannot fully meet the load demand, forcing the system to implement load shedding measures to maintain power balance. The load shedding amount under scenario 1 is as follows: Figure 2 As shown, these forced load cuts resulted in considerable load reduction costs, which to some extent offset the benefits of lower electricity purchase costs.

[0075] Compared to Scenario 1, Scenario 3 achieves a significant reduction in total cost by dynamically reconfiguring the distribution network topology, saving RMB 5,364.4 (approximately 7.7%). This optimization primarily stems from the complete elimination of load shedding costs. First, by eliminating islanded operation, Scenario 3 completely avoids load shedding costs, fundamentally resolving user economic losses and power reliability issues caused by power outages. Second, Scenario 3 optimizes power distribution through the coordinated operation of the main grid and microgrids, reducing microgrid operating costs by RMB 924.8 and network loss costs by RMB 809.3, demonstrating the precise control of power flow through dynamic regulation. Compared to Scenario 1, Scenario 3, through coordinated operation with the main grid and microgrids, not only significantly improves the absorption capacity of renewable energy and reduces curtailment of solar power, but also ensures reliable power supply around the clock, showcasing the dual advantages of dynamic reconfiguration technology in improving the economic efficiency and reliability of distribution network operation.

[0076] Scenario 3 reduced operating costs by 316.2 yuan (approximately 0.5%) compared to Scenario 2. Voltage fluctuation decreased from 0.0423 pu to 0.0125 pu, a reduction of 70.4%. By dynamically adjusting the tie switch status, system network loss costs were further reduced by 2.1% compared to Scenario 2, demonstrating that dynamically adjusting the tie switch can more flexibly balance power flow and suppress voltage fluctuations. As shown in Table 1, Scenario 3, through the implementation of a dynamic tie switch adjustment strategy, achieved a comprehensive improvement in system performance while maintaining unchanged power supply reliability. This strategy effectively reduced the operating costs of both the main grid and the microgrid by optimizing the switch status in real time. Regarding voltage quality, the system exhibited significant improvement, with voltage fluctuation range precisely controlled at a more optimal level.

[0077] Table 1 Switch Actions in Scenario 3

[0078] In the process of distribution-microgrid collaborative fault recovery considering dynamic network reconfiguration, the microgrid demonstrates its dynamic response capability to distribution network load fluctuations through multi-source collaborative optimization scheduling strategies. The microgrid output in scenario 3 is as follows: Figure 3 As shown. During the [0:00, 4:00) period, the system is in a low-load period. At this time, the photovoltaic output of the microgrid is zero, the gas turbine maintains a stable output, and together with the wind power output, forms the basic power supply. Energy storage is generally in a charging state and maintains system balance through power exchange with the distribution network. During the [4:00, 12:00) period, the load rapidly increases, and during the [7:00, 12:00) period, the photovoltaic output increases synchronously. The energy storage flexibly switches its charging and discharging modes according to the changes in photovoltaic output. The photovoltaic system both absorbs local power generation and sends surplus power back to the distribution network. During the [12:00, 15:00) period, the load remains high, and the energy storage in each microgrid discharges at high power, effectively supporting the afternoon load peak of the distribution network. During the [15:00, 18:00) period, load demand decreases, the energy storage charging and discharging strategies differ significantly, and the trading volume fluctuates more, reflecting the system's dynamic adjustment capability in response to evening load changes. Between 18:00 and 21:00, the load increases again, the photovoltaic output is zero, the gas turbine continues to operate stably, and the energy storage adopts different strategies according to the needs of each microgrid. Between 21:00 and 24:00, the load drops, the system enters a stable state, the energy storage performs a small charge, returns to its initial state of charge, and provides accurate initial conditions for the next cycle.

[0079] (2) Comparative analysis of the computational performance of approximate models For the accurate OFR model of microgrids, this invention adopts kThe model was approximated using the first-order approximation. Table 2 shows a comparison of the active and reactive power decomposition errors under the first to third-order approximations. As can be seen from Table 2, under the second-order approximation, the decomposition error of active and reactive power is already very small, almost negligible, indicating that the model at this order has high accuracy. Although the third-order approximation significantly increases the model complexity compared to the second-order approximation, it contributes almost nothing to improving the decomposition error.

[0080] Table 2 Comparison of decomposition errors at orders 1-3

[0081] in, L k for k The specific steps of the collaborative optimization algorithm, combining the path set selected by the approximate model with the established distribution-microgrid collaborative fault recovery model and equivalent projection solution method, are as follows: Step 1: Establish an optimization function with the objectives of electricity purchase cost, voltage deviation, network loss, load reduction and microgrid operating cost, and set a limit on the maximum number of switching operations for network reconfiguration.

[0082] Step 2: Based on k The first-order approximation method simplifies the microgrid OFR model, calculates the feasible domain boundary of active / reactive power in each time period, and uploads it to the distribution network layer as a collaborative optimization constraint to achieve information interaction under privacy protection.

[0083] Step 3: Based on the equivalent projection theory, eliminate variables within the microgrid and construct a dimensionality-reduced model containing only coordination and cost variables, forming a framework for decomposing the distribution network layer optimization problem and the microgrid layer sub-problems.

[0084] Step 4: The distribution network layer solves for the optimal coordination variables based on the OFR feasible region uploaded by the microgrid. and optimal cost variables Simultaneously satisfying network reconfiguration constraints and power flow security constraints, a new power grid structure that satisfies constraints such as radial topology, power flow security, and equipment capacity is sought in each time period, and a switching operation scheme is generated.

[0085] Step 5: Each microgrid receives the data from the distribution network. and As boundary conditions, the total output is decomposed into distributed resources such as wind power, photovoltaics, and energy storage through power balance constraints and DER operation constraints.

[0086] Step 6: Verify whether the refactored system meets all constraints. k Check if the decomposition error of the approximate model meets the requirements; if decomposition error exists, adjust accordingly. kThe order of the approximate model is recalculated; otherwise, the network topology is updated, switching operations are performed, and the scheduling plan for each microgrid DER is output.

[0087] Step 7: Based on the switching operation actions and the scheduling plans of each microgrid DER, evaluate the fault recovery effect, calculate performance parameters such as comprehensive cost indicators, output the optimal collaborative recovery strategy between distribution and microgrid, and the process ends.

[0088] Among them, the method for verifying the reconstructed system and evaluating the fault recovery effect analysis is to write a program based on the model, and the program can directly solve whether the result meets the requirements.

Claims

1. A method for power-micro coordination fault recovery considering network dynamic reconfiguration, characterized in that, A distribution-microgrid collaborative fault recovery model considering network dynamic reconfiguration is established, and the distribution-microgrid collaborative fault recovery is completed through the distribution-microgrid collaborative fault recovery model, including the following steps. Step S1: The distribution-microgrid collaborative fault recovery model takes the minimum of the sum of the power purchase cost, the voltage deviation cost, the network loss cost, the load reduction cost and the microgrid operation cost of the distribution network as the target, and establishes a target function by comprehensively considering the distribution network constraint condition and the microgrid constraint condition, and sets a limit on the maximum number of switch operations for network reconfiguration; Step S2: aggregate the active and reactive power feasible region FR of the distributed energy resources DER of the microgrid, calculate the upper and lower limits of the microgrid output by establishing a quadratic approximation model of the microgrid operation feasible region OFR, and upload to the distribution network to participate in coordinated optimization operation; k Step S2: aggregate the active and reactive power feasible region FR of the distributed energy resources DER of the microgrid, calculate the upper and lower limits of the microgrid output by establishing a quadratic approximation model of the microgrid operation feasible region OFR, and upload to the distribution network to participate in coordinated optimization operation; Step S3: in establishing the k approximation model, the decision variables in the distribution network and the microgrid are divided into coordination variables x and internal variables y , without changing the optimality of the system, by means of equivalent projection, the internal variables y of the microgrid are eliminated, a reduced dimension model about the microgrid is constructed, only about the internal variables x and the cost variables C , each microgrid submits the equivalent projection model of the reduced dimension to participate in the collaborative optimization operation of the distribution network layer, forming a decomposition framework of the distribution network layer optimization problem and the microgrid layer sub-problem; that is, in the coupling of the distribution network and the microgrid, the internal variables y of the microgrid only appear in the microgrid constraint conditions, and no longer appear in the microgrid layer objective function, protecting the privacy information of the microgrid layer; Step S4: The distribution network layer solves the optimal coordination variable based on the OFR feasible region uploaded on the microgrid and the optimal cost variable while meeting the network reconfiguration constraint and the power flow safety constraint, respectively finding a new structure of the power grid meeting the constraint condition in each period to generate a switch operation scheme; Step S5: Microgrid layer with and Calculate the internal variables of the microgrid as boundary conditions. The optimal solution, i.e. the optimal operating point of the microgrid, is to decompose the total output of the microgrid to each DER, so that the microgrid can also operate optimally. Step S6: Check whether the reconstructed micro-grid system meets all the constraints, and check whether the decomposition error of the approximate model meets the requirements. If there is a decomposition error, adjust the order of the approximate model k Step S6: Check whether the reconstructed micro-grid system meets all the constraints, and check whether the decomposition error of the approximate model meets the requirements. If there is a decomposition error, adjust the order of the approximate model k Step S6: Check whether the reconstructed micro-grid system meets all the constraints, and check whether the decomposition error of the approximate model meets the requirements. If there is a decomposition error, adjust the order of the approximate model Step S7: Based on the scheduling plan generated in step S6, the effect of fault recovery is evaluated, the comprehensive cost index and other performance parameters are calculated, the optimal collaborative recovery strategy of the distribution-microgrid is output, and the process ends. 2.The method of claim 1, wherein the method further comprises: The distribution network constraint conditions include distribution network power flow constraints, node power balance constraints, safe operation constraints, distributed photovoltaic inverter control constraints and distribution network network reconfiguration constraints. 3.The method of claim 1, wherein the method further comprises: The microgrid constraint conditions include wind turbine output constraints, photovoltaic active and reactive power output constraints, micro gas turbine active and reactive power output constraints, energy storage system output constraints and microgrid power balance constraints. 4.The method of claim 1, wherein the method further comprises: The basic quantities required for modeling the active and reactive power output FR of the DER of the microgrid are the maximum and minimum power that can be output and the energy demand over time, and the power and energy boundary model is used to model the FR of the DER individual: ； In the formula, denotes t active power output of the microgrid at the moment, , are t lower and upper limits of the microgrid output at the moment, , are t lower and upper limits of the microgrid energy boundary at the moment, is the minimum operating time in the dispatch cycle; According to the characteristics of the DER, the DER in the microgrid is divided into two categories, the DER without constraints on input and output energy and limited to the time duration of power output is classified as a generator-like flexibility resource, and the DER with constraints on input and output energy and limited to the time duration of power output is classified as a storage-like flexibility resource; The power and energy boundary model of the generator-like flexibility resource is in the following form: ； In the formula, , are respectively the lower limit and the upper limit of the output of the generator flexibility resource at the time class, , are respectively t the lower limit and the upper limit of the aggregated energy of the generator flexibility resource at the time class. For the class of energy storage flexibility resources, the time t The upper and lower energy bounds are derived as follows: ； In the formula, It is the initial charge state of a type of energy storage flexibility resource. , They are respectively t The upper limit of active power for charging and discharging of time-sensitive energy storage resources; the specified upper and lower energy limits are respectively the maximum energy capacity of the energy storage resources. 90% and 10%, variables and These represent the upper and lower limits of energy for flexible energy storage resources, respectively. The scheduling period; The accurate operation feasible region is screened by using a binary structure to convert into a matrix inequality form, which is represented as: ； wherein, represents the feasible region vectors arranged in descending order of time; is all the trajectory sets of the complete binary structure; represents the trajectory the dimensional column vector; , respectively represent the upper and lower limits of the operating feasible region corresponding to the trajectory respectively represent the upper and lower limits of the operating feasible region corresponding to the trajectory is the matrix transposition operation.

5. The method of claim 1, wherein the method further comprises: The k-order approximation is to select those paths with no more than k non-zero nodes to construct the constraints; the OFR model under the k-order approximation is: ； In the formula, the definition is... And establish the trajectory and feasible region vector. The correspondence is obtained in the equivalent form Then the matrix inequality is equivalent to: This serves as the precise operational feasible region model for the microgrid; among which, For trajectory exist The value at time; Trajectory at time 1-t Summation of values; t To accumulate to the specified time; Take 1- t time; The feasible domain power vectors are arranged in descending order of time. 6.The method of claim 1, wherein the method further comprises: The total power decomposition model of the microgrid is: ； wherein: is the decomposition error, denotes the microgrid layer constraints, denotes the m-th microgrid n the specific output of the n-th DER in the m-th microgrid, k K denotes the number of DERs in the microgrid, N denotes the set of microgrids, is the index of the last non-zero element in the binary tree path.​

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