As an important component of the smart grid, electric vehicles (EVs) could be a good measure against energy shortages and environmental pollution. A main way of energy supply to EVs is to swap battery from the swap station. Based on the characteristics of EV battery swap station, the coordinated charging optimal control strategy is investigated to smooth the load fluctuation. Shuffled frog leaping algorithm (SFLA) is an optimization method inspired by the memetic evolution of a group of frogs when seeking food. An improved shuffled frog leaping algorithm (ISFLA) with the reflecting method to deal with the boundary constraint is proposed to obtain the solution of the optimal control strategy for coordinated charging. Based on the daily load of a certain area, the numerical simulations including the comparison of PSO and ISFLA are carried out and the results show that the presented ISFLA can effectively lower the peakvalley difference and smooth the load profile with the faster convergence rate and higher convergence precision.
Over the past decades, many issues, such as energy shortages, serious environmental pollution, and global warming, have increasingly become worldwide concerns. EVs have emerged as a new traffic tool. Compared with internal combustion engine vehicles (ICEVs), which burn fossil fuels, EVs are driven by electricity. They demonstrate considerable advantages in solving the energy crisis and reducing the emissions of carbon dioxide, as well as in providing a means to drastically reduce the manmade pollution. More and more governments, car manufacturers, and energy companies are getting active in development and production of EVs [
With the largescale introduction of EVs, the power grid will face a significant challenge. Many domestic and foreign scholars have carried out researches on the impact of EVs on power distribution system [
The SFLA is a global optimization algorithm proposed by Eusuff et al. [
In this paper, based on the characteristics of the EV battery swap station, the ISFLAbased optimal control strategy for coordinated charging has been investigated. Through the discretization of the solution vector, an ISFLA based on the reflecting method to deal with the boundary constraint is proposed. The comparison of PSO and ISFLA shows that the presented ISFLA can lower the peakvalley difference and smooth the load profile with the faster convergence rate and higher convergence precision.
As a bioinspired optimization technique, the SFLA is a metaheuristic optimization method, which imitates and models the behavior of frogs searching for food laid on discrete stones randomly located in a pond. In SFLA there is a population, which consists of a set of frogs (solutions). The set of frogs is partitioned into subsets referred to as memeplexes. Different memeplexes are considered as different cultures of frogs, and each memeplex performs a local search. Within each memeplex, the individual frogs hold ideas, which can be influenced by those of other frogs, and evolve through a process of memetic evolution. Frog leaping improves an individual’s meme and enhances its performance towards the goal. After a predefined number of memetic evolution steps, ideas are passed among memeplexes in a shuffling process. The local search and the shuffling processes continue until the defined convergence criteria are satisfied.
The SFLA involves a population of possible solutions defined by a set of
In each memeplex the frogs with the best and the worst fitness are represented by
If
Largescale charging behavior of the EV will have a serious impact on the grid. Coordinated charging of the EV battery swap station can reduce the difference between the growing load peak and offpeak and save the costs of grid operation.
In the EV battery swap station, the typical strategy for battery charging is a twostage method. The first stage has a constant current and limited pressure and the second stage has a constant pressure and limited current. Charging load power can be expressed as
In the first stage, to facilitate the modeling and analysis, the charging voltage is treated as the linear representation of
In order to investigate the optimal control strategy for coordinated charging, the total charging duration
Then an integer
Substituting (
Obviously, the accuracy of (
According to the “technical guide for electric vehicle batteryswap station” presented by the State Grid Corporation of China (SGCC), a single EV battery charger is used to charge a single battery box. Inside the battery box, the battery pack consists of a plurality of battery cells. The battery mentioned in this paper refers to the battery pack. There are two types of batteries in the EV battery swap station, namely, the regulated battery connected to the EV battery charger and participating in the grid charging optimization by controlling its charging start time and the full charged reserve battery disconnected to the charger and used when not meeting the demand for swapping battery. Only the regulatedbattery is considered in this paper.
In order to investigate the optimal control strategy for coordinated charging of the EV battery swap station, some assumptions are made as follows.
: battery
The battery can be swapped into and swapped out of the station at any time in one section. To facilitate the optimal control, we suppose that the battery could be charged from the section next to that of swapping in and be swapped out of the station from the section next to that of full charged. Then the startcharging time
To ensure that all batteries are full charged at the end of the
If there are
Based on assumptions
There are
In this paper, the position of the virtual frog consists of the startcharging time of every battery needed for coordinated charging, so the dimension of solution space is equal to the number
Based on the assumptions,
Dealing with the boundary constraint may affect the performance of the algorithm. In general, there are three basic approaches, namely, absorbing, reflecting, and damping. Using the reflecting method, when the updating position of the frog after
When
when
The overall process of the ISFLA can be described in the following main steps.
Set the parameters of
The initial population is formed by
Firstly sort the
Repeat the following operations for
If the convergence criteria are met, stop and output the best frog
In this ISFLA, the convergence criteria are defined as the maximum number of shuffling iterations for whole population (
In this paper, the optimization objective is one area’s daily load profile which includes the charging loads generated by the EV battery swap station. The optimization period
In the EV market, there are different battery types such as NiMH, Lead Acid, and LiIon. And the market share of LiIon with its technical advantages has increased annually. The “E6 pioneer” EV developed by BYD Co., Ltd., has been configured a LiIon battery with the energy density of 100 W·h per kilogram (i.e., a battery of 600 kg can store power of 60 kW·h for each charging). Its parameters are shown in Table
Basic parameters of battery.
Type 


Constant current charging duration (min)  Constant voltage charging duration (min) 

LiIon  58.8  120  90  150 
In consideration of the charging continuity constraint and based on the battery parameters, the average charging power of each section in the multisection charging model can be calculated and shown in Table
Average charging power of each section.
Section  1  2  3  4 
 
Charging power (kW)  6.45  6.18  2.52  0.85 
A certain area daily load power before regulation can be predicted and shown in Table
Certain area daily load before regulation.
Time (h)  Power (MW)  Time (h)  Power (MW)  Time (h)  Power (MW)  Time (h)  Power (MW) 

1  5.25  7  9  13  8  19  17.75 
2  4.25  8  10.5  14  7.5  20  16 
3  4  9  9.5  15  7.75  21  14.25 
4  4  10  9.25  16  8.25  22  9.75 
5  4.25  11  9.75  17  13  23  7.25 
6  5.75  12  12  18  18  24  5.75 
At the beginning of one optimization period, there are 600 batteries in the swap station, including 350 full charged batteries, 200 unfull changed batteries, and 50 reserved batteries. All batteries except the reserved batteries participate in the optimal control of coordinated charging. By predicting the demand of EV owners for swapping batteries during each optimization section, the number
Predicted number of batteries swapped in during each optimization section.
Time (h)  1  2  3  4  5  6  7  8  9  10  11  12 
 
Number  3  3  1  2  10  18  53  68  46  31  17  24 
 
Time (h)  13  14  15  16  17  18  19  20  21  22  23  24 
 
Number  30  30  37  50  67  42  28  28  25  18  13  6 
The main parameters of ISFLA are set and shown in Table
Parameters of ISFLA.
Parameter 






Value  50  10  5  5  100 
Area load profile under different conditions.
In Figure
Convergence characteristics of ISFA and PSO.
Clearly, the convergence rate of ISFLA is much faster than that of PSO and the minimum variance of the load profile generated by ISFLA is less than that generated by PSO. Under different conditions, the variances of the load profile are shown in Table
Variances under different conditions.
Condition  Uncoordinated charging  Coordinated charging  

ISFLA  PSO  
Variance (kW^{2})  1.836  1.615  1.737 
Result  —  Declining 12.04%  Declining 5.40% 
With ISFLA, the distribution of batteries according to the startcharging time in the optimization period
Distribution of batteries starting charging.
In Figure
For a fixed population
Global convergence value.
Memeplex  5  10  20  40 


1.616  1.615  1.6139  1.6137 
Iterations of ISFLA with different memeplexes.
In Figure
As a main way of energy supply to EVs, the optimal control strategy for coordinated charging of the swap station is very important in smoothing the load profile. Based on the characteristics of the EV battery swap station, a multisection charging power model of battery is presented and an ISFLA in reflecting method to deal with the boundary constraint is proposed to achieve coordinated charging of batteries. In numerical simulations, the comparison of PSO and ISFLA is made, and the results show that the presented ISFLA can effectively lower the peakvalley difference and smooth the load profile with the faster convergence rate and higher convergence precision.
This work was supported by the National HighTech Research & Development Program of China (“863” Program) (Grant no. 2012AA050210), the National Natural Science Foundation of China (Grant no. 51177011), and Provincial Science and Technology Supporting Program (Grant no. BE2011174).