Distributed alternating current optimal power flow solving method based on multi-branch neural network

Abstract

The invention discloses a distributed alternating current optimal power flow solving method based on a multi-branch neural network. The method comprises the following steps: establishing an alternating current optimal power flow model; on the basis of a complex network theory, a power system is modeled into a weighted graph, and community division is performed on the weighted graph by using a Louvain algorithm; a multi-branch DNN model is trained for the whole power system, and the model is used for learning the mapping relation between input features and output features; the trained DNN model uses the input features to provide prediction voltages of non-zero injection nodes in the region; calculating the voltage of the ZIBs by using a Kron simplification method; and based on the voltage of the ZIBs and the provided load, obtaining the predicted active and reactive load values, and obtaining the demand load through the predicted load values. According to the method, the network scale can be effectively reduced, the training efficiency is improved, the solution accuracy is improved, and the flexibility and robustness enable the method to more powerfully cope with a future complex power system optimization task.

Description

Technical Field

[0001] The present invention relates to the technical field of power system optimization, and particularly to a distributed alternating current optimal power flow solving method based on a multi-branch neural network. Background Art

[0002] Alternating current optimal power flow (AC-OPF) is a core problem in power system optimization. Its goal is to optimize system operation while meeting power demand and grid constraints, such as minimizing generation costs or achieving other objective functions. AC-OPF improves economy, reliability, and sustainability by comprehensively considering physical characteristics of the power system, such as voltage, power factor, and network impedance. In the context of the continuous increase in the proportion of renewable energy, AC-OPF is of great significance for the efficient management of power supply and demand, optimization of resource allocation, and reduction of operating costs. At the same time, it can ensure the stability and security of the power system.

[0003] Most of the traditional methods for solving AC-OPF are based on mathematical models or meta-heuristic algorithms. However, these methods often face problems of local optimal solutions or high computational complexity when dealing with high-dimensional or complex problems. To address these challenges, in recent years, the application of machine learning methods in AC-OPF has gradually emerged and shown significant potential. Machine learning-based solutions can be mainly divided into hybrid methods and independent methods. Hybrid methods usually use deep learning models to assist traditional physical solvers to accelerate the optimization process, such as predicting hot start points, simplifying constraints, or accelerating iterations. However, such methods still need to solve the power flow equations, and the calculation speed is limited to a certain extent. In contrast, independent methods directly predict the optimal power flow solution through end-to-end learning, which can significantly improve the computational efficiency and solve constraint problems through a "prediction - reconstruction" framework. However, the model scale is usually large, and there are problems of long training time and high optimization difficulty when facing large-scale power systems. In addition, the current above-mentioned solving methods are all based on single-branch neural networks, and there are problems such as high non-convexity in the optimization process, poor model expression ability, and poor generalization ability.

[0004] Therefore, how to provide a distributed alternating current optimal power flow solving method based on a multi-branch neural network has become an urgent technical problem for those skilled in the art. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a distributed alternating current optimal power flow solving method based on a multi-branch neural network, which can effectively reduce the network scale, improve the training efficiency, enhance the accuracy of the solution, and its flexibility and robustness enable it to more effectively cope with future complex power system optimization tasks.

[0006] The present invention adopts the following technical solutions to solve the technical problems:

[0007] A distributed AC optimal power flow solving method based on a multi-branch neural network, comprising the following steps:

[0008] S1. Establish an AC optimal power flow model;

[0009] S2. Power grid area division: Based on complex network theory, the power system is 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 power system corresponds to a vertex of the graph, and the branches are represented as the edges in the graph, and the weight of the edge reflects the impedance or reactance of the branch; subsequently, the Louvain algorithm is used to perform community division on this weighted graph to identify different network modules;

[0010] S3. Distributed machine learning method based on a multi-branch neural network: Train a multi-branch DNN model for the entire power system, where the sub-networks correspond to the divided regions, and are allowed to have arbitrary architectures, depths, and continuous activation functions; in the extreme case, when the sub-network is selected as a single neuron, the multi-branch structure is simplified to a single-hidden-layer neural network; use this model to learn the mapping relationship between input features and output features; the trained DNN model uses the input features to provide the predicted voltages of non-zero injection nodes within the region; use the Kron reduction method to calculate the voltages of ZIBs; subsequently, based on the voltages of ZIBs and the provided loads, obtain the predicted active and reactive load values, and obtain the demand load through the predicted load values.

[0011] In step S1, the method for establishing the AC optimal power flow model is as follows:

[0012]

[0013] Among them, represents the set of all nodes; represents the set of generator 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 represent the admittance and susceptance respectively; P i and Q i represent the net active and reactive injections; Q gi 、P di and Q di represent reactive power generation, active load, and reactive load respectively; V i and θ i represent the voltage magnitude and phase angle respectively; θ ij represents the angle difference, which is composed of θij = 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 represent the upper and lower bounds of a certain variable x;

[0014] By the Kron reduction method, as shown in Eqs. (10)-(12), Eqs. (2)-(5) are expressed in Cartesian coordinate form, thereby removing the ZIBs from the AC-OPF model, as follows:

[0015]

[0016]

[0017] where is the set of ZIBs regarded as internal nodes in the Kron reduction.

[0018] Furthermore, in step S2, the evaluation of the power grid area division effect depends on the modularity Q, and its calculation formula is as follows:

[0019]

[0020] 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 s j respectively represent the strength of vertices i and j, which is the node degree; when vertices i and j belong to the same area, that is, c i = c j at this time, the value of δ( c i, c j) is 1, otherwise 0.

[0021] Furthermore, in step S2, the method of using the Louvain algorithm to perform community division on this weighted graph is as follows:

[0022] Regarding each node as an independent area, first, calculate the increment of modularity when each node moves to an adjacent area, and select the area with the largest gain; then, the nodes with the same label are merged into a supernode to form a larger area; this process is iterated until the modularity cannot be further improved.

[0023] Furthermore, in step S3, this model is used to learn the mapping relationship between the input feature X and the output feature Y α The input feature vector X is represented as follows:

[0024]

[0025] Among them, represents the set of all nodes in the power grid;

[0026] Output feature Y α is represented as follows:

[0027]

[0028] Among them, is the output of the sub-network corresponding to each area a, is the set of all nodes in area a, is the set of ZIBs in area a; V and θ are the node voltage amplitude and angle respectively. In the area with a balanced node, the voltage angle of the balanced node is set to zero and excluded from ; w and b are the scaling and offset coefficient matrices respectively.

[0029] Furthermore, in step S3, the trained DNN model uses the input feature X a to provide the predicted voltage of the non-zero injection nodes Calculate the voltage of ZIBs using the Kron reduction method Subsequently, based on and the provided load P d 、Q d , calculate the left side of equation (5); then directly calculate the remaining solution variables and the auxiliary variable without solving the non-linear power flow equation; for each node i: 1) If only a generator or a load exists, directly obtain its predicted active and reactive power generation, i.e., and or the predicted active and reactive power loads, i.e., and 2) If a generator and a load coexist, then set and to the given load values P di and Q di , and then directly calculate and After obtaining , calculate the objective function using equation (1).

[0030] Furthermore, the trained loss function is shown as follows:

[0031]

[0032] Among them, k obj and kd is a positive constant, is the objective loss in (1), is designed to find a feasible solution that satisfies the inequality constraints (6)-(9), while is designed to meet the required load;

[0033] is the penalty for constraint violation during training, expressed as follows:

[0034]

[0035] where k g , and k z are positive constants, calculated from the loss function value; and are the penalty terms for constraint violations of power generation, branch flow, branch angle, and ZIBs voltage magnitude during training, respectively;

[0036]

[0037]

[0038] where, here is the active and reactive power of the branch derived from the predicted voltage; is the demand load (P d , Q d ) and the penalty term for the deviation between the predicted load , expressed as follows:

[0039]

[0040] Furthermore, it also includes S4 to improve the prediction performance through post-processing:

[0041] After checking the inequality constraints (6)-(9), if there are any constraint violations, the corresponding voltage magnitude and angle will be adjusted according to the following process:

[0042]

[0043] where, represents the output feature vector of the prediction process, including the predicted voltage magnitude and angle, represents the output feature vector after post-processing, and ΔY represents the correction amount, which is determined as follows:

[0044]

[0045] where, represents F YThe pseudo-inverse; V and θ represent the voltage amplitude and angle respectively; and x represent the upper and lower bounds of a certain variable x; The inequality constraints (6)-(9) are represented in a compact form as Equation (26), where f represents the inequality constraint vector and Y represents the output feature vector; For each inequality constraint f i (Y), the equation error Δf i is defined as Equation (27), taking the part where each constraint exceeds the upper and lower limits; The value of ΔY is adaptively adjusted using Δf through Equation (25), and the adjusted value is kept within the limit range to ensure voltage constraints.

[0046] Furthermore, it also includes S5 to verify the effectiveness of the present invention through the IEEE 30-bus standard test system example:

[0047] First, based on the Louvain algorithm, using the branch reactive power as the weight, the system is divided into corresponding partitions; The dataset used for DNN learning contains 1000 samples, which are divided according to the 80-20% training-test ratio; The optimal solution considered as the benchmark is calculated using the solver IPOPT as the true value of the benchmark; The total load curve within a certain period is normalized to obtain the daily load data, and the performance of DeepOPF-MB is evaluated.

[0048] Furthermore, the hidden layer of the DNN model uses the rectified linear unit activation function, and the output layer uses the Sigmoid activation function.

[0049] A distributed AC optimal power flow solution method based on a multi-branch neural network disclosed by the present invention has the following beneficial effects:

[0050] The present invention proposes a distributed AC optimal power flow solution method based on a multi-branch neural network. Using the multi-branch neural network helps to better capture the complexity and non-linear relationships of the system, improve the optimization performance, reduce the generation cost, and improve the system operation efficiency. Secondly, this method can enhance the constraint satisfaction rate of the system, better handle the load and branch constraints, and improve the system stability and security. Through the accurate predictions in terms of load, generator power, and generation cost shown by the actual example, this technical solution is expected to improve the accuracy and reliability of system decision-making and operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 is the method flow chart of the present invention;

[0052] Figure 2 is the regional division example diagram of the IEEE 9-bus system of the present invention;

[0053] Figure 3 Schematic diagram of DeepOPF-MB of the present invention;

[0054] Figure 4 Comparison diagram of the results of DeepOPF-MB of the present invention;

[0055] Figure 5 Comparison diagram of the predicted power generation cost and the actual power generation cost of the present invention. Specific embodiments

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0057] In order to further improve the expression ability and solution efficiency of the model, the present invention introduces a multi-branch neural network to solve practical engineering problems. This multi-branch design has the following remarkable advantages: First, compared with traditional single-branch neural networks, multi-branch neural networks exhibit lower non-convexity during the optimization process, which helps to accelerate convergence and improve the final performance. Second, multi-branch neural networks allow parallel processing of different features, enabling the network to independently learn diverse feature representations in each branch, thereby enhancing the model's expression ability and generalization ability. This characteristic not only reduces the risk of overfitting but also makes the model more adaptable when facing complex datasets. In addition, multi-branch neural networks have high scalability and can increase the model capacity by adding branches without significantly modifying the overall structure, thus flexibly adapting to different task requirements. Finally, due to the independent processing of features by each branch, multi-branch neural networks show stronger robustness when dealing with noise or data missing. By combining physical information to optimize the loss function or designing variable decomposition strategies, the present invention can effectively reduce the network scale, improve the training efficiency, enhance the accuracy of the solution, and its flexibility and robustness make it more powerful in dealing with future complex power system optimization tasks.

[0058] Refer to Figure 1 A distributed alternating current optimal power flow solution method based on a multi-branch neural network disclosed by the present invention includes the following steps:

[0059] S1, establish an alternating current optimal power flow model;

[0060] The AC-OPF model is an important mathematical framework for optimizing the power distribution of an AC power grid. This model aims to effectively coordinate the generation, transmission, and distribution of electricity while considering various constraints and objectives such as cost minimization and system reliability. The model describes the strategy for achieving optimal power dispatch while satisfying grid constraints, covering key aspects such as power balance, network constraints, and generator output limits, providing a theoretical basis for the efficient management and decision-making of power systems. The method for establishing the AC optimal power flow model is as follows:

[0061]

[0062] Among them, represents the set of all nodes; represents the set of generating nodes; E represents the set of branches; P gi represents the active power generation of node i, and C i (P gi ) represents its cost; (i, j) represents the branch from node i to node j, and G ij and B ij represent admittance and susceptance respectively; P i and Q i represent net active and reactive power injections; Q gi 、P di and Q di represent reactive power generation, active power load, and reactive power load respectively; V i and θ i represent voltage magnitude and phase angle respectively; θ ij represents the angle difference, calculated by θ ij =θ i -θ j ; P ij 、Q ij and S ij represent the active, reactive, and apparent power of branch (i, j) respectively; and x represent the upper and lower bounds of a certain 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 flow is given by Equations (2)-(3); Kirchhoff's circuit law is enforced by Equation (4); the net power injection is given by Equation (5), while Equations (6) enforce the active and reactive power generation limits, Equation (7) guarantees the voltage magnitude limit, and Equations (8)-(9) limit the voltage phase angle and branch flow respectively;

[0063] Since there are usually a large number of zero-injection buses (ZIBs) in the actual power system, removing the voltages of ZIBs from the prediction can greatly reduce the size of the DNN model. By the Kron reduction method, as shown in Eqs. (10)-(12), Eqs. (2)-(5) can be expressed in the Cartesian coordinate system, thus removing ZIBs from the AC-OPF model, as follows:

[0064]

[0065] where, is the set of ZIBs regarded as internal nodes in the Kron reduction.

[0066] S2, Power grid area division: Based on complex network theory, the power system is 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 power system corresponds to a vertex of the graph, while the branches are represented as edges in the graph, and the weight of the edge reflects the impedance or reactance of the branch; subsequently, the Louvain algorithm is used to perform community division on this weighted graph to identify different network modules; the evaluation of the power grid area division effect depends on the modularity Q, and its calculation formula is as follows:

[0067]

[0068] where, W represents the sum of the weights of all edges; A ij is the value of vertices i and j in the adjacency matrix; s i and s j represent the strengths of vertices i and j respectively, which are the node degrees; when vertices i and j belong to the same area, that is, c i = c j , the value of δ(c i , c j ) is 1, otherwise it is 0.

[0069] The method of using the Louvain algorithm to perform community division on this weighted graph is as follows:

[0070] Regarding each node as an independent area, first, calculate the increment of modularity when each node moves to an adjacent area, and select the area with the largest gain; then, the nodes with the same label are merged into a super node to form a larger area; this process is iterated until the modularity cannot be further improved. Figure 2 is an example of the division of the IEEE 9-node system.

[0071] S3, Distributed machine learning method based on multi-branch neural network: The schematic diagram of the proposed DeepOPF-MB is as Figure 3As shown. By using the power grid partitioning method in S2, the entire system can be divided into multiple regions. A multi-branch DNN model is trained for the entire power system, where the sub-networks correspond to the respective divided regions and are allowed to have arbitrary architectures, depths, and continuous activation functions; in the extreme case, when the sub-network is selected as a single neuron, the multi-branch structure simplifies to a single-hidden-layer neural network; this model is used to learn the mapping relationship between the input feature X and the output feature Y α between them; the trained DNN model uses the input feature to provide the predicted voltage of the non-zero injection nodes within the region; the Kron reduction method is used to calculate the voltage of the ZIBs; subsequently, based on the voltage of the ZIBs and the provided load, the predicted active and reactive load values are obtained, and the demand load is obtained through the predicted load values.

[0072] Use this model to learn the mapping relationship between the input feature X and the output feature Y α between them. The input feature vector X is represented as follows:

[0073]

[0074] where represents the set of all nodes in the power grid;

[0075] The output feature Y α is represented as follows:

[0076]

[0077] where is the output of the sub-network corresponding to each region a, is the set of all nodes in region a, is the set of ZIBs in region a; V and θ are the node voltage magnitude and angle respectively. In the region with a slack node, the voltage angle of the slack node is set to zero and excluded from ; w and b are the scaling and offset coefficient matrices respectively.

[0078] The trained DNN model uses the input feature X a to provide the predicted voltage of the non-zero injection nodes Use the Kron reduction method to calculate the voltage of the ZIBs Subsequently, based on and the provided load P d 、Q d , calculate the left side of equation (5); then directly calculate the remaining solution variables and the auxiliary variables There is no need to solve the non - linear power flow equations; for each node i: 1) If there is only a generator or a load, directly obtain its predicted active and reactive power generations, i.e., and or the predicted active and reactive power loads, i.e., and 2) If both a generator and a load co - exist, set and to the given load values P di and Q di , then directly calculate and using Equation (5). After obtaining , calculate the objective function using Equation (1).

[0079] The loss function for training is shown as follows:

[0080]

[0081] where K obj and k d are positive constants, is the objective loss in (1), is designed to find the feasible solutions that satisfy the inequality constraints (6) - (9), while is designed to meet the required load; the Kirchhoff's circuit law in Equation (4) is automatically satisfied because the net power injection can always be calculated using the predicted node voltages. Specifically, is the penalty for violating the constraints during training, expressed as follows:

[0082]

[0083] where k g , and k z are positive constants calculated from the loss function values; and are the penalty terms for violating the generation, branch flow, branch angle, and ZIBs voltage magnitude constraints during training, respectively;

[0084]

[0085]

[0086] where, here are the active and reactive powers of the branch derived from the predicted voltage; is the demand load (P d , Q d ) and the predicted load The penalty term for the deviation therebetween is expressed as follows:

[0087]

[0088] The present invention further includes S4, improving the prediction performance through post-processing:

[0089] To enhance the feasibility of the predicted solution, a post-processing method is adopted. After checking the inequality constraints (6)-(9), if there are any constraint violations, the corresponding voltage magnitudes and angles will be adjusted according to the following process:

[0090]

[0091] wherein, represents the output feature vector of the prediction process, including the predicted voltage magnitude and angle, represents the output feature vector after post-processing, and ΔY represents the correction amount, which is determined as follows:

[0092]

[0093] wherein, represents the pseudo-inverse of F Y ; V and θ respectively represent the voltage magnitude and angle; and x represent the upper and lower bounds of a certain variable x; the inequality constraints (6)-(9) are expressed in a compact form as Equation (26), where f represents the inequality constraint vector and Y represents the output feature vector; for each inequality constraint f i (Y), the equation error Δf i is defined as Equation (27), taking the part where each constraint exceeds the upper and lower limits; the value of ΔY is adaptively adjusted through Equation (25) using Δf, and the adjusted value is kept within the limit range to ensure the voltage constraint.

[0094] The present invention further includes S5, verifying the effectiveness of the present invention through an example of the IEEE 30-bus standard test system:

[0095] First, based on the Louvain algorithm, using the branch reactive power as the weight, the system is divided into corresponding partitions. The dataset used for DNN learning contains 1000 samples, which are divided according to an 80 - 20% training - test ratio. The present invention calculates the optimal solution considered as the benchmark using the solver IPOPT 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 the Bonneville Power Administration from 6:00 am to 12:00 pm on August 2, 2016. This results in a high load change rate of over 40%, verifying the effectiveness of the proposed method in dealing with systems with significant load changes.

[0096] The following metrics are used to evaluate the performance of DeepOPF - MB:

[0097] 1) Optimality loss: Evaluate the average relative deviation of DeepOPF - MB from the optimal objective obtained by the IPOPT solver. The deviation is denoted as η opt .

[0098] 2) Constraint satisfaction rate: Evaluate the effectiveness of DeepOPF - MB by measuring the percentage of constraints satisfied. Respectively use η V , and to represent the constraint satisfaction rates of P g , Q g , V, branch power, and branch angle.

[0099] 3) Load satisfaction rate: Used to evaluate the percentage of load satisfied in the power system. and respectively represent the satisfaction rates of P d and Q d .

[0100] 4) Training time: Represents the time consumed by the DNN model during the training process, denoted as t train .

[0101] The multi - branch neural network distributed machine learning method for solving the AC optimal power flow problem proposed in the present invention is compared with different technical methods, and the technical methods for comparison include:

[0102] M0: The distributed AC optimal power flow solution method DeepOPF - MB based on the multi - branch neural network proposed in the present invention.

[0103] M1: Similar to DeepOPF - MB, the only difference is that the neural network uses a single - branch neural network.

[0104] M2: Similar to DeepOPF-MB, the only difference is the random decomposition of features and predictors.

[0105] 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. The learning rate for all three methods is 0.0001, and the penalty coefficient k of the objective function obj is set to 0.0001, and the hidden layer parameters are 32-32.

[0106] Table 1 shows the comparison of simulation experiment results of different technical methods.

[0107]

[0108] Table 1

[0109] Table 1 shows that in the IEEE 30-bus system, compared with M1, DeepOPF-MB performs relatively better in terms of optimality loss, load satisfaction rate, and branch constraint satisfaction rate. At the same time, the training time of DeepOPF-MB is reduced by 11.7% compared with M1. This indicates that the multi-branch neural network exhibits greater flexibility and modeling ability in DeepOPF-MB, which helps to capture system complexity and nonlinear relationships more accurately. This enables DeepOPF-MB to optimize the system more effectively, reduce the optimality loss, and improve the constraint satisfaction rate. Its advantages are also reflected in better handling of system load and branch constraints, showing stronger adaptability to more effectively regulate the system to meet various constraint conditions. Compared with M2, DeepOPF-MB performs significantly better in terms of optimality loss, which indicates that reasonable and appropriate power network partitioning can improve the performance of the DNN model.

[0110] Figure 4 shows the predicted solutions and their true values of DeepOPF-MB in the IEEE 30-bus system, including 10 samples randomly selected from the test dataset. In Figure 4 (a) and Figure 4 (b), taking the load of node 12 and the power of node 4 as examples, it is observed that the predicted values of load and generator power are extremely close to the true values, with remarkable accuracy. Figure 5 shows the approximation degree between the predicted target and the actual value. The predicted generation cost is highly consistent with the actual generation cost, highlighting the reliability of the model. These results collectively demonstrate the potential advantages and practical value of DeepOPF-MB in power system prediction and optimization, with important application prospects.

[0111] The present invention proposes a distributed AC optimal power flow solution method based on a multi-branch neural network. Utilizing the multi-branch neural network helps to better capture the complexity and non-linear relationships of the system, improve the optimization performance, reduce the generation cost, and enhance the system operation efficiency. Secondly, this method can enhance the constraint satisfaction rate of the system, better handle the load and branch constraints, and improve the system stability and security. Through the accurate predictions in terms of load, generator power, and generation cost demonstrated by actual case studies, this technical solution is expected to improve the accuracy and reliability of system decision-making and operation. In summary, the proposed technical solution may bring higher efficiency, reliability, and flexibility to the optimization and management of power systems, providing important technical support and innovative ideas for the development of future power systems.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. However, such modifications or replacements 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 distributed AC optimal power flow solution method based on a multi-branch neural network, characterized in that: Includes the following steps: S1, establish AC optimal power flow model; S2, grid area division: Based on complex network theory, the power system is 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 power system corresponds to a vertex of the graph, and the branch is represented as an edge in the graph, and the weight of the edge reflects the impedance or reactance of the branch; then, the Louvain algorithm is used to perform community division on this weighted graph to identify different network modules; S3, a distributed machine learning method based on a multi-branch neural network: a multi-branch DNN model is trained for the entire power system, in which the sub-networks correspond to the divided regions, and arbitrary architectures, depths, and continuous activation functions are allowed; in extreme cases, when the sub-network is selected as a single neuron, the multi-branch structure is simplified to a single hidden layer neural network; the model is used to learn the mapping relationship between input features and output features; the trained DNN model uses the input features to provide the predicted voltage of the non-zero injection nodes in the region; the Kron simplification method is used to calculate the voltage of the ZIBs; then, based on the voltage of the ZIBs and the provided load, the predicted active and reactive load values ​​are obtained, and the demand load is obtained through the predicted load value.

2. A distributed AC optimal power flow solution method based on a multi-branch neural network according to claim 1, characterized in that: In step S1, the method for establishing the AC optimal power flow model is as follows: 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 Indicates the upper and lower bounds of a variable x; By using Kron's simplified method, as shown in equations (10)-(12), equations (2)-(5) are expressed in Cartesian coordinates, thereby removing ZIBs from the AC-OPF model, as follows: in, is the set of ZIBs that are considered internal nodes in the Kron simplification.

3. A distributed AC optimal power flow solution method based on a multi-branch neural network according to claim 2, characterized in that: In step S2, the evaluation of the effect of the power grid area division depends on the modularity Q, which is calculated 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.

4. A distributed AC optimal power flow solution method based on a multi-branch neural network according to claim 3, characterized in that: In step S2, the method of using the Louvain algorithm to divide the weighted graph into communities is as follows: Each node is regarded 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 super node to form a larger region. This process is iterated until the modularity cannot be further improved.

5. A distributed AC optimal power flow solution method based on a multi-branch neural network according to claim 4, characterized in that: In step S3, the model is used to learn the input feature X and the output feature Y α The mapping relationship between them, the input feature vector X is expressed as follows: in, Represents the set of all nodes in the power grid; Output feature Y α It is expressed as follows: in, is the output of the sub-network corresponding to each region a, is the set of all nodes in region a, is the set of ZIBs in region a; V and θ are the node voltage amplitude and angle, respectively. In the region with a balanced node, the voltage angle of the balanced node is set to zero and is changed from excluded; w and b are the scaling and offset coefficient matrices respectively.

6. A distributed AC optimal power flow solution method based on a multi-branch neural network according to claim 5, characterized in that: In step S3, the trained DNN model uses the input feature X a To provide a predicted voltage at a non-zero injection node Calculation of voltage of ZIBs using Kron simplified method Subsequently, based on and the load P provided 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 There is no need to solve the nonlinear power flow equation; for each node i: 1) If only a generator or load exists, directly obtain its predicted active and reactive power generation, that is, and or the 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).

7. A distributed AC optimal power flow solution method based on a multi-branch neural network according to claim 6, characterized in that: The loss function of training is as follows: Among them, k obj and k d is a normal number, is the target loss in (1), is designed to find feasible solutions that satisfy the inequality constraints (6)-(9), while Designed to meet the required loads; 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, calculated from the loss function value; 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. A distributed AC optimal power flow solution method based on a multi-branch neural network according to claim 7, characterized in that: Also included is S4, which improves prediction performance through post-processing: 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 x represents the upper and lower bounds of a variable x; the inequality constraints (6)-(9) are expressed in a compact form as equation (26), 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 (27), take the part of each constraint that exceeds the upper and lower limits; use Δf to adaptively adjust the value of ΔY through formula (25), and the adjusted The value of is kept within limits to ensure voltage constraints.

9. A distributed AC optimal power flow solution method based on a multi-branch neural network according to claim 8, characterized in that: It also includes S5, and verifies the effectiveness of the present invention through an IEEE 30-node standard test system example: 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-MB is evaluated.

10. A distributed AC optimal power flow solution method based on a multi-branch 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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