Electric vehicle charging scheduling optimization algorithm based on improved NSGA-II algorithm

Abstract

The invention relates to an electric vehicle charging scheduling optimization algorithm based on an improved NSGA-I algorithm. The electric vehicle charging scheduling optimization algorithm comprises the following steps: step 1, initialization input: randomly generating relevant parameters of a power grid end and an electric vehicle end in a city electric vehicle charging process; step 2, establishing an electric vehicle charging scheduling optimization model, and constructing a dual-objective decision optimization model by taking the minimization of the charging cost of an electric vehicle end and the minimization of the load variance of a power grid end as objectives; 3, algorithm solving: simulating a specific charging scene of the urban electric vehicle, solving the established mathematical model by using an improved NSGA-I algorithm, obtaining a Pareto optimal solution set of electric vehicle charging scheduling through multiple iterations, and recommending multiple feasible optimized charging schemes for the electric vehicle; the method is high in solving capability, can provide a Pareto optimal solution set, is high in expansibility, and is higher in flexibility.

Description

Technical Field

[0001] The present invention relates to the technical field of electric vehicle charging scheduling, and in particular to an electric vehicle charging scheduling optimization algorithm based on an improved NAGA-II algorithm. Technical Background

[0002] In recent years, increasing the proportion of new energy in the power system and building a new clean power system have become new goals for the development of the power grid industry. Compared with traditional fuel vehicles, new energy electric vehicles have significant green and environmentally friendly characteristics, and its future market growth is foreseeable, which will also become an important breakthrough point for the green transformation and upgrading of the automobile and power industries.

[0003] With the massive growth in the number of electric vehicles, the impact of electric vehicle charging load on the power grid is becoming more and more significant. Due to the uncertainty of electric vehicle users' charging demand, disorderly charging may cause large fluctuations in the power grid load, posing challenges to the safety and stability of the power grid. However, different charging users have different charging behavior preferences. For example, operating vehicles such as taxis are more sensitive to prices and prefer DC fast charging, while private cars are not so sensitive and prefer AC slow charging. In the face of heterogeneous charging needs of users with different charging behavior preferences, it is of great significance to study effective active charging scheduling methods to guide electric vehicle users to charge in an orderly manner, which can not only ensure lower charging costs for users, but also smooth out the fluctuations in power system grid load.

[0004] Therefore, the present invention proposes an electric vehicle charging scheduling optimization based on an improved NSGA-II algorithm that takes into account user charging behavior preferences to solve the above problems. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm with strong optimization and adaptability, which recommends multiple charging schemes for electric vehicles with different charging preferences, while reducing the cost of electric vehicles and the load variance at the power grid end.

[0006] The present invention provides an electric vehicle charging scheduling optimization algorithm based on an improved NSGA-II algorithm, comprising the following steps:

[0007] Step 1, set initial parameters: generate grid-side and electric vehicle-side related parameters during the charging process of urban electric vehicles. Grid-side parameters mainly include the location information of charging stations and charging piles, the charging power and price of charging piles, the transformer power of charging stations and the connection relationship with charging piles. Electric vehicle-side parameters mainly include the charging user type of the electric vehicle to be charged, the initial location and destination information of the electric vehicle, the battery capacity of the electric vehicle, and the battery initial state of charge SOC during the charging process;

[0008] Step 2: Establish a mathematical model: Establish an electric vehicle charging scheduling optimization model that takes into account user charging behavior, and build a dual-objective decision-making optimization model with the goal of minimizing the charging cost of the electric vehicle end and minimizing the load variance of the power grid end;

[0009] Step 3: Algorithm solution: For the charging scenario of electric vehicles, the improved NSGA-II algorithm is used to solve the established mathematical model. Through multiple iterations, the Pareto optimal solution set of electric vehicle charging scheduling is obtained, and a variety of feasible optimized charging schemes are recommended for electric vehicles.

[0010] In the above-mentioned electric vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm, the step 2 of establishing an electric vehicle charging scheduling optimization model considering user charging behavior mainly includes the following steps:

[0011] Step 2.1, define mathematical symbols: use represents a collection of electric vehicles, There are I electric cars in the area, and the destination of each car is represented by τ i Indicates that the starting point is ξ i Indicates that k represents the user type, There are K types of users, Represents a collection of charging stations. There are L charging stations in the area. Represents a collection of charging piles. For convenience, we use Indicates the charging pile with serial number m at the lth charging station. In addition, and They represent the available and unavailable charging pile sets of charging station l, use represents the set of transformers of charging station l, For convenience, we use represents the transformer with serial number w at the lth charging station, represents the set of charging piles connected to transformer w at the lth charging station;

[0012] Step 2.2: Set the objective function: Considering the charging cost at the charging user end and the load variance at the grid end, formula (1) represents the cost at the vehicle end, including the mileage cost α i , time cost β i , and charging cost γ i , formula (2) represents the load variance of the grid, including the load variance of the charging station The load variance of the transformer in the same charging station

[0013]

[0014] Among them, the mileage cost α in formula (1) i , time cost β i , and charging cost γ i The calculation is as follows:

[0015]

[0016] Mileage cost α i It is defined as the mileage cost required for electric vehicle user i to travel from the starting point to the charging station and from the charging station to the destination, as shown in formula (3). The parameters and represents the distance from the starting point of electric vehicle user i to the charging pile with the serial number m at the lth charging station and the distance from the charging pile to the destination. The parameter μ i and ω i represents the weight coefficient set according to user preference,

[0017] Time cost β i Defined as the driving time from the starting point to the charging station Charging time and the time to reach the destination after charging is completed The sum of the total time cost is shown in formula (4), and the parameter ρ i ,θ i , δ i is the weight coefficient, and equation (5) calculates the charging time of electric vehicle user i. The parameter and Respectively represent the state of charge (SOC) of the battery before and after charging, parameter C i represents the battery capacity of electric vehicle user i, parameter P lm represents the charging power of the charging pile with the serial number m at the lth charging station,

[0018] Charging cost for electric vehicle user i γ i As shown in formula (6), the parameter M lm represents the charging price of the charging pile with the serial number m at the lth charging station, and the parameter σ i represents the weight coefficient,

[0019] The load variance of the charging station in formula (2) The load variance of the transformer in the same charging station The calculation is as follows:

[0020]

[0021] From the grid side, the load variance of the charging station It is defined as the load variance of all charging stations in the region. As shown in formula (7), the load of the lth charging station is recorded as The calculation results are shown in formula (8), which includes the load generated by the scheduling plan and the load of the charging pile in use. The parameter P lm represents the charging power of the charging pile with the serial number m at the lth charging station, and the average load of each charging station The calculation is shown in formula (9):

[0022] The charging load calculation of the transformer with serial number w at the lth charging station is shown in formula (10). The total load and average load of the transformer at the lth charging station are calculated by formula (11) and formula (12) respectively. Formula (13) and formula (14) calculate the transformer variance of the i-th charging station and all charging stations respectively.

[0023] Step 2.3, set the decision variable: z ilm When it is 1, it means that electric vehicle user i is recommended to charge at the charging pile with the serial number m at the lth charging station, otherwise z ilm =0, as shown below:

[0024]

[0025] Step 2.4, set constraints: The constraint expression for recommending a charging station to each electric vehicle user is as follows:

[0026]

[0027] The constraint expression for each electric vehicle user's remaining battery capacity to reach the recommended charging station is as follows:

[0028]

[0029] in, represents the power of electric vehicle user i when triggering charging demand, C i represents the battery capacity of electric vehicle user i, Θ represents the battery life of the electric vehicle per 100 kilometers,

[0030] The constraint expression that the charging power of the charging pile cannot exceed the maximum output power of the charging station is as follows:

[0031]

[0032] Among them, P lmax represents the maximum output power of all charging piles at the lth charging station,

[0033] The constraint expression that the charging power of the charging pile cannot exceed the maximum output power of the transformer to which it is connected is as follows:

[0034]

[0035] Among them, P lwmax Represents the maximum output power of all transformers in the lth charging station.

[0036] In the above-mentioned charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm, solving the model using the improved NSGA-II algorithm in step 3 includes the following steps:

[0037] Step 3.1, condition setting: set the population size and number of iterations, where each individual in the population represents a recommended charging plan for all electric vehicles (recommended to specific available charging piles);

[0038] Step 3.2, encoding: according to the order of available charging piles, the electric vehicle is arranged to the available charging piles by integer encoding. The value of the available charging pile for which the charging task is arranged is set to the electric vehicle number, and the value of the charging pile for which no charging task is arranged is set to 0;

[0039] Step 3.3, generate the initial population: arrange all electric vehicles with charging needs to the available charging piles to generate a population individual, and generate the initial solution individual of the set population size;

[0040] Step 3.4, population selection: merge the parent population with the newly generated next generation population, perform fast non-dominated sorting on the merged population and calculate the crowding distance, and select individuals of the population size as the new population;

[0041] Step 3.5, crossover operator: Set the crossover rate to 0.9, randomly select two individuals from the new population as parents, generate a MC random number between [0,1], if the first random number is greater than the crossover probability, the two parent individuals will not crossover, if the first random number is less than or equal to the crossover probability, select the designed random crossover and single-point crossover with probabilities of 0.5 and 0.5 respectively, until the offspring of the population size is generated,

[0042] Step 3.6, mutation operator: Set the mutation rate to 0.01. For each individual, generate a second random number between [0,1]. If the second random number is greater than the mutation rate, no mutation will be performed. If the second random number is less than or equal to the mutation probability, randomly select one of the three designed mutation methods with probabilities of 0.2, 0.4, and 0.4 respectively to obtain the next generation population.

[0043] Step 3.7, repair operator: Since crossover and mutation may cause chromosomes to be infeasible, it is necessary to repair the chromosomes after crossover and mutation;

[0044] Step 3.8, fast non-dominated sorting: Based on the Pareto dominance relationship, fast non-dominated sorting is one of the most important sorting techniques in implementing multi-objective algorithms. It can quickly arrange individuals in the population according to their levels and provide a basis for the selection of the population;

[0045] Step 3.9, crowding distance: Based on the result of stratifying the individuals in the population by the fast non-dominated sorting algorithm, in order to compare the performance of individual solutions in the same layer, the NAGA-II algorithm introduces the crowding distance to measure the density and diversity between individuals in the same non-dominated sorting layer.

[0046] In the above-mentioned electric vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm, the selection of the population in step 3.4 adopts the following method:

[0047] The parent generation and the new offspring generated by crossover and mutation are placed together at the same time, and the individuals are stratified by fast non-dominated sorting and the crowding distance is calculated. Individuals are selected from the non-dominated layer from low to high to join the new population until a certain proportion of the population size (for example, 70%) is reached. Then, one is randomly selected from the remaining unselected non-dominated layer and all are added to the selected individuals. If the selected individuals still do not reach the population size, the operation is repeated until the randomly selected non-dominated layer is larger than the population size. At this time, the remaining individuals are selected from the crowding degree of the non-dominated layer from large to small, so that the population size is the set size.

[0048] In the above-mentioned electric vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm, the crossover operator of the population in step 3.5 includes the following methods:

[0049] Random crossover: Randomly select two chromosomes and randomly generate a number (within the range of 0 to the chromosome length) as the initial crossover point. At the same time, search backward until three non-zero numbers (i.e. the numbers of the three vehicles with charging needs) are found. The smaller cutoff point of the two chromosomes is taken as the cutoff crossover point, and then the gene fragments of the two chromosomes within the range of the initial crossover point and the cutoff crossover point are crossed. If after the randomly generated initial crossover point appears, neither chromosome can search backward for three non-zero numbers, the processing method is to end at the last bit of the chromosome.

[0050] In the above-mentioned electric vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm, the crossover operator of the population in step 3.5 includes the following methods:

[0051] Single-point crossover: randomly select a chromosome, randomly select a car, and exchange them with the genes at the corresponding position on another chromosome.

[0052] In the above-mentioned electric vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm, the population mutation operator in step 3.6 includes the following three methods:

[0053] Random mutation: randomly select a car and randomly assign its location to another available charging station;

[0054] Variation oriented to reduce the cost of electric vehicles: find the car with the highest cost of electric vehicles in the current arrangement plan, re-arrange it to the charging station closest to the destination, and then arrange it to the charging pile with the smallest transformer load at the current charging station. If the charging pile with the smallest transformer load and the available charging piles are empty sets, then choose the next charging pile with the smallest transformer load. At the same time, check whether the electric vehicle’s power is sufficient to reach the charging station closest to the destination. If not, determine the next closest charging station to the destination.

[0055] Mutation oriented to reduce grid load variance cost: find the charging station with the largest load in the current arrangement (the load is calculated by two parts, one is the charging pile in use, and the other is the load increased due to our arrangement). If it includes our arranged car, find the corresponding electric car and arrange it to the charging pile with the smallest transformer load in the charging station with the smallest load. If it includes multiple arranged cars, randomly select the number of a car for arrangement.

[0056] In the above-mentioned electric vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm, the population repair operator in step 3.7 includes the following two methods:

[0057] Fix the situation of duplicate vehicles: if the same vehicle number appears twice in a chromosome, the vehicle number corresponding to the position with the highest cost on the electric vehicle side is set to 0, and the other one is retained;

[0058] Fix the situation where there are missing vehicles: If a chromosome is missing the number of a vehicle that needs to be charged, the missing vehicle will be arranged to the available charging pile with the smallest transformer load under the current arrangement plan. If the charging pile with the smallest transformer load and the available charging piles are empty sets, the next charging pile with the smallest transformer load will be selected. At the same time, check whether the electric vehicle’s power is sufficient to arrive at this time. If not, determine the next available charging pile with the smallest transformer load until the remaining power is sufficient to arrive.

[0059] In the above-mentioned charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm, the fast dominated non-dominated sorting of the population in step 3.8 is performed according to the following steps:

[0060] Step 3.8.1: Initialization: For each individual p in the population, calculate its dominating solution set S p and the number of individuals n that dominate p p , S p The initial value is n p The initial value is 0;

[0061] Step 3.8.2: Nondominated Sorting: Find n p = 0, that is, individuals that are not dominated by any other individuals, put them into the first layer (F1) and save them in the result set. For all individuals in F1, traverse their domination solution set S p , for S p For each individual in p If -1 is followed by 0, it is put into the second layer (F2) and saved in the result set.

[0062] Step 3.8.3: Repeat step 3.8.2 until all individuals are stratified. In each cycle, the stratified individuals are no longer considered, and finally all stratified individuals are saved in a result set.

[0063] In the above-mentioned electric vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm, the crowding distance of the population in step 3.9 is performed according to the following steps:

[0064] Step 3.9.1: Initialization: For each individual i in the population, set its crowding degree d i The initial value is 0;

[0065] Step 3.9.2: Perform a fast non-dominated sort on the population and calculate the crowding distance between individuals in the same layer according to the following formula:

[0066]

[0067] f m [i-1] and f m [i+1] represents the fitness values ​​of the two adjacent individuals of individual i after the feature sorting of the mth dimension, and They represent the maximum and minimum fitness values ​​of the population in the m-th dimension feature respectively. For points on the boundary, their crowding degree is set to infinity.

[0068] The advantages of the present invention are:

[0069] (1) The present invention takes into account the characteristic attributes of different electric vehicles (initial location information and destination location information, etc.) and their charging behavior preferences (distance, time and price sensitivity, etc.) to establish an electric vehicle charging scheduling optimization model. After setting relevant parameters in the model, reasonable charging demand points and related structural information of charging stations are generated as inputs of the model, which has high flexibility.

[0070] (2) The present invention aims to minimize the two objectives of charging cost at the electric vehicle end and load variance at the power grid end, and establishes an electric vehicle charging scheduling model based on multiple objectives by taking into account the availability status information of the charging piles.

[0071] (3) The electric vehicle charging scheduling optimization model established by the present invention is solved based on the improved NSGA-II algorithm. By improving the selection operator of the population, the diversity of the population is expanded, which is conducive to searching for a better Pareto optimal solution set.

[0072] (4) The present invention combines the two objectives of electric vehicle scheduling by designing a variety of crossover and mutation operators, including operators for increasing randomness and operators for improving the solution of the objective function, which is conducive to providing more diverse and excellent solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0074] Figure 1 To generate an initial location information map of electric vehicles and charging stations;

[0075] Figure 2 It is an overall flow chart of the electric vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm of the present invention;

[0076] Figure 3 It is a flow chart of the improved NSGA-II algorithm of the present invention;

[0077] Figure 4 It is a coding structure diagram of the present invention;

[0078] Figure 5 is the degree of improvement of the objective function of the electric vehicle end in 100 iterations of the present invention;

[0079] Figure 6 is the degree of improvement of the objective function of the power grid in 100 iterations of the present invention;

[0080] Figure 7 It is the Pareto optimal solution set obtained by the present invention in 100 iterations. DETAILED DESCRIPTION

[0081] The following embodiments can enable those skilled in the art to more fully understand the present invention, but the present invention is not limited to the scope of the embodiments.

[0082] This example considers that different charging stations are distributed in an area. Each charging station has a certain number of charging piles and transformers, and each transformer may be connected to one or more charging piles. At a certain moment, there are different types of electric vehicle users distributed in different locations. Each electric vehicle user has his own destination. Based on this, suitable charging solutions are recommended for them according to their electric vehicle charging behavior preferences. When making decisions, the available status of the charging piles in the system is known. For example Figure 1 As shown, the initial location information of the electric vehicle and the charging station is generated.

[0083] This example considers two types of electric vehicle users, private cars and commercial vehicles, with equal probability distribution. The sensitivity coefficients of the two to distance, time and charging cost are given below.

[0084] Table 1 Charging behavior preference sensitivity coefficients for different user types

[0085]

[0086] Below are other relevant parameters in the model, including the battery capacity of the electric vehicle, the charging power of the fast and slow charging piles, the charging price of the charging piles, the range of the electric vehicle, and the maximum output power of the charging station and transformer.

[0087] Table 2 Other parameter values ​​in the model

[0088]

[0089]

[0090] According to the "Shanghai New Energy Vehicle Big Data Research Report (2022)", the initial charging battery state of electric vehicles obeys the distribution shown in Tables 3 and 4.

[0091] Table 3 Distribution

[0092]

[0093] Table 4 Distribution

[0094]

[0095] The electric vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm is adopted to improve and optimize the electric vehicle charging cost and grid load variance. After the relevant parameters are given, the solution is based on the above two objectives.

[0096] like Figure 2 ,The electric vehicle charging scheduling optimization algorithm based on the improved NSGA-II algorithm includes the following steps:

[0097] Step 1, set initial parameters: Generate relevant parameters of the power grid and electric vehicle during the charging process of urban electric vehicles. The power grid parameters mainly include the location information of charging stations and charging piles, the charging power and price of charging piles, the power of charging station transformers and the connection relationship with charging piles. The electric vehicle parameters mainly include the charging user type of the electric vehicle to be charged, the initial location and destination information of the electric vehicle, the battery capacity of the electric vehicle, and the initial state of charge (SOC) of the battery during the charging process.

[0098] Step 2: Establish a mathematical model: Establish an electric vehicle charging scheduling optimization model that takes into account user charging behavior, and build a dual-objective decision-making optimization model with the goal of minimizing the charging cost of the electric vehicle end and minimizing the load variance of the power grid end;

[0099] Step 3, algorithm solution: simulate the specific charging scenario of urban electric vehicles, use the improved NSGA-II algorithm to solve the established mathematical model, and through multiple iterations, obtain the Pareto optimal solution set of electric vehicle charging scheduling, and recommend multiple feasible optimized charging solutions for electric vehicles. Figure 3 As shown in FIG. 1 , the electric vehicle active scheduling optimization algorithm based on the improved NSGA-II algorithm specifically includes the following steps:

[0100] Step 3.1, condition setting: set the population size to 200 and the number of iterations to 100, where each individual in the population represents a recommended charging plan for all electric vehicles (recommended to specific available charging piles);

[0101] Step 3.2, Coding: Use integer coding to arrange electric vehicles to available charging piles according to the order of available charging piles. The value of the available charging pile for which charging tasks are arranged is set to the electric vehicle number, and the value of the charging pile for which no charging tasks are arranged is set to 0; the coding structure is as follows Figure 4 shown.

[0102] Step 3.3, generate the initial population: arrange all electric vehicles with charging needs to available charging piles to generate a population individual, and generate individuals of the set population size;

[0103] Step 3.4, population selection: merge the parent population with the newly generated next generation population, perform fast non-dominated sorting on the merged population and calculate the crowding distance, and select individuals of the population size as the new population;

[0104] The population is selected using the following method:

[0105] The parent generation and the new offspring generated by crossover and mutation are placed together at the same time, and the individuals are stratified by fast non-dominated sorting and the crowding distance is calculated. Individuals are selected from the non-dominated layer from low to high to join the new population until a certain proportion of the population size (for example, 70%) is reached. Then, one is randomly selected from the remaining unselected non-dominated layer and all are added to the selected individuals. If the selected individuals still do not reach the population size, the operation is repeated until the randomly selected non-dominated layer is larger than the population size. At this time, the remaining individuals are selected from the crowding degree of the non-dominated layer from large to small, so that the population size is the set size.

[0106] Step 3.5, crossover operator: Set the crossover rate to 0.9, randomly select two individuals from the new population as parents, generate a MC random number between [0,1], if the first random number is greater than the crossover probability, the two parent individuals will not cross over, if the first random number is less than or equal to the crossover probability, select the designed random crossover and single-point crossover with probabilities of 0.5 and 0.5 respectively, until the offspring of the population size is generated.

[0107] The crossover operator of the population includes the following two methods:

[0108] Random crossover: Randomly select two chromosomes, randomly generate a number (0 to the length of the chromosome) as the initial crossover point, and search backwards until three non-zero numbers (i.e. the numbers of the three vehicles with charging requirements) are found, and the smaller cutoff point of the two chromosomes is taken as the cutoff crossover point, and then the gene fragments of the two chromosomes within the range of the initial crossover point and the cutoff crossover point are crossed. If after the randomly generated initial crossover point appears, the two chromosomes cannot search backwards for three non-zero numbers, the processing method is to stop at the last digit of the chromosome.

[0109] Single-point crossover: randomly select a chromosome, randomly select a car, and exchange them with the genes at the corresponding position on another chromosome.

[0110] 3.6 Mutation operator: Set the mutation rate to 0.01. For each individual, generate a second random number between [0,1]. If the second random number is greater than the mutation rate, no mutation will be performed. If the second random number is less than or equal to the mutation probability, randomly select one of the three designed mutation methods with probabilities of 0.2, 0.4, and 0.4 respectively to obtain the next generation population.

[0111] The mutation operators of the population include the following three methods:

[0112] Random mutation: randomly select a car and randomly assign its location to another available charging station;

[0113] Variation oriented to reduce the cost of electric vehicles: find the car with the highest cost of electric vehicles in the current arrangement plan, re-arrange it to the charging station closest to the destination, and then arrange it to the charging pile with the smallest transformer load at the current charging station. If the charging pile with the smallest transformer load and the available charging piles are empty sets, then choose the next charging pile with the smallest transformer load. At the same time, check whether the electric vehicle has enough power to reach the charging station closest to the destination. If not, determine the next closest charging station to the destination;

[0114] Mutation oriented to reduce grid load variance cost: find the charging station with the largest load in the current arrangement (the load is calculated by two parts, one is the charging pile in use, and the other is the load increased due to our arrangement). If it includes our arranged car, find the corresponding electric car and arrange it to the charging pile with the smallest transformer load in the charging station with the smallest load. If it includes multiple arranged cars, randomly select the number of a car for arrangement.

[0115] 3.7 Repair operator: Since crossover and mutation may cause chromosomes to be infeasible, it is necessary to repair the chromosomes after crossover and mutation;

[0116] The population repair operator includes the following two methods:

[0117] Fix the situation of duplicate vehicles: if the same vehicle number appears twice in a chromosome, the vehicle number corresponding to the position with the highest cost on the electric vehicle side is set to 0, and the other one is retained;

[0118] Fix the situation of missing vehicles: If a chromosome is missing the number of a vehicle that needs to be arranged for charging, the missing vehicle will be arranged to the available charging pile with the smallest transformer load under the current arrangement plan. If the charging pile with the smallest transformer load and the available charging piles are empty sets, the next charging pile with the smallest transformer load will be selected. At the same time, check whether the electric vehicle has enough power to reach the destination. If not, determine the next available charging pile with the smallest transformer load until the remaining power is sufficient to reach the destination.

[0119] 3.8 Fast non-dominated sorting: Based on the Pareto dominance relationship, fast non-dominated sorting is one of the most important sorting techniques in implementing multi-objective algorithms. It can quickly arrange individuals in the population according to their levels and provide a basis for the selection of the population.

[0120] The fast dominated non-dominated sorting of a population is performed as follows:

[0121] Step 3.8.1: Initialization: For each individual p in the population, calculate its dominating solution set S pand the number of individuals n that dominate p p . S p The initial value is n p The initial value is 0;

[0122] Step 3.8.2: Nondominated Sorting: Find n p = 0, that is, individuals that are not dominated by any other individuals, put them into the first layer (F1) and save them in the result set. For all individuals in F1, traverse their domination solution set S p , for S p For each individual in p If -1 is followed by 0, it is placed in the second layer (F2) and saved in the result set.

[0123] Step 3.8.3: Repeat step 3.8.2 until all individuals are stratified. In each cycle, the stratified individuals are no longer considered, and finally all stratified individuals are saved in a result set.

[0124] 3.9 Crowding distance: Based on the result of arranging individuals in a population into layers based on the fast non-dominated sorting algorithm, in order to compare the performance of individual solutions in the same layer, the NAGA-II algorithm introduces the crowding distance to measure the density and diversity between individuals in the same non-dominated sorting layer.

[0125] The congestion distance calculation is performed according to the following steps:

[0126] Step 3.9.1: Initialization: For each individual i in the population, set its crowding degree d i The initial value is 0;

[0127] Step 3.9.2: Perform a fast non-dominated sort on the population and calculate the crowding distance between individuals in the same layer according to the following formula:

[0128]

[0129] f m [i-1] and f m [i+1] represents the fitness values ​​of the two adjacent individuals of individual i after the feature sorting of the mth dimension, and They represent the maximum and minimum fitness values ​​of the population in the mth dimension. For points on the boundary, set their crowding to infinity.

[0130] In the improved NSGA-II algorithm, the crossover rate is set to 0.9, and a crossover mode of two crossover operators is randomly selected with the same probability of 0.5. The mutation rate is set to 0.01. Random mutation, mutation oriented to reduce the cost of electric vehicles, and mutation oriented to reduce the variance cost of grid load are randomly selected with probabilities of 0.2, 0.4, and 0.4, respectively. The population size is set to 200, and the algorithm termination condition is 100 iterations.

[0131] Table 5 shows the improvement of the objective function by the improved NSGA-II algorithm in the case of 10 vehicles. The results show that the improved NSGA-II algorithm can improve the electric vehicle cost and grid load variance. Figure 5 and Figure 6 The improved NSGA-II algorithm is shown to improve the cost of electric vehicles and the load variance of the power grid. Figure 7 It can be seen that the NSGA-II algorithm can find multiple sets of Pareto optimal solutions for the current charging recommendation task.

[0132] Table 5 Improvement of the objective function by the improved NSGA-II algorithm

[0133]

[0134] Next, a sensitivity analysis is conducted on the number of electric vehicles, considering the impact of 10, 20, 30, 40 and 50 electric vehicles on the experimental results. The experimental results are shown in Table 6. As can be seen from Table 6, as the number of electric vehicles increases, the minimum cost of electric vehicles also increases, which is consistent with the actual situation. However, the grid variance has both rising and falling trends, which is related to our assumption that there are currently some charging piles in use. As the number of electric vehicles connected to the grid increases, the load variance of the grid will fluctuate and show an upward and downward trend. Table 6 also shows that as the number of vehicles increases, the improvement cost of electric vehicles shows a significant downward trend between 10 and 30 vehicles, and only slightly increases between 30 and 50 vehicles, which means that when the number of available charging piles is fixed, the increase in the number of electric vehicles makes the optimization space of electric vehicles tend to decrease. However, when the number of electric vehicles reaches 30, the stability of the grid will be significantly improved. In other words, for grid operators, orderly guiding an appropriate number of electric vehicles to access the grid can effectively improve the volatility of the grid.

[0135] Table 6 Comparison of objective function optimization under different EV numbers

[0136]

[0137]

[0138] Those skilled in the art should understand that the present invention is not limited to the above embodiments, and the above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, and these changes and improvements fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. An electric vehicle charging scheduling optimization algorithm based on an improved NSGA-II algorithm, comprising the following steps: Step 1: Set initial parameters: Generate relevant parameters of the grid and electric vehicle during the charging process of urban electric vehicles; Step 2: Establish a mathematical model: Establish an electric vehicle charging scheduling optimization model that takes into account user charging behavior, and build a dual-objective decision-making optimization model with the goal of minimizing the charging cost of the electric vehicle end and minimizing the load variance of the power grid end; Step 3: Algorithm solution: For the charging scenario of electric vehicles, the improved NSGA-II algorithm is used to solve the established mathematical model. Through multiple iterations, the Pareto optimal solution set of electric vehicle charging scheduling is obtained, and a variety of feasible optimized charging schemes are recommended for electric vehicles.

2. The charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm according to claim 1 is characterized in that: The step 2 of establishing an electric vehicle charging scheduling optimization model taking into account user charging behavior mainly includes the following steps: Step 2.1, define mathematical symbols: use represents a collection of electric vehicles, There are I electric cars in the area, and the destination of each car is represented by τ i Indicates that the starting point is ξ i Indicates that k represents the user type, There are K types of users, Represents a collection of charging stations. There are L charging stations in the area. Represents a collection of charging piles. For convenience, we use Indicates the charging pile with serial number m at the lth charging station. In addition, and They represent the available and unavailable charging pile sets of charging station l, use represents the set of transformers of charging station l, For convenience, we use represents the transformer with serial number w at the lth charging station, represents the set of charging piles connected to transformer w at the lth charging station; Step 2.2: Set the objective function: Considering the charging cost at the charging user end and the load variance at the grid end, formula (1) represents the cost at the vehicle end, including the mileage cost α i , time cost β i , and charging cost γ i , formula (2) represents the load variance of the grid, including the load variance of the charging station The load variance of the transformer in the same charging station Among them, the mileage cost α in formula (1) i , time cost β i , and charging cost γ i The calculation is as follows: Mileage cost α i It is defined as the mileage cost required for electric vehicle user i to travel from the starting point to the charging station and from the charging station to the destination, as shown in formula (3). The parameters and represents the distance from the starting point of electric vehicle user i to the charging pile with the serial number m at the lth charging station and the distance from the charging pile to the destination. The parameter μ i and ω i represents the weight coefficient set according to user preference, Time cost β i Defined as the driving time from the starting point to the charging station Charging time and the time to reach the destination after charging is completed The sum of the total time cost is shown in formula (4), and the parameter ρ i ,θ i , δ i is the weight coefficient, and equation (5) calculates the charging time of electric vehicle user i. The parameter and Respectively represent the state of charge (SOC) of the battery before and after charging, parameter C i represents the battery capacity of electric vehicle user i, parameter P lm represents the charging power of the charging pile with the serial number m at the lth charging station, Charging cost for electric vehicle user i γ i As shown in formula (6), the parameter M lm represents the charging price of the charging pile with the serial number m at the lth charging station, and the parameter σ i represents the weight coefficient, The load variance of the charging station in formula (2) The load variance of the transformer in the same charging station The calculation is as follows: From the grid side, the load variance of the charging station It is defined as the load variance of all charging stations in the region. As shown in formula (7), the load of the lth charging station is recorded as The calculation results are shown in formula (8), which includes the load generated by the scheduling plan and the load of the charging pile in use. The parameter P lm represents the charging power of the charging pile with the serial number m at the lth charging station, and the average load of each charging station The calculation is shown in formula (9): The charging load calculation of the transformer with serial number w at the lth charging station is shown in formula (10). The total load and average load of the transformer at the lth charging station are calculated by formula (11) and formula (12) respectively. Formula (13) and formula (14) calculate the transformer variance of the lth charging station and all charging stations respectively. Step 2.3, set the decision variable: z ilm When it is 1, it means that electric vehicle user i is recommended to charge at the charging pile with the serial number m at the lth charging station, otherwise z ilm =0, as shown below: Step 2.4, set constraints: The constraint expression for recommending a charging station to each electric vehicle user is as follows: The constraint expression for each electric vehicle user's remaining battery capacity to reach the recommended charging station is as follows: in, represents the power of electric vehicle user i when triggering charging demand, C i represents the battery capacity of electric vehicle user i, Θ represents the battery life of the electric vehicle per 100 kilometers, The constraint expression that the charging power of the charging pile cannot exceed the maximum output power of the charging station is as follows: Among them, P lmax represents the maximum output power of all charging piles at the lth charging station, The constraint expression that the charging power of the charging pile cannot exceed the maximum output power of the transformer to which it is connected is as follows: Among them, P lwmax Represents the maximum output power of all transformers in the lth charging station.

3. The charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm according to claim 1 is characterized in that: In step 3, solving the model using the improved NSGA-II algorithm includes the following steps: Step 3.1, condition setting: set the population size and number of iterations, where each individual in the population represents a recommended charging plan for all electric vehicles (recommended to specific available charging piles); Step 3.2, encoding: according to the order of available charging piles, the electric vehicle is arranged to the available charging piles by integer encoding. The value of the available charging pile for which the charging task is arranged is set to the electric vehicle number, and the value of the charging pile for which no charging task is arranged is set to 0; Step 3.3, generate the initial population: arrange all electric vehicles with charging needs to the available charging piles to generate a population individual, and generate the initial solution individual of the set population size; Step 3.4, population selection: merge the parent population with the newly generated next generation population, perform fast non-dominated sorting on the merged population and calculate the crowding distance, and select individuals of the population size as the new population; Step 3.5, crossover operator: Set the crossover rate to 0.9, randomly select two individuals from the new population as parents, generate a MC random number between [0,1], if the first random number is greater than the crossover probability, the two parent individuals will not crossover, if the first random number is less than or equal to the crossover probability, select the designed random crossover and single-point crossover with probabilities of 0.5 and 0.5 respectively, until the offspring of the population size is generated, Step 3.6, mutation operator: Set the mutation rate to 0.

01. For each individual, generate a second random number between [0,1]. If the second random number is greater than the mutation rate, no mutation will be performed. If the second random number is less than or equal to the mutation probability, randomly select one of the three designed mutation methods with probabilities of 0.2, 0.4, and 0.4 respectively to obtain the next generation population. Step 3.7, repair operator: Since crossover and mutation may cause chromosomes to be infeasible, it is necessary to repair the chromosomes after crossover and mutation; Step 3.8, fast non-dominated sorting: Based on the Pareto dominance relationship, fast non-dominated sorting is one of the most important sorting techniques in implementing multi-objective algorithms. It can quickly arrange individuals in the population according to their levels and provide a basis for the selection of the population. Step 3.9, crowding distance: Based on the result of stratifying the individuals in the population by the fast non-dominated sorting algorithm, in order to compare the performance of individual solutions in the same layer, the NAGA-II algorithm introduces the crowding distance to measure the density and diversity between individuals in the same non-dominated sorting layer.

4. The charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm according to claim 1 is characterized in that: The selection of population in step 3.4 is carried out by the following method: The parent generation and the new offspring generated by crossover and mutation are placed together at the same time, and the individuals are stratified by fast non-dominated sorting and the crowding distance is calculated. Individuals are selected from the non-dominated layer from low to high to join the new population until a certain proportion of the population size (for example, 70%) is reached. Then, one is randomly selected from the remaining unselected non-dominated layer and all are added to the selected individuals. If the selected individuals still do not reach the population size, the operation is repeated until the randomly selected non-dominated layer is larger than the population size. At this time, the remaining individuals are selected from the crowding degree of the non-dominated layer from large to small, so that the population size is the set size.

5. The charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm according to claim 3 is characterized in that: The crossover operator of the population in step 3.5 includes the following methods: Random crossover: Randomly select two chromosomes and randomly generate a number (within the range of 0 to the chromosome length) as the initial crossover point. At the same time, search backward until three non-zero numbers (i.e. the numbers of the three vehicles with charging needs) are found. The smaller cutoff point of the two chromosomes is taken as the cutoff crossover point, and then the gene fragments of the two chromosomes within the range of the initial crossover point and the cutoff crossover point are crossed. If after the randomly generated initial crossover point appears, neither chromosome can search backward for three non-zero numbers, the processing method is to end at the last bit of the chromosome.

6. The charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm according to claim 3 is characterized in that: The crossover operator of the population in step 3.5 includes the following methods: Single-point crossover: randomly select a chromosome, randomly select a car, and exchange them with the genes at the corresponding position on another chromosome.

7. The charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm according to claim 3 is characterized in that: The population mutation operator in step 3.6 includes the following three methods: Random mutation: randomly select a car and randomly assign its location to another available charging station; Variation oriented to reduce the cost of electric vehicles: find the car with the highest cost of electric vehicles in the current arrangement plan, re-arrange it to the charging station closest to the destination, and then arrange it to the charging pile with the smallest transformer load at the current charging station. If the charging pile with the smallest transformer load and the available charging piles are empty sets, then choose the next charging pile with the smallest transformer load. At the same time, check whether the electric vehicle’s power is sufficient to reach the charging station closest to the destination. If not, determine the next closest charging station to the destination. Mutation oriented towards reducing grid load variance cost: find the charging station with the largest load in the current arrangement (the load is calculated by two parts, one is the charging pile in use, and the other is the load increased due to our arrangement). If it includes our arranged cars, find the corresponding electric car and arrange it to the corresponding charging pile with the smallest transformer load in the charging station with the smallest load. If it includes multiple cars arranged by us, randomly select the number of a car for arrangement.

8. The charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm according to claim 3 is characterized in that: The population repair operator in step 3.7 includes the following two methods: Fix the situation of duplicate vehicles: if the same vehicle number appears twice in a chromosome, the vehicle number corresponding to the position with the highest cost on the electric vehicle side is set to 0, and the other one is retained; Fix the situation where there are missing vehicles: If a chromosome is missing the number of a vehicle that needs to be charged, the missing vehicle will be arranged to the available charging pile with the smallest transformer load under the current arrangement plan. If the charging pile with the smallest transformer load and the available charging piles are empty sets, the next charging pile with the smallest transformer load will be selected. At the same time, check whether the electric vehicle’s power is sufficient to arrive at this time. If not, determine the next available charging pile with the smallest transformer load until the remaining power is sufficient to arrive.

9. The charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm according to claim 3 is characterized in that: The fast dominated non-dominated sorting of the population in step 3.8 is performed according to the following steps: Step 3.8.1: Initialization: For each individual p in the population, calculate its dominating solution set S p and the number of individuals n that dominate p p , S p The initial value is n p The initial value is 0; Step 3.8.2: Nondominated Sorting: Find n p = 0, that is, individuals that are not dominated by any other individuals, put them into the first layer (F1) and save them in the result set. For all individuals in F1, traverse their domination solution set S p , for S p For each individual in p If -1 is followed by 0, it is put into the second layer (F2) and saved in the result set. Step 3.8.3: Repeat step 3.8.2 until all individuals are stratified. In each cycle, the stratified individuals are no longer considered, and finally all stratified individuals are saved in a result set.

10. The charging scheduling optimization algorithm for electric vehicles based on the improved NSGA-II algorithm according to claim 3 is characterized in that: The crowding distance of the population in step 3.9 is performed according to the following steps: Step 3.9.1: Initialization: For each individual i in the population, set its crowding degree d i The initial value is 0; Step 3.9.2: Perform a fast non-dominated sort on the population and calculate the crowding distance between individuals in the same layer according to the following formula: f m [i-1] and f m [i+1] represents the fitness values ​​of the two adjacent individuals of individual i after the feature sorting of the mth dimension, and They represent the maximum and minimum fitness values ​​of the population in the m-th dimension feature respectively. For points on the boundary, their crowding degree is set to infinity.

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