Power distribution network transient voltage linearization prediction method
By constructing a graph neural network prediction model and linearizing it, and embedding it into the load recovery optimization model, the problem of integrating transient voltage safety assessment and recovery optimization is solved, and efficient and real-time distribution network fault recovery decision-making is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-26
- Publication Date
- 2026-03-27
AI Technical Summary
Existing technologies struggle to achieve integrated and collaborative solutions for transient voltage safety assessment and load recovery optimization, failing to balance transient safety with decision-making timeliness. Traditional methods suffer from high computational complexity and time consumption, and neural network models are difficult to directly embed into optimization models.
A graph neural network prediction model is constructed, which is then transformed into a mixed-integer linear programming model through linearization. This model is then embedded as a transient safety constraint into the load recovery optimization model to form a unified optimization model. The Big-M method is used to precisely linearize the nonlinear activation function, and the model is solved by combining it with a mixed-integer second-order cone programming model.
It realizes the integrated solution of transient voltage safety constraints and load restoration optimization, improves the safety and timeliness of distribution network fault restoration, meets the real-time requirements of online decision-making, and enhances the grid restoration capability under the background of high proportion of new energy access.
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Figure CN121749147A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of power system safety and stability and optimal dispatching, and particularly relates to a linear prediction method for transient voltage of a distribution network. BACKGROUND
[0002] With the promotion of the "double carbon" goal, the energy structure transformation is accelerating. After a high proportion of new energy (such as wind power and photovoltaic power) is connected to the power grid, its intermittency and volatility make transient voltage safety a key factor restricting the recovery capability of the distribution network. The safety and timeliness of load recovery after a fault directly affect power supply reliability, and especially in extreme weather or complex disaster scenarios, fast recovery of power supply is of great importance.
[0003] Existing technologies mostly use sequential load recovery or transactional control, rely on steady-state flow models, focus on static constraints such as flow balance, voltage out-of-limit, line transmission capacity, and take maximizing the amount of load recovery as the goal. However, these methods cannot directly reflect the transient voltage dynamic process and can only be verified through post-simulation, making it difficult to embed transient safety margin in the optimization model. In the actual recovery process, the batched load input, dynamic adjustment of network topology and fast response characteristics of new energy power supply often trigger significant transient processes, leading to transient voltage drop exceeding the standard, insufficient voltage recovery, and even causing transient instability, which seriously threatens the safe and stable operation of the power grid. Existing transient safety assessment mainly relies on time-domain simulation tools such as electromagnetic transient programs, which have high computational complexity and time-consuming problems, making it difficult to be repeatedly called in load recovery optimization with multiple time periods and multiple fault scenarios, and unable to adapt to the real-time requirements of online decision-making. Graph neural networks can utilize both the topology structure and the operating data of the power grid, and are used for fast prediction of safety indicators such as voltage and frequency after a fault. However, deep models are essentially nonlinear and non-explicit black-box forms, with forward mapping being a high-dimensional nonlinear function, making it difficult to directly embed them into mainstream load recovery optimization models such as mixed integer linear programming (MILP) as constraints. If an outer iteration correction or heuristic algorithm is used for indirect integration, it will also face problems such as poor convergence, insufficient interpretability, and difficulty in ensuring the stability of the solution, limiting the practical application of transient safety constraints in load recovery optimization.
[0004] Therefore, existing technologies cannot achieve integrated and collaborative solving of transient safety assessment and load recovery optimization, and cannot balance transient safety and decision-making timeliness. SUMMARY
[0005] The application aims to provide a power distribution network transient voltage linearization prediction method, which can realize efficient prediction of transient voltage characteristics by using the strong fitting capability of a neural network, accurately linearize the neural network model and embed it into a power grid load restoration decision model, ensure the efficiency of optimization solution, and realize explicit satisfaction of transient voltage safety constraints.
[0006] To achieve the above-mentioned purpose, the technical scheme adopted by the application is as follows: A power distribution network transient voltage linearization prediction method comprises the following steps: Based on multi-working-condition transient simulation data of the power distribution network, a graph neural network prediction model is constructed; The graph neural network prediction model is trained to take the transient voltage amplitude as the prediction target, and a trained graph neural network prediction model is obtained; The trained graph neural network prediction model is linearized, that is, the nonlinear activation function therein is linearized, and the graph neural network prediction model is converted into a mixed integer linear programming model; Real-time state data of the power distribution network are taken as input, forward calculation logic defined by the mixed integer linear programming model is executed, and the prediction result of the transient voltage of the power distribution network is output; A load restoration optimization model is constructed, which takes the minimization of the total cost of the restoration process as the optimization target and contains power flow balance constraints, voltage safety constraints, line capacity constraints and switch operation constraints; The mixed integer linear programming model is embedded into the load restoration optimization model as a transient safety constraint, forming a unified optimization model; The unified optimization model is solved, and a load restoration scheme satisfying the transient voltage safety constraint is output.
[0007] Further, the transient voltage amplitude is the lowest voltage amplitude in a specific time window after fault clearing.
[0008] Further, the graph neural network adopts a hybrid structure combining edge multilayer perceptron and graph convolution network, which is used to process node features and edge features at the same time.
[0009] Further, the edge multilayer perceptron is used for nonlinear transformation and aggregation of line features, and the graph convolution network is used to capture the propagation characteristics of electrical quantities on the topology.
[0010] Further, the training of the graph neural network prediction model adopts Huber Loss as the loss function, and combines early stopping strategy and cross-validation to ensure the model generalization ability.
[0011] Further, the linearization process introduces auxiliary continuous variables and binary variables to the ReLU activation function using the Big-M method to construct an equivalent set of linear constraints.
[0012] Further, the load restoration optimization model is a mixed integer second-order cone programming model, and the total restoration process cost includes distributed power generation cost, line loss cost and switch operation cost.
[0013] Further, the transient security constraint is defined as: the transient voltage value predicted by the mixed integer linear programming model should be within the preset transient voltage safety limit range.
[0014] Further, the solving process of the unified optimization model uses branch and bound and second-order cone relaxation technology to quickly converge to the optimal solution through continuous optimization sub-problems.
[0015] The power distribution network transient voltage linearization prediction method provided by the application realizes integrated solving of transient security constraints and load restoration optimization through the linearizable embedded neural network transient voltage prediction method, and has the following significant beneficial effects compared with the prior art: Firstly, by constructing a multi-working-condition transient simulation data set and using a graph neural network structure, the power grid topology and operation data are fully utilized to realize high-precision prediction of transient voltage indicators, avoiding the problems of high complexity and long time consumption of traditional time-domain simulation calculation.
[0016] Secondly, the Big-M method is used to accurately linearize the segmented nonlinear activation function in the neural network, auxiliary variables are introduced to construct a mixed integer linear constraint set, and the black box model is converted into an analyzable explicit expression, solving the problem that the neural network cannot be directly embedded in the optimization model.
[0017] Thirdly, the linearized transient voltage prediction model is used as a security constraint term and is uniformly modeled with the steady-state power flow equation and load restoration constraints to form a complete optimization framework, so that the restoration decision satisfies both static operation constraints and transient security criteria.
[0018] Finally, through the integrated process of "fast prediction-linear embedding-optimization decision", the explicit satisfaction of transient voltage security constraints is realized under the premise of ensuring the solving efficiency, which significantly improves the safety and timeliness of power distribution network fault restoration under the background of high proportion of new energy access, and provides reliable technical support for online decision-making. BRIEF DESCRIPTION OF DRAWINGS
[0019] Figure 1 is the overall framework diagram of the application; Figure 2 is the graph neural network prediction model training flowchart of the application; Figure 3 A linearization and forward propagation flowchart of the present application. DETAILED DESCRIPTION
[0020] In order to make the purposes, technical solutions and advantages of the present application clearer, the present application is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific examples described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in the various embodiments of the present application described below can be combined with each other as long as they do not conflict with each other.
[0021] The present application models the power grid as a graph structure with node features and edge features, adopts a neural network structure combining edge multi-layer perceptron (Edge-MLP) and graph convolution network (GCN), fully utilizes topology, electrical parameters, operating conditions and restoration decision information, and realizes high-precision and high-efficiency prediction of post-fault transient voltage indicators. All nonlinear activation functions in the network are precisely linearized by Big-M, and the original nonlinear "black box" mapping is converted into a set of linear equations, inequalities and binary variables; the linearized neural network is embedded into the load restoration optimization model as a transient security constraint, realizing integrated solution of load restoration decision and transient security assessment. The overall framework of the present application is shown in Figure 1 .
[0022] The present embodiment provides a power distribution network transient voltage linearization prediction method, which comprises: based on power distribution network multi-condition transient simulation data, constructing a graph neural network prediction model; training the graph neural network prediction model to take transient voltage amplitude as the prediction target, obtaining a trained graph neural network prediction model; linearizing the trained graph neural network prediction model, i.e. linearizing the nonlinear activation function therein, converting the graph neural network prediction model into a mixed integer linear programming model; taking real-time state data of the power distribution network as input, executing the forward calculation logic defined by the mixed integer linear programming model, and outputting the prediction result of the transient voltage of the power distribution network; constructing a load restoration optimization model, which takes the minimization of the total cost of the restoration process as the optimization objective and contains power flow balance constraints, voltage security constraints, line capacity constraints and switch operation constraints; embedding the mixed integer linear programming model as a transient security constraint into the load restoration optimization model to form a unified optimization model; solving the unified optimization model to output a load restoration scheme that satisfies the transient voltage security constraint. The method process is described in detail below.
[0023] 1. Based on transient simulation data of distribution networks under multiple operating conditions, a graph neural network prediction model is constructed. A distribution network simulation model is established in electromagnetic transient simulation software (such as PSCAD), setting various fault types, fault locations, fault clearing times, load connection methods, and topology operations. Through the above simulation settings, transient voltage response data under different recovery strategies and operating conditions are generated, forming the dataset required for training and validation. In the load recovery scenario, the distribution network topology can be abstracted as a graph structure: (1) Where V is the set of nodes, encompassing core power grid components such as generators, load nodes, buses, and switching stations. E is the set of edges, including physical connections such as transmission lines, transformers, and tie lines. Edge weights characterize the switching status of switches and circuit breakers, reflecting dynamic topology changes under different recovery schemes. Node features are used to characterize the attributes and operating status of each bus. Each bus or power aggregation point is considered an independent node i∈V, and information about the generators, loads, capacitors, and reactance devices connected to it serves as node features. For each transmission line or transformer, the corresponding edge (i,j)∈E has electrical parameters such as resistance, reactance, rated capacity, and turns ratio as edge features.
[0024] To balance physical constraints with subsequent Big-M linearization, the aforementioned recovery decision variables are encoded as graph features, uniformly standardized or scaled across intervals to form bounded feature tensors. The influence of disturbances on the system voltage distribution is learned through graph convolution. Sliding window aggregation is applied to the time-series features, compressing key information from the transient process into finite-dimensional graph feature inputs. The lower and upper bounds of the feature values are determined by the range of equipment ratings, operating limits, and simulation conditions.
[0025] 2. Train the graph neural network prediction model, using the transient voltage amplitude as the prediction target, to obtain the trained graph neural network prediction model. The transient voltage amplitude is the lowest voltage amplitude within a specific time window after the fault is cleared. After data preparation is completed, the training phase of the graph neural network prediction model begins. This process enables the model to accurately learn the complex nonlinear mapping relationship between different grid states and transient voltage responses. The training process is as follows: Figure 2 As shown.
[0026] The graph neural network employs a hybrid structure combining an edge-multilayer perceptron and a graph convolutional network to simultaneously process node and edge features. The edge-multilayer perceptron performs nonlinear transformations and aggregations on line features, while the graph convolutional network captures the propagation characteristics of electrical quantities across the topology. The training of the graph neural network prediction model uses Huber Loss as the loss function, combined with an early stopping strategy and cross-validation to ensure the model's generalization ability.
[0027] A hybrid architecture combining Edge-MLP and Graph Convolutional Network (GCN) is adopted, using the power grid topology as the graph input. Considering node and edge features, the multi-condition dataset samples are divided into training, validation, and test sets. Huber Loss (which takes into account the mean squared error characteristics) is used as the loss function to train the model. Cross-validation and performance evaluation are used to ensure that the model has good generalization ability for unseen conditions, and it is used to predict the transient safety margin of load restoration schemes under fault disturbances. After the model parameters are fixed, the trained network is used as the basis for subsequent linearization and optimized embedding.
[0028] To fully account for the impact of line characteristics on transient voltage, edge characteristics of the Edge-MLP layer are adopted. A nonlinear transformation is performed to construct edge embedding vectors. These vectors are then activated using ReLU to obtain the first layer of edge features. A second linear transformation is then applied to obtain more edge embedding vectors. Finally, these features are aggregated to each source node to form supplementary node-level edge feature information. (2) (3) Through two layers of GCNConv, the node features are first linearly transformed, and then the adjacency matrix is normalized. A graph convolution is performed, and the convolution result, edge aggregation result, and bias term are superimposed to obtain the first-layer pre-activation value. ReLU activation is then applied to obtain the first-layer node hidden vector. Similarly, a second-layer graph convolution is performed on the first-layer output. A linear transformation is first performed, then the pre-activation value is obtained by adding a bias term to the adjacency matrix. ReLU activation is then applied to obtain the second-layer node hidden vector, achieving layer-by-layer updating of node features and graph-level feature propagation. The formula is expressed as: (4) in, For activation function, As a trainable weight matrix, this structure can capture the propagation characteristics of electrical quantities in the network topology, enabling physical consistency in node voltage prediction.
[0029] The lowest voltage amplitude within a certain period after fault clearance is used as the node transient voltage index (transient voltage amplitude), and prediction is completed through the linear output layer: (5) Among them, V ̂ i Let be the predicted voltage at node i. For the trainable output layer weight matrix, For bias terms, These are the hidden features of the nodes output by the second layer of the convolutional network.
[0030] The training part uses Huber Loss as the loss function, and the objective function is the regression error of the node voltage. (6) The Adam optimizer is used, and strategies such as learning rate decay, batch training, and early-stopping of the validation set are set to avoid overfitting. The prediction error of the model under different fault types and load levels is evaluated by cross-validation to ensure that the model meets the accuracy requirements for transient voltage prediction.
[0031] The multi-condition dataset is divided proportionally into training, validation, and test sets to ensure the model has good generalization ability for unseen conditions. The trained model will serve as the basis for subsequent linearization and embedding optimization to predict the transient voltage safety margin under different load recovery schemes during fault disturbances.
[0032] Through the above systematic training process, a high-precision graph neural network model that can accurately predict the transient voltage of the distribution network is finally obtained, laying the foundation for subsequent linearization transformation and optimized embedding.
[0033] 3. The trained graph neural network prediction model is linearized, specifically its nonlinear activation function, transforming it into a mixed-integer linear programming model. This linearization process employs the Big-M method, introducing auxiliary continuous and binary variables into the ReLU activation function to construct an equivalent set of linear constraints. After training and validating the graph neural network model, this crucial linearization process is necessary. The aim is to transform the trained nonlinear graph neural network prediction model into a mixed-integer linear programming model, enabling it to be embedded as constraints in subsequent optimization problems. The linearization process is as follows: Figure 3 As shown.
[0034] All nonlinear activations in the neural network use the ReLU function, where z is the pre-activation amount and h is the activated feature. (7) The piecewise nonlinearity of the ReLU function is a major obstacle preventing the direct embedding of the model into the optimization problem. The Big-M method transforms the piecewise nonlinear ReLU function into a linear constraint by introducing auxiliary continuous variables, binary variables, and a large M value. To achieve linearizable embedding of the model, the Big-M exact linearization technique transforms all nonlinear activation functions in Edge-MLP and GCN networks into equivalent mixed-integer linear constraints, making the black-box model explicit and enabling it to be directly analyzed and solved analytically by the MILP (Mixed Integer Linear Programming) solver.
[0035] Introducing an auxiliary continuous variable h and a 0-1 binary variable s, and defining a lower bound L and an upper bound U for the input z, we construct an equivalent set of linear constraints for each ReLU function, i.e., a general set of linear constraints: (8) Where 𝐿 and 𝑈 represent the lower and upper bounds of the pre-activation quantity of the unit, respectively. The values are first determined based on the physical constraints of the input features, including equipment ratings and system operating limits (e.g., bus voltage is generally limited to [0.90, 1.10] pu, and distributed power output is constrained by rated capacity, etc.). Based on this, the boundaries are tightened by combining the statistical distribution of the model training data to avoid excessively wide values due to extreme samples. Furthermore, based on the neural network weights and biases, the values corresponding to each neuron are calculated through layer-by-layer interval propagation. When the input features are normalized, The typical order of magnitude is usually 100. Or smaller.
[0036] By expanding the above constraints across the entire network, the neural network, which was originally composed of multiple nonlinear mappings, is transformed into a set of linear equations, inequalities, and a finite number of binary variables, thus forming a MILP (Mixed Integer Linear Programming) model that is strictly consistent with the original network output.
[0037] Edge-MLP networks are used to mine the impact of edge features on transient voltages. The linearization process is as follows.
[0038] Calculate the pre-activation amount of the first layer: (9) in For edge feature dimension, , These are the weight matrix and bias term of the first layer of Edge-MLP, respectively, where p is the edge index and k is the hidden layer feature index.
[0039] Substitute the general constraints and let : (10) Calculate the pre-activation amount of the second layer: (11) in For the hidden layer feature dimension, , These are the weight matrix and bias term of the second layer of Edge-MLP, respectively.
[0040] Substitute the general constraints and let : (12) The source point average aggregation process for edge embedding is represented as follows: (13) in Let be the out-degree of node i, which is the number of directed branches from node i to other nodes. Let i be the source node of edge p. The k-th dimension edge aggregation feature of node i can be calculated by the activation amount of the second layer of Edge-MLP using equation (13).
[0041] The out-degree of each node can be calculated based on the topology and power flow information. The direction of the directed edge in the power grid topology is determined according to the power transmission relationship of the distribution network: taking the power source node as the starting point, along the power transmission direction during normal operation or load recovery, the branch direction is defined as pointing from the upstream node to the downstream node; if the branch power direction is variable, the direction of the directed edge is determined by the power flow direction under the current operating state or recovery decision.
[0042] GCN convolutional networks are used to capture the propagation characteristics of electrical quantities on a topology. The linearization process is as follows.
[0043] Calculate the pre-activation amount of the first layer of GCN (fusion of node features and edge aggregation features): (14) in , These are the weight matrix and bias terms of the first layer of the GCN, respectively. For rows and bias terms, To obtain the normalized adjacency matrix, it is constructed from the distribution network topology: First, the original adjacency matrix is obtained based on the node-branch connection relationships. If node With nodes If there is an electrical connection (branch / switch is in the ON state), then ,otherwise To introduce self-connection and perform symmetric normalization, let... The normalized adjacency matrix is defined as The value is determined solely by the distribution network topology and switch status, and can be used to express the normalized coupling relationship between nodes.
[0044] Substitute the general constraints and let : (15) Calculate the pre-activation amount of GCN layer 2: (16) in , These are the weight matrix and bias terms of the second layer of the GCN, respectively. For rows and bias terms.
[0045] Substitute the general constraints and let : (17) The hidden features output from the second layer of the GCN are mapped through a linear layer to obtain the final transient voltage prediction. There is no nonlinear activation, and linear constraints are directly constructed. (18) in, , These are the output layer weight matrix and the bias term, respectively.
[0046] Furthermore, the boundary constraints for node features and edge features in linearization are defined as follows: (19) The pre-activation threshold is defined as: (20) Through the above hierarchical linearization process, the overall neural network can be represented as: (twenty one) in It is a piecewise linear function formed by combining Edge-MLP, two layers of GCN, and an output layer. P, Q, and E represent the input sets of this mapping. P and Q are the net active and net reactive power injection vectors of each node at the current recovery time, respectively, and are normalized using per-unit values or rated base values. E is the set of distribution network topology and line information, including edge sets and their switch connectivity states, and line electrical parameters, used to construct edge features, which together determine the graph convolution propagation and the final transient voltage prediction output. The relevant weight matrix and bias term parameters of each network layer are derived from the best prediction model after training.
[0047] This linearized model (mixed-integer linear programming model) is strictly consistent with the output of the original neural network and contains only linear equations, inequalities, and a finite number of 0-1 binary variables. It can be directly analyzed by MILP (mixed-integer linear programming) / MIQCP (mixed-integer second-order cone programming) solvers, perfectly adapting to the constraint embedding requirements of the load recovery optimization model. This transformation is the key technology for achieving deep integration of transient safety constraints and static optimization.
[0048] 4. Using real-time distribution network status data as input, execute the forward computation logic defined by the mixed-integer linear programming model to output the predicted results of the distribution network transient voltage. After completing the neural network linearization to obtain the mixed-integer linear programming model, the prediction application stage begins. Using real-time distribution network status data (including switch status, generation output, and load level) as input, execute the forward computation logic defined by the mixed-integer linear programming model.
[0049] This process essentially involves solving a defined system of linear equations. Since all nonlinear elements have been transformed into linear constraints using the Big-M method, the computation does not require iterative optimization; it can be directly obtained by forward propagation along the computation graph using efficient linear algebra operations.
[0050] This method boasts extremely high computation speed, operating in the millisecond range, and provides deterministic results, meeting the real-time requirements of online applications. The final output consists of transient voltage predictions for each critical bus, particularly the minimum voltage amplitude within a specific time window after fault clearance, providing an immediate and reliable transient safety margin assessment for subsequent optimization decisions.
[0051] 5. A load restoration optimization model is constructed. This model aims to minimize the total cost of the restoration process and includes power flow balance constraints, voltage safety constraints, line capacity constraints, and switch operation constraints. The load restoration optimization model is the core carrier for achieving integrated decision-making in this invention.
[0052] The load restoration optimization model is a mixed-integer second-order cone programming (MIQCP) model. The total cost of the restoration process includes distributed generation costs, line loss costs, and switching operation costs. A MIQCP model is constructed, centered on network reconfiguration and considering both power flow feasibility and switching operation costs. The optimal switching operation sequence is determined through joint optimization of node electrical states, line power flow, switch configuration, and radial structure. The ultimate goal is to restore the distribution network after a fault to a stable operating state that satisfies all constraints, maximize load restoration, and simultaneously consider the economic efficiency and restoration efficiency of system operation.
[0053] Taking into account both the economic efficiency and recovery efficiency of system operation, the objective function consists of three parts: the generation cost of distributed power sources, the line loss cost, and the switching operation cost. (twenty two) in, This is a collection of non-switching circuits whose connectivity remains fixed. This is a set of controllable switching circuits, whose connectivity is determined by a binary variable, used to describe network reconfiguration. Two types of circuits are modeled separately in the objective function and constraints to distinguish the operational characteristics of fixed and reconfigurable topologies. For the cost of distributed power generation, For line loss costs, The switching operation cost is represented by units of yuan / (kWh), yuan / (kWh), and yuan / operation, respectively. Its values are set based on market electricity prices, equipment operation and maintenance experience, and dispatching experience, reflecting the weighting relationships of different optimization objectives. This objective function ensures both effective recovery and economic efficiency of system operation.
[0054] To ensure the physical feasibility and operational safety of the recovery plan, the model includes a comprehensive constraint system. This model is based on a simplified DistFlow power flow relationship, and the constraint equations consider factors such as power flow balance, electrical safety, switch operation, and radial topology. Specifically, the constraints include the following: (23a) (23b) (24a) (24b) (25) (26) (27) (28) (29) (30) (31) The model is constructed based on a simplified DistFlow power flow relationship, and the constraint equations consider factors such as power flow balance, electrical safety, switching operation, and radial topology. Here, L is the set of edges in the distribution network, used to describe the electrical connections between nodes, including all electrical branches involved in operation and optimization modeling, including distribution lines and transformers equivalent to branch models. Controllable switching lines and non-switching lines are respectively represented by sets... and The symbols i and j represent distribution network node indices, indicating bus or power aggregation nodes. Indicates the connection node With nodes A side road.
[0055] The constraint equations for the approximate active power flow and reactive power flow equations are expressed as equations (23a) and (23b). and P represents the resistance and reactance parameters of branches i and j, respectively. These values can be obtained from equipment nameplate data or the operating database and then normalized. ijQ ij Representing branches The active and reactive power on the power grid are determined by the power flow balance relationship. ij X represents the amplitude of the branch current. l branch road The switch state variables are used to describe the on / off state of controllable switch lines. The initial state is given by real-time operating data of the distribution network. For ordinary lines, the traditional second-order conical linearized voltage drop model of the distribution network is used to reflect the influence of line impedance, active and reactive power flow, and current on the voltage drop. For lines with switches, the voltage difference is determined by introducing auxiliary variables. Whether the constraint effect is exerted depends on the switching state and the large M constraint, realizing the flexible release of voltage coupling in the on-off state, as expressed by equations (24a) and (24b), respectively, V i V represents the voltage amplitude at node i. Equation (25) is a typical second-order cone power flow relaxation form, ensuring the physical consistency of voltage, current, and power flow. Equation (26) limits the operating range of node voltage, realizing dual control of compliant voltage at energized nodes and zero voltage at unenergized nodes. min With V max These are the lower and upper limits, respectively, and their values are determined according to the power distribution network operation regulations. Current and power flow capacity constraints are achieved through switch state variables. To clarify the upper and lower limits of line current and active and reactive power flow, and to avoid invalid power flow when the switch is opened, it is expressed as equation (27), where P max Q max and I max This represents the maximum allowable active and reactive power transmission capacity and the upper limit of allowable current for the branch, used to characterize the thermal stability constraints of the line and transformer. The values are determined based on the rated parameters of the equipment. Equation (28) introduces auxiliary variables... This linearizes the absolute value of the switching action deviation, providing support for calculating the switching operation cost. Indicates the switch connection status. This indicates the initial state of the switch connection. Equation (29) defines the switch direction constraint; if the switch is closed, only one direction of power flow structure is allowed to exist. ij This indicates whether the power flow follows the branch from node A to node B. Equation (30) represents the unique incoming line constraint of the node, ensuring that a legal radial topology without loops or islands is formed after the distribution network is restored. Equation (31) clarifies the value range of all decision variables, ensuring the legality of the decision variables and providing strict physical constraints and operational boundary guarantees for load restoration optimization.
[0056] Through the aforementioned comprehensive constraint system, a rigorous and well-considered load restoration optimization model was constructed. This model provides a solid static optimization foundation for subsequent embedding of transient voltage safety constraints, ensuring the feasibility and safety of the restoration scheme at the static level. This model is solved using commercial solvers such as CPLEX or Gurobi, effectively handling practical distribution network restoration optimization problems.
[0057] 6. The mixed-integer linear programming model is embedded as a transient safety constraint into the load recovery optimization model to form a unified optimization model.
[0058] After completing the precise linearization of the neural network, the resulting transient voltage linearization model is embedded as a transient safety constraint into the load restoration optimization model. The optimization objective is to minimize the total cost of the restoration process. This objective indirectly maximizes the load restoration amount after a fault by balancing generation, losses, and operating costs. While considering static constraints such as power flow, voltage, line capacity, switch operation, and network structure, the embedded linear neural network ensures transient voltage safety.
[0059] The linearized prediction model (mixed-integer linear programming model, MILP) is embedded as a transient safety constraint into the constructed load recovery optimization model (mixed-integer second-order cone programming model, MIQCP). Specifically, the transient safety constraint refers to the requirement that the transient voltage value predicted by the mixed-integer linear programming model should be within a preset transient voltage safety limit. The core of the embedding process is to compare the predicted output of the linearized model with the preset safety limit to form the constraint conditions. (32) in, The linearized prediction model provides the transient voltage prediction for node i at time t. and These are the lower and upper limits of the transient voltage safety for node i, respectively. This constraint ensures that the voltage remains within a safe range throughout the entire transient process.
[0060] The linearized transient voltage model can be expressed as follows: ,in It is a piecewise linear function formed by combining Edge-MLP, GCN, and the output layer. The specific method for directly incorporating this model into the load recovery optimization model is as follows: Variable correlation: This involves linking real-time operating state variables (power generation output) in the load recovery optimization model. , Network topology (E, etc.) is used as input to the linearized prediction model; Constraint addition: Based on the original optimization model constraint system, the transient voltage safety constraint described in formula (32) is added; Model unification: All constraints (equality, inequality and integer constraints) of the linearized prediction model and the constraints of the load recovery optimization model together constitute a unified mathematical programming problem.
[0061] The unified optimization model formed through the above embedding operations has the following characteristics: Integrity: It includes both static operational constraints (power flow balance, equipment capacity, topology radial shape, etc.) and transient safety constraints; Coordination: Automatically balances steady-state and transient safety when optimizing recovery schemes; Solvability: The unified model retains the mixed-integer second-order cone programming (MIQCP) structure and can be solved directly by commercial solvers.
[0062] The constraint embedding method employed in this invention has significant advantages: it considers transient safety during the optimization phase, avoiding the iterative process of "optimizing first and then verifying," and provides a forward-looking safety assessment; the linearized model has fast computation speed, and embedding it does not significantly increase the complexity of the optimization problem; it ensures that the final recovery scheme meets safety requirements throughout the entire process (steady-state + transient). Through these methods, an integrated solution for transient safety assessment and recovery optimization is achieved, providing reliable technical support for rapid and safe recovery of distribution networks after faults.
[0063] 7. Solve the unified optimization model and output a load restoration scheme that satisfies the transient voltage safety constraints. The unified optimization model with embedded transient safety constraints is solved using a commercial mathematical programming solver (such as CPLEX, Gurobi, etc.). The solution process of the unified optimization model uses branch and bound and second-order cone relaxation techniques to quickly converge to the optimal solution through continuous optimization of subproblems. The core flow of the solution algorithm is as follows: Branch and bound framework: Construct a search tree by enumerating all possible combinations of integer variables (switch states) in the system; Node processing: Solve the continuous slack subproblem at each tree node to obtain the lower bound of the objective function value under the current branch; Pruning strategy: Use relaxation solution information to prune infeasible and non-optimal branches, greatly reducing the search space; Convergence criterion: When the optimality gap is less than the preset tolerance, the algorithm terminates and outputs the global optimal solution.
[0064] The solver first performs continuous relaxation on the original MIQCP problem, relaxing the integer variables into continuous variables, thus obtaining a continuous second-order cone programming problem. It then enters the branch and bound main loop: the branch strategy selects the integer variable whose fraction is closest to 0.5 (such as the switch state). Branching, generating two child nodes ( =0 and =1); Boundary calculation: Solve the relaxed SOCP problem at each node to obtain the objective function boundary of that branch; Feasibility assessment: Check whether the current relaxed solution satisfies the integer property requirement and all constraints. By continuously repeating the branching, bounding, and pruning process, the solver gradually narrows down the possible range of the optimal solution until it finds the global optimal solution that satisfies all integer constraints and transient safety requirements.
[0065] After the model converges, it outputs a complete load recovery scheme, including: Switch operation sequence: a scheme for switch state changes in each time period to ensure the fewest possible operations; Power generation output plan: Optimization of active and reactive power output of distributed power sources; Load restoration plan: maximizing the amount and distribution of restored load; System operating status: prediction results of electrical quantities such as node voltage amplitude and line power flow; Transient safety margin: Assessment of the transient voltage safety boundary of critical busbars.
[0066] The solution results were verified for completeness to ensure that all constraints (static operating constraints and transient safety constraints) were strictly satisfied. The radial topology was free of circulating currents and islanding, and the transient voltage remained within safe limits throughout the entire process. The recovery scheme was feasible in a real system. This solution process fully considered various practical constraints of distribution network recovery. Through rigorous mathematical optimization methods, it ensured that the final scheme achieved optimal results in both static safety and transient stability, providing reliable decision support for the rapid and safe recovery of the distribution network after a fault.
[0067] In summary, this invention achieves efficient collaboration between transient voltage safety assessment and recovery optimization decision-making, effectively solving the problem of rapid and safe recovery in high-proportion renewable energy distribution networks.
[0068] Embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0069] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0070] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0071] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0072] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.
Claims
1. A method for linearizing and predicting transient voltages in a distribution network, characterized in that, Includes the following steps: A graph neural network prediction model is constructed based on transient simulation data of multiple operating conditions in the power distribution network. The graph neural network prediction model is trained with transient voltage amplitude as the prediction target to obtain the trained graph neural network prediction model. The trained graph neural network prediction model is linearized, that is, the nonlinear activation function is linearized, and the graph neural network prediction model is transformed into a mixed integer linear programming model. The real-time status data of the distribution network is used as input, and the forward calculation logic defined by the mixed integer linear programming model is executed to output the prediction result of the transient voltage of the distribution network. A load restoration optimization model is constructed. The model aims to minimize the total cost of the restoration process and includes power flow balance constraints, voltage safety constraints, line capacity constraints, and switch operation constraints. The mixed-integer linear programming model is embedded as a transient safety constraint into the load recovery optimization model to form a unified optimization model; Solve the unified optimization model to output a load recovery scheme that satisfies the transient voltage safety constraint.
2. The method for linearizing and predicting transient voltages in a distribution network according to claim 1, characterized in that, The transient voltage amplitude is the lowest voltage amplitude within a specific time window after the fault is cleared.
3. The method for linearizing and predicting transient voltages in a distribution network according to claim 1, characterized in that, The graph neural network adopts a hybrid structure that combines edge multilayer perceptron and graph convolutional network to process node features and edge features simultaneously.
4. The method for linearizing and predicting transient voltages in a distribution network according to claim 3, characterized in that, The edge multilayer perceptron is used to perform nonlinear transformation and aggregation of line features, and the graph convolutional network is used to capture the propagation characteristics of electrical quantities on the topology.
5. The method for linearizing and predicting transient voltages in a distribution network according to claim 1, characterized in that, The training of the graph neural network prediction model uses Huber Loss as the loss function, and combines early stopping strategy and cross-validation to ensure the model's generalization ability.
6. The method for linearizing and predicting transient voltages in a distribution network according to claim 1, characterized in that, The linearization process employs the Big-M method, which introduces auxiliary continuous variables and binary variables into the ReLU activation function to construct an equivalent set of linear constraints.
7. The method for linearizing and predicting transient voltages in a distribution network according to claim 1, characterized in that, The load restoration optimization model is a mixed integer second-order cone programming model, and the total cost of the restoration process includes the distributed generation cost, line loss cost, and switching operation cost.
8. The method for linearizing and predicting transient voltages in a distribution network according to claim 1, characterized in that, The transient safety constraint is defined as follows: the transient voltage value predicted by the mixed integer linear programming model should be within the preset transient voltage safety limit range.
9. The method for linearizing and predicting transient voltages in a distribution network according to claim 1, characterized in that, The solution process of the unified optimization model uses branch and bound and second-order cone relaxation techniques to quickly converge to the optimal solution by continuously optimizing subproblems.