A Decentralized AC Optimal Power Flow Solution Based on Physical Information Neural Network

Abstract

This invention discloses a distributed AC optimal power flow solution method based on a physical information neural network (PINN), comprising: establishing an AC optimal power flow model; modeling the power system network as a weighted graph based on complex network theory, using the Louvain algorithm to partition the weighted graph into communities, and decomposing the feature variables and prediction variables within each region; independently training a DNN model for each region, using the input feature vector to provide the predicted voltage of non-zero injected nodes within the region, and obtaining the voltage of all non-zero injected nodes by merging the prediction results of all DNN models; calculating the voltage of ZIBs using the Kron simplification method; calculating net active power based on the predicted voltage and the provided load, obtaining the predicted load, and obtaining the demand load through the predicted load. This invention optimizes generation costs by adjusting controllable variables, ensuring power system stability and cost-effectiveness.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a method for solving distributed AC optimal power flow based on physical information neural networks. Background Technology

[0002] AC Optimal Power Flow (AC-OPF) refers to the optimization process of adjusting the output power of generators in a power system from the perspective of optimizing power system operation, in order to minimize generation costs while satisfying node power balance and all physical constraints. However, with the introduction of a large amount of renewable energy and large-scale new equipment, grid operation faces higher uncertainties, and the AC-OPF problem needs to be addressed more frequently to maintain the balance between generation and load.

[0003] Existing solution methods based on physical models can be mainly divided into mathematical optimization and metaheuristic algorithms. Mathematical optimization methods mainly include gradient methods, Newton's method, linear programming, quadratic programming, and interior-point methods. These methods accurately simulate complex constraints and optimization objectives using mathematical formulas, thus ensuring the feasibility of the optimal solution. However, when facing a power grid with large-scale integration of renewable energy sources, the complexity and computational requirements of these methods may lead to scalability issues. Unlike traditional mathematical methods, metaheuristic algorithms such as genetic algorithms, particle swarm optimization, and ant colony optimization are a series of algorithms that simulate the laws of genetic evolution and animal behavior in nature. They have good global search capabilities and can effectively handle discontinuous and non-convex problems, but they lack performance guarantees and have high computational complexity.

[0004] In recent years, widely used data-driven machine learning algorithms mainly include hybrid methods and independent methods. Hybrid methods utilize deep neural networks (DNNs) as auxiliary tools to accelerate the optimization process of physics-based solvers, and mainly include hot-start prediction, constraint simplification, constraint screening, iterative acceleration, and adversarial learning. These methods still require solving power flow equations, resulting in relatively slow computation speeds. Unlike hybrid methods, independent methods can directly predict solutions to optimal power flow problems, achieving higher computational speeds through end-to-end training. Some studies have proposed a "prediction-reconstruction" framework to solve DC optimal power flow problems while ensuring inequality constraints are met. Other studies use this framework to solve AC-OPF problems by predicting decision variables and reconstructing the remaining variables using power flow equations. Still other studies incorporate physical information into the loss function, improving the accuracy of predicted solutions. However, when dealing with large-scale systems, these methods require large DNNs and long training times. To reduce the size of DNNs and improve training efficiency, the predicted variables can be decomposed based on the principles of power flow calculation.

[0005] Distributed optimization methods can significantly improve the solution speed of AC-OPF. Existing distributed optimal power flow algorithms mainly employ mathematical optimization techniques including the Alternating Direction Multiplier Method (ADMM) and the Lagrange relaxation method based on dual decomposition. These methods are easy to implement and debug, and have wide adaptability. However, as traditional mathematical optimization methods, they suffer from slow convergence speed and high computational complexity. Some studies have also used machine learning methods to obtain a near-optimal "primitive-dual" solution for hot-starting the ADMM algorithm. This method can accelerate the convergence speed of AC-OPF problem solving, but it still requires solving an optimization problem, thus limiting the computational acceleration.

[0006] Therefore, how to provide a distributed AC optimal power flow solution based on physical information neural networks has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a distributed AC optimal power flow solution method based on physical information neural networks, which optimizes power generation costs by adjusting controllable variables, thereby ensuring the stability and cost-effectiveness of the power system.

[0008] The present invention solves the technical problem by adopting the following technical solution:

[0009] A distributed AC optimal power flow solution based on a physical information neural network includes the following steps:

[0010] S1, Establish the optimal power flow model for communication;

[0011] S2, Power Grid Regional Division and Variable Decomposition: Based on complex network theory, the power system network is modeled as a weighted graph. The Louvain algorithm is used to divide the weighted graph into communities to identify different network modules. The power system network is divided into multiple non-overlapping regions, and the feature variables and predictive variables in each region are decomposed.

[0012] S3, a distributed machine learning method based on physical information neural networks: For each region, an independent DNN model is trained to learn the mapping relationship between the input feature vector and the output feature vector; the trained DNN model uses the input feature vector to provide the predicted voltage of non-zero injection nodes in the region; by merging the prediction results of all DNN models, the voltage of all non-zero injection nodes is obtained; the voltage of ZIBs is calculated using the Kron simplification method; subsequently, based on the predicted voltage and the provided load, the net active power is calculated; then, the predicted load is obtained by using the obtained net active power value, and the demand load is obtained by using the predicted load.

[0013] Furthermore, in S1, the method for establishing the optimal power flow model is as follows:

[0014] The standard AC-OPF model is adopted, as shown in equations (1)-(9):

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] in, Represents the set of all nodes; Denotes the set of generator nodes; E represents the set of branches; P represents the set of generator nodes. gi C represents the active power of the generator at node i. i (P gi (i,j) represents the power generation cost; (i,j) represents the branch from node i to node j, G ij and B ij Let P represent the admittance and susceptance of branch (i,j), respectively; i and Q i Q represents the net injected active and reactive power; gi P di and Q di V represents the generator reactive power, load active power, and load reactive power at node i, respectively; i and θ i θ represents the voltage magnitude and voltage angle at node i, respectively; ij The voltage angle difference between node i and node j is represented by θ. ij =θ i -θ j ;P ij and Q ij Let i and j represent the active and reactive power of the branch (i,j), respectively. and x It represents the upper and lower bounds of a variable x; Let (i,j) represent the maximum apparent power flow of the branch; the optimization objective of the AC-OPF model is to minimize the total generation cost in equation (1) while ensuring that all constraints in equations (2)-(9) are satisfied.

[0025] According to the Kron simplification principle, for zero-injection nodes ZIBs, equations (2)-(5) are expressed in Cartesian coordinates, and ZIBs are removed from the AC-OPF model, as follows:

[0026]

[0027]

[0028]

[0029] in, It is the set of ZIBs that are considered internal nodes in the Kron simplification method.

[0030] Furthermore, in S2, the method for dividing the weighted graph into communities using the Louvain algorithm is as follows:

[0031] The Louvain algorithm initializes each node as a separate region. First, it calculates the increment of modularity when each node moves to an adjacent region and selects the region with the largest gain. Then, nodes with the same label are merged into a supernode to form a larger region. The above steps are iterated until the modularity can no longer be improved.

[0032] Furthermore, the modularity Q is used to evaluate the effectiveness of the partitioning, and the calculation formula is as follows:

[0033]

[0034] Where W represents the sum of all edge weights; A ij These are the values ​​of vertices i and j in the adjacency matrix; s i and s j Let represent the strengths of vertices i and j, respectively, and let be their degree; when vertices i and j belong to the same region, i.e., c... i =c j At that time, δ(c) i ,c j The value of ) is 1, otherwise it is 0.

[0035] Furthermore, in S2, the method for decomposing the feature variables and predictor variables is as follows:

[0036] Suppose a power system network is divided into k non-overlapping regions. For each region a, the input feature vector X... a It is expressed as follows:

[0037]

[0038] in, This represents the set of nodes in region a; Represents the set of neighboring nodes of region a; the output feature vector of region a It is expressed as follows:

[0039]

[0040] in, Let ZIBs be the set of regions a; in regions with slack nodes, set the voltage angle of the slack nodes to zero and set it from... Excluded from the list.

[0041] Furthermore, in S3, the voltage magnitude of the zero-injection nodes ZIBs is calculated using the Kron simplification method. and angle Subsequently, based on the predicted voltage and the provided load P d Q d Calculate the left side of equation (5); then, directly calculate the remaining solution variables using the obtained left-side values. and auxiliary variables There is no need to solve the nonlinear power flow equations; for each node i: 1) if only generators or loads exist, directly obtain their predicted active and reactive power generation (i.e. and ) or active and reactive loads (i.e. and 1) If the generator and the load coexist, then... and Set to a given load value P di and Q di Then, calculate directly using equation (5). and In acquiring Then, the objective function is calculated using equation (1).

[0042] Furthermore, the loss function for each region a is shown in the following equation:

[0043]

[0044] Where, k obj and k d It is a positive number. It is the target in (1). It was designed to find feasible solutions that satisfy the inequality constraints (6)-(9), while Designed to meet the required load; Kirchhoff's circuit laws in equation (4) are automatically satisfied, and net power injection is calculated using the predicted node voltage; The penalty for violating the rules during training is shown as follows:

[0045]

[0046] Where, k g , and k z It is a positive number; and These are penalties for violations of constraints on power generation, branch flow, branch angle, and ZIBs voltage amplitude during training.

[0047]

[0048]

[0049]

[0050]

[0051] in, Here The active and reactive power of the branch are derived from the predicted voltage; It is the demand load (P) d Q d ) and forecast load The penalty for deviation between them is expressed as follows:

[0052]

[0053] Furthermore, S4 is also included, which improves prediction performance through post-processing methods, as follows:

[0054] After checking the inequality constraints (6)-(9), if any constraint violation is found, the corresponding voltage magnitude and angle will be adjusted according to the following procedure:

[0055]

[0056] in, This represents the output feature vector of the prediction process, containing the predicted voltage magnitude and angle. This represents the output feature vector after post-processing, and ΔY represents the correction amount, which is determined as follows:

[0057]

[0058]

[0059]

[0060] in, F represents Y The pseudo-inverse; V and θ represent the voltage amplitude and angle, respectively; and x Let f represent the upper and lower bounds of a variable x; the inequality constraints (6)-(9) are expressed in compact form as equation (20), where f represents the inequality constraint vector and Y represents the output feature vector; for each inequality constraint f i (Y), equation error Δf i Defined as equation (21), the portion of each constraint exceeding the upper and lower limits is taken; the value of ΔY is adaptively adjusted using Δf through equation (19), and the adjusted value is... The value is kept within the limit to ensure voltage constraint.

[0061] Furthermore, S6's effectiveness was verified through a test system example based on the IEEE 30 / 118 node standard, using the following method:

[0062] First, based on the Louvain algorithm, the system is divided into corresponding partitions using branch reactive power as weights; the dataset used for DNN learning contains 1000 samples and is divided according to a training-test ratio of 80-20%; the solver IPOPT is used to calculate the optimal solution considered to be the baseline, which is used as the true value of the baseline; the total load curve over a certain period of time is normalized to obtain daily load data, and the performance of DeepOPF-DP is evaluated.

[0063] Furthermore, the hidden layers of the DNN model use the modified linear unit activation function, while the output layer uses the sigmoid activation function.

[0064] The distributed AC optimal power flow solution method based on physical information neural network disclosed in this invention has the following beneficial effects:

[0065] This invention provides a decentralized AC optimal power flow solution method based on a physical information neural network. It enables decentralized learning of the load-solution mapping and incorporates physical information into the training process, improving training efficiency and better satisfying all physical constraints. This method optimizes generation costs by adjusting controllable variables, ensuring power system stability and cost-effectiveness. Attached Figure Description

[0066] Figure 1 This is a flowchart of the method of the present invention;

[0067] Figure 2 This is an example diagram of the region division of the IEEE 9-node system of the present invention;

[0068] Figure 3 This is a schematic diagram of the DeepOPF-DP of the present invention;

[0069] Figure 4 This is a comparison chart of the results of DeepOPF-DP of the present invention;

[0070] Figure 5 This is a comparison chart of the predicted power generation cost and the actual power generation cost of this invention. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] refer to Figure 1 The present invention discloses a method for solving distributed AC optimal power flow based on physical information neural networks, comprising the following steps:

[0073] S1, Establish the optimal power flow model for communication;

[0074] S2, Power Grid Regional Division and Variable Decomposition: Based on complex network theory, the power system network is modeled as a weighted graph. The Louvain algorithm is used to divide the weighted graph into communities to identify different network modules. The power system network is divided into multiple non-overlapping regions, and the feature variables and predictive variables in each region are decomposed.

[0075] S3, a distributed machine learning method based on physical information neural networks: For each region, an independent DNN model is trained to learn the mapping relationship between the input feature vector and the output feature vector; the trained DNN model uses the input feature vector to provide the predicted voltage of non-zero injection nodes in the region; by merging the prediction results of all DNN models, the voltage of all non-zero injection nodes is obtained; the voltage of ZIBs is calculated using the Kron simplification method; subsequently, based on the predicted voltage and the provided load, the net active power is calculated; then, the predicted load is obtained by using the obtained net active power value, and the demand load is obtained by using the predicted load.

[0076] In S1, the specific method for establishing the optimal power flow model is as follows:

[0077] The AC-OPF model is an important mathematical framework for optimizing power allocation in AC power grids. This model aims to effectively coordinate power generation, transmission, and distribution while considering various constraints and objectives such as cost minimization and system reliability. It describes strategies for achieving optimal power dispatch under grid constraints, covering key aspects such as power balance, network constraints, and generator output limitations, providing a theoretical foundation for efficient power system management and decision-making. Its simplified description is as follows:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] in, Represents the set of all nodes; E represents the set of generating nodes; E represents the set of branches; P represents the set of generating nodes. gi C represents the active power generation of node i. i (P gi (i, j) represents its cost; (i, j) represents the branch from node i to node j, G ij and B ij P represents admittance and susceptance, respectively; i and Q i Indicates net active and reactive power injection; Q gi P di and Q di These represent reactive power generation, active load, and reactive load, respectively; V i and θ i θ represents the voltage amplitude and phase angle, respectively. ij Representing the angular difference, by θ ij =θ i -θ j Calculation yielded; P ij Q ij and S ij These represent the active, reactive, and apparent power of branch (i,j), respectively. and x Let x represent the upper and lower bounds of a variable x. The AC-OPF model minimizes the total generation cost in equation (1) while ensuring that all constraints in equations (2)-(9) are satisfied. Branch power flow is given by equations (2)-(3). Kirchhoff's circuit laws are enforced by equation (4). Net power injection is given by equation (5), while equation (6) enforces active and reactive power generation limits, equation (7) guarantees voltage amplitude limits, and equations (8)-(9) limit voltage phase angle and branch flow, respectively.

[0088] Since real power systems typically contain a large number of zero-injection buses (ZIBs), removing the voltages of ZIBs from the prediction can significantly reduce the size of the DNN model. Using the Kron simplification method, as shown in equations (10)-(12), equations (2)-(5) can be expressed in Cartesian coordinates, thus removing ZIBs from the AC-OPF model, as follows:

[0089]

[0090]

[0091]

[0092] in, It is the set of ZIBs that are considered internal nodes in Kron simplification.

[0093] In S2, the specific methods for dividing the power grid region and decomposing variables are as follows:

[0094] Based on complex network theory, a power system can be modeled as a weighted graph G(V,E), where V and E represent the sets of nodes and edges, respectively. In this model, each node in the system corresponds to a vertex in the graph, while branches are represented as edges, and the weights of the edges typically reflect the impedance or reactance of the branch. Subsequently, the Louvain algorithm is used to partition this weighted graph into communities to identify different network modules. The evaluation of the partitioning effect usually depends on the modularity Q, which is calculated as follows:

[0095]

[0096] Where W represents the sum of all edge weights; A ij These are the values ​​of vertices i and j in the adjacency matrix; s i and s j Let represent the strengths of vertices i and j, respectively, and let be the node degrees. When vertices i and j belong to the same region (i.e., c...),... i =c j When ), δ(c)i ,c j The value of ) is 1, otherwise it is 0.

[0097] The initial step of Louvain's algorithm is to treat each node as an independent region. First, it calculates the increment in modularity when each node moves to an adjacent region and selects the region with the largest gain. Then, nodes with the same label are merged into a supernode, forming a larger region. This process is iterated until no further improvement in modularity can be achieved. Figure 2 This is an example of partitioning an IEEE 9-node system.

[0098] For the k non-overlapping regions, for each region a, the input feature vector X a It can be represented as follows:

[0099]

[0100] in, This represents the set of nodes in region a; This represents the set of neighboring nodes of region a.

[0101] The reason for considering only the load within the region and its neighboring nodes as input is that, according to the power flow equations (2)-(5), the load at node i is P i and Q i The calculation is only related to the set and The nodes in G are related, while the remaining nodes are due to G. ij =0 and B ij =0, therefore it has no effect on the calculation at node i. Furthermore, this decomposition method makes the mapping between the load and the solution smoother, thereby improving the efficiency of learning.

[0102] Output feature vector of region a It can be represented as follows:

[0103]

[0104] in, Let ZIBs be the set of regions a. In regions with slack nodes, the voltage angle of the slack nodes is set to zero, and it is then removed from... Excluded from the list.

[0105] S3. The specific details of the distributed machine learning method based on physical information neural networks are as follows:

[0106] The schematic diagram of the proposed DeepOPF-DP is as follows: Figure 3As shown, by using the power network partitioning method in S2, the entire system can be divided into multiple regions. For each region, a DNN model is trained independently to learn the input features X. a With output Y a The mapping relationship between them. A well-trained DNN model uses input X. a To provide the predicted voltage of non-zero injection nodes within the region. By merging the predictions from all DNN models, the voltages of all non-zero injection nodes can be obtained. The voltages of ZIBs are then calculated using the Kron simplification method. Subsequently, based on the predicted voltage and the provided load P d Q d The left side of equation (5) can be calculated. Then, the remaining solution variables can be directly calculated using the obtained left-side values. and auxiliary variables There is no need to solve the nonlinear power flow equations. Specifically, for each node i: 1) if only generators or loads exist, the predicted active and reactive power generation is directly obtained (i.e., and ) or predicted active and reactive loads (i.e. and 1) If the generator and the load coexist, then... and Set to a given load value P di and Q di Then, calculate directly using equation (5). and In acquiring Then, the objective function is calculated using equation (1).

[0107] The loss function for each region a is shown in the following equation:

[0108]

[0109] Where, k obj and k d It is a positive number. It is the target in (1). It was designed to find feasible solutions that satisfy the inequality constraints (6)-(9), while Designed to meet the required load. Kirchhoff's circuit laws in equation (4) can be automatically satisfied because the net power injection can always be calculated using the predicted node voltage. Specifically, The penalty for violating the rules during training is shown as follows:

[0110]

[0111] Where, kg , and k z It is a positive number; and These are penalties for violations of constraints on power generation, branch flow, branch angle, and ZIBs voltage amplitude during training.

[0112]

[0113]

[0114]

[0115]

[0116] in, Here The active and reactive power of the branch are derived from the predicted voltage. It is the demand load (P) d Q d ) and forecast load The penalty for deviation between them is expressed as follows:

[0117]

[0118] The present invention also includes S4, which improves prediction performance through post-processing methods, as follows:

[0119] To enhance the feasibility of the predicted solution, a post-processing method was adopted. After checking the inequality constraints (6)-(9), if any constraint violation exists, the corresponding voltage magnitude and angle will be adjusted according to the following process:

[0120]

[0121] in, This represents the output feature vector of the prediction process, containing the predicted voltage magnitude and angle. Let represent the output feature vector after post-processing, and ΔY represent the correction amount, which is determined as follows:

[0122]

[0123]

[0124]

[0125] in, F represents Y The pseudo-inverse; V and θ represent the voltage amplitude and angle, respectively; and xLet f represent the upper and lower bounds of a variable x; the inequality constraints (6)-(9) are expressed in compact form as equation (20), where f represents the inequality constraint vector and Y represents the output feature vector; for each inequality constraint f i (Y), equation error Δf i Defined as equation (21), the portion of each constraint exceeding the upper and lower limits is taken; the value of ΔY is adaptively adjusted using Δf through equation (19), and the adjusted value is... The value is kept within the limit to ensure voltage constraint.

[0126] This invention also includes S6, verifying its effectiveness through a computational example using the IEEE 30 / 118 node standard test system, as follows:

[0127] First, based on the Louvain algorithm, the system is divided into corresponding partitions using branch reactive power as weights. The dataset used for DNN learning contains 1000 samples, divided according to an 80-20% training-to-test ratio. We use the solver IPOPT to compute the optimal solution considered as the baseline, which serves as the true value for the baseline. Load data was generated by scaling the default load using the normalized daily total load curve from the Bonneville Electricity Authority between 6:00 AM and 12:00 PM on August 2, 2016. This resulted in a high load variation rate of over 40%, validating the effectiveness of the proposed method in handling systems with significant load variations.

[0128] The following metrics were used to evaluate the performance of DeepOPF-DP:

[0129] 1) Optimality Loss: Evaluates the average relative deviation of DeepOPF-DP from the optimal objective obtained by the IPOPT solver. The deviation is denoted as η. opt .

[0130] 2) Constraint Satisfaction Rate: The effectiveness of DeepOPF-DP is evaluated by measuring the percentage of constraints satisfied. This is achieved using... η V , and To represent P g Q g V represents the constraint satisfaction rate of branch power and branch angle.

[0131] 3) Load fulfillment rate: Used to assess the percentage of load fulfillment in a power system. and P d and Q d The satisfaction rate.

[0132] 4) Training time: Represents the longest time consumed by the DNN model during parallel training, denoted as t. train .

[0133] The distributed machine learning method for solving the AC optimal power flow problem proposed in this invention is compared with different technical methods, including:

[0134] M0: DeepOPF-DP, a distributed AC optimal power flow solution method based on physical information neural network proposed in this invention.

[0135] M1: Modify the existing DeepOPF-V using the Korn simplification method for fair comparison. The input to the DNN model is the load of all nodes, and the output is the voltage magnitude and angle of the non-ZIB region.

[0136] M2: Similar to DeepOPF-DP, the only difference is the random decomposition of features and predictor variables.

[0137] M3: Similar to DeepOPF-DP, the only difference is that the loss function does not include physical information.

[0138] The DNN model uses the modified linear unit activation function in the hidden layers and the sigmoid activation function in the output layer. The maximum number of iterations and the mini-batch size are set to 6000 and 50, respectively, k. d k g , and k z All parameters are set to 1. Due to the different dimensions of the input data, the neural network structure of DeepOPF-DP may differ from that of M1, while other parameters remain the same for all comparison methods. The training parameters for M0, M1, M2, and M3 are shown in Table 1.

[0139]

[0140]

[0141] Table 1

[0142] Table 2 shows a comparison of simulation results for different technical methods.

[0143]

[0144] Table 2

[0145] Table 2 shows that, compared to M1 and M2, DeepOPF-DP performs better in terms of optimality loss, load satisfaction rate, and branch constraint satisfaction rate in both the 30-node and 118-node systems. This indicates that reasonable and appropriate power network partitioning can improve the performance of DNN models. Compared to M1, training time is reduced by 5.6% and 12.0% in the 30-node and 118-node systems, respectively, due to the smaller input and output dimensions after partitioning. Furthermore, as shown in the results for the 118-node system, the reduction in training time is even more significant when the input and output dimensions are further reduced compared to the overall size. Compared to M3, DeepOPF-DP shows a significant improvement in optimality loss and power satisfaction rate, indicating that adding physical information to the loss function makes the model's results more consistent with physical constraints.

[0146] Figure 4 The paper presents the predicted solutions and their true values ​​of DeepOPF-DP in the IEEE 30-node and 118-node systems, including 10 samples randomly selected from the test dataset. Figure 4 (a) shows the load on node 14 in the 118-node system. Figure 4 (b) represents the power of node 2 in a 30-node system. Figure 4 (a) and Figure 4 In (b), taking node 14 in the IEEE 118-node system and node 2 in the 30-node system as examples, it was observed that the predicted values ​​of load and generator power were very close to the actual values. Figure 5 This demonstrates the degree of approximation between the predicted target and the actual value. Figure 5 (a) is a comparison chart of the predicted generation cost and the actual generation cost of a 30-node system. Figure 5 (b) A comparison chart of the predicted and actual power generation costs of a 30-node system. Figure 5 (a) and Figure 5 (b) It can be seen that the predicted generation cost is highly consistent with the actual generation cost, highlighting the feasibility of the predicted solution. These results demonstrate the significant potential of the proposed method in power system optimization problems, providing a reliable solution for achieving accurate generation cost optimization and system stability.

[0147] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for solving distributed AC optimal power flow based on physical information neural networks, characterized in that, Includes the following steps: S1, Establish the optimal power flow model for communication; S2, Power Grid Area Division and Variable Decomposition: Based on complex network theory, the power system network is modeled as a weighted graph, and the Louvain algorithm is used to divide the weighted graph into communities to identify different network modules; The power system network is divided into multiple non-overlapping regions, and the characteristic variables and predictor variables within each region are decomposed. S3, a distributed machine learning method based on physical information neural networks: For each region, an independent DNN model is trained to learn the mapping relationship between the input feature vector and the output feature vector; the trained DNN model uses the input feature vector to provide the predicted voltage of non-zero injection nodes in the region; by merging the prediction results of all DNN models, the voltage of all non-zero injection nodes is obtained; the voltage of ZIBs is calculated using the Kron simplification method; subsequently, based on the predicted voltage and the provided load, the net active power is calculated; then, the predicted load is obtained by using the obtained net active power value, and the demand load is obtained by using the predicted load; In S2, the method for dividing the weighted graph into communities using the Louvain algorithm is as follows: The Louvain algorithm initializes each node as a separate region. First, it calculates the increment of modularity when each node moves to an adjacent region and selects the region with the largest gain. Then, nodes with the same label are merged into a supernode to form a larger region. The above steps are iterated until the modularity can no longer be improved. Use modularity Q The effectiveness of the partitioning is evaluated using the following formula: (13) in, W This represents the sum of the weights of all edges; It is the vertex i and j The value in the adjacency matrix; and Representing vertices respectively i and j The strength is the node degree; when the vertex... i and j Belonging to the same area, that is = hour, The value is 1 if it is 1, otherwise it is 0. The characteristic feature is that, in S2, the method for decomposing the feature variables and predictor variables is as follows: Suppose a power system network is divided into k For each region, there are non-overlapping regions. a Input feature vector It is expressed as follows: (14) in, Indicates the region a The set of nodes in; Indicates the region a The set of neighboring nodes; region a The output feature vector It is expressed as follows: (15) in, For the region a The ZIBs set; in the region with slack nodes, the voltage angle of the slack nodes is set to zero and it is removed from... Excluded from the list.

2. The method for solving distributed AC optimal power flow based on a physical information neural network according to claim 1, characterized in that, In S1, the method for establishing the optimal power flow model is as follows: The standard AC-OPF model is adopted, as shown in equations (1)-(9): (1) (2) (3) (4) (5) (6) (7) (8) , (9) in, Represents the set of all nodes; Represents the set of generator nodes; E Represents the set of branches; Represents a node i The active power of the generator, Indicates its power generation cost; i , j ) indicates from node i To the node j The side road, and They represent the branches ( i , j Admittance and susceptance; and This indicates the net injected active and reactive power; , and Representing nodes respectively i The generator reactive power, load active power and load reactive power; and Representing nodes respectively i Voltage amplitude and voltage angle; Represents a node i With nodes j The voltage angle difference, i.e. = - ; and They represent the branches ( i , j The active and reactive power of ) and Represents a variable x The upper and lower bounds; Indicates branch ( i , j The maximum apparent power flow of the AC-OPF model is to minimize the total power generation cost in equation (1) while ensuring that all constraints in equations (2)-(9) are satisfied. According to the Kron simplification principle, for zero-injection nodes ZIBs, equations (2)-(5) are expressed in Cartesian coordinates, and ZIBs are removed from the AC-OPF model, as follows: (10) (11) (12) in, It is the set of ZIBs that are considered internal nodes in the Kron simplification method.

3. The method for solving distributed AC optimal power flow based on a physical information neural network according to claim 2, characterized in that, In S3, the voltage magnitude of the zero-injection nodes ZIBs is calculated using the Kron simplified method. and angle Subsequently, based on the predicted voltage and the provided load... , Calculate the left side of equation (5); then, directly calculate the remaining solution variables using the obtained left-side values. , ) and forecasted load ( , No need to solve nonlinear power flow equations; for each node i 1) If only generators or loads exist, directly obtain their predicted active and reactive power generation. and or active and reactive loads and ; 2) If the generator and load coexist, then... and Set to the given load value and Then, calculate directly using equation (5). and In obtaining Then, the objective function is calculated using equation (1).

4. The method for solving distributed AC optimal power flow based on a physical information neural network according to claim 3, characterized in that, For each region a The loss function is shown in the following equation: (16) in, and It is a positive number. It is the target in formula (1). It was designed to find feasible solutions that satisfy the inequality constraints (6)-(9), while Designed to meet the required load; Kirchhoff's circuit laws in equation (4) are automatically satisfied, and net power injection is calculated using the predicted node voltage; The penalty for violating the rules during training is shown as follows: (17) in, , , and It is a positive number; , , and These are penalties for violations of constraints on power generation, branch flow, branch angle, and ZIBs voltage amplitude during training. , (18) (19) (20) (21) in, Here ( , The active and reactive power of the branch are derived from the predicted voltage. It is demand load ( , ) and predicted load ( , The penalty for deviation between () is expressed as follows: (22)。 5. The method for solving distributed AC optimal power flow based on a physical information neural network according to claim 4, characterized in that, It also includes S4, which improves prediction performance through post-processing methods, as follows: After checking the inequality constraints (6)-(9), if any constraint violation is found, the corresponding voltage magnitude and angle will be adjusted according to the following procedure: (18) in, This represents the output feature vector of the prediction process, containing the predicted voltage magnitude and angle. This represents the output feature vector after post-processing. The correction amount is determined as follows: (19) (20) (21) in, express The false reversal; and These represent the voltage amplitude and angle, respectively. and Represents a variable x The upper and lower bounds; the inequality constraints (6)-(9) are expressed in compact form as equation (20), where Represents the inequality constraint vector. For each inequality constraint Equation error Defined as equation (21), it takes the portion of each constraint that exceeds the upper and lower limits; it is used through equation (19). Adaptive adjustment The adjusted value The value is kept within the limit to ensure voltage constraint.

6. The method for solving distributed AC optimal power flow based on a physical information neural network according to claim 5, characterized in that, It also includes S6, whose effectiveness was verified through a test system example based on the IEEE 30 / 118 node standard, as follows: First, based on the Louvain algorithm, the system is divided into corresponding partitions using branch reactive power as weights; the dataset used for DNN learning contains 1000 samples and is divided according to a training-test ratio of 80-20%; the solver IPOPT is used to calculate the optimal solution considered to be the baseline, which is used as the true value of the baseline; the total load curve over a certain period of time is normalized to obtain daily load data, and the performance of DeepOPF-DP is evaluated.

7. The method for solving distributed AC optimal power flow based on a physical information neural network according to claim 6, characterized in that, The hidden layers of the DNN model use the modified linear unit activation function, and the output layer uses the sigmoid activation function.

Images