Optimization method of virtual power plant based on multi-agent collaborative power sharing double-layer nested game based on risk assessment and user satisfaction

Abstract

The present invention discloses a virtual power plant optimization method based on a two-layer nested game of multi-agent collaborative power sharing based on risk assessment and user satisfaction. The field belongs to the field of virtual power plant optimization, including: constructing a two-layer optimization study of multi-virtual power plant nested games of multi-agent collaboration for multi-scenario risk assessment and user satisfaction. As the upper-level leader, the distribution network operator interacts with the lower-level virtual power plant alliance through price guidance to achieve balanced management of risks and benefits. By sharing idle resources and responding to price signals, members of the virtual power plant alliance optimize internal power transactions and enhance system flexibility and responsiveness. Quantitative indicators of user satisfaction are added to the model to optimize the virtual power plant scheduling strategy to ensure that user comfort and service quality requirements are met while improving economic benefits.

Description

Technical Field

[0001] The present invention belongs to the field of virtual power plant optimization, and in particular relates to a multi-agent collaborative power sharing double-layer nested game virtual power plant optimization method based on risk assessment and user satisfaction. Background Art

[0002] Against the backdrop of a global energy crisis and environmental pollution, the development of clean energy has become crucial for alleviating environmental pressures and promoting energy structural transformation. Virtual power plants (VPs) aggregate distributed energy resources, such as wind power, photovoltaics, energy storage, and adjustable loads, effectively participating in market transactions and grid dispatch, promoting the rational consumption of energy. However, the randomness and volatility of distributed energy resources pose challenges to grid stability. Optimizing the energy management of VPs is crucial for ensuring energy supply and user quality.

[0003] Existing research focuses on optimal energy scheduling within virtual power plants (VPPs), user satisfaction after demand response, and the coordinated optimization of multiple VPPs. Literature analyzes user electricity demand and proposes energy consumption reduction strategies, but often overlooks user comfort. Optimal scheduling strategies must balance energy efficiency and user satisfaction, enhancing comfort while reducing energy consumption. With the reform of trading mechanisms, VPPs are participating in market competition, facing a shift from single VPP scheduling optimization to coordinated optimization of multiple VPPs. Strategies include VPP energy management that considers optimal power flow in the distribution network and establishing energy sharing platforms to facilitate direct electricity trading between VPPs. Game theory has become an effective tool for analyzing balance of interests, but it has limitations in addressing unequal contributions. To address this, incentive mechanisms, improved game methods, and profit distribution models have been proposed to achieve more equitable distribution of benefits. Existing research has not fully considered the risks associated with the stochastic nature of distributed energy resources. Conditional value at risk (CVA) is widely used in power market risk assessment, but the two-tier operational risk issues associated with nested games involving multiple agents and multiple VPPs require further research. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a virtual power plant optimization method based on risk assessment and user satisfaction using a multi-agent collaborative power sharing two-layer nested game, including:

[0005] Calculate the uncertainty of distributed energy resources within virtual power plants based on risk value theory and build a multi-scenario risk assessment model;

[0006] Build an optimized virtual power plant dispatch model based on user participation and satisfaction;

[0007] A nested game two-level optimization model is constructed based on the interactive problem in the coordinated dispatch of multiple agents and multiple virtual power plants;

[0008] The virtual power plant is optimized based on the risk assessment model, the virtual power plant scheduling model and the nested game two-layer optimization model.

[0009] Preferably, in the multi-scenario risk assessment model, the average loss of the portfolio risk loss exceeding the risk value under the set confidence level is:

[0010] ;

[0011] in, For investment portfolio The loss function is Represents a continuous random factor that may affect the loss function;

[0012] The expression for calculating the conditional risk value of the multi-scenario risk assessment model is:

[0013] ;

[0014] in, is the number of discrete scenarios; For the The value of a random variable in a discrete scenario, For risk value.

[0015] Preferably, the process of building an optimized virtual power plant dispatch model based on user participation and satisfaction includes:

[0016] User engagement and satisfaction were defined as the degree of change in the load curve before and after the response;

[0017] Building flexible economic compensation based on user participation in demand response;

[0018] The virtual power plant scheduling model is constructed based on the degree of change of the load curve before and after the response and the flexible economic compensation.

[0019] Preferably, the expression for the degree of change of the load curve before and after the response is:

[0020] ;

[0021] in, 、 are the electric load power before and after response respectively.

[0022] Preferably, the calculation expression of the flexible economic compensation is:

[0023] ;

[0024] in, Cost of flexible loads participating in demand response; 、 are the cost coefficients for shifting load and interrupting load to participate in demand response; 、 are the transfer and interruption load powers participating in demand response, respectively.

[0025] Preferably, the process of constructing the nested game two-layer optimization model includes:

[0026] Construct the upper-level model of dynamic pricing for distribution network operators based on the upper-level objective function and upper-level constraints;

[0027] Constructing a lower-level virtual power plant aggregate model based on lower-level objective functions and lower-level constraints

[0028] Based on the KKT condition, the upper-level model of dynamic pricing of the distribution network operator and the lower-level virtual power plant aggregate model are solved to obtain the nested game two-level optimization model.

[0029] Preferably, the upper layer objective function is:

[0030] ;

[0031] in, 、 、 are the virtual power plant serial number, time, and scene respectively; correspondingly, is its quantitative value; is the scenario probability; are the on-grid electricity price and the grid electricity price respectively; are the purchase and sale prices of electricity of the virtual power plant respectively; They are the electricity purchase and sales of the virtual power plant; is the risk aversion coefficient; the risk value of the virtual power plant benefits; is the confidence level; is an auxiliary variable, indicating that the operating profit of the virtual power plant in each scenario exceeds proportion;

[0032] The upper-level constraints include: electricity price constraints and conditional risk value constraints.

[0033] Preferably, the lower layer objective function is:

[0034] ;

[0035] ;

[0036] in, are the costs of transactions within the virtual power plant aggregate; Payment costs for transactions within the virtual power plant aggregator; is the Nash game bargaining coefficient; They are gas turbine operating cost, adjustable load participation demand response cost, and user satisfaction conversion cost; is the gas turbine cost coefficient; are the cost coefficients for shifting load and interrupting load to participate in demand response; Convert the cost coefficient to the user satisfaction index; is the energy storage charging and discharging cost coefficient; is the charging and discharging power of energy storage; Output power for the gas turbine; are the transfer and interruption load powers participating in demand response, respectively; are the electric load power before and after the response respectively;

[0037] The lower-level constraints include: power balance constraints, gas turbine constraints, power purchase and sales constraints, electric vehicle constraints, commercial load constraints, battery energy storage system constraints, air conditioning constraints, demand response constraints and revenue constraints.

[0038] Preferably, the process of solving the upper-level model of dynamic pricing of the distribution network operator and the lower-level virtual power plant aggregate model based on the KKT condition includes: using the KKT condition to convert the upper-level model of dynamic pricing of the distribution network operator and the lower-level virtual power plant aggregate model into a nonlinear single-layer problem containing complementary relaxation conditions and bilinear products, and then using the Big-M method to process the complementary relaxation conditions of the Lagrange multipliers and constraints, and linearizing the bilinear product through strong duality theory, and finally forming an equivalent nested game two-level optimization model.

[0039] Compared with the prior art, the present invention has the following advantages and technical effects:

[0040] 1. By introducing the conditional value at risk theory and building a multi-scenario risk assessment model, we can effectively manage and quantify the risks in virtual power plant operations, improve the distribution network operators' ability to cope with uncertainty, and thus enhance the stability and reliability of the entire power system.

[0041] 2. The two-layer nested game model enhances the virtual power plant's responsiveness to market price signals, improving the system's flexibility and adaptability, enabling it to better adapt to market changes and user needs. The multi-virtual power plant collaborative dispatch model promotes effective collaboration among different virtual power plants, improves overall dispatch efficiency, and achieves optimal resource allocation. Idle power is shared among virtual power plants, optimizing power resource allocation, improving energy efficiency, reducing costs, and increasing economic benefits. Through precise pricing strategies and flexible power-sharing mechanisms, virtual power plants enhance their competitiveness in the electricity market and are better able to participate in market competition.

[0042] 3. Optimizing the consumption of distributed renewable energy, reducing pressure on the environment, promoting the use of clean energy, and contributing to the sustainable development of the environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0044] Figure 1 This is a schematic diagram of an energy trading framework according to an embodiment of the present invention;

[0045] Figure 2 A schematic diagram of a nested game two-layer optimization model according to an embodiment of the present invention;

[0046] Figure 3 Schematic diagram of a typical wind power and photovoltaic output scenario according to an embodiment of the present invention;

[0047] Figure 4 Schematic diagram of the efficient frontier curve of returns with respect to conditional value at risk according to an embodiment of the present invention;

[0048] Figure 5 This is a schematic diagram of the optimization results of the virtual power plant aggregated resources according to an embodiment of the present invention;

[0049] Figure 6 This is a schematic diagram of nested electricity price optimization results according to an embodiment of the present invention;

[0050] Figure 7 A schematic diagram of interactive power optimization results according to an embodiment of the present invention;

[0051] Figure 8 This is a schematic diagram of the interactive electricity price optimization results according to an embodiment of the present invention;

[0052] Figure 9 This is a schematic diagram of the demand response positivity optimization results according to an embodiment of the present invention. DETAILED DESCRIPTION

[0053] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0054] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0055] Example 1

[0056] This embodiment provides a virtual power plant optimization method based on risk assessment and user satisfaction using a multi-agent collaborative power sharing two-layer nested game, including:

[0057] Calculate the uncertainty of distributed energy resources within virtual power plants based on risk value theory and build a multi-scenario risk assessment model;

[0058] Build an optimized virtual power plant dispatch model based on user participation and satisfaction;

[0059] A nested game two-level optimization model is constructed based on the interactive problem in the coordinated dispatch of multiple agents and multiple virtual power plants;

[0060] The virtual power plant is optimized based on the risk assessment model, the virtual power plant scheduling model and the nested game two-layer optimization model.

[0061] This example addresses the risk management challenges associated with the uncertainty of distributed energy resources within virtual power plants (VPPs). It introduces conditional value-at-risk theory and constructs a multi-scenario risk assessment model. In this model, distribution network operators, acting as top-level leaders, interact with the VPP consortium through price guidance to achieve a balanced management of risks and benefits.

[0062] To address user engagement and satisfaction, this embodiment adds a quantitative indicator of user satisfaction, including demand response mechanisms, to the model. By considering the economics and satisfaction of user load adjustments, the virtual power plant's dispatch strategy is optimized, ensuring that user comfort and service quality requirements are met while improving system economics.

[0063] To address the interaction issues in the coordinated scheduling of multiple entities and multiple virtual power plants, this embodiment proposes a two-layer nested model for power sharing, in which the virtual power plant alliance serves as the lower-level follower. Members optimize internal power transactions by sharing idle resources and responding to upper-level price signals, thereby enhancing the system's flexibility and responsiveness.

[0064] The nested game-based two-layer optimization model constructed in this embodiment forms a closed-loop decision-making and feedback mechanism, enabling all entities to benefit from power sharing. In a two-layer problem, the solution to the inner layer depends on the solution to the outer layer. The KKT condition is a method for solving two-layer problems by transforming them into a single-layer problem, simplifying the solution.

[0065] The framework of the multi-agent collaborative power sharing nested game two-layer optimization model for risk assessment and user satisfaction is as follows:

[0066] Virtual power plants (VPPs) aggregate distributed renewable energy, gas turbines, interruptible loads, and shiftable loads. Distributed renewable energy includes wind power and photovoltaics, interruptible loads include residential air conditioners, and shiftable loads include electric vehicles, commercial loads, and battery energy storage systems. In the future, different VPPs will be owned by different stakeholders, creating a competitive landscape with multiple decision-makers. The uncertainty of distributed energy resources, conflicts of interest among operators, and the complexity of coordinated planning limit the potential of VPPs in the electricity market.

[0067] To solve the above problems, the present invention establishes a two-layer nested game structure consisting of a distribution network operator and a virtual power plant aggregate that aggregates distributed energy resources, which solves the risk management problem caused by the uncertainty of distributed energy resources within the virtual power plant and realizes power sharing and optimization of collaborative scheduling of multiple virtual power plants. By introducing the conditional risk value theory to construct a multi-scenario risk assessment model, the distribution network operator interacts with the lower-level virtual power plant aggregate through pricing strategies to achieve balanced management of risks and benefits. The Nash game model of power sharing among lower-level aggregate members allows virtual power plants to share idle resources and respond to price signals, optimize internal power transactions, and improve the flexibility and responsiveness of the system. Through quantitative indicators of user satisfaction, while meeting user comfort requirements, flexible loads are actively guided to participate in demand response.

[0068] In order to consider the uncertain risks of wind and solar power output and market electricity prices, this paper adopts the conditional value at risk theory. Distribution network operators interact with the underlying virtual power plant aggregates through pricing strategies to achieve balanced management of risks and benefits.

[0069] Conditional VaR is an improvement on VaR, which is defined as: during a specific investment period, the average loss of the portfolio risk exceeding the VaR under a set confidence level is:

[0070]

[0071] Where: For investment portfolio The loss function is Represents a continuous random factor that may affect the loss function.

[0072] Calculating the conditional value at risk is equivalent to solving a linear constraint problem with discrete variables, which simplifies the calculation process. The specific calculation method in a discrete scenario is as follows:

[0073]

[0074] Where: is the number of discrete scenarios; For the The value of a random variable under a discrete scenario. This formula assumes that the probability of all discrete scenarios occurring is equal; For risk value.

[0075] Due to the volatility of renewable energy generation, actual power generation may deviate from expectations. This deviation has a significant impact on the power grid, and attention should be paid to its average level and probability of occurrence. The conditional risk value can reflect both the magnitude of the deviation and the likelihood of occurrence. The definition of renewable energy output deviation is as follows:

[0076]

[0077] Where: Contribute to the new energy plan, Make practical contributions to new energy.

[0078] The user engagement and satisfaction questions were constructed as follows:

[0079] Demand response projects guide users to use energy rationally, optimize terminal energy consumption curves, and improve the energy efficiency of virtual power plants. In a humanized scheduling environment, formulating demand response scheduling methods based solely on the optimal benefits of the main body will lead to a decline in user satisfaction, resistance, and a significant reduction in enthusiasm. Therefore, scheduling strategies that consider user satisfaction are extremely important. Users usually arrange their electricity usage plans according to the production and lifestyle that best suits them, so that users are most satisfied with their electricity usage methods. However, after users participate in demand response, they need to change their original electricity usage plans to respond to the load scheduling of the virtual power plant and form a new electricity load curve. Defining satisfaction with electricity usage methods The degree of change in the load curve before and after the response.

[0080]

[0081]

[0082] Where: 、 are the electric load power before and after response respectively.

[0083] Virtual power plants (VPPs) aggregate distributed renewable energy, gas turbines, interruptible loads, and shiftable loads. Interruptible loads include residential air conditioners, while shiftable loads include electric vehicles, commercial loads, and battery energy storage systems. These flexible loads participate in demand response, and the VPP is compensated based on the amount of demand response it participates in, thus taking the cost of flexible load compensation into account.

[0084]

[0085] Where: Cost of flexible loads participating in demand response; 、 are the cost coefficients for shifting load and interrupting load to participate in demand response; 、 are the transfer and interruption load powers participating in demand response, respectively.

[0086] 1. The two-level optimization model of the nested game between the distribution network operator and the virtual power plant aggregate is constructed as follows:

[0087] S1: Game-theorizing dynamic pricing model for upper-level distribution network operators

[0088] The distribution network operator aims to maximize the overall objective, which includes the costs and benefits of power trading with the upper grid and the virtual power plant aggregate, while controlling the risk aversion coefficient to account for uncertainty. The decision model of the distribution network operator is as follows.

[0089] (1) Objective function

[0090] The objective function consists of two items: one is the revenue generated by the distribution network operator trading electricity with the grid; the other is the risk-return trade-off.

[0091]

[0092] Where: 、 、 are the virtual power plant serial number, time, and scene respectively; correspondingly, is its quantitative value; is the scenario probability; are the on-grid electricity price and the grid electricity price respectively; are the purchase and sale prices of electricity of the virtual power plant respectively; They are the electricity purchase and sales of the virtual power plant; is the risk aversion coefficient; the risk value of the virtual power plant benefits; is the confidence level; is an auxiliary variable, indicating that the operating profit of the virtual power plant in each scenario exceeds proportion.

[0093] (2) Constraints

[0094] 1) Electricity price constraints

[0095] To prevent distribution network operators from setting high purchase prices and low sales prices for virtual power plant aggregates out of self-interest, the purchase and sales prices set by distribution network operators should meet the following constraints.

[0096]

[0097]

[0098] Where: are the minimum values ​​of the purchase and sale prices of electricity respectively; are the maximum values ​​of electricity purchase and sale prices respectively; are the average values ​​of electricity purchase and sale prices, respectively.

[0099] 2) Conditional Value-at-Risk Constraints

[0100]

[0101] S2: Game-theoretic lower-layer virtual power plant aggregate model

[0102] Guided by the distribution network operator's strategy, virtual power plants (VPPs) achieve mutual benefit through energy exchange with the distribution network operator. Nash game theory is used to analyze the energy interactions between VPPs, encouraging them to share resources and optimize costs. This mechanism facilitates energy trading among VPPs and fairly distributes revenue based on their contributions. By evaluating the VPPs' response to electricity price signals, distribution network operators can develop effective market mechanisms to ensure that VPPs adopt optimal operating strategies under electricity price incentives.

[0103] (1) Objective function

[0104] Each member of the virtual power plant aggregate aims to maximize its own comprehensive benefits, including the income from purchasing and selling electricity, the interactive benefits among members, demand response costs, energy storage costs, gas turbine operating costs, and user satisfaction conversion costs.

[0105]

[0106]

[0107] Where: are the costs of transactions within the virtual power plant aggregate; Payment costs for transactions within the virtual power plant aggregator; is the Nash game bargaining coefficient; They are gas turbine operating cost, adjustable load participation demand response cost, and user satisfaction conversion cost; is the gas turbine cost coefficient; are the cost coefficients for shifting load and interrupting load to participate in demand response; Convert the cost coefficient to the user satisfaction index; is the energy storage charging and discharging cost coefficient; is the charging and discharging power of energy storage; Output power for the gas turbine; are the transfer and interruption load powers participating in demand response, respectively; are the electric load power before and after response respectively.

[0108] (2) Constraints

[0109] 1) Power balance constraints

[0110]

[0111] Where: It is the internal transaction volume of the virtual power plant aggregate; are wind and solar output power respectively.

[0112] 2) Gas turbine constraints

[0113]

[0114] Where: is the maximum output power of the gas turbine; is the maximum ramp power constraint of the gas turbine.

[0115] 3) Constraints on electricity purchase and sales

[0116]

[0117] Where: are the maximum values ​​of electricity purchased and sold respectively.

[0118] 4) Electric vehicle constraints

[0119] This paper assumes that the daily mileage distribution of electric vehicles and fuel vehicles is similar. The probability density function of the time when a vehicle is connected to the grid is similar to the normal distribution function and is expressed as:

[0120]

[0121] The probability density function of the time when a vehicle is disconnected from the grid can be expressed as:

[0122]

[0123] The probability density of the daily mileage of electric vehicles is as follows:

[0124]

[0125] Where: The daily mileage of electric vehicles.

[0126] Estimate the amount of electricity required based on the daily driving distance of the electric vehicle as follows:

[0127]

[0128] Where: The power consumption per kilometer for electric vehicles; is the discharge efficiency of electric vehicles.

[0129] Taking into account user participation in demand response, the charging capacity of electric vehicles should be within a reasonable range to ensure users' daily travel needs and meet the following constraints.

[0130]

[0131] Where: They are the initial load of electric vehicles, the load transferred by participating in demand response, the maximum transfer amount, and the load of electric vehicles after transfer; The amount of electricity in the electric vehicle when it leaves the vehicle; Charging efficiency for electric vehicles; The positive response to electric vehicles.

[0132] 5) Commercial load constraints

[0133]

[0134] Where: They are the initial load of commercial load, load transferred by participating in demand response, maximum transfer amount and commercial load after transfer; The responsiveness of commercial loads.

[0135] 6) Battery Energy Storage System Constraints

[0136]

[0137] Where: is the maximum charge and discharge power of the battery energy storage system; The charging and discharging efficiency of the battery energy storage system; are the battery energy storage system's capacity and maximum capacity respectively.

[0138] 7) Air conditioning constraints

[0139]

[0140] Where: They are the initial load of air conditioner, interruption load of participating demand response, maximum interruption amount and air conditioner load after interruption; The responsiveness of the air conditioner; is the indoor and outdoor temperature; are the equivalent thermal resistance and capacitance of the building, respectively.

[0141] 8) Demand response constraints

[0142]

[0143] 9) Revenue Constraints

[0144]

[0145] Constraints ensure that the collective interests of the power sharing model outweigh individual operations, the balance of transaction funds and the balanced distribution of benefits.

[0146] 2. The solution process of the nested game two-level optimization model is as follows:

[0147] In a two-layer problem, the solution to the inner layer depends on the solution to the outer layer. The KKT condition is a method for solving two-layer problems. It transforms the two-layer problem into a single-layer problem, simplifying the solution. To solve the nested game two-layer optimization model constructed by this invention, the lower-layer virtual power plant internal energy trading model is first decomposed into two independent sub-problems, namely P1 and P2.

[0148] P1: Aggregate benefit maximization problem

[0149]

[0150] P2: Benefit distribution issues

[0151]

[0152] In order to speed up the solution and reduce the number of iterations, the power function of the above equation is logarithmically processed.

[0153]

[0154] To address a bilevel optimization problem involving bilinear terms, the KKT condition is used to transform the low-level problem into a nonlinear single-level problem involving complementary slack conditions and bilinear products. The Big-M method is then used to address the complementary slack conditions of the Lagrange multipliers and constraints. The bilinear product is linearized using strong duality theory, ultimately forming an equivalent single-level mixed-integer linear programming model. This model is solved using the YALMIP toolbox and the CPLEX solver in the MATLAB environment.

[0155] The equivalent single-level mixed integer linear programming formula is as follows:

[0156]

[0157] The complementary slack conditions corresponding to the inequalities are shown below.

[0158]

[0159] In the above formula, there are nonlinear constraints. We introduce 0-1 Boolean variables and use the Big-M method to transform the nonlinear constraints into mixed integer linear constraints, as shown in the following formula:

[0160]

[0161] Where: is the introduced dual variable; is a sufficiently large number; Boolean variable introduced for the complementary slack condition.

[0162] The following example analyzes the scene generation, as described below:

[0163] The simulation uses a provincial electricity market in China as an example. A simplified example is used to verify the proposed two-layer nested game model, using one operator and three regional virtual power plants. Figure 1 Energy trading framework, Figure 2 Nested game two-level optimization model, Figure 3 Typical wind power and photovoltaic output scenarios. The grid's time-of-use electricity prices are shown in Table 1, the gas turbine and battery energy storage operating parameters are shown in Tables 2 and 3, and the probability of each scenario is shown in Table 4.

[0164] Table 1

[0165]

[0166] Table 2

[0167]

[0168] Table 3

[0169]

[0170] Table 4

[0171]

[0172] Using the CVaR theory, we assess the uncertainty risk of wind and solar power output, allowing distribution network operators to balance risk and return. We set the confidence level α to 0.95 and the risk aversion coefficient between 0.01 and 1. Table 5 shows the analysis of the expected return and CVaR values ​​of distribution network operators under different risk aversion coefficients.

[0173] Table 5

[0174]

[0175] As shown in Table 5, as the risk aversion coefficient gradually increases, the distribution network operator's attitude towards risk gradually changes from aggressive to conservative, the expected return gradually decreases, and the loss caused by risk also gradually decreases. In the operation strategy, it is more inclined to set a higher electricity selling price and a lower electricity purchase price. According to the calculation results in Table 5, the efficient frontier curve of the distribution network operator's expected return with respect to CvaR is obtained, as shown in Figure 4 shown.

[0176] This paper divides the distribution network operators' attitudes towards risk into five categories according to the degree of risk aversion: radical, partially radical, neutral, partially conservative, and conservative. Figure 4 As shown. Figure 4 It can be seen that when the distribution network operator has an aggressive attitude towards risk, the expected return changes little as the degree of risk acceptance increases; when the distribution network operator has a conservative attitude towards risk, the expected return increases slowly as the degree of risk acceptance increases; when the distribution network operator is relatively conservative, the expected return is linearly related to the degree of risk acceptance, and the higher the degree of risk acceptance, the greater the expected return.

[0177] To verify the economic viability of the proposed game model, combined with the analysis in the previous section, we established the following two game models for comparative simulations, considering a risk aversion coefficient of α = 0.1. Scenario 1: A master-slave game model between the distribution network operator and the virtual power plant. Scenario 2: A nested game with two-level optimization.

[0178] After optimization and calculation, the benefits of distribution network operators participating in the energy market, as well as the benefits and operating costs of each virtual power plant entity, are shown in Tables 6 and 7, respectively, for each scenario. The payment costs of electricity transactions between virtual power plants, derived from the sharing of idle power among the virtual power plants in the lower layer of the nested game, are shown in Table 8.

[0179] Table 6

[0180]

[0181] Table 7

[0182]

[0183] Table 8

[0184]

[0185] A comparison shows that the proposed approach (Scenario 2) increases the total revenue of distribution network operators by 17,434.28 yuan compared to Scenario 1. This is because, after considering the nested game, the virtual power plant's dependence on power purchases from the distribution network operator decreases while its dependence on power sales increases. Furthermore, the price of power purchased from the virtual power plant is lower, which increases the distribution network operator's revenue. The complementary utilization of energy by members of the virtual power plant aggregate through idle power trading increases the aggregate's total revenue. Virtual Power Plant 1's profit increases by 7,391.8 yuan, Virtual Power Plant 2's by 7,681.26 yuan, and Virtual Power Plant 3's by 6,470.84 yuan. This is because the introduction of the Nash game reduces the aggregate's total cost while improving the benefits of each member, ensuring a fair distribution of the benefits of cooperation. In summary, the proposed nested game reduces costs and increases revenue for each entity through underlying power sharing and optimization of each entity. This demonstrates the economic viability of the nested game model established in this paper.

[0186] Under the two game modes, each virtual power plant aggregates resources to optimize output. Figure 5 As shown, the game electricity price is Figure 6 shown. Figure 5 The left figure shows the output of equipment in virtual power plant 1-3 under scenario 1, and the right figure shows the output of equipment in virtual power plant 1-3 under scenario 2.

[0187] Depend on Figure 5 As can be seen, the power generated by the virtual power plant's internal entities not only meets internal demand at certain times but also generates revenue by selling excess electricity to the market. Of the three virtual power plants, Virtual Power Plant 3 has the highest load demand, while Virtual Power Plant 2 has the lowest. A vertical analysis shows that when the power generated by the virtual power plant's internal entities is insufficient to meet internal demand, the cost of purchasing electricity from the market exceeds the cost of gas turbine generation, so gas turbine generation is prioritized. During certain periods of insufficient power, energy storage discharge is used to meet demand. At other times, excess power is allocated based on the electricity sales price and the electricity purchase price during other periods. However, Virtual Power Plant 1, due to its high internal power generation, is sufficient to meet demand, and the high cost factor of installing a gas turbine, does not use gas turbine generation throughout the entire period. Power generation is high at noon, and the remaining power is traded at the electricity sales price set by the distribution network operator. A horizontal analysis shows that under both game modes, the right-hand figure, due to the power-sharing Nash game model, considers transactions between virtual power plants during power shortages or surpluses. At certain moments, internal equipment output and surplus power sales fluctuate. This is due to the transaction costs of each virtual power plant and the price of electricity negotiated between them. This also promotes local energy consumption and reduces other costs. Secondly, the post-response load curve shows that the nested game's post-response load curve is smoother. This is the optimal value for adjustable load participation in demand response, considering user satisfaction. This shows that the nested game constructed in this paper has a good peak-shaving and valley-filling effect on the scheduling of controllable loads.

[0188] Depend on Figure 6 It can be seen that regardless of the game framework, the upper echelon seeks to maximize its own interests. This means that the electricity pricing pattern set by distribution network operators remains unchanged, with higher sales prices and lower purchase prices. Therefore, under both game frameworks, distribution network operators will purchase electricity at the same price from virtual power plants, ensuring the lowest electricity purchase costs for distribution network operators. However, the price set by virtual power plants from distribution network operators in the nested game is higher than that in the one-master-multiple-slave game and is closer to the price ceiling. This is because the virtual power plants share power, reducing the amount of electricity they can sell to distribution network operators. Therefore, distribution network operators set higher prices to mitigate losses caused by the decrease in traded electricity.

[0189] The interactive power between virtual power plant aggregates is as follows Figure 7 As shown, the game electricity price is Figure 8 shown.

[0190] Figure 7-8 It can be seen that the Nash game electricity price setting is related to the amount of electricity exchanged between individual virtual power plants. At every moment, there are always virtual power plant aggregates purchasing and selling electricity. From the perspective of electricity purchase, the party with a smaller purchase amount sets a lower transaction price, while the party with a larger transaction volume sets a higher transaction price. After the Nash game participants trade in power sharing, the benefits of participating in power sharing are more equitable and reasonable. The greater the amount of power shared, the higher the benefits. At the same time, the nested game model ensures that the upper and lower levels of the entities optimize their output, resulting in increased profits.

[0191] Figure 6 and 8 By comparison, the Nash game electricity price is lower than the master-slave game price. This is because the nested power-sharing game model encourages energy trading between virtual power plant aggregates. Excess energy can be consumed locally, reducing the impact of grid connection on grid stability and lowering the costs of virtual power plant aggregates. This demonstrates the economic viability of this proposed game model.

[0192] This paper constructs flexible load models such as air conditioners, electric vehicles, commercial loads, and energy storage to participate in demand response, and accesses the system through the user satisfaction evaluation index created. Finally, the response positivity of air conditioners, electric vehicles, and commercial loads in the three virtual power plants obtained through optimization is as follows: Figure 9 shown.

[0193] As shown in the figure, air conditioning response activity is low during hot noon and afternoon hours due to the urgent need for cooling. However, response activity is higher during milder mornings and evenings, as demand for air conditioning decreases during these times, making users more willing to participate in demand response. Electric vehicle response activity decreases continuously during vehicle usage and rest periods, but steadily increases during non-working hours. Commercial load response activity reaches its lowest point during periods of peak business activity, slowly declines during normal business hours, and rises during periods of low business activity, giving commercial users greater flexibility in adjusting their electricity usage. Multiple factors, including load characteristics, user behavior, market mechanisms, and incentives, interact to cause fluctuations in load response activity over time.

[0194] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A virtual power plant optimization method based on risk assessment and user satisfaction for multi-agent collaborative power sharing and double-layer nested game, characterized in that: include: Calculate the uncertainty of distributed energy resources within virtual power plants based on risk value theory and build a multi-scenario risk assessment model; Build an optimized virtual power plant dispatch model based on user participation and satisfaction; A nested game two-level optimization model is constructed based on the interactive problem in the coordinated dispatch of multiple agents and multiple virtual power plants; Optimizing the virtual power plant based on the risk assessment model, the virtual power plant scheduling model and the nested game two-layer optimization model; The process of constructing the nested game two-layer optimization model includes: Construct the upper-level model of dynamic pricing for distribution network operators based on the upper-level objective function and upper-level constraints; Construct a lower-level virtual power plant aggregate model based on the lower-level objective function and lower-level constraints; Solving the upper-layer dynamic pricing model of the distribution network operator and the lower-layer virtual power plant aggregate model based on the KKT condition to obtain the nested game two-layer optimization model; The upper objective function is: ； in, 、 、 are the virtual power plant serial number, time, and scene respectively; correspondingly, is its quantitative value; is the scenario probability; are the on-grid electricity price and the grid electricity price respectively; are the purchase and sale prices of electricity of the virtual power plant respectively; They are the electricity purchase and sales of the virtual power plant; is the risk aversion coefficient; the risk value of the virtual power plant benefits; is the confidence level; is an auxiliary variable, indicating that the operating profit of the virtual power plant in each scenario exceeds proportion; The upper-level constraints include: electricity price constraints and conditional risk value constraints; The lower layer objective function is: ； ； in, are the costs of transactions within the virtual power plant aggregate; Payment costs for transactions within the virtual power plant aggregator; is the bargaining coefficient of Nash game; They are gas turbine operating cost, adjustable load participation demand response cost, and user satisfaction conversion cost; is the gas turbine cost coefficient; are the cost coefficients for shifting load and interrupting load to participate in demand response; Convert the cost coefficient to the user satisfaction index; is the energy storage charging and discharging cost coefficient; is the charging and discharging power of energy storage; Output power for the gas turbine; are the transfer and interruption load powers participating in demand response, respectively; are the electric load power before and after the response respectively; The lower-level constraints include: power balance constraints, gas turbine constraints, power purchase and sales constraints, electric vehicle constraints, commercial load constraints, battery energy storage system constraints, air conditioning constraints, demand response constraints and revenue constraints.

2. The method according to claim 1, characterized in that In the multi-scenario risk assessment model, the average loss of the portfolio risk loss exceeding the risk value under the set confidence level is: ； in, For investment portfolio The loss function is Represents a continuous random factor that may affect the loss function; The expression for calculating the conditional risk value of the multi-scenario risk assessment model is: ； in, is the number of discrete scenarios; For the The value of a random variable in a discrete scenario, For risk value.

3. The method according to claim 1, characterized in that The process of building an optimized virtual power plant dispatch model based on user engagement and satisfaction includes: User engagement and satisfaction were defined as the degree of change in the load curve before and after the response; Building flexible economic compensation based on user participation in demand response; The virtual power plant scheduling model is constructed based on the degree of change of the load curve before and after the response and the flexible economic compensation.

4. The method according to claim 3, characterized in that The expression for the degree of change of the load curve before and after the response is: ； in, 、 are the electric load power before and after response respectively.

5. The method according to claim 3, characterized in that The calculation expression of the flexible economic compensation is: ； in, Cost of flexible loads participating in demand response; 、 are the cost coefficients for shifting load and interrupting load to participate in demand response; 、 are the transfer and interruption load powers participating in demand response, respectively.

6. The method according to claim 1, characterized in that The process of solving the upper-level dynamic pricing model of the distribution network operator and the lower-level virtual power plant aggregate model based on the KKT condition includes: using the KKT condition to transform the upper-level dynamic pricing model of the distribution network operator and the lower-level virtual power plant aggregate model into a nonlinear single-layer problem containing complementary relaxation conditions and bilinear products, and then using the Big-M method to process the complementary relaxation conditions of the Lagrange multipliers and constraints, and linearizing the bilinear product through strong duality theory, finally forming an equivalent nested game two-level optimization model.

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