A game optimization solution method for plug-in electric vehicle charging problem

Abstract

The application discloses a game optimization solving method for plug-in electric vehicle charging problems, comprising the following steps: constructing an intelligent charging station business scenario model and a cost function of a plug-in electric vehicle; obtaining a joint strategy vector through a charging strategy and performing variable replacement to obtain initial linear constraints of the charging strategy; based on the initial linear constraints, constructing F(x) according to the cost function and the joint strategy vector; evaluating individuals in a genetic algorithm population through F(x) to obtain elite individuals; performing local search on the elite individuals through a cosine annealing algorithm and a particle swarm optimization algorithm, and forming a next generation population with new individuals obtained through selection, crossover and mutation, and iterating, outputting a population individual with F(x) closest to 0, and restoring the population individual to a charging strategy of the plug-in electric vehicle through variable replacement. The application converges to Nash equilibrium quickly under a large-scale PEV scenario, and avoids dependence of traditional methods on convexity and continuous differentiability.

Description

Technical Field

[0001] This invention relates to the field of automobile charging, and in particular to a game-theoretic optimization method for solving the charging problem of plug-in electric vehicles. Background Technology

[0002] With the rapid development of smart grids, the widespread adoption of plug-in electric vehicles (PEVs) has presented new challenges to energy management. A lack of coordination in PEV charging behavior can lead to peak grid loads, increased energy costs, and even system collapse. Therefore, considering that each PEV is pursuing its own minimum cost, researching efficient optimization algorithms to solve the game equilibrium in the PEV charging problem is of great significance.

[0003] Smart charging stations (SCS), as the core infrastructure for charging plug-in electric vehicles (PEVs), involve coordinating the charging behavior of multiple PEVs under limited resource conditions. SCSs are typically deployed in residential or commercial areas, integrating an aggregator unit responsible for unified management of the charging process. PEV charging demands exhibit significant spatiotemporal heterogeneity, specifically manifested in different initial energy levels, termination energy requirements, battery capacity limitations, and personalized charging time windows for each vehicle. Simultaneously, the SCS itself must adhere to maximum load constraints to prevent system overload risks. Furthermore, it is assumed that PEVs are absolutely rational, determining their own charging strategies based on the price set by the aggregator to minimize costs.

[0004] Game theory provides a rigorous mathematical framework for analyzing multi-agent interaction problems. Nash equilibrium (NE) is defined as a strategy combination state where no participant can improve their payoff by unilaterally deviating from their current strategy. This concept provides a theoretical foundation for analyzing multi-agent competition and cooperation. In the charging scenario of plug-in electric vehicles (PEVs), the interaction of charging strategies among multiple PEVs can be modeled as a non-cooperative game, where solving for Nash equilibrium becomes a core challenge. Furthermore, due to the numerous linear constraints (such as battery capacity, charging time window, and grid load limitations) and the mutual constraints between PEV strategies, the solution process must consider these constraints, leading to the generalized Nash equilibrium (GNE) problem. Traditional solution methods (such as iterative optimal response algorithms or Newton's method) can solve Nash equilibria under specific conditions, but their effectiveness depends on the assumptions of problem convexity and continuous differentiability, making it difficult to extend to higher-dimensional strategy spaces, especially facing scalability and practicality challenges in smart grid scenarios. Evolutionary algorithms, due to their powerful global search capabilities, can be introduced into the field of game equilibrium solving. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings and deficiencies of the prior art and provide a game-theoretic optimization solution method for the charging problem of plug-in electric vehicles.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A game-theoretic optimization method for solving the charging problem of plug-in electric vehicles includes the following steps:

[0008] S1. Construct a smart charging station business scenario model, and based on the smart charging station business scenario model, construct a cost function for plug-in electric vehicles; the smart charging station business scenario model includes charging strategies.

[0009] S2. Obtain the joint policy vector through the charging policy, and perform variable substitution on the joint policy vector to obtain the initial linear constraints of the charging policy.

[0010] S3. Based on the initial linear constraints, construct the inverse fitness function according to the cost function and the joint policy vector;

[0011] S4. Initialize the genetic algorithm population, which is a set of joint policy vectors obtained by sampling. An individual in the population represents a joint policy vector. Evaluate and select several individuals whose inverse fitness function is less than a preset value in parallel as elite individuals. Perform local search on the elite individuals using cosine annealing and particle swarm optimization algorithms. Population individuals become new individuals through selection, crossover and mutation. The new individuals and the elite individuals after local search form the next generation population.

[0012] S5. Iterate through the next generation of individuals, output the individual whose inverse fitness function is closest to 0, and restore the individual to the charging strategy of a plug-in electric vehicle by variable substitution.

[0013] Step S1 involves constructing a smart charging station business scenario model, as detailed below:

[0014] Plug-in electric vehicles (PEVs) are abbreviated as PEVs, and smart charging stations (SCSs) are abbreviated as SCSs. The charging requirement for the i-th PEV to travel from its arrival at the SCS and then to its departure from the SCS is defined as follows:

[0015] (1)

[0016] Where N represents the total number of PEVs. This represents the time when the i-th PEV arrives at the SCS. This represents the time when the i-th PEV leaves the SCS. This represents the charging strategy of the i-th PEV at time t. This indicates the total amount of charge required by the PEV during the entire charging process.

[0017] During all PEV charging periods, the battery charge at any given time t will be maintained within a reasonable range, as calculated below:

[0018] (2)

[0019] in, This represents the lower limit of the safe range of the i-th PEV battery capacity. This represents the upper limit of the safe range of the i-th PEV battery capacity. This represents the initial battery charge of the i-th PEV upon arrival at the SCS;

[0020] The amount of charge at any time t is limited, and the specific calculation is as follows:

[0021] (3)

[0022] in, This represents the lower bound of the charging strategy for the i-th PEV battery per unit time. This represents the upper limit of the charging strategy for the i-th PEV battery unit time.

[0023] To ensure that the total charge of all PEVs does not exceed the total load of the SCS at any time t, the following constraint is defined:

[0024] (4)

[0025] in, This refers to the load capacity of the SCS.

[0026] The cost function is calculated in detail as follows:

[0027] The cost of a PEV is directly proportional to its electricity consumption; the cost of the i-th PEV... The specific calculation formula is as follows:

[0028] (5)

[0029] in, The total cost of all PEVs is less than or equal to the total energy cost of the SCS.

[0030] The specific calculation formula is as follows:

[0031] (6)

[0032] in, For electricity price, Let be the energy consumed over time t. This represents the proportion of all PEV costs to the total SCS power consumption cost. and These are two values ​​in the electricity price formula, obtained through direct observation;

[0033] Electricity consumption per unit time t The definition is as follows:

[0034] (7)

[0035] Simplifying formulas (5) to (7), the final cost of the i-th PEV is... for: .

[0036] Step S2 involves implementing the charging strategy for all PEVs. The joint policy vector x is obtained, specifically calculated as follows:

[0037] ;

[0038] According to formulas (1) to (4), the joint policy vector x is reduced to the following constraint form:

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] Where A is m n is a matrix, m is the number of equations, n is the dimension of x, and b is the m-th matrix. 1 column vector, and For m 1 column vector, Denotes the lower bound of each dimension of x. This represents the upper bound of each dimension of x; For p n is a matrix, and p is the number of constraints excluding upper and lower bound constraints and equality constraints. For p 1 column vector;

[0044] Using the equation, By performing variable substitution and eliminating several variables, we obtain... The inequality is transformed into:

[0045] ;

[0046] ;

[0047] ;

[0048] Still remember for Therefore, the PEV charging strategy satisfies the initial linear constraint:

[0049] ;

[0050] ;

[0051] .

[0052] Step S3 is to... Recorded as Let the joint strategy vector be . ; Let i be the charging strategy that the i-th PEV can control. Joint policy vector The charging strategies that can be controlled by other PEVs except for the i-th PEV;

[0053] Constructing the inverse fitness function The specific definition is as follows: ;

[0054] in, For each individual in the population, i.e., the joint policy vector x, and satisfying the initial linear constraints;

[0055] In F(x), the part before the plus sign is the local evaluation term, i.e., from the joint policy vector. local neighborhood The sampling generates several charging strategies for the i-th PEV. The charging strategy adopted by the current i-th PEV Compare costs;

[0056] The sampling strategy for the local evaluation items is as follows:

[0057] When evaluating the i-th PEV, the fixed Without moving, the sampled Make the joint policy vector Constraints must be met:

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] ;

[0063] in, Represents the neighborhood radius vector;

[0064] Randomly generate a unit vector , Except for the position that the i-th PEV can decide, all other values ​​are 0. Substitute them into the following formula to calculate:

[0065] ;

[0066] ;

[0067] ;

[0068] Thus, the calculation is obtained lower bound and the Upper Realm ;

[0069] The specific calculations are as follows:

[0070] ;

[0071] As a new Continue iterating to generate the next one Several obtained through iterative generation To satisfy the requirement of approximately uniform sampling points in the linearly constrained region;

[0072] In F(x), the part after the plus sign is the global evaluation term, which is derived from the joint policy vector. The feasible domain of the i-th PEV Charging strategy for sampling the i-th PEV The charging strategy adopted by the current i-th PEV Compare costs;

[0073] The sampling strategy for the global evaluation item is as follows:

[0074] When evaluating the i-th PEV, the fixed Without moving, the sampled Make the joint policy vector Satisfy the initial linear constraints;

[0075] Parallel CUDA computation is introduced into the sampling of local and global evaluation terms. Through parallel computation by CUDA threads, the final sampling result of each CUDA thread is used as the basis for the local and global evaluation terms. .

[0076] In step S4, the next generation population specifically refers to:

[0077] Initialize the genetic algorithm population: Find an initial solution that satisfies the initial linear constraints. ,by Using the initial point, sample within the feasible region. A solution that is approximately uniformly distributed in the feasible region is used as the initial population individuals;

[0078] All individuals in the population are evaluated in parallel using inverse fitness, and CUDA is used for parallel computation. Several individuals with inverse fitness less than a preset value are identified as elite individuals. After local search of these elite individuals using cosine annealing and particle swarm optimization algorithms, the elite individuals after local search are introduced into the next generation of the population. Other individuals in the next generation of the population are generated through selection, crossover, and mutation.

[0079] During the selection process, the individual's adverse fitness is normalized, specifically as follows:

[0080] ;

[0081] individual The probability of being selected is:

[0082] ;

[0083] To ensure that the offspring of two individuals remain within the feasible region after crossover, individuals and The following crossover process is adopted:

[0084] ;

[0085] ;

[0086] Individuals generated by crossover With probability The mutation is performed, and a PEV site is randomly selected. :

[0087] ;

[0088] By sampling approximately uniformly within the feasible region, a single point of PEV is sampled. New charging strategy Through reassembly, new individuals are formed and become part of the next generation of the population. :

[0089] ;

[0090] in, Individuals generated by crossover In addition to the points Charging strategies for other locations besides [the main point].

[0091] The initial solution The specific calculations are as follows:

[0092] Inequality constraints With boundary constraints , Standardization transformation:

[0093] Introducing slack variables , transformed Introducing variable substitution ,but Boundary constraints are transformed into Introducing variables , transformed Boundary constraints are transformed into Since a feasible solution is found, the objective function is a constant 0. Therefore, the standardized model is:

[0094] ;

[0095] ;

[0096] ;

[0097] ;

[0098] right The less-than-zero parts are negated and artificial variables are introduced; the auxiliary objective function is optimized using the simplex method.

[0099] ;

[0100] If the auxiliary objective function is optimal If the artificial variables are found to be true, then a feasible solution exists; otherwise, no feasible solution exists. Removing artificial variables from the feasible solutions yields the solution obtained from the given information. A feasible solution is found, and then the original variables are restored. This is the initial solution. .

[0101] The cosine annealing algorithm is specifically as follows:

[0102] The search radius is updated using a cosine annealing algorithm with hot restart. , For the current iteration round of the genetic algorithm, whenever for When it is a multiple of, the maximum search radius Halve; This is a hyperparameter representing the hot restart period of the search radius. The updated formula is:

[0103] ;

[0104] For elite individuals Randomly select several PEVs in random order, and traverse the i-th PEV in random order to perform the following operations:

[0105] fixed Middle opponent strategy Optimize their own strategies To minimize the objective function It must satisfy the initial linear constraint and the rectangular constraint, specifically:

[0106] ;

[0107] .

[0108] The particle swarm optimization algorithm is specifically as follows:

[0109] Initialize all particles by randomly generating multiple joint policy vectors within the rectangular constraint area and assigning them to the particles. Random initial position:

[0110] ;

[0111] Random initial particles speed:

[0112] ;

[0113] particles Historical best position Set as current position As the globally optimal position Minimize the objective function During the particle swarm search iteration process, the velocity and position updates for each generation of particles are as follows:

[0114] ;

[0115] ;

[0116] in, For inertial weights, and The updated particle is the acceleration factor. Location If it exceeds the rectangular constraint, it will be corrected to fall within the rectangular constraint range:

[0117] ;

[0118] ;

[0119] Calculate the updated particles If the objective function is smaller than the objective function of the particle before the update and satisfies the initial linear constraints, then update... and After iterative comparison in particle swarm search as well as The particles with smaller objective functions are selected as the elite individuals after the final local search.

[0120] Meanwhile, this invention provides:

[0121] A server includes a processor and a memory, the memory storing at least one program, which is loaded and executed by the processor to implement the game optimization solution method for the above-mentioned plug-in electric vehicle charging problem.

[0122] A computer-readable storage medium storing at least one program, which is loaded and executed by a processor to implement the above-described game-theoretic optimization solution method for the plug-in electric vehicle charging problem.

[0123] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0124] 1. This invention can quickly converge to the generalized Nash equilibrium in large-scale plug-in electric vehicle scenarios, avoiding the dependence of traditional methods on convexity and continuous differentiability, and significantly reducing the implementation threshold and computational overhead of the algorithm.

[0125] 2. This invention introduces initial linear constraints for sampling, enabling the charging strategy to explore efficiently within the constraint space, and significantly improves search efficiency and convergence speed through a parallel sampling strategy.

[0126] 3. This invention improves the accuracy and robustness of the Nash equilibrium solution, i.e. the final PVE charging strategy, by constructing an inverse fitness function, taking into account both global exploration and local development capabilities.

[0127] 4. Traditional technical solutions are difficult to apply directly to smart charging application scenarios. This invention introduces combined multi-constraint conditions into the defined inverse fitness function, which can efficiently solve Nash equilibrium and is more suitable for smart charging application scenarios.

[0128] 5. This invention can be extended to other multi-party game scenarios, such as smart grids and household electricity. Attached Figure Description

[0129] Figure 1 This is a schematic diagram of the intelligent charging station described in this invention.

[0130] Figure 2 This is a flowchart of the game-theoretic optimization solution method for the charging problem of plug-in electric vehicles described in this invention.

[0131] Figure 3 This diagram illustrates how three CUDA threads sample points in the feasible region in parallel, resulting in an approximately uniform distribution.

[0132] Figure 4 This diagram illustrates the use of CUDA threads to evaluate population inverse fitness in parallel.

[0133] Figure 5 This is a schematic diagram of a local search for elite individuals.

[0134] Figure 6 This is a line graph showing the strategy of 10 PEVs obtained from the results of this invention.

[0135] Figure 7 Line graph comparing the sum of the final charging strategy for PEV at each moment with the total load. Detailed Implementation

[0136] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0137] like Figure 2 A game-theoretic optimization method for solving the charging problem of plug-in electric vehicles includes the following steps:

[0138] S1. Construct a smart charging station business scenario model, and based on the smart charging station business scenario model, construct a cost function for plug-in electric vehicles; the smart charging station business scenario model includes charging strategies.

[0139] S2. Obtain the joint policy vector through the charging policy, and perform variable substitution on the joint policy vector to obtain the initial linear constraints of the charging policy.

[0140] S3. Based on the initial linear constraints, construct the inverse fitness function according to the cost function and the joint policy vector;

[0141] S4. Initialize the genetic algorithm population, which is a set of joint policy vectors obtained by sampling. An individual in the population represents a joint policy vector. Evaluate and select several individuals whose inverse fitness function is closest to 0 in parallel as elite individuals. Perform local search on the elite individuals using cosine annealing and particle swarm optimization algorithms. Population individuals become new individuals through selection, crossover, and mutation. The new individuals and the elite individuals after local search form the next generation population.

[0142] S5. Iterate through the next generation of individuals, output the individual whose inverse fitness function is closest to 0, and restore the individual to the charging strategy of a plug-in electric vehicle by variable substitution.

[0143] In step S1, modeling and analysis are performed for the smart charging station business scenario: Define the process of the i-th plug-in electric vehicle (PEV) arriving at and leaving the smart charging station (SCS) (e.g., ...). Figure 1 The required charging capacity is as follows:

[0144] (1)

[0145] Where N represents the total number of PEVs. and These represent the arrival and departure times of the i-th PEV at the SCS, respectively. This represents the charging strategy of the i-th PEV at time t, where time t is typically expressed in hours. This indicates the total amount of charge required by the PEV during the entire charging process.

[0146] Considering safety, battery life, and performance, the battery charge level at any given time t must be maintained within a reasonable range during all PEV charging cycles:

[0147] (2)

[0148] in, , This represents the upper and lower limits of the safe range of the power of the i-th PEV battery. It is defined as the initial battery charge when the i-th PEV just arrives at the SCS.

[0149] Similarly, the amount of charge at any time t needs to be limited:

[0150] (3)

[0151] in, , This represents the upper and lower limits of the charging strategy for the i-th PEV battery per unit time. To ensure that the total charge of all PEVs at any time t does not exceed the total load of the SCS, the following constraints are defined:

[0152] (4)

[0153] This refers to the load capacity of the SCS.

[0154] When the SCS is operating, the PEV strives to minimize its own cost while satisfying the linear constraints mentioned above. The cost function of the PEV is defined as follows: the cost of the PEV is proportional to the electricity consumption, and the cost of the i-th PEV is... for:

[0155] ;

[0156] in, The total cost of all PEVs must be less than or equal to the total energy cost of the SCS. The specific calculation formula is as follows:

[0157] ;

[0158] in, The electricity price can be used to determine the electricity consumption per unit time t. A linear relationship is presented. Let t be the energy consumed over time t. This represents the proportion of all PEV costs to the total SCS power consumption cost. When SCS can achieve a balance of payments, it can achieve a balance of payments; when At that time, SCS can generate profits;

[0159] Electricity consumption per unit time t The definition is as follows:

[0160] ;

[0161] Simplifying the above formula, we get the cost of the i-th PEV. for: ;

[0162] Charging strategies for all PEVs First, according to ( The joint policy vector is formed in a manner that also serves as the individual in the genetic algorithm:

[0163] ;

[0164] The cost of the i-th PEV It can be written as , Let i be the charging strategy that the i-th PEV can control. Joint policy vector The charging strategies that other PEVs can control. For a PEV to satisfy all the above linear constraints, it can be reduced to the following form:

[0165] (Constraints corresponding to formula (1))

[0166] (Constraints corresponding to formula (3))

[0167] (Constraints corresponding to formula (3))

[0168] (Constraints corresponding to formulas (2) and (4))

[0169] Where A is m n is a matrix, m is the number of equations, n is the dimension of the x vector, and b is the value of m. 1 column vector, and For m A column vector, representing the upper and lower bounds of each dimension of x. For p n is a matrix, and p is the number of constraints excluding upper and lower bound constraints and equality constraints. For p 1. Column vector.

[0170] Using the equation, By performing variable substitution and eliminating several variables, we obtain... The inequality is transformed into:

[0171] ;

[0172] ;

[0173] ;

[0174] For ease of representation, please remember for Therefore, the PEV charging strategy must satisfy linear constraints, namely the initial linear constraints mentioned below:

[0175] ;

[0176] ;

[0177] ;

[0178] Calculation of the inverse fitness function. To ensure the operation of the genetic algorithm, a fitness function needs to be defined. The higher the fitness, the better the individual. For convenience, an inverse fitness function is defined here. The joint strategy vector is the individual Inverse fitness function The smaller the value, the better the individual. (Inverse fitness function) Defined as:

[0179] ;

[0180] in For each individual, and satisfying the initial linear constraints, The meaning is: to evaluate from two aspects The main assessment adopts a joint strategy. The degree to which each PEV adheres to its own charging strategy, and the more each PEV adheres to the current joint strategy. adverse fitness The closer it is to 0.

[0181] The first aspect is the partial evaluation item, from... local neighborhood The strategy of sampling a large number of i-th PEVs The strategy adopted by the current i-th PEV Compare costs, the less Better than the current strategy If the i-th PEV adheres to the current strategy, then the i-th PEV will persist in the current strategy.

[0182] The second aspect is the overall evaluation item, from... The feasible domain of the i-th PEV The strategy of sampling a large number of i-th PEVs The strategy adopted by the current i-th PEV Compare costs, the less Better than the current strategy If the i-th PEV adheres to the current strategy, then the i-th PEV will persist in the current strategy.

[0183] The calculation requires all of both sides Summation is performed. To balance the scale differences between the two terms, the local evaluation term needs to be divided by the distance between the two points during calculation. Since both terms need to consider whether the sampling results satisfy the linear constraint (i.e., sampling within the feasible region) when sampling, directly performing uniform sampling and only accepting points that satisfy the constraint can easily lead to not sampling a feasible solution. The sampling method should be as follows:

[0184] First of all, for Sampling of local evaluation terms, when evaluating the i-th PEV, is fixed. Immovable, sampling Make the joint policy vector Constraints must be met:

[0185] ;

[0186] ;

[0187] ;

[0188] ;

[0189] ;

[0190] This represents the neighborhood radius vector, and is generally taken as a small value. This is to randomly and uniformly sample such... Randomly generate a unit vector ,Require Except for the position that the i-th PEV can decide, all other values ​​are 0. Substitute them into the following formula to calculate:

[0191] ;

[0192] ;

[0193] ;

[0194] Finally calculated upper and lower boundaries and This yields a set of linear constraints that satisfy all linear constraints. :

[0195] ;

[0196] As a new Continue this process to produce the next one. This process of continuous iteration, this series These will be approximately uniform sampling points across the region satisfying the linear constraints; this uniformity will ensure the rationality of the inverse fitness function evaluation. Similarly, for The sampling of global evaluation terms follows the same process and must satisfy the initial linear constraints;

[0197] This sampling evaluation method samples a large number of samples in a serial iterative manner. This would significantly impact the algorithm's running speed; therefore, CUDA parallel computing is introduced, where a large number of threads can perform computations simultaneously. Through parallel computation using CUDA threads, the number of iterations required in the aforementioned serial iterations can be significantly reduced while still approximating approximately uniform sampling within the feasible region. Figure 3 This diagram illustrates parallel sampling with three CUDA threads running.

[0198] In summary, to achieve uniform sampling evaluation, a large number of CUDA threads should be started, with each thread iterating several times according to the above iterative method, and the final sampled data from each CUDA thread should be taken. These large quantities These constitute the sampling points required for inverse fitness assessment.

[0199] Initialize the genetic algorithm population. Find the initial solution that satisfies the initial linear constraints using the simplex method. ,by Starting from a point, sample within the feasible region (the region that satisfies the constraints). The solutions that are approximately uniformly distributed in the feasible region are used as the initial population individuals, and the sampling method is as described above. Sampling of global evaluation items.

[0200] The initial solution The specific implementation is as follows:

[0201] Inequality constraints With boundary constraints , Standardization transformation Introducing slack variables , transformed Introducing variable substitution ,but Boundary constraints are transformed into Introducing variables , transformed Boundary constraints are transformed into Since a feasible solution is found, the objective function can be a constant of 0. Therefore, the standardized model is:

[0202] ;

[0203] ;

[0204] ;

[0205] ;

[0206] like ,but and Merge to form basic variables; otherwise, it is necessary to... The less-than-zero parts are inverted and artificial variables are introduced. At this point, the identity matrix is ​​obtained, satisfying the operating conditions of the simplex method. The auxiliary objective function is then optimized using the simplex method.

[0207] ;

[0208] If the auxiliary objective function is optimal If the original problem has a feasible solution, then it does not; otherwise, it has no feasible solution. Removing artificial variables from the feasible solutions yields the solution. A feasible solution is found, and then the original variables are restored. That is, a feasible solution Also known as the initial solution .

[0209] The standardized model described above requires the simplex method for solution. Here, we further simplify the model, which can be represented in the standard form of a general linear programming problem as follows:

[0210] ;

[0211] st

[0212] ;

[0213] in, The objective function value, As decision variables, The coefficients of the objective function, These are the constraint coefficients. Let be the constant term on the right-hand side of the constraint, and Setting the non-basic variables to 0, we can calculate the basic feasible solution consisting of the basic variables. Then, we use the simplex method. The steps of the simplex method are as follows:

[0214] 1: Optimality test

[0215] Calculate the test number corresponding to the current basic feasible solution. The test number is used to determine whether the current solution is optimal. For maximization problems, the test number ( ),in These are the coefficients of the objective function corresponding to the basic variables. If all test numbers ( If a test number exists, then the current basic feasible solution is the optimal solution; If the solution is not optimal, then iteration is required.

[0216] 2: Determine the entering variable

[0217] Entering variables are non-basic variables that increase the value of the objective function. The non-basic variable with the largest test number is selected as the entering variable. Corresponding (This refers to the variable that enters the base). If there are multiple variables with the largest test numbers, any one of them can be chosen.

[0218] 3: Determine the basic variables

[0219] To ensure that the solution remains feasible after iteration, the basic variables need to be determined according to the minimum ratio rule; the constant terms corresponding to the basic variables need to be calculated. The constraint coefficients corresponding to the entering variables ( The ratio of ), i.e. The corresponding basic variables are the out-of-basic variables; if all If the objective function is unbounded, then the problem has no optimal solution.

[0220] 4: Basis Transformation and Iterative Calculation

[0221] Using the intersection element (pivot element) of the column corresponding to the entering basic variable and the row corresponding to the exit basic variable as the core, elementary row operations are used to transform the pivot element into 1 and the other elements in the column containing the pivot element into 0, resulting in a new basis matrix and the corresponding basic feasible solution; repeat steps 1-4 until the optimal solution is found or the problem is determined to be unbounded.

[0222] The population is evaluated in parallel using inverse fitness. This parallel approach primarily utilizes CUDA parallel computation, as shown in the following example. Figure 4 As shown, a number of individuals in the current population with the closest adverse fitness to 0 are designated as elite individuals. These elite individuals must undergo a local search to enter the next generation of the population. Other individuals in the next generation are generated through selection, crossover, and mutation.

[0223] During the selection process, individual adverse fitness needs to be normalized:

[0224] ;

[0225] individual Probability of being selected:

[0226] ;

[0227] To ensure that the offspring of two individuals remain within the feasible region after crossover, individuals and The following crossover process is adopted:

[0228] ;

[0229] ;

[0230] Individuals generated by crossover With probability The mutation is performed, and a PEV site is randomly selected. :

[0231] ;

[0232] By sampling approximately uniformly within the feasible region, a point of PEV is sampled. New charging strategy Through reassembly, new individuals are formed and become part of the next generation of the population. :

[0233] ;

[0234] Local search process for elite individuals: updating the search radius using a cosine annealing algorithm with hot restart. , For the current iteration round of the genetic algorithm, whenever for When it is a multiple of, the maximum search radius Halve; This is a hyperparameter representing the hot restart period of the search radius. The updated formula is:

[0235] ;

[0236] For elite individuals Randomly select several PEVs in random order, and traverse the i-th PEV in random order to perform the following operations:

[0237] fixed Middle opponent strategy Optimize their own strategies To minimize the objective function It must satisfy the initial linear constraint and the rectangular constraint, specifically:

[0238] ;

[0239] ;

[0240] like Figure 5 The steps for optimizing the i-th PEV using the particle swarm optimization algorithm for local search are as follows:

[0241] Initialize all particles by randomly generating multiple joint policy vectors within the rectangular constraint area and assigning them to the particles. Random initial position:

[0242] ;

[0243] Random initial particles speed:

[0244] ;

[0245] particles Historical best position Set as current position As the globally optimal position Minimize the objective function During the particle swarm search iteration process, the velocity and position updates for each generation of particles are as follows:

[0246] ;

[0247] ;

[0248] in, For inertial weights, and The updated particle is the acceleration factor. Location If it exceeds the rectangular constraint, it will be corrected to fall within the rectangular constraint range:

[0249] ;

[0250] ;

[0251] Calculate the updated particles If the objective function is smaller than the objective function of the particle before the update and satisfies the initial linear constraints, then update... and After iterative comparison in particle swarm search as well as The particles with smaller objective functions are selected as the elite individuals after the final local search.

[0252] Elite individuals obtained after completing the particle swarm optimization search for all i-th PEVs are used as the next generation of population individuals.

[0253] Particle swarm optimization (PSO) algorithm searches for and selects individuals that undergo crossover and mutation to form the next generation of the population. The number of iterations is:

[0254] ;

[0255] Repeat steps S3 to S4 until the specified number of iterations is reached. .

[0256] Finally, the population individual whose inverse fitness function is closest to 0 is output, and this population individual is restored to the charging strategy of plug-in electric vehicle through variable substitution in step S2.

[0257] Table 1 shows when At that time, the parameter table for the charging problem of 10 PEVs was used, and the remaining parameters were configured as follows: , ,when , The rest of the time .

[0258] Table 1

[0259]

[0260] This invention will be run under this problem to find the Nash equilibrium solution. All the final PEV charging strategies are as follows: Figure 6 As shown in the figure, each broken line represents the charging strategy of a PEV (player) at each moment. It is not difficult to observe that in order to gain greater benefits, the PEV not only charges but also discharges, but these decisions are made under the premise of satisfying the amount of charging required for itself from arriving at the SCS to leaving the SCS. Figure 7 This demonstrates how, in the PEV charging strategies obtained by the present invention, the summation of all PEV strategies at each time step is performed to check whether it exceeds the total load of the SCS at that time step. Figure 7 The summation line of the middle strategy is always above 0, indicating that although PEVs discharge, this electricity is transferred to other PEVs that are charging at the same time, and there is no electricity returned to SCS. Through this electricity exchange between PEVs, higher benefits are obtained.

[0261] Regarding the final result Perform verification, verification To determine if a solution is close to Nash equilibrium, we iterate through each i-th PEV while fixing the policies of all other PEVs. We check if any of the policies available to the current i-th PEV (PEV i) is a better charging policy. If not, it is considered optimal. When all PEVs do not change their policies, it is proven to be a Nash equilibrium. Since brute-force comparison of all policies is infeasible in continuous policies, a sampling method is used. 200,000 feasible policies are sampled for each PEV, and five independent experiments are conducted. The experimental results are shown in Table 2. On average, each PEV is dominated by 798.1 policies across multiple experiments. This indicates that in the current... Under these conditions, approximately 4% of the strategies are better than the current strategy for each PEV.

[0262] Table 2

[0263]

[0264] Each PEV samples 400,000 feasible strategies. Table 3 shows the dominance of each PEV among these sampled feasible strategies. PEVs 7, 8, and 9 sampled better strategies, while the remaining PEVs maintained their current strategies. PEV 9 had the most dominated strategies, but this only accounted for 17704 / 400000 = 4.4% of the total sampled strategies, a very small percentage. This demonstrates the effectiveness of the method proposed in this invention. It is quite close to the Nash equilibrium solution.

[0265] Table 3

[0266]

[0267] Meanwhile, this invention provides:

[0268] A server includes a processor and a memory, the memory storing at least one program, which is loaded and executed by the processor to implement the game optimization solution method for the above-mentioned plug-in electric vehicle charging problem.

[0269] A computer-readable storage medium storing at least one program, which is loaded and executed by a processor to implement the above-described game-theoretic optimization solution method for the plug-in electric vehicle charging problem.

[0270] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A game-theoretic optimization method for solving the charging problem of plug-in electric vehicles, characterized in that, Includes the following steps: S1. Construct a smart charging station business scenario model, and based on the smart charging station business scenario model, construct a cost function for plug-in electric vehicles; the smart charging station business scenario model includes charging strategies. S2. Obtain the joint policy vector through the charging policy, and perform variable substitution on the joint policy vector to obtain the initial linear constraints of the charging policy. S3. Based on the initial linear constraints, construct the inverse fitness function according to the cost function and the joint policy vector; S4. Initialize the genetic algorithm population, which is a set of joint policy vectors obtained by sampling. An individual in the population represents a joint policy vector. Evaluate and select several individuals whose inverse fitness function is less than a preset value in parallel as elite individuals. Perform local search on the elite individuals using cosine annealing and particle swarm optimization algorithms. Population individuals become new individuals through selection, crossover and mutation. The new individuals and the elite individuals after local search form the next generation population. S5. Iterate through the next generation of individuals, output the individual whose inverse fitness function is closest to 0, and restore the individual to the charging strategy of a plug-in electric vehicle by variable substitution.

2. The game-theoretic optimization solution method for the plug-in electric vehicle charging problem according to claim 1, characterized in that, Step S1 involves constructing a smart charging station business scenario model, as detailed below: Plug-in electric vehicles (PEVs) are abbreviated as PEVs, and smart charging stations (SCSs) are abbreviated as SCSs. The charging requirement for the i-th PEV to travel from its arrival at the SCS and then to its departure from the SCS is defined as follows: ；（1） Where N represents the total number of PEVs. This represents the time when the i-th PEV arrives at the SCS. This represents the time when the i-th PEV leaves the SCS. This represents the charging strategy of the i-th PEV at time t. This indicates the total amount of charge required by the PEV during the entire charging process. During all PEV charging periods, the battery charge at any given time t will be maintained within a reasonable range, as calculated below: ；（2） in, This represents the lower limit of the safe range of the i-th PEV battery capacity. This represents the upper limit of the safe range of the i-th PEV battery capacity. This represents the initial battery charge of the i-th PEV upon arrival at the SCS; The amount of charge at any time t is limited, and the specific calculation is as follows: ；（3） in, This represents the lower bound of the charging strategy for the i-th PEV battery per unit time. This represents the upper limit of the charging strategy for the i-th PEV battery unit time. To ensure that the total charge of all PEVs does not exceed the total load of the SCS at any time t, the following constraint is defined: ；（4） in, This refers to the load capacity of the SCS. The cost function is calculated in detail as follows: The cost of a PEV is directly proportional to its electricity consumption; the cost of the i-th PEV... The specific calculation formula is as follows: ；（5） in, The total cost of all PEVs is less than or equal to the total energy cost of the SCS. The specific calculation formula is as follows: ；（6） in, For electricity price, Let be the energy consumed over time t. This represents the proportion of all PEV costs to the total SCS power consumption cost. and These are two values ​​in the electricity price formula, obtained through direct observation; Electricity consumption per unit time t The definition is as follows: ；（7） Simplifying formulas (5) to (7), the final cost of the i-th PEV is... for: 。 3. The game-theoretic optimization solution method for the plug-in electric vehicle charging problem according to claim 1, characterized in that, Step S2 involves implementing the charging strategy for all PEVs. The joint policy vector x is obtained, specifically calculated as follows: ； According to formulas (1) to (4), the joint policy vector x is reduced to the following constraint form: ； ； ； ； Where A is m n is a matrix, m is the number of equations, n is the dimension of x, and b is the m-th matrix. 1 column vector, and For m 1 column vector, Denotes the lower bound of each dimension of x. This represents the upper bound of each dimension of x; For p n is a matrix, and p is the number of constraints excluding upper and lower bound constraints and equality constraints. For p 1 column vector; Using the equation, By performing variable substitution and eliminating several variables, we obtain... The inequality is transformed into: ； ； ； Still remember for Therefore, the PEV charging strategy satisfies the initial linear constraint: ； ； 。 4. The game-theoretic optimization solution method for the plug-in electric vehicle charging problem according to claim 1, characterized in that, Step S3 is to... Recorded as Let the joint strategy vector be . ; Let i be the charging strategy that the i-th PEV can control. Joint policy vector The charging strategies that can be controlled by other PEVs except for the i-th PEV; Constructing the inverse fitness function The specific definition is as follows: ； in, For each individual in the population, i.e., the joint policy vector x, and satisfying the initial linear constraints; In F(x), the part before the plus sign is the local evaluation term, i.e., from the joint policy vector. local neighborhood The sampling generates several charging strategies for the i-th PEV. The charging strategy adopted by the current i-th PEV Compare costs; The sampling strategy for the local evaluation items is as follows: When evaluating the i-th PEV, the fixed Without moving, the sampled Make the joint policy vector Constraints must be met: ； ； ； ； ； in, Represents the neighborhood radius vector; Randomly generate a unit vector , Except for the position that the i-th PEV can decide, all other values ​​are 0. Substitute them into the following formula to calculate: ； ； ； Thus, the calculation is obtained lower bound and the Upper Realm ; The specific calculations are as follows: ； As a new Continue iterating to generate the next one Several obtained through iterative generation To satisfy the requirement of approximately uniform sampling points in the linearly constrained region; In F(x), the part after the plus sign is the global evaluation term, which is derived from the joint policy vector. The feasible domain of the i-th PEV Charging strategy for sampling the i-th PEV The charging strategy adopted by the current i-th PEV Compare costs; The sampling strategy for the global evaluation item is as follows: When evaluating the i-th PEV, the fixed Without moving, the sampled Make the joint policy vector Initial linear constraints must be met; Parallel CUDA computation is introduced into the sampling of local and global evaluation terms. Through parallel computation by CUDA threads, the final sampling result of each CUDA thread is used as the basis for the local and global evaluation terms. .

5. The game-theoretic optimization solution method for the plug-in electric vehicle charging problem according to claim 1, characterized in that, In step S4, the next generation population specifically refers to: Initialize the genetic algorithm population: Find an initial solution that satisfies the initial linear constraints. ,by Using the initial point, sample within the feasible region. A solution that is approximately uniformly distributed in the feasible region is used as the initial population individuals; All individuals in the population are evaluated in parallel using inverse fitness, and CUDA is used for parallel computation. Several individuals with inverse fitness less than a preset value are identified as elite individuals. After local search of these elite individuals using cosine annealing and particle swarm optimization algorithms, the elite individuals after local search are introduced into the next generation of the population. Other individuals in the next generation of the population are generated through selection, crossover, and mutation. During the selection process, the individual's adverse fitness is normalized, specifically as follows: ； individual The probability of being selected is: ； To ensure that the offspring of two individuals remain within the feasible region after crossover, individuals and The following crossover process is adopted: ； ； Individuals generated by crossover With probability The mutation is performed, and a PEV site is randomly selected. : ； By sampling approximately uniformly within the feasible region, a single point of PEV is sampled. New charging strategy Through reassembly, new individuals are formed and become part of the next generation of the population. : ； in, Individuals generated by crossover In addition to the points Charging strategies for other locations besides [the main point].

6. The game-theoretic optimization solution method for the plug-in electric vehicle charging problem according to claim 5, characterized in that, The initial solution The specific calculations are as follows: Inequality constraints With boundary constraints , Standardization transformation: Introducing slack variables , transformed Introducing variable substitution ,but Boundary constraints are transformed into Introducing variables , transformed Boundary constraints are transformed into Since a feasible solution is found, the objective function is a constant of 0. Therefore, the standardized model is: ； ； ； ； right Invert the less than 0 parts and introduce artificial variables; Optimize the auxiliary objective function using the simplex method: ； If the auxiliary objective function is optimal If so, then a feasible solution exists; Otherwise, there is no feasible solution; By removing artificial variables from the feasible solutions, we obtain... A feasible solution is found, and then the original variables are restored. This is the initial solution. .

7. The game-theoretic optimization solution method for the plug-in electric vehicle charging problem according to claim 5, characterized in that, The cosine annealing algorithm is specifically as follows: The search radius is updated using a cosine annealing algorithm with hot restart. , For the current iteration round of the genetic algorithm, whenever for When it is a multiple of, the maximum search radius Halve; This is a hyperparameter representing the hot restart period of the search radius. The updated formula is: ； For elite individuals Randomly select several PEVs in random order, and traverse the i-th PEV in random order to perform the following operations: fixed Middle opponent strategy Optimize their own strategies To minimize the objective function It must satisfy the initial linear constraint and the rectangular constraint, specifically: ； 。 8. The game-theoretic optimization solution method for the plug-in electric vehicle charging problem according to claim 5, characterized in that, The particle swarm optimization algorithm is specifically as follows: Initialize all particles by randomly generating multiple joint policy vectors within the rectangular constraint area and assigning them to the particles. Random initial position: ； Random initial particles speed: ； particles Historical best position Set as current position As the globally optimal position Minimize the objective function During the particle swarm search iteration process, the velocity and position updates for each generation of particles are as follows: ； ； in, For inertial weights, and The updated particle is the acceleration factor. Location If it exceeds the rectangular constraint, it will be corrected to fall within the rectangular constraint range: ； ； Calculate the updated particles If the objective function is smaller than the objective function of the particle before the update and satisfies the initial linear constraints, then update... and After iterative comparison in particle swarm search as well as The particles with smaller objective functions are selected as the elite individuals after the final local search.

9. A server, characterized in that, The server includes a processor and a memory, the memory storing at least one program, which is loaded and executed by the processor to implement the game optimization solution method for the plug-in electric vehicle charging problem as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, The storage medium stores at least one program, which is loaded and executed by a processor to implement the game optimization solution method for the plug-in electric vehicle charging problem as described in any one of claims 1 to 8.

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