Interconnected distribution network multi-period distributed power supply restoration method based on space-time domain decomposition

Abstract

The application discloses a kind of interconnection distribution network multi-period distributed power supply recovery method based on space-time field decomposition.First, establish interconnected distribution network power supply recovery global optimization model;Then, global optimization problem is decomposed in space domain, so that interconnected distribution network power supply recovery global optimization model is decomposed into each distribution network subzone space decomposition optimization model;Further, each distribution network subzone optimization subproblem is decomposed in time domain, and each distribution network subzone time decomposition optimization model is obtained;Finally, inner solver uses ADMM algorithm to solve each time period each distribution network subzone time decomposition optimization model, obtains the local optimal solution of each distribution network subzone, and is passed to outer solver;Outer solver uses ADMM algorithm to solve global optimal solution.Through space-time double-dimension decomposition, large-scale multi-period interconnected distribution network optimization problem is decomposed into multiple small-scale subproblems and parallelly solved, and the solving scale and computational complexity of single subproblem are significantly reduced, and the real-time performance of fault recovery is improved.

Description

Technical Field

[0001] This invention belongs to the field of power supply restoration technology after a fault in an interconnected distribution network. Specifically, it is a multi-period distributed power supply restoration method for interconnected distribution networks based on spatiotemporal domain decomposition. It is applicable to scenarios where large-scale new energy sources and energy storage are connected to the distribution network, enabling efficient power supply restoration and scheduling of the distribution network after a fault occurs. It can effectively solve problems such as high complexity of multi-period scheduling and heavy communication burden. Background Technology

[0002] Against the backdrop of accelerated global energy transition, the large-scale integration of distributed power sources, represented by photovoltaics and wind power, is gradually upgrading traditional distribution networks into interconnected distribution networks with multi-entity collaboration and interaction between power sources, grids, loads, and storage. However, extreme weather and equipment failures can easily trigger localized or large-scale power outages in distribution networks. The intermittent nature of new energy sources, the time-coupled characteristics of energy storage state of charge (SOC), and the multi-regional collaboration requirements of interconnected distribution networks pose challenges to traditional centralized power restoration methods, including large solution scale, low computational efficiency, and insufficient data privacy protection. Distributed architectures avoid infringing on user privacy and improve solution speed. Therefore, promoting distributed collaborative control of interconnected distribution networks is crucial for enhancing the power restoration capabilities of distribution networks, aiming to solve distributed power restoration decisions in interconnected distribution networks when main transformers experience extreme faults, and fully leveraging the network flexibility between interconnected distribution networks.

[0003] Existing power restoration research largely focuses on single-time, single-region distribution networks, failing to fully consider the cross-time constraints of energy storage SOC and the spatial coordination requirements of interconnected distribution networks under multi-time scenarios. This limits the economics and feasibility of restoration strategies. Existing distributed research often focuses on spatial subsystem decomposition, achieving coordination only through boundary variables such as single tie-line power, neglecting the deep correlation between fault propagation timing characteristics and spatial resource distribution. This easily leads to restoration path conflicts and resource allocation imbalances. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the technical problem this invention aims to solve is to provide a multi-period distributed power supply restoration method for interconnected distribution networks based on spatiotemporal domain decomposition. By using a two-dimensional "space-time" decomposition, this method aims to solve technical problems such as low solution efficiency, complex spatiotemporal constraint coupling, and insufficient data privacy protection in the multi-period power supply restoration of large-scale interconnected distribution networks.

[0005] The present invention solves the aforementioned technical problem by adopting the following technical solution: A method for restoring distributed power supply across multiple time periods in an interconnected distribution network based on spatiotemporal domain decomposition, characterized by the following steps: Step S1: Establish a global optimization model for power supply restoration of the interconnected distribution network, the compact form of which is as follows: (1) In the formula, The scheduling period; This represents the number of normal distribution network sub-areas. and The objective functions are for the normal distribution network sub-area and the faulty distribution network sub-area, respectively. and They are respectively and Optimization variables for the network sub-area at all times; and They are respectively and Optimization variables for faulty distribution network sub-areas at any given time; and These are the feasible regions for optimizing variables in normal distribution network sub-areas and faulty distribution network sub-areas, respectively. and These are the operational constraints for normal distribution network sub-areas and faulty distribution network sub-areas, respectively. , Equation constraints for time coupling within normal and faulty distribution network sub-areas; The boundary equality constraints are for the normal distribution network sub-area and the faulty distribution network sub-area. for Boundary variables of the normal distribution network sub-region at all times; express Boundary variables of the faulty distribution network sub-area at any given moment; Step S2: Decompose the global optimization problem in the spatial domain, thereby decomposing the global optimization model for power supply restoration of the interconnected distribution network into spatial decomposition optimization models for each distribution network sub-area; The spatial decomposition optimization model for faulty distribution network sub-areas is as follows: (14) In the formula, An augmented Lagrangian function for the spatial decomposition of faulty distribution network sub-regions; The dual multiplier for the spatial decomposition of faulty distribution network sub-regions; This is a transpose operation; for Spatial consensus variables at any given time; The penalty factor for the spatial decomposition of faulty distribution network sub-areas; It is an L2 norm; The normal distribution network sub-area spatial decomposition optimization model is as follows: (15) In the formula, The augmented Lagrangian function for the spatial decomposition of normal distribution network sub-regions; The dual multiplier for the spatial decomposition of sub-regions in a normal distribution network; The penalty factor for the spatial decomposition of normal distribution network sub-areas; Step S3: Decompose the optimization sub-problems of each distribution network sub-area in the time domain to obtain the time decomposition optimization model of each distribution network sub-area; The time decomposition optimization model for the faulty distribution network sub-area is as follows: (16) In the formula, An augmented Lagrangian function for the time decomposition of faulty distribution network sub-areas; express The dual multiplier of the time decomposition of the fault distribution network sub-area; for Energy storage SOC in the distribution network sub-area during constant failure; for Global State of Charge (SOC) at any given moment; for Penalty factor for time decomposition of distribution network sub-area in case of moment failure; Similarly, the time decomposition optimization model for a normal distribution network sub-area is as follows: (17) In the formula, The augmented Lagrangian function for the time decomposition of a normal distribution network sub-area; for The dual multiplier of the time decomposition of the normal distribution network sub-area at any given time; for The energy storage SOC of the distribution network sub-area is always normal; for The penalty factor for the time decomposition of the normal distribution network sub-area at all times; Step S4: The inner solver uses the ADMM algorithm to solve the time decomposition optimization model of each distribution network sub-area in each time period, obtains the local optimum solution of each distribution network sub-area, and passes it to the outer solver; Given the boundary variables of the distribution network sub-regions, the spatial consensus variables, global energy storage SOC, the dual multipliers of spatial decomposition, the dual multipliers of temporal decomposition, and the penalty factors of temporal decomposition of each distribution network sub-region are initialized. Solve the time decomposition optimization model of each distribution network sub-area independently for each time period to obtain the current local solution of each distribution network sub-area; Update the global energy storage SOC using equation (18): (18) In the formula, for Time of the first The next iteration of global energy storage SOC; for Time of the first The energy storage SOC of the next iteration distribution network sub-region; , for Time of the first Energy storage SOC of sub-regions in both fault and normal distribution networks; , for Time of the first Dual multipliers and penalty factors of time decomposition of normal distribution network sub-regions in the next iteration; This refers to the number of interactions between the distribution network and energy storage. Update the dual multipliers of the time decomposition of the distribution network sub-region using equation (19): (19) In the formula, For the first Dual multipliers of the time decomposition of sub-regions in the next iteration; The original residual and dual residual of the global energy storage SOC are calculated according to equation (20): (20) If both the original residual and the dual residual of the global energy storage SOC are less than or equal to their respective convergence thresholds, the iteration ends, and the local optimal solution for each distribution network sub-region is output; otherwise, the global variables of the energy storage SOC and the dual multipliers of the time decomposition of the distribution network sub-region are updated, letting... The aforementioned iterative process is repeated until convergence is achieved; the local optimal solutions of each distribution network sub-region are passed to the outer solver. Step S5: The outer solver uses the ADMM algorithm to find the global optimum. Adjacent distribution network sub-areas exchange boundary variables through coupled branches, and update spatial consensus variables according to equation (21); (twenty one) In the formula, For the first Spatial consensus variables for the normal distribution network sub-region in the next iteration; , For the first Boundary variables for the normal distribution network sub-area and the faulty distribution network sub-area in the next iteration; , For the first Dual multipliers and penalty factors for the spatial decomposition of normal distribution network sub-regions in the next iteration; The number of distribution network sub-regions participating in spatial decomposition; The dual multipliers of the spatial decomposition of normal and faulty distribution network sub-regions are updated using equation (22): (twenty two) In the formula, , For the first The dual multipliers of the spatial decomposition of normal and faulty distribution network sub-regions in the next iteration. For the first Penalty factor for spatial decomposition of faulty distribution network sub-regions in the next iteration; Calculate the original residuals and dual residuals of the spatial consensus variables according to equation (23): (twenty three) If the original residuals and dual residuals of the spatial consensus variables are less than or equal to their respective convergence thresholds, the iteration ends, and the global optimal solution, i.e., the optimal power supply restoration scheme, is output; otherwise, the spatial consensus variables and the dual multipliers of the spatial decomposition for each distribution network sub-region are updated, letting... Then return to step S4 and repeat the aforementioned iterative process until convergence is achieved, thus obtaining the global optimal solution.

[0006] Furthermore, the objective function for the faulty distribution network sub-area is: (2) In the formula, Indicates the time step; This represents the set of nodes in the faulty distribution network sub-area. A set of feeder switches; Cost of power outages; express Time Node The net load active power; for Time Node Load pickup status; This indicates the on-grid electricity price for active power in the distribution network; Represented by node The set of the starting nodes of the branches of the terminal nodes; Indicates a branch The resistance; and They represent Time Branch The active and reactive power; express The root node voltage at time t; Indicates the cost of switching operations; for time Discrete variables of the feeder switch state of the branch; express The initial state variables of the feeder switch at any given time; This indicates the cost of penalties for curtailing solar power. express Time Node The reduction in photovoltaic active power at the location; Indicates the operating cost of energy storage; for Time Node The active power of energy storage at the location; The objective function for a normal distribution network sub-area is: (3) In the formula, Indicates a normal distribution network sub-area The set of nodes; express Time Branch The transmission current; Represents a node The set of upstream nodes.

[0007] Compared with the prior art, the present invention has the following beneficial effects: 1. The "space-time" dual-dimensional decomposition framework proposed in this invention handles the spatial coordination between subnets and the temporal coupling constraints within subnets through the inner and outer ADMM layers respectively. It decomposes the optimization problem of large-scale multi-time period interconnected distribution networks into multiple small-scale sub-problems that are solved in parallel, which significantly reduces the solution scale and computational complexity of a single sub-problem and improves the real-time performance of fault recovery.

[0008] 2. This invention proposes a discrete variable relaxation and smoothing strategy to transform the non-convex discrete optimization problem into a continuous SOCP model, effectively suppressing variable oscillations during the iteration process, ensuring the stability and convergence of the solution, and improving the solution accuracy. Under the distributed architecture, each distribution network sub-area only needs to exchange boundary variables, without sharing all internal data, which reduces the communication burden, protects data privacy, and enhances the scalability and practicality of the algorithm in multi-entity scheduling scenarios. By comprehensively considering multiple optimization objectives such as renewable energy consumption, energy storage operation, and load restoration, this invention improves the power restoration rate while reducing system operating costs and renewable energy curtailment rates, achieving a balance between the economy and reliability of power restoration. Attached Figure Description

[0009] Figure 1 This is the overall flowchart; Figure 2 This is an example of an interconnected power distribution network topology. Figure 3 The graph shows the changes of the original residuals and dual residuals of the spatial consensus variables as a function of the number of iterations in the example. Figure 4 This is a diagram showing the voltage distribution at the nodes of the distribution network. Detailed Implementation

[0010] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, but this does not limit the scope of protection of this application.

[0011] like Figure 1 As shown, this invention provides a multi-period distributed power supply restoration method for interconnected distribution networks based on spatiotemporal domain decomposition, comprising the following steps: Step S1: Establish a global optimization model for power supply restoration of the interconnected distribution network, the compact form of which is as follows: (1) In the formula, The scheduling period; Indicates the number of normal distribution network sub-areas; and These are the normal distribution network sub-areas. Objective function for faulty distribution network sub-areas; and They are respectively and Normal network distribution sub-area at all times Optimization variables; and They are respectively and Optimization variables for faulty distribution network sub-areas at any given time; and These are the normal distribution network sub-areas. The feasible domain of optimization variables for faulty distribution network sub-areas; and These are the normal distribution network sub-areas. Operating constraints of the faulty distribution network sub-area; Normal distribution network sub-area Internal time-coupling equality constraints; The time coupling equation constraint condition within the faulty distribution network sub-area; Normal distribution network sub-area Boundary equality constraints with faulty distribution network sub-regions; for Normal network distribution sub-area at all times Boundary variables; express Boundary variables of the faulty distribution network sub-area at any given time.

[0012] (1) The objective function of the fault distribution network sub-region is to minimize the sum of load loss cost, distributed photovoltaic active power loss cost, grid loss cost and switch operation cost. Further expressed as: (2) In the formula, Indicates the time step, in this embodiment =1h; This represents the set of nodes in the faulty distribution network sub-area. A set of feeder switches; Cost of power outages; express Time Node The net load active power; for Time Node Load pickup status, This indicates that the load was not picked up. This indicates that power has been restored to the load; This indicates the on-grid electricity price for active power in the distribution network; Represented by node The set of the starting nodes of the branches of the terminal nodes; Indicates a branch The resistance; and They represent Time Branch The active and reactive power; express The root node voltage at time t; Indicates the cost of switching operations; for time Discrete variables of feeder switch states in branch circuits. express When the feeder switch is closed, express The feeder switch is off at any time; express The initial state variables of the feeder switch at any given time; This indicates the cost of penalties for curtailing solar power. express Time Node The reduction in photovoltaic active power at the location; Indicates the operating cost of energy storage; for Time Node The active power of energy storage at the location.

[0013] (2) Considering the minimum sum of active power loss cost, grid loss cost, and energy storage operation cost of distributed photovoltaic power generation as the optimization objective, the objective function of the normal distribution network sub-area is as follows: Further expressed as: (3) In the formula, Indicates a normal distribution network sub-area The set of nodes; express Time Branch The transmission current; Represents a node The set of upstream nodes.

[0014] (3) Operational constraints of faulty distribution network sub-area These include power flow equation constraints, safe operation constraints, distributed photovoltaic operation constraints, energy storage operation constraints, and radiative topology constraints; i) Power flow equation constraint: (4) In the formula, Represented by node It is the set of branch end nodes of the first node; , express Time Branch The active and reactive power; and They are respectively Time Node Injected active and reactive power; and They are respectively Time Node , The voltage; branch road The reactance value; for Time Node Load pickup status; , They are respectively Time Node The active and reactive power of the load; , They are respectively Time Node The active and reactive power of photovoltaic power generation; express Time Node The reduction in photovoltaic active power at the location; for Time Node The active power of the energy storage device; For branches containing feeder switches, the Big M method needs to be used to relax the branch voltage equations, as shown below: (5) In the formula, M represents a very large constant.

[0015] ii) Safety operation constraints: (6) In the formula, and Representing branches Maximum active and reactive power allowed to be transmitted; and These represent the lower and upper limits of the node voltage for safe operation of the distribution network, respectively. Indicates a branch Maximum transmission current; Indicates a branch Maximum transmission capacity.

[0016] iii) Operational constraints of distributed photovoltaic systems: (7) In the formula, This represents the power factor angle of a photovoltaic inverter. Minimum power factor Set to 0.95; for Time Node Photovoltaic installed capacity at the location.

[0017] iv) Energy storage operation constraints: (8) In the formula, and They represent Time Node The charging and discharging power of the energy storage device; , They represent Time Node In the charging and discharging state of energy storage, if and A '+' indicates charging, and a '-' indicates discharging. , express , Time Node The energy storage SOC (State of Charge) at the location; and Representing nodes respectively The charging and discharging efficiency of the energy storage is less than 1; and They represent Time Node The lower and upper limits of the energy storage SOC.

[0018] v) Radiation topology constraints (9) In the formula, and express The upstream and downstream relationships between time nodes. express Time Node yes The parent node, express Time Node yes The parent node; Represents all nodes A set of boundary nodes that have upstream and downstream relationships.

[0019] To facilitate the solution, the binary feeder switch variables are relaxed to continuous variables in the interval [0, 1] and incorporated into the SOCP model for solution; the exponential moving average smoothing formula is introduced to obtain the discrete variables of the feeder switch state. (10) In the formula, , They are respectively , Time Branch The feeder switch state is a continuous variable; For smoothing coefficients, .

[0020] (4) Normal operation constraints of distribution network sub-areas It includes power flow equation constraints, safe operation constraints, distributed photovoltaic operation constraints, and energy storage operation constraints. The safe operation constraints, distributed photovoltaic operation constraints, and energy storage operation constraints are the same as those of the faulty distribution network sub-area. The power flow equation constraints are as follows: (11) (5) Time coupling equation constraints within each distribution network sub-region , for: (12) Boundary variables of normal distribution network sub-regions Boundary variables of faulty distribution network sub-regions Then the boundary equality constraints of the normal and faulty distribution network sub-regions are... for: (13) In the formula, , They represent Normal network distribution sub-area at all times Boundary nodes of faulty distribution network sub-areas The voltage; , They represent Normal network distribution sub-area at all times via line Active and reactive power transmitted to the faulty distribution network sub-area; , They represent Faulty distribution network sub-area through lines From the normal distribution network sub-area The active and reactive power absorbed.

[0021] Step S2: Decompose the global optimization problem in the spatial domain, thereby decomposing the global optimization model for power supply restoration of the interconnected distribution network into spatial decomposition optimization models for each distribution network sub-area; In the spatial dimension, the interconnected distribution network is decomposed into multiple distribution network sub-regions (including normal distribution network sub-regions and faulty distribution network sub-regions). The power injection and node voltage at the boundaries of each distribution network sub-region are used as spatial consensus variables. The consistency constraints of the spatial consensus variables are introduced into the objective function through the augmented Lagrangian function. The spatial coordination between distribution network sub-regions is coordinated by iteratively updating the spatial consensus variables and the dual multiplier, so as to ensure the consistency of boundary variables.

[0022] By spatial decomposition, the global optimization model for power supply restoration in interconnected distribution networks is decomposed into independent spatial decomposition optimization models for faulty and normal distribution network sub-areas, thereby transforming the global optimization problem into optimization sub-problems for each distribution network sub-area; the spatial decomposition optimization model for the faulty distribution network sub-area is as follows: (14) In the formula, An augmented Lagrangian function for the spatial decomposition of faulty distribution network sub-regions; The dual multiplier represents the spatial decomposition of a faulty distribution network sub-region; This is a transpose operation; for Spatial consensus variables at any given time; The penalty factor for the spatial decomposition of faulty distribution network sub-areas; It is an L2 norm.

[0023] The normal distribution network sub-area spatial decomposition optimization model is as follows: (15) In the formula, The augmented Lagrangian function for the spatial decomposition of normal distribution network sub-regions; Indicates a normal distribution network sub-area Dual multipliers of spatial decomposition; This is the penalty factor for the spatial decomposition of normal distribution network sub-areas.

[0024] Step S3: Decompose the optimization sub-problems of each distribution network sub-area in the time domain to obtain the time decomposition optimization model of each distribution network sub-area; The optimization sub-problems of normal and faulty distribution network sub-areas are decomposed into single-time-period optimization sub-problems in the time domain. Adjacent time periods are coupled into energy storage SOCs. ADMM is used to handle the cross-time-period coupling constraints of energy storage SOCs in each distribution network sub-area, so as to realize the parallel solution of single-time-period optimization sub-problems. The time decomposition optimization model for the faulty distribution network sub-area is expressed as follows: (16) In the formula, An augmented Lagrangian function for the time decomposition of faulty distribution network sub-areas; express The dual multiplier of the time decomposition of the fault distribution network sub-area; for Energy storage SOC in the distribution network sub-area during constant failure; for Global State of Charge (SOC) at any given moment; for The penalty factor for time decomposition of the distribution network sub-area during time-lapse.

[0025] Similarly, the time decomposition optimization model for a normal distribution network sub-area is expressed as: (17) In the formula, The augmented Lagrangian function for the time decomposition of a normal distribution network sub-area; for The dual multiplier of the time decomposition of the normal distribution network sub-area at any given time; for The energy storage SOC of the distribution network sub-area is always normal; for The penalty factor for the time decomposition of the normal distribution network sub-area at all times.

[0026] Step S4: The inner solver uses the ADMM algorithm to solve the time decomposition optimization model of the normal and faulty distribution network sub-areas for each time period, and obtains the local optimal solutions for the normal and faulty distribution network sub-areas: Given the boundary variables of the distribution network sub-region For spatial consensus variables Global Energy Storage SOC Dual multipliers of spatial decomposition Dual multipliers of time decomposition Penalty factor for time decomposition of faulty distribution network sub-area Penalty factor for time decomposition of normal distribution network sub-area Perform initialization; Solve independently from arrive The time decomposition optimization models for faulty distribution network sub-areas and normal distribution network sub-areas in each time period are shown in equations (16) and (17). The current local solution corresponding to each model is obtained, including boundary variables, energy storage SOC, feeder switch status, etc. in each time period. The global energy storage SOC is updated using Equation (18) by utilizing the energy storage SOC of each distribution network sub-area for each time period; (18) In the formula, for Time of the first The next iteration of global energy storage SOC; for Time of the first The energy storage SOC of the next iteration distribution network sub-region; , for Time of the first The energy storage SOC of the faulty distribution network sub-area and the normal distribution network sub-area in the next iteration; , for Time of the first Dual multipliers and penalty factors of time decomposition of normal distribution network sub-regions in the next iteration; This refers to the number of interactions between the distribution network and energy storage. Update the dual multipliers of the time decomposition of the distribution network sub-region using equation (19): (19) In the formula, For the first Dual multipliers of the time decomposition of sub-regions in the next iteration; The original residual and dual residual of the global energy storage SOC are calculated according to equation (20): (20) If both the original residual and the dual residual of the global energy storage SOC are less than or equal to their respective convergence thresholds, then the iteration ends, and the local optimal solutions for the normal and faulty distribution network sub-regions are output; otherwise, the global variables of the energy storage SOC and the dual multipliers of the time decomposition of the distribution network sub-regions are updated, letting... The aforementioned iterative process is repeated until convergence is achieved; the local optimal solutions of the normal distribution network sub-region and the faulty distribution network sub-region are passed to the outer solver.

[0027] Step S5: The outer solver uses the ADMM algorithm to find the global optimum. Adjacent distribution network sub-areas exchange boundary variables through coupled branches. Update the spatial consensus variables according to equation (21); (twenty one) In the formula, For the first Spatial consensus variables for the normal distribution network sub-region in the next iteration; , For the first Boundary variables for the normal distribution network sub-area and the faulty distribution network sub-area in the next iteration; , For the first Dual multipliers and penalty factors for the spatial decomposition of normal distribution network sub-regions in the next iteration; The number of distribution network sub-regions participating in spatial decomposition.

[0028] Based on boundary variables and spatial consensus variables, the dual multipliers of the spatial decomposition of normal distribution network sub-areas and faulty distribution network sub-areas are updated by equation (22); (twenty two) In the formula, , For the first The dual multipliers of the spatial decomposition of normal and faulty distribution network sub-regions in the next iteration. For the first Penalty factor for spatial decomposition of faulty distribution network sub-regions in the next iteration; Calculate the original residuals and dual residuals of the spatial consensus variables according to equation (23): (twenty three) If the original residuals and dual residuals of the spatial consensus variables are less than or equal to their respective convergence thresholds, the iteration ends and the global optimal solution, i.e., the optimal power supply restoration scheme, is output; otherwise, the spatial consensus variables and the dual multipliers of the spatial decomposition of each distribution network sub-region are updated according to equations (21) and (22), and let Then return to step S4 and repeat the aforementioned iterative process until convergence.

[0029] Example This embodiment selects a typical fault—a large-scale power outage caused by a main transformer failure in a distribution network—to verify the feasibility and effectiveness of the proposed method. A 2-IEEE 33 distribution network is used for simulation, with the topology as follows: Figure 2 As shown, during normal operation, the inter-grid interconnection switch TS1 is a normally open switch. The baseline capacity of the entire network is set at 10MVA, and the baseline voltage is the rated voltage of each voltage level network. The upper and lower limits for safe operation of the distribution network node voltage are 0.95pu and 1.05pu, respectively, and the photovoltaic curtailment penalty cost is also mentioned. On-grid tariff for active power in distribution networks Cost of power outage The operating cost of energy storage is The installation information for distributed photovoltaic and energy storage is shown in Table 1. An extreme fault is assumed in the main transformer of the second distribution network sub-area (referred to as the faulty distribution network sub-area), resulting in a complete power outage across the network.

[0030] Table 1. Location and Capacity of Photovoltaic and Energy Storage Installations in Distribution Networks

[0031] Figure 3 This illustrates the variation of the original and dual residuals of the spatial consensus variables with the number of iterations in the method of this invention. The convergence thresholds for the original and dual residuals are set as follows: The 53rd iteration satisfied the convergence condition, and the iteration process was stable and oscillating. The voltage distribution at the distribution network nodes is as follows: Figure 4 As shown, the voltage range of all nodes in the distribution network system is controlled within the safe operating range, and no voltage exceedance occurs. This result verifies the effectiveness of the discrete variable relaxation and smoothing strategy adopted in this invention, effectively suppressing the solution fluctuations caused by the discrete variables of the switches, and ensuring the stable convergence of the two-layer ADMM algorithm in handling the multi-time period power restoration problem.

[0032] Any aspects not covered in this invention are applicable to existing technologies.

Claims

1. A method for restoring distributed power supply in multi-period interconnected distribution networks based on spatiotemporal domain decomposition, characterized in that, Includes the following steps: Step S1: Establish a global optimization model for power supply restoration of the interconnected distribution network, the compact form of which is as follows: (1) In the formula, The scheduling period; This represents the number of normal distribution network sub-areas. and The objective functions are for the normal distribution network sub-area and the faulty distribution network sub-area, respectively. and They are respectively and Optimization variables for the network sub-area at all times; and They are respectively and Optimization variables for faulty distribution network sub-areas at any given time; and These are the feasible regions for optimizing variables in normal distribution network sub-areas and faulty distribution network sub-areas, respectively. and These are the operational constraints for normal distribution network sub-areas and faulty distribution network sub-areas, respectively. , Equation constraints for time coupling within normal and faulty distribution network sub-areas; The boundary equality constraints are for the normal distribution network sub-area and the faulty distribution network sub-area. for Boundary variables of the normal distribution network sub-region at all times; express Boundary variables of the faulty distribution network sub-area at any given moment; Step S2: Decompose the global optimization problem in the spatial domain, thereby decomposing the global optimization model for power supply restoration of the interconnected distribution network into spatial decomposition optimization models for each distribution network sub-area; The spatial decomposition optimization model for faulty distribution network sub-areas is as follows: (14) In the formula, An augmented Lagrangian function for the spatial decomposition of faulty distribution network sub-regions; The dual multiplier for the spatial decomposition of faulty distribution network sub-regions; This is a transpose operation; for Spatial consensus variables at any given time; The penalty factor for the spatial decomposition of faulty distribution network sub-areas; It is an L2 norm; The normal distribution network sub-area spatial decomposition optimization model is as follows: (15) In the formula, The augmented Lagrangian function for the spatial decomposition of normal distribution network sub-regions; The dual multiplier for the spatial decomposition of sub-regions in a normal distribution network; The penalty factor for the spatial decomposition of normal distribution network sub-areas; Step S3: Decompose the optimization sub-problems of each distribution network sub-area in the time domain to obtain the time decomposition optimization model of each distribution network sub-area; The time decomposition optimization model for the faulty distribution network sub-area is as follows: (16) In the formula, An augmented Lagrangian function for the time decomposition of faulty distribution network sub-areas; express The dual multiplier of the time decomposition of the fault distribution network sub-area; for Energy storage SOC in the distribution network sub-area during constant failure; for Global State of Charge (SOC) at any given moment; for Penalty factor for time decomposition of distribution network sub-area in case of moment failure; The normal distribution network sub-area time decomposition optimization model is as follows: (17) In the formula, The augmented Lagrangian function for the time decomposition of a normal distribution network sub-area; for The dual multiplier of the time decomposition of the normal distribution network sub-area at any given time; for The energy storage SOC of the distribution network sub-area is always in normal operation; for The penalty factor for the time decomposition of the normal distribution network sub-area at all times; Step S4: The inner solver uses the ADMM algorithm to solve the time decomposition optimization model of each distribution network sub-area in each time period, obtains the local optimum solution of each distribution network sub-area, and passes it to the outer solver; Given the boundary variables of the distribution network sub-regions, the spatial consensus variables, global energy storage SOC, dual multipliers of spatial decomposition, dual multipliers of temporal decomposition, and penalty factors of temporal decomposition of each distribution network sub-region are initialized. Solve the time decomposition optimization model of each distribution network sub-area independently for each time period to obtain the current local solution of each distribution network sub-area; Update the global energy storage SOC using equation (18): (18) In the formula, for Time of the first The next iteration of global energy storage SOC; for Time of the first The energy storage SOC of the next iteration distribution network sub-region; , for Time of the first Energy storage SOC of sub-regions in both fault and normal distribution networks; , for Time of the first Dual multipliers and penalty factors of time decomposition of normal distribution network sub-regions in the next iteration; This refers to the number of interactions between the distribution network and energy storage. Update the dual multipliers of the time decomposition of the distribution network sub-region using equation (19): (19) In the formula, For the first Dual multipliers of the time decomposition of sub-regions in the next iteration; The original residual and dual residual of the global energy storage SOC are calculated according to equation (20): (20) If both the original residual and the dual residual of the global energy storage SOC are less than or equal to their respective convergence thresholds, then the iteration ends, and the local optimal solution of each distribution network sub-region is output; otherwise, the global variables of the energy storage SOC and the dual multipliers of the time decomposition of the distribution network sub-region are updated, letting... The aforementioned iterative process is repeated until convergence is achieved; the local optimal solutions of each distribution network sub-region are passed to the outer solver. Step S5: The outer solver uses the ADMM algorithm to find the global optimum. Adjacent distribution network sub-areas exchange boundary variables through coupled branches, and update spatial consensus variables according to equation (21); (21) In the formula, For the first Spatial consensus variables for the normal distribution network sub-region in the next iteration; , For the first Boundary variables for the normal distribution network sub-area and the faulty distribution network sub-area in the next iteration; , For the first Dual multipliers and penalty factors for the spatial decomposition of normal distribution network sub-regions in the next iteration; The number of distribution network sub-regions participating in spatial decomposition; The dual multipliers of the spatial decomposition of normal and faulty distribution network sub-regions are updated using equation (22): (22) In the formula, , For the first The dual multipliers of the spatial decomposition of normal and faulty distribution network sub-regions in the next iteration. For the first Penalty factor for spatial decomposition of faulty distribution network sub-regions in the next iteration; Calculate the original residuals and dual residuals of the spatial consensus variables according to equation (23): (23) If the original residuals and dual residuals of the spatial consensus variables are less than or equal to their respective convergence thresholds, the iteration ends, and the global optimal solution, i.e., the optimal power supply restoration scheme, is output; otherwise, the spatial consensus variables and the dual multipliers of the spatial decomposition for each distribution network sub-region are updated, letting... Then return to step S4 and repeat the aforementioned iterative process until convergence is achieved, thus obtaining the global optimal solution.

2. The method for multi-period distributed power supply restoration of interconnected distribution networks based on spatiotemporal domain decomposition according to claim 1, characterized in that, The objective function for the faulty distribution network sub-area is: (2) In the formula, Indicates the time step; This represents the set of nodes in the faulty distribution network sub-area. A set of feeder switches; Costs associated with power outages; express Time Node The net load active power; for Time Node Load pickup status; This indicates the on-grid electricity price for active power in the distribution network; Represented by node The set of the starting nodes of the branches of the terminal nodes; Indicates a branch The resistance; and They represent Time Branch The active and reactive power; express The root node voltage at time t; Indicates the cost of switching operations; for time Discrete variables of the feeder switch state of the branch; express The initial state variables of the feeder switch at any given time; This indicates the cost of penalties for curtailing solar power. express Time Node The reduction in photovoltaic active power at the location; Indicates the operating cost of energy storage; for Time Node The active power of energy storage at the location; The objective function for a normal distribution network sub-area is: (3) In the formula, Indicates a normal distribution network sub-area The set of nodes; express Time Branch The transmission current; Represents a node The set of upstream nodes.

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