A Game Theory-Based Site Selection Optimization Method for Electric Vehicle Charging Stations

Abstract

This invention discloses a game theory-based method for optimizing the location of electric vehicle charging stations, relating to the field of electric vehicle charging station location technology. The method includes the following steps: randomly placing charging station nodes and recording the initial coordinates of all nodes; constructing a game theory model for the electric vehicle charging station; calculating the utility function values ​​corresponding to all strategies for each charging station node in the current iteration, identifying the strategy corresponding to the maximum utility, and updating the node coordinate set; ending the iteration when a Nash equilibrium is reached or the maximum number of iterations is reached; and applying the obtained optimal Nash equilibrium solution to the location planning of the electric vehicle charging station to achieve a balance between the total cost and coverage of the charging station. This invention can provide the optimal location for electric vehicle charging stations, improving coverage and reducing costs.

Description

Technical Field

[0001] This invention relates to the field of electric vehicle charging station site selection technology, and more specifically to a game theory-based method for optimizing electric vehicle charging station site selection. Background Technology

[0002] With the widespread use of electric vehicles, the optimal site selection of charging stations has become a critical issue that urgently needs to be addressed. The site selection of electric vehicle charging stations requires comprehensive consideration of multiple factors, including construction costs, service coverage, charging convenience, and service quality. However, these objectives often have certain interrelationships. For example, reducing the number of charging stations may lower construction costs, but it may shrink the service coverage; conversely, expanding coverage usually requires adding more charging stations, thereby increasing construction costs. This trade-off between stakeholders constitutes an NP-hard problem, and traditional methods struggle to effectively balance the needs of different stakeholders, leading to unreasonable charging station site selection, resource waste, and inconvenience for users. Therefore, a new method is urgently needed to achieve the scientific site selection of electric vehicle charging stations. Summary of the Invention

[0003] In view of this, the present invention provides a method for optimizing the location of electric vehicle charging stations based on game theory, which solves the problems existing in the background technology.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] A game theory-based method for optimizing the location of electric vehicle charging stations includes the following steps:

[0006] The charging station nodes are randomly placed, and the initial coordinates of all nodes are recorded. A game theory model of electric vehicle charging stations is constructed based on game theory.

[0007] Calculate the utility function value for all policies of each charging station node in the current iteration, find the policy corresponding to the maximum utility, and update the node coordinate set. ;

[0008] The iteration ends when Nash equilibrium is reached or the maximum number of iterations is reached. The obtained optimal Nash equilibrium solution is then applied to the site selection planning of electric vehicle charging stations to achieve a balance between the total cost and coverage of charging stations.

[0009] Optionally, the game model for electric vehicle charging stations includes: player set I Strategy Space S and utility function u ;

[0010] Player Collection I It consists of all electric vehicle charging stations in the study area, denoted as ;in,N This represents the total number of all electric vehicle charging stations in the study area, for the player. i Indicates electric vehicle charging station i ;

[0011] Strategy Space S Including player collection I The strategy of all players, players i The strategy is denoted as ;in, Indicates charging station node i Location, Indicates the area under study excluding charging station nodes i Locations of other charging station nodes; , Indicates charging station node i The coordinates of the current position;

[0012] Utility function u Used to evaluate players i The benefits of using strategies, players i Revenue includes charging station nodes i Costs and charging station nodes i Service coverage; for each player i The utility function is expressed as:

[0013]

[0014] Where: Indicates the current player i Total cost Indicates the current player i The coverage area and This represents the constant coefficient.

[0015] Optionally, the utility function value can be calculated as follows:

[0016] The utility function of charging stations is related to construction costs and coverage. For these two different metrics, the utility function is normalized. The normalized construction cost is then calculated. Represented as:

[0017]

[0018] Where: This represents the maximum sum of the cost and service coverage of a charging station. This represents the minimum sum of the cost of a charging station and its service coverage.

[0019] After normalization Monotonicity processing:

[0020]

[0021] The final utility function is expressed as:

[0022]

[0023] Where: This represents the construction cost after monotonicity treatment. Indicates the current player i The coverage area and This represents the constant coefficient.

[0024] Optionally, the method for updating the node coordinate set is as follows:

[0025] Based on the optimal response strategy convergence mechanism, the strategy corresponding to the maximum utility is found. That is, the node coordinates corresponding to the maximum utility function value, and update them to the node coordinate set. ;

[0026]

[0027] Where: k Indicates the first k One iteration is defined as the update of all charging station nodes once. Indicates the area under study excluding charging station nodes i The locations of other charging station nodes, Indicates the first i The utility value of each charging station node.

[0028] Alternatively, the optimal Nash equilibrium solution can be obtained in the following ways:

[0029] After each iteration, check if the termination condition is met. k -1st iteration and the k The difference between iterations does not exceed the threshold. ,Right now If the algorithm converges to Nash equilibrium, the iteration ends; otherwise, it enters the next iteration and continues to adjust the node strategy until Nash equilibrium or the maximum number of iterations is reached.

[0030] Alternatively, the specific method for determining Nash equilibrium is as follows:

[0031] for and A strategy combination It is a game G If the Nash equilibrium is reached, then the following equation holds:

[0032]

[0033] In the formula: Indicates charging station node i The strategy under Nash equilibrium, i.e., charging station nodes i The optimal address location; Including charging station nodes i The strategies of other charging station nodes under Nash equilibrium;

[0034] If the game G If it is an exact potential game, then the potential function is... The following equation is satisfied:

[0035]

[0036] When electric vehicle charging station nodes i From action Switch to At that time, the change in the potential function of the game is equal to the change in the utility function of the electric vehicle charging station nodes;

[0037] The exact potential game is defined as follows:

[0038]

[0039] In the formula: m This represents the strategy for all electric vehicle charging station nodes. This represents the total cost of all electric vehicle charging station nodes. This indicates the coverage area of ​​all electric vehicle charging station nodes;

[0040] When electric vehicle charging station nodes i Separately from its strategy Change to At that time, the potential function of the proposed game changes as follows:

[0041]

[0042] At this time, from arrive The change in total coverage area is equal to that affected only by nodes i Changes in the affected area, i.e., nodes i The overall uncovered area during the relocation process is only related to the node. i The cost change of the entire charging station is only related to the node. i from arrive Relevant, therefore:

[0043]

[0044]

[0045] Simplifying, we get:

[0046]

[0047] Therefore, if the game G It is a game of power, and It is its potential function. If it is the strategy combination that maximizes it, then It's a game of strategy. G The Nash equilibrium.

[0048] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a game theory-based method for optimizing the location of electric vehicle charging stations, which improves the coverage of electric vehicle charging stations and reduces their cost. According to the method of the present invention, a balance can be found between the total cost and coverage of electric vehicle charging stations, and the optimal location of the electric vehicle charging station can be determined. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0050] Figure 1 A flowchart of the electric vehicle charging station site selection optimization method based on game theory provided by the present invention;

[0051] Figure 2 A utility function value diagram for different numbers of charging stations provided by the present invention;

[0052] Figure 3 A comparison diagram of charging station site selection provided by the present invention;

[0053] Figure 4 A comparison chart of charging station coverage for GTL and RL provided by this invention;

[0054] Figure 5 A cost comparison chart of GTL and RL charging stations provided for this invention. Detailed Implementation

[0055] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0056] This invention discloses a game theory-based method for optimizing the location of electric vehicle charging stations, such as... Figure 1 As shown, it includes the following steps:

[0057] The charging station nodes are randomly placed, and these initial positions are used as the starting point for algorithm iteration. The initial coordinates of all nodes are recorded for comparison and adjustment in subsequent iterations. A game theory model of electric vehicle charging stations is constructed based on game theory.

[0058] In each iteration, the utility function value corresponding to all policies of each charging station node in the current iteration is calculated, the policy corresponding to the maximum utility (i.e., the node coordinates corresponding to the maximum effect function value) is found, and the node coordinate set is updated. ;

[0059] The iteration ends when Nash equilibrium is reached or the maximum number of iterations is reached. The obtained optimal Nash equilibrium solution is then applied to the site selection planning of electric vehicle charging stations to achieve a balance between the total cost and coverage of charging stations.

[0060] Furthermore, this embodiment constructs a game theory model for electric vehicle charging stations based on game theory. Game theory-based location (GTL) includes: player set I Strategy Space S and utility function u ;

[0061] Player Collection I (Player set): The player set is the foundation of the game model and consists of all electric vehicle charging stations in the study area, denoted as . ;in, N This represents the total number of all electric vehicle charging stations in the study area, for the player. i Indicates electric vehicle charging station i ;

[0062] Strategy Space S (Strategy space): The strategy space is the set of actions that each player can choose. In the charging station location problem, the strategy space includes the possible locations of the charging station. S Includes player collection I The strategy of all players, playersi The strategy is denoted as ;in, Indicates charging station node i Location, Indicates the area under study excluding charging station nodes i Locations of other charging station nodes; , Indicates charging station node i The coordinates of the current location; for each charging station node i Changing its strategy means changing its location within the study area. Each player evaluates their utility function value after adopting a strategy to determine the merits of the current strategy and to provide a basis for subsequent strategy adjustments.

[0063] Utility function u (Utility function): The utility function is used to evaluate players. i In the electric vehicle charging station site selection problem, the benefits of using strategies... i Revenue includes charging station nodes i Costs and charging station nodes i Service coverage; for each player i The utility function is expressed as:

[0064]

[0065] Where: Indicates the current player i Total cost Indicates the current player i The coverage area and This represents the constant coefficient.

[0066] The outcome of the game among all electric vehicle charging station nodes is a series of coordinates for all nodes. Selecting charging station locations based on these coordinates allows for a performance balance between cost and service coverage. This balance not only meets user demand for charging facilities but also reduces construction costs for charging station operators, achieving a win-win situation.

[0067] Furthermore, the specific method for calculating the utility function value is as follows:

[0068] The utility function of a charging station is related to its construction cost and coverage. Since cost and service coverage are two different metrics, they cannot be directly added together to form the final utility function. Therefore, this embodiment normalizes the utility function for both metrics to ensure comparisons are made on the same scale. The normalized construction cost is then used to calculate the utility function. Expressed as:

[0069]

[0070] In the formula: This represents the maximum sum of the cost and service coverage of a charging station. This represents the minimum sum of the cost of a charging station and its service coverage.

[0071] After normalization Monotonicity processing:

[0072]

[0073] The final utility function is expressed as:

[0074]

[0075] In the formula: This represents the construction cost after monotonicity treatment. Indicates the current player i The coverage area and This represents the constant coefficient.

[0076] Furthermore, the specific method for updating the node coordinate set is as follows:

[0077] To ensure that the GTP algorithm can effectively converge to the Nash equilibrium solution, this embodiment uses the optimal response strategy convergence mechanism as shown in the following formula to find the strategy corresponding to the maximum utility. That is, the node coordinates corresponding to the maximum utility function value, and update them to the node coordinate set. ;

[0078]

[0079] In the formula: k Indicates the first k One iteration is defined as the update of all charging station nodes once. Indicates the area under study excluding charging station nodes i The locations of other charging station nodes, Indicates the first i The utility value of each charging station node.

[0080] Furthermore, the specific method for obtaining the optimal Nash equilibrium solution is as follows:

[0081] After each iteration, check if the termination condition is met. k -1st iteration and the k The difference between iterations does not exceed the threshold. ,Right now If the results of the two iterations are very close, the algorithm converges to Nash equilibrium and the iteration ends; otherwise, it enters the next iteration and continues to adjust the node strategy until Nash equilibrium or the maximum number of iterations is reached.

[0082] After explicitly defining the GTL, the solution to the GTL depends on the existence of a Nash equilibrium. When each charging station node in the game chooses its optimal response strategy, and the strategies of other nodes remain unchanged, no charging station node will actively deviate from its current strategy choice, thus achieving a Nash equilibrium in the game. At this point, the strategy choice of each charging station node is stable, and it is impossible to obtain a higher utility value by unilaterally changing the strategy.

[0083] Furthermore, this embodiment discloses a method for determining Nash equilibrium, specifically as follows:

[0084] Definition 1 (Nash Equilibrium): For and A strategy combination It is a game G If the Nash equilibrium is reached, then the following equation holds:

[0085]

[0086] Where: Indicates charging station node i The strategy under Nash equilibrium, i.e., charging station nodes i The optimal address location; Including charging station nodes i The strategies of other charging station nodes under Nash equilibrium; there are many ways to prove the existence of Nash equilibrium, and exact potential game is a special game that can guarantee the existence of Nash equilibrium;

[0087] Definition 2 (Exact Potential Game and Exact Potential Function): If the game G If it is an exact potential game, then the potential function is... The following equation is satisfied:

[0088]

[0089] in, , and In other words, when electric vehicle charging station nodes... i From action Switch to At that time, the change in the potential function of the game is equal to the change in the utility function of the electric vehicle charging station nodes;

[0090] Theorem: If there exists a potential function in the GTL, then the game is an exact potential game;

[0091] By changing the policy of one node while keeping the policies of the other nodes unchanged, it is proven that GTL is an exact potential game.

[0092] Proof: Define an exact potential game as follows:

[0093]

[0094] In the formula: m This represents the strategy for all electric vehicle charging station nodes. This represents the total cost of all electric vehicle charging station nodes. This indicates the coverage area of ​​all electric vehicle charging station nodes;

[0095] When electric vehicle charging station nodes i Separately from its strategy Change to At that time, the potential function of the proposed game changes as follows:

[0096]

[0097] At this time, from arrive The change in total coverage area is equal to that affected only by nodes i Changes in the affected area (unaffected by any other neighboring nodes), i.e., nodes i The overall uncovered area during the relocation process is only related to the node. i This is relevant because the strategies of other nodes have not changed, and the cost change of the entire charging station is only related to the nodes. i from arrive Relevant, therefore:

[0098]

[0099]

[0100] Simplifying, we get:

[0101]

[0102] The above proves It is a potential function, and GTL is a potential game. If the game... G It is a game of power, and It is its potential function. If it is the strategy combination that maximizes it, then It's a game of strategy. G The Nash equilibrium exists in the GTL (Geometric Transmission Time) because the node strategies in the selection of electric vehicle charging station locations are finite and bounded.

[0103] In the actual site selection and planning of electric vehicle charging stations, due to the influence of multiple practical factors such as geographical constraints, random location (RL) has long been regarded as the benchmark site selection strategy. To better reflect real-world application scenarios and verify the effectiveness of the proposed GTL algorithm in charging station site selection optimization, a comparative analysis of the GTL algorithm and RL is conducted. The proposed GTL (Game Theory Location) algorithm is simulated using MATLAB to evaluate the total cost of electric vehicle charging stations and the coverage of the GTL algorithm. The total cost of an electric vehicle charging station is the sum of the construction costs of each charging station based on its location, while the coverage rate is the ratio of the total area of ​​circular areas with a radius of 2 centered on each charging station to the area of ​​the study area.

[0104] Table 1 shows the simulation parameters for three different regions, with the simulation scenario based on urban electric vehicle charging station planning. To better reflect real-world applications, the study area was divided into multiple ring-shaped coverage areas to simulate the differentiated cost distribution between the city center and the outer areas. The construction cost of charging stations closer to the city center is higher, while the cost in the outer areas is lower. The cost of a charging station located within the first ring is... The cost of a charging station located within the Second Ring Road is The cost of charging stations located within the Third Ring Road is The optimal service area radius of charging stations The value is 2. In the simulation, the initial locations of the charging stations are randomly distributed within the study area. In each iteration, their locations are adjusted according to the GTL algorithm to maximize the utility function value.

[0105] Table 1 Simulation parameters for three different regions

[0106]

[0107] Figure 2 The utility function values ​​are plotted for different numbers of charging stations. This is the utility function value of the current number of charging stations, showing the trend of utility function value changing with the number of charging stations. It is a key indicator used to evaluate the merits of charging station site selection, and consists of charging station cost and charging station coverage. As can be seen from the graph, the utility function value reaches its peak when the number of charging stations is 25. This indicates that at this number, the optimal trade-off is achieved between the construction cost and service coverage of charging stations. At this point, the site selection not only minimizes the total cost but also maximizes the service coverage, ensuring the efficient operation of electric vehicle charging stations. When the number of charging stations is small, increasing the number of charging stations significantly improves the utility function value due to the increased service coverage and relatively stable costs. However, when the number of charging stations exceeds 25, the effect of further increasing the number of charging stations on improving the utility function value begins to weaken, and may even decrease. This is because the charging station site selection is too dense, leading to overlapping coverage areas and increased charging station costs.

[0108] Figure 3 The image shows a comparison of charging station locations, where (a) represents RL and (b) represents GTL. Figure 3 The diagram shows the charging station distribution under RL and GTL when the number of charging stations is 25. Comparative analysis reveals that the charging station distribution under GTL is more uniform, effectively avoiding waste of charging resources and coverage blind spots. Under RL, there is significant overlap in the charging station distribution, which not only increases construction costs but may also lead to a decrease in service efficiency. This is because in GTL, the coverage gain of charging station nodes is incorporated into the utility function of the game theory model. GTL's coverage gain can further improve the coverage rate of charging stations, achieving optimal site selection. Furthermore, the number of charging stations near the central area under the RL distribution is significantly higher than under the GTL distribution. This is because the balance between charging station construction costs and service demand is not fully considered. Conversely, in GTL, the cost gain of charging station nodes is also incorporated into the utility function of the game theory model. GTL's cost gain can reduce the total cost of charging stations, maximizing cost-effectiveness and finding a better balance between total cost and service coverage.

[0109] Figure 4This chart compares the charging station coverage of GTL and RL. In the chart, the triangles represent the charging station coverage of GTL, and the squares represent the charging station coverage of RL. The comparative analysis shows that as the number of charging stations in the study area gradually increases, the charging station coverage of both GTL and RL shows an increasing trend. However, GTL's coverage is consistently significantly higher than RL's, demonstrating GTL's superiority in improving charging station coverage. Because GTL's game theory model considers the coverage gain of charging station nodes, the nodes dynamically adjust their positions as their utility value increases, thereby expanding the coverage area and providing more convenient charging services for electric vehicle users.

[0110] Figure 5 This chart compares the charging station costs of GTL and RL. In the chart, the triangles represent the charging station costs of GTL, while the squares represent the charging station costs of RL. As the number of charging station nodes in the study area increases, the costs of both GTL and RL show an upward trend, but the cost increase of GTL is significantly less than that of RL. This is because the game theory model in GTL considers cost-benefit, thereby maximizing cost-effectiveness. In the GTL model, charging station nodes dynamically adjust their locations based on changes in utility function values ​​to reduce total costs. This not only optimizes the location of charging stations but also effectively reduces the costs for charging station builders.

[0111] In summary, to address the site selection optimization problem of electric vehicle charging stations, this embodiment proposes a game theory-based method for electric vehicle charging station site selection optimization, which improves the coverage rate of electric vehicle charging stations and reduces their costs. According to the method of this invention, a balance can be found between the total cost and coverage rate of electric vehicle charging stations, and the optimal location of the charging station can be determined.

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

[0113] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing the location of electric vehicle charging stations based on game theory, characterized in that, Includes the following steps: The charging station nodes are randomly placed, and the initial coordinates of all nodes are recorded. A game theory model of electric vehicle charging stations is constructed based on game theory. Calculate the utility function value for all policies of each charging station node in the current iteration, find the policy corresponding to the maximum utility, and update the node coordinate set. ; The iteration ends when Nash equilibrium is reached or the maximum number of iterations is reached. The obtained optimal Nash equilibrium solution is then applied to the site selection planning of electric vehicle charging stations to achieve a balance between the total cost and coverage of charging stations. The game model for electric vehicle charging stations includes: player set I Strategy Space S and utility function u ; Player Collection I It consists of all electric vehicle charging stations in the study area, denoted as ;in, N This represents the total number of all electric vehicle charging stations in the study area, for the player. i Indicates electric vehicle charging station i ; Strategy Space S Including player collection I The strategy of all players, players i The strategy is denoted as ;in, Indicates charging station node i Location, Indicates the area under study excluding charging station nodes i Locations of other charging station nodes; , Indicates charging station node i The coordinates of the current position; Utility function u Used to evaluate players i The benefits of using strategies, players i Revenue includes charging station nodes i Costs and charging station nodes i Service coverage; for each player i The utility function is expressed as: In the formula: Indicates the current player i Total cost Indicates the current player i The coverage area and Indicates constant coefficients; The specific method for calculating the utility function value is as follows: The utility function of charging stations is related to construction costs and coverage. For these two different metrics, the utility function is normalized. The normalized construction cost is then calculated. Represented as: In the formula: This represents the maximum sum of the cost and service coverage of a charging station. This represents the minimum sum of the cost of a charging station and its service coverage. After normalization Monotonicity processing: The final utility function is expressed as: Where: This represents the construction cost after monotonicity treatment. Indicates the current player i The coverage area and This represents the constant coefficient.

2. The method for optimizing the location of electric vehicle charging stations based on game theory according to claim 1, characterized in that, The specific method for updating the node coordinate set is as follows: Based on the optimal response strategy convergence mechanism, the strategy corresponding to the maximum utility is found. That is, the node coordinates corresponding to the maximum utility function value, and update them to the node coordinate set. ; In the formula: k Indicates the first k One iteration is defined as the update of all charging station nodes once. Indicates the area under study excluding charging station nodes i The locations of other charging station nodes, Indicates the first i The utility value of each charging station node.

3. The method for optimizing the location of electric vehicle charging stations based on game theory according to claim 1, characterized in that, The specific method for obtaining the optimal Nash equilibrium solution is as follows: After each iteration, check if the termination condition is met. k -1st iteration and the k The difference between iterations does not exceed the threshold. ,Right now If the algorithm converges to Nash equilibrium, the iteration ends; otherwise, it enters the next iteration and continues to adjust the node strategy until Nash equilibrium or the maximum number of iterations is reached.

4. The method for optimizing the location of electric vehicle charging stations based on game theory according to claim 1, characterized in that, The specific method for determining Nash equilibrium is as follows: for and A strategy combination It is a game G If the Nash equilibrium is reached, then the following equation holds: Where: Indicates charging station node i The strategy under Nash equilibrium, i.e., charging station nodes i The optimal address location; Including charging station nodes i The strategies of other charging station nodes under Nash equilibrium; If the game G If it is an exact potential game, then the potential function is... The following equation is satisfied: When electric vehicle charging station nodes i From action Switch to At that time, the change in the potential function of the game is equal to the change in the utility function of the electric vehicle charging station nodes; The exact potential game is defined as follows: In the formula: m This represents the strategy for all electric vehicle charging station nodes. This represents the total cost of all electric vehicle charging station nodes. This indicates the coverage area of ​​all electric vehicle charging station nodes; When electric vehicle charging station nodes i Separately from its strategy Change to At that time, the potential function of the proposed game changes as follows: At this time, from arrive The change in total coverage area is equal to that affected only by nodes i Changes in the affected area, i.e., nodes i The overall uncovered area during the relocation process is only related to the node. i The cost change of the entire charging station is only related to the node. i from arrive Relevant, therefore: Simplifying, we get: ， Therefore, if the game G It is a game of power, and It is its potential function. If it is the strategy combination that maximizes it, then It's a game of strategy. G The Nash equilibrium.

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