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.

在以往的教学评价中，教学评价缺乏学生的参与，教师和教育主管部门通常是教学评价的主导，这样的评价结果对于学生而言是被动的。学生很难激发出自主学习的主人翁意识，也无法主动反思和调控自己的学习策略，认识自我。教师在评价中占主导地位就会导致学生不能深刻了解评价标准和学习进程，无法发现和分析学习中的具体问题，无法自己探明下一步的努力方向。此外，教师很难做到对每个学生精准地评价。

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

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.

当然，钱塘县不大，平日里或许也碰过面，眼神躲闪着迟疑着，害羞和期盼都有那么一点儿。狂热痴迷，其实也短暂地出现过。你大概想不到，糙男人李公甫，竟然也曾为了见心上人一面而在大雨里苦等。

与此同时，技术进步、空间结构、交通拥堵对物流业能耗增长起到抑制作用，尤其技术进步在考察期内对物流业能耗增长始终起到抑制作用，这说明提高物流业技术进步，降低能耗强度，对北京物流业能耗下降至关重要。空间结构虽然总体对物流业能耗增长起到了抑制作用，但在大多数年份依然起到了促进作用，所以进一步提高城市的紧凑结构，合理布局城市功能，对缓解物流业能耗压力也具有显著的作用。有趣的是，交通拥堵在考察期内多数年份对物流业能耗增长起到了抑制作用，这可能与近年来北京市采取的机动车限号以及加大道路交通建设有关。

CS野战区是农村幼儿户外混龄区域体育活动开展的主要选择之一，这一活动的形式较为特殊，很大程度上迎合了幼儿的参与兴趣，而且满足了混龄幼儿的不同活动需要。在开展这一活动的过程中，需要设置不同的关卡，如轮胎攀爬、匍匐前进、穿越障碍、通过独木桥等，但是幼儿在刚刚参与这样的活动时，根本不知道这些活动应当如何进行，尤其是对于独木桥和匍匐前进的理解，更存在较大的差异，容易出现许多幼儿直接违规游戏的状况。作为整个游戏活动的指导者，教师有必要对幼儿的活动行为做出约束，规范幼儿的活动行为。一旦幼儿在活动的过程中出现了违规的现象，应该迅速加以纠正。

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

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

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.

Fig. 2 Energy flow of energy storage fast charging station

3.1 Charging power simplified model

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.

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.

4.环境保护。养殖场对环境的影响已成为我们国家的一项基本国策，我们应从特定的自然条件出发，有效利用资源和保护环境，对畜禽养殖、畜产品加工、养殖业粪便处理等方面都做到合理配制和循环利用，切实保护生态环境，有效实施畜粪污综合利用和无害化治理，实现环境友好发展，确保养猪业和环境保护的和谐统一，实现畜牧业的可持续发展。

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.

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

(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

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.

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.

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.

Fig. 7 Revenue of charging station

TND理论提倡邻里社区的最佳规模是半径400m，这样可以保证邻里中心到边界的距离在居民5min步行范围内。目前，工业园区的邻里中心分布已经成形，针对其服务半径不能覆盖所有社区的问题，可以考虑建设多层级的邻里中心，在覆盖盲区或边缘地带建立可以满足基本需求的小型综合服务体，并在城市层面上形成多层级的邻里中心模式。

国内外文献主要从监督与咨询职能、高管薪酬、内部控制质量、盈余管理等多个视角对具有海外背景的独立董事影响企业现金持有水平进行研究。

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).

淮河水系复杂，支流众多，人类活动对流域下垫面影响大，加之治淮工程的不断实施，对产流、汇流及洪水传播时间都有较大影响。近年，极端天气事件明显增多，水旱灾害的突发性、反常性、不可预见性更加突出，特别是小范围、短历时、超强降雨不断出现，成为防汛工作中新的焦点、难点。今后，应继续加强预测预报工作，努力提高预报精度和质量。

（3）分析曲线，随泡制吋间增加，亚硝酸盐含量变化趋势均表现为________，并在第_____天均达到最大值。

References

[1] Li J, Zhang H, Xia X et al (2017) Optimal planning of electric vehicle fast charging facilities in urban areas.Electric Power Construction, 38(01): 17-22

[2] Jia L, Hu Z, Song Y et al (2017) Joint planning of distribution networks with distributed energy storage systems and electric vehicle charging stations. Proceedings of the CSEE, 37(01): 73-84

[3] Lou Y, Zhang Y, Jia Y et al (2013) Research on shifting the grid peak load by EV charging discharging and storage integrative station. Electrical Automation, 35(5): 41-43

[4] Yang M, Liu G, Fang X et al (2013) Discussion on operation mode of charging-discharging-storage integrated station considering power network statuses. Power System Technology,37(5): 1202-1208

[5] Liu F, Yang X, Shi S et al (2015) Economic operation of microgrid containing charging-swapping-storage integrated station under uncertain factors of wind farm and photovoltaic generation, Power System Technology, 39(3): 669-676

[6] Guo B, Niu M, Lai X et al (2018) Application research on large-scale battery energy storage system under Global Energy Interconnection framework. Globle Energy Interconnection,1(1): 79-86

[7] Fang C, Zhang Y, Wang Y et al (2017) Optimized capacity allocation of fast charging station with energy storage based on queuing theory. Modern Electric Power, 34(147): 62-66

[8] Ding H, Hu Z, Song Y (2015) Value of the energy storage system in an electric bus fast charging station. Applied Energy

[9] M. R. Sarker, H. Pandzic, K. Sun and M. A. Ortega-Vazquez(2018) Optimal operation of aggregated electric vehicle charging stations coupled with energy storage, IET Generation,Transmission & Distribution, 12(5): 1127-1136

[10] Cheng Q, Liu L, Cheng Z et al (2016) Real-time operation strategy for PV-based EV charging station considering charging demand and random events. In: Transactions of China Electrotechnical Society, 31(18): 142-150

[11] Su S, Jiang X, Wang W et al (2015) Optimal energy management for microgrids considering electric vehicles and photovoltaic energy storage. Automation of Electric Power Systems, 39(9): 164-171

[12] J. Ugirumurera and Z. J. Haas (2017) Optimal Capacity Sizing for Completely Green Charging Systems for Electric Vehicles.IEEE Transactions on Transportation Electrification, 2017: 565-577

[13] Zhou N, Pu S, Wang Q et al (2013) Control strategy of energy storage buffer system for fast charging electric vehicle station.Power System Protection and Control, 2013(17): 127-134

[14] Li R, Su H (2011) Optimal allocation of charging facilities for electric vehicles based on queuing theory. Automation of Electric Power Systems, 35(14): 58-61

[15] Ge S, Feng L, Liu H et al (2013) Planning of charging stations on highway considering power distribution and driving mileage.Electric Power Automation Equipment, 33(7): 111-116

[16] SafakBayram, George Michailidis (2013) Electric Power Allocation in a Network of Fast Charging Stations. IEEE Transactions on Selected Areas in Communications, 31(7):1235-1246

[17] M. Whaiduzzaman, A. Naveed and A. Gani (2018) MobiCoRE:Mobile Device Based Cloudlet Resource Enhancement for Optimal Task Response, IEEE Transactions on Services Computing, 11(1): 144-154

[18] K. Yunus, H. Z. De La Parra and M. Reza (2011) Distribution grid impact of Plug-In Electric Vehicles charging at fast charging stations using stochastic charging model. In: Proceedings of the 2011 14th European Conference on Power Electronics and Applications, Birmingham, 2011