Electric vehicle charging demand response regulation and control method based on differential game model

Abstract

The invention provides an electric vehicle charging demand response regulation and control method based on a differential game model, and the method comprises the following steps: S1, constructing a differential game optimization model of a power grid and an electric vehicle, and obtaining an optimal strategy according to the charging condition of the electric vehicle through setting the electricity price of different time periods, so as to achieve the maximum income; s2, the power grid side considers the influence of the peak-valley difference of the power grid, the charging power of the electric vehicle in unit time and the total charging amount of the electric vehicle in game time on the power grid load, and adjusts the charging habit of an electric vehicle user by regulating and controlling the time-of-use electricity price, so that the power grid load is optimal; s3, the electric vehicle selects the optimal charging power to minimize the cost by combining the satisfaction income of the electric vehicle user, the charging cost of the electric vehicle and the battery loss cost of the electric vehicle according to the electricity price information given by the power grid and combining the charging demand of the electric vehicle; and S4, solving the game model by using feedback Nash equilibrium to obtain an optimal strategy of the game of the two parties.

Description

Technical Field

[0001] The present invention relates to the technical field of electric vehicle charging optimization strategies, and particularly to a method for regulating electric vehicle charging demand response based on a differential game model. Background Art

[0002] In recent years, the number of electric vehicles has increased sharply, but the growth rate of electric vehicles is significantly higher than that of public charging piles. This is mainly due to the large investment in the construction of charging stations, which will exacerbate the range anxiety of electric vehicle owners. To solve the above problems, it is necessary to optimize the scheduling and management of electric vehicle charging points. Electric vehicles have the ability to store electrical energy. When electric vehicle owners have no travel demand or have excess electricity, the electrical energy stored in electric vehicles can be used as idle resources to participate in the grid demand response on a large scale through charging stations, reducing the peak shaving pressure on the grid.

[0003] In the traditional centralized management interaction mechanism, intelligent charging stations collect information of all electric vehicle users, and then transfer the electric vehicle load to the low-load period by updating the charging price in real time. However, the prior art does not consider the internal loss problem of the battery during the charging and discharging process (the internal loss of the battery will directly affect its service life), does not consider the problem that the charging and discharging of electric vehicles are dynamically changing (the charging and discharging of electric vehicles and the change of grid load will change with time, which belongs to a dynamic change problem, so it should be studied in combination with dynamic game according to the actual situation), and does not evaluate the economy of reasonably arranging charging behavior by combining the satisfaction benefits brought by electric vehicle users to adjusting their own charging habits (the economic benefits brought by electric vehicle users adjusting their own charging behaviors can be directly reflected by the satisfaction of electric vehicle users). Summary of the Invention

[0004] The purpose of the present invention is to provide a method for regulating electric vehicle charging demand response based on a differential game model to solve the problems raised in the above background art.

[0005] The present invention is realized through the following technical solutions:

[0006] A method for regulating electric vehicle charging demand response based on a differential game model, the method comprising the following steps:

[0007] Step S1: Construct a differential game optimization model for the power grid and electric vehicles. The differential game optimization model for the power grid and electric vehicles divides a day into 24 time periods, sets the power grid strategy as time-of-use electricity price, and the power grid feeds back the electricity price information to electric vehicle users. By setting the electricity price in different time periods, the optimal strategy is obtained according to the charging situation of electric vehicles, so as to maximize its profit;

[0008] Step S2: During the game between the two parties, the grid side considers the peak-valley difference of the grid, the charging power of electric vehicles per unit time, and the impact of the total charging amount of electric vehicles during the game time on the grid load, and adjusts the charging habits of electric vehicle users by regulating time-of-use electricity prices to optimize the grid load;

[0009] Step S3: During the game between the two parties, the electric vehicle combines the satisfaction revenue of the electric vehicle user, the charging cost of the electric vehicle, and the battery loss cost of the electric vehicle, and selects the optimal charging power according to the electricity price information given by the grid and its own charging needs to minimize its cost;

[0010] Step S4: Use the feedback Nash equilibrium to solve the game model to obtain the optimal strategies for the game between the two parties.

[0011] Specifically, the specific steps of step S1 include:

[0012] Let the time-of-use electricity price be r 1 (t), and the strategy of the electric vehicle is:

[0013] Among them, represents the strategy of the i-th electric vehicle;

[0014] Let x i (t) represent the battery power of the electric vehicle at time t, represents the change rate of the electric vehicle battery power, then there is:

[0015]

[0016] Among them, k represents the charging probability of each time period, and μ represents the charging efficiency of the electric vehicle battery.

[0017] Specifically, the consideration of the impact of the peak-valley difference on the grid load in step S2 specifically includes:

[0018] Let P T (t) and P D (t) represent the peak load and valley load respectively, P T (t)-P D (t) represents the peak-valley difference. Assuming the load Q = P T (t)-P D (t), according to the relationship between the load and the electricity price Q = α 1 r 1 (t)+β 1 , minimizing the peak-valley difference can be equivalent to: min[(α 1 r 1 (t)+β 1 ) 2 , where α1 and β 1 Both represent parameters of the relationship between load and electricity price.

[0019] Specifically, the consideration of the impact of the charging power per unit time on the grid load in step S2 specifically includes:

[0020] By introducing the parameter θ 1 , representing the unit cost of charging power during the game time, Let \(C(t)\) represent the charging cost of the electric vehicle, then the charging power per unit time is

[0021] Specifically, the consideration of the impact of the total charging amount of electric vehicles during the game time on the grid load in step S2 specifically includes:

[0022] By introducing \(x'(t)\) i , representing the amount of electricity that the electric vehicle still needs to purchase from the grid, and according to the objective function \(J\) of the grid under the influence of the above factors 1 is expressed as:

[0023]

[0024] where \(a\) represents the discount rate of the grid, \(t\) 0 represents the starting time of the game, and \(T\) represents the ending time of the game.

[0025] Specifically, the consideration of the impact of the satisfaction benefit of electric vehicle users on the cost of electric vehicles in step S3 specifically includes:

[0026] Introduce α 2 , representing the correction factor for adjusting the electricity consumption behavior of electric vehicle users. The larger its value, the greater the satisfaction of electric vehicle users with adjusting their own charging behavior. Then the impact of the satisfaction benefit of electric vehicle users on the cost of electric vehicles is where represents the charging cost.

[0027] Specifically, the consideration of the impact of the battery loss of electric vehicles on the cost of electric vehicle users in step S3 specifically includes:

[0028] Introduce β 2 as the loss cost rate of the electric vehicle battery, representing the battery loss caused by unit charging amount, used to measure the consumption of the battery during the charging process. Then the battery loss cost of the electric vehicle is β 2 [x i (t) - x i (0)], and according to the above factors, the objective function of the electric vehicle is expressed as follows:

[0029]

[0030] where x i (0) represents the initial power of the i-th electric vehicle, and b represents the discount rate of the electric vehicle.

[0031] Specifically, the step S4 specifically includes:

[0032] For the power grid, let the strategy set be the feedback Nash equilibrium solution of the differential game optimization model of the power grid objective function. There exists a continuously differentiable function u(t, x i ): [t 0 , T] × R n →R, satisfying the following equation:

[0033]

[0034] And take the first derivative of its r 1 (t), and we get:

[0035]

[0036] where u t (t, x i ) represents a real-valued function of the derivative with respect to t, represents a real-valued function of the derivative with respect to x. k represents the charging probability of each time period, μ represents the charging efficiency of the electric vehicle battery, x i represents the power of the electric vehicle battery at time t, represents the loss of the electric vehicle battery life over time, R represents the set of real numbers, and R n represents the set of n-dimensional real numbers.

[0037] For the electric vehicle, let the strategy set be the feedback Nash equilibrium solution of the differential game optimization model of the electric vehicle objective function. There exists a continuously differentiable function v i (t, x i ): [t 0 , T] × R n →R, satisfying the following equation:

[0038]

[0039] And take the first derivative of it , and we get:

[0040]

[0041] where v i (t, x i ) represents a real-valued function, represents a real-valued function of the derivative with respect to t.

[0042] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0043] A method for regulating electric vehicle charging demand response based on a differential game model provided by the present invention solves the problem of disordered charging of electric vehicles by using a differential game model under the demand response framework. This model can effectively coordinate the relationship between the power grid and electric vehicles, and can effectively help the power grid reduce the peak-valley difference while reducing the cost of electric vehicles. Description of the Drawings

[0044] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings described below are only the preferred embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0045] Figure 1 It is a flowchart of the steps of a method for regulating electric vehicle charging demand response based on a differential game model provided by the present invention. Detailed Embodiments

[0046] In order to make the objectives, technical solutions, and advantages of the present invention more obvious, the exemplary embodiments according to the present invention will be described in detail below with reference to the drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments of the present invention. It should be understood that the present invention is not limited by the exemplary embodiments described herein. Based on the embodiments of the present invention described herein, all other embodiments obtained by those skilled in the art without creative efforts shall fall within the protection scope of the present invention.

[0047] In the following description, a large number of specific details are given to provide a more thorough understanding of the present invention. However, it is obvious to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some well-known technical features are not described.

[0048] It should be understood that the present invention can be implemented in different forms and should not be construed as limited to the embodiments presented herein. On the contrary, providing these embodiments will make the disclosure thorough and complete, and will fully convey the scope of the present invention to those skilled in the art.

[0049] The purpose of the terms used herein is only to describe specific embodiments and is not a limitation of the present invention. As used herein, the singular forms "a", "an" and "the" are also intended to include the plural forms unless the context clearly dictates otherwise. It should also be understood that the terms "comprising" and / or "including", when used in this specification, identify the presence of the stated features, integers, steps, operations, elements and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups. As used herein, the term "and / or" includes any and all combinations of the associated listed items.

[0050] To thoroughly understand the present invention, detailed structures will be presented in the following description to illustrate the technical solutions proposed by the present invention. The optional embodiments of the present invention are described in detail below. However, in addition to these detailed descriptions, the present invention may also have other embodiments.

[0051] See Figure 1 , a method for regulating electric vehicle charging demand response based on a differential game model, the method comprising the following steps:

[0052] Step S1: Construct a differential game optimization model for the power grid and electric vehicles. The differential game optimization model for the power grid and electric vehicles divides a day into 24 time periods, sets the power grid strategy as time-of-use electricity price, and the power grid feeds back the electricity price information to electric vehicle users. By setting the electricity price for different time periods and obtaining the optimal strategy according to the charging situation of electric vehicles, the maximum benefit can be achieved.

[0053] Step S2: During the process of the two-party game, the power grid side considers the peak-valley difference of the power grid, the charging power of electric vehicles per unit time, and the impact of the total charging amount of electric vehicles during the game time on the power grid load, and adjusts the charging habits of electric vehicle users by regulating the time-of-use electricity price to optimize the power grid load.

[0054] Step S3: During the process of the two-party game, the electric vehicle combines the satisfaction benefit of the electric vehicle user, the charging cost of the electric vehicle, and the battery loss cost of the electric vehicle, and selects the optimal charging power to minimize its cost according to the electricity price information given by the power grid and its own charging demand.

[0055] Step S4: Use the feedback Nash equilibrium to solve the game model to obtain the optimal strategies for the two-party game.

[0056] Specifically, step S1 specifically includes:

[0057] Let the time-of-use electricity price be r 1 (t), and the strategy of the electric vehicle is:

[0058] Wherein, denotes the strategy of the \(i\)-th electric vehicle, which is also the charging power corresponding to the electricity price in each time period; the goal of the electric vehicle user is to minimize the charging cost of the electric vehicle. It looks for the most favorable charging time period according to the electricity price given by the power grid to minimize its cost.

[0059] Let \(x\) i (t) denote the battery level of the electric vehicle at time \(t\), which is called the state of the system. denotes the rate of change of the battery level of the electric vehicle, which is also called the change of the system state. The change of the system state is related to the strategies \(r\) of both sides of the game 1 (t), and the state of the system itself. Specifically, it is manifested in: (1) The influence of the strategy \(r\) of the power grid 1 (time-of-use electricity price) on the rate of change of the battery level of the electric vehicle - during the peak load period of the power grid, the electricity price is relatively high, and the charging power of the electric vehicle is relatively low, so the rate of change of the battery level of the electric vehicle will also be affected. This part is an indirect influence; (2) The influence of the strategy of the electric vehicle (charging power) on the rate of change of the battery level of the electric vehicle - the magnitude of the charging power of the electric vehicle will directly affect the rate of change of the battery level of the electric vehicle. The rate of change of the battery level will increase as the charging power of the electric vehicle increases, and vice versa; (3) The influence of the state \(x\) of the system itself i (t) on the rate of change of the battery level of the electric vehicle - the higher the charging efficiency of the electric vehicle battery, the higher the energy conversion efficiency during the charging process of the electric vehicle, and the faster the rate of change of the electric vehicle battery will be. In summary, the dynamic change of the system state can be described by the following stochastic differential equation:

[0060]

[0061] where \(k\) represents the charging probability in each time period, and its value range is [0 - 1], and \(\mu\) represents the charging efficiency of the electric vehicle battery.

[0062] Exemplarily, during the process of the game between the two sides, the power grid aims to adjust the charging habits of electric vehicle users by regulating the time-of-use electricity price to optimize its own load. There are three factors affecting the power grid load, namely, the peak-valley difference of the power grid, the charging power of electric vehicles per unit time, and the total charging amount of electric vehicles during the game time.

[0063] Specifically, the consideration of the influence of the peak-valley difference on the power grid load in step S2 specifically includes:

[0064] Let \(P\) T (t) and \(P\) D (t) represent the peak load and valley load respectively, \(P\)T (t)-P D (t) represents the peak-valley difference. Assume the load Q = P T (t)-P D (t). According to the relationship between the load and the electricity price Q = α 1 r 1 (t)+β 1 , minimizing the peak-valley difference is equivalent to: min[(α 1 r 1 (t)+β 1 ) 2 , where α 1 and β 1 both represent the parameters of the relationship between the load and the electricity price.

[0065] Specifically, considering the impact of the charging power per unit time on the grid load in step S2 specifically includes:

[0066] Because the charging power is different under different electricity prices at different times. By studying the charging power at different times of a day, we can understand the charging habits of electric vehicle users for different electricity prices on that day, which will provide a reference for the adjustment of the electricity price the next day. For this reason, by introducing the parameter θ 1 , representing the unit cost within the charging power during the game time, representing the charging cost of the electric vehicle, then the charging power per unit time is

[0067] Specifically, considering the impact of the total charging amount of electric vehicles during the game time on the grid load in step S2 specifically includes:

[0068] Because the level of the total charging amount of electric vehicles in the grid will directly affect the fluctuation of the grid load. At the same time, how to balance the electricity consumption of EVs with other uses (such as household electricity, industry, commercial electricity, etc.) is also an issue that the grid needs to consider. For this reason, by introducing x’ i (t), representing the electricity that the electric vehicle still needs to purchase from the grid, according to the objective function J of the grid under the influence of the above factors 1 is expressed as:

[0069]

[0070] where a represents the discount rate of the grid, t 0 represents the start time of the game, and T represents the end time of the game.

[0071] Exemplarily, based on the electricity price information provided by the power grid and in combination with its own charging demand, the electric vehicle selects the optimal charging power to minimize its cost. The cost of the electric vehicle is described in terms of the satisfaction benefit of the electric vehicle user, the charging cost of the electric vehicle, and the battery loss cost of the electric vehicle.

[0072] Specifically, the consideration of the impact of the satisfaction benefit of the electric vehicle user on the cost of the electric vehicle in step S3 specifically includes:

[0073] Introduce α 2 , representing a correction factor for adjusting the electricity consumption behavior of electric vehicle users, whose value range is [0 - 1]. The larger its value, the greater the satisfaction of electric vehicle users with adjusting their own charging behavior. Then the impact of the satisfaction benefit of electric vehicle users on the cost of the electric vehicle is Among them, represents the charging cost.

[0074] Specifically, the consideration of the impact brought by the charging cost of the electric vehicle in step S3 specifically includes: If the charging cost is too high, then the electric vehicle user will appropriately adjust their charging method, stagger charging during peak electricity consumption periods, or choose to charge during off-peak electricity consumption periods to minimize the charging cost.

[0075] Specifically, the consideration of the impact of the battery loss of the electric vehicle on the cost of the electric vehicle user in step S3 specifically includes:

[0076] Introduce β 2 as the loss cost rate of the electric vehicle battery, representing the battery loss caused by unit charging amount, used to measure the consumption of the battery during the charging process. Then the battery loss cost of the electric vehicle is β 2 [x i (t) - x i (0)], and the objective function of the electric vehicle under the influence of the above factors is expressed as follows:

[0077]

[0078] Among them, x i (0) represents the initial power of the i-th electric vehicle, and b represents the discount rate of the electric vehicle.

[0079] Specifically, step S4 specifically includes:

[0080] For the power grid, let the strategy set be the feedback Nash equilibrium solution of the differential game optimization model of the power grid objective function. There exists a continuously differentiable function u(t, x i ): [t 0 , T] × R n →R, satisfying the following equation:

[0081]

[0082] And take the first derivative of its r 1 (t), we get:

[0083]

[0084] where u t (t, x i ) represents a real-valued function that is differentiated with respect to t, represents a real-valued function that is differentiated with respect to x, k represents the charging probability for each time period, μ represents the charging efficiency of the electric vehicle battery, x i represents the battery level of the electric vehicle at time t, represents the degradation of the electric vehicle battery life over time, R represents the set of real numbers, and R n represents the n-dimensional set of real numbers.

[0085] For an electric vehicle, let the strategy set be the feedback Nash equilibrium solution of the differential game optimization model of the electric vehicle's objective function. There exists a continuously differentiable function v i (t, x i ): [t 0 , T] × R n → R, satisfying the following equation:

[0086]

[0087] And take the first derivative of it , we get:

[0088]

[0089] where v i (t, x i ) represents a real-valued function, represents a real-valued function that is differentiated with respect to t.

[0090] Exemplarily, if the state equation of the system satisfies a stochastic differential equation, the objective function satisfies the grid objective function and the electric vehicle objective function, and the functions for which the optimal solutions exist are A(t), B(t), C i (t) and D i (t), then we have:

[0091] u(t, x i ) = exp[-a(t - t 0 )][A(t)x i + B(t)]

[0092] v i(t, x i ) = exp[-b(t - t 0 )][C i (t)x i + D i (t)]

[0093] Where A'(t) represents the reciprocal of A(t).

[0094] Taking the partial derivatives of u(t, x i ) with respect to t and x i respectively, we get:

[0095] u t (t, x i ) = {-a[A(t)x i + B(t)] + A'(t)x i + B'(t)}exp[-a(t - t 0 )]

[0096]

[0097] For the power grid, we have:

[0098]

[0099] Where A'(t) represents the reciprocal of A(t), and B'(t) represents the reciprocal of B(t).

[0100] We can obtain:

[0101]

[0102] In summary, for the power grid, its optimal strategy is:

[0103]

[0104] Taking the partial derivatives of v i (t, x i ) with respect to t and x i respectively, we get:

[0105]

[0106] For electric vehicles, we have:

[0107]

[0108] Where C i '(t) represents the reciprocal of C i (t), and D i '(t) represents the reciprocal of D i (t).

[0109] It can be obtained that:

[0110]

[0111] In summary, for an electric vehicle, its optimal strategy (optimal cost) is:

[0112]

[0113] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for regulating and controlling charging demand of electric vehicles based on a differential game model, characterized in that: The method comprises the following steps: Step S1: constructing a differential game optimization model of the power grid and electric vehicles, wherein the differential game optimization model of the power grid and electric vehicles divides a day into 24 time periods, sets the power grid strategy as a time-of-use electricity price, and feeds back electricity price information to electric vehicle users. By setting electricity prices in different time periods, the optimal strategy is obtained according to the charging conditions of the electric vehicles to maximize their benefits; Step S2: During the game between the two parties, the grid side considers the peak-to-valley difference of the grid, the charging power of electric vehicles per unit time, and the impact of the total charging amount of electric vehicles during the game time on the grid load, and adjusts the charging habits of electric vehicle users by regulating the time-of-use electricity price to optimize the grid load; Step S3: In the process of the game between the two parties, the electric vehicle combines the satisfaction benefits of the electric vehicle users, the charging cost of the electric vehicle and the battery loss cost of the electric vehicle, and according to the electricity price information given by the power grid and its own charging needs, selects the optimal charging power to minimize its cost; Step S4: Use feedback Nash equilibrium to solve the game model and obtain the optimal strategy for the game between the two parties.

2. The electric vehicle charging demand response control method based on a differential game model according to claim 1 is characterized in that: The step S1 specifically includes: Assuming the time-of-use electricity price is r1(t), the strategy of electric vehicles is: in, represents the strategy of the i-th electric car; Let x i (t) represents the battery charge of the electric vehicle at time t, Represents the rate of change of the battery power of the electric vehicle, then: Among them, k represents the charging probability in each time period, and μ represents the charging efficiency of the electric vehicle battery.

3. The electric vehicle charging demand response control method based on the differential game model according to claim 2 is characterized in that: The influence of the peak-to-valley difference on the grid load considered in step S2 specifically includes: Let P T (t) and P D (t) represent the peak load and valley load respectively, P T (t)-P D (t) represents the peak-to-valley difference, assuming that the load Q = P T (t)-p D (t), according to the relationship between load and electricity price Q = α1r1(t) + β1, minimizing the peak-to-valley difference can be equivalent to: min[(α1r1(t) + β1) 2 ], where α1 and β1 represent the parameters of the relationship between load and electricity price.

4. The electric vehicle charging demand response control method based on a differential game model according to claim 3 is characterized in that: The influence of the charging power per unit time on the grid load considered in step S2 specifically includes: By introducing the parameter θ1, it represents the unit cost of charging power during the game time. represents the charging cost of electric vehicles, then the charging power per unit time is 5. The electric vehicle charging demand response control method based on a differential game model according to claim 4 is characterized in that: The influence of the total charging amount of electric vehicles on the grid load during the game time considered in step S2 specifically includes: By introducing x' i (t), represents the amount of electricity that electric vehicles need to purchase from the power grid. The objective function J1 of the power grid under the influence of the above factors is expressed as: Among them, a represents the discount rate of the power grid, t0 represents the starting time of the game, and T represents the ending time of the game.

6. The electric vehicle charging demand response control method based on a differential game model according to claim 5 is characterized in that: The influence of the satisfaction benefit of electric vehicle users on the cost of electric vehicles in step S3 specifically includes: α2 is introduced to represent the correction factor for adjusting the electricity consumption behavior of electric vehicle users. The larger its value is, the greater the satisfaction of electric vehicle users in adjusting their own charging behavior is. Then the impact of the satisfaction benefits of electric vehicle users on the cost of electric vehicles is: in, Indicates the charging cost.

7. The electric vehicle charging demand response control method based on a differential game model according to claim 6 is characterized in that: The influence of the battery loss of the electric vehicle on the cost of the electric vehicle user is considered in step S3 specifically including: β2 is introduced as the loss cost rate of electric vehicle batteries, which represents the battery loss caused by unit charging amount and is used to measure the battery consumption during the charging process. The battery loss cost of electric vehicles is β2[x i (t)-x i (0)], the objective function of electric vehicles under the influence of the above factors is expressed as follows: Among them, x i (0) represents the initial power of the i-th electric vehicle, and b represents the discount rate of the electric vehicle.

8. The electric vehicle charging demand response control method based on a differential game model according to claim 7 is characterized in that: The step S4 specifically includes: For the power grid, the strategy set The feedback Nash equilibrium solution of the differential game optimization model of the power grid objective function exists as a continuous differentiable function u(t,x i ):[t0,T]×R n →R, satisfies the following equation: And take the first-order derivative of r1(t), we get: Among them, u t (t,x i ) represents a real-valued function derived with respect to t, represents a real-valued function derived with respect to x, k represents the charging probability in each time period, μ represents the charging efficiency of the electric vehicle battery, and x i represents the battery charge of the electric vehicle during period t, represents the depreciation of the battery life of electric vehicles over time, R represents a real number set, R n Represents the set of n-dimensional real numbers. For electric vehicles, the strategy set is the feedback Nash equilibrium solution of the differential game optimization model of the electric vehicle objective function. There exists a continuous differentiable function v i (t,x i ):[t0,T]×R n →R, satisfies the following equation: And Find the first-order derivative and we get: Among them, v i (t,x i ) represents a real-valued function, represents a real-valued function whose derivative is with respect to t.

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