A master-slave game pricing method for virtual power plant balancing service

Abstract

This invention discloses a master-slave game-theoretic pricing method for virtual power plant balancing services, belonging to the technical field of electricity market and virtual power plant collaborative operation. The method includes: constructing a master-slave game framework between the balancing service provider and multiple virtual power plants, establishing an upper-level pricing model and a lower-level decision-making model; transforming the two-level game model into a mixed-integer linear programming model based on KKT conditions and duality theory; and obtaining the optimal balancing service price, the proportion of electricity purchased by each virtual power plant, and the compensation strategy of the balancing service provider through an optimization solver. This invention introduces the balancing service provider as an independent market entity to provide electricity balancing services to virtual power plants, replacing the traditional deposit model and relieving the financial pressure on enterprises; it achieves synergistic optimization of interests between the two parties through the master-slave game model, improving resource allocation efficiency and system operational flexibility. This method can be widely applied to power systems with a high proportion of renewable energy access, supporting the commercial operation of virtual power plants and the stable operation of the electricity market.

Description

Technical Field

[0001] This invention relates to the field of power system operation and power market trading technology, and in particular to a master-slave game pricing method for virtual power plant balancing services, applicable to the collaborative operation and market-based trading between virtual power plants and balancing service providers in power systems with a high proportion of renewable energy. Background Technology

[0002] Driven by the "dual-carbon" strategic goals, renewable energy sources, represented by wind power and photovoltaics, are rapidly becoming the mainstay of energy structure transformation. As the installed capacity of wind and solar power continues to climb, the inherent intermittency and volatility of these technologies increasingly highlight the contradiction between them and the safe and stable operation of the power grid, placing higher demands on the power system's flexible adjustment capabilities. Virtual Power Plants (VPPs), as a solution to this challenge, utilize the Internet of Things, big data, and advanced control technologies to deeply aggregate and intelligently coordinate diverse distributed energy resources (DERs), such as distributed generator sets, energy storage devices, and controllable loads, achieving optimized resource allocation and flexible system adjustment.

[0003] However, the commercial operation of virtual power plants still faces multiple challenges. Under the backdrop of power market reform, virtual power plants need to participate as independent entities in the medium- and long-term electricity market, spot market, and ancillary services market. However, the distributed resources they aggregate are affected by uncertainties such as natural conditions and user behavior, which may lead to insufficient power supply and consequently, risks of penalties for deviations in electricity trading assessments or default compensation. On the other hand, virtual power plants participating in the electricity market need to submit performance guarantees. The traditional margin deposit model ties up a large amount of working capital, limiting their technological upgrades and resource aggregation capabilities.

[0004] Therefore, power balancing services, as an innovative tool for transferring performance risks and optimizing capital allocation, are gradually becoming a core component of virtual power plant risk management. In 2024, the first virtual power plant power transaction performance guarantee insurance policy in China was implemented at State Grid Shandong Integrated Energy Company, relieving the company's financial pressure by replacing margin deposits with premium payments. This case marks the formal entry of insurance mechanisms into the virtual power plant field, providing the industry with a new paradigm for risk hedging. However, the design of current power balancing service products still faces many challenges: How to design insurance clauses that cover multiple risks such as technical failures and market fluctuations? How to establish a premium pricing model adapted to the characteristics of virtual power plants?

[0005] In summary, existing research on pricing mechanisms for virtual power plant balancing services still has the following shortcomings: First, it lacks a systematic model for collaborative pricing between virtual power plants and balancing service providers; second, it does not fully consider the price response behavior and risk preferences of virtual power plants; and third, traditional pricing methods fail to achieve optimal synergy between the interests of both parties, resulting in low market efficiency. Therefore, there is an urgent need for a pricing method for balancing services that can achieve synergy between the interests of virtual power plants and balancing service providers and improve system operating efficiency. Summary of the Invention

[0006] The purpose of this invention is to provide a master-slave game pricing method for virtual power plant balancing services, in order to solve the problems of imperfect pricing mechanisms, low market efficiency, and unreasonable resource allocation in existing technologies, and to achieve synergy of interests and optimized risk allocation between virtual power plants and balancing service providers.

[0007] To achieve the above objectives, the present invention provides the following solution:

[0008] A master-slave game pricing method for virtual power plant balancing services, the method comprising:

[0009] Step 1: Construct a joint trading framework between Balance Service Providers (BSPs) and multiple Virtual Power Plants (VPPs), clarify the market roles of BSPs as balance service providers and VPPs as balance service buyers, and define two paths for BSPs to compensate VPPs for shortfalls in electricity: compensation using their own energy storage or compensation by purchasing electricity from the real-time balance market.

[0010] Step 2: Based on the supply and demand relationship and risk transfer characteristics between BSP and multiple VPP in the electricity market, construct a Stackelberg master-follower game model to simulate the dynamic game behavior of market leaders and followers, and establish an upper-level pricing model with the goal of maximizing BSP profits and a lower-level decision-making model with the goal of minimizing VPP costs.

[0011] Step 3: Based on the KKT conditions and duality theory, the two-layer master-slave game model is transformed into a mixed integer linear programming model that can be solved efficiently;

[0012] Step 4: Solve the mixed-integer linear programming model using the optimization solver to obtain the optimal balance service price, the proportion of electricity purchased by each VPP, and the BSP compensation strategy under equilibrium conditions.

[0013] Furthermore, the construction of the Stackelberg master-follower game model simulating the dynamic game behavior of market leaders and followers specifically includes:

[0014] Assuming the BSP is the upper-level leader, its decision variables include the uniform balancing service price λser for all VPPs and the self-owned energy storage compensation ratio z for each VPP.i ;

[0015] Multiple VPPs are designated as lower-level followers, and the decision variable for each VPP is the proportion of electricity purchased from the BSP for balancing services. ;

[0016] Establish the sequential decision-making relationship between BSP and VPP: BSP first publishes the price λ ins Each VPP decides its purchase ratio accordingly. Ultimately, both parties settled accounts and provided compensation based on the actual shortfall in electricity consumption.

[0017] Furthermore, the establishment of the upper-level pricing model aimed at maximizing BSP profits specifically includes:

[0018] BSP's Balancing Service Revenue: The BSP sells power balancing services to VPPs and receives balancing service revenue. For the i-th VPP, the balancing service revenue obtained by the BSP is:

[0019]

[0020] In the formula: The balanced service revenue that BSP obtains in the i-th VPP; The unit power balance service price set by the BSP in the game; The contracted electricity volume sold by the i-th VPP; The proportion of the ith VPP's decision to purchase balance services in the game.

[0021] BSP's compensation costs: As the provider of balancing services, BSP's compensation terms for VPPs are as follows:

[0022] If the actual power deficit of VPPs Less electricity than the amount purchased for balancing service a day ago BSP only compensates VPPs for the actual shortfall; if the actual shortfall in electricity volume for wind VPPs is... More electricity than the balancing service The BSP reimburses the VPPs for the entire balancing service volume, while the wind power generator bears the remaining deviation penalty cost. Therefore, the balancing service provider reimburses the i-th VPP for the specified volume. for:

[0023]

[0024] BSPs can choose two methods to compensate VPPs that have purchased balancing services for insufficient power:

[0025] Approach 1: Utilize the BSP's own energy storage resources. The unit cost for compensating the i-th VPP is... The unit cost varies with the distance between each VPP and BSP; the greater the distance, the higher the cost.

[0026] Approach 2: From real-time balancing market to market-based electricity purchase prices Compensation will be provided by purchasing electricity.

[0027] The compensation cost incurred by the BSP for the i-th VPP is:

[0028]

[0029] In the formula: C i com Z represents the cost of compensation paid by the BSP to the i-th VPP. i Let z be the proportion of the compensation electricity of the i-th VPP that the BSP uses its own energy storage to compensate for. i c is the proportion of electricity purchased by the BSP from the real-time balancing market to compensate the i-th VPP for its compensation electricity; own,i The unit cost of BSP using its own energy storage to compensate for the i-th VPP; N i λ is the compensation charge of the BSP for the i-th VPP; buy The unit price of electricity purchased by the BSP from the real-time balancing market.

[0030] The objective function of BSP in this model is to maximize the total revenue C. BSP The objective function expression is as follows:

[0031]

[0032] Price Constraints: To ensure that VPPs are willing to transact with BSP for balancing services, the balancing service price set by BSP should meet the following constraints:

[0033]

[0034] Compensation and capacity constraints:

[0035]

[0036]

[0037] In the formula: P avail This represents the total energy storage capacity owned by the BSP.

[0038] Furthermore, the establishment of the lower-level decision-making model with the objective of minimizing VPP cost specifically includes:

[0039] The balancing service fee paid by VPPs: VPPs purchase power balancing services from BSPs to reduce their own deviation penalty costs. The insurance fee paid by the i-th VPP to the BSP is:

[0040]

[0041] Deviation penalty cost borne by VPP: If the amount of electricity purchased by VPP from balancing services is sufficient to cover the shortfall, then VPP will not incur any deviation penalty; if the amount of electricity purchased by VPP from balancing services is insufficient to cover the shortfall, then VPP will incur the remaining deviation penalty cost.

[0042] The deviation charge that the i-th VPP needs to bear as an additional deviation penalty is:

[0043]

[0044] The deviation penalty cost borne by the i-th VPP is:

[0045]

[0046] In the formula: λ pen T represents the deviation penalty coefficient, indicating the unit price of the deviation penalty imposed by the market or dispatching agency; i The deviation power that VPP needs to bear as an additional deviation penalty.

[0047] The cost of the i-th VPP due to insufficient power: The objective function of each VPP is to minimize its own additional cost C due to insufficient power. i VPP The target expression is as follows:

[0048]

[0049] Optional, lower-level decision constraints:

[0050]

[0051] Optionally, the transformation of the two-level master-slave game model into an efficiently solvable mixed-integer linear programming model based on KKT conditions and duality theory specifically includes:

[0052] Since the lower-level decision problem contains a max function, we introduce... Instead of the max function, that is

[0053]

[0054] Using the methods for handling max functions in mathematical programming, Equivalently represented as linear inequality constraints:

[0055]

[0056] Similarly, regarding the higher-level problem... It can be used To indicate:

[0057]

[0058] The lower-level problem can then be rewritten as:

[0059]

[0060] The dual problem of the lower-level problem is obtained as follows:

[0061]

[0062] In the formula: , For the corresponding dual variable.

[0063] The duality theorem for linear programming states that the objective function values ​​of the primal and dual problems are equal at the optimal solution. Therefore, for the lower-level linear programming problem, the following equation can be obtained:

[0064]

[0065] Under KKT constraints, the upper-level objective function expression is equivalent to:

[0066]

[0067] This formula is linear with respect to the decision variables at both the upper and lower levels.

[0068] In the lower-level game decision-making process of this paper, the equilibrium service price is given for the follower VPPs. If the lower-level linear programming problem is replaced by its KKT conditions, the optimization problem can be eliminated, transforming the two-level problem into a single-level problem. The optimal solution of the lower-level optimization problem is expressed as the constraint conditions of the upper-level variables. Let the dual variable be... , Then the KKT conditions for the lower-level optimization problem are:

[0069]

[0070] In the formula: , These are dual variables. The lower-level optimization can be transformed into constraints using KKT conditions.

[0071] In summary, the BSP's balancing service pricing game with VPPs can be transformed into the following mixed-integer linear programming problem:

[0072]

[0073] The optimal solution of this mixed-integer linear programming problem This constitutes the equilibrium point of the original master-slave game.

[0074] Furthermore, the step of solving the mixed-integer linear programming model using an optimization solver specifically includes:

[0075] Input the transformed mixed-integer linear programming model into the business optimization solver;

[0076] Set the solution accuracy and time limits, and execute the solution algorithm;

[0077] Extract and output the global optimal solution, including the optimal balancing service price λ. ins Optimal purchase ratio for each VPP (vpponent platform) b i BSP optimal compensation ratio z i And the corresponding BSP profit and VPP cost.

[0078] Compared with existing technologies, this technology has the following advantages:

[0079] This invention provides a master-slave game-theoretic pricing method for virtual power plant (BSP) balancing services. Addressing the deviation assessment risks and capital occupation issues faced by virtual power plants in a high-proportion renewable energy power market, it proposes a market-based pricing mechanism for balancing services based on Stackelberg game theory. This invention is the first to introduce master-slave game theory into the pricing problem of virtual power plant power balancing services, constructing a two-level game model between BSPs and VPPs. This model accurately characterizes the strategic interactions between the two parties in risk transfer and pricing, providing theoretical support for the design of balancing service market mechanisms. By using KKT conditions and duality theory, the complex two-level model is transformed into a mixed-integer linear programming problem, ensuring efficient solution and global optimality. By optimizing the dynamic compensation ratio of BSPs' "own energy storage + market-purchased electricity," resource allocation efficiency and operational revenue are significantly improved. This invention achieves synergy of interests and optimized risk allocation between virtual power plants and balancing service providers, improving the overall operational efficiency and flexibility of the power market.

[0080] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0081] Figure 1 This is a flowchart of an embodiment of the present invention;

[0082] Figure 2 This is a transaction framework diagram between the balancing service provider and the virtual power plant in an embodiment of the present invention;

[0083] Figure 3 This is a structural diagram of the master-slave game model in an embodiment of the present invention;

[0084] Figure 4 This is a schematic diagram of the probability distribution of the virtual power plant's power shortage in an embodiment of the present invention;

[0085] Figure 5 This is a three-dimensional relationship diagram of BSP price-cost-revenue in an embodiment of the present invention;

[0086] Figure 6 This is a comparison chart of VPPs costs when purchasing and not purchasing the balancing service in this embodiment of the invention;

[0087] Figure 7 This is a comparison chart of VPPs cost savings under master-slave game theory and cost-plus pricing methods in embodiments of the present invention. Detailed Implementation

[0088] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0089] This invention provides an optimization method for pricing and compensation strategies of virtual power plant power balancing services based on a master-slave game theory approach. It aims to address issues such as high deviation assessment risks, large capital outlays, and imperfect balancing service pricing mechanisms faced by virtual power plants participating in the electricity market in existing technologies. By introducing a balancing service provider (BSP) and constructing a master-slave game model between the BSP and multiple virtual power plants, this invention achieves coordinated optimization of balancing service prices and compensation strategies. This reduces the operating costs of virtual power plants, increases the revenue of the balancing service provider, and promotes the safe and stable operation of the power system.

[0090] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0091] Figure 1 The flowchart is an embodiment of the present invention, such as Figure 1 As shown, a master-slave game pricing method for virtual power plant balancing services is described, the method comprising:

[0092] Step 101: Construct a joint transaction framework between the balancing service provider and multiple virtual power plants, clarify the market roles of BSP as the seller of balancing services and VPPs as the buyer of balancing services, and define two paths for BSP to compensate VPPs for shortfall in electricity: compensation using its own energy storage or compensation by purchasing electricity from the real-time balancing market.

[0093] Step 102: Based on the supply and demand relationship and risk transfer characteristics between BSP and multiple VPP in the electricity market, construct a Stackelberg master-follower game model to simulate the dynamic game behavior of market leaders and followers, and establish an upper-level pricing model with the goal of maximizing BSP profits and a lower-level decision-making model with the goal of minimizing VPP costs.

[0094] Step 103: Based on the KKT conditions and duality theory, the two-layer master-slave game model is transformed into a mixed integer linear programming model that can be solved efficiently;

[0095] Step 104: Solve the mixed-integer linear programming model using the optimization solver to obtain the optimal balance service price, the proportion of electricity purchased by each VPP, and the BSP compensation strategy under equilibrium conditions.

[0096] Figure 2 This is a transaction framework diagram of the balancing service provider and virtual power plants in an embodiment of the present invention. The diagram clearly shows the market roles of the BSP as the balancing service provider and the VPPs as the buyers. There are two paths for the BSP to compensate the VPPs for the shortfall in electricity: Path 1 is that the BSP directly compensates using its own energy storage resources, and the compensation cost is related to the geographical distance of the VPPs (denoted by c). own,i (Indicated); Path 2 is for BSP to obtain prices from the real-time balancing market. Compensation is provided after electricity is purchased. VPPs then decide the proportion of electricity they will purchase from BSPs for balancing services based on their own forecast deviations. This is to avoid the risk of deviation assessment.

[0097] Figure 3 This is a diagram illustrating the master-slave game model structure in an embodiment of the present invention. The diagram reveals the Stackelberg game relationship between the BSP and VPPs: the upper-level leader, the BSP, aims to maximize its own profit by formulating a balanced service price and compensation strategy. i (That is, the proportion of electricity compensated by using one's own energy storage); lower-level follower VPPs, on the other hand, decide on the proportion of electricity to purchase from balancing services with the goal of minimizing their own costs. The strategies of both sides influence each other, eventually leading to a Nash equilibrium.

[0098] To verify the effectiveness of the proposed model, this invention uses a case study of the balancing service transaction between a BSP and five VPPs in a certain region. The probability distribution of power shortage for each VPP is as follows: Figure 4As shown, this distribution is based on statistical analysis of historical operating data and reflects the output deviation characteristics of each VPP. Tables 1 and 2 provide basic data such as aggregated resource parameters and contracted power volume for each VPP.

[0099] Table 1. Aggregated resource parameters for each VPP

[0100] (Unit: MWh) wind power Photovoltaics Hydropower Energy storage Interruptible VPP1 40 60 75 10 15 VPP2 35 80 85 31 19 VPP3 45 90 35 0 10 VPP4 75 95 10 24 16 VPP5 60 100 110 20 10

[0101] Table 2 Summary of VPP parameters

[0102] (Unit: MWh) Pi <![CDATA[X i ]]> <![CDATA[c own,i ($ / MWh)]]> VPP1 200 50 26 VPP2 250 70 22 VPP3 180 80 36 VPP4 220 100 31 VPP5 300 90 27

[0103] The transformed mixed-integer linear programming model was solved using the Yalmip toolbox and the Gurobi solver. The equilibrium solution of the master-slave game was obtained, including the optimal balancing service price, the optimal purchase ratio of each VPP, and the optimal compensation ratio of the BSP, as shown in Tables 3 and 4.

[0104] Table 3 Optimal Purchase Ratio

[0105] VPP1 VPP2 VPP3 VPP4 VPP5 <![CDATA[b i (%)]]> 0.2148 0.2423 0.3994 0.4094 0.2608 Battery capacity (MWh) 42.96 60.57 71.89 90.06 78.24

[0106] Table 4 Optimal Compensation Ratio

[0107] VPP1 VPP2 VPP3 VPP4 VPP5 zi(%) 1 1 0 0 0.2104

[0108] Figure 5 This is a three-dimensional relationship diagram of BSP price, cost, and revenue in an embodiment of the present invention. The diagram shows the trend of BSP revenue changes with the balancing service pricing and average compensation cost: revenue first increases and then decreases as the price increases, indicating the existence of an optimal pricing point; average cost increases as the price increases because the price increase leads to a decrease in the amount of VPPs purchased, and after the BSP's own energy storage is depleted, it is forced to use more expensive real-time market electricity for compensation, thereby pushing up the average cost.

[0109] Figure 6 This is a cost comparison chart for VPPs with and without purchasing balancing services in this embodiment of the invention. The chart shows that without purchasing balancing services, VPPs bear the full deviation penalty, resulting in a total cost of $14,099.71. However, after purchasing balancing services using the method of this invention, the total cost drops to $11,597.20, saving $2,502.51, an average reduction of 17.74%. This demonstrates that introducing balancing services can effectively reduce the operational risks and costs of VPPs.

[0110] Figure 7This is a comparison chart of cost savings for VPPs under master-slave game theory and cost-plus pricing in this embodiment of the invention. Comparing the method of this invention with the traditional cost-plus pricing method (plus rate of 15%), the results show that under master-slave game pricing, the cost of each VPP is lower than that under the cost-plus method, and the overall social welfare is increased by $2258.18. This verifies the superiority of the method of this invention in balancing the interests of both parties and improving the overall efficiency of the system.

[0111] This invention provides an optimization method for pricing and compensation strategies of virtual power plant power balancing services based on a master-slave game theory approach, achieving synergistic optimization of pricing and compensation strategies for power balancing services. The specific steps include: first, establishing a joint trading framework between BSPs and VPPs, clarifying two compensation paths: self-owned energy storage and real-time market power purchase; second, constructing a Stackelberg game model with BSPs as leaders and VPPs as followers; and then, based on KKT conditions and duality theory, transforming the two-level nonlinear problem into a single-level mixed-integer linear programming problem to obtain the globally optimal solution. Compared to the drawbacks of traditional cost-plus pricing methods that only price from the service provider's perspective and ignore the price response of VPPs, as well as the limitation of the margin model tying up working capital, this invention accurately characterizes the strategic interaction between the two parties, achieving synergistic benefits, and providing an efficient solution that yields the globally optimal solution. Simultaneously, the proposed dual compensation path significantly improves the resource utilization efficiency of BSPs. The method provided by this invention significantly reduces the operating costs and deviation assessment risks of VPPs and frees up their working capital; it increases BSP revenue and promotes the development of the balancing service market; it optimizes resource allocation to improve the capacity for renewable energy consumption; and it provides innovative risk management tools for virtual power plants to participate in the electricity market, helping the new power system to operate safely and efficiently, and has significant engineering application value.

[0112] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0113] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A master-slave game pricing method for virtual power plant balancing services, characterized in that, Includes the following steps: Construct a master-slave game framework between the balancing service provider and multiple virtual power plants, in which the balancing service provider is the upper-level leader and the virtual power plants are the lower-level followers; Establish an upper-level pricing model with the goal of maximizing the profits of service providers, and make decisions on balancing service prices and compensation strategies for each virtual power plant. Establish a lower-level decision-making model to determine the proportion of electricity to purchase balancing services, with the goal of minimizing the total cost of the virtual power plant due to the electricity shortage. Based on KKT conditional and dual theory, the master-slave game model is transformed into a single-layer mixed integer linear programming model. Solving the mixed-integer linear programming model yields the optimal balancing service price, the proportion of electricity purchased by each virtual power plant, and the compensation strategy under equilibrium conditions.

2. The master-slave game pricing method for virtual power plant balancing services according to claim 1, characterized in that, The balancing service provider has its own energy storage resources and can purchase electricity through the real-time balancing market to compensate for the power shortage of the virtual power plant in two ways.

3. The master-slave game pricing method for virtual power plant balancing services according to claim 1, characterized in that, The virtual power plant includes at least one distributed resource among wind power, photovoltaic power, energy storage, and interruptible loads, and its power deficit follows a probability distribution based on historical operating data.

4. The master-slave game pricing method for virtual power plant balancing services according to claim 1, characterized in that, The objective function of the upper-level pricing model is: In the formula: C BSP The balanced service revenue that BSP obtains in the i-th VPP; The unit power balance service price set by the BSP in the game; The contracted electricity volume sold by the i-th VPP; The proportion of the ith VPP's decision to purchase balance services in the game; z i Let z be the proportion of the compensation electricity of the i-th VPP that the BSP uses its own energy storage to compensate for. i c is the proportion of electricity purchased by the BSP from the real-time balancing market to compensate the i-th VPP for its compensation electricity; own,i The unit cost of the BSP using its own energy storage to compensate for the i-th VPP; Ni is the amount of electricity compensated by the BSP for the i-th VPP; λ buy The unit price of electricity purchased by the BSP from the real-time balancing market.

5. The master-slave game pricing method for virtual power plant balancing services according to claim 1, characterized in that, The objective function of the lower-level decision model is: where: λ pen is the deviation penalty coefficient, representing the market or the dispatching agency imposed deviation penalty unit price; T i is the deviation electricity that the VPP needs to additionally bear the deviation penalty.

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