Grid investment portfolio game optimization method based on graph neural network and quantum evolution

Abstract

The invention relates to the technical field of power grid investment portfolio, and discloses a power grid investment portfolio game optimization method based on a graph neural network and quantum evolution, and the method comprises the steps: collecting data, and obtaining a sample data set; constructing a power grid graph structure; constructing a graph neural network GNN model, and training the graph neural network GNN model by using the power grid graph structure and the sample data set; performing feature extraction on the power grid graph structure and the power grid investment project by using the trained GNN model to obtain a project comprehensive benefit evaluation index; constructing a non-cooperative game model taking a power grid company, a power generation party and a user side as subjects, and predicting project benefit indexes of each subject after game by using a GNN model; the three subjects respectively construct revenue functions to obtain game equilibrium solutions; and inputting the game equilibrium solution into the quantum evolution algorithm model, and outputting a final optimal portfolio scheme. The optimal investment portfolio scheme gives consideration to a global optimization objective and multi-agent game balance, and provides scientific and feasible decision support for power grid investment decision.

Description

Technical Field

[0001] This invention relates to the field of power grid portfolio technology, and more specifically to a power grid portfolio game optimization method based on graph neural networks and quantum evolution. Background Technology

[0002] The high proportion of renewable energy grid integration presents numerous challenges to power grid planning and operation: the randomness, volatility, and intermittency of renewable energy output increase the difficulty of balancing power supply and demand; the large-scale grid connection of power electronic equipment reduces system inertia, requiring traditional stability control theories relying on synchronous machine inertia to adapt and improve. Furthermore, the large-scale integration of renewable energy, the increasingly complex grid structure, strong cross-regional AC / DC coupling, and the increasing number of voltage levels significantly increase the difficulty of coordination between different voltage levels and the sending and receiving grids, making cascading reactions more likely after a fault. Simultaneously, the scale of power grid projects is continuously expanding, with transmission and transformation projects often involving investments of hundreds of billions of yuan, long industrial chains, and strong radiating effects, placing higher demands on overall project management. Planning coordination between different regions and voltage levels is becoming increasingly complex, but under the existing system and mechanisms, there is a lack of integrated planning for each link—source-grid-load-storage—often resulting in independent actions and low resource utilization efficiency. Against this backdrop, how to optimize the allocation of various engineering investments and improve overall coordination and economy while meeting carbon emission constraints has become a pressing technical challenge in power grid investment planning.

[0003] For a long time, power grid planning has relied primarily on human experience and qualitative analysis: planners, based on load growth forecasts, planning guidelines, and their own experience, gradually propose solutions to current power grid problems. This expert-driven decision-making approach is feasible when project scale and constraints are relatively limited, but it is susceptible to cognitive biases and limitations of experience in highly complex scenarios. Furthermore, algorithms such as genetic algorithms and artificial fish swarm algorithms are widely used in power grids due to their low computational cost, simple implementation, and effectiveness in nonlinear discrete optimization problems. However, these heuristic algorithms also have shortcomings in accuracy and reliability: they are prone to getting trapped in local optima and struggle to balance global search capability with convergence speed. Due to limitations in model accuracy and algorithm performance, traditional planning results often fail to meet the requirements of safety, economy, and flexibility, and cannot fully satisfy the needs of modern power grid portfolio optimization.

[0004] Existing power grid investment optimization methods often focus on a single objective, such as maximizing economic benefits. Traditional optimization methods typically lack the ability to comprehensively consider multiple objectives, which may lead to incomplete optimization results and fail to meet the multidimensional needs of complex power grid investment decisions. Specifically, single-objective optimization methods cannot balance the priorities and importance of different investment projects, resulting in some investment schemes that may affect the overall efficiency and reliability of the power grid being ignored or underestimated.

[0005] Existing optimization methods typically require multiple stages of manual calculations or simple heuristics for decision-making. These steps can lead to lengthy computational processes and slow response times. When faced with a large number of candidate investment projects and complex power grid topologies, these methods are computationally inefficient and cannot provide timely decision support. Especially when it comes to investment decisions involving large-scale power grids, the slow response time of traditional methods severely impacts decision-making efficiency, thereby affecting the timeliness of investment plan implementation.

[0006] Existing optimization methods for power grid planning and investment decisions often rely on traditional mathematical modeling and simulation tools. However, these methods may face high error rates in practical applications, especially given the variable power grid topology and complex interrelationships between projects. The accuracy and predictive power of traditional methods often fall short of the requirements for precise decision-making. Particularly in the modeling process of nonlinear and high-dimensional data, the accumulation of errors can lead to biased decisions, ultimately affecting the effectiveness of power grid investment.

[0007] A game-theoretic optimization method for power grid portfolios based on graph neural networks and quantum evolution is needed. This method should accurately capture the nonlinear relationships between power grid topology and nodes, generate precise benefit assessments for each candidate portfolio, and provide high-precision predictions for decision-making. This would reduce the error rate, avoid error accumulation and prediction bias in traditional methods, and thus provide a more reliable basis for decision-making. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a power grid portfolio game optimization method based on graph neural networks and quantum evolution.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] S1: Collect power grid topology data, meteorological data, node load data, and power grid investment project data, and obtain a sample dataset after preprocessing;

[0011] S2: Construct the power grid graph structure, which includes a node set, an edge set, a node feature matrix, and an edge feature matrix;

[0012] S3: Construct a graph neural network (GNN) model and train the GNN model using a power grid graph structure and a sample dataset to obtain the trained GNN model;

[0013] S4: Use the trained GNN model to extract features from the power grid graph structure and power grid investment projects to obtain the node and edge features in the power grid graph structure and the comprehensive benefit evaluation index of the projects.

[0014] S5: Construct a non-cooperative game model with the power grid company, power generation party, and user side as the main parties, and use the trained GNN model to predict the project benefit indicators of each party after the game.

[0015] S6: The power grid company, the power generation party, and the user side each construct a revenue function based on the project benefit indicators of each entity. Each entity iterates its strategy with the goal of maximizing its own revenue until the Stackelberg equilibrium is reached, thus obtaining the game equilibrium solution.

[0016] S7: The game equilibrium solution is input into the quantum evolution algorithm model to perform initial qubit observation and fitness evaluation;

[0017] S8: Based on the fitness evaluation results, the probability amplitude of the qubits is adjusted using the quantum rotation gate. At the same time, every few generations, the better portfolio scheme obtained by the quantum evolution algorithm is returned to the non-cooperative game model constraints for verification. The current better portfolio scheme is checked to see if it meets the payoff function and constraints of the non-cooperative game model. If the verification fails, the quantum evolution algorithm is used again to adjust and optimize the better portfolio scheme until a better portfolio scheme that can pass the verification is obtained.

[0018] S9: Substitute the validated portfolio proposal back into the non-cooperative game model. The three parties—the power grid company, the power generator, and the user—adjust their strategies based on their respective payoff functions and constraints. Then, feed the adjusted portfolio proposal back into the quantum population of the quantum evolution algorithm model to correct the fitness evaluation function and determine whether the termination condition is met: whether the maximum number of iterations Tmax has been reached. When the convergence condition is met, output the individual with the highest fitness in the current population as the final optimal portfolio proposal. If the termination condition is not met, repeat steps S7, S8, and S9 until the preset maximum number of iterations is reached, and output the final optimal portfolio proposal.

[0019] The present invention has the following beneficial effects:

[0020] (I) Current methods lack consideration for multi-stakeholder game dynamics, making it difficult to achieve collaborative optimization of power grid investment decisions. Existing power grid investment portfolio optimization methods typically assume centralized planning by a single decision-making entity, neglecting the interactive game relationships between multiple investment entities. Stakeholders may have different goals and interests; traditional methods lack a game theory perspective and cannot effectively address the conflict and coordination issues under multi-stakeholder decision-making, resulting in investment schemes failing to achieve global equilibrium. This invention integrates a game theory-driven mechanism into the optimization framework, introducing a multi-stakeholder game model to characterize the decision-making interactions between different investment entities. This solves the problem of decision incoordination caused by the lack of consideration for multi-stakeholder game dynamics in existing technologies, achieving collaborative optimization and balance of power grid investment decisions with the participation of multiple stakeholders.

[0021] (II) The current lack of effective modeling for the complex topological relationships of power grids leads to inaccurate investment scheme evaluations. Power grids are characterized by numerous nodes and complex topological networks. Existing technologies often use simplified models or fragment the network structure, failing to fully consider the interrelationships between various components of the power grid. Therefore, existing methods cannot effectively address the problem of accurately evaluating the impact of investments in a particular region or equipment on the overall power grid performance, resulting in optimization results that may not reach the optimal level. This invention introduces a graph neural network model for topological perception and feature extraction of the power grid, modeling each node and its connections in a graph structure to fully explore the dependencies and network effects between nodes. Based on this, this invention can accurately characterize the impact of investment schemes on the overall power grid, solving the problem of inaccurate evaluations caused by the lack of characterization of power grid topological relationships in traditional methods, and ensuring that optimization decisions consider the complex interrelationships of the entire power grid.

[0022] (III) Currently, the power grid lacks efficient global optimization capabilities, easily getting trapped in local optima and struggling to converge quickly in complex search spaces. Power grid portfolio optimization is a high-dimensional and complex combinatorial optimization problem with a vast space of alternative solutions and numerous constraints. Traditional optimization algorithms often face the dilemma of low computational efficiency or only reaching local optima, failing to effectively solve the problem of obtaining a globally optimal solution within a reasonable time. To address this deficiency, this invention combines quantum evolution algorithms for global search optimization. Quantum evolution algorithms utilize quantum parallelism and probabilistic evolution mechanisms to improve population diversity and search depth, significantly enhancing the ability to escape local optima traps and improving convergence speed. By applying quantum evolution algorithms to power grid portfolio optimization, this invention solves the problem of insufficient global search capabilities in large-scale combinatorial optimization, enabling efficient optimization to obtain higher-quality power grid portfolio solutions.

[0023] (iv) This application utilizes graph neural network-driven power grid topology modeling and rapid evaluation. It employs graph neural networks (GNNs) to represent the power grid topology and model node features, serving as a portfolio value evaluator. This deep model can efficiently approximate the solution of complex power grid planning problems and can be used to quickly predict the power grid state and benefits under different investment schemes. Compared to traditional optimization calculation models, the GNN model can significantly improve computational speed while maintaining accuracy, thus supporting real-time evaluation and comparison of candidate project combinations. Game theory mechanisms ensure the equilibrium of multi-entity investment strategies. A game theory model is introduced into the decision-making process to characterize the collaborative and competitive relationships among multiple investment entities or strategies, thereby obtaining an equilibrium solution that balances the interests of all parties. Unlike centralized optimization methods that only pursue global optimality and may ignore individual returns, this invention ensures that the objectives of each participant are considered through strategic game theory, making the optimization results more feasible and practically valuable. This game theory-driven decision-making mechanism effectively promotes cooperation among stakeholders, resulting in a "win-win" investment portfolio solution that better aligns with the actual operation of the electricity market. The global optimization search using the quantum evolution algorithm (QEA) performs a global optimization search for the power grid investment portfolio. QEA draws on quantum computing principles, using qubits to encode candidate solutions and updating the population through operations such as quantum superposition and quantum rotation gates. Compared to traditional genetic algorithms, the quantum evolution algorithm has advantages such as smaller population size, faster convergence speed, and stronger global search capabilities. This means the algorithm is better able to avoid premature convergence and find the globally optimal combination of power grid investments with a higher probability. By introducing QEA, this invention can efficiently lock in the optimal solution even in a vast combinatorial search space, improving the performance and effectiveness of optimization. The three-layer integrated intelligent optimization framework organically combines the aforementioned GNN evaluation layer, game theory decision-making layer, and quantum optimization layer, forming an innovative methodological system that integrates "predictive evaluation + strategic game theory + global optimization." First, a trained GNN model is used to evaluate the grid operation status and multi-dimensional performance of each investment portfolio in real time. Second, game analysis is performed based on the GNN evaluation results to adjust strategies and achieve equilibrium in the payouts of all participants. Finally, a quantum evolution algorithm is used to search for the optimal investment portfolio globally. These three methods work together to achieve comprehensive intelligent optimization decision-making for grid investment project portfolios across multiple objectives, including economic benefits, power supply reliability, and clean energy consumption. This significantly improves the scientific rigor and practicality of large-scale grid investment planning, such as the Liaoning power grid.

[0024] By combining Graph Neural Networks (GNNs), multi-agent game theory models, and Quantum Evolutionary Algorithms (QEAs), the effectiveness and efficiency of power grid investment planning are significantly improved. On one hand, by using GNNs to model the power grid topology and its spatiotemporal characteristics, the evaluation of planning schemes becomes more accurate and reliable, significantly improving the prediction accuracy of power grid operating status and risks such as power outages. On the other hand, this invention introduces a game theory framework to coordinate the decision-making interactions among stakeholders—source, grid, load, and storage—enabling them to reach optimal strategies such as Nash equilibrium in the planning process. This achieves coordinated planning for distributed power source integration and grid expansion, overcoming the problems of poor coordination and low resource utilization efficiency caused by existing fragmented approaches. While meeting carbon emission constraints, this invention achieves optimized and coordinated allocation of investments in multiple projects within a large power grid. Compared to existing optimal technical solutions, it further improves the security, economy, and overall coordination of the planning results. This invention, by integrating game theory-driven Graph Neural Networks (GNNs) and Quantum Evolutionary Algorithms (QEAs), overcomes the problem of existing methods focusing only on a single objective. Through a multi-objective optimization framework, it can simultaneously consider factors such as the economic benefits, reliability, security, and new energy integration of the power grid. This invention enables power grid investment optimization to improve the overall stability and sustainability of the power grid while ensuring economic benefits, avoiding the single-objective limitations of traditional methods. The optimization method of this invention is based on the combination of GNN and QEA, using a deep learning model to efficiently approximate the power grid state and leveraging a quantum evolution algorithm to quickly find the optimal solution globally. Compared with traditional methods, this invention significantly improves computational efficiency and response speed, especially when dealing with large-scale power grid investments, enabling rapid evaluation of the benefits of different investment portfolios and real-time decision support. Through an integrated intelligent optimization framework, this invention reduces lengthy computational processes and enhances the immediate responsiveness of the decision-making process. By employing GNN as an intelligent evaluator for the power grid, this invention accurately captures the nonlinear relationships between the power grid topology and nodes. After training, the GNN model can generate accurate benefit assessments for each candidate investment portfolio and provide high-precision predictions for decision-making. This high-precision optimization effectively reduces the error rate, avoiding error accumulation and prediction bias in traditional methods, thus providing a more reliable basis for decision-making. Attached Figure Description

[0025] Figure 1 This is a system structure diagram of the optimization method according to an embodiment of the present invention;

[0026] Figure 2 This is a technical roadmap of the optimization method according to an embodiment of the present invention;

[0027] Figure 3 It is the equilibrium solution of the three parties in a non-cooperative game. Detailed Implementation

[0028] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0029] A power grid portfolio game optimization method based on graph neural networks and quantum evolution is characterized by the following steps:

[0030] S1: Collect power grid topology data, meteorological data, node load data, and power grid investment project data, and obtain a sample dataset after preprocessing;

[0031] S2: Construct the power grid graph structure, which includes a node set, an edge set, a node feature matrix, and an edge feature matrix;

[0032] S3: Construct a graph neural network (GNN) model and train the GNN model using a power grid graph structure and a sample dataset to obtain the trained GNN model;

[0033] S4: Use the trained GNN model to extract features from the power grid graph structure and power grid investment projects to obtain the node and edge features in the power grid graph structure and the comprehensive benefit evaluation index of the projects.

[0034] S5: Construct a non-cooperative game model with the power grid company, power generation party, and user side as the main parties, and use the trained GNN model to predict the project benefit indicators of each party after the game.

[0035] S6: The power grid company, the power generation party, and the user side each construct a revenue function based on the project benefit indicators of each entity. Each entity iterates its strategy with the goal of maximizing its own revenue until the Stackelberg equilibrium is reached, thus obtaining the game equilibrium solution.

[0036] S7: The game equilibrium solution is input into the quantum evolution algorithm model to perform initial qubit observation and fitness evaluation;

[0037] S8: Based on the fitness evaluation results, the probability amplitude of the qubits is adjusted using the quantum rotation gate. At the same time, every few generations, the better portfolio scheme obtained by the quantum evolution algorithm is returned to the non-cooperative game model constraints for verification. The current better portfolio scheme is checked to see if it meets the payoff function and constraints of the non-cooperative game model. If the verification fails, the quantum evolution algorithm is used again to adjust and optimize the better portfolio scheme until a better portfolio scheme that can pass the verification is obtained.

[0038] S9: Substitute the validated portfolio proposal back into the non-cooperative game model. The three parties—the power grid company, the power generator, and the user—adjust their strategies based on their respective payoff functions and constraints. Then, feed the adjusted portfolio proposal back into the quantum population of the quantum evolution algorithm model to correct the fitness evaluation function and determine whether the termination condition is met: whether the maximum number of iterations Tmax has been reached. When the convergence condition is met, output the individual with the highest fitness in the current population as the final optimal portfolio proposal. If the termination condition is not met, repeat steps S7, S8, and S9 until the preset maximum number of iterations is reached, and output the final optimal portfolio proposal.

[0039] The process of constructing the power grid diagram structure in S2 specifically includes:

[0040] The process of constructing the power grid graph structure includes: extracting power grid features, constructing the power grid graph structure, and representing it as G=(V,E,X). V ,X E ), where V is the set of nodes, representing substations, load centers, and renewable energy access points; E is the set of edges, representing transmission lines and transformer connections; X V ∈R ∣V∣×dv This is a node feature matrix, where each row corresponds to a feature vector of a node, including load level, equipment status, and renewable energy output; X E ∈R ∣E∣×de Let R be the edge feature matrix, which includes line capacity, impedance, and operating status, and R represents the set of all real numbers.

[0041] In S3, a graph convolutional neural network is used as the basic structure of the graph neural network (GNN) model. The input includes the power grid diagram structure and the sample dataset. The graph neural network (GNN) model is trained under supervised learning conditions. The graph neural network (GNN) model is shown in the following equation (1):

[0042]

[0043] in, = +I represents the adjacency matrix with added self-loops. It is the original adjacency matrix. It is the identity matrix; for The degree matrix; Let the nodes of the l-th layer be represented as follows: =XV; The weight matrix is ​​trainable. For activation functions; This represents the node representation of the (l+1)th layer.

[0044] The training loss function for supervised learning is the mean squared error plus a regularization term:

[0045]

[0046] in, This represents the total loss value. This represents the number of training samples; For sample index; It is the benefit evaluation indicator for the i-th power grid project portfolio scheme; These are the predicted values ​​from the Graph Neural Network (GNN) model. λ is the variance of the sample error term; λ is the regularization coefficient. As a regularization term, the trained GNN model can predict the comprehensive benefits of any power grid project portfolio scheme of the current power grid company. It replaces traditional time-consuming simulation calculations, providing real-time and accurate evaluation support for subsequent game theory and optimization.

[0047] In S4, the process of using the trained GNN model to extract features from the power grid graph structure and power grid investment projects, and obtaining the node and edge features in the power grid graph structure as well as the comprehensive benefit evaluation index of the projects, includes:

[0048] The power grid topology map and candidate power grid investment project information are incorporated into the trained GNN model through node feature enhancement; the final layer output of the GNN model is the embedding representation of each node. This forms a comprehensive benefit evaluation vector y∈R K Where K represents the number of evaluation indicators, the comprehensive benefit evaluation vector must include at least economic benefits, reliability, security, and renewable energy integration rate. The comprehensive benefit evaluation vector is essentially the overall comprehensive indicator. It is essentially a comprehensive indicator that is further subdivided into three main indicators.

[0049] The above predictions are used to assess the overall effectiveness of subsequent quantitative investment plans. Node and edge features are extracted after the GNN model is trained and are used for subsequent game theory and benefit evaluation. Here, the comprehensive project benefit evaluation index is an overall project content evaluation index, while the project indicators for each entity mentioned later refer to indicators that are relevant to the interests of each of the three parties.

[0050] The process of constructing a non-cooperative game model in S5 with power grid companies, power generation enterprises, and users as the main participants, and using the trained GNN model to predict the project benefit indicators of each participant after the game, includes:

[0051] The non-cooperative game model involves power grid companies, power generation companies, and users. The strategy space represents the combinations of power grid investment projects that each entity can choose. In this model, the power grid company, power generation companies, and users form a closed-loop game: the power grid company uses a GNN model to obtain the comprehensive benefits of the predicted investment portfolio, formulates the portfolio plan and electricity price, and applies these to power generation companies and users respectively. Power generation companies, based on the investment plan and electricity price given by the power grid company, determine the scale of new energy installations on the supply side. Users participate in demand response based on electricity prices, adjusting transferable load to reduce electricity purchase costs. The trained GNN model is used to predict the project benefit indicators of each entity under different strategies, obtaining the revenue assessment value for each entity.

[0052] This approach abstracts the decision-making process as a multi-agent non-cooperative game. Power grid investment and electricity prices, generation investment and renewable energy scale, and load demand response all influence each other, forming a multi-agent game system for source-grid-load coordinated planning. The power grid company uses a GNN model to obtain the comprehensive benefits of the predicted investment portfolio schemes, formulates investment plans and on-grid electricity prices, and applies them to both generation companies and users. Generation companies, based on the investment plans and electricity prices provided by the power grid company, determine the scale of renewable energy installations on the supply side; users, on the demand side, participate in demand response based on electricity prices, adjusting transferable load to reduce electricity purchase costs. Then, the trained GNN model is used to predict the project benefit indicators of each agent under different strategies, i.e., the profit assessment values ​​of each agent, as input for game analysis.

[0053] In step S6, the power grid company, power generation enterprise, and user side each construct a benefit function based on the benefit indicators of their respective projects. Each entity iterates its strategy with the goal of maximizing its own utility until a Stackelberg equilibrium is reached. The process of obtaining the game equilibrium solution includes:

[0054] 1) Game Theory Model of Power Grid Company:

[0055] With the goal of maximizing economic benefits, the power grid company constructs the following revenue function:

[0056]

[0057] in, Investment plan for the power grid company; The scale of new energy investment by power generation companies; For user-side demand response process; p is the feed-in tariff; The total demand after the user response; ∈{0,1} indicates whether to invest in the project, where 0 means not to invest in the current project and 1 means to invest in the current project; For project investment costs; It is the failure cost predicted by the GNN model; this failure cost is also one of the comprehensive benefit indicators predicted by GNN, but it appears in the form of a negative benefit.

[0058] The constraints that the power grid company needs to meet include:

[0059] Power grid company's investment budget constraints:

[0060]

[0061] in, Indicates the project investment cost; Indicates whether the project has been invested in; N represents the number of projects invested in by the power grid company; This indicates the power grid company's investment budget;

[0062] Power grid companies' line capacity constraints:

[0063]

[0064] Where (i, j) represents a line in the power grid that connects node i and node j; E is the set of edges, which is the set of all lines in the power grid; This represents the active power flowing through line (i, j) under the combined strategies of the power grid company;

[0065] Node voltage constraints for power grid companies:

[0066]

[0067] in, The lower and upper limits of the allowable voltage at node i. The voltage magnitude of node i under the combined strategies of the power grid enterprise is a function;

[0068] 2) Game theory model for power generation companies:

[0069] Power generation companies, aiming to maximize profits, construct the following revenue function:

[0070]

[0071] in, This reflects the scale of new energy investment by power generation companies and is also part of their current strategy. A function representing the amount of electricity generated from new energy sources; Represents a government subsidy function; This indicates the investment cost per unit capacity; This represents the operation and maintenance costs of power generation companies; This represents the wind and solar power curtailment loss function;

[0072] The constraints that power generation companies need to meet include:

[0073] Maximum deployable capacity constraint:

[0074]

[0075] in, Represents the scale of new energy investment by power generation companies. This represents the maximum investment scale for the operation of power generation enterprises.

[0076] Output fluctuation constraints:

[0077]

[0078] in, Fluctuations in the output of new energy sources by power generation companies; This indicates the maximum permissible power output fluctuation.

[0079] 3) User-side game theory model:

[0080] The goal on the user side is to reduce electricity purchase costs and maintain business efficiency. The following revenue function is constructed:

[0081]

[0082] in, The actual electricity consumption of the user In response to compensation; This indicates the loss of productivity or comfort due to the response. This represents the unit cost coefficient incurred by large electricity customers due to losses in production or comfort.

[0083] Demand response is constrained by business flexibility and comfort levels; therefore, the constraints that users need to meet include:

[0084] Demand responsiveness constraints:

[0085]

[0086] in, This represents the degree of user-side participation in responding to user needs. To the maximum permissible level of demand response;

[0087] Minimum power consumption guarantee:

[0088]

[0089] in, This refers to the actual electricity consumption of users after demand response is implemented. This is the minimum electricity consumption that large electricity customers must meet;

[0090] The Stackelberg master-slave game model is used to solve the game equilibrium. The power grid company, as the leader, first announces the investment plan. and grid connection price Power generation companies and users, as followers, each choose their optimal response after observing the leader's strategy. and Each agent continuously adjusts its decisions through strategy iteration until a Stackelberg equilibrium is reached, meaning there exists a strategy combination ( This makes:

[0091]

[0092] Game equilibrium solution ( ( ) represents the optimal portfolio scheme after considering multi-party game.

[0093] In step S6, the effectiveness of the power grid investment project portfolio is quantified to construct the revenue function for each entity. The power grid company's revenue function integrates electricity sales revenue, investment costs, transmission losses, and fault costs; the power generation company's revenue function considers electricity sales revenue, subsidies, investment, and operation and maintenance costs; and the user's revenue function includes reduced electricity expenses and compensation costs. The power grid company chooses to maximize economic benefits, the power generation company chooses to maximize profits, and the user chooses to reduce electricity purchase costs and maintain business efficiency. As described above, each party's utility function pursues its own utility maximization.

[0094] Step S7 involves inputting the game equilibrium solution into the quantum evolution algorithm model, and the process of initializing qubit observations and fitness evaluation includes:

[0095] A quantum bit string is used to encode the power grid investment portfolio. Unlike classical encoding, quantum encoding can exist in a superposition of two quantum states simultaneously, allowing a single "chromosome" to express a superposition of multiple states at the same time. The encoding is as follows:

[0096] (14)

[0097] In the formula: |0> and |1> represent the "0" and "1" of the quantum state, respectively; , Let be two complex numbers representing the probability magnitudes of quantum states, satisfying the normalization condition | |2+| |2=1;

[0098] Considering the complex decision-making space involving multiple stakeholders and projects, a piecewise real-number encoding method is adopted: each decision variable, such as whether an investment project is implemented, the scale of new energy installed capacity, and the degree of demand response participation, corresponds to a set of qubits. The individual chromosome encoding is as follows:

[0099] (15)

[0100] in, This represents the preprocessed chromosome, where m is the number of qubits encoding each variable, and Nd is the number of decision variables. , Let be the probability amplitude of the i-th qubit of the j-th variable. For each individual, observe the binary string s generated by its qubit. i Convert to real number x i :

[0101] (16)

[0102] In the formula: s i A binary string generated for observing qubits; bin2dec(s i ) represents the conversion of a binary string to a decimal number; m is the number of qubits encoded for each variable; To define the upper and lower bounds of the value range of the i-th decision variable, an initial quantum population is constructed. A quantum chromosome population of a certain size is randomly initialized. The classical portfolio scheme obtained through the initial quantum state bit observation process of formulas (15) and (16) is input into the trained GNN model to quickly predict the project benefit index of the scheme. At the same time, combined with the game equilibrium solution, a comprehensive fitness function is constructed:

[0103]

[0104] in, To score for economic benefits, For power supply reliability score, The score represents the renewable energy absorption capacity score, and w1, w2, and w3 are the weighting coefficients for the economic benefit score, power supply reliability score, and renewable energy absorption capacity score, respectively. As a penalty term for violating the game equilibrium constraint, it is used to balance the global optimization goal with the interests of each subject. The predicted project benefit index is used as the fitness value of the chromosome to evaluate the merits of each scheme in the current population.

[0105] In step S8, the probability amplitude of the qubits is adjusted using a quantum rotation gate based on the fitness evaluation results. Simultaneously, every few generations, the process of returning the better portfolio solutions obtained by the quantum evolution algorithm to the non-cooperative game model for verification includes:

[0106] Specifically, the probability amplitude of the qubits is adjusted using a quantum rotation gate mechanism. Through the adjustment of the quantum rotation gate, the quantum population gradually evolves towards a higher fitness. The quantum rotation gate is the core operation of the quantum evolution algorithm. Based on the current optimal solution or individual fitness, the rotation angle of each qubit is adjusted so that the probability amplitude tends to generate a better solution. The chromosome update and evolution process is realized through the rotation operation of the quantum rotation gate, as shown in equations (18) and (19).

[0107] (18)

[0108] (19)

[0109] In the formula: U(θ) is the quantum rotation gate, used to adjust the state of the qubit; θ is the rotation angle; Let be the probability amplitude of the k-th generation qubit; This represents the probability magnitude when the number of iterations is k+1.

[0110] (20)

[0111] In the formula: Maximum and minimum rotation angles; T max This represents the maximum number of iterations. Initially, a larger rotation angle is used to enhance global search capabilities, while later the rotation angle is reduced to improve local fine-grained search capabilities.

[0112] The fundamental operation of quantum crossover is the temporary exchange of current optimal solutions among individuals. After an individual completes the crossover operation, it will be influenced by other individuals, changing its evolutionary direction. The steps are as follows: First, through a roulette wheel approach, individuals in the population... Select 2 individuals and Secondly, start with the individual. Local optimal objective As Local optimal solution, and utilize quantum rotation gate pairs Update; then, by individual Local optimal objective As Local optimal solution, and utilize quantum rotation gate pairs The process involves updating the population; finally, each population returns its local optimum target value, generating a new population.

[0113] Quantum mutation reduces the probability of an individual falling into a local optimum by altering the evolutionary process at a certain stage. By setting the mutation probability as shown in equation (20), mutation occurs when the random probability is less than the mutation probability, i.e., the α and β values ​​of the individual are swapped, thus reversing the direction of evolution.

[0114] (twenty one)

[0115] In the formula: P m T is the mutation probability; k is the decay coefficient; T max This represents the maximum number of iterations.

[0116] Monitor the improvement of population fitness over several consecutive generations. Every preset number of generations, return the optimal portfolio solution found by the quantum evolution algorithm to the non-cooperative game model: use this solution as the initial strategy, and re-perform the three-way game iteration to verify whether the solution meets the payoff requirements and constraints of each subject.

[0117] In step S9, in the non-cooperative game model, the three parties—the power grid company, the power generator, and the user—adjust their strategies based on their respective payoff functions and constraints. The adjusted portfolio strategy is then fed back into the quantum population of the quantum evolution algorithm model to correct the fitness evaluation function and determine whether the termination condition is met, i.e., whether the maximum number of iterations T has been reached. max When the convergence condition is met, the individual with the highest fitness in the current population is output as the final optimal portfolio solution.

[0118] If the termination condition is not met, repeat steps S7, S8, and S9 until the preset maximum number of iterations is reached, and output the final optimal portfolio solution.

[0119] Specifically, this includes:

[0120] The portfolio solutions obtained after the three parties adjust their strategies through non-cooperative game theory are fed back to the quantum population to guide the quantum rotation gate update direction, making the population evolution closer to the game equilibrium region. This adjusts the probabilities of quantum crossover and mutation, maintaining population diversity while satisfying game constraints, and imposing stronger elimination pressure on individuals that violate key constraints, thereby correcting the fitness evaluation function. This feedback mechanism achieves an organic integration of "global optimization" and "local game equilibrium," ensuring that the final solution is both theoretically optimal and practically feasible, and acceptable to all parties.

[0121] Based on the portfolio scheme information obtained through the quantum evolution algorithm, it is determined whether the termination condition is met, i.e., whether the maximum number of iterations has been reached. If the convergence condition is met, the individual with the highest fitness in the current population is output as the final optimal power grid portfolio scheme. If the convergence condition is not met, steps S7 to S9 are repeated to update the quantum population through quantum rotation gate, quantum crossover, and quantum mutation to generate a new generation of candidate portfolio schemes. Then, the benefits of the new generation of portfolio schemes are quickly evaluated using the GNN model. The fitness is calculated based on the constraints in the game equilibrium formula, and excellent individuals are selected to be retained for the next generation. The optimal portfolio scheme is periodically fed into the next generation. The non-cooperative game model is validated by revising the game equilibrium solution and fitness function based on the adjustment results of each agent until the convergence condition is met. The individual with the highest fitness in the current population is output as the final optimal power grid investment portfolio. The optimal power grid investment portfolio includes: the power grid company's investment decision, selecting and implementing power grid infrastructure projects and investment arrangements; the power generation party's investment decision, recommending the scale and layout of new energy projects; the user-side participation plan, suggesting the demand response scale and incentive mechanism design, as well as comprehensive benefit indicators; and multi-dimensional quantitative indicators of the power grid investment portfolio's economic benefits, power supply reliability, new energy absorption capacity, and carbon emission reduction effect. At this point, the optimal solution simultaneously takes into account the global optimization objective and the multi-agent game balance, providing scientific and feasible decision support for power grid investment decisions.

[0122] The optimal portfolio proposal corresponding to the current best individual in the quantum population is used as the initial strategy input to a non-cooperative game model. The three parties—the power grid company, the power generator, and the user—adjust their strategies according to their respective payoff functions and constraints. Through several rounds of game iteration, the strategies of each party gradually converge to a new Stackelberg equilibrium, making the adjusted portfolio proposal more aligned with the interests and practical feasibility of each party. Simultaneously, the fitness evaluation of the quantum evolution algorithm is updated based on the adjusted portfolio proposal.

[0123] For example, such as Figure 3 As shown in the non-cooperative game, each entity iterates its strategy with the goal of maximizing its own profit: Power grid company: Based on the comprehensive benefits of the GNN output, it weighs investment costs, electricity prices, transmission losses, and fault costs, and tends to adjust its investment plan from A→B→C. Power generation company: Given the grid connection price and grid constraints, the larger the installed capacity of new energy, the higher the profit, thus favoring investment plans B and C. User side: Under dynamic electricity prices and demand response subsidies, the total cost of electricity purchase is lowest and the profit is highest under plan C.

[0124] The Stackelberg equilibrium solution obtained through strategy iteration is as follows: the power grid company chooses investment scheme C, the power generation company allocates a high proportion of renewable energy capacity, and the user side undertakes a strong demand response participation. At this time, investment scheme C is the game equilibrium solution for the power grid company, power generation company, and user side under non-cooperative game. The initial equilibrium scheme is generation 0; the quantum evolution algorithm encodes the investment portfolio (such as line reinforcement capacity, energy storage configuration, demand response depth, and other decision variables) with qubit strings and searches for a better combination in the neighborhood of scheme C; after the qubit string is updated by the rotation gate, the optimal scheme obtained in generation 20 improves both the total system revenue and the renewable energy access rate compared to the initial equilibrium scheme. By returning this scheme to step S7, it is verified that it can still maintain the improvement or at least no decrease of the revenue of all three parties under the non-cooperative game framework, realizing the coordinated optimization of "source-grid-load".

[0125] Table 1. Examples of partial iteration results of the quantum evolution algorithm from generation 0 to 20.

[0126]

[0127] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A power grid portfolio game optimization method based on graph neural networks and quantum evolution, characterized in that, Includes the following steps: S1: Collect power grid topology data, meteorological data, node load data, and power grid investment project data, and obtain a sample dataset after preprocessing; S2: Construct the power grid graph structure, which includes a node set, an edge set, a node feature matrix, and an edge feature matrix; S3: Construct a graph neural network (GNN) model and train the GNN model using a power grid graph structure and a sample dataset to obtain the trained GNN model; S4: Use the trained GNN model to extract features from the power grid graph structure and power grid investment projects to obtain the node and edge features in the power grid graph structure and the comprehensive benefit evaluation index of the projects. S5: Construct a non-cooperative game model with the power grid company, power generation party, and user side as the main parties, and use the trained GNN model to predict the project benefit indicators of each party after the game. S6: The power grid company, the power generation party, and the user side each construct a revenue function based on the project benefit indicators of each entity. Each entity iterates its strategy with the goal of maximizing its own revenue until the Stackelberg equilibrium is reached, thus obtaining the game equilibrium solution. S7: The game equilibrium solution is input into the quantum evolution algorithm model to perform initial qubit observation and fitness evaluation; S8: Based on the fitness evaluation results, the probability amplitude of the qubits is adjusted using the quantum rotation gate. At the same time, every few generations, the better portfolio scheme obtained by the quantum evolution algorithm is returned to the non-cooperative game model constraints for verification. The current better portfolio scheme is checked to see if it meets the payoff function and constraints of the non-cooperative game model. If the verification fails, the quantum evolution algorithm is used again to adjust and optimize the better portfolio scheme until a better portfolio scheme that can pass the verification is obtained. S9: Substitute the validated portfolio proposal back into the non-cooperative game model. The three parties—the power grid company, the power generator, and the user—adjust their strategies based on their respective payoff functions and constraints. Then, feed the adjusted portfolio proposal back into the quantum population of the quantum evolution algorithm model to correct the fitness evaluation function and determine whether the termination condition is met: whether the maximum number of iterations Tmax has been reached. When the convergence condition is met, output the individual with the highest fitness in the current population as the final optimal portfolio proposal. If the termination condition is not met, repeat steps S7, S8, and S9 until the preset maximum number of iterations is reached, and output the final optimal portfolio proposal.

2. The power grid portfolio game optimization method based on graph neural networks and quantum evolution according to claim 1, characterized in that, The process of constructing the power grid graph structure includes: extracting power grid features, constructing the power grid graph structure, and representing it as G=(V,E,X). V ,X E ), where V is the set of nodes, representing substations, load centers, and renewable energy access points; E is the set of edges, representing transmission lines and transformer connections; X V ∈R ∣V∣×dv This is a node feature matrix, where each row corresponds to a feature vector of a node, including load level, equipment status, and renewable energy output; X E ∈R ∣E∣×de Let R be the edge feature matrix, which includes line capacity, impedance, and operating status, and R represents the set of all real numbers.

3. The power grid portfolio game optimization method based on graph neural networks and quantum evolution according to claim 2, characterized in that, In S3: A graph convolutional neural network (GNN) is used as the basic structure of the GNN model. The input includes a power grid diagram structure and a sample dataset. Supervised learning training is performed on the GNN model. The GNN model is shown in the following equation: in, = +I represents the adjacency matrix with added self-loops. It is the original adjacency matrix. It is the identity matrix; for The degree matrix; Let the nodes of the l-th layer be represented as follows: =XV; The weight matrix is ​​trainable. For activation functions; This represents the nodes at level l+1; The training loss function for supervised learning is the mean squared error plus a regularization term: in, This represents the total loss value. This represents the number of training samples; For sample index; It is the benefit evaluation indicator for the i-th power grid project portfolio scheme; These are the predicted values ​​from the Graph Neural Network (GNN) model. λ is the variance of the sample error term; λ is the regularization coefficient. As a regularization term, the trained GNN model can predict the overall benefits of any power grid project portfolio scheme of the current power grid company.

4. The power grid portfolio game optimization method based on graph neural networks and quantum evolution according to claim 1, characterized in that, The process of using a trained GNN model to extract features from the graph structure of the power grid and power grid investment projects, and obtaining the node and edge features in the power grid graph structure as well as the comprehensive benefit evaluation index of the projects, includes: The power grid topology map and candidate power grid investment project information are incorporated into the trained GNN model through node feature enhancement; the final layer output of the GNN model is the embedding representation of each node. This forms a comprehensive benefit evaluation vector y∈R K Where K is the number of evaluation indicators, the comprehensive benefit evaluation vector includes at least economic benefits, reliability, security and new energy access rate.

5. The power grid portfolio game optimization method based on graph neural networks and quantum evolution according to claim 1, characterized in that, The process of constructing a non-cooperative game model with the power grid company, power generation party, and user side as the main participants, and using the trained GNN model to predict the project benefit indicators of each participant after the game, includes: The non-cooperative game model involves power grid companies, power generation companies, and users. The strategy space represents the power grid investment project combinations that each entity can choose. In this model, the power grid company, power generation companies, and users form a closed-loop game: the power grid company uses a GNN model to obtain the comprehensive benefits of the predicted investment portfolio, formulates investment plans and electricity prices, and applies these to power generation companies and users respectively. Power generation companies, based on the investment plans and electricity prices provided by the power grid company, determine the scale of new energy installations on the supply side. Users participate in demand response based on electricity prices, adjusting transferable loads to reduce electricity purchase costs. The trained GNN model is used to predict the project benefit indicators of each entity under different strategies, obtaining the revenue assessment value for each entity.

6. The power grid portfolio game optimization method based on graph neural networks and quantum evolution according to claim 1, characterized in that, The power grid company, power generation enterprise, and user side each construct a benefit function based on the benefit indicators of their respective projects. Each entity iterates its strategy with the goal of maximizing its own utility until a Stackelberg equilibrium is reached. The process of obtaining the game equilibrium solution includes: 1) Game Theory Model of Power Grid Company: With the goal of maximizing economic benefits, the power grid company constructs the following revenue function: in, Investment plan for the power grid company; The scale of new energy investment by power generation companies; For user-side demand response process; p is the feed-in tariff; The total demand after the user response; ∈{0,1} indicates whether to invest in the project, where 0 means not to invest in the current project and 1 means to invest in the current project; For project investment costs; It is the failure cost predicted by the GNN model; The constraints that the power grid company needs to meet include: Power grid company's investment budget constraints: in, Indicates the project investment cost; Indicates whether the project has been invested in; N represents the number of projects invested in by the power grid company; This indicates the power grid company's investment budget; Power grid companies' line capacity constraints: Where (i, j) represents a line in the power grid that connects node i and node j; E is the set of edges, which is the set of all lines in the power grid; This represents the active power flowing through line (i, j) under the combined strategies of the power grid company; Node voltage constraints for power grid companies: in, The lower and upper limits of the allowable voltage at node i. The voltage amplitude at node i under the combined strategies of the power grid enterprise; 2) Game theory model for power generation companies: Power generation companies, aiming to maximize profits, construct the following revenue function: in, This reflects the scale of new energy investment by power generation companies and is also part of their current strategy. A function representing the amount of electricity generated from new energy sources; Represents a government subsidy function; This indicates the investment cost per unit capacity; This represents the operation and maintenance costs of power generation companies; This represents the wind and solar power curtailment loss function; The constraints that power generation companies need to meet include: Maximum deployable capacity constraint: in, Represents the scale of new energy investment by power generation companies. This represents the maximum investment scale for the operation of power generation enterprises. Output fluctuation constraints: in, Fluctuations in the output of new energy sources by power generation companies; This indicates the maximum permissible power output fluctuation. 3) User-side game theory model: The goal on the user side is to reduce electricity purchase costs and maintain business efficiency. The following revenue function is constructed: in, The actual electricity consumption of the user In response to compensation; This indicates the loss of productivity or comfort due to the response. This represents the unit cost coefficient incurred by large electricity customers due to losses in production or comfort. The constraints that the user side needs to meet include: Demand responsiveness constraints: in, This represents the degree of user-side participation in responding to user needs. To the maximum permissible level of demand response; Minimum power consumption guarantee: in, This refers to the actual electricity consumption of users after demand response is implemented. This is the minimum power consumption that must be met by the user. The Stackelberg master-slave game model is used to solve the game equilibrium. The power grid company, as the leader, first announces the investment plan. and grid connection price The power generator and the user, as followers, each select the optimal response after observing the leader's strategy. and Each agent continuously adjusts its decisions through strategy iteration until a Stackelberg equilibrium is reached, meaning there exists a strategy combination ( This makes: Game equilibrium solution ( ( ) represents the optimal portfolio scheme after considering multi-party game.

7. The power grid portfolio game optimization method based on graph neural networks and quantum evolution according to claim 4, characterized in that, The process of inputting the game equilibrium solution into the quantum evolution algorithm model to perform initial qubit observation and fitness evaluation includes: The power grid portfolio is encoded using a qubit string, and the encoding is as follows: (14) In the formula: |0> and |1> represent the "0" and "1" of the quantum state, respectively; , Let be two complex numbers representing the probability magnitudes of quantum states, satisfying the normalization condition | |2+| |2=1; Using segmented real-number encoding, each decision variable corresponds to a set of qubits, and the individual chromosome is encoded as follows: (15) in, This represents the preprocessed chromosome, where m is the number of qubits encoding each variable. For the number of decision variables, , Let be the probability amplitude of the i-th qubit of the j-th variable. For each individual, observe the binary string generated by its qubit. Convert to real number : (16) In the formula: A binary string generated for observing qubits; To convert a binary string to a decimal number; m is the number of qubits encoded for each variable; , To define the upper and lower bounds of the value range of the i-th decision variable, an initial quantum population is constructed. A quantum chromosome population of a certain size is randomly initialized. The classical portfolio scheme obtained through the initial quantum state bit observation process of formulas (15) and (16) is input into the trained GNN model to quickly predict the project benefit index of the scheme. At the same time, combined with the game equilibrium solution, a comprehensive fitness function is constructed: in, Score based on economic benefits; Score for power supply reliability; Score for new energy absorption capacity; , , These are the weighting coefficients for economic benefit score, power supply reliability score, and new energy absorption capacity, respectively. As a penalty term for violating the game equilibrium constraint, it is used to balance the global optimization goal with the interests of each subject. The predicted project benefit index is used as the fitness value of the chromosome to evaluate the merits of each investment portfolio scheme in the current population.

8. The power grid portfolio game optimization method based on graph neural networks and quantum evolution according to claim 7, characterized in that, The validated portfolio proposal is then reintroduced into the non-cooperative game model. The power grid company, power generator, and user adjust their strategies based on their respective payoff functions and constraints. The adjusted portfolio proposal is then fed back into the quantum population of the quantum evolution algorithm model to correct the fitness evaluation function and determine if the termination condition is met: whether the maximum number of iterations Tmax has been reached. When the convergence condition is met, the individual with the highest fitness in the current population is output as the final optimal portfolio proposal. If the termination condition is not met, steps S7, S8, and S9 are repeated until the preset maximum number of iterations is reached. The process of outputting the final optimal portfolio solution includes: The optimal portfolio proposal corresponding to the current best individual in the quantum population is used as the initial strategy input to the non-cooperative game model. The three parties—the power grid company, the power generator, and the user—adjust their strategies according to their respective payoff functions and constraints. Through several rounds of game iteration, the strategies of each party gradually converge to a new Stackelberg equilibrium, making the adjusted portfolio proposal more in line with the interests and practical feasibility of each party. Simultaneously, the fitness evaluation of the quantum evolution algorithm is updated based on the adjusted portfolio proposal. The key information obtained from the non-cooperative game model verification is fed back to the quantum population. The key information includes the sensitive constraints, strategy preferences, and equilibrium point characteristics of each subject. This guides the update direction of the quantum rotation gate, making the population evolution closer to the game equilibrium region, adjusting the probability of quantum crossover and mutation, maintaining population diversity under the premise of satisfying game constraints, and exerting stronger elimination pressure on individuals that violate key constraints. Based on the modified fitness evaluation function, determine whether the termination condition is met; if it is met, output the individual with the highest fitness in the current population as the final optimal portfolio solution; if it is not met, return to step S7 to continue iterative optimization until the preset maximum number of iterations is reached.

9. The power grid portfolio game optimization method based on graph neural networks and quantum evolution according to claim 1, characterized in that, The optimal power grid investment portfolio includes: power grid company investment decisions, selection of power grid infrastructure projects and investment arrangements; power generation company investment decisions, recommended scale and layout of new energy projects; user-side participation plans, suggested demand response scale and incentive mechanism design, and comprehensive benefit indicators; as well as multi-dimensional quantitative indicators of the power grid investment portfolio's economic benefits, power supply reliability, new energy absorption capacity, and carbon emission reduction effect.

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