Multi-subject electric vehicle charging collaborative optimization method based on dynamic game and behavior correction

Abstract

The invention discloses a multi-subject electric vehicle charging collaborative optimization method based on dynamic game and behavior correction, and the method comprises the steps: S1, building a dynamic power grid cost function based on the geographic distribution of a plurality of electric vehicle aggregators in a power distribution network and a charging station control relation; s2, constructing a two-stage non-cooperative game model, and analyzing a second-stage game according to a reverse induction method; then analyzing the game of the first stage based on the equilibrium result of the second stage; s3, correcting irrational behaviors: in the game, adjusting subjective evaluation of the aggregator on the charging time through a probability weighting function, and correcting cognitive deviation of the aggregator on low / high probability events; integrating the subjective probability into expected income calculation; and S4, based on an inertia weight updating rule, iteratively adjusting each aggregator mixing strategy until convergence. According to the invention, the peak load of the power grid can be effectively reduced, the energy utilization efficiency is improved, and the system is ensured to still operate efficiently and stably when facing uncertainty of user behaviors.

Description

Technical Field

[0001] The present invention mainly relates to the technical field of electric vehicles, and in particular to a multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction. Background Art

[0002] With the increasing popularity of electric vehicles, effectively managing their charging behavior to reduce pressure on the power grid, optimize energy efficiency, and lower operating costs has become a critical research area. Existing charging management systems often fail to fully account for the dynamic changes in grid load and the diversity of user behavior, leading to problems such as grid overload and energy waste during peak hours. Especially in areas with high EV density, irrational charging behavior can lead to grid instability, increase power supply costs, and impact the overall safety and reliability of the grid.

[0003] Furthermore, traditional charging strategies typically employ fixed electricity pricing mechanisms or simple time-of-use pricing strategies, which lack flexibility and adaptability and fail to effectively incentivize users to charge during off-peak hours. Furthermore, users' actual charging behavior can be influenced by a variety of factors, such as personal preferences and unexpected demand. These irrational behaviors further complicate system scheduling. Summary of the Invention

[0004] In response to the technical problems existing in the existing technology, the present invention provides a multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction, which effectively reduces the peak load of the power grid, improves energy utilization efficiency, and ensures that the system maintains efficient and stable operation in the face of user behavior uncertainty.

[0005] In order to solve the above technical problems, the technical solution proposed by the present invention is: A multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction includes the following steps: S1. Establish an energy cost model: Based on the geographic distribution of multiple EV aggregators in the distribution grid and the control relationships between charging stations, a dynamic grid cost function is constructed. This cost function integrates real-time electricity prices, time-of-use electricity prices, and grid base load to optimize charging start time and energy distribution. This cost function includes a real-time electricity price term and a target energy consumption deviation cost term. The target energy consumption deviation cost is calculated by using a preset penalty coefficient and the target energy consumption for the time period. The total cost of the aggregator is determined by combining the charging time, electricity price, and deviation cost. S2. Construct a two-stage non-cooperative game model. According to the reverse induction method, we first analyze the second stage game, that is, at a given charging start time Under the condition of , solve the Nash equilibrium of each subgame; then, based on the equilibrium results of the second stage, analyze the first stage game, that is, how the aggregator chooses the optimal charging start time; S3. Correcting Irrational Behavior: In the game, a probability-weighted function is used to adjust the aggregator's subjective assessment of charging time, correcting their cognitive bias towards low / high probability events. This also incorporates subjective probability into the expected return calculation, replacing the traditional utility model. S4. Solve the ε-Nash equilibrium: Based on the inertia weight update rule, iteratively adjust the mixed strategy of each aggregator until convergence. In each iteration, the mixed strategy is updated by weighting the historical strategy and the current best response strategy, and the expected return is dynamically calculated in combination with the model of the previous step. The iteration termination condition is that the strategy update amount is less than the preset threshold to ensure the practical feasibility and robustness of the equilibrium solution.

[0006] Preferably, in step S1, the power grid cost function is specifically: (1) In the formula, and is the positive on-grid electricity price constant at time t, Specifically , the unit electricity price is , The basic load of the power grid.

[0007] Preferably, the target energy consumption deviation cost is specifically: (2) Where, is an aggregator i In time t target energy consumption; is the corresponding penalty coefficient.

[0008] Preferably, the total cost of the aggregator for: (3) Where, is an aggregator i Time to start charging; is the aggregator i at time t electricity bills paid; is the cost of the deviation from the target energy consumption.

[0009] Preferably, the specific process of step S2 is: 1) The second stage: Aggregators select Determine charging energy At a given charging start time After that, each aggregator decides the specific charging energy distribution To maximize its own benefits, solve the Nash equilibrium of each sub-game, and each aggregator chooses the optimal charging energy given the strategies of other aggregators. , the local optimization problem is: (4) Indicates the local optimum of charging energy; represents the charging amount of the remaining agents except aggregator i; represents the actual energy consumption of agents other than aggregator i; The Nash equilibrium is: (5) The superscript * indicates the optimal charging energy after Nash equilibrium; 2) Phase 1: Aggregators choose to participate in the charging time game Each aggregator determines the best time to start charging based on the choices of other aggregators , allowing aggregators to charge during periods of lower electricity prices to maximize their profits while avoiding conflicts with other aggregators; The profit function is: (6) The expected return under the mixed strategy is: (7) represents the objective probability of the j-th user under aggregator i choosing the charging start time, and j represents the j-th user under aggregator i.

[0010] Preferably, in step S3, the specific process of adjusting the aggregator's subjective assessment of charging time by a probability weighting function and correcting its cognitive bias for low / high probability events is as follows: The probability weighting function of Prelec is used to describe the subjective evaluation of the aggregator on the choice of charging time, namely: (8) Where a is the objective probability of the event; is the weight parameter of aggregator i, 0< ≤1; when = 1, the aggregator's behavior is rational, consistent with expected utility theory; when When <1, the aggregator exhibits irrational behavior and tends to overestimate low-probability events and underestimate high-probability events.

[0011] Preferably, in step S3, the subjective probability is incorporated into the expected return calculation, specifically: Under prospect theory, the expected return of an aggregator is considered as a probability-weighted function ,Right now: (10) Aggregator i chooses the charging start time The objective probability of is the charging start time chosen by aggregator i for other aggregators r subjective probability assessment.

[0012] Preferably, the specific process of step S4 is: An iterative algorithm based on the inertia weight update rule gradually adjusts the mixed strategy of each aggregator until it converges to the ϵ-Nash equilibrium; In each iteration k, the mixed strategy of each aggregator i is updated : (11) β is the inertia weight, 0<β<1; is the best response strategy of aggregator i in iteration k, defined as: (12) Aggregator i chooses a pure strategy The expected return at time , based on the mixed strategies of other aggregators in the previous iteration ; The algorithm terminates when the following conditions are met: (13) Where, 、 represents the charging capacity in each iteration k and the charging capacity in iteration k-1; ε is a small positive number, which represents the convergence threshold of the policy update.

[0013] The present invention also discloses a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the method described above are executed.

[0014] The present invention further discloses a multi-agent electric vehicle charging collaborative optimization system based on dynamic game and behavior correction, including an interconnected memory and a processor, wherein a computer program is stored on the memory, and when the computer program is run by the processor, the steps of the above method are executed.

[0015] Compared with the prior art, the advantages of the present invention are: The present invention optimizes the charging time and power consumption of each EV aggregator through subgame perfect ε-Nash equilibrium analysis, thereby effectively reducing the peak load of the power grid, improving energy utilization efficiency, and ensuring that the system maintains efficient and stable operation in the face of user behavior uncertainty.

[0016] This paper coordinates charging behavior among multiple electric vehicle aggregators by constructing a two-stage non-cooperative game model. This model not only considers real-time and time-of-use electricity prices but also incorporates subgame perfect ε-Nash equilibrium analysis to address potential irrational user behavior. By optimizing the charging time and power allocation of each aggregator, this method significantly reduces peak grid load and improves grid efficiency while ensuring user demand. This provides an efficient, flexible, and robust solution for electric vehicle charging management in smart grids.

[0017] This invention simulates the competitive interaction between multiple electric vehicle aggregators by constructing a two-stage non-cooperative game model and incorporating prospect theory. This ensures that subgame-perfect ϵ-Nash equilibrium is achieved even in the presence of irrational user behavior. This system uses a purchased energy cost function to optimize charging start time and energy distribution, effectively reducing charging costs and smoothing the grid load curve. It then solves the Nash equilibrium using an iterative best response algorithm, demonstrating its efficiency and robustness in practical applications. This innovative approach significantly improves the flexibility and stability of electric vehicle charging management and is applicable to the field of smart grid technology. This invention can effectively manage electric vehicle charging behavior under aggregators to reduce pressure on the grid, optimize energy efficiency, and reduce operating costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a flow chart of an embodiment of the multi-agent electric vehicle charging collaborative optimization method of the present invention. DETAILED DESCRIPTION

[0019] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0020] like Figure 1 As shown, the multi-stakeholder electric vehicle charging method provided by the embodiment of the present invention includes the following steps: S1. Establish an energy cost model: Based on the geographic distribution of multiple EV aggregators and the control relationships between charging stations in the distribution grid, a dynamic grid cost function is constructed. This cost function integrates real-time electricity prices, time-of-use electricity prices, and grid base load to optimize charging start time and energy distribution. This cost function includes a real-time electricity price term and a target energy consumption deviation cost term. The target energy consumption deviation cost is calculated using a preset penalty coefficient and a target energy consumption amount for a time period. The total cost of the aggregator is determined by combining charging time, electricity prices, and deviation costs. S2. Construct a two-stage non-cooperative game model. According to the reverse induction method, we first analyze the second stage game, that is, at a given charging start time Under the condition of , solve the Nash equilibrium of each subgame; then, based on the equilibrium results of the second stage, analyze the first stage game, that is, how the aggregator chooses the optimal charging start time; S3. Correcting Irrational Behavior: In the game, a probability-weighted function is used to adjust the aggregator's subjective assessment of charging time, correcting their cognitive bias towards low / high probability events. This also incorporates subjective probability into the expected return calculation, replacing the traditional utility model. S4. Solve the ε-Nash equilibrium: Based on the inertia weight update rule, iteratively adjust the mixed strategy of each aggregator until convergence. In each iteration, the mixed strategy is updated by weighting the historical strategy and the current best response strategy, and the expected return is dynamically calculated in combination with the model of the previous step. The iteration termination condition is that the strategy update amount is less than the preset threshold to ensure the practical feasibility and robustness of the equilibrium solution.

[0021] In step S1, an energy cost model for electric vehicle aggregators is established, namely: A distribution grid consists of multiple electric vehicle aggregators, each of which controls a group of EV charging stations located in a local geographic area. A dynamic grid cost function is used, combining real-time electricity prices and time-of-use electricity prices to encourage electric vehicles to charge during off-peak hours. The grid cost function is: (1) In the formula, and is the positive on-grid electricity price constant at time t; , the unit electricity price is , It is the basic load of the power grid; is an aggregator i In time t actual energy consumption.

[0022] Model the target energy consumption deviation cost based on the deviation between the actual energy consumption and the target energy consumption at time t : (2) Where, is an aggregator i In time t target energy consumption; is the corresponding penalty coefficient; Cost of available aggregators : (3) Where, is the time when aggregator i starts charging; is the electricity cost paid by aggregator i at time t; is the cost of the deviation from the target energy consumption.

[0023] In step S2, a two-stage non-cooperative game model is constructed. According to the reverse induction method, the second stage game is first analyzed, that is, at a given charging start time Under this scenario, we solve the Nash equilibrium of each subgame. Then, based on the equilibrium results of the second stage, we analyze the first stage game, that is, how the aggregator chooses the optimal charging start time.

[0024] The two-stage model is as follows: 1) The second stage: Aggregators select Determine charging energy At a given charging start time After that, each aggregator decides the specific charging energy distribution To maximize its own benefits. Solve the Nash equilibrium of each sub-game, and each aggregator chooses the optimal charging energy given the strategies of other aggregators. , the local optimization problem is: (4) Indicates the local optimum of charging energy; represents the charging amount of the remaining agents except aggregator i; represents the actual energy consumption of agents other than aggregator i; The Nash equilibrium is: (5) The superscript * indicates the optimal charging energy after Nash equilibrium; 2) Phase 1: Aggregators choose to participate in the charging time game Each aggregator determines the best time to start charging based on the choices of other aggregators , allowing aggregators to charge during periods of lower electricity prices to maximize their profits while avoiding conflicts with other aggregators.

[0025] Profit Function for: (6) Expected returns under mixed strategies for: (7) represents the objective probability of the jth user under aggregator i choosing the charging start time, and j represents the jth user under aggregator i; In step S3, irrational behavior is considered in combination with prospect theory, namely: Prospect theory is used to adjust the perceived weight of probabilistic events to better reflect the actual user decision-making patterns and enhance the adaptability and flexibility of the system. Prelec’s probability weighting function is used to describe the aggregator’s subjective evaluation of charging time selection, namely: (8) Where a is the objective probability of the event. is the weight parameter of aggregator i, 0< ≤1. When = 1, the aggregator's behavior is rational, consistent with expected utility theory. When <1, the aggregator exhibits irrational behavior and tends to overestimate low-probability events and underestimate high-probability events.

[0026] In the first stage of the game, the aggregator needs to choose the charging start time Under the expected utility theory (EUT), the expected revenue of the aggregator is: (9) Under prospect theory, the expected return of an aggregator takes into account the probability weighted function ,Right now: (10) Aggregator i chooses the charging start time The objective probability of is the charging start time chosen by aggregator i for other aggregators r subjective probability assessment.

[0027] In step S4, the ε-Nash equilibrium under the mixed strategy is solved, that is: An iterative algorithm based on the inertia weight update rule gradually adjusts the mixed strategy of each aggregator until it converges to the ε-Nash equilibrium.

[0028] In each iteration k, the mixed strategy of each aggregator i is updated : (11) β is the inertia weight, 0<β<1. is the best response strategy of aggregator i in iteration k, defined as: (12) Aggregator i chooses a pure strategy The expected return at time , based on the mixed strategies of other aggregators in the previous iteration .

[0029] The algorithm terminates when the following conditions are met: (13) Where, 、 represents the charging capacity in each iteration k and the charging capacity in iteration k-1; ε is a small positive number, which represents the convergence threshold of the policy update.

[0030] The present invention optimizes the charging time and power consumption of each EV aggregator through subgame perfect ε-Nash equilibrium analysis, thereby effectively reducing the peak load of the power grid, improving energy utilization efficiency, and ensuring that the system maintains efficient and stable operation in the face of user behavior uncertainty.

[0031] This paper coordinates charging behavior among multiple electric vehicle aggregators by constructing a two-stage non-cooperative game model. This model not only considers real-time and time-of-use electricity prices but also incorporates subgame perfect ε-Nash equilibrium analysis to address potential irrational user behavior. By optimizing the charging time and power allocation of each aggregator, this method significantly reduces peak grid load and improves grid efficiency while ensuring user demand. This provides an efficient, flexible, and robust solution for electric vehicle charging management in smart grids.

[0032] This invention simulates the competitive interaction between multiple electric vehicle aggregators by constructing a two-stage non-cooperative game model and incorporating prospect theory. This ensures that subgame-perfect ϵ-Nash equilibrium is achieved even in the presence of irrational user behavior. This system uses a purchased energy cost function to optimize charging start time and energy distribution, effectively reducing charging costs and smoothing the grid load curve. It then solves the Nash equilibrium using an iterative best response algorithm, demonstrating its efficiency and robustness in practical applications. This innovative approach significantly improves the flexibility and stability of electric vehicle charging management and is applicable to the field of smart grid technology. This invention can effectively manage electric vehicle charging behavior under aggregators to reduce pressure on the grid, optimize energy efficiency, and reduce operating costs.

[0033] The present invention also discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the above-described method. The present invention further discloses a multi-agent electric vehicle charging collaborative optimization system based on dynamic game theory and behavior correction, comprising an interconnected memory and a processor, the memory having a computer program stored thereon, which, when executed by the processor, performs the steps of the above-described method. The medium and system of the present invention correspond to the above-described method and also have the advantages described by the above-described method.

[0034] The present invention can implement all or part of the process steps in the above-described method embodiments through hardware associated with computer program instructions. The computer program can be stored in a computer-readable storage medium. When executed by a processor, the computer program can implement the steps of the above-described method embodiments. The computer program includes computer program code, which can be in source code form, object code form, executable file, or some intermediate form. Computer-readable storage media include any entity or device capable of carrying computer program code, recording media, USB flash drives, removable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media. Memory is used to store computer programs and / or modules. The processor implements various functions by running or executing the computer programs and / or modules stored in the memory and accessing data stored in the memory. The memory may include a high-speed random access memory and may also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, at least one disk storage device, a flash memory device, or other volatile solid-state storage device.

[0035] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions based on the principles of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction, characterized in that: Including steps: S1. Establish an energy cost model: Based on the geographic distribution of multiple EV aggregators in the distribution grid and the control relationships between charging stations, a dynamic grid cost function is constructed. This cost function integrates real-time electricity prices, time-of-use electricity prices, and grid base load to optimize charging start time and energy distribution. This cost function includes a real-time electricity price term and a target energy consumption deviation cost term. The target energy consumption deviation cost is calculated by using a preset penalty coefficient and the target energy consumption for the time period. The total cost of the aggregator is determined by combining the charging time, electricity price, and deviation cost. S2. Construct a two-stage non-cooperative game model. According to the reverse induction method, we first analyze the second stage game, that is, at a given charging start time Under the condition of , solve the Nash equilibrium of each subgame; then, based on the equilibrium results of the second stage, analyze the first stage game, that is, how the aggregator chooses the optimal charging start time; S3. Correcting Irrational Behavior: In the game, a probability-weighted function is used to adjust the aggregator's subjective assessment of charging time, correcting their cognitive bias towards low / high probability events. This also incorporates subjective probability into the expected return calculation, replacing the traditional utility model. S4. Solve the ε-Nash equilibrium: Based on the inertia weight update rule, iteratively adjust the mixed strategy of each aggregator until convergence. In each iteration, the mixed strategy is updated by weighting the historical strategy and the current best response strategy, and the expected return is dynamically calculated in combination with the model of the previous step. The iteration termination condition is that the strategy update amount is less than the preset threshold to ensure the practical feasibility and robustness of the equilibrium solution.

2. The multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction according to claim 1 is characterized in that: In step S1, the grid cost function is specifically: (1) In the formula, and is the positive on-grid electricity price constant at time t, Specifically , the unit electricity price is , The basic load of the power grid.

3. The multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction according to claim 2 is characterized in that: The target energy consumption deviation cost is specifically: (2) Where, is an aggregator i In time t target energy consumption; is the corresponding penalty coefficient.

4. The multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction according to claim 3 is characterized in that: Aggregator total cost for: (3) Where, is an aggregator i Time to start charging; is an aggregator i In time t electricity bills paid; is the cost of the deviation from the target energy consumption.

5. The multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction according to any one of claims 1 to 4, characterized in that: The specific process of step S2 is: 1) The second stage: Aggregators select Determine charging energy At a given charging start time After that, each aggregator decides the specific charging energy distribution To maximize its own benefits, solve the Nash equilibrium of each sub-game, and each aggregator chooses the optimal charging energy given the strategies of other aggregators. , the local optimization problem is: (4) Indicates the local optimum of charging energy; represents the charging amount of the remaining agents except aggregator i; represents the actual energy consumption of agents other than aggregator i; The Nash equilibrium is: (5) The superscript * indicates the optimal charging energy after Nash equilibrium; 2) Phase 1: Aggregators choose to participate in the charging time game Each aggregator determines the best time to start charging based on the choices of other aggregators , allowing aggregators to charge during periods of lower electricity prices to maximize their profits while avoiding conflicts with other aggregators; The profit function is: (6) The expected return under the mixed strategy is: (7) represents the objective probability of the j-th user under aggregator i choosing the charging start time, and j represents the j-th user under aggregator i.

6. The multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction according to claim 5 is characterized in that: In step S3, the specific process of adjusting the aggregator's subjective assessment of charging time through the probability weighting function to correct its cognitive bias towards low / high probability events is as follows: The probability weighting function of Prelec is used to describe the subjective evaluation of the aggregator on the choice of charging time, namely: (8) Where a is the objective probability of the event; is the weight parameter of aggregator i, 0< ≤1; when = 1, the aggregator's behavior is rational, consistent with expected utility theory; when When <1, the aggregator exhibits irrational behavior and tends to overestimate low-probability events and underestimate high-probability events.

7. The multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction according to claim 6 is characterized in that: In step S3, the subjective probability is incorporated into the expected return calculation, specifically: Under prospect theory, the expected return of an aggregator is considered as a probability-weighted function ,Right now: (10) Aggregator i chooses the charging start time The objective probability of is the charging start time chosen by aggregator i for other aggregators r subjective probability assessment.

8. The multi-agent electric vehicle charging collaborative optimization method based on dynamic game and behavior correction according to claim 7 is characterized in that: The specific process of step S4 is: An iterative algorithm based on the inertia weight update rule gradually adjusts the mixed strategy of each aggregator until it converges to the ϵ-Nash equilibrium; In each iteration k, the mixed strategy of each aggregator i is updated : (11) β is the inertia weight, 0<β<1; is the best response strategy of aggregator i in iteration k, defined as: (12) Aggregator i chooses a pure strategy The expected return at time , based on the mixed strategies of other aggregators in the previous iteration ; The algorithm terminates when the following conditions are met: (13) Where, 、 represents the charging capacity in each iteration k and the charging capacity in iteration k-1; ε is a small positive number that represents the convergence threshold for policy updates.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the computer program performs the steps of the method according to any one of claims 1 to 8.

10. A multi-agent electric vehicle charging collaborative optimization system based on dynamic game and behavior correction, comprising a memory and a processor connected to each other, wherein a computer program is stored on the memory, characterized in that: When the computer program is executed by a processor, the computer program performs the steps of the method according to any one of claims 1 to 8.

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