Electric energy dispatching method and device for virtual power plant multi-subject system game

Abstract

The invention relates to an electric energy dispatching method for virtual power plant multi-subject system game, which comprises the following steps: acquiring and constructing a Wasserstein distance fuzzy set of electricity price and renewable energy output based on historical power plant data, and respectively establishing a superior power grid electricity price predicted value and a fuzzy set constraint of renewable energy output; establishing a VPP multi-subject collaborative transaction optimization model among an operator, an electric vehicle charging station and a producer, and reconstructing the VPP multi-subject collaborative transaction optimization model based on a Wasserstein distance fuzzy set and a maximum harsh lower bound method; and for the reconstructed VPP multi-agent collaborative transaction optimization model, establishing a game equilibrium model based on a non-cooperative game theory, and solving through a stationary point optimization method to obtain an electric energy scheduling scheme among multiple agents of the virtual power plant. Compared with the prior art, the method has the advantages that the robustness of game decision results is improved, and the flexibility and intelligence of electric energy utilization are improved.

Description

Technical Field

[0001] The present invention relates to the field of power plant dispatching methods, and in particular to an electric energy dispatching method and device for a virtual power plant multi-agent system game. Background Art

[0002] With the increasing scarcity of natural resources and environmental pollution, smart grid technology has received widespread attention from the power industry in various countries.

[0003] Current research on virtual power plant decision-making ignores the complex competitive and strategic interactions between stakeholders, making it difficult to achieve optimal overall returns. When all stakeholders participate in decision-making, their strategy spaces become mutually constrained, and the decision domains become coupled, making the classic Nash equilibrium inapplicable. However, the generalized Nash equilibrium addresses games where the decision space of each entity depends on the strategies of all other entities and ensures fair competition among all decision-making entities involved.

[0004] The invention with publication number CN108596464A discloses an economic dispatch method for electric vehicles and cloud energy storage based on dynamic non-cooperative game, including: (1) establishing an economic optimization dispatch model for electric vehicle agents, (2) establishing a three-party non-cooperative game model, and (3) using a particle swarm algorithm to solve the above model and determine the final Nash equilibrium point.

[0005] However, this solution directly uses the particle swarm algorithm to solve the three-party game problem model, without considering the uncertainty of energy output and the physical limits of energy output, resulting in low reliability and poor robustness. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned existing technologies, such as not considering the uncertainty of energy output, not considering the physical limits of energy output, low reliability and poor robustness, and to provide an energy scheduling method and device for multi-agent system game of virtual power plant.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A method for dispatching electric energy based on a multi-agent system game of a virtual power plant comprises the following steps:

[0009] Obtain and construct Wasserstein distance fuzzy sets of electricity prices and renewable energy output based on historical power plant data;

[0010] Based on the Wasserstein distance fuzzy set, a Wasserstein fuzzy set constraint for the upper grid electricity price forecast value and a Wasserstein fuzzy set constraint for the renewable energy output are respectively established;

[0011] Establish a VPP multi-agent collaborative transaction optimization model among operators, electric vehicle charging stations, and prosumers, and reconstruct the VPP multi-agent collaborative transaction optimization model based on the Wasserstein distance fuzzy set and maximum worst lower bound method;

[0012] For the reconstructed VPP multi-agent collaborative transaction optimization model, a game equilibrium model is established based on non-cooperative game theory, and the power scheduling scheme among multiple agents of the virtual power plant is obtained through the stationary point optimization method.

[0013] Furthermore, the VPP multi-agent collaborative transaction optimization model includes: a VPP operator distributed blue optimization transaction decision model, an electric vehicle charging station DRCC transaction decision model, and a prosumer DRCC transaction strategy model;

[0014] The VPP operator's distributed robust optimization transaction decision model, the electric vehicle charging station DRCC transaction decision model, and the prosumer DRCC transaction strategy model all include DRCC-based power balance constraints;

[0015] The VPP multi-agent collaborative transaction optimization model is reconstructed based on the Wasserstein distance fuzzy set. Specifically, according to the random variables of renewable energy output, the maximum worst lower bound of the renewable energy output of each agent is solved to obtain the DRCC problem; based on the Wasserstein fuzzy set constraints of the renewable energy output, the DRCC problem is reconstructed to transform it into a linear problem, and the maximum worst lower bound of the new energy output of each agent is solved by a commercial solver, thereby converting the DRCC-based power balance constraints of each agent into DRCC-equivalent power balance constraints.

[0016] Furthermore, the expression of the Wasserstein fuzzy set constraint of the renewable energy output is:

[0017]

[0018] Where, is the probability distribution of renewable energy output samples; The poor probability distribution of renewable energy output forecast values; is the Wasserstein distance between the empirical distribution and the true distribution of renewable energy output; θ res ,ξ res Obedience A random variable; Π res (dθ res ,dξ res ) is θ res and ξ res The joint probability distribution of 2 is the support set of the random variable; εres The radius of the Wasserstein sphere for renewable energy output; is the probability distribution; β res Confidence level in contributing to renewable energy.

[0019] Furthermore, based on the Wasserstein fuzzy set constraints of the renewable energy output, the DRCC problem is reconstructed to be converted into a linear problem expression as follows:

[0020]

[0021] Where, is the worst lower bound of renewable energy output; α is the confidence level, ε res The radius of the Wasserstein sphere that produces renewable energy; P t res,min 、P t res,max are the minimum and maximum output of renewable energy respectively; w t,m 、 z t,m 、v t is an auxiliary variable; For the sample set The mth sample of renewable energy output at time t; N res The number of samples that contributed renewable energy.

[0022] Furthermore, the DRCC-based power balance constraints of each subject are converted into DRCC-equivalent power balance constraints as follows:

[0023] The expression of the power balance constraint after DRCC equivalent of the VPP operator's distributed robust optimization transaction decision model is:

[0024]

[0025] The expression of the power balance constraint after DRCC equivalent of the DRCC transaction decision model of the electric vehicle charging station is:

[0026]

[0027] The expression of the power balance constraint after DRCC equivalent of the prosumer DRCC trading strategy model is:

[0028]

[0029] Furthermore, the calculation expression of the game equilibrium model established for the reconstructed VPP multi-agent collaborative transaction optimization model is:

[0030]

[0031] Where C i 、x i 、X i are the objective function, decision variables, and strategy space of participant i respectively; x -i is the decision variable of all participants except participant i; g i is the inequality constraint of participant i; h i is the equality constraint for participant i.

[0032] Furthermore, the energy dispatching scheme among multiple entities of the virtual power plant obtained by the stationary point optimization method is specifically as follows:

[0033] According to the game equilibrium model, the stationary point optimization method is used to transform the equivalent KKT system of each subject and the corresponding constraints in parallel. The big M method is used to convert it into a mixed integer linear programming problem, which is solved by a commercial solver to obtain the electricity price strategy of each subject, which is used as a guide for power scheduling.

[0034] Furthermore, the objective function of the VPP operator's distributed robust optimization transaction decision model is expressed as:

[0035]

[0036] Where, F vppo Distribute the objective function value of the robust optimization transaction decision model for VPP operators; C EO 、R EO are the expectations of the power purchase cost and power sales revenue of the VPP operator and the upper grid under the worst probability distribution; R C&P 、C ESS 、C GT are the revenue from electricity sales by the VPP operator to EV charging stations and prosumers, the energy storage degradation cost, and the gas turbine operating cost; is the probability distribution expectations; are the fuzzy sets of electricity purchase and sale prices; P t g,buy 、P t g,sell They are the electricity purchased and sold by VPP operators from the power grid; P t C&P is the clearing electricity price and transaction power of the VPP operator’s transactions with EV charging stations and prosumers, where a positive transaction power represents the VPP operator selling electricity to other entities, and a negative value represents the purchase of electricity; c dep is the degradation coefficient of the energy storage device; is the charging and discharging power of the energy storage device; ρ gasis the natural gas price; V t gas The amount of gas consumed by the gas turbine; is the time period; sup is the supremum, which aims to find the worst scenario in the fuzzy set; inf is the infimum, which aims to find the worst scenario in the fuzzy set;

[0037] The constraints of the VPP operator's distributed robust optimization transaction decision model also include power balance constraints with other entities, fuel turbine operation constraints, energy storage operation constraints, and upper and lower limit constraints on the transaction volume of electricity purchases and sales to the power grid and other entities.

[0038] Furthermore, the objective function of the DRCC transaction decision model for electric vehicle charging stations is expressed as follows:

[0039]

[0040] Where, F evcs is the cost function of the electric vehicle charging station, P is the clearing electricity price for transactions between VPP operators and EV charging stations and prosumers; t CS The power traded between the EV charging station and the VPP operator. A positive value indicates that the EV charging station purchases electricity from the VPP operator, while a negative value indicates that the EV charging station sells electricity. is the unit utility of EV in period t; are the charging and discharging power of EV respectively; is the charging and discharging efficiency of EV;

[0041] The constraints of the electric vehicle charging station DRCC transaction decision model include: EV constraints and EV charging station power purchase and sale constraints.

[0042] Furthermore, the objective function of the prosumer DRCC transaction strategy model is expressed as:

[0043]

[0044] Where, F pro The cost of electricity for prosumers; P is the clearing electricity price for transactions between VPP operators and EV charging stations and prosumers; t Pro C is the power traded between the prosumer and the VPP operator. A positive value indicates that the prosumer purchases electricity from the VPP operator, while a negative value indicates that the prosumer sells electricity. DR P is the penalty cost of user demand response for prosumers; t Pro,in 、P t Pro,out are the inflow and outflow loads of the prosumer respectively; P tPro,cut load shedding for prosumers; are the unit penalty prices for prosumers to shift and curtail load, respectively.

[0045] Compared with the prior art, the present invention has the following advantages:

[0046] (1) Based on historical power plant data, the present invention analyzes the relationship between electric motors and renewable energy output, and constructs a Wasserstein distance fuzzy set of electric power prices and renewable energy output; solves the maximum worst lower bound of renewable energy output for each subject in the VPP multi-subject collaborative transaction optimization model, and reconstructs the problem to be solved based on the Wasserstein fuzzy set of renewable energy output to transform it into a linear problem, making it easier to solve the maximum worst lower bound of each subject's new energy output through a commercial solver. In addition, the constraints of each subject take into account the upper and lower limit constraints of random variables, thereby improving the robustness of the game decision-making results, and the probability of default is relatively low. Under the condition of limited information, a reliable but not overly conservative strategy is implemented to deal with uncertainty;

[0047] Finally, by establishing a generalized Nash equilibrium problem to describe the non-cooperative game model, the suboptimal decision-making of VPP and the potential loss of interests of internal entities were effectively avoided, the overall interests were maximized, and the flexibility and intelligence of electricity utilization were improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A flowchart of an electric energy dispatching method based on a multi-agent system game of a virtual power plant provided in an embodiment of the present invention;

[0049] Figure 2 Schematic diagram of a multi-agent VPP transaction model optimization process taking into account DRCC provided in an embodiment of the present invention;

[0050] Figure 3 A schematic diagram of a multi-agent VPP non-cooperative game solving method provided in an embodiment of the present invention;

[0051] Figure 4 A schematic diagram of a sample set of electricity prices of a higher-level power grid provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0053] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0054] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0055] Example 1

[0056] like Figure 1 As shown, this embodiment provides an energy scheduling method for a virtual power plant multi-agent system game, comprising the following steps:

[0057] S1: Obtain and construct Wasserstein distance fuzzy sets of electricity prices and renewable energy output based on historical power plant data;

[0058] S2: Based on the Wasserstein distance fuzzy set, the Wasserstein fuzzy set constraints of the upper grid electricity price forecast value and the Wasserstein fuzzy set constraints of the renewable energy output are established respectively;

[0059] S3: Establish a VPP multi-agent collaborative transaction optimization model among operators, electric vehicle charging stations, and prosumers, and reconstruct the VPP multi-agent collaborative transaction optimization model based on Wasserstein distance fuzzy sets and the maximum worst lower bound method;

[0060] S4: For the reconstructed VPP multi-agent collaborative transaction optimization model, a game equilibrium model is established based on non-cooperative game theory, and the power scheduling plan among multiple subjects of the virtual power plant is obtained through the stationary point optimization method.

[0061] Specifically, step S1 is as follows:

[0062] The Wasserstein fuzzy sets of grid electricity prices and renewable energy output are constructed based on historical data, and the neighborhood range of the probability distribution of random variables is defined by the radius of the Wasserstein sphere.

[0063] Step S2 is specifically as follows:

[0064] The Wasserstein fuzzy set constraints of the upper-level power grid electricity price forecast value are established based on the uncertain set of Wasserstein distance:

[0065]

[0066] Where: Sample electricity price for power grid purchase and sales The probability distribution of Forecast value of electricity purchase and sales price for the power grid The bad probability distribution of θ p ,ξ p Obedience A random variable; Π p is θ p ,ξ p The joint probability distribution of ; ε p is the radius of the Wasserstein sphere for grid electricity purchase and sales prices; β p The confidence level of the power grid purchase and sales price.

[0067] Wasserstein fuzzy set constraints for renewable energy output:

[0068]

[0069] Where: is the probability distribution of renewable energy output samples; is the bad probability distribution of renewable energy output forecast value; θ res ,ξ res Obedience A random variable; Π res is θ res and ξ res The joint probability distribution of ; ε res is the radius of the Wasserstein sphere of renewable energy output; β res Confidence level in contributing to renewable energy.

[0070] In step S3, the VPP multi-agent collaborative transaction optimization model includes: a VPP operator distributed blue optimization transaction decision model, an electric vehicle charging station DRCC transaction decision model, and a prosumer DRCC transaction strategy model;

[0071] The VPP operator's distributed blue-stick optimization transaction decision model, the electric vehicle charging station DRCC transaction decision model, and the prosumer DRCC transaction strategy model all include DRCC-based power balance constraints;

[0072] The VPP multi-agent collaborative transaction optimization model is reconstructed based on the Wasserstein distance fuzzy set. Specifically, according to the random variables of renewable energy output, the maximum worst lower bound of renewable energy output of each agent is solved to obtain the DRCC problem; based on the Wasserstein fuzzy set constraints of renewable energy output, the DRCC problem is reconstructed to transform it into a linear problem, and the maximum worst lower bound of new energy output of each agent is solved through a commercial solver, thereby converting the DRCC-based power balance constraints of each agent into DRCC-equivalent power balance constraints.

[0073] Specifically, the objective function of the VPP operator's distributed robust optimization transaction decision model is:

[0074]

[0075] Where: C EO 、R EO are the expectations of the power purchase cost and power sales revenue of the VPP operator and the upper grid under the worst probability distribution; R C&P 、C ESS 、C GT are the revenue from electricity sales by the VPP operator to EV charging stations and prosumers, the energy storage degradation cost, and the gas turbine operating cost; is the probability distribution expectations; are the fuzzy sets of electricity purchase and sale prices; P t g ,buy 、P t g,sell They are the electricity purchased and sold by VPP operators from the power grid; P t C&P is the clearing electricity price and transaction power of the VPP operator’s transactions with EV charging stations and prosumers, where a positive transaction power represents the VPP operator selling electricity to other entities, and a negative value represents the purchase of electricity; c dep is the degradation coefficient of the energy storage device; is the charging and discharging power of the energy storage device; ρ gas is the natural gas price; V t gas The amount of gas consumed by the gas turbine; is the time period; sup is the supremum, which aims to find the worst scenario (maximum electricity purchase cost) in the fuzzy set; inf is the infimum, which aims to find the worst scenario (minimum electricity sales revenue) in the fuzzy set.

[0076] Trading power balance constraints with other entities:

[0077]

[0078] Where: P t Pro P is the transaction power between the prosumer and the VPP operator. A positive value indicates that the prosumer purchases electricity from the VPP operator, while a negative value indicates that the prosumer sells electricity. t CS is the transaction power between the EV charging station and the VPP operator. A positive value indicates that the EV charging station purchases electricity from the VPP operator, while a negative value indicates that the EV charging station sells electricity. is the dual variable.

[0079] Power balance constraints based on DRCC:

[0080]

[0081] Where: P t EO,L is the load of the VPP operator; P t GT is the power generation capacity of the gas turbine; are the charging and discharging power of energy storage respectively; is the fuzzy set of renewable energy generation output of VPP operators; expresses the probability that the inequality holds; 1-α is the confidence level of the chance constraint.

[0082] In addition to the above constraints, the VPP operator model also includes fuel turbine operation constraints, energy storage operation constraints, and upper and lower limit constraints on the purchase and sale of electricity from the power grid and other entities.

[0083] Cluster EVs into N groups based on historical data type The proportion of EVs of type v is

[0084] The goal of the above electric vehicle charging station DRCC transaction decision model is to minimize the cost function F evcs :

[0085]

[0086] Where: U EV is the utility of EV; N EV The average number of EVs served by the charging station in a day; Represents the type set of EV, there are N type Elements is the unit utility of EV in period t; are the charging and discharging power of EV respectively; is the charge and discharge efficiency of the EV.

[0087] Power balance constraints based on DRCC:

[0088]

[0089] Where: is the random variable of photovoltaic power output of EV charging station; is the fuzzy set of photovoltaic power generation output of EV charging station.

[0090] In addition to the above constraints, the electric vehicle charging station model also includes EV constraints and EV charging station power purchase and sales constraints.

[0091] The DRCC trading strategy model for prosumers takes minimizing the electricity cost of prosumers as its decision-making objective:

[0092]

[0093] Where: C DR P is the penalty cost of user demand response for prosumers; t Pro,in 、P t Pro,out are the inflow and outflow loads of the prosumer respectively; P t Pro,cut load shedding for prosumers; are the unit penalty prices for prosumers to shift and curtail load, respectively.

[0094] Power balance constraints based on DRCC:

[0095]

[0096] Where: P t Pro,L is the total load of prosumers; is the random variable of the photovoltaic power output of the prosumer; is the fuzzy set of photovoltaic power generation output of prosumers.

[0097] In addition to the above constraints, the prosumer model also includes upper and lower limit constraints on load reduction, upper and lower limit constraints on load transfer (in and out), transfer load balance constraints and upper and lower limit constraints on electricity purchase and sales.

[0098] like Figure 2 As shown, in order to obtain the maximum worst lower bound of renewable energy output in each subject, it is necessary to solve the same type of DRCC problem. Therefore, the random variable of renewable energy output is defined as The worst lower bound of each entity's renewable energy output is solved through the following general problem:

[0099]

[0100] Where: The worst lower bound for renewable energy output.

[0101] The DRCC problem is reconstructed based on the Wasserstein fuzzy set of renewable energy output:

[0102]

[0103] Where: P t res,min 、P t res,max are the minimum and maximum output of renewable energy respectively; w t,m 、 z t,m 、v t is an auxiliary variable; For the sample set The mth sample of renewable energy output at time t; N res The number of samples that contributed renewable energy.

[0104] Therefore, the DRCC problem can be transformed into a linear problem. The maximum worst lower bound of each entity's renewable energy output can be solved using a commercial solver, thereby converting the power balance constraints of each entity into DRCC equivalent power balance constraints:

[0105] Considering the VPP operator power balance constraints after DRCC equivalence:

[0106]

[0107] Considering the DRCC equivalent, the power balance constraints of the EV charging station are:

[0108]

[0109] Considering the power balance constraints of prosumers after DRCC equivalence:

[0110]

[0111] Step S4 is specifically as follows:

[0112] Based on the three elements of the game model, the present invention models the multi-agent non-cooperative game as a generalized Nash equilibrium problem:

[0113]

[0114] Where: C i 、x i 、X i are the objective function, decision variables, and strategy space of participant i respectively; x -i is the decision variable of all participants except participant i; g i is the inequality constraint of participant i; h i is the equality constraint for participant i.

[0115] The multi-agent VPP transaction decision model established by the present invention is divided according to the architecture of non-cooperative game. Different from the traditional method of constructing equivalent equilibrium models based on variational inequalities, the present invention does not require distributed algorithms such as the alternating direction multiplier method (ADMM) for solution (which relies on the strict monotonicity of the mapping operator to ensure convergence), but adopts the stationary point optimization method to transform the equivalent KKT system of each subject and establish its conditions in parallel, and uses the big M method to convert it into a mixed integer linear programming (MILP) problem, and solves it through a commercial solver. Under the conditions that the objective function is strongly convex and the constraint set is tight, this method can guarantee convergence to a unique equilibrium point, avoid the oscillation risk of the traditional ADMM algorithm in non-monotonic conditions, and still ensure good computational efficiency when the number of subjects increases. See the specific solution process. Figure 3 .

[0116] Given that GNEP can exhibit different equilibrium states, including no equilibrium, a finite number of equilibria, or an infinite number of equilibria, the existence and uniqueness of the equilibrium can be verified by directly combining the KKT conditions to calculate and determine fixed points. Considering that the Nash equilibrium solution of the model proposed in this article exists and is not unique, to study the analytical properties of the generalized Nash equilibrium, a stationary point optimization method is used to solve the equilibrium solution of this multi-agent game, using the minimization of the overall cost of the VPP system as the criterion for screening fixed points. Based on this, the equilibrium state of the multi-agent game of the VPP system, consisting of VPP operators, prosumers, and EV charging stations, is defined to achieve optimal economic benefits. The specific process is as follows:

[0117] Write a KKT system for each subject

[0118]

[0119] where i represents the VPP operator, EV charging station, and prosumer, respectively; σ is the dual variable of the equality constraint h; and ψ is the dual variable of the inequality constraint g.

[0120] The equilibrium point solution is as follows:

[0121]

[0122] Where: x EO 、x Pro 、x CS are the decision variables of each subject; Represents the KKT system of each subject; C TO The overall cost of VPP is as follows:

[0123] C TO =C EO′ -R EO′ +C ESS +CGT -U EV +C DR (18)

[0124] Unlike the master-slave game model, where the transaction price is determined by the upper-level leader, under the KKT condition under market equilibrium, the transaction price between the VPP operator and other entities is equivalent to the dual variable in the global coupling constraint (4). From an economic perspective, this price is determined by the supply and demand relationship of each entity. Therefore, this pricing scheme truly reflects the value of electricity in the VPP system and is fair to all entities.

[0125] The effectiveness of the technology used in this invention is verified and explained by means of scientific demonstration below.

[0126] The verification environment is set as follows: the renewable energy source of the VPP operator is wind power generation, and the EV charging station serves 100 EVs. In order to characterize the uncertainty of grid electricity prices, the electricity price data in Table 1 is used as the initial data. The Monte Carlo simulation method based on the Latin hypercube sampling is used to generate 10,000 sets of electricity price sample sets, and the scenario reduction is performed based on the comprehensive optimal scenario reduction method with corrloss weights to minimize the correlation loss before and after the scenario reduction. The electricity price sample scenario after reduction is shown in Figure 4 The relevant parameters of the gas turbine and energy storage are shown in Tables 2 and 3. The different EV types and parameters in the EV charging station are shown in Table 4. The upper and lower bounds of renewable energy output are determined by the maximum and minimum values ​​of historical data. Wasserstein distance ε s =ε b =0.02,ε res =1, confidence level α=70%.

[0127] Table 1: Time-of-use electricity price data of the power grid

[0128] plan time Electricity purchase price / (yuan / kWh) Electricity sales price (yuan / kWh) Valley Time 00:00-07:00，22:00-24:00 0.40 0.20 usually 07:00-11:00，14:00-18:00 0.75 0.40 Peak Hour 11:00-14:00，18:00-22:00 1.20 0.60

[0129] Table 2: Gas turbine related parameters

[0130]

[0131] Table 3: VPP operator energy storage parameters

[0132]

[0133] Table 4: Electric vehicle parameters

[0134] type Maximum charge and discharge power / kW Battery capacity / kWh Initial power / kWh Entry and exit time / h A 6 40 15 10-24 B 6 32 16 2-9 C 6 24 12 13-22 D 6 40 25 1-8 E 10 64 25 11-23

[0135] S1: Optimization of non-cooperative game model based on generalized Nash equilibrium. It should be noted that:

[0136] In order to verify the optimization effect of the non-cooperative game model constructed by the present invention, the following four schemes were designed and compared with the test results to verify the advantages of the method proposed in the present invention in terms of economy and applicability.

[0137] Option 1: All stakeholders belong to a unified entity, and there is no competition between them.

[0138] Option 2: Build a VPP model based on the Stackelberg game, with the VPP operator as the upper-level leader to decide the transaction electricity price, and EV charging stations and prosumers as followers, adjusting their own electricity purchase and sales strategies in response to the VPP's electricity price.

[0139] Solution 3: A VPP generalized Nash equilibrium model with the same stakeholders was constructed, converted into a variational inequality problem, and solved using a distributed algorithm.

[0140] Solution 4: A VPP generalized Nash equilibrium model with the same stakeholders was constructed and solved using the stationary point optimization method.

[0141] Table 5: Comparison of cost results of each entity under different schemes

[0142] plan VPP operator cost / yuan EV charging station cost / yuan Smart prosumer cost / yuan VPP total cost / yuan one 3822.59 -644.78 6797.93 9975.74 two 3893.25 -583.74 7323.20 10632.71 three 4039.82 -649.21 6787.45 10178.06 Four 3858.95 -661.77 6523.47 9720.66

[0143] Table 5 shows that in Option 1, VPP operators have lower costs, while EV charging stations and prosumers have higher costs. This suggests that ignoring competition among stakeholders can lead to harming the interests of some stakeholders in order to optimize overall benefits. Therefore, VPPs must effectively manage competition among stakeholders and adopt a non-cooperative game approach.

[0144] In a comparison of three non-cooperative game models, Option 4 outperformed Option 2. In Option 2, the three stakeholders suffered significant losses, leading to increased total costs. This is because, as price takers of VPP pricing, EV charging stations and prosumers lack market competitiveness and have a distinct master-slave relationship with the VPP. Furthermore, the transaction price is subject to upper and lower limits. In Option 4, the transaction price, serving as the dual variable of the global coupling constraint, depends on the supply and demand relationships of each VPP system entity, thereby reducing the losses for each entity. Furthermore, compared to Option 3's GNE, which uses variational inequalities and a distributed algorithm to solve it, the costs for VPP operators and prosumers are reduced, the revenue for EV charging stations is increased, and the overall economic performance is superior, providing greater guidance for practical application research.

[0145] In order to verify the scalability of the method proposed in this invention and the effectiveness of the solution algorithm, a multi-agent expansion scale test scenario was constructed to compare the computational efficiency differences of the two solution methods.

[0146] Table 6: Computational efficiency results

[0147] Total number of entities Mode 3 calculation time / s Mode 4 calculation time / s 10 237.21 35.52 50 748.14 41.95 100 4873.57 54.36

[0148] As shown in Table 6, as the total number of EV charging stations and prosumers increases from 50 to 100, the computation time for Scheme 3 increases (by 551.42%). In contrast, the computation time for Scheme 4, proposed in this paper, increases slightly (by only 29.58%), but remains acceptable within the day-ahead market. Therefore, in practice, the proposed method maintains good adaptability when the number of VPP aggregation entities increases.

[0149] S2: DRCC model optimization model based on Wasserstein distance. It should be noted that:

[0150] To verify the effectiveness of DRCC, five uncertainty processing methods are designed and compared, including the traditional sample average approximation (SAA), SO, RO, moment information-based DRCC (M-DRCC) and Wasserstein distance-based DRCC (W-DRCC).

[0151] To comprehensively evaluate the superiority of the proposed method, 500 sets of renewable energy output data were selected as the original sample set, and an additional 500 sets of samples were selected for out-of-sample testing to verify the model's generalization ability. During the testing process, out-of-sample costs were calculated and default probabilities were statistically analyzed to demonstrate the reliability of each method.

[0152] Table 7: Comparison of solution results of five processing methods

[0153] Uncertainty handling methods SAA SO RO M-DRCC W-DRCC VPP total cost / yuan 9647.89 9538.21 10377.53 9769.48 9720.66 Out-of-sample costs 9857.24 9798.10 10917.46 9743.91 9705.43 Probability of Default 13.56％ 28.48％ 0％ 1.27％ 0.73％

[0154] The results show that the RO method incurs higher costs than the other four methods. This is because the RO method makes decisions based solely on upper and lower bounds of uncertainty, resulting in overly conservative trading schemes that are robust but have low economic benefits. The SAA method has higher operating costs, primarily because it cannot fully cover low-probability events, resulting in more conservative trading. Since the SO method assumes that renewable energy output conforms to a precise probability distribution, this may lead to wind and solar power curtailment by various VPP entities. Although optimistic operating strategies can generate higher returns, they will affect the reliability of each entity's operation and lack robustness.

[0155] Because DRCC involves worst-case scenarios and considers upper and lower bounds on random variables, the decisions of each entity are more conservative than those of SO and SAA. However, DRCC's default probability is relatively low, demonstrating that its approach can leverage the inherent information about uncertainty described in fuzzy sets to guide decision-making, enabling reliable yet conservative strategies to address uncertainty when information is limited. At the same time, DRCC's out-of-sample costs are reduced, effectively preventing economic losses in extreme situations. Furthermore, compared to M-DRCC, Wasserstein fuzzy sets capture the overall characteristics of the probability distribution rather than just some statistical characteristics, making W-DRCC superior to M-DRCC in terms of cost-effectiveness and reliability.

[0156] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A method for dispatching electric energy based on multi-agent system game of virtual power plant, characterized in that: The following steps are involved: Obtain and construct Wasserstein distance fuzzy sets of electricity prices and renewable energy output based on historical power plant data; Based on the Wasserstein distance fuzzy set, a Wasserstein fuzzy set constraint for the upper grid electricity price forecast value and a Wasserstein fuzzy set constraint for the renewable energy output are respectively established; Establish a VPP multi-agent collaborative transaction optimization model among operators, electric vehicle charging stations, and prosumers, and reconstruct the VPP multi-agent collaborative transaction optimization model based on the Wasserstein distance fuzzy set and maximum worst lower bound method; For the reconstructed VPP multi-agent collaborative transaction optimization model, a game equilibrium model is established based on non-cooperative game theory, and the power scheduling scheme among multiple agents of the virtual power plant is obtained through the stationary point optimization method.

2. The electric energy dispatching method of a virtual power plant multi-agent system game according to claim 1 is characterized in that: The VPP multi-agent collaborative transaction optimization model includes: a VPP operator distributed blue optimization transaction decision model, an electric vehicle charging station DRCC transaction decision model, and a prosumer DRCC transaction strategy model; The VPP operator's distributed robust optimization transaction decision model, the electric vehicle charging station DRCC transaction decision model, and the prosumer DRCC transaction strategy model all include DRCC-based power balance constraints; The VPP multi-agent collaborative transaction optimization model is reconstructed based on the Wasserstein distance fuzzy set. Specifically, according to the random variables of renewable energy output, the maximum worst lower bound of the renewable energy output of each agent is solved to obtain the DRCC problem; based on the Wasserstein fuzzy set constraints of the renewable energy output, the DRCC problem is reconstructed to transform it into a linear problem, and the maximum worst lower bound of the new energy output of each agent is solved by a commercial solver, thereby converting the DRCC-based power balance constraints of each agent into DRCC-equivalent power balance constraints.

3. The electric energy dispatching method of a virtual power plant multi-agent system game according to claim 2 is characterized in that: The expression of the Wasserstein fuzzy set constraint of renewable energy output is: Where, is the probability distribution of renewable energy output samples; The poor probability distribution of renewable energy output forecast values; is the Wasserstein distance between the empirical distribution and the true distribution of renewable energy output; θ res ,ξ res Obedience A random variable; Π res (dθ res ,dξ res ) is θ res and ξ res The joint probability distribution of 2 is the support set of the random variable; ε res The radius of the Wasserstein sphere for renewable energy output; is the probability distribution; β res Confidence level in contributing to renewable energy.

4. The electric energy dispatching method of a virtual power plant multi-agent system game according to claim 3 is characterized in that: The expression of reconstructing the DRCC problem into a linear problem based on the Wasserstein fuzzy set constraint of the renewable energy output is: Where, is the worst lower bound of renewable energy output; α is the confidence level, ε res The radius of the Wasserstein sphere that produces renewable energy; P t res,min 、P t res,max are the minimum and maximum output of renewable energy respectively; w t,m 、 z t,m 、v t is an auxiliary variable; For the sample set The mth sample of renewable energy output at time t; N res The number of samples that contributed renewable energy.

5. The electric energy dispatching method of a virtual power plant multi-agent system game according to claim 4 is characterized in that: The specific conversion of the DRCC-based power balance constraints of each subject into the DRCC-equivalent power balance constraints is: The expression of the power balance constraint after DRCC equivalent of the VPP operator's distributed robust optimization transaction decision model is: The expression of the power balance constraint after DRCC equivalent of the DRCC transaction decision model of the electric vehicle charging station is: The expression of the power balance constraint after DRCC equivalent of the prosumer DRCC trading strategy model is:

6. The electric energy dispatching method of a virtual power plant multi-agent system game according to claim 5 is characterized in that: The calculation expression of the game equilibrium model established for the reconstructed VPP multi-agent collaborative transaction optimization model is: Where C i 、x i 、X i are the objective function, decision variables, and strategy space of participant i respectively; x -i is the decision variable of all participants except participant i; g i is the inequality constraint of participant i; h i is the equality constraint for participant i.

7. The electric energy dispatching method of a virtual power plant multi-agent system game according to claim 6 is characterized in that: The energy dispatching scheme among multiple entities of the virtual power plant obtained by the stationary point optimization method is specifically as follows: According to the game equilibrium model, the stationary point optimization method is used to transform the equivalent KKT system of each subject and the corresponding constraints in parallel. The big M method is used to convert it into a mixed integer linear programming problem, which is solved by a commercial solver to obtain the electricity price strategy of each subject, which is used as a guide for power scheduling.

8. The electric energy dispatching method of a virtual power plant multi-agent system game according to claim 2 is characterized in that: The objective function of the VPP operator's distributed robust optimization transaction decision model is expressed as: Where, F vppo Distribute the objective function value of the robust optimization transaction decision model for VPP operators; C EO 、R EO are the expectations of the power purchase cost and power sales revenue of the VPP operator and the upper grid under the worst probability distribution; R C&P 、C ESS 、C GT are the revenue from electricity sales by the VPP operator to EV charging stations and prosumers, the energy storage degradation cost, and the gas turbine operating cost; is the probability distribution expectations; are the fuzzy sets of electricity purchase and sale prices; P t g,buy 、P t g,sell They are the electricity purchased and sold by VPP operators from the power grid; P t C&P is the clearing electricity price and transaction power of the VPP operator’s transactions with EV charging stations and prosumers, where a positive transaction power represents the VPP operator selling electricity to other entities, and a negative value represents the purchase of electricity; c dep is the degradation coefficient of the energy storage device; is the charging and discharging power of the energy storage device; ρ gas is the natural gas price; V t gas The amount of gas consumed by the gas turbine; is the time period; sup is the supremum, which aims to find the worst scenario in the fuzzy set; inf is the infimum, which aims to find the worst scenario in the fuzzy set; The constraints of the VPP operator's distributed robust optimization transaction decision model also include power balance constraints with other entities, fuel turbine operation constraints, energy storage operation constraints, and upper and lower limit constraints on the transaction volume of electricity purchases and sales to the power grid and other entities.

9. The electric energy dispatching method of a virtual power plant multi-agent system game according to claim 2 is characterized in that: The objective function of the DRCC transaction decision model for electric vehicle charging stations is expressed as follows: Where, F evcs is the cost function of the electric vehicle charging station, P is the clearing electricity price for transactions between VPP operators and EV charging stations and prosumers; t CS Trading power with VPP operators for EV charging stations; is the unit utility of EV in period t; are the charging and discharging power of EV respectively; is the charging and discharging efficiency of EV; The constraints of the electric vehicle charging station DRCC transaction decision model include: EV constraints and EV charging station power purchase and sale constraints.

10. The electric energy dispatching method of a virtual power plant multi-agent system game according to claim 2, characterized in that: The objective function of the prosumer DRCC trading strategy model is expressed as: Where, F pro The cost of electricity for prosumers; P is the clearing electricity price for transactions between VPP operators and EV charging stations and prosumers; t Pro Prosumers trade power with VPP operators; C DR P is the penalty cost of user demand response for prosumers; t Pro,in 、P t Pro ,out are the inflow and outflow loads of the prosumer respectively; P t Pro,cut load shedding for prosumers; are the unit penalty prices for prosumers to shift and curtail load, respectively.

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