Power distribution network load recovery method and device, electronic equipment and storage medium

Abstract

The embodiment of the invention discloses a power distribution network load recovery method and device, electronic equipment and a storage medium. The method comprises the following steps: constructing a power distribution network centralized optimization model based on a load recovery amount, a distributed energy utilization rate and a voltage drop; the centralized optimization model comprises connectivity and radial constraint, capacity constraint and power balance and voltage constraint; decomposing the power distribution network into at least two subsystems, and establishing an objective function for each subsystem; the connectivity, the radial performance and the coordination among the subsystems are optimized and adjusted; and calculating the distributed optimization problem of each subsystem by adopting a penalty driving distributed alternating direction multiplier algorithm so as to recover the load of the power distribution network. By adopting the scheme, the power distribution network is decomposed into at least two subsystems, the distributed optimization model is established, and the penalty-driven distributed alternating direction multiplier algorithm is combined, so that the load can be quickly recovered after the fault occurs, and the recovery efficiency of the power distribution network is improved.

Description

Technical Field

[0001] Embodiments of the present invention relate to the technical field of power systems, and in particular to a distribution network load recovery method, device, electronic equipment, and storage medium. Background Art

[0002] With the integration of smart grid technologies, the load recovery capability of distribution networks in the face of natural disasters or cyber attacks is particularly important. Although smart grid technologies have greatly improved the resilience of distribution networks, outages in distribution systems due to unpredictable external events such as failures or attacks are still inevitable. To meet this challenge, load recovery strategies should be able to respond quickly to these events and automatically restore power supply within a reasonable time. For example, microgrids can supply critical loads after an outage, distributed energy resources can be used to power isolated microgrids, and advanced communication and control devices offer great potential for implementing efficient self-healing strategies.

[0003] Centralized optimization algorithms can converge to the global optimal solution. Current centralized recovery schemes usually rely on a central controller and require advanced communication networks to collect data from various components in the network and perform complex calculations; however, this architecture is costly and has the risk of single point failure, and it also poses a threat to data privacy. Distributed service recovery provides a potential solution, but many existing distributed recovery schemes require the convexity assumption of the problem, which is not always met in reality. In addition, many methods ignore the scalability problem in large-scale distributed networks, and most existing studies ignore the data privacy problem, which makes the existing distributed recovery schemes have limitations. Existing studies have proposed a distributed recovery framework based on the distributed alternating direction multiplier algorithm, but these methods usually cannot obtain feasible solutions when dealing with binary variables, and the strict structure adopted cannot support switching operations within the cluster. In addition, these methods ignore their inherent complexity and scalability problems when dealing with complex network topologies, and it is difficult to meet the practical application needs of large-scale distributed networks. Existing distributed alternating direction multiplier algorithm methods are mainly applied to convex optimization problems. Although some success has been achieved in non-convex problems, their convergence is still uncertain.

[0004] Therefore, how to deal with the restoration problem in a large-scale active distribution network is a technical problem that needs to be solved urgently by those skilled in the art. Summary of the invention

[0005] The embodiments of the present invention provide a distribution network load recovery method, device, electronic device and storage medium to achieve rapid load recovery after a fault occurs, thereby improving the recovery efficiency of the distribution network.

[0006] In a first aspect, an embodiment of the present invention provides a distribution network load recovery method, comprising:

[0007] Constructing a distribution network centralized optimization model based on load recovery, distributed energy utilization and voltage drop; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance and voltage constraints;

[0008] Decompose the power distribution network into at least two subsystems and establish an objective function for each subsystem;

[0009] Optimize the connectivity, radiality and coordination among subsystems;

[0010] The penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problem of each subsystem to restore the distribution network load.

[0011] In a second aspect, an embodiment of the present invention further provides a distribution network load recovery device, comprising:

[0012] A centralized optimization model building module is used to build a centralized optimization model of the distribution network based on load recovery, distributed energy utilization and voltage drop; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance and voltage constraints;

[0013] A power distribution network decomposition module, used for decomposing the power distribution network into at least two subsystems and establishing an objective function for each subsystem;

[0014] Subsystem optimization and adjustment module, used to optimize the connectivity, radiality and coordination among subsystems;

[0015] The distribution network load recovery module is used to calculate the distributed optimization problems of each subsystem using a penalty-driven distributed alternating direction multiplier algorithm to restore the distribution network load.

[0016] In a third aspect, an embodiment of the present invention further provides an electronic device, the electronic device comprising:

[0017] one or more processors;

[0018] A storage device for storing one or more programs;

[0019] When the one or more programs are executed by the one or more processors, the one or more processors implement the distribution network load recovery method described in any embodiment of the present invention.

[0020] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the distribution network load recovery method described in any embodiment of the present invention.

[0021] In a fifth aspect, an embodiment of the present invention further provides a computer program product, including a computer program, which, when executed by a processor, implements the distribution network load recovery method as described in any embodiment of the present invention.

[0022] The embodiment of the present invention provides a distribution network load recovery method, device, electronic device and storage medium, which constructs a distribution network centralized optimization model based on load recovery amount, distributed energy utilization rate and voltage drop; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance and voltage constraints; the distribution network is decomposed into at least two subsystems, and an objective function is established for each subsystem; the connectivity, radiality and coordination between each subsystem are optimized and adjusted; a penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problem of each subsystem to restore the distribution network load. The technical solution of the embodiment of the present invention is adopted, by decomposing the distribution network into at least two subsystems, establishing a distributed optimization model, and combining the penalty-driven distributed alternating direction multiplier algorithm to quickly restore the load after a fault occurs, and ensure the effective use of more distributed energy, thereby improving the recovery efficiency of the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Other features, objects and advantages of the present invention will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings. The drawings are only for the purpose of illustrating preferred embodiments and are not to be considered as limiting the present invention. Also, the same reference symbols are used throughout the drawings to represent the same parts. In the drawings:

[0024] Figure 1 is a flow chart of a distribution network load recovery method provided in an embodiment of the present invention;

[0025] Figure 2 is a flow chart of another distribution network load recovery method provided in an embodiment of the present invention;

[0026] Figure 3 is a flow chart of another distribution network load recovery method provided in an embodiment of the present invention;

[0027] Figure 4 It is a schematic diagram of distributed optimization results in an IEEE 33-node system provided in an embodiment of the present invention;

[0028] Figure 5 It is a schematic diagram of the convergence of integer variables in the recovery of an IEEE33 bus system by a penalty-driven distributed alternating direction multiplier algorithm provided in an embodiment of the present invention;

[0029] Figure 6It is a schematic diagram of the convergence of residual terms of a penalty-driven distributed alternating direction multiplier algorithm in IEEE33 bus system recovery provided in an embodiment of the present invention;

[0030] Figure 7 It is a schematic diagram of a distributed optimization result in an IEEE 123 node system provided in an embodiment of the present invention;

[0031] Figure 8 It is a schematic diagram of the convergence of integer variables in the IEEE123 bus system recovery of a penalty-driven distributed alternating direction multiplier algorithm provided in an embodiment of the present invention;

[0032] Fig. 9 It is a schematic diagram of the convergence of continuous variables of a penalty-driven distributed alternating direction multiplier algorithm in IEEE123 bus system recovery provided in an embodiment of the present invention;

[0033] Fig.10 It is a schematic diagram of the convergence of residuals of a penalty-driven distributed alternating direction multiplier algorithm in IEEE123 bus system recovery provided in an embodiment of the present invention;

[0034] Fig.11 is a structural schematic diagram of a distribution network load recovery device provided in an embodiment of the present invention;

[0035] Fig.12 It is a structural schematic diagram of an electronic device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0037] Before discussing the exemplary embodiments in more detail, it should be mentioned that some exemplary embodiments are described as processes or methods depicted as flow charts. Although the flow charts describe the operations (or steps) as sequential processes, many of the operations (or steps) therein can be implemented in parallel, concurrently or simultaneously. In addition, the order of the operations can be rearranged. The process can be terminated when its operation is completed, but can also have additional steps not included in the accompanying drawings. The process can correspond to a method, function, procedure, subroutine, subprogram, etc.

[0038] Among them, the acquisition, storage, use and processing of data in the technical solution of this application are in compliance with the relevant provisions of national laws and regulations. It should be noted that in the embodiments of this application, some existing solutions in the industry such as certain software, components or models may be mentioned, which should be considered as exemplary, and their purpose is only to illustrate the feasibility of the implementation of the technical solution of this application, but it does not mean that the applicant has or will necessarily use the solution.

[0039] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein.

[0040] Embodiment 1

[0041] Figure 1 This is a flow chart of a distribution network load recovery method provided in an embodiment of the present invention. This embodiment is applicable to the case of distribution network load recovery. The method of this embodiment can be executed by a distribution network load recovery device, which can be implemented in hardware and / or software. The device can be configured in a distribution network load recovery server. The method specifically includes the following steps:

[0042] S110, construct a distribution network centralized optimization model based on load recovery, distributed energy utilization and voltage drop.

[0043] Among them, load recovery usually refers to the ability of a system or device to recover to its initial state or a higher state after experiencing a certain degree of load (such as pressure, energy consumption, etc.) under certain circumstances; in the embodiment of the present invention, the load recovery amount is used to characterize the power supply recovery capability of the distribution network. Distributed energy utilization refers to the proportion of input energy converted into useful energy in the actual operation of the distributed energy system. Voltage drop refers to the potential difference generated at both ends of the device when current passes through the electrical equipment; in the embodiment of the present invention, the voltage drop is used to characterize the normal operation of the distribution system.

[0044] In the embodiment of the present invention, a distribution network centralized optimization model is constructed based on load recovery, distributed energy utilization and voltage drop. The centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance and voltage constraints to ensure the stability and safety of system operation. The distribution network centralized optimization model is expressed as:

[0045] Minimize:F Obj =α1F Load +α2F Der +α3F V

[0046] Among them, F Obj represents the objective function of the centralized optimization model; F Load Indicates load recovery amount; F Der represents the utilization rate of distributed energy; F V represents the voltage drop; α1, α2, and α3 represent their corresponding weights respectively.

[0047] The load recovery amount has the highest proportion in the objective function, and the load recovery amount can be expressed as:

[0048]

[0049] in, Represents the total number of load nodes in the distribution network; s n represents the switch state of node n, usually a binary variable (0 or 1), indicating whether the node has been restored to power; P n Represents the load power of node n.

[0050] The distributed energy utilization rate allows more distributed energy to be injected into the system. The distributed energy utilization rate can be expressed as:

[0051]

[0052] in, Represents the node set where distributed energy resources are located; Represents the distributed energy injection power at node n.

[0053] Voltage drop is used to characterize the stability of the power distribution system. Voltage stability is crucial to the normal operation of the power distribution system. It is very important to keep the voltage of each node close to the nominal value. The voltage drop can be expressed as:

[0054]

[0055] in, Represents the square of the difference between the node voltage and the nominal voltage.

[0056] In order to simplify the analysis process, a compact optimization model is obtained, as follows:

[0057]

[0058] In the above formula, P1 represents the objective function; X, represent continuous decision variables and integer decision variables respectively; represent equality constraints and inequality constraints respectively.

[0059] S120: Decompose the power distribution network into at least two subsystems, and establish an objective function for each subsystem.

[0060] The distribution network is decomposed into at least two subsystems, each of which corresponds to a subgraph on the topological structure. l They all solve a very similar problem, and an optimization model for each subsystem is established as follows:

[0061]

[0062] ζ(lj)=H l ×H j →ε

[0063] In the above formula, Represents subsystem H l The objective function of X l , A vector representing continuous and integer variables, indicating states associated with the subsystem; Represent the continuous variables and integer variables on the boundary switches respectively. ζ(lj)

[0064] Represents the connection between two subsystems H l and H j The boundary line or overlapping area between them.

[0065] S130, optimizing and adjusting the connectivity, radiality and coordination among the subsystems.

[0066] After the power distribution network is decomposed into at least two subsystems, the connectivity, radiality and coordination between the subsystems need to be adjusted. Connectivity can refer to the connectivity between the subsystems, and the connection lines between the subsystems can be maintained by introducing boundary switches. Radiality can refer to the flow direction of current between the subsystems. Coordination can refer to the communication coordination between the subsystems, and the coordination between the subsystems can be optimized and adjusted by introducing auxiliary variable virtual commodity flows.

[0067] S140. Use a penalty-driven distributed alternating direction multiplier algorithm to calculate the distributed optimization problem of each subsystem to restore the load of the distribution network.

[0068] Among them, the Penalty-driven Distributed Alternating Direction Method of Multipliers (P-ADMM) is an optimization algorithm that combines the advantages of penalty methods and distributed computing to solve large-scale distributed optimization problems. The algorithm introduces a penalty factor to handle constraints, so that the originally difficult-to-handle constraint optimization problem can gradually approach the optimal solution through iteration; in a distributed environment, P-ADMM allows each node to perform calculations independently and exchange information through a communication mechanism to ultimately reach a global optimal solution. In the embodiment of the present invention, the distributed optimization problem of each subsystem is calculated by a penalty-driven distributed alternating direction multiplier algorithm to solve the optimization problem of the entire distribution network and restore the distribution network load.

[0069] The embodiment of the present invention provides a method for load recovery of a distribution network, which constructs a centralized optimization model of the distribution network based on the load recovery amount, the utilization rate of distributed energy, and the voltage drop; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance, and voltage constraints; the distribution network is decomposed into at least two subsystems, and an objective function is established for each subsystem; the connectivity, radiality, and coordination between the subsystems are optimized and adjusted; and a penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problems of each subsystem to restore the load of the distribution network. The technical solution of the embodiment of the present invention is adopted, by decomposing the distribution network into at least two subsystems, establishing a distributed optimization model, and combining the penalty-driven distributed alternating direction multiplier algorithm to quickly restore the load after a fault occurs, and ensure the effective utilization of more distributed energy, thereby improving the recovery efficiency of the distribution network.

[0070] Embodiment 2

[0071] Figure 2 The flowchart of a method for restoring a load in a distribution network provided in an embodiment of the present invention is shown in FIG. The embodiment of the present invention further optimizes the above embodiment on the basis of the above embodiment, and the embodiment of the present invention can be combined with each optional solution in one or more of the above embodiments. Figure 2 As shown, the distribution network load recovery method provided in the embodiment of the present invention may include the following steps:

[0072] S210, construct a centralized optimization model of the distribution network based on load recovery, distributed energy utilization and voltage drop.

[0073] In the embodiment of the present invention, a distribution network centralized optimization model is constructed with load recovery, distributed energy utilization and voltage drop as objective functions; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance and voltage constraints to ensure the stability and safety of system operation.

[0074] The load restoration problem attempts to maintain the radial topology of the distribution network while restoring the load. Sufficient conditions for the connectivity and radiality of the distribution network system are that all buses are connected to the root bus and each energized bus is connected to only one incoming arc.

[0075] Among them, connectivity constraints and radial constraints ensure that the distribution network maintains a radial topology during the restoration process, that is, each node can only be connected to the main network in one direction. The details are as follows:

[0076]

[0077] In the above formula, z mn ,z nm represents the line state from node m to node n; β mn Binary auxiliary variables representing lines m and n, ensuring that the line status of the system in different directions is consistent; f mn represents the network traffic from node m to node n; v n represents the state variable of node n (0 or 1); ε,ε F ,ε S They represent line set, faulty line set, and selectable line set respectively; Represents the set of root nodes (usually main substations) in the distribution network; Represents the set of nodes connected to node n.

[0078] The capacity constraint ensures that the decision variables of the distribution network load restoration problem are within the allowable range, as follows:

[0079]

[0080] In the above formula, represents the maximum active power of node n; represents the injected reactive power of node n; represents the maximum reactive power of node n; P mn ,Q mn Represent the active power and reactive power of line mn respectively; Respectively represent the maximum active power, reactive power and apparent power of line mn; V min ,V max Represent the minimum voltage and maximum voltage of node n respectively.

[0081] The linearized power balance equation and voltage equation for the unbalanced system are shown below:

[0082]

[0083] In the above formula, Represents the impedance of line mn, namely resistance and reactance.

[0084] The load recovery strategy proposed in the embodiment of the present invention takes into account various constraints such as the connectivity, radiality, capacity constraint and power balance of the distribution network, can ensure the stable operation of the distribution network during the load recovery process, and effectively avoid the risk of single point failure in the centralized optimization solution.

[0085] Optional, see Figure 3 ,Before building the centralized optimization model, the method also includes initializing system parameters, such as system topology, distributed energy capacity, line capacity and load demand, as well as initializing the primal variables, dual variables, penalty coefficients and auxiliary variables in the penalty-driven distributed alternating direction multiplier algorithm.

[0086] S220: Decompose the power distribution network into at least two subsystems, and establish an objective function for each subsystem.

[0087] The embodiment of the present invention proposes a decomposition method of the autonomous clustering strategy, which divides the distribution network into multiple subsystems. The subsystems exchange and coordinate data through boundary switches, which can improve the convergence speed of subproblems and penalty-driven distributed alternating direction multiplier algorithms and reduce information exchange.

[0088] As an optional but non-limiting implementation, decomposing the power distribution network into at least two subsystems and establishing an objective function for each subsystem includes:

[0089] According to the decomposition method of the autonomous clustering strategy, the distribution network is decomposed into at least two subsystems, and an objective function is established for each subsystem; wherein each subsystem corresponds to a subgraph on a topological structure.

[0090] The distribution network system is decomposed into multiple subsystems H l (l∈1,2,3,...k), each subsystem corresponds to a subgraph in the topological structure. Each subsystem H l They all solve a very similar problem, and an optimization model for each subsystem is established as follows:

[0091]

[0092] ζ(lj)=H l ×H j →ε

[0093] in, Represents subsystem H l The objective function of X l , A vector representing continuous and integer variables, indicating states associated with the subsystem; represent the continuous variable and integer variable on the boundary switch respectively; ζ(lj) represents the connection between the two subsystems H l and H j The boundary line or overlapping area between them.

[0094] S230, optimizing and adjusting the connectivity, radiality and coordination among the subsystems.

[0095] After constructing the objective function of each subsystem, the connection lines, radiality and coordination between subsystems are optimized and adjusted.

[0096] As an optional but non-limiting implementation, the optimization and adjustment of the connectivity, radiality and coordination among the subsystems includes but is not limited to steps A1-A2:

[0097] Step A1: introducing boundary switches between subsystems and modifying connectivity and radiality constraints in the centralized optimization model of the distribution network; wherein the boundary switches are used to maintain connectivity and radiality between subsystems.

[0098] Step A2: introducing auxiliary variable virtual commodity flows on the boundary lines of each subsystem to optimize the coordination between the subsystems; wherein the auxiliary variable virtual commodity flows represent the power flow between the subsystems.

[0099] After decomposing the distribution network system, boundary switches are introduced between the subsystems, and the boundary switches maintain the connectivity between the subsystems. Therefore, the connectivity constraint modification of the line with boundary switches can be expressed as:

[0100]

[0101] In the above formula, ε B Represents the boundary line set, which is located at the boundary of the subsystem and is used to connect different subsystems or subsystems with the main system; Represents the boundary node set, which are nodes located at the boundary of the subsystem and are usually connected to other subsystems or the main system through boundary switches.

[0102] Responsible for calculating H l X l and The distributed controller needs information to imitate the rest of the system to achieve the global optimal solution, which is achieved by l (Hj ) is achieved by introducing auxiliary variables on the straight line. Assume that mn is identified by ζ(lj) in H l and H j The lines between, n' and m' are the auxiliary buses introduced for decomposition. Secondly, the active power, reactive power and commodity flows into the adjacent subsystems through the boundary bus are represented by the auxiliary generators connected to. These auxiliary generators represent the l H at the busbar n' j Since this decomposition is performed along switchable lines, the above representation also depends on the line β mn' Therefore, The value of H l Calculate and share as follows:

[0103]

[0104] In the above formula, represent the active and reactive power flows at the boundary nodes, respectively; Represents virtual commodity traffic.

[0105] When β mn' When closed, m and n' are adjacent busbars; if β mn' Disconnect, these two subsystems H l ,H j Physically disconnected. To introduce the effect of variations between adjacent subsystems, the following modifications are included. Adjacent subsystems share the voltage amplitude at one end of mn'. Therefore, The coupling variables and The shared copies are as follows:

[0106]

[0107] This decomposition has important implications for the active power, reactive power, voltage and commodity flow equations on the boundary line mn' in each subsystem H l The impact of the inter-subsystem iteration (k) is as follows:

[0108]

[0109] The embodiment of the present invention proposes an autonomous clustering strategy, decomposes the distribution network into multiple subsystems and exchanges data between the subsystems through boundary switches, which significantly reduces the amount of information exchange and computational complexity and improves the convergence speed of the distributed optimization algorithm.

[0110] S240, using a penalty-driven distributed alternating direction multiplier algorithm to calculate the distributed optimization problem of each subsystem, and solving the local optimization problem of each subsystem under the conditions of radial constraints and capacity constraints.

[0111] The embodiment of the present invention uses a penalty-driven distributed alternating direction multiplier algorithm to calculate the distributed optimization problem of each subsystem. Each subsystem solves its local optimization problem under the premise of considering radiality and capacity constraints, and shares necessary boundary information with adjacent subsystems. First, the optimization objective is defined by augmenting the Lagrangian function, and the problem is decomposed into a multi-stage solution, relying on the alternating optimization of the main problem and the dual problem. At the same time, for continuous and discrete variables, the algorithm uses projection and relaxation techniques to ensure that the optimization results gradually approach the global optimal solution.

[0112] As an optional but non-limiting implementation, the penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problem of each subsystem, including but not limited to steps B1-B2:

[0113] Step B1: Replace the integer decision variables in the distributed optimization problem with continuous decision variables to decompose the distributed optimization problem of each subsystem into a multi-stage solution.

[0114] Step B2: Define the objective function through the augmented Lagrangian function, and update the augmented Lagrangian function through the scaled dual variable to optimize the objective function.

[0115] The embodiment of the present invention reformulates the distributed optimization problem by replacing integer decision variables with continuous decision variables. The augmented Lagrangian function of the problem is as follows:

[0116]

[0117] In the above formula, Y l yes The continuous relaxation version of ; ρ represents the penalty coefficient; Represent the Lagrange multiplier vectors of the continuous and integer variables of the adjacent subsystems. The augmented Lagrangian function is updated by scaling the dual variable μ = ν / ρ:

[0118]

[0119] The penalty-driven distributed alternating direction multiplier algorithm includes the state variable X l and Y l The projection of the continuous variable y to the integer set Z is given by This projection technique is embedded in the regularization term by transforming the global state vector A copy of ) is rounded to the nearest integer.

[0120] The embodiment of the present invention proposes a penalty-driven distributed alternating direction multiplier algorithm, which decomposes the problem into multiple sub-problems based on Lagrange multipliers, introduces penalty function relaxation variables to solve the distributed optimization model, and gradually approaches the optimal solution through iteration, thereby achieving rapid and effective recovery of the distribution network load.

[0121] S250, iteratively update the variables of the penalty-driven distributed alternating direction multiplier algorithm.

[0122] The penalty-driven distributed alternating direction multiplier algorithm variables include original variables, dual variables, auxiliary variables, residuals and penalty coefficients.

[0123] The primary variables, global auxiliary variables, and dual variables are updated in the (k+1)th iteration as follows:

[0124]

[0125] At the same time, the relaxed integer variables are updated. Since the relaxed integer variables are Boolean variables, in order to make them close to integer values, the penalty function is introduced into the objective function as follows:

[0126]

[0127] x s =[z nm ,z mn ,s n ]

[0128] In the above formula, φ l (x s ) represents the penalty function; L l +τφ l (x s ) represents the modified objective function; x s Represents line and load switch status; Indicates that x s Round to the nearest integer.

[0129] The residual update, stopping criterion, and penalty coefficient update of the penalty-driven distributed alternating direction multiplier algorithm in each iteration are as follows:

[0130]

[0131] δ(k+1)=(r p (k+1), r d (k+1)) ∞ ≤

[0132]

[0133] The embodiments of the present invention support complex topological structures and parallel processing of multiple subsystems in distributed computing by introducing penalty functions and auxiliary variables, thereby improving the scalability and flexibility of the algorithm in large-scale distribution networks.

[0134] S260, iteratively updating the distribution network centralized optimization model according to the distributed optimization problems of each subsystem, the local optimization problems and the variables of the penalty-driven distributed alternating direction multiplier algorithm until the distribution network centralized optimization model meets the preset convergence conditions.

[0135] Among them, after solving the distributed optimization problem and local optimization problem of each subsystem, the centralized optimization model of the distribution network is iteratively updated, and it is determined whether the updated centralized optimization model of the distribution network meets the preset convergence conditions. If the preset convergence conditions are not met, the penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problems of each subsystem, and the local optimization problems of each subsystem are solved under the conditions of radial constraints and capacity constraints; and the variables of the penalty-driven distributed alternating direction multiplier algorithm are continued to be iteratively updated until the centralized optimization model of the distribution network meets the preset convergence conditions.

[0136] The embodiment of the present invention provides a load recovery method for a distribution network, which is intended to address the load recovery problem of the distribution network under faults or natural disasters. The recovery method divides the distribution network into multiple subsystems by constructing a distributed optimization model and combining an autonomous clustering strategy, and coordinates and exchanges data between subsystems through boundary switches, thereby significantly improving the efficiency of distributed computing. A penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problems of each subsystem. In the algorithm, by introducing auxiliary variables and penalty functions, it can effectively handle the optimization problems of complex network topology and boundary conditions, and support parallel computing of multiple subsystems, thereby ensuring the convergence and rapid recovery capabilities of the system as a whole. The core of the method is to decompose the centralized optimization problem into sub-problems of multiple subsystems, each subsystem is solved independently and optimized in coordination with adjacent subsystems, thereby reducing the computational burden and improving the optimization speed. In addition, the present invention also fully considers the connectivity, radiality, power balance and capacity constraints of the distribution network to ensure that the system maintains stable operation during the load recovery process. Through the design of a distributed computing framework, the strategy improves the self-healing ability of the distribution network, can achieve rapid and effective load recovery when a fault occurs, and significantly improves the reliability and scalability of the system.

[0137] In an optional solution of the embodiment of the present invention, an improved IEEE 33-node distribution network system and an IEEE 123-node distribution network system are selected to verify the present invention. During the verification process, the load recovery effect of the distribution network based on the penalty-driven distributed alternating direction multiplier algorithm proposed in the embodiment of the present invention is verified.

[0138] The centralized and distributed algorithms are implemented using the Matlab toolbox Yalmip, and the optimization framework is solved using the Gurobi optimizer. The typical parameter values ​​used in the penalty-driven distributed alternating direction multiplier algorithm are taken as an example: τ=5, ρ=300, ∈=0.001, α1=1, α2=5, α3=5, γ1=0.1, γ2=1.5,,γ3=1.2. An emergency situation is studied in a modified IEEE 33-bus system. The rated power and rated voltage of the system are 100MVA and 12.66kV, respectively. The minimum and maximum limits of the square of the voltage amplitude are 0.95 and 1.05pu, respectively, and the substation operates at a voltage of 1p.u. See Figure 4 , the system is divided into three subsystems along {(5-6), (8-21), (9-10), (18-33), (25-29)}, and the bus sets of the subsystems are as follows: H 1 ={1-6,8,19-22,23-25,29},H 2 ={5-10,18,21,25-33},H 3 ={9-18,33}. The total number of controllable line switches in the system is 20, and all loads are switchable. The three distributed energy sources are located at The total capacity is 0.98MVA, accounting for about 25% of the total MVA demand. Figure 4 As shown, the fault occurs in line (27-28), which is located inside subsystem 2. The fault is cleared by disconnecting the faulty line. B =(5-6) and ε I =(14-15) The network is restored. The convergence of the boundary integer variables and residuals of the penalty-driven distributed alternating direction multiplier algorithm is shown in Figure 5 as well as Figure 6 shown.

[0139] See also Figure 7 , a penalty driven distributed alternating direction multiplier algorithm is studied in the improved IEEE 123 bus system. The rated power of the system is 1MVA and the rated voltage is 4.16kV. The minimum and maximum voltage amplitude square limits are 0.95 and 1.1pu respectively. Substations 1 and 2 operate at 1.0pu voltage. The system is divided into seven subsystems, and the locations of the subsystems and NRs are listed in Table 1. All ε B and ε I exist Figure 7 The total number of controllable line switches in the system is 46, and all loads can be switched. The total MVA capacity is 1.6 MVA, which is close to 40% of the total MVA requirement. The distributed energy resources connected to bus 60 operate at 1.0 pu voltage. The distributed energy resources mainly supply power to subsystem 4 (isolated area), but if necessary, excess generation will be supplied to neighboring subsystems.

[0140] Table 1 Location of subsystems and NRs

[0141]

[0142]

[0143] The embodiment of the present invention studies the distributed recovery of unbalanced systems. F ={(86-87), (35-116)}, the accidental case with two broken lines is studied. The fault of line (86-87) is an internal fault of subsystem 7, while the fault of line (35-116) is an interruption of the boundary switch. These two faults are cleared by opening the lines separately. Figure 8 , 9 , as shown in 10, close ε B ={(13-18),(117-118),(97-124),(72-76),(54-94)}, open B ={(39-66),(52-121),(60-119)}, the network is restored. Figure 7 From the perspective of the topology of the restored network, the voltage levels of subsystems 1 and 2 are regulated by substation 1, the voltage levels of subsystems 3 and 5 are regulated by substation 2, and the voltage levels of subsystems 4, 6, and 7 are regulated by GFM-DER. The convergence of the boundary integers, continuous variables, and residual terms of the PD-ADMM algorithm is shown in Figure 8 , 9 , 10. The existence of isolated campuses also shows the ability of distributed optimization algorithms in local island formation.

[0144] in, Figure 4 It is the distributed optimization result in IEEE 33-node system; Figure 5 as well as Figure 6 is the performance of the penalty driven distributed alternating direction multiplier algorithm in IEEE 33 bus system recovery; Figure 7 It is the distributed optimization result in IEEE 123 node system; Figure 8 , Fig. 9 as well as Fig.10It is the performance of the penalty-driven distributed alternating direction multiplier algorithm in the recovery of the IEEE 123 bus system. As can be seen from the figure, the penalty-driven distributed alternating direction multiplier algorithm can achieve fast recovery when a fault occurs, and has good convergence performance, ensuring the stable operation of the distributed power grid.

[0145] Embodiment 3

[0146] Fig.11 This is a schematic diagram of the structure of a distribution network load recovery device provided in an embodiment of the present invention. The technical solution of this embodiment can be applied to the situation of distribution network load recovery. The device can be implemented by software and / or hardware and is generally integrated on any electronic device with network communication function, including but not limited to: servers, computers, personal digital assistants and other devices. Fig.11 As shown, the distribution network load recovery device provided in this embodiment may include: a centralized optimization model construction module 1110, a distribution network decomposition module 1120, a subsystem optimization and adjustment module 1130 and a distribution network load recovery module 1140; wherein,

[0147] A centralized optimization model building module 1110 is used to build a centralized optimization model of the distribution network based on load recovery, distributed energy utilization, and voltage drop; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance, and voltage constraints;

[0148] A power distribution network decomposition module 1120, used to decompose the power distribution network into at least two subsystems and establish an objective function for each subsystem;

[0149] The subsystem optimization and adjustment module 1130 is used to optimize and adjust the connectivity, radiality and coordination among the subsystems;

[0150] The distribution network load recovery module 1140 is used to calculate the distributed optimization problem of each subsystem using a penalty-driven distributed alternating direction multiplier algorithm to recover the distribution network load.

[0151] Based on the above embodiment, optionally, the centralized optimization model construction module is specifically used to:

[0152] Taking load recovery, distributed energy utilization and voltage drop as objective functions, a distribution network centralized optimization model is constructed; the distribution network centralized optimization model is expressed as:

[0153] Minimize:F Obj =α1F Load +α2F Der +α3F V

[0154] Among them, FObj represents the objective function of the centralized optimization model; F Load Indicates load recovery amount; F Der represents the utilization rate of distributed energy; F V represents the voltage drop; α1, α2, and α3 represent their corresponding weights respectively.

[0155] Based on the above embodiment, optionally, the power distribution network decomposition module is specifically used to:

[0156] According to the decomposition method of the autonomous clustering strategy, the distribution network is decomposed into at least two subsystems, and an objective function is established for each subsystem; wherein each subsystem corresponds to a subgraph on a topological structure;

[0157] The objective function is established for each subsystem, which is expressed as:

[0158]

[0159] ζ(lj)=H l ×H j →ε

[0160] in, Represents subsystem H l The objective function of X l , A vector representing continuous and integer variables, indicating states associated with the subsystem; represent the continuous variable and integer variable on the boundary switch respectively; ζ(lj) represents the connection between the two subsystems H l and H j The boundary line or overlapping area between them.

[0161] Based on the above embodiment, optionally, the subsystem optimization and adjustment module is specifically used to:

[0162] Introducing boundary switches between subsystems and modifying connectivity and radiality constraints in the centralized optimization model of the distribution network; wherein the boundary switches are used to maintain connectivity and radiality between subsystems;

[0163] An auxiliary variable virtual commodity flow is introduced on the boundary line of each subsystem to optimize and adjust the coordination between the subsystems; wherein the auxiliary variable virtual commodity flow represents the power flow between the subsystems.

[0164] Based on the above embodiment, optionally, the distribution network load recovery module is specifically used to:

[0165] The penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problem of each subsystem, and the local optimization problem of each subsystem is solved under the conditions of radial constraints and capacity constraints.

[0166] Iteratively updating the variables of the penalty-driven distributed alternating direction multiplier algorithm; wherein the penalty-driven distributed alternating direction multiplier algorithm variables include original variables, dual variables, auxiliary variables, residuals and penalty coefficients;

[0167] The centralized optimization model of the distribution network is iteratively updated according to the distributed optimization problems of each subsystem, the local optimization problems and the variables of the penalty-driven distributed alternating direction multiplier algorithm until the centralized optimization model of the distribution network meets the preset convergence conditions.

[0168] Based on the above embodiment, optionally, the distribution network load recovery module is specifically used to:

[0169] The integer decision variables in the distributed optimization problem are replaced by continuous decision variables to decompose the distributed optimization problem of each subsystem into a multi-stage solution;

[0170] The objective function is defined by the augmented Lagrangian function, and the augmented Lagrangian function is updated by scaling the dual variables to optimize the objective function.

[0171] The distribution network load recovery device provided in the embodiment of the present invention can execute the distribution network load recovery method provided in any embodiment of the present invention mentioned above, and has the corresponding functions and beneficial effects of executing the distribution network load recovery method. For detailed process, please refer to the relevant operations of the distribution network load recovery method in the above embodiment.

[0172] Embodiment 4

[0173] Fig.12 1 is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. The electronic device 10 is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices (such as helmets, glasses, watches, etc.) and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present invention described and / or required herein.

[0174] like Fig.12As shown, the electronic device 10 includes at least one processor 11, and a memory connected to the at least one processor 11, such as a read-only memory (ROM) 12, a random access memory (RAM) 13, etc., wherein the memory stores a computer program that can be executed by at least one processor, and the processor 11 can perform various appropriate actions and processes according to the computer program stored in the read-only memory (ROM) 12 or the computer program loaded from the storage unit 18 to the random access memory (RAM) 13. In the RAM 13, various programs and data required for the operation of the electronic device 10 can also be stored. The processor 11, the ROM 12, and the RAM 13 are connected to each other through a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0175] A number of components in the electronic device 10 are connected to the I / O interface 15, including: an input unit 16, such as a keyboard, a mouse, etc.; an output unit 17, such as various types of displays, speakers, etc.; a storage unit 18, such as a disk, an optical disk, etc.; and a communication unit 19, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 19 allows the electronic device 10 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.

[0176] The processor 11 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the processor 11 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, digital signal processors (DSPs), and any appropriate processors, controllers, microcontrollers, etc. The processor 11 executes the various methods and processes described above, such as a distribution network load recovery method.

[0177] In some embodiments, the distribution network load recovery method may be implemented as a computer program, which is tangibly contained in a computer-readable storage medium, such as a storage unit 18. In some embodiments, part or all of the computer program may be loaded and / or installed on the electronic device 10 via the ROM 12 and / or the communication unit 19. When the computer program is loaded into the RAM 13 and executed by the processor 11, one or more steps of the distribution network load recovery method described above may be performed. Alternatively, in other embodiments, the processor 11 may be configured to execute the distribution network load recovery method in any other appropriate manner (e.g., by means of firmware).

[0178] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0179] Computer programs for implementing the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that when the computer program is executed by the processor, the functions / operations specified in the flow chart and / or block diagram are implemented. The computer program may be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a stand-alone software package, or entirely on a remote machine or server.

[0180] In the context of the present invention, a computer-readable storage medium may be a tangible medium that may contain or store a computer program for use by or in combination with an instruction execution system, device or equipment. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices or equipment, or any suitable combination of the foregoing. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0181] To provide interaction with a user, the systems and techniques described herein may be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and a pointing device (e.g., a mouse or trackball) through which the user can provide input to the electronic device. Other types of devices may also be used to provide interaction with the user; for example, the feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form (including acoustic input, voice input, or tactile input).

[0182] The systems and techniques described herein may be implemented in a computing system that includes backend components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes frontend components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such backend components, middleware components, or frontend components. The components of the system may be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), a blockchain network, and the Internet.

[0183] A computing system may include a client and a server. The client and the server are generally remote from each other and usually interact through a communication network. The client and server relationship is generated by computer programs running on the corresponding computers and having a client-server relationship with each other. The server may be a cloud server, also known as a cloud computing server or cloud host, which is a host product in the cloud computing service system to solve the defects of difficult management and weak business scalability in traditional physical hosts and VPS services.

[0184] Embodiment 5

[0185] An embodiment of the present invention further provides a computer program product, including a computer program, which, when executed by a processor, implements the distribution network load recovery method provided in any embodiment of the present application.

[0186] In the process of implementation, the computer program product can be written in one or more programming languages ​​or a combination thereof to perform the computer program code of the present invention, including object-oriented programming languages, such as Java, Smalltalk, C++, and conventional procedural programming languages, such as "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (for example, using an Internet service provider to connect through the Internet).

[0187] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the present invention can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solution of the present invention can be achieved, and this document does not limit this.

[0188] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for restoring a distribution network load, characterized in that: The method comprises: Constructing a distribution network centralized optimization model based on load recovery, distributed energy utilization and voltage drop; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance and voltage constraints; Decompose the power distribution network into at least two subsystems and establish an objective function for each subsystem; Optimize the connectivity, radiality and coordination among subsystems; The penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problem of each subsystem to restore the distribution network load.

2. The method according to claim 1, characterized in that The centralized optimization model of the distribution network is constructed based on the load recovery amount, the utilization rate of distributed energy and the voltage drop, including: Taking load recovery, distributed energy utilization and voltage drop as objective functions, a distribution network centralized optimization model is constructed; the distribution network centralized optimization model is expressed as: Minimize:F Obj =α1F Load +α2F Der +α3F V Among them, F Obj represents the objective function of the centralized optimization model; F Load Indicates load recovery amount; F Der represents the utilization rate of distributed energy; F V represents the voltage drop; α1, α2, and α3 represent their corresponding weights respectively.

3. The method according to claim 1, characterized in that Decomposing the power distribution network into at least two subsystems and establishing an objective function for each subsystem includes: According to the decomposition method of the autonomous clustering strategy, the distribution network is decomposed into at least two subsystems, and an objective function is established for each subsystem; wherein each subsystem corresponds to a subgraph on a topological structure; The objective function is established for each subsystem, which is expressed as: in, Represents subsystem H l The objective function of A vector representing continuous and integer variables, indicating states associated with the subsystem; represent the continuous variable and integer variable on the boundary switch respectively; ζ(lj) represents the connection between the two subsystems H l and H j The boundary line or overlapping area between them.

4. The method according to claim 1, characterized in that: The optimization and adjustment of connectivity, radiality and coordination among the subsystems includes: Introducing boundary switches between subsystems and modifying connectivity and radiality constraints in the centralized optimization model of the distribution network; wherein the boundary switches are used to maintain connectivity and radiality between subsystems; An auxiliary variable virtual commodity flow is introduced on the boundary line of each subsystem to optimize and adjust the coordination between the subsystems; wherein the auxiliary variable virtual commodity flow represents the power flow between the subsystems.

5. The method according to claim 1, characterized in that The penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problem of each subsystem to restore the load of the distribution network, including: The penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problem of each subsystem, and the local optimization problem of each subsystem is solved under the conditions of radial constraints and capacity constraints. Iteratively updating the variables of the penalty-driven distributed alternating direction multiplier algorithm; wherein the penalty-driven distributed alternating direction multiplier algorithm variables include original variables, dual variables, auxiliary variables, residuals and penalty coefficients; The centralized optimization model of the distribution network is iteratively updated according to the distributed optimization problems of each subsystem, the local optimization problems and the variables of the penalty-driven distributed alternating direction multiplier algorithm until the centralized optimization model of the distribution network meets the preset convergence conditions.

6. The method according to claim 5, characterized in that The penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problem of each subsystem, including: The integer decision variables in the distributed optimization problem are replaced by continuous decision variables to decompose the distributed optimization problem of each subsystem into a multi-stage solution; The objective function is defined by the augmented Lagrangian function, and the augmented Lagrangian function is updated by scaling the dual variables to optimize the objective function.

7. A distribution network load recovery device, characterized in that: The device comprises: A centralized optimization model building module is used to build a centralized optimization model of the distribution network based on load recovery, distributed energy utilization and voltage drop; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance and voltage constraints; A power distribution network decomposition module, used for decomposing the power distribution network into at least two subsystems and establishing an objective function for each subsystem; Subsystem optimization and adjustment module, used to optimize the connectivity, radiality and coordination among subsystems; The distribution network load recovery module is used to calculate the distributed optimization problems of each subsystem using a penalty-driven distributed alternating direction multiplier algorithm to restore the distribution network load.

8. An electronic device, characterized in that: include: one or more processors; A storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the distribution network load recovery method described in any one of claims 1-6.

9. A storage medium containing computer executable instructions, characterized in that: The computer executable instructions are used to execute the distribution network load recovery method as described in any one of claims 1 to 6 when executed by a computer processor.

10. A computer program product, comprising a computer program, wherein when the computer program is executed by a processor, the computer program implements the distribution network load recovery method according to any one of claims 1 to 6.

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