# Research on Electric Vehicle Charging Scheduling Strategy Based on the Multiobjective Algorithm

Authors: Xuefeng Jiang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Under the influence of the low-carbon economy, the electric vehicles have been vigorously promoted. As the main place for charging, charging stations are classified as unstable loads in the power grid because of the large fluctuation of electricity demand. If a large number of charging stations in the system are not regulated and dispatched, the stability of the system will be greatly affected, so it is vital to further study the scheduling strategy of the cars. In this paper, a scheduling model based on the multiobjective algorithm is established, in which the PSO algorithm is used in the model. And the experimental analysis shows that the model can reduce the average charging time and improve the utilization rate of charging piles.


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## Body

## 1. Introduction

Although the popularity of cars has brought great convenience to the lives of people, automobile exhaust has become the main source of urban air pollution [1, 2]. With the appearance of environmental pollution and energy shortage, electric vehicles are vigorously promoted. The charging time and habits of users are uncertain, and the charging load is random, which improve the difficulty of grid side scheduling. The unreasonable use of battery charging equipment will have a negative impact on power quality, so it is vital to further study the charging scheduling strategy [3, 4]. In the case of meeting the daily power demand, the research on the charging scheduling can not only promote the coordinated development of the system but also provide a reliable basis for the power sector to formulate policies.In recent years, scholars have made a series of research studies on the orderly charging scheduling of electric vehicles from different aspects. From the perspective of operators, reference [5] introduced an ordered charging model whose goal is to maximize economic benefits. By setting the time-of-use price policy to analyze the charging behavior under the dynamic response of the policy, the benefits of the grid side were significantly improved [5]. Taking the minimum charging cost and the optimal charging time as the objectives, references [6, 7] comprehensively analyzed the fluctuation law of regional distribution network load. By dividing the peak and valley periods, the user response behavior under the TOU price strategy was analyzed, which effectively improved the user satisfaction [6, 7]. Based on the prediction of future electricity price, the charging time is optimized from the perspective of dynamic programming [8]. Reference established the optimization model that takes the optimization of network loss of the power system as the goal and the user charging demand as the constraint, and the results show that the network loss, load change, and voltage level of the distribution network are significantly improved [9]. The situation in which large-scale electric vehicles are connected to the grid is considered, which promotes the rational utilization of resources in the distribution network and effectively promotes the coordinated development of the grid [10]. In summary, the objective of the research is relatively single, in which the influence of various factors is not considered.Firstly, this paper introduces the principle of charging scheduling, and then a scheduling model based on the multiobjective algorithm is established, in which the multiple factors is considered. Finally, 200 electric vehicles are selected to make experimental analysis on the charging scheduling model.


## 2. Principles and Methods

### 2.1. Multiobjective Optimization Theory

Multiobjective optimization means that two or more objective functions need to be solved under the same constraint conditions. The composition of multiobjective optimization mainly includes decision variables, objective functions, and constraint conditions. The objective function can be expressed asf1x,f2x,⋅⋅⋅,fmxT, and constraints are generally composed of multiple equality or inequality equations, and their general forms are shown in formulas (1) and (2):(1)minx∈Rnf1x,f2x,⋅⋅⋅,fmx,(2)s.t.gix≤0,j=1,2,⋅⋅⋅,a;hkx=0,k=1,2,⋅⋅⋅,b;where m represents the number of objective functions, gix and hkx represent the constraints.The orderly charging scheduling problem is a multiobjective problem, and there may be contradictory relationships among subobjectives. When solving this problem, it is necessary to coordinate the relationships among subobjectives as reasonably as possible, so that each subobjective function is as close to the optimal solution as possible.


### 2.2. Particle Swarm Optimization

Based on the study of natural population biology, scientists have proposed a series of swarm intelligence algorithms, among which the representative is the particle swarm algorithm. The algorithm originates from the research on the foraging behavior of bird swarm, which makes the search process of the whole group in the solution space from disorder to order. By constantly comparing the fitness of itself and other individuals in the environment, the particles adjust their search direction and gradually approach the optimal solution [11].In this model, the position and velocity of particles represent the solution of the problem, and the relevant information of particles is also changing with the increase of iteration time. When the iteration stops, the problem is solved and the relevant information of the particle represents the solution of the problem [12]. When studying the charging scheduling problem, the key is to establish a connection between the model and the reality. In this paper, the problem to be solved is the matching problem between electric vehicles and charging piles, and the ultimate goal is to make the charging time shortest which includes two aspects, one is the queuing time and the other is battery charging time that may be required in the time station to the charging station. The judgment of the scheme is mainly based on the length of the absolute charging time.Assuming that the iteration number of particle swarm isT=1,2,3,…,t, the velocity and position in the population can be expressed by formulas (3) and (4):(3)Vit=vi1t,vi2t,…,viDt,(4)Xit=xi1t,xi2t,…,xiDt,where Vit represents the velocity vector and D represents the dimension of the search space.After each iteration, the fitness value of each particle is calculated by fitness function. When the number of iterations ist, the optimal position of particle is searched which is denoted as pbestit, and the expression is shown in the following formula:(5)pbestit=Xit=xi1t,xi2t,…,xiDt,where pbestit represents the position with the best fitness, and Xit represents the position vector of the ith particle.The corresponding position update formula is shown in the following formula:(6)xidt+1=xidt+vidt+1,where xidt+1 represents the updated position vector of the ith particle and vidt+1 represents the velocity vector of the ith particle.The flow of particle swarm optimization is shown in Figure1.Figure 1
Flow chart.


## 2.1. Multiobjective Optimization Theory

Multiobjective optimization means that two or more objective functions need to be solved under the same constraint conditions. The composition of multiobjective optimization mainly includes decision variables, objective functions, and constraint conditions. The objective function can be expressed asf1x,f2x,⋅⋅⋅,fmxT, and constraints are generally composed of multiple equality or inequality equations, and their general forms are shown in formulas (1) and (2):(1)minx∈Rnf1x,f2x,⋅⋅⋅,fmx,(2)s.t.gix≤0,j=1,2,⋅⋅⋅,a;hkx=0,k=1,2,⋅⋅⋅,b;where m represents the number of objective functions, gix and hkx represent the constraints.The orderly charging scheduling problem is a multiobjective problem, and there may be contradictory relationships among subobjectives. When solving this problem, it is necessary to coordinate the relationships among subobjectives as reasonably as possible, so that each subobjective function is as close to the optimal solution as possible.


## 2.2. Particle Swarm Optimization

Based on the study of natural population biology, scientists have proposed a series of swarm intelligence algorithms, among which the representative is the particle swarm algorithm. The algorithm originates from the research on the foraging behavior of bird swarm, which makes the search process of the whole group in the solution space from disorder to order. By constantly comparing the fitness of itself and other individuals in the environment, the particles adjust their search direction and gradually approach the optimal solution [11].In this model, the position and velocity of particles represent the solution of the problem, and the relevant information of particles is also changing with the increase of iteration time. When the iteration stops, the problem is solved and the relevant information of the particle represents the solution of the problem [12]. When studying the charging scheduling problem, the key is to establish a connection between the model and the reality. In this paper, the problem to be solved is the matching problem between electric vehicles and charging piles, and the ultimate goal is to make the charging time shortest which includes two aspects, one is the queuing time and the other is battery charging time that may be required in the time station to the charging station. The judgment of the scheme is mainly based on the length of the absolute charging time.Assuming that the iteration number of particle swarm isT=1,2,3,…,t, the velocity and position in the population can be expressed by formulas (3) and (4):(3)Vit=vi1t,vi2t,…,viDt,(4)Xit=xi1t,xi2t,…,xiDt,where Vit represents the velocity vector and D represents the dimension of the search space.After each iteration, the fitness value of each particle is calculated by fitness function. When the number of iterations ist, the optimal position of particle is searched which is denoted as pbestit, and the expression is shown in the following formula:(5)pbestit=Xit=xi1t,xi2t,…,xiDt,where pbestit represents the position with the best fitness, and Xit represents the position vector of the ith particle.The corresponding position update formula is shown in the following formula:(6)xidt+1=xidt+vidt+1,where xidt+1 represents the updated position vector of the ith particle and vidt+1 represents the velocity vector of the ith particle.The flow of particle swarm optimization is shown in Figure1.Figure 1
Flow chart.


## 3. Electric Vehicle Charging Scheduling Model Based on Particle Swarm Optimization

Electric vehicles need to obtain electricity in the power grid irregularly in order to analyze the charging behavior of cars, and the charging characteristics should be clarified first. The charging equipment used by different types of cars are also different, and the charging mode of electric vehicles mainly includes four modes, one is the slow charging, one is the fast charging, one is the power charging, and the other is the wireless charging.Electric vehicle charging scheduling problem belongs to a branch of vehicle scheduling problem which aims to achieve the minimum time-consuming, the shortest path, and the lowest cost under certain constraints by formulating the vehicle route [13]. Vehicle scheduling problem is a NP-hard problem in which the computational complexity increases exponentially with the expansion of the scale.Generally, the vehicle scheduling problem can be divided into two kinds, which are static vehicle scheduling and dynamic vehicle scheduling. In the static vehicle scheduling, the scheduling center will plan the driving path of the vehicle after collecting information such as the location, demand, vehicle speed, and road network environment of the user. The vehicle follows the planned route after scheduling and the route will not change due to other factors. In dynamic vehicle scheduling, the scheduling center plans the driving path after collecting relevant requests from users. After scheduling, the scheduling center will still collect all kinds of real-time information, which can adjust the planning route in real time. The vehicle scheduling process is shown in Figure2.Figure 2
Vehicle scheduling process.The cluster effect of electric vehicle charging should be studied, which means that the influence of a large number of electric vehicles on the distribution network should be studied. Assuming that the charging time is normally distributed and independent of other electric vehicles, the total charging power is shown in the following formula:(7)Pt=∑k=1NPk,t,where k represents the electric vehicle number, T represents the time period number, and N represents the total number of electric vehicles.


### 3.1. Objective Function

From the angle of power grid security and stable operation, the objective function should make the peak load of the power grid as low as possible, and the peak-valley difference and load fluctuation as small as possible. Therefore, the objective function constructed is shown in formulas (8)–(10), which represent the minimum peak load, the minimum peak-valley difference, and the minimum load variance, respectively.(8)f1=min∑i=1NPi,t,(9)f2=minmax∑i=1NPi,t−min∑i=1NPi,t,(10)f3=min1T∑i=1NPi,t−Pav2,where N represents the number of nodes, t represents the time period, and Pav represents the average power of node i.The power quality includes three parts, one is the voltage of power supply system, one is the frequency, and the other is the waveform. In order to ensure the normal operation, the power supply voltage must be stable within the specified range; otherwise, the electrical equipment may fail, fail prematurely, or cannot operate at all. There are two main indicators to measure power quality, one is frequency offset and the other is voltage offset. In this paper, the node voltage is used as the evaluation index of power quality, which is shown in the following formula:(11)f4=min∑t=1T∑i=1NUi,t−Ui,0,where Ui,t represents the voltage of node i, Ui,0 represents the rated voltage of node i.In addition to considering the actual operation, the influence of two factors needs to be considered, one is the economic operation and the other hand is the interests of users. From the economic perspective of power grid operation, the relationship between the operation and maintenance costs and the benefits should be comprehensively considered. This paper also takes into account the input of renewable energy in the region, and the expression is shown in the following formula:(12)f5=minCm+Cs+∑t=1T−Pev,tCt−Pe,tCe,t,where Cm represents the operation and maintenance cost, Cs represents the input cost of renewable energy, Pev,t represents the charging power of electric vehicles, Ct represents the current electricity price, and Pe,t represents the generation power of renewable energy.Time-of-use electricity price is obtained by the electric power company according to the analysis of factors such as the running state in different time periods and the affordability of users in historical data. Under this electricity price mechanism, a day is divided into many time periods whose electricity price is fixed. Generally, a day is divided into several different load periods, each of which lasts for more than 1 hour. The types of load periods are generally divided into three types which are peak period, flat load period, and trough period, and the corresponding prices are set according to the types of load periods. The key content of electric vehicle charging strategy is to guide the charging behavior of users to reduce the expenditure of users and the expression is shown in the following formula:(13)f6=minCa+∑t=1TPev,tCt−CE,where Ca represents the cost of automobile maintenance and CE represents the subsidize electric vehicles.The electric vehicle charging scheduling problem is a complex problem, which needs to be considered in many aspects. This paper only considers the minimum load peak, the minimum peak-valley difference, the minimum load variance, the power quality, the user expenditure, and the grid operation economy and the user interests.


### 3.2. Constraints

In order to ensure the safe use of the battery, the charge and discharge capacity of the battery should not exceed 20% of its rated capacity per unit time. In addition to the battery state constraints, it should also meet the user demand constraints, that is, the charging level of electric vehicles after charging should meet the subsequent use needs of users.In order to ensure the safe operation, the node voltage constraint of the line and the load constraint of the distribution transformer should be satisfied in the charging and discharging process. Therefore, the expression of the definition of the constraint condition is shown in formulas (14) and (15):(14)Ui,min≤Ui,t≤Ui,max,(15)∑i=1NPi,t≤αST,where Ui,min represents the lower limit value for the voltage of node i, Ui,max represents the upper limit value for the voltage of node i, and α represents the efficiency of the transformer.


### 3.3. Electric Vehicle Charging Scheduling Model Based on Particle Swarm Optimization

As a heuristic algorithm, regional particle swarm optimization has inherent advantages in solving large-scale problems. How to establish association between the vehicle charging scheduling problem and the particle swarm optimization algorithm is the key to solve the problem. When using PSO to solve the vehicle charging scheduling problem, we need to number the charging vehicle which is denoted asEVi, and number the charging piles in the road network as Pi. In short, the charging scheduling problem of electric vehicles is to solve the problem of how to match the electric vehicles and charging piles, and the excellent matching scheme makes the vehicles in the system have less time to complete the charging. The time includes the queuing time in the time station and battery charging time which may be required to the charging station.In the algorithm, each particle represents a matching scheme of the vehicle and the charging pile, and the scheme with less time is the optimal scheme. The particle swarm algorithm process is shown in Figure3.Figure 3
Flow chart of the model.The velocity and position of particles are a vector of lengthn in which each component of the position vector represents the vehicle number to be scheduled, and the value saved by each component is the corresponding charging pile number which is in the range of [1, m].In the scheduling strategy, some basic assumptions need to be made. Assuming that the electric energy consumption per hundred kilometers of electric vehicles is certain, and the charging power of electric vehicles is also constant, so the probability density distribution of one-day charging time of electric vehicles can be obtained. The basic assumptions under the conventional charging mode of electric vehicles are as follows:(1)
The power consumption per 100 kilometers of electric vehicles is fixed at 15 kWh.(2)
The electric vehicles starts charging after the last trip back.(3)
Electric vehicles are charged with constant power in the charging process.(4)
Users will fully charge the battery every time they charge.(5)
The parameters such as charging start time, daily driving distance, and charging power are independent of each other, and the charging power and battery capacity are consistent. The daily charging power is the daily driving power consumption, and the maximum mileage of the vehicle is 200 km. The mileage is generated according to the logarithmic normal distribution, and the mileage is calculated according to 200 km when the mileage is greater than 200 km.The optimal scheduling should fully consider the influence of two factors, one is the randomness of charging and discharging and the other is the change of basic load of distribution network. When the load is at a low level, the scheduling goal should be based on economic benefits. When the power grid load is high, the scheduling goal should be based on security. In extreme cases where the power supply capacity is insufficient, the security and stability should be considered firstly.


## 3.1. Objective Function

From the angle of power grid security and stable operation, the objective function should make the peak load of the power grid as low as possible, and the peak-valley difference and load fluctuation as small as possible. Therefore, the objective function constructed is shown in formulas (8)–(10), which represent the minimum peak load, the minimum peak-valley difference, and the minimum load variance, respectively.(8)f1=min∑i=1NPi,t,(9)f2=minmax∑i=1NPi,t−min∑i=1NPi,t,(10)f3=min1T∑i=1NPi,t−Pav2,where N represents the number of nodes, t represents the time period, and Pav represents the average power of node i.The power quality includes three parts, one is the voltage of power supply system, one is the frequency, and the other is the waveform. In order to ensure the normal operation, the power supply voltage must be stable within the specified range; otherwise, the electrical equipment may fail, fail prematurely, or cannot operate at all. There are two main indicators to measure power quality, one is frequency offset and the other is voltage offset. In this paper, the node voltage is used as the evaluation index of power quality, which is shown in the following formula:(11)f4=min∑t=1T∑i=1NUi,t−Ui,0,where Ui,t represents the voltage of node i, Ui,0 represents the rated voltage of node i.In addition to considering the actual operation, the influence of two factors needs to be considered, one is the economic operation and the other hand is the interests of users. From the economic perspective of power grid operation, the relationship between the operation and maintenance costs and the benefits should be comprehensively considered. This paper also takes into account the input of renewable energy in the region, and the expression is shown in the following formula:(12)f5=minCm+Cs+∑t=1T−Pev,tCt−Pe,tCe,t,where Cm represents the operation and maintenance cost, Cs represents the input cost of renewable energy, Pev,t represents the charging power of electric vehicles, Ct represents the current electricity price, and Pe,t represents the generation power of renewable energy.Time-of-use electricity price is obtained by the electric power company according to the analysis of factors such as the running state in different time periods and the affordability of users in historical data. Under this electricity price mechanism, a day is divided into many time periods whose electricity price is fixed. Generally, a day is divided into several different load periods, each of which lasts for more than 1 hour. The types of load periods are generally divided into three types which are peak period, flat load period, and trough period, and the corresponding prices are set according to the types of load periods. The key content of electric vehicle charging strategy is to guide the charging behavior of users to reduce the expenditure of users and the expression is shown in the following formula:(13)f6=minCa+∑t=1TPev,tCt−CE,where Ca represents the cost of automobile maintenance and CE represents the subsidize electric vehicles.The electric vehicle charging scheduling problem is a complex problem, which needs to be considered in many aspects. This paper only considers the minimum load peak, the minimum peak-valley difference, the minimum load variance, the power quality, the user expenditure, and the grid operation economy and the user interests.


## 3.2. Constraints

In order to ensure the safe use of the battery, the charge and discharge capacity of the battery should not exceed 20% of its rated capacity per unit time. In addition to the battery state constraints, it should also meet the user demand constraints, that is, the charging level of electric vehicles after charging should meet the subsequent use needs of users.In order to ensure the safe operation, the node voltage constraint of the line and the load constraint of the distribution transformer should be satisfied in the charging and discharging process. Therefore, the expression of the definition of the constraint condition is shown in formulas (14) and (15):(14)Ui,min≤Ui,t≤Ui,max,(15)∑i=1NPi,t≤αST,where Ui,min represents the lower limit value for the voltage of node i, Ui,max represents the upper limit value for the voltage of node i, and α represents the efficiency of the transformer.


## 3.3. Electric Vehicle Charging Scheduling Model Based on Particle Swarm Optimization

As a heuristic algorithm, regional particle swarm optimization has inherent advantages in solving large-scale problems. How to establish association between the vehicle charging scheduling problem and the particle swarm optimization algorithm is the key to solve the problem. When using PSO to solve the vehicle charging scheduling problem, we need to number the charging vehicle which is denoted asEVi, and number the charging piles in the road network as Pi. In short, the charging scheduling problem of electric vehicles is to solve the problem of how to match the electric vehicles and charging piles, and the excellent matching scheme makes the vehicles in the system have less time to complete the charging. The time includes the queuing time in the time station and battery charging time which may be required to the charging station.In the algorithm, each particle represents a matching scheme of the vehicle and the charging pile, and the scheme with less time is the optimal scheme. The particle swarm algorithm process is shown in Figure3.Figure 3
Flow chart of the model.The velocity and position of particles are a vector of lengthn in which each component of the position vector represents the vehicle number to be scheduled, and the value saved by each component is the corresponding charging pile number which is in the range of [1, m].In the scheduling strategy, some basic assumptions need to be made. Assuming that the electric energy consumption per hundred kilometers of electric vehicles is certain, and the charging power of electric vehicles is also constant, so the probability density distribution of one-day charging time of electric vehicles can be obtained. The basic assumptions under the conventional charging mode of electric vehicles are as follows:(1)
The power consumption per 100 kilometers of electric vehicles is fixed at 15 kWh.(2)
The electric vehicles starts charging after the last trip back.(3)
Electric vehicles are charged with constant power in the charging process.(4)
Users will fully charge the battery every time they charge.(5)
The parameters such as charging start time, daily driving distance, and charging power are independent of each other, and the charging power and battery capacity are consistent. The daily charging power is the daily driving power consumption, and the maximum mileage of the vehicle is 200 km. The mileage is generated according to the logarithmic normal distribution, and the mileage is calculated according to 200 km when the mileage is greater than 200 km.The optimal scheduling should fully consider the influence of two factors, one is the randomness of charging and discharging and the other is the change of basic load of distribution network. When the load is at a low level, the scheduling goal should be based on economic benefits. When the power grid load is high, the scheduling goal should be based on security. In extreme cases where the power supply capacity is insufficient, the security and stability should be considered firstly.


## 4. Example and Result Analysis

In order to evaluate the algorithm, 200 electric vehicles are selected to analyze the charging scheduling problem, 200 electric vehicles whose remaining power is 20%∼40% of the total electricity are randomly generated in the road network. In the case of no scheduling, vehicles usually go to the nearest charging point for charging, which will cause a series of time overhead, the time cost of electric vehicle adopting the nearby charging strategy in the case of no scheduling can be got by the calculation.In order to minimize the charging time, we use the particle swarm charging scheduling algorithm to schedule the above 200 electric vehicles and the fitness evolution curve of the algorithm is shown in Figure4.Figure 4
Fitness evolution curve.The charging time of 200 electric vehicles is shown in Figure5, it can be seen that without dispatching, the total time for electric vehicles to go to the nearest charging pile to charge is 249.52 hours, and the average vehicle time is 74.86 minutes. After using the PSO charging scheduling algorithm, the total charging time of 200 electric vehicles is 177.85 hours, and the average time of each vehicle is 53.36 minutes. Compared with the case without scheduling, the average charging time of each electric vehicle can be saved by 20.5 minutes after using the scheduling algorithm, which can be seen that the average charging time of electric vehicles in the system can be effectively reduced by using the particle swarm optimization charging scheduling algorithm.Figure 5
Average charging time.The load variance of each charging station under the two scheduling strategies is calculated, the variance is 2.94 without scheduling and the variance is 0.52 when the charging scheduling algorithm is used to schedule the vehicle. Compared with the unscheduled case, the use of the charging scheduling algorithm for electric vehicles can effectively reduce the charging time cost of vehicles. In addition, the charging piles of each charging station can be fully utilized through scheduling, which improves the utilization rate of each pile and avoids the idleness of charging piles. The particle swarm vehicle charging scheduling algorithm can not only effectively reduce the average charging time but also improve the utilization rate of charging piles.


## 5. Conclusion

Firstly, this paper introduces the principle of charging scheduling, then a scheduling model based on the multiobjective algorithm is established, in which several factors are considered comprehensively. Finally, 200 electric vehicles are selected for the experimental analysis of the model, and the results show that the model can reduce the average charging time and the charging piles can been fully utilized, which avoids the idle of charging equipment.



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