Expressway multi-station electric vehicle charging scheduling optimization method

Abstract

The invention provides a highway multi-station electric vehicle charging scheduling optimization method. According to the method, the improved NSGA-II algorithm is used for carrying out multi-target iterative optimization on the charging scheduling of the multi-station electric vehicles, so that the charging scheduling of the multi-station electric vehicles on the highway is optimized, the queuing and waiting time of the vehicles in peak hours is effectively shortened, and the charging experience of users is improved. Meanwhile, the operation load balance after optimization is remarkably improved, and charging resource distribution is more reasonable. According to the method, a multi-station electric vehicle charging scheduling mathematical model and a multi-station vehicle charging global queuing model are constructed, multiple groups of Pareto optimal solutions can be output, dynamic balanced distribution of vehicle charging demands among stations is realized, the overall utilization rate of the charging stations is remarkably improved, and the charging efficiency is improved. And the phenomenon that part of stations are congested and part of stations are idle is avoided. In conclusion, a manager can flexibly select a scheduling scheme according to actual requirements, and the method has good adaptability and popularization value.

Description

Technical Field

[0001] This invention relates to the field of electric vehicle charging infrastructure management and traffic scheduling optimization, and in particular to a method for optimizing multi-site electric vehicle (EV) charging scheduling on highways. Background Technology

[0002] In recent years, with advancements in battery technology, policy incentives, and the widespread adoption of environmental protection concepts, the market penetration rate of electric vehicles has increased rapidly and is expected to maintain a high-speed growth trend in the coming years. At the same time, the widespread application of electric vehicles places higher demands on charging infrastructure, especially public charging stations along highways. As a core infrastructure supporting long-distance electric vehicle travel, the rationality of the highway charging network's layout and operational efficiency directly affect user experience and the effectiveness of industry promotion.

[0003] Currently, due to the limited number of charging stations, large distances between stations, and uneven spatial distribution, charging stations on highways generally face severe queuing and excessively long waiting times during peak traffic periods. Existing scheduling strategies primarily guide vehicles to prioritize the nearest or most convenient charging station, ignoring the overall load status of the road network. This "proximity principle" approach easily leads to extreme congestion at some stations while other stations remain idle, resulting in resource waste and a decline in overall efficiency. Meanwhile, some traditional charging scheduling optimization methods, such as dynamic programming, linear programming, and heuristic algorithms, while practical in small-scale, single-objective scenarios, often face the challenge of insufficient global optimality in the large-scale dynamic environment of highways with multiple vehicles, stations, and objectives.

[0004] Furthermore, most current research and practical systems lack comprehensive consideration of multiple factors such as vehicle travel distance, remaining battery power, station distribution, and real-time traffic flow when making charging scheduling decisions, making it impossible to achieve intelligent global collaborative scheduling across stations and time periods. As the number of electric vehicles continues to rise, congestion and queuing problems at highway charging stations will further intensify in the future, inevitably affecting users' travel experience and even hindering the further popularization of electric vehicles. Summary of the Invention

[0005] To address the shortcomings of existing technologies, the present invention aims to provide an optimized scheduling method for electric vehicle charging at multiple highway stations, significantly reducing total vehicle waiting time, improving charging station utilization, and achieving dynamic load balancing across the entire network. The method includes the following steps:

[0006] c1. Collect parameter information of charging vehicles, charging stations and road network;

[0007] c2. Construct a mathematical model for multi-site electric vehicle charging scheduling;

[0008] c3. Model and evaluate the collaborative scheduling effect of multiple charging stations for electric vehicles on highways, and establish a global queuing model for vehicle charging at multiple stations based on the mathematical model.

[0009] c4. The improved NSGA-II algorithm is used to perform multi-objective iterative optimization of electric vehicle charging scheduling at multiple sites; the final population is sorted non-dominated to obtain the Pareto optimal solution set; and a suitable solution is selected from the optimal solution set according to the requirements as the final charging scheduling scheme.

[0010] Based on the above technical content, the present invention has the following beneficial effects:

[0011] This invention utilizes an improved NSGA-II algorithm to perform multi-objective iterative optimization of multi-site electric vehicle charging scheduling, thereby optimizing multi-site electric vehicle charging scheduling on highways, effectively reducing queuing and waiting times during peak hours, and improving the user charging experience. Simultaneously, the optimized algorithm significantly improves operational load balance and results in more rational allocation of charging resources.

[0012] This invention constructs a mathematical model for multi-site electric vehicle charging scheduling and a global queuing model for multi-site vehicle charging. It can output multiple Pareto optimal solutions, realize the dynamic and balanced distribution of vehicle charging demand among various sites, significantly improve the overall utilization rate of charging stations, and avoid the phenomenon of some sites being congested and others being idle.

[0013] In summary, this invention allows managers to flexibly select scheduling schemes according to actual needs, and has good adaptability and promotional value. Attached Figure Description

[0014] Figure 1 This is a flowchart of a multi-site electric vehicle charging method according to an embodiment of this application;

[0015] Figure 2 This is a map showing the distribution of highway routes and charging stations, which is an application example of this application.

[0016] Figure 3 This application example provides a Gantt chart of charging station services under normal conditions before optimization.

[0017] Figure 4 This application example provides a Gantt chart of the charging station service under normal conditions after optimization.

[0018] Figure 5 Here is a Gantt chart of the charging pile service under normal conditions before optimization for charging station 3, an application example of this application;

[0019] Figure 6 Here is a Gantt chart of the charging pile service under normal conditions after optimization for charging station 3, an application example of this application;

[0020] Figure 7 Here is a Gantt chart of the charging station service under normal conditions before optimization, as shown in the application example 4 of this application.

[0021] Figure 8 Here is a Gantt chart of the charging pile service under normal conditions for example charging station 4 in this application;

[0022] Figure 9 This application example provides a Gantt chart of charging station services under busy conditions before optimization at charging station 0.

[0023] Figure 10 This application example provides a Gantt chart of charging station service under busy conditions after optimization at charging station 0.

[0024] Figure 11 Here is a Gantt chart of the charging station service under busy conditions before optimization, as shown in the application example 3 of this application.

[0025] Figure 12 Here is a Gantt chart of the charging station service under busy conditions after optimization for charging station 3, an application example of this application;

[0026] Figure 13 This is a schematic diagram of the vehicle charging process under busy conditions before optimization at charging station 4, an application example of this application.

[0027] Figure 14 This is a schematic diagram of the vehicle charging process under busy conditions after optimization at charging station 4, an application example of this application.

[0028] Figure 15 A schematic diagram illustrating the charging process of vehicles with initial charging stations 0, 3, and 4 under normal circumstances before optimization, as an application example of this application.

[0029] Figure 16 A schematic diagram illustrating the charging process of vehicles with the first charging stations being 0, 3, and 4 under normal circumstances after the optimization of the charging stations used in this application example;

[0030] Figure 17 A schematic diagram illustrating the charging process of vehicles at charging stations 0, 3, and 4 under busy conditions before the optimization of the charging stations used in this application example;

[0031] Figure 18 A schematic diagram illustrating the charging process of vehicles at charging stations 0, 3, and 4 under busy conditions after optimization of the charging stations used in this application example;

[0032] Figure 19 This application example provides a comparison chart of vehicle queuing times before and after optimization under normal circumstances;

[0033] Figure 20 This application example shows a comparison of vehicle queuing times before and after optimization under busy conditions. Detailed Implementation

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] like Figure 1 As shown, this application provides a method for optimizing the scheduling of electric vehicle charging at multiple stations on highways. This method can dynamically sense system status, comprehensively consider multiple objectives, and adapt to large-scale complex road networks. It aims to achieve efficient utilization of resources at each station and reasonable allocation of the overall network load, promoting the sustainable development and intelligent upgrading of highway charging networks. The method includes the following steps:

[0036] c1. Data Processing:

[0037] Collect basic information related to charging vehicles, charging stations, and road networks to provide data support for optimizing subsequent multi-site charging scheduling strategies. This includes the following steps:

[0038] c11. Obtain relevant data for charging vehicles: Based on user reservation information, historical charging records and traffic flow prediction data, collect key parameters of charging vehicles.

[0039] Furthermore, the key parameters include:

[0040] Total charging time requirement for the vehicle: The cumulative charging time required for the vehicle to complete its journey;

[0041] The set of charging stations covered by the vehicle's driving route: sorted in order of travel, denoted as Ri, which includes all charging stations that the vehicle can physically reach;

[0042] The estimated time when the vehicle is expected to arrive at the first charging station in the set, wherein the first charging station in the set is Ri[0];

[0043] The vehicle's initial battery status and destination information are used to verify the feasibility of the charging strategy and ensure that the vehicle has no risk of power loss during the journey.

[0044] c12. Obtain charging station road network modeling data: Combine the highway road network topology to collect the core parameters of charging stations and road networks.

[0045] Furthermore, the core parameters include:

[0046] Basic attribute data for each charging station: including the station's geographical location (distribution along the highway network), the number of charging piles (i.e., the number of charging spaces within the station, denoted as cj), and charging power specifications, etc.

[0047] Road network connectivity data: the accessibility between charging stations, i.e., whether there is a direct route;

[0048] Travel time between stations: The travel time between any two reachable stations is calculated based on actual road conditions and traffic flow characteristics.

[0049] c2. Mathematical modeling of the multi-site charging scheduling problem:

[0050] This study focuses on the complex real-world problem of multi-site electric vehicle charging scheduling. By precisely defining decision variables, clarifying optimization objectives, and clarifying constraints, it abstracts the problem into a mathematical model, constructing a mathematical model for multi-site electric vehicle charging scheduling. This provides a quantitative analysis and solution framework for achieving efficient allocation of charging resources. The steps include:

[0051] c21. Definition of decision variables:

[0052] set up S is a set of M electric vehicles that need charging; , ,..., } represents the set of charging stations along the highway, totaling N.

[0053] For each vehicle Using vectors This indicates its charging plan. Among them... For vehicles On the site The charging time. If >0 indicates a vehicle Choose on site Charging; if =0 indicates a vehicle Do not select this site .

[0054] The charging decisions of all vehicles are aggregated into a decision matrix. The decision matrix in which the first... Corresponding vehicle In the charging distribution at each station, the first List of corresponding sites The total charging load received is used to fully characterize the core decision-making elements of multi-site charging scheduling from a mathematical perspective.

[0055] c22. Optimization objectives are set with multi-objective optimization as the core, to balance user experience and operational efficiency. These optimization objectives include:

[0056] Minimize total wait time: Establish objective function For vehicles The cumulative waiting time at all charging stations, i.e., the time difference between arriving at the station and starting charging.

[0057] Maximizing weighted average utilization: Establishing the objective function For the site The number of charging stations; For the site No. The utilization rate of a charging pile is the ratio of effective charging time to optimization cycle. This is a weighting coefficient based on the total service time of the site.

[0058] Minimize load imbalance: Establish the objective function Where LI is the coefficient of variation of the utilization rate of each site, and its calculation formula is: This is used to measure the balance of load distribution among sites; The average number of vehicles serving all stations. The standard deviation of vehicles serving all stations.

[0059] c23. To ensure the feasibility and rationality of the charging plan, the following constraints are set:

[0060] Consistency of total charging time: Vehicle The cumulative charging time at all stations must equal the total demand, i.e. ,in For vehicles Total charging time required.

[0061] Charging only at accessible stations: Vehicles It can only charge at stations covered by its driving trajectory, meaning it can only charge at stations outside the reachable station set. The site in , must meet .

[0062] First stop must charge: Vehicle It must be the first site in its reachable site set ( Charging, i.e. .

[0063] Charging time limits: at reachable stations Charging time Need to be Within the range, This is the minimum charging time, including the minimum system service time and the time required to reach the next station using energy. This is the maximum charging time.

[0064] Maximum number of charging stations: vehicles The number of charging stations shall not exceed the upper limit. ,Right now ,in This indicates that the site has been selected. Then it means no selection.

[0065] c3. Establish a global queuing model for multi-site vehicle charging to model and evaluate the collaborative scheduling effect of multiple charging stations for electric vehicles on highways, providing a simulation verification basis for the optimization algorithm. This includes the following steps:

[0066] c31. Set initial idle time for all charging piles at each charging station. All charging stations are initially in an idle state.

[0067] c32. Integrate modeling of vehicle queuing planning and charging scheduling process, recording charging information for each vehicle at each station:

[0068] c321, All vehicles arrive according to their initial arrival time. Arrange in ascending order to ensure the model is processed in chronological order.

[0069] c322, for vehicles Each planned site Planned arrival time :

[0070] If it is the first station ;

[0071] If it is a subsequent site .

[0072] For the previous site The charging end time, For station to Travel time.

[0073] c323, Charging Station Allocation: Select Charging Station The earliest vacant charging station in the country, namely Its available time is Modeling the actual charging process, including:

[0074] Actual start time: ;

[0075] Waiting time: ;

[0076] End time: .

[0077] Update Status: Update the idle time of this charging station to = .

[0078] c324. Record the charging information for each vehicle at each station, including: Vehicle ID. Site ID Charging pile ID Charging time Planned arrival time Actual start time End time and waiting time .

[0079] c33. Based on the recorded charging information, calculate performance metrics, including:

[0080] (1) Basic indicators for a single station, including:

[0081] Number of service vehicles Deduplication statistics for charging stations Total number of vehicles in service;

[0082] Total service time, i.e., the total service time for all vehicles in Total charging time: ;

[0083] Latest end time, i.e., charging station Maximum value of all charging completion times: .

[0084] (2) Efficiency indicators, including:

[0085] Single-site utilization rate, which is the ratio of total service time to total capacity time: ;

[0086] Average utilization rate: ;

[0087] Weighted average utilization: Based on softmax normalization, highlighting the contribution of high-load sites. The weight ;

[0088] Total waiting time: .

[0089] (3) Balance indicators, including:

[0090] Load imbalance: ,in:

[0091] , which is the average number of vehicles served at each station; , which is the standard deviation of the number of vehicles served at each station.

[0092] The above steps clearly describe how the multi-site vehicle charging global queuing model simulates the vehicle charging process and calculates core performance indicators, providing a quantitative basis for optimizing multi-site charging strategies.

[0093] c4. NSGA-II-based Multi-Site Charging Scheduling Optimization: Based on the traditional NSGA-II algorithm, and considering the complex constraints of multi-site electric vehicle charging scheduling on highways, the following improved scheme is proposed. Since traditional selection, crossover, and mutation operations are difficult to generate solutions that satisfy the mathematical model constraints, this invention customizes these operators. Simultaneously, a solution repair mechanism is introduced to forcibly correct infeasible solutions, ensuring they meet constraints such as mandatory charging at the first station, charging duration range, and maximum number of stations. Through these improvements, the NSGA-II algorithm can effectively adapt to this scheduling model, ensuring that the obtained scheme outperforms traditional methods in both feasibility and optimization performance.

[0094] c41. Initial population generation:

[0095] Set each candidate solution For a decision matrix ,in Indicates vehicle The charging allocation is defined as follows: M represents the number of vehicles, and N represents the number of charging stations.

[0096] Randomly generate P items The non-negative initial matrix is ​​used to correct solutions that violate constraints, such as ensuring that the first charging station is always charged and that the total charging time is consistent. The specific steps are as follows:

[0097] For solutions that need repair Each row corresponds to a charging scheme for a single vehicle; the solution is checked row by row. And perform the following operations:

[0098] Remove unreachable stations: If the vehicle The reachable sites are concentrated in one place. but , place ;

[0099] Ensure you top up your account on the first stop: If you top up your account on the first stop of Assignment ,in Indicates the minimum charging time;

[0100] Limit the number of charging stations: If the number of active stations ( )Exceed Randomly set zeros for some sites It should be noted that the first stop is not included;

[0101] Correcting total charging time: Calculating scaling factor Adjust all non-zero values Make the total time meet the requirements;

[0102] Cutting time upper and lower limits: Limit to threshold range If the total changes, it will be redistributed proportionally to maintain the total time.

[0103] c42. Non-dominated sorting and crowding distance calculation:

[0104] For each solution in the current population, evaluate its quality using the following steps:

[0105] c421. Non-dominated sorting: For solutions If no other solution exists In all objective functions All of the above are better than or equal to And is strictly superior to at least one objective function Then it is called This is a non-dominated solution. Based on this relationship, the entire population is divided into several levels, with smaller level numbers indicating better solutions within that level.

[0106] c422. Crowding Distance Calculation: To maintain solution diversity, the crowding distance of each solution in the target space is calculated. :

[0107] For each objective function Find the solution The nearest better solution on this objective And the worst solution recently ;

[0108] Crowded distance The greater the distance, the sparser the region where the solution is located;

[0109] Assign an infinite crowding distance to solutions at the edge of the target space (such as the optimal solution for a certain target). This is to ensure that the boundary solution is not eliminated.

[0110] c43. Selection, crossover, and mutation operations:

[0111] A parent mating pool is formed, and crossover and mutation operations are performed on the individuals in the mating pool to generate the offspring population. This includes the following sub-steps:

[0112] c431. Selection operation: Based on the non-dominated sorting priority and crowding distance calculation results, the tournament selection method is used to select the parent generation to form a parent generation mating pool of size P.

[0113] c432, in the decision matrix Perform crossover operation row by row:

[0114] For any two parent individuals' decision matrices and The first in its matrix The rows are respectively denoted as and Corresponding vehicle Charging allocation. Generating offspring. At that time, and Each row is subjected to a crossover operation according to a preset crossover probability. The specific operation method randomly adopts one of the following two methods:

[0115] (1) Inheritance-based crossover:

[0116]

[0117] This indicates that the child inherits directly from the parent with probability p. The charging allocation row of a certain vehicle in the system inherits directly from its parent with probability 1−p. The charging allocation line for the corresponding vehicle.

[0118] (2) Weighted average crossover:

[0119]

[0120] in The weights are random, meaning they are applied to the parent generation. and father generation The charging allocation row for the corresponding vehicle is determined by random weights. Perform a weighted average to obtain the charging allocation row for the offspring.

[0121] c433, in the decision matrix Perform mutation operations row by row:

[0122] For the offspring generated after crossover , its first OK Mutation operations are performed using one or all of the following methods, based on preset mutation probabilities:

[0123] (1) Gaussian perturbation variation:

[0124] For each assigned site Charging time Add Gaussian noise:

[0125]

[0126] That is, charging time The superposition follows a normal distribution Gaussian noise And ensure that the charging time is non-negative.

[0127] (2) Transfer of charging time between stations:

[0128] Two stations were randomly selected for the vehicle. and Set the transfer ratio The transferable duration is:

[0129]

[0130] And execute:

[0131]

[0132] in and Is it the same vehicle at the station? and sites Charging time, The random transfer ratio is between 0.1 and 0.6, and the longer charging time between the two sites is taken first. The product of the ratio r and the shorter charging time between the two stations. Take the minimum value to ensure that the charging time of both sites is non-negative after the transfer, and that the transfer amount meets the proportional constraint.

[0133] c434. For each new offspring individual obtained after crossover and mutation operations... The solution that violates the constraints is corrected, and the correction method is as shown in step c41, to ensure that all obtained solutions meet the constraints.

[0134] c44. Elite Preservation and Population Renewal:

[0135] The parent and offspring populations are merged into a mixed population of size 2P. Steps c42 and c43 are repeated to select the P optimal individuals, forming a new generation of parent populations, thus preserving elites. The crossover and mutation operation of step c43 is then repeated in the new generation of parent populations to obtain a new generation of offspring populations, achieving population renewal.

[0136] c45. Output:

[0137] Repeat step c44 until the latest population satisfies the preset iteration termination condition, such as reaching the maximum number of iterations or the optimal solution front layer tending to converge. Perform non-dominated sorting on the final population, and use the resulting first front layer solutions as the Pareto optimal solution set for the multi-objective optimization problem. Each solution in this set corresponds to a feasible charging schedule. In practical applications, a suitable solution can be selected from the Pareto optimal solution set as the final charging schedule based on the emphasis placed on different optimization objectives.

[0138] Based on the same concept as the above method, this application also provides an application example with a highway in a certain area of ​​Zhejiang Province as the demonstration object, selecting three highway routes forming a near-ring shape and seven charging stations along the routes as the simulation network.

[0139] This application example selects the expressway network surrounding Cixi City, Ningbo City, Zhejiang Province as the research area, covering the Shenhai Expressway, Ciyu Expressway and Hangzhou Bay Ring Expressway.

[0140] c1. Data Processing:

[0141] c11. Data collection related to charging vehicles:

[0142] Vehicle data is generated based on traffic flow characteristics along the highway, with the following specific rules:

[0143] Charging demand: The charging demand at each station is determined based on the traffic flow ratio.

[0144] Under normal circumstances: based on a traffic flow ratio of 0.2%, the charging demand of the 7 stations is 20, 78, 70, 64, 20, 77, and 63 respectively.

[0145] Busy conditions: Based on a traffic ratio of 0.5%, the demand is 30, 102, 91, 85, 26, 100, and 96 respectively.

[0146] Charging time: follows a truncated exponential distribution with parameter λ=3, and the value range is limited to 15~40 minutes, which is consistent with the typical duration of high-speed fast charging scenarios.

[0147] Arrival time: The time when the vehicle arrives at the first charging station is a random value within 0 to 120 minutes, simulating the dynamic arrival process within 2 hours.

[0148] Reachable Station Sequence: Based on the road network connectivity between stations, a set of stations reachable along the driving route is randomly generated for each vehicle and sorted in the order of passage.

[0149] The final charging vehicle data is shown in Table 1:

[0150] Table 1 Partial Data Table of Charging Vehicles

[0151]

[0152] c12. Data collection for charging station and road network modeling:

[0153] Based on the location of actual charging stations obtained from the map, and combined with traffic features such as highway interchange nodes, additional stations were added, ultimately forming a network layout of 7 charging stations. The location information of the charging stations and the road traffic flow are as follows: Figure 2 As shown.

[0154] Travel time between stations: Based on the actual mileage of the expressway section and an average driving speed of 100 km / h, the travel time between each station is shown in Table 2 (unit: minutes):

[0155] Table 2 Travel timetable between different stations

[0156]

[0157] Charging pile configuration: The number of charging piles at the 7 sites was determined based on actual operating data and manual estimation, as shown in Table 3.

[0158] Table 3 Number of charging piles at different sites

[0159]

[0160] c2. Mathematical modeling of the multi-site charging scheduling problem:

[0161] c21. Definition of decision variables:

[0162] In a typical scenario, the total number of vehicles requiring charging is M=392, the total number of charging stations is N=7, and the decision variable is one. Charging distribution matrix .

[0163] c22. Optimize target setting:

[0164] The optimization objective is to minimize the total latency. Maximize average utilization and minimize load imbalance The indicators are obtained through the global queuing simulation program for multi-site vehicle charging in step c3.

[0165] c23. Constraint Setting:

[0166] The constraints include upper and lower limits for charging time. Set to 10 minutes. Set to 40 minutes, the number of charging stations per vehicle shall not exceed Set to 3 times.

[0167] c3. Global queuing simulation program for multi-site vehicle charging:

[0168] Based on the charging pile count data of the 7 charging stations obtained in step c21, a global queuing simulation program for multi-site vehicle charging is established, where each station follows the "first-come, first-served" (FCFS) principle.

[0169] c31. Initialize state:

[0170] Set initial idle time for all charging piles at the 7 charging stations: .

[0171] c32. Vehicle queuing and charging scheduling:

[0172] c321. Arrange the 392 charging vehicles according to the arrival times in Table 3. Sort in ascending order.

[0173] c322, Based on the decision matrix The OK Determine each planned site for a single vehicle VI (like (i.e., charging is required), to obtain the vehicle's planned arrival time:

[0174] Determine the station based on the reachable station sequence in Table 3. Is this the first stop for the vehicle's VI? If it is the first stop, If it is a subsequent site, For the previous site The charging end time, For station to The travel time is obtained from Table 1.

[0175] c323, Charging Station Allocation: Select Charging Station The earliest vacant charging station in the country, namely Its available time is Record the charging process:

[0176] Actual start time: ;

[0177] Waiting time: ;

[0178] End time: .

[0179] After charging is complete, update the status and update the idle time of the charging station. = .

[0180] c324 records the charging information of 392 vehicles at each station, including:

[0181] Vehicle ID Site ID Charging pile ID ;

[0182] Planned charging time Planned arrival time ;

[0183] Actual start time End time Waiting time .

[0184] c33. Performance index calculation:

[0185] Based on simulation data, the system performance indicators are calculated using the following formula:

[0186] 1. Basic indicators for a single station:

[0187] Number of vehicles in service: For charging stations Total number of vehicles in service;

[0188] Total service hours: ;

[0189] Latest end time: .

[0190] 2. Efficiency Indicators:

[0191] Single-site utilization rate: ;

[0192] Average utilization rate: ;

[0193] Weighted average utilization rate: The weight ;

[0194] Total waiting time: .

[0195] 3. Balance Indicators:

[0196] Load imbalance: ,in: , .

[0197] c4. Multi-site charging scheduling optimization based on NSGA-II:

[0198] c41. Initial population generation:

[0199] Set the core parameters of NSGA-II as follows: initial population size is 500, number of iterations is 100, crossover probability is 0.7, and mutation probability is 0.15.

[0200] 500 randomly generated Given a matrix where all values ​​are non-negative, immediately execute the solution repair procedure to correct solutions that violate the constraints. The specific steps are as follows:

[0201] ① Clear charging time for non-path stations:

[0202] Traverse the vehicle charging plan vector For all stations not accessible by vehicle Index of stations not covered by the travel route Forced settings .

[0203] ②Initialize the first station charging time (if not allocated):

[0204] If after step 1, the vector If all elements in the value are 0 (i.e., no charging time allocation), then the total charging demand of the vehicle will be calculated. All allocated to the first station ,Right now .

[0205] ③Limit the number of charging stations (≤3):

[0206] Extract vector Index of all stations with a charging time greater than 0 (denoted as...) ).

[0207] like (Exceeding the maximum allowed number of sites):

[0208] Sort by charging time from longest to shortest The first three sites were selected as the retained sites (denoted as...). );

[0209] If the first stop Not here In ), use replace The station with the shortest charging time (prioritizing the first station to charge).

[0210] Calculate the current total charging time of the retained sites. ;

[0211] Proportionally reallocate total demand: for each ,renew Other sites are set to 0.

[0212] ④ Ensure minimum charging time:

[0213] Extract vector All charging times are less than The site index, (denoted as) Calculate the difference Prioritize charging at other stations where the charging time exceeds 20 minutes ( Transfer the corresponding difference to The stations listed will be ensured to meet the minimum charging time requirement; if no such stations exist, then... The existing charging time (less than 10 minutes) of medium-sized stations is transferred to other stations with non-negative charging time, and the allocation is adjusted to ensure the rational use of resources.

[0214] ⑤ Final time calibration:

[0215] Calculate the repaired vector Total charging time ;

[0216] like Perform the following operations:

[0217] like Scale all non-zero values ​​proportionally. Make the total time equal to .

[0218] like (In extreme exceptional circumstances) All requirements will be allocated to the first battle: .

[0219] Finally, 500 feasible solutions were obtained as the initial population.

[0220] c42. Non-dominated sorting and crowd distance calculation

[0221] For a population of 500 individuals, the three optimization objective functions set in step c22 are... Perform the following processing:

[0222] Non-dominated ranking process: Determine the dominance relationship among 500 individuals in the population. For any individual... If no other individuals exist Simultaneously satisfy:

[0223] In the objective function The value of is greater than or equal to ; In the objective function The value of is greater than or equal to ; In the objective function The value of is greater than or equal to ,and At least in Strictly superior to one of the objective functions Then determine The solution is non-dominated. Based on the above rules, the 500 individuals are divided into several levels. The first level contains all non-dominated solutions, and individuals in this level are not dominated by any other individual in the population. The second level contains solutions that are dominated only by individuals in the first level, and so on, to complete the stratification of all 500 individuals.

[0224] Crowding distance calculation process: For individuals within each level, the crowding distance is calculated based on three objective functions. :

[0225] against Three objective functions are used to sort individuals within the current level according to the values ​​of each objective function.

[0226] For individuals ,exist In the dimensional sorting results, take the values ​​of its preceding adjacent individuals. Value as Take the next adjacent individual in the order of its order. Value as Calculate the difference .

[0227] Similarly, calculate Dimensional difference and Dimensional difference .

[0228] individual The crowding distance is the sum of the differences in the three dimensions, namely: .

[0229] For in or The final crowding distance for any individual that takes the optimal value on any objective function. .

[0230] c43. Selection, crossover, and mutation operations:

[0231] c431. Selection Operation: Based on the "non-dominated sorting priority" and "crowding distance" from step c42, a tournament selection method is used to select parents, forming a parent mating pool of 500 individuals. Lower crossover and mutation operations are then performed on these individuals to generate a progeny population of 500.

[0232] c432, Crossover operation: Crossover in the individual decision matrix Proceed line by line. For any two parent individuals... and The first in its matrix The rows are respectively denoted as and Corresponding vehicle Charging allocation. Generating offspring. At that time, a crossover operation is performed on each row of the matrix according to a preset crossover probability. The specific operation method is randomly selected from one of the following two methods:

[0233] Inheritance crossover:

[0234]

[0235] This means directly inheriting the charging allocation line of a certain vehicle from its parent.

[0236] Weighted average crossover:

[0237]

[0238] c433, Mutation Operation: The mutation operation is also present in the individual decision matrix. Proceed row by row. For the offspring generated after crossover... , its first OK Mutation operations are performed according to preset mutation probabilities, using one or both of the following two methods:

[0239] Gaussian perturbation variation:

[0240] For each assigned site Its charging time Add Gaussian noise:

[0241]

[0242] Inter-site charging time transfer:

[0243] Two stations were randomly selected for the vehicle. and Random sampling The transferable duration is:

[0244]

[0245] And execute:

[0246]

[0247] c434. For each new offspring individual obtained after crossover and mutation operations... The solution that violates the constraints is corrected, and the correction method is as shown in step c41, to ensure that all obtained solutions meet the constraints.

[0248] c44. Elite Preservation and Population Renewal:

[0249] The parent and offspring populations are merged into a mixed population of 1000. Steps c42 and c43 are repeated to select the 500 best individuals, forming a new generation of parent populations, thus preserving elites. The crossover and mutation operation of step c43 is then repeated in the new generation of parent populations to obtain a new generation of offspring populations, achieving population renewal.

[0250] c45. Output:

[0251] Repeat step c44 until the iteration count reaches 100. Perform non-dominated sorting on the final population, and use the solutions of the first frontier layer as the Pareto optimal solution set for the multi-objective optimization problem. A total of 91 Pareto solutions are obtained. The weights of the three optimization objectives are set to 0.7, 0.2, and 0.1, respectively. The final charging scheduling scheme is shown in Table 4.

[0252] Table 4 Final Charging Scheduling Scheme

[0253]

[0254] By comparing the system performance indicators before and after optimization, the effectiveness of the multi-site charging scheduling strategy based on NSGA-II can be verified. The following analysis will be carried out from two scenarios: normal and busy conditions. Key indicators include total waiting time, average utilization rate and load imbalance.

[0255] Under normal circumstances, there are 392 charging vehicles. After optimization with NSGA-II, the total waiting time for the Pareto optimal solution ranges from 94 to 1729 minutes, a significant reduction compared to before optimization; the average utilization rate is 52.7% to 63.9%, an improvement of approximately 16.4 to 27.6 percentage points compared to before optimization; and the load imbalance is 0.21 to 0.30, falling within the "good balance" range. Without the charging redistribution strategy, i.e., vehicles autonomously select stations, the total system waiting time is 475 minutes. After optimization, the optimal solution is 94 minutes, a reduction of approximately 80.2%; the average utilization rate is only 36.3%, which improves to 50.7% to 76.0% after optimization; and the load imbalance is 0.42, falling within the "moderate imbalance" range, which decreases to 28.6% to 50.0% after optimization, achieving a balanced distribution of station load.

[0256] Under busy conditions, there are 530 charging vehicles. The total waiting time for the Pareto optimal solution ranges from 3587 to 7754 minutes. Although the absolute value is high, it is still an improvement compared to before optimization. The average utilization rate is 68.8% to 76.0%, which is at a high level. The load imbalance is 0.15 to 0.26, and the balancing effect is better than in normal conditions. Before optimization, the total system waiting time was 4769 minutes, and after optimization, it was 3587 minutes, a reduction of about 24.8%, alleviating congestion under high demand. The average utilization rate was 50.1%, which increased to 37.3% to 51.7% after optimization, significantly improving infrastructure utilization efficiency. The load imbalance was 0.40 (moderate imbalance), which decreased to 35.0% to 62.5% after optimization, maintaining balance among sites even under high load scenarios.

[0257] In summary, regardless of whether the conditions are normal or busy, the optimization strategy significantly reduces total waiting time, improves charging pile utilization, and alleviates load imbalance, validating the applicability of NSGA-II in multi-objective charging scheduling. Even in high-demand, busy scenarios, the optimization strategy maintains a low load imbalance (LI < 0.3), indicating strong adaptability to dynamic demands. Compared to the traditional model of vehicles autonomously selecting charging stations, the optimization strategy achieves comprehensive improvements in "reducing waiting time, increasing efficiency, and promoting balance" through global scheduling, providing a feasible solution for the efficient operation of highway charging networks.

[0258] The following analysis uses total waiting time as the core indicator to compare and analyze vehicle charging conditions before and after optimization. Three charging stations with prominent charging demand characteristics were selected from the seven charging stations for analysis. Stations 0 and 4 are idle stations with low vehicle acceptance and very few vehicles queuing; Station 3 is a busy station with high charging demand and long queues are likely to occur.

[0259] Under normal circumstances, the service Gantt charts of charging stations 0, 3, and 4 before and after optimization are as follows: Figures 3-8 As shown, where Figure 3 and Figure 4 To optimize the service Gantt chart of charging station 0 before and after normal operation, Figure 5 and Figure 6 To optimize the service Gantt charts of charging station 3 before and after normal operation, Figure 7 and Figure 8 The service Gantt charts for charging station 4 before and after optimization under normal conditions are shown below. The service Gantt charts for charging stations 0, 3, and 4 before and after optimization under busy conditions are shown below. Figures 9-14 As shown, where Figure 9 and Figure 10 To optimize the service Gantt chart for charging stations 0 before and after peak hours, Figure 11 and Figure 12To optimize the service Gantt charts for the pre- and post-charging stations 3 during peak hours, Figure 13 and Figure 14 Service Gantt charts for charging station 4 before and after optimization under busy conditions are presented. In each sub-chart, the horizontal axis represents time, and the vertical axis represents the charging piles at each station. Different colored blocks represent the charging time of different vehicles at their respective charging piles, with the start and end positions of the blocks corresponding to the start and end times of vehicle charging. In both scenarios, stations 0 and 4, with low charging demand before optimization, served fewer vehicles and had low utilization rates. After optimization, these previously low-demand stations significantly increased the number of vehicles served, and the overall number of vehicles served at each station also increased, effectively revitalizing charging resources and optimizing station service efficiency.

[0260] Under normal circumstances, the vehicle charging process before and after optimization is illustrated in the diagram below. Figure 15 and Figure 16 As shown in the diagram, this illustrates the optimized charging process for vehicles before and after charging during busy periods. Figure 17 and Figure 18 As shown, the horizontal axis of each subgraph represents time, and the vertical axis represents the vehicle number that uses the corresponding station as the first charging station. In normal scenarios, before optimization, only station 3 had a small amount of queuing; after optimization, queuing was almost eliminated, and the charging process at each station was smoother. In busy scenarios, before optimization, station 3 experienced "out-of-control" queuing due to supply and demand imbalance (the red queuing strips at station 3 were dense and lasted for a long time). After optimization, through scheduling strategies, extreme queuing was distributed to stations 0 and 4, which not only kept queuing within an acceptable range but also balanced the load of each station in the road network, significantly reducing the imbalance between stations and improving overall charging efficiency.

[0261] Under normal circumstances, the total queuing time per vehicle before and after optimization is similar to... Figure 19 As shown, in busy conditions, as Figure 20 As shown, the horizontal axis represents the vehicle ID, and the vertical axis represents the difference in total queuing time, obtained by subtracting the total queuing time before and after optimization. A difference > 0 indicates an increase in queuing time after optimization, while a difference < 0 indicates a decrease in queuing time. Under normal circumstances, the optimization scheme only increases the queuing time for a very small number of vehicles, while reducing the queuing time for the vast majority of vehicles. In busy situations, although the queuing time for vehicles originally charging at stations 0 and 4 is significantly extended due to stations taking over the charging demand from other stations, the overall queuing time for vehicles at other stations is still significantly reduced, demonstrating the difference in the effectiveness and overall value of the optimization scheme in different scenarios.

[0262] With minimizing the total waiting time as the core objective, the optimized charging schemes (unit: minutes) for local vehicles under normal and busy conditions are calculated as shown in Table 5:

[0263] Table 5 Optimization Scheme for Charging Vehicles

[0264]

[0265] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for optimizing electric vehicle charging scheduling at multiple stations on highways, characterized in that, Includes the following steps: c1. Collect parameter information of charging vehicles, charging stations and road network; c2. Construct a mathematical model for multi-site electric vehicle charging scheduling; c3. Model and evaluate the collaborative scheduling effect of multiple charging stations for electric vehicles on highways, and establish a global queuing model for vehicle charging at multiple stations based on the mathematical model. c4. The improved NSGA-II algorithm is used to perform multi-objective iterative optimization of electric vehicle charging scheduling at multiple sites; the final population is sorted non-dominated to obtain the Pareto optimal solution set; and a suitable solution is selected from the optimal solution set according to the requirements as the final charging scheduling scheme.

2. The method for optimizing electric vehicle charging scheduling at multiple highway stations according to claim 1, characterized in that, Step c1 includes: c11. Collect key parameters of charging vehicles based on user reservation information, historical charging records and traffic flow prediction data; c12. Based on the highway network topology, collect the core parameters of charging stations and the road network.

3. The method for optimizing electric vehicle charging scheduling at multiple highway stations according to claim 2, characterized in that, The key parameters include: The total charging time required for the vehicle, the set of charging stations covered by the vehicle's driving route, the estimated time when the vehicle will arrive at the first charging station in the set, the initial battery status of the vehicle, and destination information.

4. The method for optimizing electric vehicle charging scheduling at multiple highway stations according to any one of claims 1-3, characterized in that, Step c2 includes: c21. Summarize the charging decisions of all vehicles into a decision matrix, wherein the decision matrix contains the first... The charging allocation for vehicles at each station corresponds to the number of stations. The total charging load received by the corresponding stations; c22. Set optimization objectives with multi-objective optimization as the core to balance user experience and operational efficiency; c23. To ensure the feasibility and rationality of the charging plan, set constraints.

5. The method for optimizing electric vehicle charging scheduling at multiple highway stations according to claim 1, characterized in that, Step c3 includes: c31. Set the initial idle time for all charging piles at each charging station; c32. Integrate modeling of vehicle queuing planning and charging scheduling process, and record the charging information of each vehicle at each station; c33. Calculate performance metrics based on recorded charging information.

6. The method for optimizing electric vehicle charging scheduling at multiple highway stations according to claim 5, characterized in that, Step c32 includes: c321. Sort all vehicles in ascending order of their initial arrival time; c322. Planned arrival time for each planned stop for all vehicles; c323. Select the earliest available charging pile in the charging station and model the actual charging process. c324. Record the charging information for each vehicle at each station.

7. A method for optimizing electric vehicle charging scheduling at multiple highway stations according to claim 5 or 6, characterized in that, The performance indicators include: Basic indicators for a single station include: number of vehicles served, total service time, and latest end time; Efficiency metrics include: single-station utilization rate, average utilization rate, weighted average utilization rate, and total waiting time; Balance indicators include: load imbalance.

8. The method for optimizing electric vehicle charging scheduling at multiple highway stations according to claim 1, characterized in that, Step c4 includes: c41. Set each candidate solution as a decision matrix, randomly generate a non-negative initial matrix, and correct solutions that violate the constraints; c42. For each solution in the current population, perform non-dominated sorting and crowding distance calculation; c43. Form a parent mating pool, perform crossover and mutation operations on the individuals in the mating pool to generate the offspring population and correct the solutions that violate the constraints; c44. Merge the parent population and the offspring population into a mixed population. Repeat steps c42 and c43 to select the best individuals and form a new generation of parent population. Repeat step c43 on the new generation of parent population to obtain a new generation of offspring population, thus achieving population renewal. c45. Repeat step c44 until the latest population satisfies the preset iteration termination condition; perform non-dominated sorting on the final population, and take the obtained first frontier layer solution as the Pareto optimal solution set of the multi-objective optimization problem; each solution in the optimal solution set corresponds to a feasible charging scheduling scheme; select a suitable solution from the optimal solution set as the final charging scheduling scheme according to the needs of different optimization objectives.

9. The method for optimizing electric vehicle charging scheduling at multiple highway stations according to claim 8, characterized in that, The method for correcting solutions that violate constraints is as follows: For solutions that need repair Each row corresponds to a charging scheme for a single vehicle, and the solution is checked row by row. And perform the following operations: Remove unreachable charging stations, ensure that the first charging station is always available, and limit the number of charging stations; Calculate the scaling factor to adjust the total charging time; limit the charging time within a threshold range; if the total charging time changes, redistribute it proportionally to maintain the total charging time constant.

10. A method for optimizing electric vehicle charging scheduling at multiple highway stations according to claim 8 or 9, characterized in that, Step c43 includes: c431. Based on the non-dominant sorting priority and crowding distance calculation results, the tournament selection method is used to select the parent mating pool; c432. When generating offspring, crossover operations are performed randomly using inheritance crossover or weighted average crossover according to a preset crossover probability for each row of the decision matrix of the two parent individuals. c433. For the offspring generated after crossover, perform mutation operations on each row using Gaussian perturbation mutation and / or inter-site charging duration transfer. c434. For each new offspring obtained after crossover and mutation operations, correct any solutions that violate the constraints to ensure that all obtained solutions comply with the constraints.

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