Modeling of fast charging station equipped with energy storage

1 Introduction

In the context of the energy crisis and environment degradation, the energy structure has been accelerating the transition of low-carbon economy, and the electrification of transportation is an important access to realize this transition. As a result, EVs are generally accepted as the clean means of transportation. Compared with traditional fuel vehicles, the pure EVs have shorter driving distance and longer charging time, in order to improve the endurance of the EVs and meet the rapid energy supply during the journey, it is necessary to establish a fast charging station in the appropriate area and plan fast charging facility for the station[1]. However, EVs arrive at charging station randomly and connect to the distribution network for fast charging, which will seriously affect the safe and stable operation of the grid. With the rapid development of battery charging technology, the fast charging mode has a serious impact on the grid. Since the energy storage can improve the electric energy demand of the EVs from the grid, reduce the cost of additional construction and retrofitting brought by the charging station, and promote the electric energy balance of supply and demand between the distribution network and the fast charging station, the energy storage can be used at charging station[2].

Recently, the research about the utilization of energy storage for fast charging station and alleviating the impact of EV charging on the grid has been gradually increasing.In order to realize the flexible interaction of the electric energy between the grid and the charging station, the energy storage system is integrated into the charging station to form a charging-discharging/swapping-storage integrated station [3-6]. The study in [7] optimizes the capacity of energy storage in the fast charging station.It shows that the energy storage not only plays a role in smoothing the load, but also saves the cost of electricity purchase. According to the operational data, the application of energy storage to the electric bus fast charging station can reduce the total cost by 22.85% [8]. Reference [9]proposes a framework to optimize the offering/bidding strategy of an ensemble of charging stations coupled with energy storage. It accounts for degradation of the energy storage, robust scheduling against price uncertainty, as well as stochastic energy demand from EVs. The results show the viability of the proposed framework in providing cost savings to an ensemble of EV charging stations. In[10,11], they apply energy storage and photovoltaic to charging station micro-grid system for reducing the impact of EV charging power on the grid, it is essential to use energy storage to meets the demand for EVs charging, and improve the local photovoltaic consumption. Accordingly,a multidimensional discrete-time Markov chain model is utilized, in which each system state is defined by the photovoltaic generation, the number of EVs and the state of energy storage[12].The work in [13] apply the energy storage in the charging station to buffer the fast charging power of the EVs, it proposed the operation mode and control strategy of the energy storage system, analyzed the dynamic characteristics of the energy storage system at different pulse charging power, and finally verified the rationality of the control strategy.

In this paper, the characteristics of charging load are determined by queuing theory. The two-dimensional continuous time parameter Markov chain is used to describe the state of charging station, and the economic model of charging station is established. Then the paper proposes a method of power quantification to simplify the model, and analyze the influence of the configuration of energy storage under different power limit of grid on the revenue.

2 Load characteristics analysis of fast charging station

The behavior of EVs arrive at the charging station has a great randomness, and the number of vehicle varies with time and follows the Poisson distribution with the parameter λ [14-16]. When EVs arrive at a charging station, they may accept charging service if the charging station has an idle charging facility. Otherwise, they will wait in line, or the EV users would not like to wait and leave the charging station. Charging vehicles obey the firstcome, first-served queuing rule, and the service quality can be described by system blocking rate.

The hybrid queuing system is a combination of waiting queuing system and loss queuing system; it allows a certain length of queuing capacity. When the queuing length exceeds the allowable capacity of the system, the new arrival vehicles are refused to enter the queuing system. Since the initial state of charge of the vehicles are different, assuming that the charging service time (grid charging and storage charging) is subject to the negative exponential distribution with the parameterµ ,the charging duration of the storage system is also subject to the negative exponential distribution with the parameter ν[16], and this paper will not consider the technology level of energy storage. If the charging station has k independent charging piles and the system allows the queuing length to be a finite capacity N, the charging station conforms to a standard M/ M /k /N hybrid queuing system model. Charging station queuing system is life-death process, the process that the EVs arrive at the charging station to receive services is born; birth rate is the arrival rate. The process that the EVs to leave after completing charging service is death, the mortality rate is the service rate.

For theM/ M /k/N hybrid queuing system, assuming that the number of EV at the charging station is n, the arrival rate and service rate are shown below.

When the number of EVs at the charging station meets the equation n＜ N, the system average arrival rate and the system average service rate are as follows.

When the number of EVs at the charging station meets the equation n≥N , the system average arrival rateλ = 0,and the charging station rejects the new arrival vehicles. As result, the system is in a loss state, as shown in Fig. 1.

Fig. 1 State transition relation

M/ M /k/N queuing system steady-state equilibrium equations are as follows[17].

Where πn is the steady-state probability of receiving service for n EVs in the charging station, and

The EVs that exceeding the allowable capacity N will be denied to enter the station, so that the system loss rate is:

The loss rate is the ratio of the number of customers who leave the charging station after ending service to the total number of arrival. It is an important indicator to measure the service quality of the fast charging station queuing system. Given the number of charging pile k,determine the loss rate correspond to different system arrival rate. Thus, it gives the maximum system arrival rate by limiting the system allowable loss rate at the given number of charging pile.

3 State modeling of fast charging station

The EVs get the power from the grid and the energy storage system. Under the condition that certain service quality is guaranteed, the grid provides with a limited charging power to the charging station system and the discharging power of the energy storage system is adjustable. The grid is used to meet the stable charging demand, while the energy storage system is used to meet the random charging demand and buffer the intermittent charging power. The energy flow of the charging station is shown in Fig. 2.

Fig. 2 Energy flow of energy storage fast charging station

3.1 Charging power simplified model

According to the distribution of charging vehicles in traditional gas stations, with reference to the statistics data of Norwegian National Oil Company [18], Monte Carlo simulations of 500 EVs in one day are performed to obtain the curve of load demand and energy storage chargingdischarging power, as shown in Fig. 3. When the charging power demand exceeds the limited power provided by the grid, the energy storage system is discharging to meets the remaining charging power demand. If the grid power is surplus and the storage capacity is not full, the grid will charge the energy storage system.

Assuming there are T charging piles in the charging station, the power of single charging pile is p, the number of grid charging pile is S, and the number of storage charging pile is R. For this reason, the maximum power provided by the grid to the charging station is quantified as S, which means S EVs can be charged at the same time.The capacity of the energy storage system is quantified as R, which is the number of charger provided by the full capacity of the energy storage system during the continuous service time μ, and r is the number of charger quantified by the discharge power of the energy storage system, r＜min{T, S+R}. L is the number of EVs allowed to be queued. Therefore, the fast charging station can theoretically provide S+R EVs for continuous charging service at the same time. Considering the inherent number of charging pile in the charging station, if S+R＞T, the actual number of effective charging pile is T, and the extra arriving EVs will queue. The system will block and deny other EVs arriving when the number of EVs reaches the queue capacity L allowed by the system.

Fig. 3 Daily power curve of charging station load demand and the energy storage for charging and discharging

3.2 Queuing model

Since the energy storage system needs the grid energy supply, the allowable queuing length is equal to the number of quantified charging pile. The service process of charging station is described by M/ M /k / Nqueuing system. Two situations as follows will result customer losing:

1) All charging piles are using for charging, and the number of EVs waiting in line reaches the allowable capacity. The next arriving EV will be refused to come in charging station.

2) Although some idle charging piles can serve, the energy storage system does not have enough power or energy to meet the charging needs and the queuing length reach the ceiling of system, the station refuse other EVs to arrive.

Considering the stochastic assumptions and operating conditions of the fast charging station, the state space of the charging station system is captured dynamically by Markov chain with two-dimensional continuous time, as shown in Fig. 4. One dimension of the state space is the number of EVs that the charging station allowed, include the EVs that are receiving service and waiting in the line. Another dimension is the capacity level of energy storage system.

(i,j)represents two-dimensional state, where 0≤i≤ S + j +L,0 ≤j≤R, for example, the state (0, 0)means that there is no EV charging in the station and the energy storage unit does not store the energy. Likewise, (i, 0)(0 ≤i≤S) indicates that there are i EVs being charged in the station but the storage energy unit still have no energy.(S+j, j) indicates that there is no surplus charging pile or power in the station, the arriving vehicles need to be queued; (S+L+j, j) indicates that the system capacity is full and refuse other EVs to arrive.

The charging process of EVs is consistent with the birth-death Markov chain. The matrix of transfer rate Q and the number of total state φ of the Markov chain as (6)and (7) respectively. It can be seen that the Markov chain is irreducible, normalized and traversed [16].

4 Economic model of fast charging station

This paper analysis the system state under a certain arrival rate without considering the charging at different time, and simplifies the analysis of the impact of different storage capacity at the charging station on economics.The revenue of fast charging station is simplified as the service fee charged for each charging EV, the cost for installation, maintenance, storage purchasing, and the compensation own to customers losing that decline service quality should subtract from the revenue. In order to calculate the revenue of charging station, the random charging model of fast charging station is divided into grid charging state, storage charging state, queuing state and loss state, as shown in Fig. 4.

The charging station obtains the profit by charging the EVs for service fee, and deducting the system cost. The profit calculated as formula (9).

Fig. 4 State space of energy storage fast charging station

Where i(s) represents the total number of EVs in the charging station at the state s, and w is the revenue for charging each vehicle. Cb is the compensation cost for declining the service quality of the charging station caused by customers losing, Ca is the cost for installation,maintenance and storage purchasing.π( s)is steadystate probability at the states≡ (i,j), the steady-state distributionπ can be solved by (10).

5 Example analysis

The birth-death Markov chain with two-dimensional continuous time is used to describe the state of the energy storage fast charging station, it analysis the performance and economy of the charging station by combining the M/ M /k/N hybrid queuing system. Due to the constraint of grid charging power and energy storage system capacity,the energy storage system can not continuously supply power for EVs, so that the state of energy storage system determine the number of EVs accommodated by the charging station. Defined the number of grid charging pile S=5, the queuing length L=S=5, the capacity of energy storage is set as R= 1, ..., 10, EV arrival rate range from 0 to 40.The system loss rate correspond to different arrival rate under different storage capacity can be obtained, as shown in Fig. 5.

As can be seen from the Fig. 5, the loss rate decreases when the capacity of the energy storage system increases.While limiting the loss rate of the fast charging station system, the arrival rate correspond to the different capacity of the energy storage system can be determined. When the EV arrival rate exceeds the service rate, it is a low probability that the energy storage unit being fully charged,as so as R increases, the system loss rate decreases less and less. Therefore, under the high arrival rate, increasing R merely can not effectively reduce the charging station system loss rate.

Fig. 5 System loss rate under different arrival rate

To ensure the service quality of charging stations, the average waiting time for queuing is limited [7]. Assuming that the maximum average waiting time for EVs is 2 minutes, the number of charging pile changes from 1 to 20,and the maximum arrival rate correspond to the number of charging pile is shown in Fig. 6.

Fig. 6 Maximum arrival rate varies with the number of charging pile

For the fast charging station, assuming the service fee of charging EVs w =1.25, the compensation cost of loss caused by the decline in the service qualityC b =1.5, single storage purchasing cost C a =0.4. According to the setting parameters, the model of energy storage fast charging station is simulated as shown in Fig. 7. The simulation takes S=4, R=5 and S=5, R=5.

Fig. 7 Revenue of charging station

The simulation results show that as the EV arrival rate increases, the revenue of charging station firstly increases and then decreases. When the arrival EVs at a low rate,the system cost is high, so the revenue is negative. When the arrival EVs at a high rate, the charging station can not support extra EVs exceeding the queuing capacity and lose a large amount of customers, the service quality of charging station will decline, and result high compensation cost. Meanwhile, the greater the charging power provided by the grid, the higher the arrival rate supported by system,the more the earnings get. Therefore, the system should set a reasonable power limit of grid, configure the appropriate energy storage capacity according to the arrival rate to achieve maximize benefit of charging station.

6 Conclusion

In this paper, the queuing model of fast charging station system is proposed according to the characteristics of EVs charging in station. The Markov chain with twodimensional continuous time is used to describe the state of energy storage fast charging station system. Then the stochastic charging model of fast charging station is established to solve the system state probability.Combining with the queuing theory and economic model,set reasonable power limit of grid, optimize the capacity of storage system. Finally, through the example analysis, it is found that as the energy storage capacity increases, the charging station can serve more EVs. However, under the condition of high arrival rate, the charging power provided by the energy storage system exceeds that provided by the grid; it can not effectively reduce the system loss rate. This paper considers a charging station with a relatively stable arrival rate. As for the arrival rate varies greatly with time,the configuration of the energy storage system should be changed according to the charging load to obtain more profit.

Acknowledgements

This work was Supported by National Key Research Program of China (2016YFB0101800); SGCC Scientific and Technological Project(520940170017); State Grid Shanghai Municipal Electric Power Company Scientific and Technological Projects (5209001500KP).