CN112434866A - Electric vehicle charging management method based on generalized Stark Berger game - Google Patents

Electric vehicle charging management method based on generalized Stark Berger game Download PDF

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CN112434866A
CN112434866A CN202011380488.7A CN202011380488A CN112434866A CN 112434866 A CN112434866 A CN 112434866A CN 202011380488 A CN202011380488 A CN 202011380488A CN 112434866 A CN112434866 A CN 112434866A
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王若谷
陈雨甜
高欣
钱涛
孙宏丽
王秀丽
李明
吴子豪
王辰曦
张小平
唐露甜
李高阳
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State Grid Corp of China SGCC
Xian Jiaotong University
Electric Power Research Institute of State Grid Shaanxi Electric Power Co Ltd
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Xian Jiaotong University
Electric Power Research Institute of State Grid Shaanxi Electric Power Co Ltd
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Abstract

The invention discloses an electric vehicle charging management method based on a generalized Stark Boger game, which comprises the following steps: collecting and sorting initial electricity prices provided by a power grid and an initial charging strategy of an electric automobile, and preparing for solving a next model; step two, establishing a generalized Starkeberg game model between a power grid and the electric automobile, wherein the power grid is used as a game leader to formulate a charging behavior of guiding the electric automobile by the electricity price, and the electric automobile is used as a game follower to determine a reasonable charging strategy and influence the formulation of the electricity price; step three, according to the known electricity price, the generalized Nash equilibrium of the electric vehicle charging amount is obtained by using a fixed step length projection algorithm and an optimal response algorithm; fourthly, determining the power grid price according to the charging strategy of the electric automobile; and step five, repeating the step three and the step four, finally obtaining the socially optimal generalized Stark-Berger equilibrium solution through the continuous game between the power grid and the electric vehicle, formulating a reasonable charging strategy by the electric vehicle, maximizing the value of the utility function, formulating a proper electricity price by the power grid, and maximizing the income.

Description

Electric vehicle charging management method based on generalized Stark Berger game
Technical Field
The invention belongs to the technical field of power systems, and relates to an electric vehicle charging management method based on a generalized Stark-Berger game.
Background
Under the double pressure of environmental pollution and energy shortage, electric automobiles are rapidly popularized as important measures for energy conservation and emission reduction. The continuous increase of the electric automobile survival rate provides a series of challenges for the development of the smart power grid, including how the electric automobile owner formulates the charging strategy, how the power grid utilizes the price of electricity to reasonably guide the electric automobile to charge … … so as to realize the high-efficiency interaction between the electric automobile and the power grid, so that the electric automobile actively participates in the operation of the power grid, and meanwhile, the power grid is ensured to obtain higher income, thus the problem that the electric automobile is urgently required to be solved when entering the network.
The game theory is an effective technology for analyzing multi-subject interactive decision, and participants achieve better selection among each other by mutually playing the game. With the rapid advance of the intellectualization of the power grid, decision-making main bodies in the power grid are more diversified, and how to decide the optimal strategy of the main bodies to maximize the benefits of all parties becomes a research hotspot. The game theory provides an effective method for optimal decision of multiple subjects and multiple targets, and is widely applied to the aspects of control, scheduling, planning and the like of modern power systems.
The charging management of the electric automobile is an effective means for realizing the high-efficiency interaction between the electric automobile and a power grid, and the research for solving the problem of interactive decision between the electric automobile and the power grid by using a game theory at present mainly comprises two categories: one type is based on cooperative game, and reasonably formulates a charging strategy by considering the electric automobile formation union so as to obtain the maximum benefit of the union; one type is based on a non-cooperative game, respective charging strategies are independently determined by considering the electric automobile, the strategy selection of participants is not limited by other people, and finally a strategy set with the maximum benefits of all parties is formed. However, the energy supply of the power grid is limited at a specific time and in a specific space, the electric vehicle inevitably faces the coupling influence of the charging amount in the charging process, at this time, the game is expanded to a generalized game, and few researches are made on the coupling constraint of considering the charging amount of the electric vehicle in the charging management of the electric vehicle.
In conclusion, under the background that the permeability of the electric vehicle is gradually improved, the research of the electric vehicle charging management method based on the generalized Starkeberge game can help an electric vehicle owner to reasonably make a charging strategy, balance the benefits and the cost of electric vehicle charging, accelerate the large-scale popularization of the electric vehicle, optimize the income of a power grid, provide a reference for the power grid to make a charging price, and fill the blank that the existing research is not focused yet.
Disclosure of Invention
The invention aims to provide an electric vehicle charging management method based on a generalized Stark-Berger game, which is used for filling the defects of the existing electric vehicle charging management method: considering the coupling constraint of the charging quantity of the electric automobile, on one hand, a reasonable charging strategy of the electric automobile is formulated, the charging benefit is maximized, on the other hand, the power grid price is determined, and the electric automobile is guided to actively charge and simultaneously the income of the power grid is maximized.
In order to achieve the purpose, the invention adopts the following technical scheme: an electric vehicle charging management method based on a generalized Stark Boger game comprises the following steps:
the method comprises the following steps: acquiring an initial electricity price and an initial charging strategy of the electric automobile;
step two: establishing a generalized Stark-Berger game model between a power grid and an electric vehicle, wherein the power grid is a leader of a game, the electric vehicle is guided to make a corresponding charging strategy according to the electricity price, the electric vehicle is a follower of the game, and the charging amount is adjusted according to the determined electricity price and the pricing strategy of a micro-grid is influenced;
step three: according to the known electricity price obtained in the first step, the generalized Nash balance of the electric vehicle charging amount is obtained by using a fixed step length projection algorithm and an optimal response algorithm;
step four: determining the power grid price according to the charging strategy of the electric vehicle obtained in the step one;
after the game among the electric automobiles reaches generalized Nash balance, the power grid optimizes the electricity price according to the electricity purchasing quantity of the electric automobiles;
step five: and repeating the third step and the fourth step, finally obtaining the socially optimal generalized Stark-Berger equilibrium solution through the continuous game between the power grid and the electric automobile, formulating a reasonable charging strategy by the electric automobile, maximizing the value of the utility function, formulating a proper electricity price by the power grid, and maximizing the income.
Further, the initial price of electricity is provided by the power grid.
Further, the specific method of the second step is as follows, assuming that the total number of electric vehicles in the power grid is N, and when the power grid price is given, the utility function defining the electric vehicle N is UnAnd satisfies the following conditions:
Figure BDA0002809203010000031
defining the utility function of the power grid to be R, and satisfying:
Figure BDA0002809203010000032
wherein xnIs the charge amount, x, of the electric vehicle n-n＝[x1,x2Kxn-1,xn+1,xn+2,KxN]Is a collection of charging strategies for all electric vehicles except the electric vehicle n, enIs the battery capacity, s, of the electric vehicle nnThe method comprises the steps that charging satisfaction degree parameters of an electric automobile n are represented, p is the electricity price established by a power grid, and E is total available electric energy after the power grid meets other load requirements; e.g. of the typenAnd snAre all constants, enAssociated with the performance of the electric vehicle, snDifferent electric vehicles e related to the battery capacity and trip demand factors of the electric vehiclesnAnd snMay be different in value;
the generalized Stark Game Process for Power networks and electric vehicles is described by the problem Γ { ({ G }), { x { (G })n}n∈ゥ,{Un}n∈,R(p),p,g(x)}；
G and the number represents the power grid and electric vehicle set of the participants of the game, R (p) and { U }n}n∈￥Set of utility functions, p and { x, representing the grid and electric vehiclesn}n∈￥Representing a set of policies for grid and electric vehicles, g (x) is a coupling constraint that all electric vehicles satisfy, g (x) ∑ xn-E and according to formula (1) satisfies g (x). ltoreq.0.
Further, the specific method of step three is as follows, if there is a behavior scheme (x) for the problem Γ defined in step two*,p*) So that the following conditions hold:
Figure BDA0002809203010000041
then (x)*,p*) Is a generalized starkeberg equilibrium solution to the problem Γ; solving the generalized Stark Berger equilibrium solution firstly needs to solve the generalized Nash equilibrium solution of the electric vehicle charging amount, the generalized Nash equilibrium problem with the public constraint can be converted into a variational inequality problem, and the related method of the variational inequality is utilized to solve the problem; when assuming that the grid electricity prices are known, equation (1) translates to nash equilibrium problem with penalty factor λ:
Figure BDA0002809203010000042
wherein
Figure BDA0002809203010000043
Is xnA feasible field of; further, the equation (4) is converted into a corresponding variational inequality problem, namely
Figure BDA0002809203010000044
Wherein
Figure BDA0002809203010000045
F is the partial derivative of the inverse of the utility function of all electric vehicles with respect to the self-charge, i.e.
Figure BDA0002809203010000046
Solving nash equilibrium of the charge quantity by using a fixed-step projection algorithm, wherein the specific flow of the algorithm is shown in fig. 3, and the value of λ is updated by equation (5):
λ(k+1)＝|λ(k)+τg(x*(λ(k)))| (14)
wherein tau isIs a fixed step size; solving for x in projection algorithm*(λ(k)) During the process, an optimal response algorithm is adopted, the specific flow of the algorithm is shown in fig. 4, in each iteration, each electric vehicle owner updates own strategy when considering the strategies of other people, and the own utility function is sequentially optimized according to the formula (6), so that the integral optimal solution is obtained;
Figure BDA0002809203010000047
wherein f isn＝-Un+λTg。
Further, the specific method in the fourth step is as follows, and according to the KKT condition, the total utility function U of all the electric vehicles satisfies:
Figure BDA0002809203010000051
in a balanced state, the Lagrange multipliers of the coupling constraint keep consistent and are uniformly expressed by lambda; according to formula (7) having-en+snxnThe power value p satisfies the formula (8) because λ ≧ 0, and + p + λ is 0:
p≤en-snxn (17)
when obtaining
Figure BDA0002809203010000052
Then, combining with the need of the power grid to maximize the income, the electricity price of the power grid is determined by the formula (9);
Figure BDA0002809203010000053
compared with the existing electric automobile charging management method, the method has the following beneficial effects: the invention considers the interactive decision problem of the electric vehicle and the power grid, and establishes a generalized Stark-Berger game model between the power grid and the electric vehicle by utilizing the correlation theory of the game theory, so that the charging strategy of the electric vehicle reaches generalized Nash equilibrium, the strategy set of the power grid and the electric vehicle reaches generalized Stark-Berger equilibrium, and the optimal social benefit is obtained. Compared with the existing method, the method provided by the invention considers the coupling constraint of the electric vehicle charging process more comprehensively and completely, fully utilizes the limited resources of the power grid in specific time and space, balances the relation between the charging benefit of the electric vehicle owner and the charging cost, considers the power grid benefit at the same time, obtains the optimal generalized Stark-Berger equilibrium of the power grid and the electric vehicle society by a variational inequality method, and not only can the electric vehicle obtain the maximum charging efficiency under the equilibrium, but also the power grid benefit is improved, and the advantages are obvious. In addition, the algorithm adopted in the invention has high convergence speed, saves the calculation time to a certain extent, and improves the efficiency of making the charging strategy and the electricity price.
Drawings
FIG. 1 is an overall process of the present invention.
Fig. 2 is a generalized starkeberg game model diagram between the power grid and the electric vehicle, which is established in the invention.
FIG. 3 is a flow chart of a fixed step projection algorithm for solving generalized Nash equilibrium in the present invention.
FIG. 4 is a flow chart of the optimal response algorithm for solving generalized Nash equilibrium in the present invention.
Fig. 5 is a schematic view of the charging scheme of the electric vehicle according to the present invention.
Fig. 6 is a power rate diagram of the power grid under the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and the detailed description.
As shown in fig. 1, the electric vehicle charging management method based on the generalized starkeberg game specifically includes the following steps:
the method comprises the following steps: and collecting and collating initial electricity prices provided by the power grid and an initial charging strategy of the electric automobile, and preparing for solving the next model.
Step two: and establishing a generalized Stark Berger game model between the power grid and the electric automobile, wherein the established model is shown in figure 2. The electric vehicle is a follower of the game, and the charging amount is adjusted according to the determined electricity price and the pricing strategy of the micro-grid is influenced.
Assuming that the total number of electric vehicles in the power grid is N, the utility function defining the electric vehicle N is U when the power price of the power grid is givennAnd satisfies the following conditions:
Figure BDA0002809203010000061
defining the utility function of the power grid to be R, and satisfying:
Figure BDA0002809203010000062
wherein xnIs the charge amount, x, of the electric vehicle n-n＝[x1,x2K xn-1,xn+1,xn+2,K xN]Is a collection of charging strategies for all electric vehicles except the electric vehicle n, enIs the battery capacity, s, of the electric vehicle nnThe method is characterized in that the charging satisfaction degree parameter of the electric automobile n is represented, p is the electricity price established by a power grid, and E is the total available electric energy after the power grid meets other load requirements. e.g. of the typenAnd snAre all constants, enAssociated with the performance of the electric vehicle, snDifferent electric vehicles e related to the battery capacity and trip demand factors of the electric vehiclesnAnd snMay be different.
In summary, the generalized starkeberg game process for the grid and electric vehicles is described by the problem Γ { ({ G }), { x { (r) })n}n∈ゥ,{Un}n∈R (p), p, G (x), G and this represent the participant's grid and electric vehicle set in the game, R (p) and { U }n}n∈￥Set of utility functions, p and { x, representing the grid and electric vehiclesn}n∈￥Representing a set of policies for grid and electric vehicles, g (x) is a coupling constraint that all electric vehicles satisfy, g (x) ∑ xn-EAnd satisfies g (x). ltoreq.0 according to formula (1).
Step three: and (4) according to the known electricity price, utilizing a fixed step length projection algorithm and an optimal response algorithm to obtain the generalized Nash equilibrium of the electric vehicle charging quantity.
For the problem Γ defined in step two, if there is a behavior scheme (x)*,p*) So that the following conditions hold:
Figure BDA0002809203010000071
then (x)*,p*) Is a generalized starkeberg equilibrium solution to the problem Γ. Solving the generalized Stark Berger equilibrium solution firstly needs to solve the generalized Nash equilibrium solution of the electric vehicle charging amount, the generalized Nash equilibrium problem with the common constraint can be converted into a variational inequality problem, and the related method of the variational inequality is utilized to solve the problem. When assuming that the grid electricity prices are known, equation (1) translates to nash equilibrium problem with penalty factor λ:
Figure BDA0002809203010000072
wherein
Figure BDA0002809203010000073
Is xnCan be used. Further, the equation (4) is converted into a corresponding variational inequality problem, namely
Figure BDA0002809203010000074
Wherein
Figure BDA0002809203010000075
F is the partial derivative of the inverse of the utility function of all electric vehicles with respect to the self-charge, i.e.
Figure BDA0002809203010000081
Solving Nash equilibrium of charge quantity by using fixed step length projection algorithm, wherein the specific flow of the algorithm is shown in figure 3, and the method adopts a formula(5) Update of the value of λ:
λ(k+1)＝|λ(k)+τg(x*(λ(k)))| (23)
where τ is a fixed step size. Solving for x in projection algorithm*(λ(k)) And then, an optimal response algorithm is adopted, the specific flow of the algorithm is shown in fig. 4, in each iteration, each electric vehicle owner updates own strategy when considering the strategies of other people, and the own utility function is sequentially optimized according to the formula (6), so that the overall optimal solution is obtained.
Figure BDA0002809203010000082
Wherein f isn＝-Un+λTg。
Step four: and determining the power price of the power grid according to the charging strategy of the electric automobile.
And when the game among the electric automobiles reaches the generalized Nash balance, the power grid optimizes the electricity price according to the electricity purchasing quantity of the electric automobiles. According to the KKT condition, the total utility function U of all electric vehicles satisfies:
Figure BDA0002809203010000083
under equilibrium conditions, the lagrange multipliers of the coupling constraint remain consistent, collectively denoted by λ. According to formula (7) having-en+snxnThe power value p satisfies the formula (8) because λ ≧ 0, and + p + λ is 0:
p≤en-snxn (26)
when obtaining
Figure BDA0002809203010000084
Then, in combination with the need to maximize the revenue of the grid, the electricity rate of the grid is determined by equation (9).
Figure BDA0002809203010000085
Step five: and repeating the third step and the fourth step, finally obtaining the socially optimal generalized Stark-Berger equilibrium solution through the continuous game between the power grid and the electric automobile, formulating a reasonable charging strategy by the electric automobile, maximizing the value of the utility function, formulating a proper electricity price by the power grid, and maximizing the income.
The process flow of the method is illustrated by a simple example.
This example is directed to an electric vehicle group in a city of west ampere that is charged by being connected to a power grid at a peak time, assuming that each electric vehicle group includes 1000 electric vehicles, the power grid has an available electric energy E of 100MWh in the region and time slot, and the initial electric price p of the time slot is 0.396 yuan/kWh, and 5 electric vehicle groups are considered, and the basic data thereof are shown in table 1.
TABLE 1 basic data of electric vehicle group
Figure BDA0002809203010000091
By using the method of the invention, according to the specific implementation of each step, the charging strategy and the power grid price of the electric vehicle can be obtained, as shown in fig. 5 and fig. 6 respectively, wherein the power grid price is p*The optimal charging strategy for each electric vehicle group is x 0.5235 yuan/kWh*＝[11.3524,24.0164,14.3115,18.6229,21.4572]MWh. The result shows that after the iteration times are 25 times, the algorithm is converged to a constant value, the algorithm convergence speed is high, and the calculation efficiency is high. In addition, generalized Nash balance among electric automobile groups can be achieved under the method, generalized Stark-Barger balance can be achieved through the game of the power grid and the electric automobiles, a reasonable charging strategy is formulated for the electric automobiles under the limited electric energy provided by the power grid, the income of the power grid is improved, and the optimal social benefit is realized.
Finally, it should be noted that: the above examples are only for illustrating the technical solutions of the present invention, and the scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solutions of the present invention and their inventive concepts within the scope of the present invention.

Claims (5)

1. The electric vehicle charging management method based on the generalized Stark Berger game is characterized by comprising the following steps of:
the method comprises the following steps: acquiring an initial electricity price and an initial charging strategy of the electric automobile;
step two: establishing a generalized Stark-Berger game model between a power grid and an electric vehicle, wherein the power grid is a leader of a game, the electric vehicle is guided to make a corresponding charging strategy according to the electricity price, the electric vehicle is a follower of the game, and the charging amount is adjusted according to the determined electricity price and the pricing strategy of a micro-grid is influenced;
step three: according to the known electricity price obtained in the first step, the generalized Nash balance of the electric vehicle charging amount is obtained by using a fixed step length projection algorithm and an optimal response algorithm;
step four: determining the power grid price according to the charging strategy of the electric vehicle obtained in the step one;
after the game among the electric automobiles reaches generalized Nash balance, the power grid optimizes the electricity price according to the electricity purchasing quantity of the electric automobiles;
step five: and repeating the third step and the fourth step, finally obtaining the socially optimal generalized Stark-Berger equilibrium solution through the continuous game between the power grid and the electric automobile, formulating a reasonable charging strategy by the electric automobile, maximizing the value of the utility function, formulating a proper electricity price by the power grid, and maximizing the income.
2. The method for managing charging of the electric vehicle based on the generalized Stark Boger game as claimed in claim 1, wherein the initial price of electricity is provided by a power grid.
3. The method for managing charging of electric vehicles based on the generalized Stark Berger game as claimed in claim 1, wherein the specific method of the second step is as follows, assuming that the total number of electric vehicles in the electric network is N, and the price of the electric power is givenThe utility function of the electric vehicle n is UnAnd satisfies the following conditions:
Figure FDA0002809201000000011
defining the utility function of the power grid to be R, and satisfying:
Figure FDA0002809201000000021
wherein xnIs the charge amount, x, of the electric vehicle n-n＝[x1,x2Kxn-1,xn+1,xn+2,KxN]Is a collection of charging strategies for all electric vehicles except the electric vehicle n, enIs the battery capacity, s, of the electric vehicle nnThe method comprises the steps that charging satisfaction degree parameters of an electric automobile n are represented, p is the electricity price established by a power grid, and E is total available electric energy after the power grid meets other load requirements; e.g. of the typenAnd snAre all constants, enAssociated with the performance of the electric vehicle, snDifferent electric vehicles e related to the battery capacity and trip demand factors of the electric vehiclesnAnd snMay be different in value;
the generalized Stark Game Process for Power networks and electric vehicles is described by the problem Γ { ({ G }), { x { (G })n}n∈ゥ,{Un}n∈,R(p),p,g(x)}；
G and the number represents the power grid and electric vehicle set of the participants of the game, R (p) and { U }n}n∈￥Set of utility functions, p and { x, representing the grid and electric vehiclesn}n∈￥Representing a set of policies for grid and electric vehicles, g (x) is a coupling constraint that all electric vehicles satisfy, g (x) ∑ xn-E and according to formula (1) satisfies g (x). ltoreq.0.
4. The method for managing charging of the electric vehicle based on the generalized Stark Boger game as claimed in claim 1 or 3, wherein the method comprisesThe specific method of step three is as follows, if there is a behavior scheme (x) for the problem Γ defined in step two*,p*) So that the following conditions hold:
Figure FDA0002809201000000022
then (x)*,p*) Is a generalized starkeberg equilibrium solution to the problem Γ; solving the generalized Stark Berger equilibrium solution firstly needs to solve the generalized Nash equilibrium solution of the electric vehicle charging amount, the generalized Nash equilibrium problem with the public constraint can be converted into a variational inequality problem, and the related method of the variational inequality is utilized to solve the problem; when assuming that the grid electricity prices are known, equation (1) translates to nash equilibrium problem with penalty factor λ:
Figure FDA0002809201000000031
wherein
Figure FDA0002809201000000032
Is xnA feasible field of; further, the equation (4) is converted into a corresponding variational inequality problem, namely
Figure FDA0002809201000000033
Wherein
Figure FDA0002809201000000034
F is the partial derivative of the inverse of the utility function of all electric vehicles with respect to the self-charge, i.e.
Figure FDA0002809201000000035
Solving nash equilibrium of the charge quantity by using a fixed-step projection algorithm, wherein the specific flow of the algorithm is shown in fig. 3, and the value of λ is updated by equation (5):
Figure FDA0002809201000000036
where τ is a fixed step size; solving for x in projection algorithm*(λ(k)) During the process, an optimal response algorithm is adopted, the specific flow of the algorithm is shown in fig. 4, in each iteration, each electric vehicle owner updates own strategy when considering the strategies of other people, and the own utility function is sequentially optimized according to the formula (6), so that the integral optimal solution is obtained;
Figure FDA0002809201000000037
wherein f isn＝-Un+λTg。
5. The electric vehicle charging management method based on the generalized Stark Berger game as claimed in claim 1, wherein the specific method of the fourth step is as follows, and according to the KKT condition, the total utility function U of all electric vehicles satisfies:
Figure FDA0002809201000000038
in a balanced state, the Lagrange multipliers of the coupling constraint keep consistent and are uniformly expressed by lambda; according to formula (7) having-en+snxnThe power value p satisfies the formula (8) because λ ≧ 0, and + p + λ is 0:
p≤en-snxn (8)
when obtaining
Figure FDA0002809201000000041
Then, combining with the need of the power grid to maximize the income, the electricity price of the power grid is determined by the formula (9);
Figure FDA0002809201000000042
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