Micro-grid optimization operation strategy based on risk management and mixed game

Abstract

A micro-grid optimization operation strategy based on risk management and mixed game comprises the following steps: establishing a multi-main-body system framework of a micro-grid containing a plurality of wind and light users, a shared energy storage network and a power distribution network, and analyzing a micro-grid benefit model based on a conditional value-at-risk theory to balance economic benefits and value-at-risk; on the basis of a master-slave game, a proper-alliance-oriented decision-making thought is fused, a master-slave alliance interaction model with the benefit maximization of an upper-layer micro-grid and a lower-layer user alliance as a target is constructed, and a multi-user electric energy sharing cooperative game model is established based on an asymmetric Nash bargaining theory; an improved differential evolution algorithm is adopted to solve the master-slave Litishan game interaction model, and the cooperative game benefit distribution problem is solved in a distributed mode through ADMM, so that the optimal solution of the multi-user electric energy sharing cooperative game model is obtained, namely, the optimal microgrid optimization operation strategy is obtained. According to the strategy, economic benefits of the microgrid and the user alliance are effectively considered, and fair distribution of cooperation benefits is realized on the premise of protecting user privacy.

Description

Technical Field

[0001] This invention relates to the field of microgrid optimization operation, and specifically to a microgrid optimization operation strategy based on risk management and hybrid game theory. Background Technology

[0002] With the advancement of urban industrialization, global energy demand continues to grow, and environmental problems caused by energy consumption are becoming increasingly severe. In response, countries worldwide have proposed green transformation goals for their energy structures. Against this backdrop, microgrids can effectively improve the utilization efficiency of renewable energy through intelligent dispatch and control. Specifically, to reduce dependence on traditional power systems, electricity users within microgrids deploy distributed energy resources and energy storage devices, realizing a shift from individual consumers to prosumers, effectively promoting local energy consumption and flexible management. Furthermore, the peer-to-peer (P2P) energy sharing system formed between prosumers and consumers promotes the democratization and competitiveness of the energy trading market. However, the conflict of interest among multiple stakeholders within a microgrid, driven by their own need to maximize economic benefits, and the autonomy of transactions also significantly increases the complexity of energy dispatch.

[0003] In existing technologies, the literature "Optimization Algorithm for Microgrid Energy Management System Based on Non-cooperative Game Theory" (Li Chendi, Chen Yuanrui, Zeng Jun, et al. Optimization Algorithm for Microgrid Energy Management System Based on Non-cooperative Game Theory [J]. Power System Technology, 2016, 40(02): 387-395.) proposes a microgrid economic optimization model based on non-cooperative complete information dynamic game theory. This model significantly improves the energy utilization efficiency on the source side and the electricity satisfaction on the load side by characterizing the game interaction relationship between the source and the load. However, there is no clear role hierarchy in non-cooperative games, and all participants are equal in the game. Under the condition of incomplete information sharing, participants will make decisions simultaneously or independently based on their own judgment. In reality, there are differences in the social status and identity of different participants, and the decision-making process usually has a clear order.

[0004] The paper "Economic Optimization Scheduling of Multi-Microgrid Systems Based on Master-Slave Game Theory under Multi-Agent Technology" (Ma Yue, Lin Hong. Economic Optimization Scheduling of Multi-Microgrid Systems Based on Master-Slave Game Theory under Multi-Agent Technology [J]. Acta Energiae Solaris Sinica, 2024, 45(01):574-582.) proposes an economic optimization scheduling strategy for multi-microgrid systems based on master-slave game theory. This strategy significantly improves the economic benefits of all parties and promotes local energy consumption by establishing a master-slave game framework for energy interaction among multi-microgrids. However, master-slave game theory focuses on individual rationality, emphasizing only the interests of each entity and neglecting the coordination and sharing of the overall benefits of the system. Cooperative game theory, on the other hand, under the premise of collective rationality, reaches a cooperative alliance through negotiation among multiple entities, jointly pursuing the maximization of overall benefits and rationally distributing the benefits brought by cooperation, emphasizing the unity of fairness and efficiency.

[0005] The paper "Capacity Configuration of Wind-Solar-Electricity-Hydrogen Microgrid Based on Cooperative Game Theory" (Chen Yi, He Shan, Xie Shaohua, et al.). *Acta Energiae Solaris Sinica*, 2024, 45(02): 395-405. This paper proposes a capacity configuration method for wind-solar-electricity-hydrogen microgrids based on cooperative game theory. This method verifies the economic efficiency and low-carbon nature under a fully cooperative game framework by exploring capacity configuration under different game modes involving different stakeholders. However, this paper does not consider the impact of source-load uncertainty, which can easily lead to intermittent energy supply-demand imbalances, thereby causing grid fluctuations and potential operational risks.

[0006] The paper "A Joint Optimization Strategy for Virtual Power Plant Participation in Main and Auxiliary Markets Considering Uncertainty Risks and Multi-Agent Collaboration" (Liu Haitao, Zhong Cong, Ma Jiayi, et al. A Joint Optimization Strategy for Virtual Power Plant Participation in Main and Auxiliary Markets Considering Uncertainty Risks and Multi-Agent Collaboration [J]. Power System Technology, 2024, 48(11): 4553-4567.) proposes a multi-agent collaborative optimization strategy for virtual power plants considering multiple uncertainties. This strategy quantifies the relationship between day-ahead market bidding returns and risks using CVaR theory, effectively coordinating the interests of virtual power plants and electric vehicle groups. However, this paper does not optimize the distribution of returns through game theory, making it difficult to guarantee fairness and potentially weakening the willingness of multiple stakeholders to participate in VPP collaboration in the long term. Summary of the Invention

[0007] To address the shortcomings or deficiencies in existing technologies, this invention provides a microgrid optimization operation strategy based on risk management and hybrid game theory. This strategy effectively balances the economic benefits of the microgrid and the user alliance, and achieves a fair distribution of cooperative benefits while protecting user privacy.

[0008] The technical solution adopted in this invention is as follows: The microgrid optimization operation strategy based on risk management and hybrid game theory includes the following steps: Step 1: A multi-entity system framework was established, including microgrids with multiple wind and solar users, shared energy storage, and distribution networks. Based on the conditional value at risk theory, a microgrid benefit model was analyzed to weigh economic benefits against risk value. Step 2: Based on the master-slave game, incorporate the decision-making idea of ​​moderate altruism, construct a master-slave altruistic game interaction model with the goal of maximizing the benefits of the upper-level microgrid and the lower-level user alliance respectively, and establish a multi-user power sharing cooperative game model based on asymmetric Nash bargaining theory. Step 3: The improved differential evolution algorithm is used to call Cplex to solve the master-slave altruistic game interaction model, and the cooperative game benefit distribution problem is solved through ADMM distributed solution to obtain the optimal solution of the multi-user power sharing cooperative game model, that is, the optimal microgrid optimization operation strategy.

[0009] In step 1, the establishment of the multi-agent system framework includes: This invention studies a microgrid with multiple wind and solar users, shared energy storage, and a distribution network, forming a multi-layered, multi-entity microgrid system framework. First, multiple users produce, consume, and store energy with the participation of shared energy storage, sharing energy within the region. Then, they engage in energy trading with the microgrid operator (MGO). The MGO, acting as the central coordinator, is responsible for formulating energy trading rules with users and coordinating energy interaction with the higher-level electricity market to ensure the safe, stable, and efficient operation of the microgrid. Through negotiation and cooperation, different entities promote flexible energy dispatch and trading, maximizing energy utilization efficiency and the economic benefits of microgrid operation.

[0010] The microgrid benefit model in step 1 includes: a: Microgrid operator benefit model: Microgrid operators (MGOs) set interactive electricity prices with users based on the grid's time-of-use pricing. They generate revenue through electricity purchases and sales with the grid and users, including revenue generated between the MGO and the grid, and between the MGO and users. The specific details are as follows: (1); In equation (1), Represents total revenue; For the first The probability of each scenario; For the first Benefits of MGO interacting with the power grid in various scenarios; For the first Benefits of MGO interaction with users in various scenarios; This indicates the total number of scenes. Among them, (2); (3); In the formula, , They are respectively The period-specific MGO purchases and sells electricity from the grid at the following prices; The first In each scenario During the period, MGO purchases and sells electrical power from the grid; , They are respectively Time period MGO from the Electricity purchase and sale price for individual users; , They were respectively in the second In each scenario Time period MGO from the Electricity purchased and sold by individual users; Indicates the first One user; Indicates time; Indicates a unit time interval.

[0011] To limit the market dominance and ensure the safe operation of MGOs, MGO decisions should meet the following constraints: (4); In equation (4), This represents the probability of each scenario.

[0012] (5); In equation (5), express Time period MGO to the first The lowest electricity price for individual users; Indicate Time period MGO to the first The highest electricity price for an individual user; express Time period MGO from the The lowest electricity price for individual users; express Time period MGO from the The highest electricity price for an individual user; , This represents the maximum average electricity purchase and sale price from MGO to users, used to constrain the range of upper-level decision variables; (6); In equation (6), Indicates in In the scenario, during the time period, MGO starts from the... The maximum power consumption that an individual user can purchase; Indicates in In the first scenario, during the time period, MGO directs to the first The maximum power output for an individual user's electricity sales.

[0013] (7); Equation (4) is the scenario probability equality constraint, Equation (5) is the MGO electricity purchase and sale price inequality constraint, Equation (6) is the power transmission constraint between MGO and users, and Equation (7) is the MGO power balance constraint.

[0014] The upstream power grid has strong energy regulation capabilities and coordinates the energy balance of wind and solar users under the MGO (Maintenance, Development, and Transportation) framework. However, it is constrained by the capacity of the power interconnection lines between them, resulting in the following limitations: (8); In equation (8), This is the maximum permissible transmission power of the tie line between the upstream power grid and the MGO; The first In each scenario The time period MGO represents the 0 / 1 variables of the power purchase and sale status to the upper-level power grid.

[0015] b: Considering the microgrid benefit model of CvaR: Conditional Value at Risk (CVaR) is a risk measurement model that refers to the risk level under normal market conditions and a certain confidence level. The following steps are performed to calculate the conditional expected value of losses exceeding VaR within a given time period. Considering CVaR, the MGO benefit-maximizing model described in a) above is transformed into a cost-minimizing model: (9); In equation (9), This represents the total cost of the microgrid benefit model; is the risk preference coefficient, representing an investor's attitude towards risk, and its value ranges from [0,1]. The higher the value, the more risk-averse MGO is; to obtain higher returns, MGO can choose lower values. Lowering expected costs, conversely, a more conservative approach to MGO (Management Goals) is more likely to favor larger costs. Increase the weighting of risk aversion; It represents the conditional risk value.

[0016] The CVaR model established to measure the cost risk caused by uncertainty is as follows: (10); In equation (10), Value at risk; The value at which the MGO cost exceeds VaR; for ease of calculation, it is relaxed to the following constraint: (11); In equation (11), This indicates the price at which MGO purchases electricity from users. This indicates the price at which MGO sells electricity to users; Indicates the first In each scenario Time period The amount of electricity sold by each user to the grid; Indicates the first In each scenario Time period The power that each user purchases from the grid.

[0017] c: User benefit model: Wind and solar users in the underlying shared energy storage service aim to minimize their own operating costs, including interaction costs with MGO, shared energy storage, and other users, as well as operation and maintenance costs and penalty costs; the cost optimization model is described as follows: (12); (13); In the formula, For the first Operating costs per user; , , , , They were respectively in the second In the scenario, the first The costs of interaction between individual users and MGO, the costs of interaction with shared energy storage systems, the costs of interaction with other users, the costs of wind and solar power operation and maintenance, and the costs of penalties; Indicates the first In the scenario, the first The utility of an individual user; for Time-sharing energy storage charging and discharging service fee; , The first In each scenario Time period The charging and discharging power of energy storage leased by individual users; For the first The user and the first Between users Electricity prices during specific time periods; For the first In the scenario, the first The user and the first Between users The trading volume during the time period; For the first In the scenario, the first For individual users, the marginal cost of power generation of wind and solar generator sets can be approximated as 0 in actual operation. Therefore, this invention only considers the operation and maintenance costs during the operation phase.

[0018] , , These are the parameters for the user utility function; For the first In each scenario Time period The actual electrical load of each user; Indicates the first In the scenario, the first Wind power operation and maintenance costs for individual users; Indicates the first In the scenario, the first The cost of penalty for each user's failure to load; The unit power generation cost of wind turbines and The power generation capacity of the wind turbine at any given time; , The unit power generation cost of photovoltaic units and Power generation of photovoltaic units at all times They were respectively in the second In the scenario, the first The cost of wind and solar power curtailment and the cost of load shedding for individual users; , These are the unit penalty cost for load loss and the unit penalty cost for wind and solar power curtailment, respectively. For users to operate safely and reasonably with the participation of shared energy storage, energy storage-related constraints need to be taken into account, including charging and discharging power and energy storage state of charge continuity constraints: (13); (14); (15); (16); (17); In the formula: , The first Energy storage in various scenarios Maximum charging and discharging power during the period; The first In the scenario, the first individual users Energy storage charging and discharging status during a given period; and These refer to the energy storage charging and discharging efficiencies, respectively. Rated capacity; Self-discharge rate; The unit is the time interval for scheduling; Indicates the rated power of the energy storage; Indicates the maximum state of charge of the stored energy; This represents the minimum state of charge of energy storage; Indicates energy storage in the first In each scenario State of charge during a given time period.

[0019] Indicates the first In the scenario, the first individual users Energy storage charging power during a given time period; The representation of the first In the scenario, the first individual users Energy storage discharge power during a given time period; Indicates the first In each scenario State of charge of energy storage during a given time period.

[0020] To ensure a normal energy storage supply at the beginning of each scenario, the initial capacity is set to be equal to the end-of-day capacity, i.e., the initial state of charge. Equal to the end-of-day state of charge The formula is as follows: (18); To ensure the normal operation of the transaction, the energy interaction between users needs to consider power constraints and power balance, including the maximum power constraint of the transmission line, the constraint that the sum of the output power of the users is equal to the sum of the input power of the other users, and the power balance constraint between the two parties in the transaction, as shown in the following equation (19): (19); In equation (19), Indicates the first In the scenario, the first The user and the first Between users The trading volume during the time period; Indicates the relationship between users Maximum transaction volume during the time period; This represents the total number of users. To avoid energy grid collapse, this invention uses the Load Deficiency Rate (LPSP) and Energy Spillover Rate (SPSP) to represent power supply reliability and energy waste rate, respectively. A smaller LPSP value indicates a more stable system, and a smaller SPSP value indicates less wind and solar power curtailment. The expressions are as follows: (20); (twenty one); In the formula, Indicates the first In the scenario, the first The load power shortage rate of individual users; Indicates the first In the scenario, the first Energy overflow ratio per user; , They represent the first In each scenario Time of the first Individual user load power shortage and wasted wind and solar power; For the first In each scenario Time of the first The load requirements of each user; This represents the maximum allowable power shortage rate for the load. The maximum permissible rate of energy waste; express The power generation capacity of the photovoltaic unit at any given time; express The power generation capacity of the wind turbine at any given time.

[0021] In addition, the power balance constraint should also be satisfied: (twenty two); (twenty three); In the formula, express The power generation capacity of the photovoltaic unit at any given time; express The power generation capacity of the wind turbine at any given time; The first In each scenario Time of the first Power shortage or power surplus for individual users. The first In each scenario Time of the first The system's power deficit and excess power are for individual users. Indicates the first In the scenario, the first The user and the first Between users Trading volume during a given period; Represented as the first In each scenario Time of the first The actual load of each user.

[0022] To avoid the unreasonable phenomenon of simultaneous energy shortages and surpluses leading to wind and solar power curtailment and load shedding, the following constraints are added: (twenty four).

[0023] In step 2, 2.1: The master-slave altruistic game interaction model of the microgrid system includes: There is a conflict of interest between the MGO and the users, and their decisions have a sequential order. Therefore, a master-slave game model can be constructed between the MGO and the users. Considering that traditional Stackelberg game models are usually based on the assumption of perfect rationality, emphasizing the leader's unilateral decision-making dominance over followers, but in reality, purely self-interested game outcomes suffer from low social efficiency, the master-slave game requires a slight altruistic element to increase the fairness and coordination of transactions compared to other games. To establish a long-term stable cooperative relationship with followers and maintain the leader's prestige and influence, the leader should appropriately consider the followers' interests and make reasonable concessions to enhance their participation and thus consolidate their leadership position. Therefore, this invention integrates a moderately altruistic decision-making approach into the master-slave game model to reflect the symbiotic relationship between layers, achieving maximum benefit and minimum risk. Thus, the microgrid benefit model considering CvaR in step 1b) is reformulated as follows: (25); In equation (25), This represents the total cost of the microgrid benefit model; This represents the risk preference coefficient; Indicates the first Benefits of MGO interacting with the power grid in this scenario; Indicates the first Benefits of MGO interaction with users in specific scenarios; For wind and solar power users' operating costs; This is the altruistic ratio coefficient.

[0024] By finding a slightly altruistic equilibrium point in the master-slave game, we can simultaneously consider the multiple objectives of MGO and users, achieving a more coordinated decision outcome. The master-slave altruistic game interaction model can be represented as: (26); In equation (26), This represents a master-servant altruistic game interaction model; Represents the set of participants in a game; This represents the set of strategies for purchasing electricity from users within a single day; This represents the set of strategies for pricing electricity to users within a single day; This indicates the amount of electricity a user purchases or sells from MGO within one day; This indicates the charging and discharging capacity of the leased energy storage. This indicates the amount of electricity consumed through user interactions within a single day. This represents the cost for microgrid operators; This represents the user's cost.

[0025] The above game theory model contains three elements: participants, strategies, and utility, specifically represented as follows: 1) Participants: MGO and the user alliance are the two participants in this game.

[0026] 2) Strategy: The leader's strategy These are sets of strategies for purchasing and selling electricity to users within a single day. Follower strategies. These represent the electricity purchased or sold by users to MGO within a day, the charging and discharging of leased energy storage, and the electricity exchanged between users.

[0027] 3) Utility: The utility of each participant is the objective function defined above.

[0028] When the strategies chosen by the agent and the follower complement each other and they have no incentive to change their strategies, both the agent and the follower achieve maximum utility. This means that under the current strategies, it is impossible to obtain higher utility by changing the strategies, thus reaching a Stackelberg equilibrium. Must meet: (27); In equation (27), This represents the total cost of the microgrid efficiency model under the Stackelberg game; This represents the price at which the MGO sells electricity to users under the Stackelberg game; This represents the price at which the MGO purchases electricity from users under the Stackelberg game; This represents the amount of electricity that users purchase or sell to the MGO under the Stackelberg game.

[0029] This represents the total cost of the microgrid benefit model; This indicates the price at which MGO sells electricity to users; This indicates the price at which MGO purchases electricity from users.

[0030] This represents the total cost of the user benefit model under the Stackelberg game; This represents the charging and discharging capacity of leased energy storage under the Stackelberg game; This represents the amount of electricity exchanged between users under the Stackelberg game.

[0031] This represents the total cost of the user benefit model; This indicates the charging and discharging capacity of the leased energy storage. This indicates the amount of electricity used in interactions between users.

[0032] 2.2: Multi-user energy sharing cooperative game model: When multiple users directly trade electricity with an MGO (Multi-User Group), each user's interests are harmed because the MGO's electricity sales price is higher than its purchase price. However, if multiple users can cooperate, complementing their respective supply and demand, and trading using an intermediate electricity price, the overall revenue can be significantly improved. Therefore, this invention constructs an asymmetric Nash bargaining cooperative game model based on the cooperative relationship of lower-level users, which is a multi-user electricity sharing cooperative game model.

[0033] The asymmetric Nash bargaining cooperative game model satisfies both symmetry and Pareto optimality, as shown in the following equation. The solution that maximizes the Nash product is the equilibrium solution of the Nash bargaining game problem. (28); In equation (28), For the benefit of the negotiating party, The benefits before the main players participate in cooperative game theory, i.e., the point at which negotiations break down; Indicates the first One user; This indicates the total number of users; This indicates product calculation.

[0034] The asymmetric Nash bargaining cooperative game model is a multivariate coupled nonconvex nonlinear problem. To facilitate the solution of the model, this invention transforms the asymmetric Nash bargaining cooperative game model into two convex subproblems: The subproblem of minimizing the cost of the cooperative alliance (P1) and the subproblem of distributing the benefits (P2) are solved sequentially. After cooperation, the interaction cost between users is zero. Therefore, the cost optimization model for lower-level followers described in the microgrid benefit model is transformed into the P1 subproblem.

[0035] P1: Minimize operating costs: (29); In equation (29), This represents the total cost of the microgrid benefit model; Indicates the first The probability of each scenario; Indicates the first In the scenario, the first The interaction cost between each user and MGO; Indicates the first In the scenario, the first The cost of interaction between an individual user and a shared energy storage system; Represented as the first In the scenario, the first The utility of an individual user; This indicates the operation and maintenance costs of wind and solar power. This indicates the cost of punishment.

[0036] P2: Bargaining and profit distribution issues: (30); In equation (30), Indicates the first In the scenario, the first The cost of each user; Indicates the first In the scenario, the first The interaction cost between each user and MGO; Indicates the first In the scenario, the first The cost of interaction between an individual user and a shared energy storage system; Indicates the first In the scenario, the first The cost of interaction between each user and other users; Represented as the first In the scenario, the first The utility of an individual user; Indicates the first In the scenario, the first The maintenance and operation costs of wind and solar power for individual users; Indicates the first In the scenario, the first The cost of punishment for each user; Indicates the first The bargaining power of individual users; Since the natural logarithm is a strictly monotonically increasing convex function, taking the logarithm of the above equation yields the following result.

[0037] (31); In equation (31), Indicates the first The bargaining power of each user varies depending on their contribution in different scenarios. Users with high demand contribute less to the overall interests of the alliance, thus their bargaining power decreases; users who provide more energy contribute more to the overall interests of the alliance, thus their bargaining power increases accordingly. Therefore, to achieve a fair and reasonable distribution of benefits, this invention measures the bargaining power of a subject based on the amount of energy provided or obtained by the subject on all typical days and the changes in costs before and after cooperation. As shown in the following formula (32): (31); (33); In the formula, Indicates the first In the scenario, the first The user and the first individual users Interactive power consumption during a given time period; The maximum total electrical energy supplied to all users; This represents the maximum total electrical energy received by all users. , The first In the scenario, the first The interaction cost between users and MGO before and after collaboration.

[0038] To ensure users' willingness to cooperate, the total cost of cooperation in the cooperative game must be less than the cost before the game. Furthermore, the total payment from all parties involved in the transaction must equal the total revenue to guarantee the smooth operation of the transaction. The corresponding constraints are as follows: (34); (35).

[0039] In step 3: 3.1: Improved Differential Evolution Algorithm: Differential Evolution (DE) is a biomimetic intelligent algorithm similar to genetic algorithms. It is conceptually simple, easy to implement, less sensitive to parameters, converges quickly to a better solution, and does not require the continuity or differentiability of the objective function, making it widely applicable. Despite its many advantages, DE can still encounter problems such as slow convergence, search stagnation, and poor stability when dealing with highly complex problems. This is because a single mutation strategy struggles to dynamically adapt to changes in population size at different stages. Combining multiple mutation strategies allows for flexible switching based on the population evolution stage, balancing search capability and convergence speed.

[0040] Therefore, this invention improves the differential evolution (DE) algorithm through an adaptive combinatorial mutation strategy, as follows: (36); In equation (36), For the number of iterations The weight of the mutation strategy at that time; Indicates the number of iterations. The weight of the mutation strategy at that time; The total change is adjusted for weights. This represents the maximum value of the mutation strategy weight; This represents the minimum value of the mutation strategy weight; in this invention, the weight is adjusted from 0.8 to 0.2. As the asymptotic coefficient, this invention takes , Indicates a time interval; Indicates time.

[0041] Indicates the first Generation, First The variation vector of each individual; The basis vectors are individuals randomly selected from the population. This represents an individual randomly selected from the population, and then a mutation vector is generated using "two difference variables"; This represents a randomly selected individual, and the mutation vector is generated by combining the best individual in the population with one difference variable. This means selecting the best individual from the population and then using "two difference variables" to generate a mutation vector.

[0042] By smoothly adjusting the weights, a gradual and smooth transition is achieved in the selection of mutation strategies between adjacent stages. The mutation strategies are defined as follows: (37); In equation (37), It belongs to random integer, Indicates population size, and ; Indicates the first Generation, First The variation vector of each individual; Indicates the first Generation, First Individual; Indicates the first Generation, First Each individual; Indicates the first Generation, First Individual; Indicates the first Generation, First Individual; Indicates the first Generation, First Individual; Indicates the first Generation, First Individual; Indicates the first The best individual in the generation.

[0043] Variants The algorithm controls the magnitude of the difference between two individuals. If this difference is too large, the algorithm tends to perform a more random search, enhancing its global search capability but slowing down the convergence speed. A value much greater than 1 may cause the population to diverge and fail to evolve effectively; a value too small will weaken the mutation effect, resulting in insufficient exploration and making the population prone to getting trapped in local optima, increasing the likelihood of the algorithm prematurely converging. Therefore, this invention designs an adaptive mutation factor. The mutation factor is dynamically adjusted based on both the algorithm iteration progress and individual fitness mechanisms to balance global search and convergence speed. This is illustrated in equation (38) below: (38); (39); In the formula, For population Variable factors; These are the upper and lower limits of the variable factor, respectively. Take 0.2; , These are the current iteration count and the maximum iteration count, respectively. , , population The fitness value, the average fitness value of all current populations, and the optimal fitness value.

[0044] 3.2: Model Solution Process: a) Solution process for the master-slave game model: Considering the nonlinear characteristics of the upper-level MGO pricing decision, an improved difference decomposition is used. The lower level solves the overall energy scheduling problem after user cooperation using Cplex. This fully leverages the advantages of the improved DE algorithm's global search and the efficiency of Cplex in solving linear and integer programming problems, achieving a superior master-slave game equilibrium solution compared to a single strategy. The specific steps are as follows: Step 1. Parameter initialization: Population size The variance is 150. and initial value of cross factor Maximum number of iterations The taboo list length is 500. Maximum number of domains ; Step 2. The population is initialized to generate feasible solutions for the upper-level MGO decision variables. Cplex is called to solve the subproblem P1 of the lower-level user alliance. The fitness value of the upper-level population is calculated based on the policy feedback from the lower level. All individuals are evaluated to find the current optimal solution for both the upper and lower levels. ; Step 3. The population is evolved through mutation and crossover operations. Then, Cplex is called to solve P1 and the population fitness is calculated. Individuals are then re-evaluated. If a new solution is better than the optimal solution, the solution is accepted and the optimal solutions in the upper and lower layers are updated. .

[0045] Step 4. Determine whether the convergence criterion is met. or number of iterations If the algorithm fails to converge, it terminates, either by finding an equilibrium solution to the master-slave game problem or by failing to converge. Otherwise, it returns... Step 3 .

[0046] b) Solution process for cooperative game theory model: By solving subproblem P1, the optimal benefit for each user can be obtained. The collection of interactive power between the main body and the subject .because This indicates that there are multiple couplings between users, which can be decoupled into a dual-coupling constraint of electricity price that satisfies the expectations of both parties: The consensus is reached when one party's purchase price equals the other party's selling price; then, ADMM is used to solve the subproblem P2 in a distributed manner. ADMM effectively solves the complex interest allocation problem in cooperative game theory through decomposition, penalty, and alternating iteration techniques. This invention is based on Mosek to solve the second-order convex optimization problem of lower-level interest allocation. The specific steps are as follows: Step 1: First, calculate the Nash bargaining power value of each user after cooperation. ; Step 2: To construct the augmented Lagrangian function of subproblem P2 by adding a penalty term: (40); (41); In the formula, For the first The objective function for each user; Indicates the first The bargaining power of individual users; This represents the user's own cost; This is the optimal solution for the cooperative alliance; For the scene Next The user and the Lagrange multipliers between users; As a penalty factor; Indicates the first The user purchased the first Electricity price for individual users; Indicates the first The user purchased the first Electricity price for individual users; This represents the interaction cost between two users; Indicates the first In the scenario, the first Cost of interaction between individual users and MGO; Indicates the first In the scenario, the first The cost of interaction between an individual user and a shared energy storage system; Indicates the first In the scenario, the first The utility of an individual user; Indicates the first In the scenario, the first The operation and maintenance cost per user; Indicates the first In the scenario, the first The cost of punishment for each user.

[0047] To ensure priority for energy exchange among the cooperating entities, the negotiated price must be higher than the MGO's electricity purchase price but lower than the MGO's electricity sales price, i.e.: (42); In equation (42), This indicates the electricity price paid by the user to MGO. This indicates the price at which MGO sells electricity to users.

[0048] To ensure users' willingness to cooperate, the total cost of cooperation in the cooperative game is less than the cost before the game, that is: (43); Step 3: Initialization parameters: interactive electricity price, Lagrange multipliers, penalty parameter Number of iterations Maximum number of iterations Convergence criterion factor ; Step 4: Each user solves their local objective function to obtain their local optimal pricing strategy, and the only interaction between users is the exchange of pricing strategy information to update the decision variables. The user first based on the first Update local decisions based on individual user strategies. Then the first The user received the first Decision information of individual users To update local decisions ; (44); In equation (44), Representing a scene Next The user and the Lagrange multipliers between users; Indicates the first At the nth iteration number, the th The user and the Lagrange multipliers for electricity price constraints between individual users; Indicates the first At the nth iteration number, the th The user purchased the first Electricity price for individual users; Also indicates a scene Next The user and the Lagrange multipliers between users; Indicates the first At the nth iteration number, the th The user purchased the first Electricity price for individual users; Indicates the first At the nth iteration number, the th The user purchased the first Electricity price per user.

[0049] Step 5: Update the Lagrange multipliers: (45); In equation (45), Indicates the first At the nth iteration number, the th In the first scenario, representing the first... The user purchased the first Lagrange multipliers for each user; Indicates the first At the nth iteration number, the th In the first scenario, the... The user and the Lagrange multipliers between users; Indicates the first At the number of iterations, with the penalty factor User transaction behavior.

[0050] Step 6: Determine if the algorithm meets the convergence criterion , This represents the absolute value of the difference in electricity prices between users.

[0051] If yes, the iteration terminates, and the optimal Nash equilibrium solution is obtained; otherwise, it is determined whether the condition is met. , Indicates the maximum number of iterations; This indicates the maximum number of iterations.

[0052] If so, the algorithm does not converge; otherwise, update the number of iterations. ,return Step 4.

[0053] This invention provides a microgrid optimization operation strategy based on risk management and hybrid game theory, with the following technical effects: 1) In step 1 of this invention: Because the power output and load distribution of wind and solar renewable energy are highly random, microgrids may have potential operational risks. To address this, this paper introduces conditional value at risk into the microgrid benefit model. Its core function is to resolve the fundamental contradiction between the randomness and load volatility of wind and solar renewable energy and the balance between microgrid benefits and risks—avoiding both the pursuit of economic gains at the expense of extreme risks and overly conservative design leading to benefit loss, ultimately achieving controllable risks, stable benefits, and scientific decision-making in microgrid operation.

[0054] The following details its specific advantages from three dimensions: risk quantification, benefit optimization, and decision support: a) Risk quantification: The power output of wind and solar power generation is affected by random fluctuations in sunlight and wind speed, and load also experiences sudden fluctuations. These uncertainties can easily trigger extreme risk events. Traditional risk measurement indicators can only reflect the degree of fluctuation and cannot focus on extreme losses; while the core advantage of CVaR is that it quantifies the average loss under the worst-case scenario, accurately capturing the tail risks of microgrid operation. Specific advantages include: ①CVaR focuses on extreme scenarios outside the confidence level by setting a pre-defined confidence level and calculates the average loss value in these scenarios.

[0055] ② Power or load fluctuations in microgrids are not all risks, but traditional indicators tend to include all fluctuations in the risk category, leading to overly conservative approaches. CVaR, on the other hand, focuses on extreme fluctuations on the loss side, eliminating the interference of fluctuations on the revenue side, and is more in line with the actual definition of risk for microgrids.

[0056] b) Optimization of efficiency: The core objective of microgrid benefit models is to maximize economic returns, but high returns are often accompanied by high risks. The introduction of CVaR shifts the model from simply maximizing benefits to optimizing a benefit-risk balance, with specific advantages including: ① In the benefit model, the risk level of microgrids can be forcibly constrained by setting an upper limit for CVaR.

[0057] ② Calculate the "benefit cost required to reduce risk weight by one unit or the risk increase required to improve benefit by one unit" using CVaR. This quantitative result provides decision-makers with a clear basis—if the microgrid has high requirements for power supply reliability, "high cost and low risk" is acceptable; if it is a general park microgrid, "moderate risk and high return" can be selected.

[0058] c) Decision support: The randomness of microgrids is not fixed; CVaR's dynamic computing capabilities can support flexible decision-making in different scenarios. Specific advantages include: ① In microgrid planning, CVaR can calculate extreme risks for different climate and load scenarios, ensuring that the configuration scheme can still operate stably under the "worst scenario".

[0059] ② In real-time microgrid scheduling, CVaR can dynamically update extreme risk values ​​based on the latest wind and solar power or load forecast data.

[0060] 2) In step 2 of this invention, in the scenario of power interaction between microgrids and users, traditional master-slave game theory often focuses on "maximizing the profit of the upper-level microgrid" and "minimizing the cost of the lower-level users," which can easily lead to problems such as imbalanced resource allocation and low user participation. However, by incorporating a moderate altruistic orientation, constructing a "master-slave altruistic game interaction model," and combining it with asymmetric Nash bargaining theory to establish a multi-user power sharing cooperative game model, the essence is to modify the game objective by introducing "altruistic thinking," optimize the distribution of benefits through "cooperative bargaining," and ultimately achieve a unity of "individual rationality" and "collective rationality." Its core advantages can be elaborated from aspects such as goal synergy, fairness of benefit distribution, system efficiency, user participation, and robustness, as specifically analyzed below: a) Advantages of the master-servant altruistic game model: In traditional master-slave game theory, the relationship between microgrids and users is a one-way "manager-managed" dynamic. Users lack trust due to information asymmetry and perceived loss of benefits, resulting in generally low willingness to participate in energy sharing. The specific advantages of incorporating an altruistic orientation into the model are as follows: ① In traditional master-slave game theory, the goal of the upper-level microgrid (master) is usually "maximizing electricity sales profit," while the goal of the lower-level user alliance (slave) is "minimizing electricity purchase cost." These two goals are directly opposed—if the microgrid increases profits by raising electricity prices, it inevitably leads to increased user costs, and vice versa, creating a zero-sum dilemma where "one party benefits at the expense of the other." By incorporating the "moderate altruistic orientation," the objective functions of both the master and slave are reconstructed as "maximizing their own benefits + moderately considering the benefits of the other." This "altruistic-self" collaborative goal design makes the benefits of the master and slave no longer completely opposed, but rather forms a positive correlation of "mutual benefit," ultimately achieving a Pareto optimal solution (i.e., no other solution can improve the benefits of one party without harming the other), significantly superior to the "suboptimal solution" of traditional master-slave game theory.

[0061] ② Driven by altruism, microgrids will guide users to use energy during off-peak hours through "price signals" or "subsidy incentives," and users will also proactively adjust their energy consumption habits considering the peak-shaving pressure on the microgrid. Specifically, the altruistic goal of microgrids requires them to disclose the basis for electricity pricing and the calculation method for shared revenue, so that users can clearly understand the source of their own benefits and reduce concerns about being exploited. The master-slave game is no longer a one-way decision-making process where the microgrid sets the rules and the user passively accepts them, but a two-way interaction "from the microgrid proposing an initial plan to the user alliance providing feedback on their needs through negotiation, and then to the microgrid adjusting the plan."

[0062] ③ In addition, the introduction of altruistic orientation will significantly enhance the robustness of the system. Specifically, when photovoltaic output drops sharply, the altruistic goal of the microgrid prevents it from experiencing extreme price increases, and instead ensures stable user costs by moderately reducing its own profits.

[0063] b) Advantages of the multi-user energy sharing cooperative game model based on asymmetric bargaining theory: The core pain point of multi-user power sharing is the unfair distribution of benefits: if the sharing benefits are distributed equally based on "electricity consumption / power generation", it will dampen the enthusiasm of users who contribute highly; if the distribution is completely dominated by the microgrid, it will lead to the squeezing of user interests and ultimately disintegrate the sharing alliance.

[0064] The introduction of asymmetric Nash bargaining theory precisely solves this problem, and its advantages are reflected in two aspects: ①The core of asymmetric Nash bargaining is to reflect the actual bargaining power of each party through "bargaining power" (which is determined by the user's contribution in this invention).

[0065] ② The solution of asymmetric Nash bargaining satisfies the individual rationality constraint: that is, the benefit that each participant gains through sharing must be higher than the benefit they would have gained if they did not participate in sharing.

[0066] This allocation method avoids the inefficiency of egalitarianism and the injustice of unilateral dominance, ensuring that each participant's benefits match their contribution and needs, thus adhering to the principle of "fairness." Furthermore, this "participation equals benefit" mechanism ensures that each user has a continuous incentive to participate in sharing, preventing adverse selection in the sharing alliance and significantly improving its stability.

[0067] 3) In step 3 of the present invention: a) Advantages of using the improved differential evolution algorithm to solve the master-slave altruistic game model using Cplex. ① Chaotic initialization of the population: Traditional random initialization methods lead to uneven distribution of individuals in the population, affecting the algorithm's search efficiency and convergence performance. Chaotic maps, however, possess both randomness and determinism, exhibiting good random distribution characteristics in the solution space. Considering that Tent maps offer uniform distribution, fast computation, and ease of controlling entry into a chaotic state, this paper uses Tent maps to initialize the population, increasing population diversity, improving the algorithm's global search capability, thereby accelerating the convergence process and reducing the risk of search stagnation.

[0068] ② Adaptive combination variation: A single mutation strategy is difficult to dynamically adapt to changes in population size at different stages, while a combination of multiple mutation strategies can flexibly switch strategies according to the stage of population evolution, balancing search capability and convergence speed.

[0069] ③ Adaptive Crossover: By comprehensively considering the breadth and depth of the algorithm through adaptive crossover factors, both population diversity and optimal solutions are ensured, thereby significantly improving the algorithm efficiency.

[0070] ④ Tabu search improves difference: Tabu Search (TS) is a heuristic algorithm for solving optimization problems. It improves upon local search by maintaining an external tabu list while preserving local optima, allowing the algorithm to escape local optima. The memory function of the Derivative Algorithm (DE) and the mechanism of TS complement each other, jointly improving search efficiency: the former accelerates convergence by preserving and inheriting superior genes; the latter strengthens global search capabilities by heuristically accepting inferior solutions. The synergy of the two algorithms effectively balances global and local optimization, accelerating the solution process. The DE algorithm, through evolutionary operations, can preserve and inherit valuable information from the population. Based on this, the TS algorithm can directly search for and recombine individuals containing valuable gene information, thus avoiding repetitive and ineffective operations on similar populations. Furthermore, the TS algorithm itself possesses flexible and adaptable memory capabilities, allowing it to accept inferior solutions to escape local optima.

[0071] b) Advantages of the ADMM algorithm for solving game theory models: ①ADMM's distributed architecture: The essence of cooperative game theory is that multiple independent participants achieve "collective optimality" through collaborative decision-making. The core logic of Active Distributed Game Theory (ADMM) is to decompose the global optimization problem into local subproblems for each participant, and then achieve coordination through minimal global information exchange. This perfectly matches this requirement. Specifically, ADMM introduces dual variables (Lagrange multipliers) and consistency constraints to decompose the global objective function of cooperative game theory into local subproblems that each participant can solve independently. Furthermore, each participant only needs to transmit a small amount of information to neighboring nodes in each iteration, without uploading the original data, significantly reducing the communication overhead of distributed systems, making it particularly suitable for geographically dispersed game scenarios.

[0072] ②Advantages of ADMM in handling large-scale problems with multiple constraints: The essence of cooperative game theory is that multiple independent participants achieve collective optimality through collaborative decision-making. The core logic of ADMM is to decompose the global optimization problem into local subproblems of each subject and then achieve coordination through a small amount of global information exchange, which perfectly matches this requirement. Specifically, the decomposed local subproblems usually have lower dimensions and are mostly convex problems, which can be solved quickly through simple analytical solutions or lightweight iterations, avoiding the high complexity of global optimization.

[0073] Furthermore, cooperative game theory often involves two types of key constraints: local constraints for participants and global collaborative constraints. ADMM, through its inherent adaptability to constraints via the "multiplier method," can efficiently handle these complex constraints. Specifically, by introducing dual multipliers, ADMM transforms global collaborative constraints into penalty terms for local subproblems. This eliminates the need to strictly satisfy global constraints in each iteration; instead, it iteratively approximates the constraints, avoiding the computational bottlenecks caused by strict constraints in traditional "projection methods."

[0074] ③ADMM has features to protect user privacy: In cooperative game theory, the core data of participants is often sensitive information. Traditional centralized algorithms need to collect the raw data of all participants, posing a serious risk of privacy leakage. ADMM, on the other hand, achieves privacy protection through local computation and limited information exchange. Specifically, each participant only needs to solve subproblems based on its own private data (such as cost parameters and local constraints), without uploading the raw data to the coordinator or other participants. Privacy protection reduces participants' concerns about collaboration, decreases game deadlocks caused by "unwillingness to share data," and improves the feasibility of cooperative game theory.

[0075] ④ The ADMM algorithm is robust and adaptable to dynamic game environments: Real-world cooperative game scenarios often exhibit a dynamic nature, and traditional distributed algorithms in such scenarios require re-initialization and iteration from scratch, resulting in extremely low efficiency. ADMM, however, possesses superior robustness. If participants are added or removed from a cooperative game, ADMM only needs to adjust the number of local subproblems and the information exchange objects of the coordinator, without needing to reconstruct the entire algorithm framework. The iteration process can be seamlessly integrated, reducing the cost of dynamic adjustments. Furthermore, when external disturbances occur, ADMM responds quickly to the disturbances through "rapid updates of dual multipliers," without needing to resolve the global problem. Attached Figure Description

[0076] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is the two-layer hybrid game model architecture proposed in this invention.

[0077] Figure 2 This invention sets up an example of the electricity purchase and sale pricing strategy formulated by MGO.

[0078] Figure 3(a) shows the power optimization results of the user cooperation alliance; Figure 3(b) shows the charging and discharging services provided by shared energy storage and the corresponding SOC optimization results.

[0079] Figure 4 This is a flowchart of the microgrid optimization operation strategy of the present invention. Detailed Implementation

[0080] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0081] This invention proposes a microgrid optimization operation strategy based on risk management and hybrid game theory. First, a multi-entity system framework is established, comprising a microgrid with multiple wind and solar users, shared energy storage, and a distribution network. A microgrid benefit model is then formulated based on Conditional Value at Risk (CVaR) theory to balance economic benefits and risk value. Next, a moderately altruistic decision-making approach is incorporated into the master-slave game theory framework. This leads to the construction of master-slave altruistic game interaction models aiming to maximize the benefits of both the upper-level microgrid and the lower-level user alliance. Furthermore, a multi-user energy-sharing cooperative game model is established based on asymmetric Nash bargaining theory. Finally, an improved differential evolution algorithm is used to solve the master-slave game model using Cplex, and the cooperative game benefit allocation problem is solved using ADMM distributed algorithm to obtain the optimal solution to the game model, i.e., the optimal microgrid optimization operation strategy. The proposed strategy effectively balances the economic benefits of the microgrid and the user alliance, and achieves a fair distribution of cooperative benefits while protecting user privacy.

[0082] Figure 1This invention presents a two-layer hybrid game theory model architecture. Based on the competitive relationship between the MGO and users, and the cooperative relationship among users, a two-layer hybrid game theory model based on master-slave and cooperative game theory is constructed. The upper-layer MGO, as the leader in the master-slave game, aims to maximize its own benefits and sets the purchase and sale price of electricity based on time-of-use pricing and the lower-layer electricity purchase and sale demand. The lower-layer user cooperative alliance, as followers, aims to maximize the overall benefit of the alliance. Through the control center, it responds to the upper-layer pricing strategy to decide its own purchase and sale volume and the charging and discharging volume of shared energy storage, and coordinates the shared electricity among users. Through negotiation and cooperation, the leader and followers achieve resource sharing and optimized allocation between the upper-layer MGO and the lower-layer user alliance, while simultaneously meeting their respective energy needs, thereby achieving the goal of safe, stable, and efficient operation of the microgrid system.

[0083] Figure 2 This invention sets up a case study considering the altruistic leader MGO's electricity purchase and sale pricing strategy. From... Figure 2As can be seen, the proposed pricing strategy, while satisfying upper and lower limit constraints, achieves purchase and sale prices that fluctuate within the range of the grid's time-of-use pricing. Peak prices are observed from 10:00-14:00 and 18:00-20:00, while on-time prices are observed from 7:00-9:00 and 15:00-17:00. Prices at other times are close to off-time prices. Maintaining purchase and sale prices within the upper and lower limits set based on grid prices ensures the absolute profit of MGO leaders, and the sale price is always higher than the purchase price, preventing arbitrage by lower-level users. The sale price is lower than the upper limit during peak hours because high peak prices lead to strong load shifting intentions; to ensure their own profitability, MGOs tend to lower prices to encourage user purchases during this period. During off-peak hours, the sale price approaches the upper limit of the off-peak price because cooperation reduces the amount of electricity purchased, requiring upper-level MGOs to set higher prices to ensure their own profitability. Regarding the electricity purchase price, cooperation at the lower levels increases the wind and solar power absorption rate, reduces the amount of electricity users can feed into the grid, and decreases the arbitrage behavior of the MGO (Microgrid Organisation). Therefore, during off-peak hours when wind and solar power output is redundant, the MGO is willing to raise the electricity purchase price to encourage users to sell electricity during this period. It is worth noting that the electricity purchase and sale prices for users 1 and 2 are similar because their load distribution characteristics are similar after cooperation. However, user 3 still has a high electricity demand, so the microgrid prices slightly lower for user 3. Because this invention considers the interests of the lower levels, the electricity purchase and sale prices will not be too high or too low. When user 3's electricity demand is high between 7:00 and 16:00, the increase in the MGO's electricity sale price compared to the grid's electricity sale price is lower, thus ensuring that the interests of the lower levels are not excessively reduced, but rather slightly higher. When user 3's electricity demand is high between 1:00 and 8:00 AM and users 1 and 2's between 7:00 and 11:00 PM, the MGO (Moving Energy Purchase Price) should be higher than the grid purchase price to increase efficiency at the upper levels while simultaneously improving efficiency at the lower levels. Conversely, the MGO should be lower. In summary, the strategy proposed in this invention can encourage users to respond more actively to the MGO pricing strategy, increasing their incentive to consume energy and meet load demands, thereby avoiding large-scale wind and solar power curtailment and load shedding due to excessively high MGO pricing.

[0084] Figures 3(a) and 3(b) show the optimal scheduling scheme of the user cooperation alliance in the case of this invention. Based on the upper-level pricing results, the overall optimal scheduling scheme of the lower-level user alliance is obtained, as shown in Figures 3(a) and 3(b). The power optimization result of the user cooperation alliance is shown in Figure 3(a): positive values ​​in the figure represent users purchasing electricity from external entities, and negative values ​​represent users selling electricity to external entities. It can be clearly observed that when user 1 and user 2 have low load demand and high wind power output from 1:00 to 7:00, they sell a portion of their electricity to the MGO to generate revenue and store some excess wind power. During the peak electricity price period from 10:00 to 14:00, they release energy to compensate for load demand and avoid buying electricity at high prices. It is worth noting that for user 3, the microgrid sets a relatively favorable selling price from 1:00 to 8:00, so the alliance sells some energy through user 3 who is experiencing power shortages. During other times, users purchase electricity from the MGO to meet the electricity needs of each user at each time period.

[0085] Figure 3(b) illustrates the charging and discharging services provided by shared energy storage and the corresponding SOC optimization results. Users lease energy storage charging services during off-peak hours (1:00–6:00 and 23:00–24:00) and reach full charge by 7:00. During peak hours (10:00–13:00 and 18:00–19:00), users lease energy storage discharging services and reach near full discharge by 20:00. To meet energy storage constraints and maintain balance, users do not participate in energy storage leasing services during the periods 7:00–9:00 and 20:00–22:00, and the energy storage status remains unchanged. In summary, it can be seen that with the participation of shared energy storage, users' peak shaving and valley filling capabilities are significantly improved, and operating costs are reduced. Furthermore, from the perspective of user net load, it can be seen that energy storage effectively realizes the transfer of energy from surplus periods to shortage periods, greatly improving the absorption capacity of new energy sources.

[0086]

[0087]

[0088] Tables 1 and 2 present a comparative analysis of the benefit allocation strategies in the case studies of this invention. Table 1 shows that the asymmetric Nash bargaining proposed in this invention results in the lowest benefit for user 3 (whose contribution is the smallest), the highest share for user 2 (whose contribution is the largest), and the next highest share for user 1. The Shapley value allocation results show that each user achieved a positive benefit better than before cooperation, and the allocation was relatively fair. However, this method allocates benefits based on fixed parameters or scenarios, without considering the game process and dynamic strategy choices among participants. Such static allocation leads to inaccurate or unreasonable benefit allocation results in real-world situations and fails to adequately incentivize participants to actively cooperate and contribute. Furthermore, since Shapley allocation requires considering each participant's marginal contribution to all possible cooperation sets, the computational complexity increases exponentially with the number of cooperating users. Based on three users, the computation time for this invention with five users participating in the allocation was approximately 563 seconds, significantly highlighting this problem. Dynamic Nash bargaining effectively considers the game process and strategy choices among participants, better reflecting the interactive behavior and decision-making process in real-world situations, and does not require calculating all possible cooperation, effectively improving upon the aforementioned shortcomings. It is worth noting that users 1 and 3 gained greater benefits based on the Shapley distribution, while user 2 experienced a decrease. This is because the Nash bargaining process in dynamic allocation assumes that all participants have equal status and power, ignoring potential differences in status among participants. This can lead to unreasonable allocations, especially when market influence and contributions to the alliance differ. To address these issues, this invention employs asymmetric Nash bargaining based on contribution, ensuring that each user receives benefits proportional to their contribution to the alliance, achieving the fairest and most reasonable distribution. The changes in benefits before and after cooperation are shown in Table 2.

Claims

1. A microgrid optimization operation strategy based on risk management and hybrid game theory, characterized in that... Includes the following steps: Step 1: A multi-entity system framework was established, including microgrids with multiple wind and solar users, shared energy storage, and distribution networks. Based on the conditional value at risk theory, a microgrid benefit model was analyzed to weigh economic benefits against risk value. Step 2: Based on the master-slave game, incorporate the decision-making idea of ​​moderate altruism, construct a master-slave altruistic game interaction model with the goal of maximizing the benefits of the upper-level microgrid and the lower-level user alliance respectively, and establish a multi-user power sharing cooperative game model based on asymmetric Nash bargaining theory. Step 3: Use the improved differential evolution algorithm to solve the master-slave altruistic game interaction model, and use ADMM distributed solution to solve the cooperative game benefit distribution problem to obtain the optimal solution of the multi-user power sharing cooperative game model, that is, the optimal microgrid optimization operation strategy.

2. The microgrid optimization operation strategy based on risk management and hybrid game theory as described in claim 1, characterized in that: Step 1 includes a microgrid operator benefit model: Microgrid operators (MGOs) set interactive electricity prices with users based on the grid's time-of-use pricing. They generate revenue through electricity purchases and sales with the grid and users, including interactive revenue between the MGO and the grid, and between the MGO and users. The specific details are as follows: （1）； In equation (1), Represents total revenue; For the first The probability of each scenario; For the first Benefits of MGO interacting with the power grid in various scenarios; For the first Benefits of MGO interaction with users in various scenarios; This indicates the total number of scenes; among them, （2）； （3）； In the formula, , They are respectively The period-specific MGO purchases and sells electricity from the grid at the following prices; The first In each scenario During the period, MGO purchases and sells electrical power from the grid; , They are respectively Time period MGO from the Electricity purchase and sale price for individual users; , They were respectively in the second In each scenario Time period MGO from the Electricity purchased and sold by individual users; Indicates the first One user; Indicates time; Indicates a unit time interval.

3. The microgrid optimization operation strategy based on risk management and hybrid game theory as described in claim 2, characterized in that: To limit the market dominance and ensure the safe operation of MGOs, MGO decisions must meet the following constraints: （4）； In equation (4), Represents the probability of each scenario; （5）； In equation (5), express Time period MGO to the first The lowest electricity price for individual users; Indicate Time period MGO to the first The highest electricity price for an individual user; express Time period MGO from the The lowest electricity price for individual users; express Time period MGO from the The highest electricity price for an individual user; , This represents the maximum average electricity purchase and sale price from MGO to users, used to constrain the range of upper-level decision variables; （6）； In equation (6), Indicates in In the scenario, during the time period, MGO starts from the... The maximum power consumption that an individual user can purchase; Indicates in In the first scenario, during the time period, MGO directs to the first The maximum power output for electricity sold to a single user; （7）； Equation (4) is the scenario probability equality constraint, Equation (5) is the MGO electricity purchase and sale price inequality constraint, Equation (6) is the power transmission constraint between MGO and users, and Equation (7) is the MGO power balance constraint. The upstream power grid has strong energy regulation capabilities and coordinates the energy balance of wind and solar users under the MGO (Maintenance, Development, and Transportation) framework. However, it is constrained by the capacity of the power interconnection lines between them, resulting in the following limitations: （8）； In equation (8), This is the maximum permissible transmission power of the tie line between the upstream power grid and the MGO; The first In each scenario The time period MGO represents the 0 / 1 variables of the power purchase and sale status to the upper-level power grid.

4. The microgrid optimization operation strategy based on risk management and hybrid game theory according to claim 3, characterized in that: Step 1 also includes a microgrid benefit model that considers CvaR: Conditional Value at Risk (CVaR) is a risk measurement model that refers to the risk level under normal market conditions and a certain confidence level. The following steps are taken: The conditional expected value of loss exceeding VaR within a given time period is calculated; considering CVaR, the MGO benefit-maximizing model is transformed into a cost-minimizing model. （9）； In equation (9), This represents the total cost of the microgrid benefit model; is the risk preference coefficient, representing an investor's attitude towards risk, and its value ranges from [0,1]. The higher the value, the more risk-averse MGO is; to obtain higher returns, MGO can choose lower values. Lowering expected costs, conversely, a more conservative approach to MGO (Management Goals) is more likely to favor larger costs. Increase the weighting of risk aversion; Represents conditional risk value; To measure the cost risk caused by uncertainty, the CVaR model is established as follows: （10）； In equation (10), Value at risk; The value at which the MGO cost exceeds VaR; for ease of calculation, it is relaxed to the following constraint: （11）； In equation (11), This indicates the price at which MGO purchases electricity from users. This indicates the price at which MGO sells electricity to users; Indicates the first In each scenario Time period The amount of electricity sold by each user to the grid; Indicates the first In each scenario Time period The power that each user purchases from the grid.

5. The microgrid optimization operation strategy based on risk management and hybrid game theory according to claim 4, characterized in that: Step 1 also includes a user benefit model: Wind and solar users in the underlying shared energy storage service aim to minimize their own operating costs, including interaction costs with MGO, shared energy storage, and other users, as well as operation and maintenance costs and penalty costs; the cost optimization model is described as follows: （12）； （13）； In the formula, For the first Operating costs per user; , , , , They were respectively in the second In the scenario, the first The costs of interaction between individual users and MGO, the costs of interaction with shared energy storage systems, the costs of interaction with other users, the costs of wind and solar power operation and maintenance, and the costs of penalties; Indicates the first In the scenario, the first The utility of an individual user; for Time-sharing energy storage charging and discharging service fee; , The first In each scenario Time period The charging and discharging power of energy storage leased by individual users; For the first The user and the first Between users Electricity prices during specific time periods; For the first In the scenario, the first The user and the first Between users Trading volume during a given period; For the first In the scenario, the first For individual users, the marginal cost of wind and solar power generation can be approximated as 0 in actual operation. , , These are the parameters for the user utility function; For the first In each scenario Time period The actual electrical load of each user; Indicates the first In the scenario, the first Wind power operation and maintenance costs for individual users; Indicates the first In the scenario, the first The cost of penalty for each user's failure to load; The unit power generation cost of wind turbines and The power generation capacity of the wind turbine at any given time; , The unit power generation cost of photovoltaic units and Power generation of photovoltaic units at all times They were respectively in the second In the scenario, the first The cost of wind and solar power curtailment and the cost of load shedding for each user; , These represent the unit penalty cost for load shedding and the unit penalty cost for wind and solar power curtailment, respectively.

6. The microgrid optimization operation strategy based on risk management and hybrid game theory as described in claim 5, characterized in that: The safe and reasonable operation of users with shared energy storage participation will take into account energy storage-related constraints, including charging and discharging power and energy storage state of charge continuity constraints: （13）； （14）； （15）； （16）； （17）； In the formula: , The first Energy storage in various scenarios Maximum charging and discharging power during the period; The first In the scenario, the first individual users Energy storage charging and discharging status during a given period; and These refer to the energy storage charging and discharging efficiencies, respectively. Rated capacity; Self-discharge rate; The unit is the time interval for scheduling; Indicates the rated power of the energy storage; Indicates the maximum state of charge of the stored energy; This represents the minimum state of charge of energy storage; Indicates energy storage in the first In each scenario State of charge over a period of time; Indicates the first In the scenario, the first individual users Energy storage charging power during a given time period; The representation of the first In the scenario, the first individual users Energy storage discharge power during a given time period; Indicates the first In each scenario State of charge of energy storage during a given time period; To ensure a normal energy storage supply at the beginning of each scenario, the initial capacity is set to be equal to the end-of-day capacity, i.e., the initial state of charge. Equal to the end-of-day state of charge The formula is as follows: （18）； To ensure the normal operation of the transaction, the energy interaction between users needs to consider power constraints and power balance, including the maximum power constraint of the transmission line, the constraint that the sum of the output power of the users is equal to the sum of the input power of the other users, and the power balance constraint between the two parties in the transaction, as shown in the following equation (19): （19）； In equation (19), Indicates the first In the scenario, the first The user and the first Between users Trading volume during a given period; Indicates the relationship between users Maximum transaction volume during the time period; This indicates the total number of users.

7. The microgrid optimization operation strategy based on risk management and hybrid game theory as described in claim 6, characterized in that: Power supply reliability and energy waste rate are represented by the load deficit rate (LPSP) and energy spillover ratio (SPSP), respectively. A smaller LPSP value indicates a more stable system, and a smaller SPSP value indicates less wind and solar power curtailment. The expressions are as follows: （20）； （21）； In the formula, Indicates the first In the scenario, the first The load power shortage rate of individual users; Indicates the first In the scenario, the first Energy overflow ratio per user; , They represent the first In each scenario Time of the first Individual user load power shortage and wasted wind and solar power; For the first In each scenario Time of the first The load requirements of each user; This represents the maximum allowable power shortage rate for the load. The maximum permissible rate of energy waste; express The power generation capacity of the photovoltaic unit at any given time; express The power generation capacity of the wind turbine at any given time; In addition, the power balance constraint should also be satisfied: （22）； （23）； In the formula, express The power generation capacity of the photovoltaic unit at any given time; express The power generation capacity of the wind turbine at any given time; The first In each scenario Time of the first Power shortage and power surplus indicators for individual users; The first In each scenario Time of the first The system's power deficit and excess power are for individual users. Indicates the first In the scenario, the first The user and the first Between users Trading volume during a given period; Represented as the first In each scenario Time of the first The actual load of each user; To avoid the unreasonable phenomenon of simultaneous energy shortages and surpluses leading to wind and solar power curtailment and load shedding, the following constraints are added: （24）。 8. The microgrid optimization operation strategy based on risk management and hybrid game theory as described in claim 7, characterized in that: Step 2 includes a master-slave altruistic game interaction model for the microgrid system, as detailed below: The microgrid benefit model considering CvaR in step 1 is restated as follows: （25）； In equation (25), This represents the total cost of the microgrid benefit model; This represents the risk preference coefficient; Indicates the first Benefits of MGO interacting with the power grid in this scenario; Indicates the first Benefits of MGO interaction with users in specific scenarios; For wind and solar power users' operating costs; This is the altruistic ratio coefficient; By finding a slightly altruistic equilibrium point in the master-slave game, we can simultaneously consider the multiple objectives of MGO and users, achieving a more coordinated decision outcome; the master-slave altruistic game interaction model is represented as: （26）； In equation (26), This represents a master-servant altruistic game interaction model; Represents the set of participants in a game; This represents the set of strategies for purchasing electricity from users within a single day; This represents the set of strategies for pricing electricity to users within a single day; This indicates the amount of electricity a user purchases or sells from MGO within one day; This indicates the charging and discharging capacity of the leased energy storage. This indicates the amount of electricity consumed through user interactions within a single day. This represents the cost for microgrid operators; Indicates the user's cost; The above game theory model contains three elements: participants, strategies, and utility, specifically represented as follows: 1) Participants: MGO and the user alliance are the two participants in this game; 2) Strategy: The leader's strategy These are sets of strategies for buying and selling electricity to users within a single day; follower strategies. These represent the electricity purchased and sold by users to MGO within a day, the charging and discharging of leased energy storage, and the electricity exchanged between users. 3) Utility: The utility of each participant is the objective function defined above; When the strategies chosen by the agent and the follower complement each other and they have no incentive to change their strategies, both the agent and the follower achieve maximum utility. This means that under the current strategies, it is impossible to obtain higher utility by changing the strategies, thus reaching a Stackelberg equilibrium. Must meet: （27）； In equation (27), This represents the total cost of the microgrid efficiency model under the Stackelberg game; This represents the price at which the MGO sells electricity to users under the Stackelberg game; This represents the price at which the MGO purchases electricity from users under the Stackelberg game; This represents the amount of electricity a user buys or sells from the MGO under the Stackelberg game; This represents the total cost of the microgrid benefit model; This indicates the price at which MGO sells electricity to users; This indicates the price at which MGO purchases electricity from users; This represents the total cost of the user benefit model under the Stackelberg game; This represents the charging and discharging capacity of leased energy storage under the Stackelberg game; This represents the amount of electricity exchanged between users under the Stackelberg game. This represents the total cost of the user benefit model; This indicates the charging and discharging capacity of the leased energy storage. This indicates the amount of electricity used in interactions between users.

9. The microgrid optimization operation strategy based on risk management and hybrid game theory according to claim 8, characterized in that: Step 2 includes a multi-user energy sharing cooperative game model: The constructed asymmetric Nash bargaining cooperative game model is the multi-user power sharing cooperative game model. The asymmetric Nash bargaining cooperative game model satisfies both symmetry and Pareto optimality, as shown in the following formula. The solution that maximizes the Nash product is the equilibrium solution of the Nash negotiation game problem. （28）； In equation (28), For the benefit of the negotiating party, The benefits before the main players participate in cooperative game theory, i.e., the point at which negotiations break down; Indicates the first One user; This indicates the total number of users; Indicates product calculation; The asymmetric Nash bargaining cooperative game model is a multivariate coupled nonconvex nonlinear problem. To facilitate the solution of the model, the asymmetric Nash bargaining cooperative game model is transformed into two convex subproblems: The subproblem of minimizing the cost of the cooperative alliance, P1, and the subproblem of distributing the benefits, P2, are solved sequentially. After cooperation, the interaction cost between users is 0. Based on this, the cost optimization model of the lower-level followers described in the microgrid benefit model is transformed into the P1 subproblem. P1: Minimize operating costs: （29）； In equation (29), This represents the total cost of the microgrid benefit model; Indicates the first The probability of each scenario; Indicates the first In the scenario, the first The interaction cost between each user and MGO; Indicates the first In the scenario, the first The cost of interaction between an individual user and a shared energy storage system; Represented as the first In the scenario, the first The utility of an individual user; This indicates the operation and maintenance costs of wind and solar power. Indicates the cost of punishment; P2: Bargaining and profit distribution issues: （30）； In equation (30), Indicates the first In the scenario, the first The cost of each user; Indicates the first In the scenario, the first The interaction cost between each user and MGO; Indicates the first In the scenario, the first The cost of interaction between an individual user and a shared energy storage system; Indicates the first In the scenario, the first The cost of interaction between each user and other users; Represented as the first In the scenario, the first The utility of an individual user; Indicates the first In the scenario, the first The maintenance and operation costs of wind and solar power for individual users; Indicates the first In the scenario, the first The cost of punishment for each user; Indicates the first The bargaining power of individual users; Since the natural logarithm is a strictly monotonically increasing convex function, taking the logarithm of the above equation yields the following result; （31）； In equation (31), Indicates the first The bargaining power of each user varies depending on their contribution in different scenarios. Users with high demand contribute less to the overall interests of the alliance, thus their bargaining power decreases. Users who provide more energy contribute more to the overall interests of the alliance, thus their bargaining power increases accordingly. The bargaining power of a subject is measured by the amount of energy provided or obtained by the subject on all typical days and the changes in costs before and after cooperation, as shown in the following formula (32): （31）； （33）； In the formula, Indicates the first In the scenario, the first The user and the first individual users Interactive power consumption during a given time period; The maximum total electrical energy supplied to all users; This represents the maximum total electrical energy received by all users. , The first In the scenario, the first The interaction cost between each user and MGO before and after collaboration; To ensure users' willingness to cooperate, the total cost of cooperation in the cooperative game must be less than the cost before the game. Furthermore, the total payment from all parties involved in the transaction must equal the total revenue to guarantee the smooth operation of the transaction. The corresponding constraints are as follows: （34）； （35）。 10. The microgrid optimization operation strategy based on risk management and hybrid game theory according to claim 9, characterized in that: In step 3, the differential evolution (DE) algorithm is improved through an adaptive combinatorial mutation strategy, as follows: （36）； In equation (36), For the number of iterations The weight of the mutation strategy at that time; Indicates the number of iterations. The weight of the mutation strategy at that time; The total change is adjusted for weights. This represents the maximum value of the mutation strategy weight; This represents the minimum value of the mutation strategy weight; The asymptotic coefficient; Indicates a time interval; Indicates time; Indicates the first Generation, First The variation vector of each individual; The basis vectors are individuals randomly selected from the population. This represents an individual randomly selected from the population, and then a mutation vector is generated using "two difference variables"; This represents a randomly selected individual, and the mutation vector is generated by combining the best individual in the population with one difference variable. This means selecting the best individual from the population and then using "two difference variables" to generate a mutation vector; By adjusting the weights smoothly, a gradual and smooth transition in the selection of mutation strategies between adjacent stages is achieved; the mutation strategies are defined as follows: （37）； In equation (37), It belongs to random integer, Indicates population size, and ; Indicates the first Generation, First The variation vector of each individual; Indicates the first Generation, First Individual; Indicates the first Generation, First Each individual; Indicates the first Generation, First Individual; Indicates the first Generation, First Individual; Indicates the first Generation, First Individual; Indicates the first Generation, First Individual; Indicates the first The best individual in the generation; Design adaptive mutation factor The mutation factor is dynamically adjusted based on the dual mechanisms of algorithm iteration progress and individual fitness to balance global search and convergence speed, as shown in equation (38) below: （38）； （39）； In the formula, For population Variable factors; These are the upper and lower limits of the variable factor, respectively; , These are the current iteration count and the maximum iteration count, respectively. , , population The fitness value, the average fitness value of all current populations, and the optimal fitness value.

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