Method and system for constructing three-party evolutionary game model involving power grid company, VPP operator and user

Abstract

The invention provides a method and a system for constructing a three-party evolutionary game model involving a power grid company, a virtual power plant (VPP) operator and a user, an evolutionary game method is adopted to research interaction behaviors among a power grid, the VPP operator and the user, and the key point is to improve the anti-disaster capability of an urban energy system. The influence of long-term power system development on simulation results is studied. Key parameters in the game model are determined through numerical simulation. The evolution stability strategy of a single participant and a system is analyzed on the whole. According to a simulation result, as the unit load recovery benefit is increased from 40 to 1000, the three parties take the recovery capability into consideration more and more preferentially in decision making. In addition, within certain parameter ranges, the goal of increasing renewable energy consumption may conflict with the goal of improving power system recovery capability. The research can provide strategy suggestions for improving the long-term recovery capability of the power system, and provide valuable opinions for formulating feasible plans.

Description

Technical Field

[0001] The present invention relates to the technical field of power system management and optimization, and in particular to a method and system for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user. Background Art

[0002] In recent years, natural disasters, primarily caused by climate change, have become increasingly frequent, posing a significant threat to power supply infrastructure. Ensuring a secure and reliable power supply has become a top priority for China's power industry development. To address these challenges, power grid companies are actively developing strategic plans and implementing various measures, including adjusting production methods, to enhance power supply security. The Natural Resources Defense Council (NRDC) released a 2023 research report, "Pathways and Mechanisms for Improving Power Supply Capacity Considering Climate Risk," which emphasizes that China's power systems vary across regions with varying energy resources and stages of development. This diversity requires the development of region-specific strategies to ensure power supply in the face of medium- and long-term climate risks. The report recommends that the western region, known for its high proportion of renewable energy, improve the scalability and controllability of renewable energy generation by enhancing forecasting accuracy. In contrast, the densely populated eastern region, with its high demand, can improve power supply reliability through measures such as "residential power generation" and "community power storage." These approaches facilitate the establishment of a distributed power network and provide decentralized support. The "Measures for Electricity Demand-Side Management (2023)" include a measure encouraging the use of market mechanisms to enable qualified demand response entities to provide system emergency reserve services. The goal of this initiative is to ensure the safe and stable operation of the power system and gradually incorporate demand-side resources into the power balance through the use of virtual power plants (VPPs) and similar methods.

[0003] Currently, VPP operators have integrated a variety of flexible resources, including distributed generation (DG), energy storage, and demand-side adjustable loads, making them key to supporting a stable and secure power supply. This article focuses on enhancing system resilience by integrating DG and demand-side adjustable loads within VPPs. Energy storage, as an adjustable load, is primarily influenced by economic factors rather than user satisfaction, so it is not discussed in detail in this article.

[0004] In China, the VPP operating model primarily focuses on demand-side resources. This includes aggregating users' adjustable loads and participating in the demand response market to generate profits. In contrast, VPP development in Europe and the United States started earlier and has reached a more mature stage. For example, in Germany, VPPs have been widely integrated into various sectors, including the power generation and transmission markets. VPP operators directly manage distributed renewable energy projects and participate in the real-time buying and selling of electricity to maintain the power balance. In addition, consumers have the flexibility to choose their electricity supplier. Under Germany's Renewable Energy Act (EEG), renewable energy power producers enjoy priority in electricity pricing and are eligible for subsidies. This policy facilitates the integration of VPP-generated electricity into the grid. The power aggregated from these distributed generation resources can significantly improve the security and reliability of urban power systems.

[0005] As China's electricity market reforms progress and its "dual carbon" goals are pursued, demand for renewable energy generation continues to increase, and the development of virtual power generation projects is increasingly shifting toward a more transactional and autonomous model. Within this evolving landscape, VPP operators are emerging as dynamic market players, poised to play a key role in enhancing energy system resilience. The behavioral strategies of the power grid, VPP operators, and load-adjustable users are multifaceted and complex. Typically, these parties aim to minimize costs or maximize benefits under normal operating conditions. However, in disaster situations, priorities shift toward maximizing supply capacity. Evolutionary game theory provides a robust framework for analyzing the strategic interactions among these multiple parties. This approach optimizes strategic choices under different scenarios, considering how the interests of each participant are affected by the decisions of others. Assuming bounded rationality and incomplete information, the strategic decisions of the power grid, VPP operators, and users are interdependent and evolve over time. Evolutionary game models provide a balancing strategy that accommodates the dynamic nature of their decision-making processes.

[0006] The increasing frequency of extreme natural disasters has drawn public attention to system resilience. However, current research focuses on strengthening power system lines and increasing redundancy, with limited research on enhancing resilience through multi-agent collaboration. Summary of the Invention

[0007] The present invention is made to solve the above problems, and its purpose is to provide a method and system for constructing a three-party evolutionary game model involving power grid companies, VPP operators and users.

[0008] The present invention provides a method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator and a user, which has the following characteristics and specifically includes the following steps: S1, setting a model assumption of the three-party evolutionary game model; S2, based on the model assumption, setting model parameters, thereby constructing the three-party evolutionary game model; S3, based on the three-party evolutionary game model, constructing a profit matrix of the three participants to obtain expected profits, and using a replicator dynamic equation to describe the dynamic propagation process of the interaction strategies of the three participants, selecting a specific strategy, and obtaining a three-party dynamic replication equation; S4, modeling the expected profits to obtain a resilience profit situation; S5, analyzing the stability of the evolutionary game strategy based on the three-party dynamic replication equation and the resilience profit situation.

[0009] The method provided by the present invention for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user may also have the following features: wherein the expected benefits include the expected benefits of the power grid, the expected benefits of the VPP operator, and the expected benefits of the user when participating in RDR. The expected benefits of the power grid are as follows: Considering elasticity, the expected benefits of the power grid can be expressed as:

[0010] Y 11 =xz(R+S+D y -BM)+(1-x)zR+x(1-z)(R+SBM)+(1-x)(1-z)R (1)

[0011] Without considering elasticity, the expected benefit of the grid can be expressed as:

[0012] Y 12 =RW (2)

[0013] The average return can be expressed as:

[0014] Y1=yY 11 +(1-y)Y 12 =y(R+x(zD y +SBM))+(1-y)(RW) (3)

[0015] The expected benefits for VPP operators are as follows:

[0016] The expected revenue of a VPP operator considering elasticity can be expressed as:

[0017] X 11 =yz(U+F+G+M+D x -Q)+(1-y)zU+y(1-z)(U+F+G+ME)+(1-y)(1-z)U (4)

[0018] Without considering elasticity, the expected revenue of the VPP operator can be expressed as:

[0019] X 12 =U (5)

[0020] The average return can be expressed as:

[0021] X1=xX 11 +(1-x)X 12 =x(U+y(zD x +F+G+MQ))+(1-x)U (6)

[0022] The expected benefits for users when participating in RDR are as follows:

[0023] Z 11 =xy(C+D z )+(1-x)y(CV)+x(1-y)(CV)+(1-x)(1-y)(CV) (7)

[0024] When elastic demand is responded to, the expected benefits when users do not participate are:

[0025] Z 12 =xy(C-(1-α)V)+(1-x)y(CV)+x(1-y)(CV)+(1-x)(1-y)(CV) (8)

[0026] The average return can be expressed as:

[0027] Z1=zZ 11 +(1-z)Z 12 =z(xy(V+D z )+CV)+(1-z)(xyαV+CV) (9).

[0028] The method provided by the present invention for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user may also have the following characteristics: based on the average profits of the power grid company, the VPP operator, and the consumer, the three-party dynamic replication equation is expressed as:

[0029] F grid (y) = dy / dt = y(Y 11 -Y1)=y(1-y)(x(zD y +SBM)+W) (10)

[0030] F VPP (x) = dx / dt = x(X 11 -X1)=xy(1-x)(zD x +F+G+MQ) (11)

[0031] F user(z) = dz / dt = z(Z 11 -Z1)=xyz(1-z)((1-α)V+D z ) (12).

[0032] The method provided by the present invention for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user may also have the following features: wherein, in step S4, expected benefits are modeled using a Haotailin model and an RDR model. The Haotailin model describes the relationship between the proportion of renewable energy integrated into the grid and resilience benefits. In the Haotailin model, the resilience benefits brought about by the integration of renewable energy into the grid can be expressed as:

[0033]

[0034] Where S represents resilience benefit; C fac is the amount of renewable energy connected to the grid; S max and C max They represent the resilience benefit at the maximum point and the amount of renewable energy connected to the grid, respectively. Here, it is assumed that the resilience benefit is maximum when x1, and the maximum benefit is U1. When the amount of renewable energy connected to the grid is 0, the resilience benefit is 0; when the proportion of renewable energy is 100%, the resilience benefit is -U2. In the RDR model, two characteristic parameters, user response willingness θ and minimum incentive price λ, are selected to express the differences in user resilience demand response. When formulating incentive prices, the power grid selects different incentive mechanisms and compares their advantages. When adopting a static response incentive mechanism, the power grid company sets a static incentive price, and the response subsidy obtained by the user is the product of the incentive price and the response power, which can be expressed as:

[0035] J sta =∑λ sta ξ t (15)

[0036] Where, J sta represents the user's response subsidy under the static response mechanism, ξ t represents the user's response power at time t. Under the static incentive mechanism, when the incentive price is too low, if the user's response willingness is not high and the incentive price does not reach the minimum incentive price expected by the user, the user's response power is zero, which can be expressed as a constraint:

[0037] λ sta ≥λ sta (θ) (16)

[0038] According to the characteristics of user response, its development trend should be opposite to the trend of response willingness. The dynamic incentive mechanism of resilient demand response of power grid companies is as follows:

[0039]

[0040] Where, J dyn represents the user's response subsidy under the dynamic response incentive mechanism; It is a dynamic incentive price for unit load recovery, set by the power grid company and changes with changes in user response willingness and response ability.

[0041] The method provided by the present invention for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user may also have the following features: wherein step S5 specifically includes the following steps: In the dynamic evolutionary game, the strategy choices of the power grid, the VPP operator, and the user are all time-dependent, so the solution domains of their dynamic equations are all [0,1]. When all replicated dynamic equations are zero, the game strategy is in a stable state. From equations (18-20), E1(0,0,0), E2(1,0,0), E3(1,1,0), E4(1,0,1), E5(0,0,1), E6(0,1,0), E7(0,1,1), and E8(1,1,1) are equilibrium points of pure strategies. All stakeholders will choose a single strategy. These equilibrium points constitute the boundaries of the evolutionary game solution domain. The partial derivatives of the replicated dynamic equations with respect to y, x, and z are as follows:

[0042]

[0043] Where, F G ′(y), F V ′(x) and F U ′(z) represents the partial derivatives of the replication dynamic equations for the power grid company, VPP operator, and user, respectively. According to the stability principle of differential equations, when F(y) = 0 and F'(y) = dF(y) / dt < 0, the unilateral evolution reaches a stable state. Therefore, the ESS of the unilateral subject is found based on the replication dynamic equation, and the results of the three-party ESS are analyzed.

[0044] The method for constructing a three-party evolutionary game model involving the power grid company, the VPP operator and the user provided by the present invention may also have the following features: wherein the stability analysis of the power grid company strategy is as follows: (1) When x(zD y +SBM)+W=0, that is, the benefits obtained by the grid company when considering resilience in decision-making are the same as those when not considering resilience. And F grid When (y) = 0, the strategy choice of the power grid company has nothing to do with time and is always in a stable state. (2) When x(zD y +SBM)+W>0, that is, the grid company has more benefits if it chooses to consider resilience than if it does not, and we can get Let F grid (y) = 0, we can get y = 0 and y = 1, and substitute y = 0 and y = 1 into F respectively.G ′(y), because F G ′(0)>0,F G ′(1)<0, so y=1 is an ESS. At this time, the power grid company is in a stable state and tends to consider resilience. (3) When x(zD y +SBM)+W<0, that is, the grid company has more benefits if it chooses not to consider resilience than if it considers resilience, and we can get Let F grid (y) = 0, we can get y = 0 and y = 1, and substitute y = 0 and y = 1 into F respectively. G ′(y), because F G ′(0)<0,F G ′(1)>0, so y=0 is an ESS. At this time, the grid company is in a stable state and tends not to consider resilience.

[0045] The method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user provided by the present invention may also have the following features: wherein the VPP operator strategy stability analysis is as follows: (1) When y≠0, when zD x When +F+G+MQ=0, the VPP operator obtains the same benefits whether it considers resilience in its decision-making or not. And F VPP (x)=0, the strategy choice of VPP operator has nothing to do with time and is always in a stable state. (2) When zD x When +F+G+MQ>0, the VPP operator will gain more benefits by considering resilience than not considering resilience. Let F VPP (x) = 0, we can get x = 0 and x = 1, and substitute x = 0 and x = 1 into F respectively. V ′(x), because F V ′(0)>0,F V ′(1)<0, so x=1 is an ESS. At this time, the VPP operator is in a stable state and tends to consider resilience. (3) When zD x When +F+G+MQ<0, that is, the VPP operator chooses to have more benefits without considering resilience than considering resilience, and can get Let F VPP (x) = 0, we can get x = 0 and x = 1, and substitute x = 0 and x = 1 into F respectively. V ′(x), because F V ′(0)<0,F V ′(1)>0, so x=0 is an ESS, and VPP operators tend not to consider resilience.

[0046] The method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user provided by the present invention may also have the following characteristics: wherein the user strategy stability analysis is as follows: when y≠0 and x≠0, (1-α)V+D in formula (15) z >0, let F user (z) = 0, we can get z = 0 and z = 1, and substitute z = 0 and z = 1 into F respectively. U ′(z), because F U ′(0)>0,F U ′(1)<0, so z=1 is the ESS of the user evolution strategy. When the probability of the grid company and the VPP operator considering resilience is not 0, the user tends to consider resilience.

[0047] The present invention also provides a system for constructing a three-party evolutionary game model involving a power grid company, a VPP operator and a user, which has the following characteristics: a model assumption module, which sets the model assumptions of the three-party evolutionary game model; a model construction module, which sets the model parameters based on the model assumptions, thereby constructing the three-party evolutionary game model; an expected benefit analysis module, which constructs the benefit matrix of the three participants based on the three-party evolutionary game model, obtains the expected benefits, and uses the replicator dynamic equation to describe the dynamic propagation process of the interaction strategies of the three participants, selects a specific strategy, and obtains the three-party dynamic replication equation; a resilience benefit analysis module, which models the expected benefits and obtains the resilience benefit situation; and a stability analysis module, which analyzes the stability of the evolutionary game strategy based on the three-party dynamic replication equation and the resilience benefit situation.

[0048] Functions and effects of the invention

[0049] According to the method and system involved in constructing a three-party evolutionary game model involving power grid companies, VPP operators, and users, the present invention is a post-disaster system resilience improvement planning method. The present invention targets power grid companies, VPP operators, and users. Decisions to improve resilience include establishing new renewable energy grid connection subsidies and a resilience demand response mechanism. An evolutionary game model is constructed between the three parties to simulate decisions. The three-party ESS and system stability strategies are analyzed, and numerical simulation methods are used to verify the validity of the results and the impact of relevant parameters on the evolutionary trajectory. Based on these simulation results, decision-making recommendations are provided to power grid companies.

[0050] This paper uses evolutionary game theory to study the interactions between power grids, virtual power plant (VPP) operators, and users, with a focus on improving the resilience of urban energy systems to disasters. The impact of long-term power system development on simulation results was investigated. Key parameters in the game model were determined through numerical simulations. The evolutionary stability strategies of individual players and the system as a whole were analyzed. This paper can provide strategic recommendations for improving the long-term resilience of power systems and offer valuable insights for developing practical and feasible plans. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 This is a flowchart of a three-party evolutionary game model among a power grid company, a VPP operator, and a user in an embodiment of the present invention;

[0052] Figure 2 It is a three-party evolutionary game model framework in an embodiment of the present invention;

[0053] Figure 3 is the Hao Tailin model of renewable energy grid connection ratio and resilience benefits in the embodiment of the present invention;

[0054] Figure 4 is a phase diagram of the strategy evolution of a power grid enterprise in an embodiment of the present invention;

[0055] Figure 5 is a phase diagram of the VPP operator strategy evolution in an embodiment of the present invention;

[0056] Figure 6 is the evolution trajectory of the three parties under different initial probability settings in the embodiment of the present invention;

[0057] Figure 7 It is the evolution process of the three parties over time when the initial probability is 0.2 in the embodiment of the present invention;

[0058] Figure 8 is the effect of the unit load recovery benefit coefficient on the evolution trajectory in the embodiment of the present invention;

[0059] Figure 9 is the influence of Hao Tailin model parameters on the evolution trajectory in the embodiment of the present invention;

[0060] Figure 10 is the impact of the resilience demand response parameters on the evolution trajectory in the embodiment of the present invention;

[0061] Figure 11 It is the influence of F on the evolution trajectory in the embodiment of the present invention. DETAILED DESCRIPTION

[0062] To facilitate understanding of the technical means, creative features, objectives, and effects of the present invention, the following embodiments, combined with accompanying figures, specifically illustrate the method and system of the present invention for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user.

[0063] This paper studies the evolutionary stability strategies of various entities from the perspective of disaster resilience and explores how changes in key factors related to disaster resilience in power systems affect decision-making behavior. This study includes the following steps:

[0064] (1) Construct a three-party evolutionary game model;

[0065] (2) Present the results and analysis of numerical simulations;

[0066] (3) The main findings of the present invention are summarized and strategic recommendations are put forward.

[0067] Figure 1 It is a flowchart of a three-party evolutionary game model among a power grid company, a VPP operator, and a user in an embodiment of the present invention.

[0068] like Figure 1 As shown in the figure, the present invention constructs a three-party evolutionary game method involving power grid companies, VPP operators, and users. From the perspective of disaster resilience, the method studies the evolutionary stability strategies of each entity and explores how changes in key factors related to disaster resilience in the power system affect decision-making behavior. The method specifically includes the following steps:

[0069] S1, set the model assumptions of the three-party evolutionary game model.

[0070] like Figure 2 As shown in Figure 2, common aggregated resources in VPPs include small thermal power units, distributed renewable energy generators, energy storage stations, and demand response users. The following analysis focuses on distributed renewable energy and demand response users.

[0071] Figure 2 It is a three-party evolutionary game model framework in an embodiment of the present invention.

[0072] like Figure 2 As shown, the present invention is based on the following assumptions:

[0073] Assumption 1: Grid companies, VPP operators, and users are assumed to exhibit bounded rationality. Due to limitations in their ability to obtain and process market information, these participants cannot achieve complete rationality.

[0074] Hypothesis 2: One resilience strategy employed by power grid companies is to provide subsidies to VPP operators to support the construction and integration of new renewable energy generation facilities. These subsidies cover the costs associated with installing poles, towers, and transmission lines. Their primary purpose is to diversify the energy mix and enhance the resilience of the supply system. The grid company allocates these subsidies specifically to VPP operators to connect new renewable energy sources. Integrating these energy sources diversifies the grid's supply mix and reduces the risk of large-scale load disruptions during extreme events. Failure to consider resilience could result in penalty costs for the grid company.

[0075] Hypothesis 3: Another resilience strategy for grid companies is to establish a flexible demand response (RDR) mechanism. Through this mechanism, VPP operators send response signals to consumers, who then use electric vehicles to provide backup energy to support the response. This enhances the overall resilience of the energy system. The economic benefits generated by the demand response process are shared by three parties: the grid company, the VPP operator, and consumers.

[0076] Hypothesis 4: VPP operators' strategies depend on whether they prioritize resilience. If so, as previously discussed, VPP operators will participate in resilience enhancement programs established by grid companies. This participation enables them to receive grid company subsidies for renewable energy, green certificate subsidies, and profits from participating in RDR programs. However, this approach requires investment in new renewable energy facilities and the associated costs. Without prioritizing resilience, VPP operators will neither benefit from these advantages nor bear the costs.

[0077] Hypothesis 5: If resilience is prioritized, grid companies have two options: increasing the share of renewable energy in their supply mix and implementing RDR mechanisms. This paper hypothesizes that when resilience is prioritized, grid companies will implement both strategies simultaneously. Conversely, if resilience is not prioritized, neither strategy will be implemented. Similarly, when VPP operators prioritize resilience, they will adopt both strategies simultaneously. If resilience is not prioritized, neither strategy will be adopted.

[0078] Hypothesis 6: Consumers' strategies depend on their prioritization of resilience. If consumers prioritize resilience, they will participate in demand response programs and profit from them. Conversely, if consumers do not prioritize resilience, they will not receive any demand response benefits. Furthermore, the strategies adopted by the grid company and VPP operator significantly influence the losses consumers incur during a disaster. Assuming both resilience strategies are implemented simultaneously, consumers will face no losses during a disaster. Otherwise, they will incur loss costs. The total energy supplied is allocated between the two strategies, with the proportion of renewable energy represented by ɑ and the proportion supplied through RDR as 1-ɑ.

[0079] Assumption 7: In the event of a disaster, even after the grid has implemented measures such as dispatching thermal power units and repairing lines, some unmet load may still be met. For the sake of simplicity, this unmet load is assumed to be infinite and must be addressed through the increased integration of renewable energy and flexible demand response measures described in this invention.

[0080] S2, based on the model assumptions, set the model parameters to construct a three-party evolutionary game model.

[0081] Table 1 Parameter settings

[0082]

[0083]

[0084] As shown in Table 1, based on the assumptions in step S1 above, the model parameters of each participant in the evolutionary game are constructed.

[0085] S3, based on the three-party evolutionary game model, constructs the payoff matrix of the three participants to obtain the expected payoff, and uses the replicator dynamic equation to describe the dynamic propagation process of the interaction strategies of the three participants. A specific strategy is selected to obtain the three-party dynamic replication equation.

[0086] To simulate the interaction and cooperation mechanisms, a payoff matrix for the three participants was constructed. This model, introduced in this paper, is a three-party evolutionary game involving the power grid company, the VPP operator, and consumers. Both the power grid company and the VPP operator must decide whether to incorporate resilience into their strategic decisions. Similarly, consumers must decide whether to participate in the RDR program. The payoff matrix of this evolutionary game outlines the rewards and penalties each participant receives based on their chosen strategy and their interactions with each other.

[0087] Table 2 Game payoff matrix considering elasticity

[0088]

[0089] Table 3 Game payoff matrix without considering elasticity

[0090]

[0091]

[0092] As shown in Table 2-3, it is a remuneration matrix, where the remuneration is expressed in the format of (grid, VPP operator, user).

[0093] Expected benefits include the expected benefits of the power grid, the expected benefits of the VPP operator, and the expected benefits of users participating in RDR.

[0094] The expected benefits to the grid are as follows:

[0095] Taking elasticity into account, the expected benefit of the power grid can be expressed as:

[0096] Y 11 =xz(R+S+D y -BM)+(1-x)zR+x(1-z)(R+SBM)+(1-x)(1-z)R (1)

[0097] Without considering elasticity, the expected benefit of the grid can be expressed as:

[0098] Y 12 =RW (2)

[0099] The average return can be expressed as:

[0100] Y1=yY 11 +(1-y)Y 12 =y(R+x(zD y +SBM))+(1-y)(RW) (3)

[0101] The expected benefits for VPP operators are as follows:

[0102] The expected revenue of a VPP operator considering elasticity can be expressed as:

[0103] X 11 =yz(U+F+G+M+D x -Q)+(1-y)zU+y(1-z)(U+F+G+ME)+(1-y)(1-z)U (4)

[0104] Without considering elasticity, the expected revenue of the VPP operator can be expressed as:

[0105] X 12 =U (5)

[0106] The average return can be expressed as:

[0107] X1=xX11 +(1-x)X 12 =x(U+y(zD x +F+G+MQ))+(1-x)U (6)

[0108] The expected benefits for users when participating in RDR are as follows:

[0109] Z 11 =xy(C+D z )+(1-x)y(CV)+x(1-y)(CV)+(1-x)(1-y)(CV) (7)

[0110] When elastic demand is responded to, the expected benefits when users do not participate are:

[0111] Z 12 =xy(C-(1-α)V)+(1-x)y(CV)+x(1-y)(CV)+(1-x)(1-y)(CV) (8)

[0112] The average return can be expressed as:

[0113] Z1=zZ 11 +(1-z)Z 12 =z(xy(V+D z )+CV)+(1-z)(xyαV+CV) (9).

[0114] For different entities, choosing a specific strategy is a dynamic process that evolves over time. This quantitative process can be expressed using the replicator dynamic equation. Based on the average profits of the grid company, VPP operator, and consumer, the three-party dynamic replication equation is expressed as:

[0115] F grid (y) = dy / dt = y(Y 11 -Y1)=y(1-y)(x(zD y +SBM)+W) (10)

[0116] F VPP (x) = dx / dt = x(X 11 -X1)=xy(1-x)(zD x +F+G+MQ) (11)

[0117] F user (z) = dz / dt = z(Z 11 -Z1)=xyz(1-z)((1-α)V+D z ) (12).

[0118] S4, model the expected returns and obtain the resilience returns.

[0119] Adopting resilience-enhancing strategies within a cooperative mechanism can yield specific benefits. Modeling of expected benefits includes both the Houtelin model and the RDR model. The Houtelin model describes the relationship between the proportion of renewable energy integrated into the grid and resilience benefits.

[0120] In the Haotailin model, the integration of renewable energy enhances the resilience of the city's power system, but also introduces potential instability and security risks to a stable power supply. Generally speaking, greater reliance on a single energy source reduces power supply stability. In this scenario, VPP operators face a strategic decision: how much renewable energy to integrate into the grid while also considering resilience. It is assumed that the quality of the renewable energy integrated by VPP operators remains consistent, but the proportion of renewable energy in the overall power supply varies.

[0121] Figure 3 It is the Hao Tailin model of renewable energy grid connection ratio and resilience benefits in the embodiment of the present invention.

[0122] like Figure 3 As shown, this ratio is uniformly distributed within the range [0, 1], where 0 represents no renewable energy generation and 1 represents 100% renewable energy generation. When the proportion of grid-connected renewable energy is within the range [0, x1], the resilience benefit is positive and increasing. However, as the ratio increases from [x1, 1], the benefit decreases and becomes negative between [x2, 1].

[0123] The resilience benefits brought by renewable energy integration can be expressed as:

[0124]

[0125] Where S represents resilience benefit; C fac is the amount of renewable energy connected to the grid; S max and C max They represent the resilience benefit at the maximum point and the amount of renewable energy connected to the grid. Here, it is assumed that the resilience benefit is the largest when x1, and the maximum benefit is U1. When the amount of renewable energy connected to the grid is 0, the resilience benefit is 0; when the proportion of renewable energy is 100%, the resilience benefit is -U2.

[0126] In the RDR model,

[0127] The demand response mechanism discussed in the RDR Incentive Strategy section is called RDR. In the event of an energy outage, RDR involves gathering dispersed users through VPPs to participate in demand response activities, thereby enhancing the resilience of the energy supply system. Once the grid determines the required response power and sets the incentive price, the VPP operator communicates this information to users. Based on this information, users develop response strategies to receive incentive subsidies. However, it is important to note that while users contribute backup energy to the energy system, this process can also result in a certain degree of loss in user satisfaction.

[0128] Generally speaking, user response characteristics include willingness and ability. Willingness reflects a user's understanding of resilience and their financial status; ability reflects the maximum capacity and remaining capacity that can support the load. The stronger the user's willingness and ability, the lower the minimum incentive price requirement and the greater the response load.

[0129] This paper selects two characteristic parameters, user response willingness θ and minimum incentive price λ, to represent the differences in user resilient demand response. When formulating incentive prices, the power grid selects different incentive mechanisms and compares their advantages. When a static response incentive mechanism is adopted, the power grid company sets a static incentive price, and the response subsidy received by the user is the product of the incentive price and the response power, which can be expressed as:

[0130] J sta =∑λ sta ξ t (15)

[0131] Where, J sta represents the user's response subsidy under the static response mechanism, ξ t represents the user's response power at time t. Under the static incentive mechanism, when the incentive price is too low, if the user's response willingness is not high and the incentive price does not reach the minimum incentive price expected by the user, the user's response power is zero, which can be expressed as a constraint:

[0132] λ sta ≥λ sta (θ) (16)

[0133] In real life, users do not always participate in resilient demand response in the same state. As society develops and residents' living standards improve, awareness of resilience and the maximum capacity of responsive loads increase, and users' willingness to participate in resilient demand response will gradually increase. Dynamic incentive mechanisms can be changed according to the different stages of user response willingness. Based on user response characteristics, its development trend should be opposite to the trend of response willingness. The dynamic incentive mechanism for resilient demand response of power grid companies is as follows:

[0134]

[0135] Where, J dyn represents the user's response subsidy under the dynamic response incentive mechanism; It is a dynamic incentive price for unit load recovery, set by the power grid company and changes with changes in user response willingness and response ability.

[0136] S5, based on the three-party dynamic replication equation and resilience benefits, analyze the stability of the evolutionary game strategy.

[0137] In the dynamic evolutionary game, the strategy choices of the power grid, VPP operators, and users are all time-dependent. Therefore, the solution domain of their dynamic equations is [0,1]. When all replicated dynamic equations are zero, the game strategy is in a stable state. From Equations (18-20), E1(0,0,0), E2(1,0,0), E3(1,1,0), E4(1,0,1), E5(0,0,1), E6(0,1,0), E7(0,1,1), and E8(1,1,1) are pure strategy equilibrium points. All stakeholders will choose a single strategy. These equilibrium points constitute the boundaries of the evolutionary game solution domain. The partial derivatives of the replicated dynamic equations with respect to y, x, and z are as follows:

[0138]

[0139] Where, F G ′(y), F V ′(x) and F U ′(z) represents the partial derivatives of the replication dynamic equations for the power grid company, VPP operator, and user, respectively. According to the stability principle of differential equations, when F(y) = 0 and F'(y) = dF(y) / dt < 0, the unilateral evolution reaches a stable state. Therefore, the ESS of the unilateral subject is found based on the replication dynamic equation, and the results of the three-party ESS are analyzed.

[0140] Figure 4 This is a phase diagram of the strategy evolution of the power grid enterprise in the embodiment of the present invention. Figure (a) shows the phase diagram of the strategy evolution of the power grid enterprise in the embodiment of the present invention. y +SBM)+W=0, Figure (b) shows the situation when x(zD y +SBM)+W>0, Figure (c) is when x(zD y +SBM)+W<0.

[0141] The strategic stability analysis of the power grid company is as follows:

[0142] (1) Figure 4 As shown in (a), when x(zD y +SBM)+W=0, that is, the benefits obtained by the grid company when considering resilience in decision-making are the same as those when not considering resilience. And Fgrid When (y) = 0, the strategy choice of the power grid company is independent of time and is always in a stable state.

[0143] (2) Figure 4 As shown in (b), when x(zD y +SBM)+W>0, that is, the grid company has more benefits if it chooses to consider resilience than if it does not, and we can get Let F grid (y) = 0, we can get y = 0 and y = 1, and substitute y = 0 and y = 1 into F respectively. G ′(y), because F G ′(0)>0,F G ′(1)<0, so y=1 is an ESS. At this time, the power grid company is in a stable state and tends to consider resilience.

[0144] (3) Figure 4 As shown in (c), when x(zD y +SBM)+W<0, that is, the grid company has more benefits if it chooses not to consider resilience than if it considers resilience, and we can get Let F grid (y) = 0, we can get y = 0 and y = 1, and substitute y = 0 and y = 1 into F respectively. G ′(y), because F G ′(0)<0,F G ′(1)>0, so y=0 is an ESS. At this time, the grid company is in a stable state and tends not to consider resilience.

[0145] like Figure 4 As shown, the cube can be divided into P1 and P2. P1 represents the grid company's strategy of considering resilience, with its volume VP1 representing the probability of considering resilience. P2 represents the grid company's strategy of not considering resilience, with its volume VP2 representing the probability of not considering resilience. The figure shows that whether the grid company's strategy considers resilience is related to the other two factors. As the probability of considering resilience in the strategies of VPP operators and users increases, the probability of the grid company considering resilience also increases. The grid company's strategy choice is significantly influenced by the VPP operator. When the VPP operator considers resilience, the grid must also consider resilience, and users also consider resilience. When the VPP operator does not consider resilience, the grid company also does not consider resilience. Therefore, the grid company can improve power system resilience by increasing the probability that the VPP operator considers resilience.

[0146] Figure 5 This is a phase diagram of the VPP operator strategy evolution in an embodiment of the present invention. x +F+G+MQ=0, Figure (b) shows the situation when zD x+F+G+MQ>0, Figure (c) shows the case when zD x +F+G+MQ<0.

[0147] The stability analysis of VPP operator strategies is as follows:

[0148] (1) A detailed analysis of the factors in formula (19) shows that when y = 0, F VPP (x) = 0, F V ′(x)=0, the strategy of the VPP operator is dominated by the strategy of the grid enterprise, so only the case of y≠0 is discussed here.

[0149] like Figure 5 As shown in (a), when y≠0, when zD x When +F+G+MQ=0, the VPP operator obtains the same benefits whether it considers resilience in its decision-making or not. And F VPP (x) = 0, the strategy selection of the VPP operator is independent of time and is always in a stable state.

[0150] (2) Figure 5 As shown in (b), when zD x When +F+G+MQ>0, the VPP operator will gain more benefits by considering resilience than not considering resilience. Let F VPP (x) = 0, we can get x = 0 and x = 1, and substitute x = 0 and x = 1 into F respectively. V ′(x), because F V ′(0)>0,F V ′(1)<0, so x=1 is an ESS. At this time, the VPP operator is in a stable state and tends to consider resilience.

[0151] (3) Figure 5 As shown in (c), when zD x When +F+G+MQ<0, that is, the VPP operator chooses to have more benefits without considering resilience than considering resilience, and can get Let F VPP (x) = 0, we can get x = 0 and x = 1, and substitute x = 0 and x = 1 into F respectively. V ′(x), because F V ′(0)<0,F V ′(1)>0, so x=0 is an ESS, and VPP operators tend not to consider resilience.

[0152] like Figure 5As shown, the cube is the evolution strategy of the VPP operator when y≠0, which can be divided into P3 and P4, where P3 represents the strategy of the VPP operator considering toughness, and its volume V P3 represents the probability of considering resilience. P4 is the strategy of the VPP operator not considering resilience. Its volume V P4 represents the probability without considering toughness. Figure 5 It can be seen that whether VPP operators consider resilience in their strategies is related to user strategies. As the probability of users considering resilience increases, the benefits of VPP operators considering resilience increase. Therefore, promoting the concept of resilience among users and guiding them to participate in resilience demand response can help increase VPP operators' profits.

[0153] The stability analysis of user policies is as follows:

[0154] Through detailed analysis of formula (20), it is found that only when y≠0 and x≠0, F user (z) and F U ′(z) is not always 0, so here we only discuss the case where y≠0 and x≠0.

[0155] When y≠0 and x≠0, (1-α)V+D in formula (15) z >0, let F user (z) = 0, we can get z = 0 and z = 1, and substitute z = 0 and z = 1 into F respectively. U ′(z), because F U ′(0)>0,F U ′(1)<0, so z=1 is the ESS of the user evolution strategy. When the probability of the grid company and the VPP operator considering resilience is not 0, the user tends to consider resilience.

[0156] In this embodiment, the simulation results and analysis are as follows:

[0157] To explore the strategic interactions among the three parties in the game, this section examines the equilibrium strategies and ESS of each party under the various scenarios discussed above to verify the rationality of the model. This section uses a system simulation method to analyze the evolutionary trajectory of the three parties, focusing on the evolution of the three-party game in 2022.

[0158] This study numerically investigates the urban energy system in the Lingang Special Economic Zone (SEZ) in Shanghai, China, as a case study. The SEZ is a pilot free trade zone launched by the central government in 2019. With the goal of building an internationally competitive free trade zone and improving integrated energy services, the local government has developed a highly forward-looking urban energy system plan. Furthermore, the SEZ's location on Shanghai's southeast coast makes it susceptible to extreme weather, such as typhoons. Consequently, the reliability and resilience of its energy supply are of particular concern. To support this energy planning, the local government has also developed guidelines for the application of resilient energy.

[0159] Currently, the cost of photovoltaic power generation is 0.35 yuan / kWh, and the cost of onshore wind power generation is 0.26 yuan / kWh. The grid-connected price for photovoltaic power generation is 0.415 yuan / kWh, and the grid-connected price for onshore wind power generation is 0.302 yuan / kWh. VPP operators have an equal probability of choosing to invest in distributed photovoltaic and wind power projects. Therefore, the average cost of these renewable energy projects is 0.305 yuan / kWh. The average grid-connected price is 0.358 yuan / kWh, and the green certificate revenue is 0.038 yuan / kWh. The installed capacity (μ) is assumed to be 1000 kW, and the operating life is 15 years, resulting in a total grid-connected power generation of 43.8 GWh during this period. The dispatchable electric vehicle load (ξ) is assumed to be 1000 kWh, and the unit load recovery coefficient (δ) is 500 yuan / kWh. The system is designed to handle eight load interruptions, each lasting four hours, during its design life. These criteria serve as the basis for adjusting parameters in subsequent simulation scenarios.

[0160] First, we simulate the evolutionary behavior of the three-party transaction under different initial probabilities. In this scenario, increasing the integration of renewable energy reduces unmet load by 12,800 kWh over its lifetime, while elastic demand response reduces unmet load by 8,000 kWh. The total benefits of restorative demand response are distributed among the grid, VPP operator, and users in a 5:3:2 ratio. Renewable energy sales revenue is approximately 15.664 million yuan, including 1.648 million yuan in green energy revenue and 13.328 million yuan in renewable energy construction costs. For ease of calculation, the above data are scaled down by a ratio of 1600:1, resulting in Dy = 125, Dx = 75, Dz = 50, S = 400, B = 16.5, W = 160, F = 979, G = 103, Q = 833, α = 0.62, and V = 650. The strategy of each of the three parties evolves over time and is influenced by the strategies of the other two parties, leading to adjustments in its own strategy.

[0161] Figure 6 It is the evolution trajectory of the three parties under different initial probability settings in the embodiment of the present invention. Figure 7 This is the evolution process of the three parties over time when the initial probability is assumed to be 0.2 in the embodiment of the present invention.

[0162] The evolution model was simulated many times with different initial probability values. Figure 6In the figure, different initial probabilities all tend to (1,1,1), indicating that in the 2022 scenario selected in this article, considering resilience in the decision-making of the three parties will bring positive benefits, and when all three parties cooperate, the benefits will be greater. Further analysis shows that when the grid company is more willing to consider resilience, the probability of VPP operators and users increases rapidly, and when the grid company is less willing, the growth rate of the other two parties' probability of considering resilience is slow. This evolutionary model is mainly dominated by the decision-making of the grid company. Only after the grid company proposes a plan to improve resilience can VPP operators and users participate in profit. Therefore, the grid company can set a higher probability of considering resilience to encourage VPP operators and users to participate in improving the overall resilience of society. The evolutionary trajectory between operators and users shows a linear growth trend. The decision-making plans of the two constrain each other but both evolve towards (1,1). By Figure 7 It was found that all three parties chose to improve resilience and achieved rapid response in the evolutionary iterations over time.

[0163] The results of the numerical simulation are consistent with the analysis of the three-party ESS in the previous section. The simulation results can provide a theoretical basis for the decision-making of power grid companies and VPP operators in 2022 and a scientific foundation for the game analysis of subsequent decision-making behaviors.

[0164] The inductive analysis of key parameters in the model is as follows:

[0165] To explore the impact of key parameters on the decision-making evolution trajectory and the characteristic parameters of resilience, this section conducts simulation analysis on the selection of these key parameters, including the unit load recovery benefit coefficient, Haotailin model parameters, resilience demand response parameters, and renewable energy revenue per kilowatt-hour. The following section analyzes the parameter settings and simulation results.

[0166] The impact of the unit load recovery benefit coefficient is as follows:

[0167] Table 4 Parameters related to unit load recovery benefit coefficient

[0168]

[0169]

[0170] Under the premise that other parameters remain unchanged, the key parameters affected by changing the benefit coefficient of unit load recovery are shown in Table 4.

[0171] Figure 8 It is the influence of the unit load recovery benefit coefficient on the evolution trajectory in the embodiment of the present invention.

[0172] The simulation results of the model are shown in Figure 8As can be seen in the figure, the unit load restoration benefit coefficient significantly influences the direction and speed of the evolution trajectory. When the benefits of load restoration are minimal, the three-party decision evolves toward (0, 0.93, 0.21). Not only does the grid company fail to gain sufficient benefits from its decision to support resilience, but it also has to pay additional subsidies to the VPP operator. Therefore, the grid company does not consider resilience in its decision-making. VPP operators do not bear the public opinion penalty associated with resilience loss and can still receive subsidies from the grid company for decisions that consider resilience, so they continue to evolve toward considering resilience. Although users are affected by load loss, their decision-making in the three-party game model is completely dominated by the other two parties. The figure shows that the probability of users considering resilience rises slowly, with the rate of increase gradually decreasing. This is because the grid company's decision gradually approaches zero during the evolutionary trajectory, causing users to gradually lose hope of improving resilience during the evolutionary process. As for the impact on evolution speed, as can be seen from the three scenarios approaching (1, 1, 1), as the profit coefficient increases, the evolution speed of the three parties becomes faster and faster. The increase in the profit coefficient means that the benefits obtained by grid companies and users from taking measures to improve resilience increase. The decisions of grid companies also affect the evolution of VPP operators' decisions, greatly increasing the enthusiasm of all three parties to consider resilience in their decision-making behavior.

[0173] The impact of Haotailin model parameters is as follows:

[0174]

[0175] To explore the impact of varying proportions of energy supply entities on the evolutionary trajectory, a Hotelling model of energy system resilience was developed. As before, while keeping all other parameters constant, the newly installed renewable energy capacity (representing the proportion of renewable energy in the supply mix) and the associated resilience benefits were adjusted. Results for key parameters are shown in Table 5.

[0176] Figure 9 This is the influence of Hao Tailin model parameters on the evolution trajectory in the embodiment of the present invention.

[0177] like Figure 9 The simulation results show that in scenarios Ht1 and Ht2, the proportion of renewable energy is positively correlated with resilience benefits. Increasing the proportion of renewable energy in the supply mix can improve the benefits of grid companies and VPP operators. It is worth noting that compared with Ht1, scenario Ht2 evolves faster.

[0178] Scenario Ht3 is characterized by a negative correlation between the proportion of renewable energy and resilience benefits. Simulation results show that the decisions of the three parties continue to trend toward (1, 1, 1). However, in this scenario, the VPP operator's decision is less influenced by the grid's intentions. For VPP operators, profits primarily come from the sale of electricity generated by newly added renewable energy projects. Faced with the potential decline in system resilience caused by the operator's decisions, the grid should take timely measures to restrict the operator's connection of new renewable energy projects and consider withdrawing their subsidies.

[0179] In scenario Ht4, the resilience benefits of integrating new renewable energy to the grid are negative, and the decision-making trajectories of the three parties tend to (0, 0.76, 0.31). The probability of users considering disaster resilience in their decision-making increases from 0.2 to 0.31, and they continue to participate in disaster resilience demand response to reduce losses. At this stage, grid companies can shift their strategies from strengthening the energy supply structure to improving responsiveness to support load demand. The simulation results in this section show that as the proportion of renewable energy generation affects the resilience of the power system, both grid companies and VPP operators should promptly adjust their strategies to adapt to changes in the supply structure. Such adjustments will facilitate the seamless integration of renewable energy and enhance the resilience of the power system.

[0180] The impact of resilience demand response parameters is as follows:

[0181] Table 6 Resilience demand response parameters

[0182]

[0183] Grid companies can then develop different resilience demand response systems in the future and compare the advantages and disadvantages of static and dynamic response mechanisms. With social development and economic advancement, users' awareness of the importance of resilience is increasing, and their responsiveness is also increasing. Therefore, two hypotheses are proposed: low response willingness and low response capability, and high response willingness and high response capability. Under the static mechanism, the response price for both hypotheses is the same, while the dynamic mechanism adjusts the response price. The key parameters are shown in Table 6.

[0184] Figure 10 This is the impact of the resilience demand response parameters on the evolution trajectory in the embodiment of the present invention.

[0185] like Figure 10The simulation results show that under all scenarios, the decisions of the three parties evolve toward (1,1,1), but at different speeds. This indicates that different incentive mechanisms do not affect the decision-making behavior of the three parties, and all three parties tend to consider resilience in their decisions. A comparison of the two response incentive mechanisms reveals that improving user response willingness and response capability significantly increases the speed of decision-making evolution. When response willingness and response capability are low, the difference between the two incentive mechanisms is minimal. However, when response willingness and response capability are high, the user evolution speed under the dynamic response mechanism is significantly higher than that under the static response mechanism, and users are more inclined to choose the dynamic incentive mechanism provided by the power grid to participate in demand response. It is recommended that power grid companies adopt dynamic response mechanisms in the future to promote the evolution of decision-making among the three parties towards enhancing resilience. At the same time, they should promote public awareness of the importance of energy system resilience, accelerate economic development, and promote the participation of multiple actors and factors in improving resilience.

[0186] The impact of renewable energy revenue per kilowatt-hour is as follows:

[0187] Figure 11 It is the influence of F on the evolution trajectory in the embodiment of the present invention.

[0188] Without changing other parameters, let F = 1200, 1000, 800 and 600, the simulation results are shown in Figure 11 The decline in renewable energy revenue per kilowatt-hour reduces the enthusiasm of VPP operators to consider resilience in their decision-making, slowing down the evolution towards (1,1,1).

[0189] like Figure 11 As shown in Figure (b), when F = 1200, 1000, and 800, as the revenue per kilowatt-hour decreases, the rate at which grid and VPP operators consider resilience slows down. When F is less than 600, meaning the benefits to VPP operators from ignoring resilience are greater than the benefits from considering resilience, the operators' decisions shift from considering resilience to ignoring it. However, grid companies' decisions continue to evolve toward considering resilience. In this scenario, the shift in VPP operators' decisions hinders the improvement of overall system resilience and slows the evolution of grid and user decision-making. Based on this, grid companies can adjust their decision-making strategies in a timely manner, increase subsidies to VPP operators, and encourage operators' decision-making behavior to evolve toward considering resilience, thereby improving overall system resilience.

[0190] The present invention also discloses a system for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user, comprising:

[0191] The model assumption module sets the model assumption of the three-party evolutionary game model according to the above step S1.

[0192] The model building module sets the model parameters based on the model assumptions according to the above step S2, thereby building a three-party evolutionary game model.

[0193] The expected profit analysis module, in accordance with the above step S3, constructs the profit matrix of the three participants based on the three-party evolutionary game model to obtain the expected profit, and uses the replicator dynamic equation to describe the dynamic propagation process of the interaction strategies of the three participants, selects a specific strategy, and obtains the three-party dynamic replication equation.

[0194] The resilience benefit analysis module models the expected benefits according to the above step S4 to obtain the resilience benefit situation.

[0195] The stability analysis module analyzes the stability of the evolutionary game strategy based on the three-party dynamic replication equation and the resilience benefit according to the above step S5.

[0196] According to simulation results, as the unit load restoration benefit increases from 40 to 1000, all three parties increasingly prioritize restoration capabilities in their decision-making. Notably, when the unit load restoration benefit is 40, grid companies tend to neglect restoration capabilities. To improve the resilience of the power system, especially when the proportion of renewable energy generation is high, utility grids should prioritize managing the integration of renewable energy into the grid. Furthermore, public interest in participating in dynamic demand response programs to receive incentives is growing. Furthermore, within certain parameter ranges, the goal of increasing renewable energy consumption may conflict with the goal of improving power system resilience. VPP operators are unlikely to introduce new renewable energy projects to the grid if the rate of return is less than 0.0325 yuan / kWh.

[0197] The main conclusions of the present invention are as follows:

[0198] (1) Under the constraints of random initial probability and China's actual scenario in 2022, the optimal strategy combination for the power grid, VPP operators, and users is that all three parties implement decisions that take resilience into consideration.

[0199] (2) Through the analysis of unilateral ESS and system stability, it can be seen that the grid company plays a dominant role in the three-party game model. Only when the grid company considers resilience in its decision-making and proposes a corresponding resilience-enhancing mechanism, will VPP operators and users have the opportunity to participate in the resilience mechanism proposed by the grid company to profit. Accordingly, whether the grid company considers resilience in its decision-making is also constrained by the willingness of VPP operators and users. When both VPP operators and users have a low willingness to consider resilience, the grid company will not consider resilience in its decision-making.

[0200] (3) The design of relevant parameters in the game model has a significant impact on the strategic choices of the three parties. When the unit load recovery benefit coefficient is high, the importance of resilience increases, and the three directions of evolution towards resilience increase in speed. However, when the unit load recovery benefit coefficient is low, restoring the load does not bring sufficient benefits to the power grid, and the power grid tends to ignore resilience.

[0201] (4) As time progresses, the proportion of renewable energy generation increases. At this point, the integration of new renewable energy sources into the grid does not necessarily improve power system resilience. This chapter uses the Hao Tailin model to describe this process and finds that when the power system develops to a certain level, grid companies are less inclined to continue providing subsidies to VPP operators for the integration of new renewable energy generation. At this stage, it is possible to consider replacing previous subsidies with penalty costs to avoid a decline in power system resilience.

[0202] (5) Considering the performance of the static and dynamic demand response incentive mechanisms in the three-party game model, the simulation results show that when residents' ability and willingness to participate in demand response are both low, the two response mechanisms are not much different. However, as the economic level improves and residents' willingness to respond also increases, the dynamic response incentive mechanism effectively increases the evolution speed of the three parties and is more suitable for the needs of system resilience improvement planning.

[0203] (6) The per-kilowatt-hour revenue from investing in renewable energy may decrease due to factors such as subsidy cancellation and policy slowdown. The simulation took this process into account and found that the decline in per-kilowatt-hour revenue mainly affected the decision-making behavior of VPP operators, which may cause operators to stop investing in renewable energy power generation projects, thereby affecting the resilience of the power system.

[0204] This paper provides valuable insights into long-term resilience planning for power systems and has important practical implications. Based on the simulation model results, this paper proposes the following decision-making strategy:

[0205] (1) The power grid plays a crucial role in resilience planning. Strategies related to enhancing resilience should be implemented in a timely manner, and a collaborative platform should be created to enable various stakeholders to participate in strengthening the resilience of the power system.

[0206] (2) Accurate measurement and evaluation are essential for informed decision-making. Grid companies must be well prepared for the decision-making process to ensure that the benefits of restoring each unit of load are accurately measured. These loads should be categorized based on criteria such as geographic location and importance. Decisions regarding load restoration should prioritize these categories to optimize overall benefits.

[0207] (3) In the 2022 scenario outlined in this study, grid companies provide subsidies to VPP operators for integrating new renewable energy into the grid. However, as the share of renewable energy in the power system grows, these companies should continuously monitor generation trends, promptly assess the resilience of the power system, and adjust their strategies accordingly. Over time, they should consider scaling back subsidies for integrating new renewable energy into the grid. If necessary, they could implement penalties to regulate excessive integration of renewable energy.

[0208] (4) Considering the public’s potential unfamiliarity with the newly proposed RDR mechanism, it is recommended to initially implement a simpler and more user-friendly static demand response incentive mechanism to promote public participation. Later, this static mechanism can be transformed into a dynamic mechanism to give full play to the supporting role of flexible loads and enhance the resilience of the power system.

[0209] (5) Power system planning must balance the integration of renewable energy and enhanced resilience. Simulation results show that under certain constraints, there is a conflict between the integration of renewable energy and enhanced resilience. When making decisions related to resilience, power grids should consider the dynamics of the renewable energy market. They need to actively evaluate the profitability of renewable energy projects and adjust strategies accordingly, aiming to achieve both the integration of renewable energy and enhanced resilience.

[0210] Future Outlook:

[0211] Building resilient urban energy systems in the future requires the joint efforts of grid operators, VPP operators, and users. This study established a tripartite collaborative planning model for improving urban energy system resilience. However, it has certain limitations in terms of model accuracy and practical applicability. Future work should focus on the following prospects:

[0212] (1) In the tripartite cooperation mechanism of this invention, small thermal power plants and energy storage units are not suitable for participation due to mandatory operation and exclusive revenue. However, their impact cannot be ignored because the size of their reserve power directly affects the power demand during extreme disasters. Therefore, it is crucial to establish an accurate and reliable functional model to express the mathematical relationship between these variables.

[0213] (2) In real-world scenarios, participants’ decisions may lead to risks such as reduced reserve capacity. Therefore, it is necessary to explore the integration mechanism within the model to detect decision-making risks. In addition, participants’ decisions are not solely driven by profit. Incorporating participants’ rational factors into the game model can enhance its applicability to real-world environments.

[0214] Those skilled in the art will appreciate that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user, characterized in that: The proposed method is used to study the evolutionary stability strategies of three participants: the power grid company, the VPP operator, and the user. The specific steps include: S1, set the model assumptions of the three-party evolutionary game model; S2, based on the model assumptions, setting model parameters to construct the three-party evolutionary game model; S3, based on the three-party evolutionary game model, constructing the payoff matrix of the three participants to obtain the expected payoff, and using the replicator dynamic equation to describe the dynamic propagation process of the interaction strategies of the three participants, selecting a specific strategy, and obtaining the three-party dynamic replication equation; S4, modeling the expected benefits to obtain resilience benefits; S5. Analyze the stability of the evolutionary game strategy based on the three-party dynamic replication equation and the resilience benefit.

2. The method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user according to claim 1, characterized in that: in, The expected benefits include the expected benefits of the power grid, the expected benefits of the VPP operator, and the expected benefits of users participating in RDR. The expected benefits to the grid are as follows: Taking elasticity into account, the expected benefit of the grid can be expressed as: Y 11 =xz(R+S+D y -B-M)+(1-x)zR+x(1-z)(R+S-B-M)+(1-x)(1-z)R (1) Without considering elasticity, the expected benefit of the grid can be expressed as: Y 12 =R-W (2) The average return can be expressed as: Y1=yY 11 +(1-y)Y 12 =y(R+x(zD y +S-B-M))+(1-y)(R-W) (3) The expected benefits for VPP operators are as follows: The expected revenue of a VPP operator considering elasticity can be expressed as: X 11 =yz(U+F+G+M+D x -Q)+(1-y)zU+y(1-z)(U+F+G+M-E)+(1-y)(1-z)U(4) Without considering elasticity, the expected revenue of the VPP operator can be expressed as: X 12 =U (5) The average return can be expressed as: X1=xX 11 +(1-x)X 12 =x(U+y(zD x +F+G+M-Q))+(1-x)U (6) The expected benefits for users when participating in RDR are as follows: Z 11 =xy(C+D z )+(1-x)y(C-V)+x(1-y)(C-V)+(1-x)(1-y)(C-V) (7) When elastic demand is responded to, the expected benefits when users do not participate are: Z 12 =xy(C-(1-α)V)+(1-x)y(C-V)+x(1-y)(C-V)+(1-x)(1-y)(C-V) (8) The average return can be expressed as: Z1=zZ 11 +(1-z)Z 12 =z(xy(V+D z )+C-V)+(1-z)(xyαV+C-V) (9)。 3. The method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user according to claim 1, characterized in that: in, Based on the average profits of the grid company, VPP operator and consumers, the three-party dynamic replication equation is expressed as: F grid (y)=dy / dt=y(Y 11 -Y1)=y(1-y)(x(zD y +S-B-M)+W) (10) F VPP (x)=dx / dt=x(X 11 -X1)=xy(1-x)(zD x +F+G+M-Q) (11) F user (z)=dz / dt=z(Z 11 -Z1)=xyz(1-z)((1-α)V+D z ) (12)。 4. The method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user according to claim 1, Its characteristics are: In step S4, the expected benefits are modeled, including a Haotailin model and an RDR model. The Haotailin model describes the relationship between the proportion of renewable energy integrated into the grid and the resilience benefits. In the Hao Tai Lin model, the resilience benefits brought by renewable energy grid integration can be expressed as: Where S represents resilience benefit; C fac is the amount of renewable energy connected to the grid; S max and C max They represent the resilience benefit at the maximum point and the amount of renewable energy connected to the grid. Here, it is assumed that the resilience benefit is the largest when x1, and the maximum benefit is U1. When the amount of renewable energy connected to the grid is 0, the resilience benefit is 0; when the proportion of renewable energy is 100%, the resilience benefit is -U2. In the RDR model, two characteristic parameters, user response willingness θ and minimum incentive price λ, are selected to represent the differences in user resilience demand response. When formulating incentive prices, the power grid selects different incentive mechanisms and compares their advantages. When a static response incentive mechanism is adopted, the power grid company sets a static incentive price, and the response subsidy obtained by the user is the product of the incentive price and the response power, which can be expressed as: Where, J sta represents the user's response subsidy under the static response mechanism, ξ t represents the user's response power at time t. Under the static incentive mechanism, when the incentive price is too low, if the user's response willingness is not high and the incentive price does not reach the minimum incentive price expected by the user, the user's response power is zero, which can be expressed as a constraint: l sta ≥λ sta (i) (16) According to the characteristics of user response, its development trend should be opposite to the trend of response willingness. The dynamic incentive mechanism of resilient demand response of power grid companies is as follows: Where, J dyn represents the user's response subsidy under the dynamic response incentive mechanism; It is a dynamic incentive price for unit load recovery, set by the power grid company and changes with changes in user response willingness and response ability.

5. The method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user according to claim 1, characterized in that: in, Step S5 specifically includes the following steps: In the dynamic evolutionary game, the strategy choices of the power grid, VPP operators, and users are all time-dependent. Therefore, the solution domain of their dynamic equations is [0,1]. When all replicated dynamic equations are zero, the game strategy is in a stable state. From Equations (18-20), E1(0,0,0), E2(1,0,0), E3(1,1,0), E4(1,0,1), E5(0,0,1), E6(0,1,0), E7(0,1,1), and E8(1,1,1) are pure strategy equilibrium points. All stakeholders will choose a single strategy. These equilibrium points constitute the boundaries of the evolutionary game solution domain. The partial derivatives of the replicated dynamic equations with respect to y, x, and z are as follows: Where, F G ′(y), F V ′(x) and F U ′(z) represents the partial derivatives of the replication dynamic equations for the power grid company, VPP operator, and user, respectively. According to the stability principle of differential equations, when F(y) = 0 and F'(y) = dF(y) / dt < 0, the unilateral evolution reaches a stable state. Therefore, the ESS of the unilateral subject is found based on the replication dynamic equation, and the results of the three-party ESS are analyzed.

6. The method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user according to claim 5, characterized in that: in, The grid company's strategy stability analysis is as follows: (1) When x(zD y +SBM)+W=0, that is, the benefits obtained by the grid company when considering resilience in decision-making are the same as those when not considering resilience. And F grid When (y) = 0, the strategy choice of the power grid company is independent of time and is always in a stable state. (2) When x(zD y +SBM)+W>0, that is, the grid company has more benefits if it chooses to consider resilience than if it does not, and we can get Let F grid (y) = 0, we can get y = 0 and y = 1, and substitute y = 0 and y = 1 into F respectively. G ′(y), because F G ′(0)>0,F G ′(1)<0, so y=1 is an ESS. At this time, the power grid company is in a stable state and tends to consider resilience. (3) When x(zD y +SBM)+W<0, that is, the grid company has more benefits if it chooses not to consider resilience than if it considers resilience, and we can get Let F grid (y) = 0, we can get y = 0 and y = 1, and substitute y = 0 and y = 1 into F respectively. G ′(y), because F G ′(0)<0,F G ′(1)>0, so y=0 is an ESS. At this time, the grid company is in a stable state and tends not to consider resilience.

7. The method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user according to claim 5, characterized in that: in, The stability analysis of the VPP operator strategy is as follows: (1) When y≠0, when zD x When +F+G+MQ=0, the VPP operator obtains the same benefits whether it considers resilience in its decision-making or not. And F VPP (x) = 0, the strategy selection of the VPP operator is independent of time and is always in a stable state. (2) When zD x When +F+G+MQ>0, the VPP operator will gain more benefits by considering resilience than not considering resilience. Let F VPP (x) = 0, we can get x = 0 and x = 1, and substitute x = 0 and x = 1 into F respectively. V ′(x), because F V ′(0)>0,F V ′(1)<0, so x=1 is an ESS. At this time, the VPP operator is in a stable state and tends to consider resilience. (3) When zD x When +F+G+MQ<0, that is, the VPP operator chooses to have more benefits without considering resilience than considering resilience, and can get Let F VPP (x) = 0, we can get x = 0 and x = 1, and substitute x = 0 and x = 1 into F respectively. V ′(x), because F V ′(0)<0,F V ′(1)>0, so x=0 is an ESS, and VPP operators tend not to consider resilience.

8. The method for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user according to claim 5, characterized in that: in, The user policy stability analysis is as follows: When y≠0 and x≠0, (1-α)V+D in formula (15) z >0, let F user (z) = 0, we can get z = 0 and z = 1, and substitute z = 0 and z = 1 into F respectively. U ′(z), because F U ′(0)>0,F U ′(1)<0, so z=1 is the ESS of the user evolution strategy. When the probability of the grid company and the VPP operator considering resilience is not 0, the user tends to consider resilience.

9. A system for constructing a three-party evolutionary game model involving a power grid company, a VPP operator, and a user, characterized in that: include: Model hypothesis module, setting the model hypothesis of the three-party evolutionary game model; A model construction module, which sets model parameters based on the model assumptions to construct the three-party evolutionary game model; An expected profit analysis module, based on the three-party evolutionary game model, constructs a profit matrix for the three participants to obtain expected profits, and uses a replicator dynamic equation to describe the dynamic propagation process of the interaction strategies of the three participants, selects a specific strategy, and obtains a three-party dynamic replication equation; A resilience benefit analysis module models the expected benefits to obtain resilience benefit information; The stability analysis module analyzes the stability of the evolutionary game strategy based on the three-party dynamic replication equation and the resilience benefit.

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