Bus fast-charging station orderly charging method based on data-driven energy efficiency model

Abstract

The present application relates to the technical field of bus charging, in particular to a bus fast charging station orderly charging method based on a data-driven energy efficiency model; first, the power demand meeting the operation of a bus line is determined, and then a relationship between charging energy conversion efficiency and the actual charging power of a vehicle-mounted energy storage system is established; taking the minimum actual power consumption of the charging station in a day or the minimum actual electricity cost of the charging station in a day as an objective function, wherein the charging energy conversion efficiency is considered, a nonlinear optimization objective function model is established with the power demand of the electric bus line operation, the continuity of the electric bus charging time as constraint conditions, then the nonlinear optimization objective function model is converted into a mixed integer convex programming problem using piecewise linearization, and the optimal charging plan is obtained by solving the mixed integer convex programming problem; the present scheme can further improve the energy conversion efficiency of charging on the basis of traditional orderly charging, reduce the power consumption cost of the charging station operator and the charging cost of the electric bus, and improve the economy.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bus charging, in particular to a bus fast charging station orderly charging method based on a data-driven energy efficiency model. BACKGROUND

[0002] As an important part of electric vehicles, electric buses have fixed charging locations compared with the randomness of private cars and taxis. For the same bus operation line, the running route and time are relatively fixed. The battery capacity and charging power of electric buses are much larger than those of electric private cars. One of the mainstream charging modes of electric buses is the fast charging mode of returning to the station with piles, that is, the quick charging mode. Large-scale disordered charging will have an adverse impact on the power grid, intensify the peak of the power grid, and also lead to the problem of over-planning of charging piles, increasing the construction cost and electricity cost of charging piles. In view of this problem, the research on the orderly charging of electric buses has become a hot spot. However, the current research on the orderly charging of electric vehicles is mainly based on time-of-use electricity price. The research based on time-of-use electricity price aims to reduce the charging cost of users and reduce the load peak-valley difference to guide the orderly charging of electric vehicles, without considering the charging energy conversion efficiency.

[0003] In the invention patent application with the publication number CN111619394A, the use of electricity load data of each time period in the region is obtained from the power grid. The charging type of each electric bus is determined, including not accepting charging and discharging scheduling, accepting orderly charging scheduling, and accepting orderly charging and discharging scheduling. On the power grid side, the minimum load peak-valley difference is taken as the objective function. On the electric bus operator side, the minimum electric bus charging cost is taken as the objective function. An optimization model is established by taking the battery capacity, operation time, and charging and discharging power of the electric bus as the constraint conditions, and the optimal charging and discharging time and power scheme is obtained by solving the model. However, the relationship between charging efficiency and transformer efficiency, charging machine efficiency, and battery efficiency is not considered in this scheme, resulting in waste of electric energy. SUMMARY

[0004] In view of the deficiencies in the prior art, the present application aims to provide an electric bus orderly charging method that fully considers the relationship between charging power and transformer efficiency, charging machine efficiency, and battery efficiency, which can further improve the energy conversion efficiency of charging on the basis of traditional orderly charging, reduce the electricity cost of charging station operators and the charging cost of electric buses, and improve the economy.

[0005] To solve the above technical problems, the technical solution provided by the present application is a bus fast charging station orderly charging method based on a data-driven energy efficiency model, which comprises the following steps:

[0006] S1: Determine the power demand that meets the operation of the bus line according to the operation time of the charging station, the equipment power limit, the quantity limit, and the bus departure plan;

[0007] S2: Based on the charging process energy flow topology of the charging station, measure the transformer efficiency, charger efficiency and battery efficiency, and establish the relationship between the charging energy conversion efficiency and the actual charging power of the vehicle-mounted energy storage system;

[0008] S3: Take the actual power consumption of the charging station in a day or the actual electricity cost of the charging station in a day as the objective function, consider the charging energy conversion efficiency, and establish a nonlinear optimization objective function model with the bus line operation power demand and the continuity of the electric bus charging time as the constraint conditions;

[0009] S4: Convert the nonlinear optimization objective function model in step S3 into a mixed integer convex programming problem using piecewise linearization, and solve the mixed integer convex programming problem to obtain the optimal charging plan, including the optimal charging time and corresponding charging power of each vehicle.

[0010] Further, in step S1, it is necessary to ensure that the state of charge of the vehicle-mounted energy storage system before the departure time of all buses can meet the complete line:

[0011]

[0012]

[0013] wherein j is the vehicle number; is the number of buses serving the line of vehicle j; is the first departure time, the last bus time and the departure interval of the line of vehicle j, respectively; j is the length of the line where vehicle j is located; n j is the number of times each bus in the line served by vehicle j needs to be repeated; is the starting time of vehicle j in the kth cycle; V j is the unit kilometer energy consumption of the line served by vehicle j; C p,j is the maximum energy of the vehicle-mounted energy storage system of vehicle j; soc low is the lower limit of the SOC considering the additional loss caused by the traffic condition factor to ensure the safe operation of the vehicle; represents the SOC of vehicle j before the kth cycle departure.

[0014] Further, in step S2, the relationship between the charging energy conversion efficiency considering the transformer efficiency, charger efficiency and battery efficiency and the actual charging power of the vehicle-mounted energy storage system is:

[0015]

[0016] In the formula, t represents the time of charging, P t g P is the actual consumed power of the power distribution network; P t ch P is the actual charging power of the vehicle-mounted energy storage system; P t pile P is the output power of the charging pile; η hl η is the efficiency of the transformer when reducing voltage; η ad η is the efficiency of the charger; η b η is the efficiency of the power battery in the vehicle-mounted energy storage system during the charging process.

[0017] The present application measures the relationship between the charging energy conversion efficiency considering the transformer efficiency, the charger efficiency and the battery efficiency and the actual charging power of the vehicle-mounted energy storage system through experiments.

[0018] The specific steps are: 1) the transformer efficiency, the charger efficiency and their respective output powers between them are measured by a power analyzer, which are respectively represented as

[0019] 2) η b can be described as the ratio of the actual charging battery energy to the charging process input energy to the battery, and is expressed in percentage, which is related to the charging power of the battery. The experimental steps are: ① through experiments, different P t ch corresponding η b . The specific operation of measuring the efficiency η b and the actual charging power P t ch is: charging the battery with constant current, recording the energy input to the battery during the whole charging process, and obtaining the actual charging energy of the battery through a small current discharging experiment after charging, and then calculating the actual charging power of the battery and the corresponding battery charging energy conversion efficiency η b in the charging process. ② the data obtained in step ① is fitted to obtain a model describing the relationship between η b and P t ch , that is, η b =f b (P t ch ).

[0020] 3) according to the topological flow relationship of the charging system

[0021] The relationship between the charging energy conversion efficiency considering the transformer efficiency, the charger efficiency, the battery efficiency and the actual charging power P of the vehicle energy storage system can be represented as follows: t ch hl ·η ad ·η b =f(P t ch ).

[0022] Further, in step S3, the actual power consumption of the charging station in a day is taken as the objective function:

[0023]

[0024] wherein T represents the number of unit time divided in a day;△t is the unit time, in this paper△t = 60s; J is the total number of vehicles served by the bus charging station; is the actual charging power of the jth vehicle charged by the vehicle energy storage system at time t, is the output power of the charging pile when the jth vehicle is charging at time t.

[0025] Further, in step S3, the actual electricity cost of the charging station in a day is taken as the objective function:

[0026]

[0027] c(t) is the commercial electricity price of the charging station operating city at time t.

[0028] Further, in step S4, the constraint condition of the objective function is:

[0029] Time constraint:

[0030] The following formula indicates that the bus cannot be charged when it is not at the charging station:

[0031]

[0032] The following formula indicates that all vehicles cannot be charged when the charging station stops operating:

[0033]

[0034] wherein d j,t is the charging state of the vehicle j at time t, d j,t ∈{0,1}, d j,t = 1 indicates that the vehicle is in the charging state, otherwise it is in the non-charging state; is the time set when the bus with number j is not at the charging station, wherein is the departure time of the kth round of the vehicle j,​ is the back station time of the jth vehicle in the kth round, j is the total number of rounds that the jth vehicle needs to circulate in a day; T close is the time when the charging station is closed;

[0035] Charging station device constraints:

[0036] The following formula indicates that the number of charging piles simultaneously in charging is less than or equal to the total number of charging devices N in the charging station cs :

[0037]

[0038] The following formula indicates that the maximum power of a single charging pile cannot exceed the safety power P cs ;

[0039]

[0040] The following formula indicates that the power distribution capacity of the entire charging station cannot exceed the maximum safety power P of the charging station power distribution network s :

[0041]

[0042] Travel demand constraints:

[0043] The following formula indicates that the SOC of each vehicle at the departure time of each round should be between the ratio of the energy required for a single trip to the maximum energy plus the lower limit of the SOC soc low and the set maximum SOC soc max :

[0044]

[0045] The following formula indicates the calculation formula of the SOC of the jth vehicle at the kth departure time , The SOC of the vehicle at the time is the initial SOC at the beginning of the day plus the amount of electricity charged into the vehicle by the charging behavior that has occurred before, minus the amount of electricity consumed by the previous trip.

[0046]

[0047] The following formula indicates that the amount of electricity charged in a day can meet the sum of the required energy for a day's travel, ensuring the recyclability of the charging strategy:

[0048] The following formula shows that using this charging strategy, the charging behavior of each bus is continuous in the time scale:

[0049]

[0050]

[0051] where y j,t and z j,t are the start and end decision variables of the continuous charging controlled by the vehicle numbered j during the charging process after returning to the station, y j,t , z j,t ∈{0,1}; is the set of time periods of the vehicle j after returning to the station in the charging station,

[0052] Compared with the prior art, the scheme has the following obvious advantages: the scheme fully considers the relationship between charging efficiency and transformer efficiency, charger efficiency and battery efficiency, takes the minimum actual power consumption in a day as the objective function, improves the energy conversion efficiency of electric bus charging, and improves the objective function while improving the energy conversion efficiency of charging, takes the minimum actual electricity cost of the charging station in a day as the objective function, and reduces the electricity cost and electric bus charging cost of the charging station operator.

[0053] In addition, the scheme also adopts a piecewise linearization method to linearize the established optimization objective function model including transformer efficiency, charger efficiency and battery efficiency, which makes the model easy to solve under the condition of ensuring the accuracy of the total efficiency model; the complex nonlinear model is divided into several linear operations, which improves the solving efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0054] The accompanying drawings are included to provide a further understanding of the application, and constitute a part of the specification, illustrate the application, and are used to explain the application, and do not constitute a limitation on the application. In the drawings:

[0055] Figure 1 is a step flowchart of the application;

[0056] Figure 2 is a charging station energy flow topology diagram of the application. DETAILED DESCRIPTION

[0057] The preferred examples of the application are described below in conjunction with the drawings, and it should be understood that the preferred examples described herein are only used to illustrate and explain the application, and do not limit the application.

[0058] As Figure 1 shown, the ordered charging method of the bus fast charging station based on the data-driven energy efficiency model of the application comprises the following steps:

[0059] S1: According to the operation time, equipment power limit, quantity limit and bus departure plan of the charging station, determine the power demand that meets the operation of the bus line;

[0060] S2: As Figure 2 As shown, based on the energy flow topology during the charging process at the charging station, the transformer efficiency, charger efficiency, and battery efficiency are measured, and the relationship between the charging energy conversion efficiency and the actual charging power of the on-board energy storage system is established.

[0061] S3: The objective function is to minimize the actual electricity consumption of the charging station in a day or to minimize the actual electricity cost of the charging station in a day. The nonlinear optimization objective function model is established with the charging energy conversion efficiency as a consideration and the power demand of the electric bus route and the continuity of the charging time of the electric bus as constraints.

[0062] S4: Use piecewise linearization to transform the nonlinear optimization objective function model in step S3 into a mixed integer convex programming problem. Solve the mixed integer convex programming problem to obtain the optimal charging plan, including the optimal charging time and corresponding charging power for each vehicle.

[0063] Specifically, the bus charging station needs to simultaneously meet the departure needs of multiple bus routes. The travel demand of these bus routes is determined by the departure schedule set by the operator. The table below shows the departure timetable for a certain bus station in this embodiment:

[0064]

[0065]

[0066] This invention studies the charging requirements of electric buses to ensure that the onboard energy storage system of all buses has a state of charge sufficient to meet the energy consumption for the entire route before departure.

[0067]

[0068]

[0069] In the formula, j is the vehicle number; The number of buses serving the route served by vehicle j; These represent the first departure time, last departure time, and departure interval of the route for vehicle j; l j n is the length of the route in which vehicle j is located; j The number of times each bus on the route served by vehicle j needs to run repeatedly; Let V be the starting time of vehicle j in the kth cycle; j Energy consumption per unit kilometer of the route served by vehicle j; C p,j The maximum energy of the vehicle's onboard energy storage system; SOC lowTo consider the additional loss caused by factors such as traffic conditions, ensure the SOC safety lower limit of the safe operation of the vehicle; SOC of the vehicle j before the start of the kth cycle.

[0070] In step S2, the relationship between the charging energy conversion efficiency considering the transformer efficiency, the charging machine efficiency and the battery efficiency and the actual charging power of the vehicle-mounted energy storage system is:

[0071]

[0072] In the formula, t represents the charging time, P t g P is the actual power consumed by the power distribution network; P t ch P is the actual charging power of the vehicle-mounted energy storage system; P t pile P is the output power of the charging pile; η hl η is the efficiency of the transformer when reducing voltage; η ad η is the charging machine efficiency; η b η is the efficiency of the power battery in the vehicle-mounted energy storage system during the charging process.

[0073] The application measures the relationship between the charging energy conversion efficiency considering the transformer efficiency, the charging machine efficiency and the battery efficiency and the actual charging power of the vehicle-mounted energy storage system through experiments.

[0074] The specific steps are: 1) the relationship between the transformer efficiency, the charging machine efficiency and their respective output power is measured by the power analyzer, which is respectively represented as

[0075] 2) η b can be described as the ratio of the actual charging battery energy to the charging process input energy to the battery, and is expressed by percentage, which is related to the charging power of the charged battery, and the experimental steps are: ① through experiments, different P t ch corresponding to η b . The specific operation of measuring the efficiency η b and the actual charging power P t ch is: charging the battery with constant current, recording the energy input to the battery during the whole charging process, and obtaining the actual charging energy of the battery through the small current discharging experiment after charging, and then calculating the actual charging power of the battery and the corresponding battery charging energy conversion efficiency η b of the charging process. ② fitting the data obtained in step ① to obtain the description of η b and P tch The model of the relationship, i.e. η b = f b (P t ch ).

[0076] 3) According to the charging system topology flow relationship

[0077]

[0078] The charging energy conversion efficiency considering the transformer efficiency, charger efficiency and battery efficiency and the actual charging power P t ch of the vehicle-mounted energy storage system, i.e. η hl · η ad · η b = f(P t ch ).

[0079] The daily required power of the electric bus charging station can be determined by the bus schedule and can be expressed as:

[0080]

[0081] The daily required power is determined by the bus schedule and the route length, and the charging station energy conversion efficiency η in a single day can be expressed as:

[0082]

[0083] In the formula, C ostg is the actual power consumption of the charging station in a day, and thus the charging station energy conversion efficiency is the highest, which is equivalent to finding the minimum actual power consumption, so it is equivalent to taking the minimum actual power consumption of the charging station in a day as the objective function under the premise of considering the charging energy conversion efficiency.

[0084] In order to reflect the influence of the dynamic charging energy efficiency of the bus fast charging station, the embodiment compares four different scenarios:

[0085] Scenario one: without using any scheduling strategy, the bus charges as soon as it arrives at the station;

[0086] Scenario two: ordered charging with the minimum power consumption as the target, the objective function is:

[0087]

[0088] In the formula, T represents the number of unit times divided in a day; △t is the unit time, in this paper, △t = 60s; J is the total number of vehicles served by the bus charging station; The actual charging power of the jth vehicle at time t, P t pile The output power of the charging pile when the jth vehicle is charging at time t.

[0089] Scenario three: the goal is to minimize the daily operating electricity cost, considering the energy conversion efficiency of electric vehicles, and the objective function is:

[0090]

[0091] Where c(t) is the commercial electricity price of the charging station operating city at time t.

[0092] Scenario four: the goal is to minimize the daily operating electricity cost, without considering the charging energy conversion efficiency of electric buses, and P t g t pile t ch The objective function is:

[0093]

[0094] The constraints of the above optimization problem are as follows:

[0095] S3.1: Time constraints:

[0096] The following formula indicates that the bus cannot be charged when it is not at the charging station:

[0097]

[0098] The following formula indicates that all vehicles cannot be charged when the charging station stops operating:

[0099]

[0100] Where d j,t is the charging state of vehicle j at time t, d j,t ∈{0,1}, d j,t =1 vehicle is in charging state, otherwise it is in non-charging state; is the set of time when the jth bus is not at the charging station, where is the departure time of the kth round of vehicle j, is the back station time of the kth round of vehicle j, n j is the total number of rounds that vehicle j needs to circulate in a day; T close is the closing time of the charging station.

[0101] S3.2: Charging station equipment constraints:

[0102] ​​The following formula indicates that the number of charging piles charging simultaneously is less than or equal to the total number N of charging equipment in the charging station. cs :

[0103]

[0104] The following formula indicates that the maximum power of a single charging pile must not exceed the safe power P. cs ;

[0105]

[0106] The following formula indicates that the total power distribution capacity of the charging station must not exceed the maximum safe power P of the charging station's power distribution network. s :

[0107]

[0108] S3.3: Constraints on travel demand:

[0109] The following formula indicates that the State of Charge (SOC) of each vehicle at the start of each cycle should be between the ratio of the energy required for a single trip to the maximum energy, plus the minimum SOC lower limit for the protection battery. low and the set maximum SOC value. max between:

[0110]

[0111] The following formula represents the departure time of vehicle j on the kth time. The formula for calculating the State of Charge (SOC) of a vehicle at that time. The vehicle's SOC at any given time is the SOC at the beginning of the day plus the amount of electricity charged into the vehicle during previous charging activities, minus the electricity consumed during previous trips.

[0112]

[0113] The following formula represents the total amount of electricity charged in a day that can meet the daily travel needs, ensuring the cyclicality of the charging strategy:

[0114]

[0115] The following formula shows that, using this charging strategy, the charging behavior of each bus is continuous over time:

[0116]

[0117]

[0118] In the formula, y j,t and z j,tis a continuous charging start and end decision variable of the vehicle numbered j during the charging process after returning to the station, y j,t , z j,t ∈{0,1}; is a set of time periods of the vehicle j after returning to the station in the charging station,

[0119] Since the transformer efficiency, charger efficiency and battery efficiency measured by experiments are nonlinear, the optimization objective established is a nonlinear optimization model, and in this embodiment, piecewise linearization is used for processing, and the formula is:

[0120]

[0121]

[0122]

[0123]

[0124] In the formula, is an auxiliary constraint parameter, and subscript x corresponds to the xth segment after linearization, represents that the charging power is located in the xth segment of the piecewise linearization after the broken line segment, and the value is and are the upper and lower limit values of the xth segment of the segmented interval power P li,x ; K η,x and B η,x are linearization coefficients, reflecting the influence of the charging power ; W x ={1,2,3}.

[0125] Finally, the optimization objective obtained by the above steps is a linearization model, and the optimal charging plan is obtained by solving the optimization model, including the optimal charging time of each vehicle and the corresponding charging power P t ch and the corresponding P t pile . This embodiment compares four scenarios, and the results show that the power consumption of scenario two is reduced compared to scenario one, and the cost of scenario three is lower than that of scenario four. Through the comparison results, it can be known that the ordered charging method of the bus fast charging station considering the dynamic charging energy conversion efficiency can reduce the power consumption, i.e., improve the charging energy conversion efficiency, and at the same time reduce the power consumption cost of the charging station operator and the charging cost of the electric bus.

[0126] Finally, it should be noted that the above only describes the preferred examples of the present application, and is not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art will appreciate that modifications can be made to the technical solutions described in the foregoing embodiments, or some of the technical features thereof can be replaced equivalently, without departing from the spirit and principle of the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for bus fast-charging station orderly charging based on data-driven energy efficiency model, characterized in that, The method comprises the following steps: S1: determining the power demand of the bus line operation according to the operation time of the charging station, the equipment power limit, the quantity limit and the bus departure plan; S2: based on the energy flow topology of the charging process of the charging station, the transformer efficiency, the charger efficiency and the battery efficiency measured by experiment, a relationship between the charging energy conversion efficiency and the actual charging power of the vehicle-mounted energy storage system is established; S3: taking the minimum actual power consumption of the charging station in a day or the minimum actual electricity cost of the charging station in a day as the objective function, wherein the charging energy conversion efficiency is considered, a nonlinear optimization objective function model is established with the power demand of the electric bus line operation, the continuity of the charging time of the electric bus as the constraint conditions; S4: using piecewise linearization to convert the nonlinear optimization objective function model in step S3 into a mixed integer convex programming problem, and solving the mixed integer convex programming problem to obtain the optimal charging plan, including the optimal charging time and the corresponding charging power of each vehicle.

2. The data-driven energy efficiency model based bus fast-charging station ordered charging method of claim 1, wherein, In step S1, it is necessary to ensure that the state of charge of the vehicle-mounted energy storage system before the departure time of all buses can meet the complete line operation: where j is the vehicle number; the number of buses serving the route for vehicle j; the first departure time, the last departure time and the departure interval of the route for vehicle j, respectively; j the length of the route for vehicle j; j the number of times each bus needs to repeat the route for vehicle j; the start time of the kth cycle for vehicle j; j the energy consumption per kilometer for the route for vehicle j; p,j the maximum energy of the energy storage system for vehicle j; low the lower limit of the SOC for the safety of the vehicle, considering the additional loss caused by the traffic conditions; the SOC of vehicle j before the kth cycle.

3. The data-driven energy efficiency model based method for bus fast-charging station ordered charging of claim 1, wherein, In step S2, the relationship between the charging energy conversion efficiency considering the transformer efficiency, the charger efficiency and the battery efficiency and the actual charging power of the vehicle-mounted energy storage system is: where t represents the time of charging, P t g P is the actual consumed power of the distribution network; P t ch P is the actual charging power of the vehicle-mounted energy storage system; P t pile P is the output power of the charging pile; η hl η is the efficiency of the transformer when reducing voltage; η ad η is the efficiency of the charger; η b η is the efficiency of the power battery in the vehicle-mounted energy storage system during charging.

4. The data-driven energy efficiency model based method for ordered charging of buses at fast-charging stations of claim 1, wherein, In step S3, the minimum actual power consumption of the charging station in a day is taken as the objective function: In the formula, T represents the number of unit time divided in a day; Δt is a unit time, Δt = 60s; J is the total number of vehicles served by the bus charging station; Pj(t) is the actual charging power of the jth vehicle at time t; Pj(t) is the actual charging power of the jth vehicle at time t; Pj(t) is the actual charging power of the jth vehicle at time t; t ch the transformer efficiency, charger efficiency, and battery efficiency corresponding to the actual charging power P 5. The data-driven energy efficiency model based method for bus fast-charging station ordered charging of claim 1, wherein, In step S3, the minimum actual electricity cost of the charging station in a day is taken as the objective function: c(t) is the commercial electricity price of the charging station operation city t.

6. The data-driven energy efficiency model based method for ordered charging of buses at fast-charging stations of claim 4-5, wherein, In step S3, the constraint conditions of the objective function are: Time constraint: The following formula indicates that the bus cannot be charged when it is not in the charging station: The following formula indicates that all vehicles cannot be charged when the charging station stops business: where d j,t is the state of charge of vehicle j at time t, d j,t ∈ {0, 1}, d j,t = 1 if the vehicle is in charging state, otherwise in non-charging state; is the set of time when bus j is not at charging station, where is the departure time of vehicle j in the kth round, is the return time of vehicle j in the kth round, n j is the total number of rounds vehicle j has to circulate in a day; T close is the time when charging station is closed; Charging station equipment constraint: The number of charging piles simultaneously in charging is less than or equal to the total number N of charging devices in the charging station cs : The maximum power of a single charging pile shall not exceed the safety power P cs ; The following formula indicates that the power distribution capacity of the entire charging station must not exceed the maximum safe power P of the power distribution network of the charging station s : Travel demand constraint: The following formula indicates that the SOC of the vehicle at the departure time of each cycle should be between the ratio of the energy required for a single trip and the maximum energy plus the lower SOC limit soc low and the set maximum SOC soc max : The formula below represents the vehicle j at the kth departure time The formula for calculating the vehicle SOC at the kth departure time, The SOC of the vehicle at the kth departure time is the SOC at the initial time of the day plus the amount of electricity charged into the vehicle before this time, minus the amount of electricity consumed before the trip. The following formula represents that the amount of electricity charged in a day can meet the sum of the required electric energy for a day's travel, ensuring the recyclability of the charging strategy: The following formula shows that the charging behavior of each bus in the time scale is continuous by using the charging strategy: where y j,t and z j,t are the start and end decision variables for controlling consecutive charging for vehicle j after returning to the station, y j,t , z j,t ∈ {0, 1}; is the set of time periods for vehicle j after returning to the station,

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