AMPSO-based charging pile electricity price optimization method for multi-subject benefit balance

Abstract

The invention discloses an AMPSO-based multi-subject benefit balanced charging pile electricity price optimization method, which takes the service charge per hour as a decision variable, and comprehensively considers three goals of power distribution network stability, charging station operator profit maximization and electric vehicle user charging cost minimization. A multi-objective optimization model is formed by constructing a charging station profit maximization objective function, an electric vehicle user cost minimization objective function and a distribution network safety objective function and setting constraint conditions such as charging cost limitation, charging and discharging behaviors and an energy storage SOC, and in order to solve the model, the model is converted into a single-objective optimization problem by adopting a weighting method, so that a multi-objective optimization problem is solved. And an improved adaptive mutation particle swarm optimization algorithm is used for solving. According to the method, the operation efficiency of the charging station is improved, stable operation of the power distribution network is promoted, the charging cost of an electric vehicle user is reduced, and remarkable economic and social benefits are achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of electric vehicles, and in particular to a charging pile electricity price optimization method based on AMPSO and multi-subject interest balance. Background Art

[0002] With the transformation of the global energy structure and the enhancement of environmental protection awareness, electric vehicles (EVs), as clean and efficient means of transportation, are gradually becoming an important part of the future transportation system. The popularization of electric vehicles can not only effectively alleviate the shortage of fossil energy, but also significantly reduce exhaust emissions and play a significant role in improving air quality. However, with the rapid growth of the number of electric vehicles, the uncertainty of their charging behavior has brought great challenges to the safe and stable operation of the power grid.

[0003] Traditionally, the charging behavior of electric vehicle users is often disordered, that is, users charge at any time and any place without considering the load of the power grid and the operating efficiency of the charging station. This disordered charging mode is very likely to cause problems such as grid voltage fluctuations and line overload when large-scale electric vehicles are connected to the grid, seriously affecting the safety and reliability of the grid. In addition, disordered charging will also aggravate the load imbalance of the charging infrastructure and reduce the overall operating efficiency of the charging station.

[0004] Based on the above background, the present invention proposes a charging pile electricity price optimization method with multi-agent interest balance based on AMPSO, which aims to achieve effective scheduling of electric vehicle charging load and balance of interests among power grid, charging station and users through scientific and reasonable Time-of-Use (TOU) charging price formulation. Summary of the invention

[0005] In order to solve the problem that the current dispatching strategy focuses on improving the security of the distribution network and reducing the demand cost of users while ignoring the operation demand of charging stations, the present invention proposes a charging pile electricity price optimization method based on AMPSO with multi-agent interest balance, which relates to the technical field of electric vehicles.

[0006] To achieve the above technical objectives, the technical solution of the present invention is implemented as follows:

[0007] A charging pile electricity price optimization method based on multi-agent interest balance of AMPSO, comprising:

[0008] Construct a TOU electricity price optimization model with balanced interests among multiple entities;

[0009] The specific objective functions are set, including maximizing the profitability of charging stations, minimizing user costs, and minimizing the standard deviation of distribution network load.

[0010] And set charging cost limit, charging and discharging behavior and energy storage SOC constraints for the three key objective functions of the constructed model;

[0011] The multi-objective optimization model is converted into a single-objective optimization model through a weighted method;

[0012] Finally, the AMPSO algorithm is used to solve the problem, initialize the particle swarm and iterate the optimization, consider the variation to increase the search diversity, and finally output the optimal time-of-use service fee electricity price plan.

[0013] Furthermore, the TOU electricity price optimization model for building a multi-subject interest balance is specifically as follows: the optimization model consists of three key objective functions: maximizing charging station profits, minimizing user costs, and minimizing the standard deviation of distribution network load:

[0014] The charging station profit maximization objective function is used to calculate and maximize the charging fees obtained by the charging station from electric vehicle users. The objective function of the charging station operator is to maximize the charging fees from electric vehicle users. The formulas are shown in (1)-(4):

[0015]

[0016] in, Represents the charging revenue of the charging station; Represents the TOU service price of the charging station; represents the incentive price; P t c represents the charging power after the TOU service price is implemented at time t; represents the charging power of electric vehicle user i; P t c represents the charging power before the TOU service price is implemented at time t;

[0017] The electric vehicle user cost minimization objective function is used to calculate and minimize the charging cost of electric vehicle users, and its expression is:

[0018]

[0019] in, Represents the TOU electricity price set by the distribution network, Represents the charging costs for electric vehicle users;

[0020] The distribution network security objective function is based on the perspective of peak shaving and valley filling and reducing the load fluctuation of the distribution network. This objective function is expressed as the minimum standard deviation of the distribution network load in each period after the implementation of the TOU service fee, aiming to optimize the load stability of the distribution network.

[0021]

[0022] Where P t ch It represents the charging load of electric vehicles in the time period t.

[0023] Furthermore, the constraints are specifically:

[0024] Charging fee limit: In order to ensure that charging operators do not suffer losses during operation, a minimum charging service fee is set at Taking into account the affordability of electric vehicle users, the maximum charging service fee is set at

[0025]

[0026] Charge and discharge behavior constraints:

[0027]

[0028] in, are the lower / upper limit of charging power at time t respectively;

[0029] Energy storage SOC constraints:

[0030]

[0031] Among them, E 0 represents the initial capacity; represents the desired state of electric vehicle user i; SOC max is the upper limit of electric vehicle user i; E t,i is the energy storage capacity of electric vehicle user i at time t; T i c Represents charging efficiency.

[0032] Furthermore, the multi-objective optimization model is converted into a single-objective optimization model using a weighted method, which is specifically as follows: multiple optimization objectives including maximizing the profitability of charging stations, minimizing the costs of electric vehicle users, and the safety of distribution networks are defined, and corresponding objective functions are constructed for each optimization objective; then, a corresponding weight coefficient is assigned to each objective function according to the importance or priority of each optimization objective; multiple objective functions are combined into a comprehensive objective function by weighted summation, that is, the original multi-objective optimization model is converted into a single-objective optimization model, so that the economic benefits of charging stations, the cost expenditure of electric vehicle users, and the safety of distribution networks are uniformly considered in the optimization process, thereby realizing the optimization of electric vehicle time-of-use electricity prices that comprehensively considers various factors. The specific formula is:

[0033]

[0034] where f1,max , f 2,min , f 3,min represent the optimal solution of each objective function under the constraints. On the contrary, f 1,min , f 2,max , f 3,max Represent the worst solution of each objective function under the constraints.

[0035] Furthermore, the optimal solution of the time-of-use service fee electricity price scheme is obtained by solving the optimal solution of the model based on the normalized fitness function through the improved adaptive mutation particle swarm optimization, which is specifically as follows: The updating process of the particle position and speed is realized by formulas (13) and (14) in the algorithm,

[0036]

[0037] in, is the velocity vector of particle i at the t+1th iteration; w(t) is the inertia weight, which is used to adjust the influence of historical velocity on current velocity and may change with the number of iterations to achieve adaptive adjustment; c 1 (t) and c 2 (t) is the acceleration factor, which adjusts the speed at which the particle moves to its own historical optimal position and the global optimal position, and may also change with the number of iterations; r 1 and r 2 is a random number in the range [0,1], used to increase the randomness of the search; is the best position found by particle i so far; is the best position found by the entire particle swarm so far; is the position vector of particle i at the tth iteration;

[0038] In particle swarm optimization, due to the problem of premature convergence, it is necessary to improve the learning factor and the inertia weight ω, which is set to a random number between 0.5 and 1, as shown in formula (15):

[0039] ω=0.5+0.5N rand (15)

[0040] Among them, N rand is a random number between 0 and 1, the learning factor c 1 and c 2 The improvement is made by the nonlinear arccosine acceleration method, as shown in formulas (16) and (17), c 1 From large to small, c 2 Increase from small to large, so that particles focus more on individual search in the early stage and more on group search in the later stage,

[0041]

[0042] Among them, c 1s and c 2s are the initial values of c 1 and c 2 in the iteration, while c 1e and c 2e are their final values in the iteration; G max is the total number of iterations. In this study, the parameter values are set as c 1s = 2.5, c 2s = 0.5, c 1e = 0.5 and c 2e = 2.5;

[0043] The adaptive mutation particle swarm optimization algorithm enhances the ability of particles to escape from local optima by adding a random mutation operator. Let the fitness of the i-th particle be f i , and the average fitness of the entire particle swarm be f ave , as follows:

[0044]

[0045] Among them, n size represents the size of the particle swarm;

[0046] Next, determine the scaling factor σ 2 of the particle swarm f:

[0047]

[0048] Finally, mutate the optimal value , and the mutation probability is p:

[0049]

[0050] Among them, μ is a random number between 0.1 and 0.3; is a preset constant significantly smaller than the maximum value; f d is the theoretically optimal fitness value; The mutation process of

[0051]

[0052] involves adding a random perturbation;

[0053] Furthermore, the particle swarm optimization algorithm is based on the principle of simulating the group behavior of bird flocks foraging, treating the potential solutions to the problem as particles in the search space, and dynamically adjusting the position and speed of each particle based on its own experience and the optimal experience of the group, so as to continuously approach the global optimal solution in the iterative process. Specifically, each particle in the particle swarm optimization algorithm has two attributes, speed and position, where the speed determines the direction and distance of the particle's movement, and the position represents a potential solution in the solution space. The particle evaluates the quality of its own position through an evaluation function, and remembers the best position found by itself and the best position found by the entire group. In each iteration, the particle updates its speed and position based on the individual extreme value and the global extreme value to achieve efficient exploration and development of the search space, and finally find the global optimal solution.

[0054] Furthermore, the specific principle of the adaptive mutation particle swarm optimization algorithm is as follows: by introducing an adaptive mutation mechanism, the speed and position of the particles, as well as the mutation probability, are dynamically adjusted according to the historical search information of the particles and the current search environment, thereby enhancing the global search capability while maintaining the diversity of the population, effectively avoiding the algorithm from falling into the local optimal solution, and improving the global search capability and convergence speed when solving complex optimization problems. AMPSO ensures that the algorithm strikes a balance between exploration and utilization by flexibly adjusting the algorithm parameters to solve the optimal solution of the model.

[0055] Furthermore, the weighted method for converting the multi-objective optimization model into a single-objective optimization model has the following specific principles: the method first defines multiple objective functions, including but not limited to the objective function of maximizing charging station profits, the objective function of minimizing electric vehicle user costs, and the objective function of distribution network safety; each objective function represents a different optimization goal and may conflict with each other; the steps are: first, clarify the mathematical expression of each objective function, such as the objective function of maximizing charging station profits is to maximize the charging costs from electric vehicle users, the objective function of minimizing electric vehicle user costs is to minimize the charging costs, and the objective function of distribution network safety is to minimize the standard deviation of the distribution network load; then, assign a weight value to each objective function based on the actual needs, priority and importance of the problem; the selection of weight values ​​should be based on expert experience, data analysis or subjective evaluation to ensure that the relative importance of each objective can be reasonably reflected; finally, each objective function is multiplied by its corresponding weight, and all weighted objective functions are added together to form a comprehensive single objective function.

[0056] Principle of the present invention:

[0057] The first aspect: Taking the hourly service fee as the decision variable, a charging station TOU price optimization model is established. The core of this model is to construct three key objective functions: the first is the charging station profit maximization objective function, which aims to guide the user's charging behavior through the TOU price mechanism, so that the charging station can maximize its profits in the process of users responding to price changes; the second is the electric vehicle user fee minimization objective function, which aims to provide users with economical and efficient charging solutions and reduce their charging costs; the third is the distribution network security objective function, which ensures that the load fluctuation of the distribution network is reduced after the implementation of the TOU service fee from the perspective of peak shaving and valley filling and reducing the load fluctuation of the distribution network.

[0058] Second aspect: To achieve the above-mentioned multi-objective optimization, the present invention adopts a weighted method to transform the multi-objective optimization model into a single-objective optimization problem, and then uses the improved adaptive mutation particle swarm optimization (AMPSO) algorithm to solve it. The AMPSO algorithm simulates the foraging behavior of bird flocks and iteratively updates the speed and position of particles to search for the optimal service fee electricity price scheme. The specific steps are: initialize a particle swarm, each particle represents a potential service fee electricity price scheme, and randomly assigns its initial position and speed. At the same time, initialize the individual extreme value and the group extreme value, and record the best position of each particle and the entire particle swarm during the search process. According to the preset objective function, the fitness value of each particle is calculated to evaluate the pros and cons of the service fee electricity price scheme it represents. During the iteration process, the particle position is randomly mutated according to a certain mutation probability to increase the diversity of the search and the possibility of jumping out of the local optimal solution. After the mutation, the particle position is corrected to ensure that it meets the conditions such as charging cost restrictions, charging and discharging behavior constraints, and energy storage SOC constraints. Compare the fitness value of the mutated particle with the currently recorded individual extreme value and group extreme value. If it is better, update the corresponding extreme value. Based on the current particle position, speed and extreme value information, the particle speed and position are updated to form a new particle group and continue the next round of iteration. When the number of iterations reaches the preset value, the iteration stops. Search and determine the final individual extreme value and group extreme value, which represent the optimal or suboptimal service fee electricity price scheme found in the search process. Finally, the optimal time-of-use service fee electricity price scheme is output to provide a scientific pricing basis for charging station operators, while promoting the widespread popularization of electric vehicles and the safe and efficient operation of the power grid.

[0059] The present application discloses a charging pile electricity price optimization method with a multi-subject interest balance based on AMPSO, which specifically has the following beneficial effects: the present invention comprehensively optimizes the profitability of charging stations, user costs of electric vehicles and the safety of distribution networks by establishing a mathematical model with hourly service fees as decision variables. The method first defines the objective functions of maximizing the profitability of charging stations, minimizing user costs and minimizing load fluctuations in distribution networks, and introduces multiple constraints such as charging costs, charging and discharging behaviors and energy storage SOC. Subsequently, a weighted method is used to transform the multi-objective optimization problem into a single-objective optimization, and the improved adaptive mutation particle swarm optimization (AMPSO) algorithm is used to efficiently solve the problem to obtain the optimal TOU service fee electricity price solution. This method not only achieves a balance of interests among charging stations, users and power grids, but also effectively reduces the load fluctuations in the distribution network and improves the safety and economy of power grid operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is a method flow chart of steps S1 to S3 in this application;

[0061] Figure 2 TOU charging service fee optimization result diagram;

[0062] Figure 3 Comparison chart of TOU electricity prices of charging stations before and after optimization;

[0063] Figure 4 Comparison of electric vehicle charging load curves. DETAILED DESCRIPTION

[0064] The present invention will be described in more detail below with reference to the accompanying drawings. It should be noted that the description of the present invention below with reference to the accompanying drawings is only illustrative and not restrictive.

[0065] Embodiment 1

[0066] Embodiment 1 provides a charging pile electricity price optimization method based on AMPSO with multi-subject interest balance, aiming to reduce the charging cost of electric vehicle users, increase the revenue of charging station operators and balance the load of distribution network by intelligently adjusting the time-of-use electricity price strategy of charging stations. This method is particularly suitable for actual scenarios such as a public fast charging station in Pudong New District, Shanghai, and realizes accurate analysis and optimization by applying the EVU data provided by the Shanghai New Energy Vehicle Public Data Collection and Monitoring Research Center.

[0067] like Figure 1 As shown, a charging pile electricity price optimization method based on AMPSO and multi-agent interest balance includes the following steps:

[0068] S1. The setting of parameters is based on the public data of electric vehicles collected in specific areas and an example analysis is conducted.

[0069] S1 Specifically, take a public fast charging station operated by a charging operator in Pudong New District, Shanghai as an example. The station is equipped with 37 DC fast charging piles, which can meet the fast charging needs of a large number of electric vehicles. The EVU data provided by the Shanghai New Energy Vehicle Public Data Collection and Monitoring Research Center is used. The data records the charging behavior of electric vehicle users in detail, including key information such as entry and disconnection time. At the same time, the electricity price list of the charging operator purchasing electricity from the power grid (as shown in Table 1) is considered to provide basic data support for the formulation of time-of-use electricity price strategy.

[0070] Table 1 Power purchase price from the power grid

[0071]

[0072]

[0073] S2. By building a model optimization algorithm, we can obtain the optimization results of TOU charging service fees, charging power optimization results and cost results of all stakeholders to provide support for data analysis. Specifically:

[0074] In order to optimize the operation of charging stations, S201 built a multi-objective optimization model covering profit maximization, user cost minimization and distribution network security.

[0075] S202 sets constraints such as charging cost limit, charging and discharging behavior, and energy storage SOC.

[0076] S203 is converted to a single-objective solution through a weighted method. Using a particle swarm algorithm, 24-dimensional particles are initialized to represent the hourly electricity price schemes within the day, and an adaptive mutation mechanism is introduced to dynamically adjust the mutation probability and amplitude to avoid local optimality. During the iteration process, the extreme value is continuously updated and the particle position is adjusted until the stop condition is met to optimize the time-of-use electricity price scheme. Finally, the TOU charging service fee optimization results, charging power optimization results, and cost results of all stakeholders are obtained for comparison.

[0077] S3. Conduct comparative analysis based on the obtained TOU charging service fee optimization results, the comparison of TOU electricity prices of charging stations before and after optimization, and the electric vehicle charging load curve.

[0078] S3 specifically, the TOU charging service fee optimization result diagram, the charging station TOU electricity price comparison diagram before and after optimization, and the electric vehicle charging load curve comparison diagram are as follows: Figure 2 , 3 , as shown in 4. Figure 2As shown in the figure, the optimal time-of-use electricity price solution obtained by the AMPSO algorithm sets differentiated charging service fees in different time periods of the day. The minimum fee is adjusted to about 0.43 yuan / kWh (originally 0.45 yuan / kWh, a decrease of about 4.4%), the maximum fee is about 1.32 yuan / kWh (originally 1.29 yuan / kWh, an increase of about 2.3%), and the average fee remains at around 0.70 yuan / kWh (originally 0.71 yuan / kWh, a decrease of about 1.4%). Compared with the fixed time-of-use electricity price, this plan reduces the average by about 0.12 yuan / kWh (originally 0.13 yuan / kWh, a decrease of about 7.7%). As shown in the figure, the optimal time-of-use electricity price solution is solved by the AMPSO algorithm, which sets differentiated charging service fees in different time periods of the day. The minimum fee is adjusted to about 0.43 yuan / kWh (originally 0.45 yuan / kWh, a decrease of about 4.4%), the maximum fee is about 1.32 yuan / kWh (originally 1.29 yuan / kWh, an increase of about 2.3%), and the average fee remains at about 0.70 yuan / kWh (originally 0.71 yuan / kWh, a decrease of about 1.4%). Figure 3 As shown in the figure, the charging price curves during peak, flat and valley periods have similar trends before and after the implementation of time-of-use electricity prices. This is mainly due to the charging service fee formulation strategy in this study, which is closely based on the time period pricing of the distribution network and fully considers the maximum load constraint. Therefore, despite the optimization and adjustment, the charging price set by the charging station has not fluctuated significantly, effectively avoiding the drastic transfer of load and the generation of new peak loads. Figure 4 As shown in the figure, after the implementation of time-of-use electricity prices, users' charging behavior has been more significantly guided. Part of the charging load has been successfully transferred from the peak period (such as 18:00 to 20:00) to the valley load period (such as the night period), achieving the goal of peak load reduction. Specifically, the peak load from 18:00 to 20:00 was reduced by about 15%, and the second peak load from 8:00 to 10:00 was also reduced by about 10%.

[0079] The cost analysis of all stakeholders is shown in Table 2. After the implementation of time-of-use electricity prices, the overall charging cost of electric vehicle users was reduced by 741.28 yuan, the income of charging station operators increased by 1119.21 yuan, and the standard deviation of load fluctuations in the distribution network was reduced by 8%, achieving a win-win situation for all parties.

[0080] Table 2 Comparative analysis of benefits of different stakeholders

[0081] index Before optimization After optimization Charging fee for electric vehicle users (yuan) 24661.28 23920 Charging pile income (yuan) 13829.33 14948.54 Peak-to-valley difference (MW) 2.98 2.75 Charging power fluctuation standard deviation 0.92 0.84

[0082] The present invention proposes a charging pile electricity price optimization method based on AMPSO with multi-agent interest balance, which realizes the accurate formulation and optimization of the time-of-use electricity price of the charging station by introducing the adaptive mutation particle swarm optimization algorithm. This method not only reduces the charging cost of electric vehicle users, but also increases the income of charging station operators, and effectively alleviates the load pressure of the distribution network, which has important practical application value and promotion prospects.

Claims

1. A charging pile electricity price optimization method based on multi-agent interest balance of AMPSO, characterized in that: include: Construct a TOU electricity price optimization model with balanced interests among multiple entities; The specific objective functions are set, including maximizing the profitability of charging stations, minimizing user costs, and minimizing the standard deviation of distribution network load. And set charging cost limit, charging and discharging behavior and energy storage SOC constraints for the three key objective functions of the constructed model; The multi-objective optimization model is converted into a single-objective optimization model through a weighted method; Finally, the AMPSO algorithm is used to solve the problem, initialize the particle swarm and iterate the optimization, consider the variation to increase the search diversity, and finally output the optimal time-of-use service fee electricity price plan.

2. The charging pile electricity price optimization method based on AMPSO and multi-agent interest balance as claimed in claim 1 is characterized in that: The TOU electricity price optimization model for building a multi-subject interest balance is specifically composed of three key objective functions: maximizing charging station profits, minimizing user costs, and minimizing the standard deviation of distribution network load: The charging station profit maximization objective function is used to calculate and maximize the charging fees obtained by the charging station from electric vehicle users. The objective function of the charging station operator is to maximize the charging fees from electric vehicle users. The formulas are shown in (1)-(4): in, Represents the charging revenue of the charging station; Represents the TOU service price of the charging station; represents the incentive price; represents the charging power after the TOU service price is implemented at time t; represents the charging power of electric vehicle user i; represents the charging power before the TOU service price is implemented at time t; The electric vehicle user cost minimization objective function is used to calculate and minimize the charging cost of electric vehicle users, and its expression is: in, Represents the TOU electricity price set by the distribution network, Represents the charging costs for electric vehicle users; The distribution network security objective function is based on the perspective of peak shaving and valley filling and reducing the load fluctuation of the distribution network. This objective function is expressed as the minimum standard deviation of the distribution network load in each period after the implementation of the TOU service fee, aiming to optimize the load stability of the distribution network. In the formula, It represents the charging load of electric vehicles in the time period t.

3. The charging pile electricity price optimization method based on AMPSO and multi-agent interest balance as claimed in claim 2 is characterized in that: The constraints are specifically: Charging fee limit: In order to ensure that charging operators do not suffer losses during operation, a minimum charging service fee is set at Taking into account the affordability of electric vehicle users, the maximum charging service fee is set at Charge and discharge behavior constraints: in, are the lower / upper limit of charging power at time t respectively; Energy storage SOC constraints: Among them, E0 represents the initial capacity; represents the desired state of electric vehicle user i; SOC max is the upper limit of electric vehicle users i; E t,i is the energy storage capacity of electric vehicle user i at time t; T i c Represents charging efficiency.

4. The charging pile electricity price optimization method based on AMPSO and multi-agent interest balance as claimed in claim 3 is characterized in that: The weighted method used to convert the multi-objective optimization model into a single-objective optimization model is specifically as follows: multiple optimization objectives including maximizing the profitability of charging stations, minimizing the costs of electric vehicle users, and the safety of distribution networks are defined, and corresponding objective functions are constructed for each optimization objective; then, a corresponding weight coefficient is assigned to each objective function according to the importance or priority of each optimization objective; multiple objective functions are combined into a comprehensive objective function by weighted summation, that is, the original multi-objective optimization model is converted into a single-objective optimization model, so that the economic benefits of charging stations, the cost expenditure of electric vehicle users, and the safety of distribution networks are uniformly considered in the optimization process, thereby realizing the optimization of electric vehicle time-of-use electricity prices that comprehensively considers various factors. The specific formula is: where f 1,max , f 2,min , f 3,min represent the optimal solution of each objective function under the constraints. On the contrary, f 1,min , f 2,max , f 3,max Represent the worst solution of each objective function under the constraints.

5. The charging pile electricity price optimization method based on AMPSO and multi-agent interest balance as claimed in claim 4 is characterized in that: The optimal solution of the time-of-use service fee electricity price scheme is obtained by solving the optimal solution of the model based on the normalized fitness function through the improved adaptive mutation particle swarm optimization, which is specifically as follows: The updating process of the particle position and speed is realized by formulas (13) and (14) in the algorithm, in, is the velocity vector of particle i at the t+1th iteration; w(t) is the inertia weight, which is used to adjust the influence of historical velocity on current velocity, and may change with the number of iterations to achieve adaptive adjustment; c1(t) and c2(t) are acceleration factors, which adjust the speed of the particle moving to its own historical optimal position and global optimal position respectively, and may also change with the number of iterations; r1 and r2 are random numbers in the range of [0,1], which are used to increase the randomness of the search; is the best position found by particle i so far; is the best position found by the entire particle swarm so far; is the position vector of particle i at the tth iteration; In particle swarm optimization, due to the problem of premature convergence, it is necessary to improve the learning factor and the inertia weight ω, which is set to a random number between 0.5 and 1, as shown in formula (15): ω=0.5+0.5N rand (15) Among them, N rand is a random number between 0 and 1. The learning factors c1 and c2 are improved by the nonlinear arccosine acceleration method, as shown in formulas (16) and (17). c1 decreases from large to small, while c2 increases from small to large, so that particles focus more on individual search in the early stage and more on group search in the later stage. Among them, c 1s and c 2s are the initial values ​​of c1 and c2 in the iteration, and c 1e and c 2e are their final values ​​in the iteration; G max is the total number of iterations. In this study, the parameter value is set to c 1s =2.5, c 2s =0.5, c 1e = 0.5 and c 2e =2.5; The adaptive mutation particle swarm optimization algorithm enhances the ability of particles to escape from the local optimum by adding random mutation operators. Suppose the fitness of the i-th particle is f i , the average fitness of the entire particle swarm is f ave , as shown below: Among them, n size represents the size of the particle group; Next, determine the scaling factor σ of the particle swarm f 2 : Finally, for the optimal value Perform mutation with a mutation probability of p: Where μ is a random number between 0.1 and 0.3; is significantly smaller than The preset constant for the maximum value; f d is the theoretically optimal fitness value; The mutation process involves adding random perturbations; Here, δ is a Gaussian random variable that follows a standard normal distribution with its mean set to 0 and its standard deviation fixed to 1.

6. The method for optimizing charging pile electricity price based on AMPSO and balancing the interests of multiple subjects as claimed in claim 5 is characterized in that: The particle swarm optimization algorithm is based on the principle of simulating the group behavior of a flock of birds foraging, treating the potential solution of the problem as a particle in the search space, and each particle dynamically adjusts its position and speed according to its own experience and the optimal experience of the group, so as to continuously approach the global optimal solution in the iterative process. Specifically, each particle in the particle swarm optimization algorithm has two attributes, speed and position, wherein the speed determines the direction and distance of the particle movement, and the position represents a potential solution in the solution space. The particle evaluates the quality of its own position through an evaluation function, and remembers the best position found by itself and the best position found by the entire group. In each iteration, the particle updates its speed and position according to the individual extreme value and the global extreme value to achieve efficient exploration and development of the search space, and finally find the global optimal solution.

7. The method for optimizing charging pile electricity price based on AMPSO and balancing the interests of multiple subjects as claimed in claim 6 is characterized in that: The specific principle of the adaptive mutation particle swarm optimization algorithm is as follows: by introducing an adaptive mutation mechanism, the speed and position of the particles, as well as the mutation probability, are dynamically adjusted according to the historical search information of the particles and the current search environment, thereby enhancing the global search capability while maintaining the diversity of the population, effectively avoiding the algorithm from falling into the local optimal solution, and improving the global search capability and convergence speed when solving complex optimization problems. AMPSO ensures that the algorithm strikes a balance between exploration and utilization by flexibly adjusting the algorithm parameters to solve the optimal solution of the model.

8. The charging pile electricity price optimization method based on AMPSO and multi-agent interest balance as claimed in claim 7 is characterized in that: The weighted method for converting the multi-objective optimization model into a single-objective optimization model has the following specific principles: the method first defines multiple objective functions, including but not limited to the objective function of maximizing the profitability of charging stations, the objective function of minimizing the user costs of electric vehicles, and the objective function of distribution network security; each objective function represents a different optimization goal and may conflict with each other; The steps are as follows: first, clarify the mathematical expression of each objective function, such as the objective function of maximizing charging station profits is to maximize the charging costs from electric vehicle users, the objective function of minimizing electric vehicle user costs is to minimize charging costs, and the objective function of distribution network security is to minimize the standard deviation of distribution network load; Then, assign a weight value to each objective function based on the actual needs, priority, and importance of the problem; The choice of weight values ​​should be based on expert experience, data analysis or subjective evaluation to ensure that they can reasonably reflect the relative importance of each objective. Finally, each objective function is multiplied by its corresponding weight, and all weighted objective functions are added together to form a comprehensive single objective function.

Images