Power distribution network load restoration method and apparatus, electronic device, and storage medium

Abstract

A power distribution network load restoration method and apparatus, an electronic device, and a storage medium. The method comprises: building a centralized optimization model for a power distribution network on the basis of a load recovery capacity, a distributed energy utilization rate and a voltage drop (S110); decomposing the power distribution network into at least two subsystems, and establishing an objective function for each subsystem (S120); optimizing and adjusting the connectivity, radiality and coordination between the subsystems (S130); and using a penalty-driven distributed alternating direction method of multipliers to solve the distributed optimization problem of each subsystem, so as to restore the load of the power distribution network (S140).

Description

Methods, devices, electronic equipment and storage media for power distribution network load restoration

[0001] This application claims priority to Chinese Patent Application No. 202411715596.3, filed with the Chinese Patent Office on November 27, 2024, the entire contents of which are incorporated herein by reference. Technical Field

[0002] This application relates to the field of power system technology, such as a method, apparatus, electronic device, and storage medium for power distribution network load restoration. Background Technology

[0003] With the integration of smart grid technology, the load recovery capability of distribution networks in the face of natural disasters or cyberattacks has become particularly important. Although smart grid technology greatly improves the resilience of distribution networks, power outages due to unpredictable external events such as faults or attacks remain unavoidable. To address this challenge, load recovery strategies should be able to respond quickly to these events and automatically restore power supply within a reasonable timeframe. 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 equipment offers significant potential for achieving efficient self-healing strategies.

[0004] Centralized optimization algorithms can converge to the global optimum. Current centralized recovery schemes typically rely on a central controller, requiring advanced communication networks to collect data from network components and perform complex calculations. However, this architecture is costly, carries a single point of failure risk, and poses a threat to data privacy. Distributed service recovery offers a potential solution, but many distributed recovery schemes in related technologies require the assumption of problem convexity, which is not always met in reality. Furthermore, many methods neglect scalability issues in large-scale distributed networks, and most research ignores data privacy, limiting the scope of distributed recovery schemes in related technologies. Research in related technologies has proposed distributed recovery frameworks based on distributed alternating direction multiplier algorithms, but these methods often fail to obtain feasible solutions when dealing with binary variables, and the strict structure they employ cannot support intra-cluster switching operations. Moreover, these methods ignore the inherent complexity and scalability issues when dealing with complex network topologies, making it difficult to meet the practical application requirements of large-scale distributed networks. Distributed alternating direction multiplier algorithms in related technologies are mainly applied to convex optimization problems. Although some success has been achieved in non-convex problems, their convergence remains uncertain. Summary of the Invention

[0005] This application provides a method, apparatus, electronic device, and storage medium for power distribution network load restoration, so as to achieve rapid load restoration after a fault occurs, thereby improving the restoration efficiency of the power distribution network.

[0006] In a first aspect, embodiments of this application provide a method for restoring loads in a power distribution network, including:

[0007] A centralized optimization model for the distribution network 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.

[0008] The power distribution network is decomposed into at least two subsystems, and an objective function is established for each subsystem;

[0009] The connectivity, radiality, and coordination between the subsystems are optimized and adjusted.

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

[0011] Secondly, embodiments of this application also provide a power distribution network load restoration device, comprising:

[0012] The centralized optimization model construction module is configured to construct a centralized optimization model of the distribution network based on load recovery, distributed energy utilization rate, and voltage drop; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance, and voltage constraints;

[0013] The power distribution network decomposition module is configured to decompose the power distribution network into at least two subsystems and establish objective functions for each subsystem.

[0014] The subsystem optimization and adjustment module is configured to optimize and adjust the connectivity, radiality, and coordination between subsystems.

[0015] The distribution network load recovery module is configured to use a penalty-driven distributed alternating direction multiplier algorithm to calculate the distributed optimization problem of each subsystem in order to restore the distribution network load.

[0016] Thirdly, embodiments of this application also provide an electronic device, which includes:

[0017] At least one processor;

[0018] A storage device configured to store at least one program;

[0019] When the at least one program is executed by the at least one processor, the at least one processor implements the power distribution network load restoration method described in any embodiment of this application.

[0020] Fourthly, embodiments of this application also provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the power distribution network load restoration method described in any embodiment of this application.

[0021] Fifthly, embodiments of this application also provide a computer program product, including a computer program that, when executed by a processor, implements the power distribution network load restoration method as described in any embodiment of this application.

[0022] This application provides a method, apparatus, electronic device, and storage medium for power distribution network load restoration. It constructs a centralized optimization model of the power distribution network based on load restoration 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 power distribution network is decomposed into at least two subsystems, and an objective function is established for each subsystem. The connectivity, radial direction, and coordination between the subsystems 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 power distribution network load. By decomposing the power distribution network into at least two subsystems, establishing a distributed optimization model, and combining it with a penalty-driven distributed alternating direction multiplier algorithm, the technical solution of this application can quickly restore the load after a fault occurs and ensure the effective utilization of more distributed energy resources, thereby improving the restoration efficiency of the power distribution network. Attached Figure Description

[0023] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings. The drawings are for illustrative purposes only and are not intended to limit the scope of this application. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0024] Figure 1 is a flowchart of a power distribution network load restoration method provided in an embodiment of this application;

[0025] Figure 2 is a flowchart of another power distribution network load restoration method provided in the embodiments of this application;

[0026] Figure 3 is a flowchart of another power distribution network load restoration method provided in the embodiments of this application;

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

[0028] Figure 5 is a schematic diagram of the convergence of an integer variable in the recovery of an IEEE 33 bus system provided in an embodiment of this application using a penalty-driven distributed alternating direction multiplier algorithm.

[0029] Figure 6 is a schematic diagram of the convergence of the residual term in the recovery of an IEEE 33 bus system provided in an embodiment of this application using a penalty-driven distributed alternating direction multiplier algorithm.

[0030] Figure 7 is a schematic diagram of the distributed optimization results in an IEEE 123-node system provided in an embodiment of this application;

[0031] Figure 8 is a schematic diagram of the convergence of an integer variable in the recovery of an IEEE 123 bus system provided in an embodiment of this application using a penalty-driven distributed alternating direction multiplier algorithm.

[0032] Figure 9 is a schematic diagram of the convergence of a penalty-driven distributed alternating direction multiplier algorithm provided in the embodiments of this application for continuous variables in the recovery of an IEEE 123 bus system;

[0033] Figure 10 is a schematic diagram of the convergence of residuals in the recovery of an IEEE 123 bus system provided in an embodiment of this application using a penalty-driven distributed alternating direction multiplier algorithm.

[0034] Figure 11 is a structural schematic diagram of a power distribution network load restoration device provided in an embodiment of this application;

[0035] Figure 12 is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0036] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the application and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present application, not the entire structure.

[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 flowcharts. Although the flowcharts describe the operations (or steps) as sequential processes, many of the operations (or steps) may be performed in parallel, concurrently, or simultaneously. Furthermore, the order of the operations may be rearranged. The process may be terminated when its operation is completed, but may also have additional steps not included in the figures. The process may correspond to a method, function, procedure, subroutine, subroutine, etc.

[0038] The acquisition, storage, use, and processing of data in this application comply with relevant national laws and regulations. It should be noted that existing industry solutions such as software, components, or models may be mentioned in the embodiments of this application. These should be considered exemplary and intended only to illustrate the feasibility of implementing the technical solution of this application, but do not imply that the applicant has already used or necessarily used such a solution.

[0039] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in sequences other than those illustrated or described herein.

[0040] Example 1

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

[0042] S110. A centralized optimization model for the distribution network is constructed based on load recovery, distributed energy utilization rate, and voltage drop.

[0043] Load recovery capacity typically refers to the ability of a system or device to recover to its initial or higher state after experiencing a certain level of load (such as stress or energy consumption) under certain conditions. In this embodiment, load recovery capacity is used to characterize the power supply recovery capability of the power distribution network. Distributed energy utilization rate refers to the proportion of input energy converted into usable energy in the actual operation of a distributed energy system. Voltage drop refers to the potential difference generated across the electrical equipment when current flows through it. In this embodiment, voltage drop is used to characterize the normal operation of the power distribution system.

[0044] In this embodiment, a centralized optimization model for the distribution network is constructed based on load recovery, distributed energy utilization, and voltage drop. This centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance, and voltage constraints to ensure the stability and security of the system operation. The centralized optimization model for the distribution network is expressed as: Minimize:F Obj =α1F Load +α2F Der +α3F V

[0045] Among them, F ObjF represents the objective function of the lumped optimization model; Load Indicates the amount of load recovery; F Der Indicates the utilization rate of distributed energy; F V α1 represents the voltage drop; α2, α3 represent their respective weights.

[0046] The load recovery amount has the highest weight in the objective function, and the load recovery amount can be expressed as:

[0047] in, This represents the total number of load nodes in the power distribution network; s n The switch state of node n is represented by a binary variable (0 or 1), indicating whether the node has been restored to power; P n This represents the load power of node n.

[0048] Distributed energy utilization rate enables more distributed energy to be injected into the system, which can be expressed as:

[0049] in, This represents the set of nodes where distributed energy resources are located; This represents the distributed energy injection power at node n.

[0050] Voltage drop is used to characterize the stability of a power distribution system. Voltage stability is crucial for the normal operation of a power distribution system, and maintaining the voltage at each node close to its nominal value is very important. The voltage drop can be expressed as:

[0051] in, This represents the square of the difference between the node voltage and the nominal voltage.

[0052] To simplify the analysis process, a compact optimization model was obtained, as follows:

[0053] P1:

[0054] st

[0055] In the above formula, P1 represents the objective function; X, These represent continuous decision variables and integer decision variables, respectively. These represent equality constraints and inequality constraints, respectively.

[0056] S120. Decompose the power distribution network into at least two subsystems and establish objective functions for each subsystem.

[0057] The distribution network is decomposed into at least two subsystems, each corresponding to a subgraph in the topology, and each subsystem H l They all solved a very similar problem, and an optimization model was built for each subsystem, as shown below:

[0058] P2:

[0059] st ζ(lj)=H l ×H j →ε

[0060] In the above formula, Representative subsystem H l The objective function; X l , A vector representing continuous and integer variables, indicating the state associated with the subsystem; These represent continuous and integer variables on the boundary switch, respectively. ζ(lj) represents the connection between the two subsystems H. l and H j The boundary lines or overlapping areas between them.

[0061] S130. Optimize and adjust the connectivity, radiality, and coordination between the subsystems.

[0062] After decomposing the power distribution network into at least two subsystems, adjustments need to be made to the connectivity, radial orientation, and coordination between these subsystems. Connectivity refers to the interconnectivity between subsystems, which can be maintained by introducing boundary switches. Radial orientation refers to the direction of current flow between subsystems. Coordination refers to the communication coordination between subsystems, which can be optimized by introducing an auxiliary variable, virtual commodity flow.

[0063] S140. The penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problem of each subsystem in order to restore the load of the distribution network.

[0064] 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. This algorithm introduces a penalty factor to handle constraints, enabling previously difficult-to-handle constrained optimization problems to gradually approach the optimal solution through iteration. In a distributed environment, P-ADMM allows each node to perform calculations independently and exchange information through communication mechanisms, ultimately reaching the global optimum. In this embodiment, the Penalty-driven Distributed Alternating Direction Method of Multipliers is used to calculate the distributed optimization problem of each subsystem to solve the optimization problem of the entire power distribution network and restore the load of the power distribution network.

[0065] This application provides a method for distribution network load restoration, which constructs a centralized optimization model of the distribution network based on load restoration 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, radial direction, and coordination between the subsystems 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. By decomposing the distribution network into at least two subsystems, establishing a distributed optimization model, and combining it with a penalty-driven distributed alternating direction multiplier algorithm, the method can quickly restore the load after a fault occurs and ensure the effective utilization of more distributed energy resources, thereby improving the restoration efficiency of the distribution network.

[0066] Example 2

[0067] Figure 2 is a flowchart of a power distribution network load restoration method provided in an embodiment of this application. This embodiment further optimizes the aforementioned embodiments and can be combined with various optional schemes from one or more of the above embodiments. As shown in Figure 2, the power distribution network load restoration method provided in this embodiment may include the following steps:

[0068] S210. A centralized optimization model for the distribution network is constructed based on load recovery, distributed energy utilization rate, and voltage drop.

[0069] In this embodiment, a centralized optimization model for the distribution network is constructed using 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 security of system operation.

[0070] The load restoration problem attempts to maintain the radial topology of the distribution network while restoring the load. A sufficient condition for the connectivity and radiality of a distribution network system is that all buses are connected to the root bus and each energized bus is connected to only one incoming arc.

[0071] Connectivity constraints and radial constraints ensure that the distribution network maintains its radial topology during restoration, meaning that each node can only connect to the main network in one direction. Specifically: 0≤f nm ≤z nm 0≤f mn ≤z mn β nm ≤v n

[0072] In the above formula, z mn ,z nm Represents the path status from node m to node n; β mn The binary auxiliary variables representing lines m and n ensure that the line states of the system are consistent in different directions; f mn v represents the network traffic from node m to node n; n The state variables (0 or 1) representing node n; ε, ε F ,ε S These represent the set of lines, the set of faulty lines, and the set of selectable lines, respectively. This represents the set of root nodes (usually main substations) in a distribution network; This represents the set of nodes connected to node n.

[0073] Capacity constraints ensure that the decision variables for the distribution network load restoration problem are within acceptable limits, as follows:

[0074] In the above formula, This represents the maximum active power of node n; Represents the injected reactive power at node n; P represents the maximum reactive power at node n; mn Q mn These represent the active power and reactive power of line mn, respectively; These represent the maximum active power, reactive power, and apparent power of line mn, respectively; V min V max These represent the minimum and maximum voltages of node n, respectively.

[0075] The linearized power balance equation and voltage equation for the unbalanced system are shown below:

[0076] In the above formula, This represents the impedance of line mn, i.e., resistance and reactance.

[0077] The load restoration strategy proposed in this application takes into account various constraints such as the connectivity, radiality, capacity constraints, and power balance of the distribution network, which can ensure the stable operation of the distribution network during the load restoration process and effectively avoid the risk of single point of failure in centralized optimization schemes.

[0078] Optionally, as shown in Figure 3, the method before constructing the centralized optimization model also includes initializing system parameters, such as system topology, distributed energy capacity, line capacity and load demand, as well as initializing the original variables, dual variables, penalty coefficients and auxiliary variables in the penalty-driven distributed alternating direction multiplier algorithm.

[0079] S220. Decompose the power distribution network into at least two subsystems and establish objective functions for each subsystem.

[0080] This application proposes a decomposition method for autonomous clustering strategies, which divides the power distribution network into multiple subsystems. Data exchange and coordination between the subsystems are achieved through boundary switches. This can improve the convergence speed of subproblems and the penalty-driven distributed alternating direction multiplier algorithm, and reduce information exchange.

[0081] As an optional but non-limiting implementation, the method of decomposing the power distribution network into at least two subsystems and establishing an objective function for each subsystem includes:

[0082] Based on the decomposition method of the autonomous clustering strategy, the power 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 topology.

[0083] The power distribution network system is decomposed into multiple subsystems H l (l∈1,2,3,...k), each subsystem corresponds to a subgraph on a topological structure. Each subsystem H l They all solved a very similar problem, and an optimization model was built for each subsystem, as shown below:

[0084] P2:

[0085] st ζ(lj)=H l ×H j →ε

[0086] Among them, P2: Representative subsystem H l The objective function; X l , A vector representing continuous and integer variables, indicating the state associated with the subsystem; These represent the continuous and integer variables on the boundary switch, respectively; ζ(lj) represents the connection between the two subsystems H. l and H j The boundary lines or overlapping areas between them.

[0087] S230. Optimize and adjust the connectivity, radiality, and coordination between the subsystems.

[0088] After constructing the objective functions for each subsystem, the connections, radiality, and coordination between the subsystems are optimized and adjusted.

[0089] As an optional but non-limiting implementation, the optimization and adjustment of the connectivity, radiality, and coordination between the subsystems includes, but is not limited to, steps A1-A2:

[0090] Step A1: Introduce boundary switches between subsystems and modify the connectivity and radial constraints in the centralized optimization model of the distribution network; wherein, the boundary switches are used to maintain connectivity and radiality between subsystems.

[0091] Step A2: Introduce auxiliary variable virtual commodity flow on the boundary line of each subsystem to optimize and adjust the coordination between subsystems; wherein, the auxiliary variable virtual commodity flow represents the power flow between subsystems.

[0092] In this system, after decomposing the distribution network system, boundary switches are introduced between each subsystem to maintain connectivity between them. Therefore, the modification of connectivity constraints for lines with boundary switches can be expressed as follows: 0≤f nm ≤z nm 0≤f mn ≤z mn

[0093] In the above formula, ε B Represents the set of boundary lines, which are located at the boundaries of a subsystem and are used to connect different subsystems or a subsystem to the main system; This represents the set of boundary nodes, which are nodes located at the boundaries of a subsystem and are typically connected to other subsystems or the main system via boundary switches.

[0094] Responsible for calculating H l X l and The distributed controller needs information to mimic the rest of the system in order to achieve a globally optimal solution, which is achieved through H l (H j This is achieved by introducing an auxiliary variable along the straight line. Assume mn is identified by ζ(lj) in H. l and H j The lines between them, n' and m' are auxiliary buses introduced for decomposition. Secondly, the active power, reactive power, and commodity flow into neighboring subsystems via the boundary buses are represented by the auxiliary generators connected to them. These auxiliary generators represent those in H l H at bus n' j Since this decomposition is performed along a switchable line, the above representation also depends on line β. mn' The state of. Therefore, The value is determined by H l Calculate and share, as follows:

[0095] In the above formula, These represent the active and reactive power flows at the boundary nodes, respectively. This represents the traffic of virtual goods.

[0096] When β mn' When closed, m and n' are adjacent generatrices; if β mn' Disconnect, these two subsystems H l H j Physically disconnected. To introduce the effects of variations between adjacent subsystems, the following modifications are included: Adjacent subsystems share the voltage magnitude at one end of mn'. Therefore, Coupling variables and common

[0097] The shared copies are as follows:

[0098] This decomposition applies the active power, reactive power, voltage, and commodity flow equations at the boundary line mn' to each subsystem H. l The effects of the inter-subsystem iteration (k) are shown below:

[0099] This application proposes an autonomous clustering strategy to decompose the power distribution network into multiple subsystems and exchange data between the subsystems through boundary switches, thereby reducing the amount of information exchange and computational complexity, and improving the convergence speed of the distributed optimization algorithm.

[0100] S240. The distributed optimization problem of each subsystem is calculated using the penalty-driven distributed alternating direction multiplier algorithm, and the local optimization problem of each subsystem is solved under the conditions of radiality constraint and capacity constraint.

[0101] This application employs a penalty-driven distributed alternating direction multiplier algorithm to compute the distributed optimization problem for each subsystem. Each subsystem, considering radial and capacity constraints, solves its local optimization problem and shares necessary boundary information with neighboring subsystems. First, the optimization objective is defined using an augmented Lagrangian function, decomposing the problem into multi-stage solutions that rely on alternating optimization of the principal and dual problems. Simultaneously, for both continuous and discrete variables, the algorithm uses projection and relaxation techniques to ensure that the optimization results progressively approach the global optimum.

[0102] As an optional but non-limiting implementation, the method of using a penalty-driven distributed alternating direction multiplier algorithm to calculate the distributed optimization problem of each subsystem includes, but is not limited to, steps B1-B2:

[0103] 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.

[0104] Step B2: Define the objective function using the augmented Lagrangian function, and update the augmented Lagrangian function by scaling the dual variables to optimize the objective function.

[0105] This application's embodiment reformulates the distributed optimization problem by replacing integer decision variables with continuous decision variables. The augmented Lagrangian function for this problem is shown below:

[0106] In the above formula, Y l yes The continuous relaxation version; ρ represents the penalty coefficient; Let these be the Lagrange multiplier vectors representing the continuous and integer variables of the consistency constraints in adjacent subsystems, respectively. The augmented Lagrange function is updated by scaling the dual variable μ = ν / ρ.

[0107] The penalty-driven distributed alternating direction multiplier algorithm includes the application of state variable X l and Y l The joint optimization. The projection of the continuous variable y onto the set of integers Z is determined by... This projection technique is embedded in the regularization term, by projecting the global state vector... A copy (i.e.) This is achieved by rounding to the nearest integer.

[0108] This application proposes a penalty-driven distributed alternating direction multiplier algorithm. The algorithm decomposes the problem into multiple subproblems based on Lagrange multipliers and introduces a penalty function slack variable to solve the distributed optimization model. Through iteration, the algorithm gradually approaches the optimal solution, thereby achieving rapid and effective recovery of the distribution network load.

[0109] S250, Iteratively update the variables of the penalty-driven distributed alternating direction multiplier algorithm.

[0110] The penalty-driven distributed alternating direction multiplier algorithm variables include original variables, dual variables, auxiliary variables, residuals, and penalty coefficients.

[0111] The primary variables, global auxiliary variables, and dual variables are updated in the (k+1)th iteration as follows:

[0112] Simultaneously update the relaxed integer variable. Since the relaxed integer variable is a Boolean variable, to make it closer to an integer value, a penalty function is introduced into the objective function, as shown below: L l +τφ l (x s ) x s =[z nm ,z mn ,s n ]

[0113] In the above formula, φ l (x s ) represents the penalty function; L l +τφ l (x s () represents the corrected objective function; x s Indicates the status of line and load switches; Indicates x s Round to the nearest integer.

[0114] The residual update, stopping criterion, and penalty coefficient update in each iteration of the penalty-driven distributed alternating direction multiplier algorithm are shown below: δ(k+1)=(r p (k+1), r d (k+1)) ∞ ≤∈

[0115] The embodiments of this application, by introducing penalty functions and auxiliary variables, support the parallel processing of complex topologies and multiple subsystems in distributed computing, thereby improving the scalability and flexibility of the algorithm in large-scale distribution networks.

[0116] S260. Based on the distributed optimization problem, local optimization problem, and variables of the penalty-driven distributed alternating direction multiplier algorithm of each subsystem, the centralized optimization model of the distribution network is iteratively updated until the centralized optimization model of the distribution network meets the preset convergence condition.

[0117] The process involves iteratively updating the centralized optimization model of the distribution network after solving the distributed and local optimization problems of each subsystem, and determining whether the updated model meets the preset convergence conditions. If the preset convergence conditions are not met, a 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 radial and capacity constraints. The variables of the penalty-driven distributed alternating direction multiplier algorithm are then iteratively updated until the centralized optimization model of the distribution network meets the preset convergence conditions.

[0118] This application provides a load restoration method for distribution networks, aiming to address the load restoration problem of distribution networks under faults or natural disasters. This restoration method constructs a distributed optimization model, combines it with an autonomous clustering strategy, divides the distribution network into multiple subsystems, and uses boundary switches for coordination and data exchange between subsystems, significantly improving the efficiency of distributed computing. A penalty-driven distributed alternating direction multiplier algorithm is employed to compute the distributed optimization problem of each subsystem. This algorithm, by introducing auxiliary variables and a penalty function, effectively handles optimization problems with complex network topologies and boundary conditions, supports parallel computing of multiple subsystems, and ensures global convergence and rapid recovery capability. The core of this method lies in decomposing the centralized optimization problem into sub-problems of multiple subsystems. Each subsystem is solved independently and optimized collaboratively with adjacent subsystems, reducing computational burden and improving optimization speed. Furthermore, this application fully considers the connectivity, radiality, power balance, and capacity constraints of the distribution network to ensure stable system operation during load restoration. Through the design of the distributed computing framework, this strategy improves the self-healing capability of the distribution network, enabling rapid and effective load restoration when faults occur, and enhancing system reliability and scalability.

[0119] In one optional embodiment of this application, the improved IEEE 33-node distribution network system and the IEEE 123-node distribution network system are selected for verification. During the verification process, the focus is on verifying the distribution network load recovery effect based on the penalty-driven distributed alternating direction multiplier algorithm proposed in the embodiments of this application.

[0120] Centralized and distributed algorithms were implemented using the Matlab toolbox Yalmip, and the optimization framework was solved using the Gurobi optimizer. The typical parameter values ​​used in the penalty-driven distributed alternating direction multiplier algorithm were τ = 5, ρ = 300, ∈ = 0.001, α1 = 1, α2 = 5, α3 = 5, γ1 = 0.1, γ2 = 1.5, γ3 = 1.2. An emergency situation was studied in the modified IEEE 33-node system. The system's rated power and rated voltage were 100 MVA and 12.66 kV, respectively. The minimum and maximum limits of the squared voltage amplitude were 0.95 and 1.05 pu, respectively, and the substation operated at 1 p.u. voltage. Referring to Figure 4, the system was 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. Three distributed energy units are located in... The total capacity is 0.98 MVA, approximately 25% of the total MVA requirement. As shown in Figure 4, the fault occurs on line (27-28), located within subsystem 2. The fault is cleared by disconnecting the faulty line. Disconnecting line ε... B = (5-6) and ε I = (14-15) Recover the network. The convergence of the boundary integer variables and residuals of the penalty-driven distributed alternating direction multiplier algorithm is shown in Figures 5 and 6.

[0121] Referring to Figure 7, a penalty-driven distributed alternating direction multiplier algorithm was studied in an improved IEEE 123 bus system. The system has a rated power of 1 MVA and a rated voltage of 4.16 kV. The minimum and maximum voltage amplitude square limits are 0.95 and 1.1 pu, respectively. Substations 1 and 2 operate at 1.0 pu. 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 As shown in Figure 7, the system contains a total of 46 controllable circuit switches, 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 power source connected to bus 60 operates at 1.0 pu. The distributed power source primarily supplies power to subsystem 4 (isolation area), but excess power generation will supply neighboring subsystems if needed.

[0122] Table 1. Location of Subsystems and NR

[0123] This application's embodiments study the distributed recovery of unbalanced systems, in ε F In the case of {(86-87), (35-116)}, an unexpected situation with two broken lines was studied. The fault in line (86-87) is an internal fault of subsystem 7, while the fault in line (35-116) is an interruption of the boundary switch. Both faults are cleared by opening the lines separately. As shown in Figures 8, 9, and 10, ε is closed. B ={(13-18),(117-118),(97-124),(72-76),(54-94)}, open ε B ={(39-66), (52-121), (60-119)}, the network is restored. From the topology of the restored network in Figure 7, 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 are shown in Figures 8, 9, and 10. The existence of isolated campuses also demonstrates the ability of distributed optimization algorithms in the formation of local islands.

[0124] Figure 4 shows the distributed optimization results in the IEEE 33-node system; Figures 5 and 6 show the performance of the penalty-driven distributed alternating direction multiplier algorithm in the recovery of the IEEE 33 bus system; Figure 7 shows the distributed optimization results in the IEEE 123-node system; and Figures 8, 9, and 10 show 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 figures, the penalty-driven distributed alternating direction multiplier algorithm can achieve rapid recovery in the event of a fault and has good convergence performance, ensuring the stable operation of the distributed power grid.

[0125] Example 3

[0126] Figure 11 is a schematic diagram of a distribution network load restoration device provided in an embodiment of this application. The technical solution of this embodiment is applicable to distribution network load restoration. This device can be implemented by software and / or hardware and is generally integrated into any electronic device with network communication capabilities, including but not limited to: servers, computers, personal digital assistants, etc. As shown in Figure 11, the distribution network load restoration 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 restoration module 1140; wherein...

[0127] The centralized optimization model construction module 1110 is used to construct a centralized optimization model of the distribution network based on load recovery, distributed energy utilization rate, and voltage drop; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance, and voltage constraints.

[0128] The power distribution network decomposition module 1120 is used to decompose the power distribution network into at least two subsystems and establish objective functions for each subsystem;

[0129] The subsystem optimization and adjustment module 1130 is used to optimize and adjust the connectivity, radiality, and coordination between subsystems.

[0130] 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 in order to restore the distribution network load.

[0131] Based on the above embodiments, optionally, the centralized optimization model construction module is specifically used for:

[0132] A centralized optimization model for the distribution network is constructed using load recovery, distributed energy utilization rate, and voltage drop as objective functions; the centralized optimization model for the distribution network is expressed as: Minimize: F Obj =α1F Load +α2F Der +α3F V

[0133] Among them, F Obj F represents the objective function of the lumped optimization model; Load Indicates the amount of load recovery; F Der Indicates the utilization rate of distributed energy; F V α1 represents the voltage drop; α2, α3 represent their respective weights.

[0134] Based on the above embodiments, optionally, the power distribution network decomposition module is specifically used for:

[0135] Based on the decomposition method of the autonomous clustering strategy, the power 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 topology.

[0136] The objective function established for each subsystem is expressed as follows:

[0137] P2:

[0138] st ζ(lj)=H l ×Hj →ε

[0139] Among them, P2: Representative subsystem H l The objective function; X l , A vector representing continuous and integer variables, indicating the state associated with the subsystem; These represent the continuous and integer variables on the boundary switch, respectively; ζ(lj) represents the connection between the two subsystems H. l and H j The boundary lines or overlapping areas between them.

[0140] Based on the above embodiments, optionally, the subsystem optimization and adjustment module is specifically used for:

[0141] Boundary switches are introduced between subsystems, and the connectivity and radial constraints in the centralized optimization model of the distribution network are modified; wherein, the boundary switches are used to maintain the connectivity and radial constraints between subsystems.

[0142] Auxiliary variable virtual commodity flow is introduced on the boundary line of each subsystem to optimize and adjust the coordination between subsystems; wherein, the auxiliary variable virtual commodity flow represents the power flow between subsystems.

[0143] Based on the above embodiments, optionally, the power distribution network load restoration module is specifically used for:

[0144] The distributed optimization problem of each subsystem is calculated using a penalty-driven distributed alternating direction multiplier algorithm, and the local optimization problem of each subsystem is solved under radial and capacity constraints.

[0145] The variables of the penalty-driven distributed alternating direction multiplier algorithm are iteratively updated; wherein, the variables of the penalty-driven distributed alternating direction multiplier algorithm include original variables, dual variables, auxiliary variables, residuals and penalty coefficients;

[0146] The centralized optimization model of the distribution network is iteratively updated based on the distributed optimization problem, local optimization problem, and variables of the penalty-driven distributed alternating direction multiplier algorithm of each subsystem until the centralized optimization model of the distribution network meets the preset convergence condition.

[0147] Based on the above embodiments, optionally, the power distribution network load restoration module is specifically used for:

[0148] Integer decision variables in distributed optimization problems are replaced with continuous decision variables to decompose the distributed optimization problems of each subsystem into multi-stage solutions.

[0149] 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.

[0150] The power distribution network load restoration device provided in this application embodiment can execute the power distribution network load restoration method provided in any of the above embodiments of this application, and has the corresponding functions and effects of executing the power distribution network load restoration method. For details, please refer to the relevant operations of the power distribution network load restoration method in the foregoing embodiments.

[0151] Example 4

[0152] Figure 12 is a schematic diagram of an electronic device provided in an embodiment of this application. 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 processors, cellular phones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the present application described and / or claimed herein.

[0153] As shown in Figure 12, the electronic device 10 includes at least one processor 11 and a memory, such as a read-only memory (ROM) 12 or a random access memory (RAM) 13, communicatively connected to the at least one processor 11. The memory stores computer programs executable by the at least one processor. The processor 11 can perform various appropriate actions and processes based on the computer programs stored in the ROM 12 or loaded from storage unit 18 into the RAM 13. The RAM 13 can also store various programs and data required for the operation of the electronic device 10. The processor 11, ROM 12, and RAM 13 are interconnected via a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0154] Multiple components in electronic device 10 are connected to I / O interface 15, including: input unit 16, such as keyboard, mouse, etc.; output unit 17, such as various types of displays, speakers, etc.; storage unit 18, such as disk, optical disk, etc.; and communication unit 19, such as network card, modem, wireless transceiver, etc. Communication unit 19 allows electronic device 10 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0155] Processor 11 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 11 include, but are not limited to, central processing unit (CPU), graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, digital signal processors (DSPs), and any suitable processor, controller, microcontroller, etc. Processor 11 performs the various methods and processes described above, such as distribution network load restoration methods.

[0156] In some embodiments, the power distribution network load restoration method may be implemented as a computer program tangibly contained in a computer-readable storage medium, such as storage unit 18. In some embodiments, part or all of the computer program may be loaded and / or installed on electronic device 10 via ROM 12 and / or communication unit 19. When the computer program is loaded into RAM 13 and executed by processor 11, one or more steps of the power distribution network load restoration method described above may be performed. Alternatively, in other embodiments, processor 11 may be configured to perform the power distribution network load restoration method by any other suitable means (e.g., by means of firmware).

[0157] Various embodiments 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-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0158] Computer programs used to implement the methods of this application 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, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0159] In the context of this application, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. Alternatively, a computer-readable storage medium can be a machine-readable signal medium. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0160] To provide interaction with a user, the systems and techniques described herein can 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 pointing device (e.g., a mouse or trackball) through which the user provides input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0161] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or computing systems that include middleware components (e.g., application servers), or computing systems that include frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0162] A computing system can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system to address the shortcomings of traditional physical hosts and VPS services, such as high management difficulty and weak business scalability.

[0163] Example 5

[0164] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the power distribution network load restoration method provided in any embodiment of this application.

[0165] In the implementation of the computer program product, computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0166] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this application can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this application can be achieved, and this is not limited herein.

Claims

1. A method for restoring load in a distribution network, comprising: A centralized optimization model for the distribution network 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. The power 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. A penalty-driven distributed alternating direction multiplier algorithm is used to calculate the distributed optimization problem of each subsystem in order to restore the load of the distribution network.

2. The method according to claim 1, wherein, The centralized optimization model for the distribution network based on load recovery, distributed energy utilization rate, and voltage drop includes: A centralized optimization model for the distribution network is constructed, using load recovery, distributed energy utilization, and voltage drop as objective functions. This centralized optimization model is expressed as follows: Minimize:F Obj =α1F Load +α2F Der +α3F V Among them, F Obj F represents the objective function of the lumped optimization model; Load Indicates the amount of load recovery; F Der Indicates the utilization rate of distributed energy; F V α1 represents the voltage drop; α2, α3 represent their respective weights.

3. The method of claim 1, wherein, The process of decomposing the power distribution network into at least two subsystems and establishing objective functions for each subsystem includes: Based on the decomposition method of the autonomous clustering strategy, the power 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 topology. The objective function is established for each subsystem, expressed as: ζ(lj)=H l ×H j →ε Continuous and integer variables on; ζ(lj) represents the connection between two subsystems H l and H j The boundary lines or overlapping areas between them.

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

5. The method of claim 1, wherein, The method employs a penalty-driven distributed alternating direction multiplier algorithm to calculate the distributed optimization problem of each subsystem for restoring the distribution network load, including: The distributed optimization problem of each subsystem is calculated using a penalty-driven distributed alternating direction multiplier algorithm, and the local optimization problem of each subsystem is solved under radial and capacity constraints. The variables of the penalty-driven distributed alternating direction multiplier algorithm are iteratively updated; wherein, the variables of the penalty-driven distributed alternating direction multiplier algorithm include original variables, dual variables, auxiliary variables, residuals and penalty coefficients; The centralized optimization model of the distribution network is iteratively updated based on the distributed optimization problem, local optimization problem, and variables of the penalty-driven distributed alternating direction multiplier algorithm of each subsystem until the centralized optimization model of the distribution network meets the preset convergence condition.

6. The method according to claim 5, wherein, The distributed optimization problem of each subsystem is calculated using the penalty-driven distributed alternating direction multiplier algorithm, including: Integer decision variables in distributed optimization problems are replaced with continuous decision variables to decompose the distributed optimization problems of each subsystem into multi-stage solutions. 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 power distribution network load restoration device, comprising: The centralized optimization model construction module is configured to construct a centralized optimization model of the distribution network based on load recovery, distributed energy utilization rate, and voltage drop; the centralized optimization model includes connectivity and radial constraints, capacity constraints, power balance, and voltage constraints; The power distribution network decomposition module is configured to decompose the power distribution network into at least two subsystems and establish objective functions for each subsystem. The subsystem optimization and adjustment module is configured to optimize and adjust the connectivity, radiality, and coordination between subsystems. The distribution network load restoration module is configured to use a penalty-driven distributed alternating direction multiplier algorithm to calculate the distributed optimization problem of each subsystem in order to restore the distribution network load.

8. An electronic device, comprising: At least one processor; A storage device configured to store at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the power distribution network load restoration method according to any one of claims 1-6.

9. A storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the power distribution network load restoration method as described in any one of claims 1-6.

10. A computer program product comprising a computer program that, when executed by a processor, implements the power distribution network load restoration method according to any one of claims 1-6.

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