A direct current micro-grid optimal power flow model based on GNN assisted convex relaxation verification, a system thereof and a memory

Abstract

The application discloses a kind of based on GNN auxiliary convex relaxation verification direct current microgrid optimal power flow model and its system and memory.The model includes: based on MPPT-DGs and droop control establishes the non-convex power flow optimization model of distributed power generation unit and constant power load, it is accurately convex relaxation using SOCP structure, then microgrid is abstracted into graph model, extract the structure and electrical characteristics of node and edge as GNN input, and set SOCP structure relaxation, collectively input to AI-Verifier module, then based on KKT condition and construct consistency synchronization item, form distributed coordination, then introduce physical guided GCNs architecture, quickly converge to global optimal solution, and verify model performance by experiment.Based on the system provided with computer program above, it can effectively solve the problems of communication data packet loss, frequent failure and low reliability faced by centralized optimization method in large-scale direct current microgrid in the prior art, and realize intelligent optimization control of direct current microgrid.

Description

TECHNICAL FIELD

[0001] The application relates to an optimal power flow model, in particular to a direct-current micro-grid optimal power flow model based on GNN auxiliary convex relaxation verification, a system thereof and a memory, and belongs to the technical field of distributed control of direct-current micro-grids. BACKGROUND

[0002] With the global energy structure transforming to a high proportion of renewable energy, the wide access of photovoltaic and wind power distributed new energy at the distribution level promotes the rapid development of direct-current micro-grids in modern power systems. Direct-current micro-grids have the advantages of high energy transmission efficiency, flexible control and strong structure adaptability, and become an important platform for supporting the flexible access of wind and light storage and other new energy. However, the source-load structure in the direct-current micro-grid is highly complex, especially when the maximum power point tracking (MPPT) controlled distributed generation unit (MPPT-DG) and constant power load (CPL) are simultaneously accessed, the system power flow presents significant non-convex characteristics, strong coupling and multiple constraint characteristics, which greatly increases the difficulty of modeling and solving the power flow optimization problem.

[0003] The current mainstream power flow optimization method includes traditional centralized optimal power flow (OPF) control and approximate linearization modeling strategy. The centralized method relies on global information scheduling, although it can obtain better performance, but it faces challenges such as communication link packet loss, frequent node failure and low reliability, and it is difficult to effectively adapt to wide-area distributed large-scale direct-current micro-grid systems. At the same time, its computational complexity increases significantly with the expansion of the system size, which seriously restricts the real-time performance and engineering deployment capability. In contrast, the distributed optimization method can realize system coordinated control through information exchange between local nodes, has good scalability and robustness, and has become the research focus in the field of power flow optimization in recent years.

[0004] To alleviate the non-convexity of the power flow equation, convex relaxation strategies (such as semi-definite programming SDP) are widely introduced into the modeling of micro-grid optimal power flow. This kind of method converts the original non-convex optimization problem into a convex problem that can be analytically solved, which helps to obtain a theoretically global optimal solution. However, in actual engineering, this kind of method still faces two core challenges: (1) The relaxation accuracy is highly dependent on whether the optimization model accurately describes the key physical information such as network topology structure, voltage regulation mechanism, power balance and device nonlinear constraints, etc. Once the model is abstracted and distorted, it is easy to cause inaccurate solution or physically infeasible; (2) There is currently a lack of real-time, online and efficient relaxation accuracy determination mechanism, and existing strategies mostly rely on manual rank judgment or offline simulation analysis, which cannot adapt to dynamic operation scenarios and regulation requirements, limiting the feasibility of its engineering application. SUMMARY

[0005] In view of the problems existing in the prior art, a first object of the present application aims to provide a direct current micro-grid optimal power flow model based on GNN assisted convex relaxation verification. The model is based on a graph neural network, abstracts the direct current micro-grid into a graph structure, and combines a convex relaxation strategy including a SCOP structure, to realize the synergistic effect of "model prediction-distributed optimization", which can not only guarantee the high precision of system modeling and the physical feasibility of the solution, but also has the capabilities of fast verification, distributed efficient control, and truly meets the engineering requirements of safe, efficient and scalable operation of direct current micro-grid under high proportion of new energy access in the future.

[0006] A second object of the present application aims to provide a computer readable memory, which contains the implementation of the above-mentioned direct current micro-grid optimal power flow model and can be read and executed.

[0007] A third object of the present application is to provide a direct current micro-grid optimal power flow system based on GNN assisted convex relaxation verification. The system can effectively improve the scheduling efficiency and operation stability of the direct current micro-grid, and has high system robustness when facing power grid fluctuations, equipment disturbances or communication failures. Experiments show that the method can still converge to the global optimal solution under large-scale node number, and its performance is better than that of traditional centralized optimization method and existing distributed control algorithm.

[0008] In order to achieve the above technical purposes, the present application provides a direct current micro-grid optimal power flow model based on GNN assisted convex relaxation verification, which comprises:

[0009] Step S1, a non-convex power flow optimization model of distributed power generation unit (Droop-DGs) and constant power load (CPLs) is established based on MPPT-DGs and droop control;

[0010] Step S2, the non-convex power flow optimization model obtained in step S1 is accurately convex relaxed by using SOCP structure, auxiliary variable Q is constructed and tightening constraint is applied, and the optimal solution thereof satisfies the condition rank(Q)=1;

[0011] Step S3, the micro-grid is abstracted into a graph model, the structure and electrical characteristics of nodes and edges are extracted as GNN inputs, and the relaxation of SOCP structure is collected and input into the AI-Verifier module together, to complete the accuracy prediction of model relaxation;

[0012] Step S4, based on KKT condition and constructing a consistency synchronization term, a distributed coordination of the model based on adjacency Lagrange multiplier consistency is formed;

[0013] Step S5, a physically guided GCNs architecture is introduced, which can quickly converge to the global optimal solution while meeting the power flow physical constraints, and the model performance is verified by experiments.

[0014] As a preferred scheme, the direct current micro-grid comprises m MPPT-DGs, n Droop-DGs and h CPLs, m, n and h belong to the set of positive integers. Among them, the MPPT-DG adopts a voltage-power characteristic curve or a real-time power tracking control algorithm to adjust the output power, the CPL model adopts a constant power load equivalent model, and has a negative impedance characteristic. The introduction of non-convexity by this model is one of the key bases for the convex relaxation design of the application.

[0015] As a preferred scheme, the characteristic parameters of the non-convex power flow optimization model include current, voltage, reference voltage, average voltage, output power, admittance matrix, resistance, cost function, cost function parameter, new variable matrix Q, Lagrange function, Lagrange multiplier and synchronization term.

[0016] As a preferred scheme, the power flow equation of the non-convex power flow optimization model is:

[0017] Formula 1: ;

[0018] Formula 2: ;

[0019] The distributed control expression of the direct current micro-grid is:

[0020] Formula 3: ;

[0021] Formula 4: ;

[0022] In formulas 1-4, respectively represent the output power vector and the voltage vector of the power generation unit under droop control, are elements in the admittance matrix, is a diagonal matrix, and the diagonal elements are the resistance values of the MPPT-DG nodes and the CPL nodes, represents the instantaneous voltage value of the i-th Droop-DG node, represents the average value of the node voltage, is the reference voltage, represents the synchronization term of the i-th node.

[0023] As a preferred scheme, the non-convexity of the model is described as:

[0024] Formula 5: ;

[0025] Formula 6: ;

[0026] In formulas 5 and 6, represents the operation cost function of the direct current micro-grid, The cost function coefficient of the ith node is, The output power of the ith source node is, The power and voltage vectors of the source nodes are, s.t.p p The constraint condition introduced for the source node power is, The n-dimensional element vector is all 0. It should be noted that in formula 5, due to the existence of a nonlinear equality constraint, the OPF is a non-convex problem, and therefore, the problem must be first converted into a convex optimization problem, and the present application uses a convex relaxation technique to complete the conversion.

[0027] As a preferred scheme, the process of precisely convex relaxing the non-convex power flow optimization model by the SOCP structure is:

[0028] Formula 7: ;

[0029] Formula 8: ;

[0030] In formula 7 and formula 8, is a tightening constraint condition, the elements satisfy that is, . The process is based on the SOCP structure construction, and in the equivalent conversion process, in order to guarantee that the feasible solution domain is not expanded, compared with traditional relaxation methods such as semi-definite programming (SDP) or approximate linear models, it can still maintain the physical meaning of the solution and the mathematical rigor of the model under distributed conditions; further, the condition for determining whether the SOCP convex relaxation is accurate is: if OPF1 satisfies , then it is an accurate convex relaxation.

[0031] As a preferred scheme, the process of predicting the accuracy of the model relaxation is:

[0032] Step S3-1, abstracting the microgrid as a graph model, using admittance matrix, load micro-source position information, etc. as the physical meaning and characterization dimension of the nodes and edges of the GNNs model, and using a graph neural network (GCN) to extract spatial information from the topology of the microgrid, wherein the unweighted graph description of the microgrid G is:

[0033] Formula 9: ;

[0034] Step S3-2, respectively defining the feature vectors of the nodes and edges as:

[0035] Formula 10: ;

[0036] Formula 11:​ ;

[0037] Step S3-3, the precision prediction of the model relaxation is described based on the mapping learning function f of the micro-grid topology, the node feature vector and the edge feature vector, and the process is as follows:

[0038] Formula 12: ;

[0039] Formula 13: ;

[0040] In formulas 9-13, G represents an unweighted graph, V represents a set composed of nodes, E represents a set composed of edges, represents a feature vector of a node, respectively represent the voltage amplitude, the output power of the MPPT-DG, the power consumed by the CPL and the node type, represents a feature vector of an edge, is a line impedance, represents the distance between nodes, is an adjacency matrix, which represents the connection state between transmission lines, 1 represents connection, and 0 represents non-connection, represents the future time period the prediction accuracy of the convex relaxation model. By the admittance matrix of the power grid can be obtained, is a key representing the spatial position of the DG and the CPL.

[0041] In the present application, the key to the precision prediction of the model relaxation is the AI-Verifier module, which extracts spatial information from the micro-grid by using GCN, and then inputs the SOCP convex relaxation attribute and the node feature into the AI-Verifier to predict the accuracy. In addition, the above process can also improve the prediction accuracy of the convex relaxation model by using the spatio-temporal graph convolution network STGCNs.

[0042] As a preferred scheme, the process of distributed coordination of the model in step S4 is as follows:

[0043] Step S4-1, a consistency constraint expression is constructed by using the adjacency node Lagrange multiplier, wherein the Lagrange equation is expressed as:

[0044] Formula 14:

[0045] ;

[0046] Step S4-2, when the partial derivative of each part of the Lagrange equation is zero, the KKT condition and its consistency equivalent condition can be obtained, and the expressions are as follows:

[0047] Formula 15: ;

[0048] Formula 16: ;

[0049] Formula 17: ;

[0050] In formulas 14-17, are Lagrange multipliers, is a parameter obtained by partial derivative of the Lagrange equation L, is a synchronization term, when the system reaches a steady state, is established, and the system is stable at the optimal solution.

[0051] The global optimal control strategy with distributed consistency in the above process can avoid the problem of large amount of calculation in solving large-scale nonlinear convex OPF problems by traditional centralized method, and the equivalent synchronization term under the consistency protocol is derived based on the KKT condition, wherein the KKT consistency condition is expressed by the consistency constraint of the adjacent node Lagrange multiplier in the distributed calculation process, and the global coordination of multiple local problem solutions is realized; the consistency control strategy can be realized through the consistency mechanism, and it is ensured that the system can stably converge to the global optimal solution.

[0052] As a preferred scheme, the distributed coordination further includes a distributed controller.

[0053] As a preferred scheme, the controller iteratively updates the state based on local communication of each node to realize optimal power scheduling and voltage recovery. Since the controller only needs to exchange voltage estimation values and Lagrange multiplier update values with adjacent nodes in each iteration, it has the advantages of small communication burden and good engineering implementability.

[0054] As a preferred scheme, the expression of the physically guided GCNs architecture is:

[0055] Formula 18: ;

[0056] Formula 19: ;

[0057] In formulas 18 and 19, , are the feature matrix of the l-th layer after the physical constraint correction and the output feature matrix of the l-th layer standard graph convolution respectively, is a differentiable projection operator, is a voltage out-of-limit mask matrix, V represents a set of point feature quantities or edge feature vectors, is a matrix Hadamard product.

[0058] The distributed global optimization control strategy adopted in the application fuses graph neural networks (GNNs) and an accurate convex relaxation method, introduces a physical guiding mechanism, embeds physical constraints such as power balance in GNNs training, and realizes physical consistency modeling of the direct current micro-grid power flow characteristics. The strategy takes into account the modeling accuracy and solving efficiency, and improves the global optimal solution accuracy and robustness of large-scale systems under complex source and load structures.

[0059] The application further provides a computer readable memory containing a computer program, which can realize the direct current micro-grid optimal power flow model based on GNN assisted convex relaxation verification.

[0060] The application further provides a direct current micro-grid optimal power flow system based on GNN assisted convex relaxation verification, which comprises a programmable logic controller (100), a central processing unit (200) and the readable memory (300) described above; the programmable logic controller (100) collects direct current micro-grid data and inputs them into the central processing unit (200) and executes the computer program on the readable memory (300), and global optimization control is performed.

[0061] Compared with the prior art, the technical scheme of the application has the beneficial technical effects that:

[0062] 1) The application systematically establishes a power flow optimization model of a maximum power point tracking control distributed power generation unit (MPPT-DG) and a constant power load (CPL) at the same time, fully considers node voltage regulation constraints, power balance constraints and non-negativity constraints of optimization variables, greatly improves the engineering authenticity and adaptability of the power flow model, and further, for the inherent non-convexity of the power flow equation in the above-mentioned model, the application further introduces an auxiliary matrix variable Q, successfully relaxes the non-convex power flow optimization problem into a convex optimization problem with a second-order cone structure under the premise of strictly maintaining the original physical constraint conditions, ensures the high consistency of the solution space and the original non-convex problem in the mathematical and physical levels, and provides a solid model foundation and theoretical guarantee for realizing global optimal control in a distributed environment; tests show that in an 8-node direct current micro-grid containing 1 MPPT-DG, 3 Droop-DGs and 3 CPLs, the optimization model converges after 14 iterations, and the rank of the variable Q is 1, which shows that the convex relaxation strategy is accurate, and the consistency of the relaxation solution and the global optimal solution of the original non-convex problem is verified.

[0063] 2) In the technical solution provided by the present application, a synchronous coordination mechanism based on KKT consistency condition is constructed on the basis of the convex relaxation model, effectively solving the problems of communication data packet loss, frequent failure and low reliability faced by traditional centralized optimization methods in large-scale DC microgrid. In addition, by introducing a consistency synchronization term between the distributed controllers, global consistency approximation of the local calculation results is realized, so that each node can achieve the global optimization goal through limited adjacent communication, reducing the computational complexity when the system scale expands and improving the reliability of the system.

[0064] 3) In the technical solution provided by the present application, by introducing an AI-Verifier module based on a graph neural network, the problem that the convex relaxation strategy in the prior art needs to rely on a large number of offline tests and cannot quickly identify failure risks is effectively solved; the AI-Verifier module uses information such as node impedance matrix, power flow constraint boundary and distributed generation / load distribution structure to predict the accuracy of convex relaxation under the current topology and parameter configuration, and outputs the relaxation failure probability evaluation result. This mechanism combines the mathematical construction of the auxiliary matrix variable Q, generates the optimal relaxation strategy under the premise of keeping the original physical constraints unchanged, and significantly reduces the trial-and-error cost in the engineering deployment process. Test results show that the distributed convex optimization control strategy of the present application fusing the AI intelligent verification mechanism and introducing the graph neural network model of the physical guidance mechanism has engineering feasibility and algorithm accuracy, and lays a theoretical and practical foundation for the intelligent optimization control of the DC microgrid in the large-scale and high-proportion new energy access scene. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 The figure is the cost function convergence process diagram of the DC microgrid provided by the precise convex relaxation strategy of embodiment 1 of the present application;

[0066] Figure 2 The figure is the system architecture diagram of the AI-Verifier module based on the graph neural network in embodiment 1 of the present application;

[0067] Figure 3 The figure is the voltage value of Droop-DGs under the control method provided by embodiment 1 and comparative example 1 of the present application;

[0068] Wherein, Figure 3 (a) is the voltage value of Droop-DGs of the control method provided by embodiment 1 of the present application, Figure 3 (b) is the voltage value of Droop-DGs of the control method provided by comparative example 1 of the present application;

[0069] Figure 4 The figure is a schematic diagram of the synchronization term under the control method provided by embodiment 1 of the present application;

[0070] Figure 5 a structure diagram of an optimal power flow system provided by the present application;

[0071] Wherein, 100 is a programmable logic controller, 200 is a central processing unit, and 300 is a readable memory. DETAILED DESCRIPTION

[0072] In order to more clearly present the objects, technical solutions and advantages of the present application, the following will describe the exemplary embodiments of the present application in detail with reference to the drawings. It should be noted that the described embodiments are only examples of some embodiments of the present application, rather than all embodiments of the present application. It should be understood that the present application is not limited to the exemplary embodiments described herein. According to the embodiments described in the present application, other related embodiments can be derived by those skilled in the art without creative labor, and these derived embodiments should be included in the protection scope of the present application.

[0073] The present application provides a DC micro-grid optimal power flow model based on GNN auxiliary convex relaxation verification, and the following embodiments all adopt this model, and the specific process is as follows:

[0074] Step S1, a non-convex power flow optimization model of distributed power generation units (Droop-DGs) and constant power loads (CPLs) is established based on MPPT-DGs and droop control;

[0075] The DC micro-grid includes m MPPT-DGs, n Droop-DGs and h CPLs, and m, n and h belong to the set of positive integers;

[0076] The characteristic parameters of the non-convex power flow optimization model include current, voltage, reference voltage, average voltage, output power, admittance matrix, resistance, cost function, cost function parameter, new variable matrix Q, Lagrange function, Lagrange multiplier and synchronization term;

[0077] The power flow equation of the non-convex power flow optimization model is:

[0078] Formula 1: ;

[0079] Formula 2: ;

[0080] The distributed control expression of the DC micro-grid is:

[0081] Formula 3: ;

[0082] Formula 4: ;

[0083] In formulas 1-4, respectively represent the output power vector and the voltage vector of the power generation unit under droop control. are elements in admittance matrix, is a diagonal matrix, whose diagonal elements are resistance values of each MPPT-DG node and CPLs node, represents the instantaneous voltage value of the ith Droop-DG node, represents the average value of the node voltage, is a reference voltage, represents the synchronization term of the ith node;

[0084] The non-convexity of the model is described as:

[0085] Equation 5: ;

[0086] Equation 6: ;

[0087] In Equation 5 and Equation 6, represents the operation cost function of the DC microgrid, is the cost function coefficient of the ith node, is the output power of the ith source node, are the power and voltage vectors of the source node, respectively, s.t.p (subject to p ) represents the constraint condition introduced for the power of the source node, represents a vector with all elements being 0 in n dimensions;

[0088] Step S2, the non-convex power flow optimization model obtained in step S1 is accurately convex relaxed by using the SOCP structure, auxiliary variables Q are constructed and tightening constraints are applied, and the optimal solution satisfies the condition rank(Q)=1;

[0089] The process of accurately convex relaxing the non-convex power flow optimization model by using the SOCP structure is:

[0090] Equation 7: ;

[0091] Equation 8: ;

[0092] In Equation 7 and Equation 8, is a tightening constraint condition, whose elements satisfy that is, . The process is constructed based on the SOCP structure, and in order to guarantee that the feasible solution domain is not expanded in the equivalent transformation process, compared with traditional relaxation methods such as semi-definite programming (SDP) or approximate linear models, it can still maintain the physical meaning of the solution and the mathematical rigor of the model under distributed conditions; further, the condition for determining whether the SOCP convex relaxation is accurate is: if OPF1 satisfies is the exact convex relaxation;

[0093] Step S3, abstracting the microgrid as a graph model, extracting the structure and electrical characteristics of nodes and edges as GNN input, and then collecting the SOCP structural relaxation together as input to the AI-Verifier module to complete the accuracy prediction of the model relaxation;

[0094] The process of the accuracy prediction of the model relaxation is:

[0095] Step S3-1, abstracting the microgrid as a graph model, using admittance matrix, load micro-source position information, etc. as the physical meaning and representation dimension of the nodes and edges of the GNNs model, and using graph neural network (GCN) to extract spatial information from the topology of the microgrid, wherein the unweighted graph description of the microgrid G is:

[0096] Formula 9: ;

[0097] Step S3-2, respectively define the feature vectors of nodes and edges as:

[0098] Formula 10: ;

[0099] Formula 11: ;

[0100] Step S3-3, based on the mapping learning function f of the microgrid topology, node feature vector and edge feature vector, describe the accuracy prediction of the model relaxation, the process is:

[0101] Formula 12: ;

[0102] Formula 13: ;

[0103] In formulas 9-13, G represents an unweighted graph, V represents a set composed of nodes, E represents a set composed of edges, represents the feature vector of the node, respectively represent the voltage amplitude, the output power of the MPPT-DG, the power consumed by the CPL, and the node type, represents the feature vector of the edge, is the line impedance, represents the distance between nodes, is the adjacency matrix, which represents the connection state between transmission lines, 1 represents connection, and 0 represents no connection, represents the future time period the prediction accuracy of the inner convex relaxation model;

[0104] Step S4, based on the KKT condition and constructing a consistent synchronization term, forming a distributed coordination based on the consistency of the adjacency Lagrange multiplier model;

[0105] The process of the distributed coordination is:

[0106] Step S4-1, constructing a consistent constraint expression through the adjacency node Lagrange multiplier, wherein the Lagrange equation is expressed as:

[0107] Formula 14:

[0108] ;

[0109] Step S4-2, when the partial derivative of each part of the Lagrange equation is zero, the KKT condition and its consistent equivalent condition can be obtained, and the expressions are respectively:

[0110] Formula 15: ;

[0111] Formula 16: ;

[0112] Formula 17: ;

[0113] In formulas 14-17, is a Lagrange multiplier, is a parameter obtained by partial derivative of the Lagrange equation L, is a synchronization term, when the system reaches a steady state, is established, and the system is stable at the optimal solution;

[0114] Step S5, introducing a physically guided GCNs architecture, which converges to the global optimal solution quickly while meeting the physical constraints of power flow, and verifying the performance of the model through experiments;

[0115] The expression of the physically guided GCNs architecture is:

[0116] Formula 18: ;

[0117] Formula 19: ;

[0118] In formulas 18 and 19, 、 is the feature matrix of the lth layer after physical constraint correction and the output feature matrix of the lth layer standard graph convolution respectively, is a differentiable projection operator, is a voltage out-of-limit mask matrix, V represents a set of point feature quantities or edge feature vectors, is a matrix Hadamard product.

[0119] The application also provides a computer memory containing a computer program, which can realize the GNN-assisted convex relaxation verification-based direct-current micro-grid optimal power flow model.

[0120] The application also provides a GNN-assisted convex relaxation verification-based direct-current micro-grid optimal power flow system, which comprises a programmable logic controller (100), a central processing unit (200) and the readable memory (300) described above; the programmable logic controller (100) collects direct-current micro-grid data and inputs the data into the central processing unit (200) and executes the computer program on the readable memory (300) to perform global optimization control.

[0121] Embodiment 1

[0122] By using the above model, the reference voltage of the direct-current micro-grid system is set as , and the cost function coefficient is set as , and the simulation results are shown in Figure 1 and Table 1.

[0123] ;

[0124] By constructing a relaxation model with a second-order cone structure, the optimal power flow problem converges to the optimal stable solution at the 14th iteration, and the rank of the auxiliary variable matrix Q is 1, that is , which fully proves the accuracy of the convex relaxation strategy, that is, the optimal solution obtained by the relaxation problem is consistent with the global optimal solution of the original optimization problem.

[0125] In addition, the optimal voltage value of each Droop-DG and the corresponding synchronization term are calculated in this embodiment, and the results are , which further verifies the condition of , indicating that in the distributed optimization problem based on the second-order cone relaxation, the KKT consistency condition is strictly satisfied, thereby proving that the minimum value obtained is the optimal solution of the relaxation optimization problem, and verifying the accuracy of the proposed relaxation method.

[0126] Secondly, in order to verify the technical advantages of the AI-Verifier in the model provided by the application, this embodiment also verifies the technical advantages of the AI-Verifier in the model provided by the application, and the process is as follows: in the convex relaxation prediction of common micro-grid including IEEE-33 direct-current micro-grid, the system can obtain the network node admittance matrix Y, the upper and lower limits of voltage, the current limit and other power flow optimization boundary conditions, and the distribution density and position of DG / CPL, etc. These information is used as a training data set.

[0127] By using GCN to capture the spatial layout of the micro-grid, convolution operations are performed on the graph data, and the overall prediction framework is as follows Figure 4As shown in the IEEE-33 node DC microgrid improved network, a plurality of random tests are carried out, and the prediction accuracy of the AI-Verifier on the convex relaxation model is 93.6%. This proves that the AI-Verifier proposed in the application as an intelligent enhancement module for relaxation accuracy effectively improves the intelligent level and real-time reliability of the control system without destroying the original control logic, and has important engineering practical value for the wide deployment of the DC microgrid.

[0128] Thirdly, through the distributed coordination process in the model provided by the application, the stable state of the observation system and its steady-state value are observed, and the results are as shown in Figure 3 (a) and Table 2.

[0129] ;

[0130] As shown in Table 2, the synchronization term obtained satisfies the KKT consistency condition, and the value of the total cost function of the system is stabilized at consistent with the theoretical optimal solution of the original optimization problem, fully indicating that the control method provided by the application can effectively drive the system to converge to the global optimal solution, even if the system is stabilized at the optimal solution; and the system voltage is finally stabilized at about 38V, further verifying the effectiveness and engineering applicability of the control method provided by the application in realizing voltage recovery and global optimization of power flow.

[0131] Further, the model provided by the application introduces a physical guided GCNs architecture to deeply embed the physical law of the power system into the neural network through a double-channel constraint fusion mechanism, extracts the microgrid topology features by using the graph convolution through the forward propagation channel, and checks and corrects the features that violate the physical law by using the physical constraint channel.

[0132] In order to correct the power balance, a correction layer is introduced in the above process:

[0133] Formula 20: ;

[0134] Wherein is the real part, represents the node power, and U and Y represent the node voltage vector and admittance matrix respectively. is the node injection power vector, is an adaptive correction coefficient.

[0135] In the DC microgrid simulation test of IEEE-33 nodes, compared with the traditional GNN method, the voltage constraint violation rate of the system is reduced by 12%, the iteration steps required in the optimization process are significantly reduced, and the relaxation accuracy is improved by 3% after adopting the decentralized distributed communication topology structure and introducing the graph neural network model with physical guidance mechanism. The results show that the physically guided GNN not only performs better in model convergence efficiency and physical consistency of the solution, but also significantly enhances the applicability and promotion potential of the convex relaxation strategy in complex microgrid scenarios.

[0136] Comparative Example 1

[0137] The comparative example is exactly the same as example 1, except that the control strategy based on the approximate economic dispatch formula (Consensus-Based Distributed Economic Dispatch Control Method in Power, DOI: 10.1109 / TSG.2017.2756041.) is used, that is:

[0138] Formula 21: ;

[0139] The results are shown in Figure 3 (b) and Table 3.

[0140] ;

[0141] As can be seen from Table 3, the obtained synchronization term is , which does not meet the consistency condition of the KKT condition of the original optimization problem, indicating that the method cannot make the system stable at the theoretical optimal solution. At the same time, the corresponding total cost function value is , which is significantly higher than the optimal value achieved in example 1 of the present application, further verifying the insufficient performance of the method in cost minimization. In contrast, the control strategy provided in example 1 of the present application not only ensures the consistency convergence of the synchronization term, but also effectively reduces the system operating cost, which is significantly superior to the existing approximate dispatch method, fully proving the significant advantage of the proposed method in global optimization performance.

Claims

1. A DC microgrid optimal power flow model based on GNN-assisted convex relaxation verification, characterized by: include: Step S1, establishing a non-convex power flow optimization model of distributed generation units Droop-DGs and constant power loads CPLs based on MPPT-DGs and droop control; Step S2: Using the SOCP structure to perform precise convex relaxation on the non-convex power flow optimization model obtained in step S1, construct the auxiliary variable Q and impose a tight constraint, so that its optimal solution satisfies the condition rank(Q)=1; Step S3: Abstract the microgrid into a graph model, extract the structural and electrical characteristics of nodes and edges as GNN input, and then combine the SOCP structural relaxation and input them into the AI-Verifier module to complete the accuracy prediction of the model relaxation; Step S4: Based on the KKT condition and the consistency synchronization term, a distributed coordination of the model based on the consistency of the adjacent Lagrange multiplier is formed; Step S5: Introduce a physics-guided GCNs architecture to quickly converge to the global optimal solution while satisfying the physical constraints of the power flow, and verify the model performance through experiments; The process of predicting the accuracy of the model relaxation is: Step S3-1: Abstract the microgrid into a graph model. Use the admittance matrix and load microsource location information as the physical meaning and representation dimension of the nodes and edges of the GNNs model. Use the Graph Convolutional Network (GCN) to extract spatial information from the microgrid topology. The unweighted graph description of the microgrid topology G is: Formula 9: ; Step S3-2: Define the feature vectors of nodes and edges as: Formula 10: ; Formula 11: ; Step S3-3, based on the microgrid topology, node feature vectors and edge feature vectors, the mapping learning function f describes the accuracy prediction of the model relaxation, and the process is as follows: Formula 12: ; Formula 13: ; In formulas 9 to 13, G represents an unweighted graph, V represents a set of nodes, and E represents a set of edges. represents the feature vector of the node, They represent the voltage amplitude, the output power of MPPT-DGs, the power consumed by CPLs, and the node type, respectively. represents the eigenvector of the edge, is the line impedance, Represents the distance between nodes, is the adjacency matrix, which indicates the connection status between transmission lines. 1 indicates connection and 0 indicates disconnection. Indicates future time period Prediction accuracy of the convex relaxation model.

2. A DC microgrid optimal power flow model based on GNN-assisted convex relaxation verification according to claim 1, characterized in that: The DC microgrid includes m MPPT-DGs, n Droop-DGs and h CPLs, where m, n and h belong to a set of positive integers; The characteristic parameters of the non-convex power flow optimization model include: current, voltage, reference voltage, average voltage, output power, admittance matrix, resistance, cost function, cost function parameter, new variable matrix Q, Lagrangian function, Lagrangian multiplier and synchronization term.

3. A DC microgrid optimal power flow model based on GNN-assisted convex relaxation verification according to claim 1, characterized in that: The power flow equation of the non-convex power flow optimization model is: Formula 1: ; Formula 2: ; The distributed control expression of the DC microgrid is: Formula 3: ; Formula 4: ; In formulas 1 to 4, They are respectively represented as the output power vector and voltage vector of the power generation unit under droop control, are all elements in the admittance matrix, is a diagonal matrix whose diagonal elements are the resistance values ​​of each MPPT-DGs node and CPLs node. represents the instantaneous voltage value of the i-th Droop-DG node, represents the average value of the node voltage, is the reference voltage, Represents the synchronization item of the i-th node.

4. A DC microgrid optimal power flow model based on GNN-assisted convex relaxation verification according to claim 3, characterized in that: The non-convexity of the model is described as: Formula 5: ; Formula 6: ; In Equation 5 and Equation 6, represents the operating cost function of the DC microgrid, is the cost function coefficient of the i-th node, is the output power of the i-th source node, are the power and voltage vectors of the source node respectively. stp (subject to p) represents the constraints introduced on the power of the source node. Represents an n-dimensional vector whose elements are all zero.

5. The DC microgrid optimal power flow model based on GNN-assisted convex relaxation verification according to claim 4, characterized in that: The process of performing accurate convex relaxation of the non-convex power flow optimization model by the SOCP structure is as follows: Formula 7: ; Formula 8: ; In Equation 7 and Equation 8, To tighten the constraints, , whose elements satisfy ,Right now .

6. A DC microgrid optimal power flow model based on GNN-assisted convex relaxation verification according to claim 5, characterized in that: The process of distributed coordination of the model in step S4 is as follows: Step S4-1: Construct a consistency constraint expression through adjacent node Lagrange multipliers, where the Lagrange equation is expressed as: Equation 14: ； Step S4-2: When the partial derivatives of each part of the Lagrangian equation are zero, the KKT condition and its consistency equivalent condition can be obtained, and their expressions are: Equation 15: ; Equation 16: ; Equation 17: ; In formulas 14 to 17, are all Lagrange multipliers, is the parameter obtained by the partial derivative of the Lagrange equation L, is the synchronization term. When the system reaches a steady state, Established, the system is stable at the optimal solution; The distributed coordination also includes a distributed controller; the controller iteratively updates the state based on local communication of each node to achieve optimal power scheduling and voltage recovery.

7. The DC microgrid optimal power flow model based on GNN-assisted convex relaxation verification according to claim 1, characterized in that: The expression of the physical guided GCNs architecture is: Equation 18: ; Equation 19: ; In formulas 18 and 19, 、 are the feature matrix after the correction of the physical constraints of the lth layer and the output feature matrix of the lth layer standard graph convolution, is a differentiable projection operator, is the voltage limit-crossing mask matrix, V represents the set of point characteristic quantities or edge characteristic vectors, is the matrix Hadamard product.

8. A computer-readable memory comprising a computer program, characterized in that: The computer program can implement the DC microgrid optimal power flow model based on GNN-assisted convex relaxation verification as described in any one of claims 1 to 7.

9. A DC microgrid optimal power flow system based on GNN-assisted convex relaxation verification, characterized by: include: A programmable logic controller (100), a central processing unit (200) and a readable memory (300) as claimed in claim 8; the programmable logic controller (100) collects DC microgrid data and inputs it into the central processing unit (200) and executes the computer program on the readable memory (300) to perform global optimization control.

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