Distributed alternating current optimal power flow solving method based on physical information neural network

Abstract

The invention discloses a distributed alternating current optimal power flow solving method based on a physical information neural network. The method comprises the following steps: establishing an alternating current optimal power flow model; the method comprises the following steps of: modeling a power system network into a weighted graph based on a complex network theory, performing community division on the weighted graph by utilizing a Louvain algorithm, and decomposing a characteristic variable and a prediction variable in each region; for each region, independently training a DNN model, providing predicted voltages of non-zero injection nodes in the region by using an input feature vector, and obtaining voltages of all the non-zero injection nodes by combining prediction results of all the DNN models; calculating the voltage of the ZIBs by using a Kron simplification method; and calculating net active power based on the predicted voltage and the provided load to obtain a predicted load, and obtaining a demand load through the predicted load. The power generation cost is optimized by adjusting the controllable variables, and the stability and the cost effectiveness of the power system are ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a distributed AC optimal power flow solving method based on a physical information neural network. Background Art

[0002] AC Optimal Power Flow (AC-OPF) refers to the optimization process of adjusting the output power of generators in the system from the perspective of optimizing the operation of the power system, and minimizing the power generation cost under the conditions of satisfying the node power balance and all physical constraints. However, with the introduction of a large number of renewable energy sources and large-scale new equipment, the operation of the power grid faces higher uncertainty, and the AC-OPF problem needs to be solved more frequently to maintain the balance between power generation and load.

[0003] Existing physical model-based solution methods can be mainly divided into mathematical optimization and meta-heuristic algorithms. Mathematical optimization methods mainly include gradient method, Newton method, linear programming, quadratic programming and interior point method. These methods use mathematical formulas to accurately simulate complex constraints and optimization objectives, thereby ensuring the feasibility of the optimization solution. However, when faced with large-scale renewable energy access to the power grid, the complexity and computational requirements of these methods may lead to scalability problems. Different from traditional mathematical methods, meta-heuristic algorithms such as genetic algorithms, particle swarm algorithms, and ant colony algorithms 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 non-continuous and non-convex problems, but lack performance guarantees and have high computational complexity.

[0004] In recent years, the widely used data-driven machine learning algorithms mainly include hybrid methods and independent methods. Hybrid methods use deep neural networks (DNNs) as auxiliary tools to accelerate the optimization process of physics-based solvers, mainly including hot start point prediction method, constraint simplification method, constraint screening method, iterative acceleration method, adversarial learning method, etc. These methods still need to solve the power flow equation, resulting in relatively slow calculation speed. Unlike hybrid methods, independent methods can directly predict the solution of the optimal power flow problem and achieve higher calculation speed through end-to-end training. Some studies have proposed a "prediction-reconstruction" framework to solve the DC optimal power flow problem while ensuring that inequality constraints are met. Other studies have used this framework to solve the AC-OPF problem by predicting decision variables and reconstructing the remaining variables using the power flow equation. Some studies have also added physical information to the loss function to improve the accuracy of the predicted solution. However, when facing large-scale systems, the DNNs of these methods are large in scale and take a long time to train. In order to reduce the scale of DNNs and improve training efficiency, the predicted variables can be decomposed based on the power flow calculation principle.

[0005] Decentralized optimization methods can greatly improve the solution speed of AC-OPF. The existing decentralized optimal power flow algorithms mainly use mathematical optimization techniques including the alternating direction method of multipliers (ADMM) and the Lagrangian relaxation method based on dual decomposition. These methods are easy to implement and debug and have wide adaptability, but as traditional mathematical optimization methods, they have problems of slow convergence and high computational complexity. Some studies have also used machine learning methods to obtain a near-optimal "primal-dual" solution for hot-starting the ADMM algorithm. This method can accelerate the convergence speed of solving the AC-OPF problem, but it still needs to solve the optimization problem, so the acceleration computing power is limited.

[0006] Therefore, how to provide a distributed communication optimal power flow solution method based on physical information neural network has become a technical problem that technical personnel in this field urgently need to solve. Summary of the invention

[0007] In view of this, the purpose of the present invention is to provide a distributed AC optimal power flow solution method based on physical information neural network, which optimizes the power generation cost by adjusting the controllable variables to ensure 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 method based on physical information neural network includes the following steps:

[0010] S1, establish AC optimal power flow model;

[0011] S2, 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 perform community division on the weighted graph to identify different network modules; the power system network is divided into multiple non-overlapping regions, and the characteristic variables and predictor variables in each region are decomposed;

[0012] S3, a decentralized machine learning method based on physical information neural network: for each area, a DNN model is trained independently 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 the non-zero injection nodes in the area; the voltage of all non-zero injection nodes is obtained by merging the prediction results of all DNN models; the voltage of ZIBs is calculated using the Kron simplification method; then, the net active power is calculated based on the predicted voltage and the provided load; the predicted load is then obtained by using the obtained net active power value, and the demand load is obtained through the predicted load.

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

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

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024] in, Represents the set of all nodes; represents the generator node set; E represents the branch set; P gi represents the active power of the generator at node i, C i (P gi ) represents its power generation cost; (i,j) represents the branch from node i to node j, G ij and B ij Respectively represent the admittance and susceptance of branch (i, j); P i and Q i represents the net injected active and reactive power; Q gi , P di and Q di Respectively represent the generator reactive power, load active power and load reactive power of node i; V i and θ i Respectively represent the voltage amplitude and voltage angle of node i; θ ij Represents the voltage angle difference between node i and node j, that is, θ ij =θ i -θ j ;P ij and Q ij Respectively represent the active and reactive power of branch (i, j); and x Indicates the upper and lower bounds of a variable x; represents the maximum apparent power flow of branch (i, j); the optimization objective 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;

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

[0026]

[0027]

[0028]

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

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

[0031] The Louvain algorithm initializes each node as a separate region. First, it calculates the increase 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 to form a larger region. The above steps are iterated until the modularity cannot be further improved.

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

[0033]

[0034] Where W represents the sum of all edge weights; A ij is the value of vertices i and j in the adjacency matrix; s i and j Represents the strength of vertices i and j, which is the node degree; when vertices i and j belong to the same region, that is, c i =c j When δ(c i ,c j ) is 1 if the value is true or false, otherwise it is 0.

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

[0036] Assume that 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, represents the set of nodes in area 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, is the set of ZIBs in region a; in the region with a balance node, the voltage angle of the balance node is set to zero and is changed from Excluded.

[0041] Furthermore, in S3, the voltage amplitude of the zero injection node ZIBs is calculated using the Kron simplified method and angle Then, 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 by using the obtained left side values and auxiliary variables No need to solve nonlinear power flow equations; for each node i: 1) If only a generator or load exists, directly obtain its predicted active and reactive power generation (i.e. and ) or active and reactive loads (i.e. and ); 2) If the generator and load coexist, and Set to a given load value P di and Q di , and then directly calculate through equation (5) and In getting Then, the objective function is calculated using equation (1).

[0042] Furthermore, the loss function for each region a is as follows:

[0043]

[0044] Among them, k obj and k d is a normal number, is the target in (1), is designed to find feasible solutions that satisfy the inequality constraints (6)-(9), while is designed to meet the required load; Kirchhoff's circuit laws in equation (4) are automatically satisfied and the net power injection is calculated using the predicted node voltages; is the penalty for violating the constraint during training and is expressed as follows:

[0045]

[0046] Among them, k g , and k z is a positive constant; and are the penalty terms for the violation of generation, branch flow, branch angle and ZIBs voltage amplitude constraints during training, respectively;

[0047]

[0048]

[0049]

[0050]

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

[0052]

[0053] Furthermore, S4 is included to improve the prediction performance by a post-processing method, as follows:

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

[0055]

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

[0057]

[0058]

[0059]

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

[0061] Furthermore, S6 is included, and the effectiveness is verified by an IEEE 30 / 118 node standard test system example, and the method is as follows:

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

[0063] Furthermore, the hidden layer of the DNN model uses the rectified linear unit activation function, and the output layer uses the Sigmoid activation function.

[0064] The invention discloses a distributed AC optimal power flow solution method based on physical information neural network, which has the following beneficial effects:

[0065] The present invention provides a distributed AC optimal power flow solution method based on physical information neural network, which can realize distributed learning of load-solution mapping and add physical information to the training, which not only improves the training efficiency but also better meets all physical constraints. This method optimizes the power generation cost by adjusting the controllable variables to ensure the stability and cost-effectiveness of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 is a flow chart of the method of the present invention;

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

[0068] Figure 3 Schematic diagram of 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 between the predicted power generation cost and the actual power generation cost of the present invention. DETAILED DESCRIPTION

[0071] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

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

[0073] S1, establish AC optimal power flow model;

[0074] S2, 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 perform community division on the weighted graph to identify different network modules; the power system network is divided into multiple non-overlapping regions, and the characteristic variables and predictor variables in each region are decomposed;

[0075] S3, a decentralized machine learning method based on physical information neural network: for each area, a DNN model is trained independently 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 the non-zero injection nodes in the area; the voltage of all non-zero injection nodes is obtained by merging the prediction results of all DNN models; the voltage of ZIBs is calculated using the Kron simplification method; then, the net active power is calculated based on the predicted voltage and the provided load; the predicted load is then obtained by using the obtained net active power value, and the demand load is obtained through the predicted load.

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

[0077] The AC-OPF model is an important mathematical framework for optimizing power distribution in AC power grids. The model aims to effectively coordinate the generation, transmission and distribution of electricity while considering multiple constraints and objectives such as cost minimization and system reliability. The model describes the strategy for achieving optimal power dispatch under the premise of meeting grid constraints, covering key aspects such as power balance, network constraints and generator output limitations, and provides a theoretical basis for efficient management and decision-making of power systems. Its simplified description is as follows:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] in, Represents the set of all nodes; represents the set of power generation nodes; E represents the set of branches; P gi represents the active power generation of node i, C i (P gi ) represents its cost; (i, j) represents the branch from node i to node j, G ij and B ij Respectively represent admittance and susceptance; P i and Q i represents the net active and reactive power injection; Q gi , P di and Q di Respectively represent reactive power generation, active load and reactive load; V i and θ i Respectively represent the voltage amplitude and phase angle; θ ij Represents the angle difference, θ ij =θ i -θ j Calculated; P ij , Q ij and S ij Respectively represent the active, reactive and apparent power of branch (i, j); and x represents 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. The branch power flows are given by equations (2)-(3). Kirchhoff's circuit laws are enforced by equation (4). The net power injection is given by equation (5), while equation (6) enforces active and reactive generation limits, equation (7) ensures voltage amplitude limits, and equations (8)-(9) limit voltage phase angles and branch flows, respectively.

[0088] Since there are usually a large number of zero-injection buses (ZIBs) in actual power systems, the voltage of ZIBs is removed from the prediction, which can greatly reduce the size of the DNN model. According to the Kron simplification method, as shown in equations (10)-(12), equations (2)-(5) can be expressed in the form of Cartesian coordinates, thereby removing ZIBs from the AC-OPF model, as follows:

[0089]

[0090]

[0091]

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

[0093] In S2, the specific methods of grid area division and variable decomposition are as follows:

[0094] Based on complex network theory, the power system can be modeled as a weighted graph G(V,E), where V and E represent the set of nodes and edges, respectively. In this model, each node in the system corresponds to a vertex of the graph, and the branch is represented as an edge in the graph. The weight of the edge usually reflects the impedance or reactance of the branch. Subsequently, the Louvain algorithm is used to perform community partitioning on this weighted graph 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 is the value of vertices i and j in the adjacency matrix; s i and j Represents the strength of vertex i and j, which is the node degree. When vertex i and j belong to the same region (i.e. c i =c j ), δ(ci ,c j ) is 1 if the value is true or false, otherwise it is 0.

[0097] The initial step of the Louvain algorithm is to treat each node as an independent region. First, the increase in modularity when each node moves to an adjacent region is calculated, and the region with the largest gain is selected. Then, nodes with the same label are merged into a supernode to form a larger region. This process is iterated until the modularity cannot be further improved. Figure 2 This is an example of partitioning of an IEEE 9-bus system.

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

[0099]

[0100] in, represents the set of nodes in area a; Represents the set of neighboring nodes of area a.

[0101] Only the loads in the region and its neighboring nodes are considered as input because according to the power flow equations (2)-(5), P at node i is i and Q i The calculation is only with the set and The remaining nodes are related to the nodes in G ij =0 and B ij = 0, so it has no effect on the calculation at node i. In addition, this decomposition method can make the mapping between load and solution smoother, thereby improving the efficiency of learning.

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

[0103]

[0104] in, is the set of ZIBs in region a. In the region with a balance node, the voltage angle of the balance node is set to zero and is changed from Excluded.

[0105] S3. The distributed machine learning method based on physical information neural network is as follows:

[0106] The schematic diagram of the proposed DeepOPF-DP is shown in Figure 3As shown in Figure 2, 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 feature X a With output Y a The trained DNN model uses the input X a To provide the predicted voltages at non-zero injected nodes in the region By combining the predictions of all DNN models, the voltages of all non-zero injection nodes can be obtained. The voltages of ZIBs are calculated using the Kron simplification method. Then, 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 by using the obtained left side values and auxiliary variables There is no need to solve nonlinear power flow equations. Specifically, for each node i: 1) If only a generator or load exists, directly obtain its predicted active and reactive power generation (i.e. and ) or predicted active and reactive loads (i.e. and ); 2) If the generator and load coexist, and Set to a given load value P di and Q di , and then directly calculate through equation (5) and In getting Then, the objective function is calculated using equation (1).

[0107] The loss function for each region a is as follows:

[0108]

[0109] Among them, k obj and k d is a normal number, is the target in (1), is designed to find feasible solutions that satisfy the inequality constraints (6)-(9), while is designed to meet the required load. Kirchhoff’s circuit laws in equation (4) are automatically satisfied since the net power injection can always be calculated using the predicted node voltages. Specifically, is the penalty for violating the constraint during training and is expressed as follows:

[0110]

[0111] Among them, kg , and k z is a positive constant; and are the penalty terms for violations of generation, branch flow, branch angle and ZIBs voltage amplitude constraints during training, respectively.

[0112]

[0113]

[0114]

[0115]

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

[0117]

[0118] The present invention further comprises S4, improving the prediction performance by a post-processing method, the method being as follows:

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

[0120]

[0121] in, Represents the output feature vector of the prediction process, including the predicted voltage amplitude and angle, represents the output feature vector after post-processing, and ΔY represents the correction amount, which is determined as follows:.

[0122]

[0123]

[0124]

[0125] in, Indicates F Y The pseudo-inverse of ; V and θ represent the voltage amplitude and angle respectively; and xrepresents the upper and lower bounds of a variable x; the inequality constraints (6)-(9) are expressed in a compact form as equation (20), where f represents the inequality constraint vector and Y represents the output eigenvector; for each inequality constraint f i (Y), equation error Δf i Defined as formula (21), take the part of each constraint that exceeds the upper and lower limits; use Δf to adaptively adjust the value of ΔY through formula (19), and the adjusted The value of is kept within limits to ensure voltage constraints.

[0126] The present invention further comprises S6, verifying the effectiveness through an IEEE 30 / 118 node standard test system example, the method is as follows:

[0127] First, the system is divided into corresponding partitions based on Louvain algorithm using branch reactive power as weight. The dataset used for DNN learning contains 1000 samples divided into 80-20% training-testing ratio. We use the solver IPOPT to calculate the optimal solution considered as the benchmark as the true value of the benchmark. The load data is generated by scaling the default load using the normalized daily total load curve of Bonneville Power Administration between 6:00 am and 12:00 pm on August 2, 2016. This produces a high load change rate of more than 40%, verifying the effectiveness of the proposed method in dealing with systems with significant load changes.

[0128] The following metrics are 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. η V , and To represent P g , Q g , V, constraint satisfaction rate of branch power and branch angle.

[0131] 3) Load satisfaction rate: used to evaluate the percentage of load satisfaction in the power system. and Respectively represent P d and Q d 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 the present invention is compared with different technical methods, wherein the compared technical methods include:

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

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

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

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

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

[0139]

[0140]

[0141] Table 1

[0142] Table 2 shows the comparison of simulation experimental results of different technical methods.

[0143]

[0144] Table 2

[0145] Table 2 shows that in the 30-node system and the 118-node system, DeepOPF-DP performs relatively better than M1 and M2 in terms of optimality loss, load satisfaction rate, and branch constraint satisfaction rate. This shows that reasonable and appropriate power network partitioning can improve the performance of DNN models. Compared with M1, it can be observed that the training time is reduced by 5.6% and 12.0% in the 30-node and 118-node systems, respectively, which is due to the smaller input and output dimensions after partitioning. At the same time, as shown in the results of the 118-node system, the reduction in training time is more significant when the input and output dimensions are further reduced compared to the overall scale. Compared with M3, DeepOPF-DP has significantly improved performance in terms of optimality loss and power satisfaction rate, which shows that adding physical information to the loss function can make the results produced by the model more consistent with physical constraints.

[0146] Figure 4 The predicted solutions and true values ​​of DeepOPF-DP in the IEEE 30-node system and 118-node system are shown, including 10 samples randomly selected from the test dataset. Figure 4 (a) is the load of node 14 in a 118-node system. Figure 4 (b) is 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 is observed that the predicted values ​​of load and generator power are very close to the true values. Figure 5 It shows the approximation between the predicted target and the actual value. Figure 5 (a) is a comparison chart of the predicted power generation cost and the actual power generation cost of a 30-node system. Figure 5 (b) is a comparison chart of the predicted power generation cost and the actual power generation cost of the 30-node system. Figure 5 (a) with Figure 5 (b) It can be seen that the predicted power generation cost is highly consistent with the actual power generation cost, highlighting the feasibility of the predicted solution. These results show that the proposed method has significant potential in power system optimization problems and provides a reliable solution for achieving accurate power 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, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A distributed AC optimal power flow solution method based on physical information neural network, characterized in that: The steps include: S1, establish AC optimal power flow model; S2, 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 are decomposed in each region; S3, a decentralized machine learning method based on physical information neural network: for each area, a DNN model is trained independently 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 the non-zero injection nodes in the area; the voltage of all non-zero injection nodes is obtained by merging the prediction results of all DNN models; the voltage of ZIBs is calculated using the Kron simplification method; then, the net active power is calculated based on the predicted voltage and the provided load; the predicted load is then obtained by using the obtained net active power value, and the demand load is obtained through the predicted load.

2. The method for solving the distributed AC optimal power flow based on physical information neural network according to claim 1 is characterized in that: In S1, the method of establishing the AC optimal power flow model is as follows: The standard AC-OPF model is used, as shown in equations (1)-(9): in, Represents the set of all nodes; represents the generator node set; E represents the branch set; P gi represents the active power of the generator at node i, C i (P gi ) represents its power generation cost; (i,j) represents the branch from node i to node j, G ij and B ij Respectively represent the admittance and susceptance of branch (i, j); P i and Q i represents the net injected active and reactive power; Q gi , P di and Q di Respectively represent the generator reactive power, load active power and load reactive power of node i; V i and θ i Respectively represent the voltage amplitude and voltage angle of node i; θ ij Represents the voltage angle difference between node i and node j, that is, θ ij =θ i -θ j ;P ij and Q ij Respectively represent the active and reactive power of branch (i, j); and Indicates the upper and lower bounds of a variable x; represents the maximum apparent power flow of branch (i, j); the optimization objective 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 Kron's simplification principle, for zero injection nodes ZIBs, equations (2)-(5) are expressed in the form of Cartesian coordinates, and ZIBs are removed from the AC-OPF model, as follows: in, is the set of ZIBs that are considered internal nodes in Kron's simplification method.

3. The method for solving the distributed AC optimal power flow based on physical information neural network according to claim 2 is characterized in that: In S2, the method of using Louvain algorithm to divide the weighted graph into communities is as follows: The Louvain algorithm initializes each node as a separate region. First, it calculates the increase 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 to form a larger region. The above steps are iterated until the modularity cannot be further improved.

4. The method for solving the distributed AC optimal power flow based on physical information neural network according to claim 3 is characterized in that: The modularity Q is used to evaluate the effectiveness of the partitioning. The calculation formula is as follows: Where W represents the sum of all edge weights; A ij is the value of vertices i and j in the adjacency matrix; s i and j Represents the strength of vertices i and j, which is the node degree; when vertices i and j belong to the same region, that is, c i =c j When δ(c i ,c j ) is 1 if the value is true or false, otherwise it is 0.

5. The method for solving distributed AC optimal power flow based on physical information neural network according to claim 4 is characterized in that: In S2, the method for decomposing feature variables and predictor variables is as follows: Assume that 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: in, represents the set of nodes in area a; Represents the set of neighboring nodes of region a; the output feature vector of region a It is expressed as follows: in, is the set of ZIBs in region a; in the region with a balance node, the voltage angle of the balance node is set to zero and is changed from Excluded.

6. The method for solving distributed AC optimal power flow based on physical information neural network according to claim 5 is characterized in that: In S3, the voltage amplitude of the zero injection node ZIBs is calculated using the Kron simplified method. and angle Then, 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 by using the obtained left side values and auxiliary variables No need to solve nonlinear power flow equations; for each node i: 1) If only a generator or load exists, directly obtain its predicted active and reactive power generation (i.e. and ) or active and reactive loads (i.e. and ); 2) If the generator and load coexist, and Set to a given load value P di and Q di , and then directly calculate through equation (5) and In getting Then, the objective function is calculated using equation (1).

7. The method for solving distributed AC optimal power flow based on physical information neural network according to claim 6 is characterized in that: The loss function for each region a is as follows: Among them, k obj and k d is a normal number, is the target in (1), is designed to find feasible solutions that satisfy the inequality constraints (6)-(9), while is designed to meet the required load; Kirchhoff's circuit laws in equation (4) are automatically satisfied and the net power injection is calculated using the predicted node voltages; is the penalty for violating the constraint during training and is expressed as follows: Among them, k g , and k z is a positive constant; and are the penalty terms for the violation of generation, branch flow, branch angle and ZIBs voltage amplitude constraints during training, respectively; in, Here It is the branch active and reactive power derived from the predicted voltage; is the demand load (P d , Q d ) and forecast load The penalty term for the deviation between is expressed as follows:

8. The method for solving distributed AC optimal power flow based on physical information neural network according to claim 7 is characterized in that: It also includes S4, which improves the prediction performance through post-processing methods as follows: After checking the inequality constraints (6)-(9), if there is any constraint violation, the corresponding voltage magnitude and angle will be adjusted according to the following process: in, represents the output feature vector of the prediction process, including the predicted voltage amplitude and angle, represents the output feature vector after post-processing, and ΔY represents the correction amount, which is determined as follows: in, Indicates F Y The pseudo-inverse of ; V and θ represent the voltage amplitude and angle respectively; and represents the upper and lower bounds of a variable x; the inequality constraints (6)-(9) are expressed in a compact form as equation (20), where f represents the inequality constraint vector and Y represents the output eigenvector; for each inequality constraint f i (Y), equation error Δf i Defined as formula (21), take the part of each constraint that exceeds the upper and lower limits; use Δf to adaptively adjust the value of ΔY through formula (19), and the adjusted The value of is kept within limits to ensure voltage constraints.

9. The method for solving distributed AC optimal power flow based on physical information neural network according to claim 8, characterized in that: It also includes S6, and verifies the effectiveness through the IEEE 30 / 118 node standard test system example as follows: Firstly, based on the Louvain algorithm, the system is divided into corresponding partitions using branch reactive power as weight; the dataset used for DNN learning contains 1000 samples, which are divided into 80-20% training-testing ratio; the solver IPOPT is used to calculate the optimal solution considered as the benchmark as the true value of the benchmark; the total load curve within a certain period of time is normalized to obtain the daily load data, and the performance of DeepOPF-DP is evaluated.

10. The method for solving distributed AC optimal power flow based on physical information neural network according to claim 9, characterized in that: The hidden layer of the DNN model uses the rectified linear unit activation function, and the output layer uses the Sigmoid activation function.

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