Energy-storage configuration for EV fast charging stations considering characteristics of charging load and wind-power fluctuation

0 Introduction

With the rapid increases in greenhouse emissions and fuel prices,gasoline-powered vehicles are gradually being replaced by electric vehicles (EVs) [1].EVs—as a new type of load—have strong randomicity.The centralized charging of large-scale EVs significantly affects the entire distribution network [2].Building fast charging stations to satisfy the charging demand of EVs is crucial,and infrastructure construction of charging stations for EVs is urgently needed[3].With the requirement of the cooperative generation of renewable energy and traditional units as well as the increase in the permeability of intermittent and random distributed energy in the future distribution network,it is important to cope with the influence of unpredictability in the power system [4].

Numerous researchers have focused on the influence of wind-power fluctuation in the power system.In [5],a confidence interval-based distributional robust real-time economic dispatch method considering the risk related to accommodating wind power is proposed.To reduce the impact of wind-power fluctuation,a spatiotemporal quantile regression algorithm incorporating the advantages of the hybrid neural network and quantile regression is proposed[6],along with a nonparametric probabilistic wind turbine power forecasting method based on empirical dynamic modeling [7].In [8],a method based on deep reinforcement learning is proposed for solving the uncertainties of wind generation.The energy-storage system can mitigate the load shock,and peak-load shifting is used to replace the large electricity consumption during peak hours with energy storage,improving the capacity of the power grid for wind power and increasing the economic efficiency [9].In[10],a method is proposed for improving the photovoltaic capacity of unbalanced distribution networks via robust allocation of battery ESSs.Currently,most research on the ESS configuration is focused on the fast charging stations.For example,in [12],the performance of a supercapacitor storage system is compared with that of other fast charging station storage technologies.In [13],a method using two different storage technologies is proposed for preventing the increase in the peak load.In [14],design criteria for fast charging stations were investigated,and rule-based energy management is used to determine the power between the charging device,ESS,power grid,and installed photovoltaic power-generation device.In [15]and [16],the impacts of charging stations on the medium-voltage grid were discussed.Although the application of ESSs to charging stations is investigated,more work is needed for optimizing the configuration of the ESS in the charging station.The charging station can be combined with the ESS to establish an energy-storage charging station,and the ESS can be used to arbitrage and balance the uncertain EV power demand for maximizing the economic efficiency of EV charging station investors and alleviating the fluctuation on the power system [17].In [18],the value of the ESS in fast charging stations of electric buses is quantified.The ESS as a potential supplement can reduce the charging cost of EVs through electricity price arbitrage and simultaneously reduce the network integration cost of fast charging stations.However,in [18],important factors such as the constraints of the power system,the charging demand of the ESS in charging stations,and the constraints of the charging-station components were ignored.

The effect of EV charging on the distribution network must be studied to optimize the ESS configuration.Numerous researchers have examined the effects of the EV charging load on power grids [19-21].In [11],a preliminary study on the charging-load characteristics and curves of EVs is performed by using the probability method to analyze the effects of EVs on the distribution system.In[22],two modeling methods for describing the chargingstation load were developed by analyzing the impact of the vehicle inflow on the charging load.In [23],model predictive control is applied to the optimal dispatching of distribution networks including EV.It is confirmed that this method can cope with the influence of the load uncertainty of EVs.However,few studies have focused on the application of the load characteristics of EV fast charging stations to the configuration of the ES capacity of fast charging stations.The economic indicators of energy storage are directly affected by factors such as the types,technical characteristics,lifecycle,and other parameters of the ESS [24].At present,owing to the large investment cost of the ESS and the difficulty of recovering the costs in a short time,the energy-storage configuration of EV fast charging stations must effectively cope with unpredictability(including the uncertainty of market power and distributed power supply),considering the potential cost reduction and the life of the ESS loss tradeoff,for realizing economic and efficient operation [25].In [26],the optimization of the battery energy storage system (BESS) layout,capacity and daily (24h) charge and discharge is studied considering economic,environmental and technical targets.However it does not consider the future demand for clean energy in distribution network,nor does it assess the overall value of EV fast charging stations.

On the basis of the foregoing studies,an optimal model for the ESS configuration in fast charging stations of a distribution network is established in this study.Considering the fluctuations of the random wind power as well as the charging load,the optimization objectives of the proposed model are different costs,such as the investment cost,operation cost,maintenance cost,ESS discharging benefit,wind curtailment penalty,and lifecycle cost of the energy-storage battery.Meanwhile,to improve the solving efficiency of the model,the grid power flow constraint is considered,and piecewise linearization is used to cope with the nonlinear part of the target constraint.The energy-storage configuration can not only improve the absorption capacity of volatile clean energy but also alleviate the effect of the impact charging load on the distribution network.GAMS,a platform used to solve mixed integer linear programming problems[27],is used to solve the model,which is set up and transformed in this paper.Finally,to verify the feasibility and effectiveness of the model,a simulation on an improved IEEE-69 bus system is performed to analyze the configuration results of different ES types and the effects of different DG (Distributed Generator) penetration and EV charging load proportions on the ESS configuration and economic efficiency.

1 Uncertain Sequence Scene Model

1.1 Uncertain Wind-Power Modeling

1) Initial scenario generation

a) The wind-power distribution is obtained by making a statistical prediction,which is based on the historical windpower data of typical areas.

b) The nonparametric estimation method is used to obtain the wind-power probability,and a random sampling is generated via a Monte Carlo simulation,where T represents the value of each scene period.In this study,T = 24.

c) The wind power of T time periods in each scene can be represented by a random sequence,for example,T h e w i n d-p o w e r output sequence for scene s can be expressed asThe wind-power output sequence maximizing the uncertainty of random factors is random wind-power output value.

The aforementioned steps can be used to generate an S ×T sampling matrix containing a set of S random scenes for wind power.In this study,1000 scenes are selected.

2) Scenario reduction

The multi-scenario technique is useful for describing stochastic processes.The amount of calculations for the problem,which is based on scenario optimization,mainly depends on the number of scenarios.

Generally,the number of samples obtained via Monte Carlo simulation sampling is large.The scenario cutting technique is used to reduce the number of samples with the accuracy of sample fitting maximally maintained.Then,the calculation efficiency is improved.The scenario reduction technique,which eliminates low-probability scenarios and represents similar scenes with typical scenes,is adopted to form a finite number of scene sets with a certain probability value making them very similar to the original scenario set.Fig.1 shows the annual fluctuation characteristics of the wind power.

For reducing the foregoing S × T sampling matrix to an Ss× Tmatrix,the backwardscenario reductiontechnology is usedin this study [28].Corresponding totheSs wind-power output sequence of each wind-power scene in the following model,theprobability ps correspondingtoeachscenario Ss can be obtained.1000 sets of scenarios are reduced to 10 via the probability scenario reduction.

Fig.1 Characteristics of the annual fluctuation of the wind power

1.2 Load Model of EV Fast Charging Station

First,the charging demand of a certain type of EV is modeled in a certain period of time.Then,the charging demand of EVs with different characteristics is aggregated.Thus,the demand of the fast charging station is obtained.The types of EVs,the capacity of the battery,and their proportion of the EVs number in this study are presented in [29].

1) Probability of EV daily mileage

The daily mileage represents not only the electric energy required for charging the EV connected to the grid but also the energy consumed for transportation in a day.Providing that the vehicle’s daily mileage follows an exponential distribution [30],the distribution f (x ) is given as follows:

Suppose that x is located in the interval Select the average mileage dα,which is calculated via (2) as the interval index.Its probability is given by (3),as shown in Fig.2.

Fig.2 Probability distribution of daily mileage

2) Probability of driving at each time instant

Multiply m (t ) and da to obtain the expected vehicle distance.m(t) represents the probability of driving at time t.

Thus,the battery charge state of the EVk battery at time t can be expressed as follows when the daily mileage of the EV is da:

The energy provided to EVk at time t is given as

where Lk and Δ represent the charge power (kW) and charging time (h),respectively,of the EV.Thus,thecharging demand of car considering the probability of daily mileage F(da) can be expressed as follows:

Then,the expected charging demandof the EVk at time t (taking all possible values of da and their associated probabilities into account) can be expressed as

The expected total charging demand of all the EVs in the period t can be expressed as follows,provided that there are sufficient devices to charge all the EVs arriving at the station:

Finally,to obtain the charging demands of fast charging stations on a typical weekday and weekend,the various EVs’ charging demands are aggregated.Fig.3 shows EVs’expected charging demand curves on a sample weekday and weekend.

Fig.3 EVs expected charging demand on a sample weekday and weekend

2 Optimal Configuration Model of Energy Storage of Fast Charging Station

A schematic of the charge power model of the fast charging station with the energy-storage configuration is presented in Fig.4.The flow direction of the power in the charging station is indicated by the arrows.The charging station obtains power from the power grid,through the transformer.The ESS,which stores and releases power when needed,is connected to the fast charging station by the rectifier.represents the power provided by the substation of node j to the distribution network at time t,and and represent the charge power and discharge power,respectively,of energy storage at time t.represents the charge power of the EV at time t for node j.As shown in Fig.4,when the EVs arrive at the fast charging station,the electricity that they require is provided by the grid or ESS.

Fig.4 Power flow in a fast charging station

2.1 Objective Function

The objective of this study is to minimize the investment and operation costs of the ESS in the charging station by configuring the ESS and EV charging station rationally [31].The objective in the lifecycle is expressed as

where πs represents the probability of wind-power scenario s,CINV represents the investment cost of the EV charging station,COM represents the operation and maintenance cost,TB represents the discharging benefit of energy storage,and CAM represents the wind curtailment cost.

1) Investment cost

The investment cost,which is related to the charge power,discharge power,and rated capacity,can be expressed as follows:

where andrepresent the investment costs of unit charge and discharge power and unit capacity of the ESS,respectively,and and represent the charging and discharge power of the ESS and the capacity of the ESS,respectively.

2) Annual maintenance cost

Here,is the annual average maintenance cost coefficient (yuan/kW/year) of unit power for the ESS,and ir,dr,y,and Ny represent the inflation rate,discount rate [32],battery lifecycle (years),and battery life,respectively.

3) Wind curtailment cost

The wind curtailment cost,which is added to the target cost to adapt to the consumption of clean energy,can be expressed as follows:

where represents the wind curtailment cost coefficient(yuan/kW/year),and and represent the predicted and actual values of the active power for DG,respectively.

4) Discharging benefit

The electricity price is low at a valley load and is typically high at the peak load under the conditions of the power market.To realize arbitrage,the control BESS is used to charge and discharge the grid and EVs during the tough and peak load periods [33].

Here,πt represents the electricity price at time t.

2.2 Constraints

1) Power-flow balance constraints

The power-flow model presented herein is based on the linear distflow simplified power-flow equation.

The power-flow equation contains three parts,which correspond to the nodal active power balance,nodal reactive power balance,and nodal voltmeter calculation.Here,Pij,t and Qij,t represent the active power and reactive power,respectively,of branches flowing from bus i to bus j at time t;represents the reactive power of the substation input to the distribution network; represent the active power and reactive power,respectively,emitted by the DG at time period t; represent the active load power and reactive load power,respectively,at time period t;rji and xji represent the resistance and reactance,respectively,of line ij; and Ui,t represents the voltage of bus i at time t.This model uses as the predicted active power parameter.To participate in the power flow,the optimal scheduling of the charging and discharge power is provided by the ESS in the fast charging station.

2) Node voltage constraint

Here, and represent the lower and upper limits of the voltage amplitude at bus i.In this study,the root node voltage of the network is the reference value 1.Except for the root node,the voltage is allowed to fluctuate between 0.95 and 1.05 (or between 0.93 and 1.07).

3) Branch capacity constraint

Here,Sij,max represents the maximum rated apparent power allowed to pass from node i to node j.

4) Controllable DG output constraints

Here,ωDG ,i represents the maximum proportion of the active output of the DG allowed on node i.Considering that the fan’s output can be adjusted within a certain range,ωDG,i is generally set as 20%-30%.θDG ,t represents the DG power factor angle at time t.represent the lower and upper bounds,respectively,of the power factor angle.Assuming that the DG in this model can regulate the reactive power,it can participate in reactive power optimization.

5) Energy-storage operating constraints

Here,represents the sum of the maximum charge power and discharge power of energy storage.and represent the 0/1 variables of the charging and discharging states at time t,and the sum of the two is equal to 1 at the same time.SOCe,t represents the ES nuclear power state at time t.and represent the lower and upper bounds,respectively,of the ES nuclear power state.µc and µd represent the charging and discharging efficiencies,respectively.

6) Radial network structure constraint

Here,Zij ,t represents the total number of closed branches at scenario s and time t,Nbus represents the total number of nodes,and Nf represents the total number of substations.In this study,considering that the network does not need to be reconstructed,the structure of the network frame remains radial throughout the distribution network operation.

2.3 Branch Capacity Constraint Linearization Method

The foregoing ESS optimal allocation model presents a mixed-integer nonlinear programming problem,and (19)is a quadratic constraint.To solve the foregoing constraints efficiently,the linearization method is used.The feasible region of constraint (19) is inside the circle.To obtain an equivalent linearization representation of the inside of the above power circle,the method proposed in[34]is adopted.As shown in Fig.5,this model uses the area enclosed by the inscribed positive 12-sided shape to replace the circle area,achieving a balance between the accuracy and the computational efficiency.The area enclosed by the inscribed positive 12-sided shapes can be represented as a series of linear constraints.Thus,constraint (19) becomes

The coefficients in (29),which are related to the linearized power circle constraint,change when the sides’lengths of the divided regular polygon change.

3 Case Study

3.1 Case Study System

A simulation of the improved IEEE 69-bus radical distribution network,which is shown in Fig.6,is performed to validate the effectiveness of the proposed method.Table1 presents the parameters of the ESS and DG.This paper focuses on the energy-storage capacity configuration at selected locations.

Fig.5 Diagram of the polygonal inner-linearization method

Fig.6 IEEE-69 bus distribution network with the DG and ESS

Table1 Parameters of the ESS and DG

Parameter DG1 DG2 DG3 DG4 Node 20 32 43 54 Rated capacity (kW) 300 400 300 400

The configuration results of the ESS are affected by the battery type.Thus,ESSs with four different batteries including Vanadium Redox Battery (VRB),Li-ion Battery(Li-ion),Value Regulated Lead Acid Battery (VRLA) and NaS Battery (NaS) were selected to analyze and compare their optimal configurations,as well as the benefits and cost,using the proposed method and model.Table2 presents the parameters of the four types of battery ESSs.

Table2 Parameters of different types of ESSs

Parameter VRB Li-ion VRLA NaS cP E S (yuan/kW) 2982 2996 2100 1750 cE E S (yuan/kWh) 700 1470 1036 1344 cOM ES (yuan/kW/year) 63 70 77 63 T 15 15 10 15 η 70 90 80 80

The inflation and discount rates are 1.5% and 9%,respectively [35].According to the charging characteristics of EVs,two typical days are considered:working days and non-working days.The ratio of working days to nonworking days is 5:2,and each day is divided into 24 h.The electricity price of each time period is presented in Table3 [36].

Table3 Time of use electricity prices

Time Price (yuan/kWh)Peak 11:00-13:00,20:00-21:00 1.4409 High 10:00-15:00,18:00-21:00 1.3222 Shoulder 7:00-10:00,15:00-18:00,21:00-23:00 0.8395 Valley 23:00-7:00 0.3818

3.2 Optimal Configuration Results for Different Types of Energy Storage

The GAMS is used to solve the proposed model and method.Taking ESS1 as an example,the lifecycle configuration results,including the rated power and rated capacity of the four batteries,are presented in Table4.The unit of cost and benefit is 10,000 yuan.

Table4 Configuration results for different types of ESSs

Parameter VRB Li-ion VRLA NaS Pemax/MW 0.49 0.41 0.25 0.48 Wemax/(MW·h) 1.43 1.15 0.7 1.20 CINV(103 yuan) 1206.87 1382.25 1058.34 1034.98 TB (103 yuan) 3946.09 2404.03 2550.24 2903.12 Annual return on investment 21.1% 11.5% 24.1% 18.7%

According to the proposed objective function,different BESSs exhibited different configuration results and investment-income relationships,as shown in Table4.The investment and maintenance cost increases in the following order:VRLA,NAS,VRB,and Li-ion.The total returns increases in the following order:Li-ion,NAS,VRLA,and VRB.

Because the cost and efficiency of different ESSs are different,the ESSs have different economic performance.Compared with VRLA and NAS batteries,although the Li-ion battery is efficient,its unit investment cost is high.Regarding the annual return on investment,VRLA is better than VRB,which has good economy but a short lifecycle.VRB has higher cost performance and economic advantages than the other batteries,which make it more suitable in power-system applications.In this study,VRB is selected as the object of analysis to optimize the ES configuration in the EV fast charging station.

3.3 Energy-Storage Allocation Economy Analysis

VRB is selected as the battery type in the optimal energy-storage configuration,and the model is solved for two cases:with and without the ESS.Table5 presents the relationship between the investment cost and the income for these two cases.

Table5 Costs of different cases

CINV/103 yuan TB/103yuan CAW /yuan COM /yuan Without ESS 0 0 209835.7 0 With ESS 1206.87 3946.09 116388.4 8453289

Table5 indicates the following.1) The ESS configuration increases the investment,operation,and maintenance costs.The total investment cost for the case with the ESS is higher than that without installation.With an increase in the amount of equipment,the operation and maintenance costs increase.2) The wind curtailment cost after the installation of the energy storage is 44.53% lower than that without the energy storage.Fig.7 presents a comparison of the wind curtailment before and after the configuration of the energy-storage,which is the weighted average of 10 windpower scenarios.As shown,the wind-curtailment capacity is significantly reduced with the configuration of the energy storage.However,the wind-abandoning phenomenon cannot be eliminated,because of the wind power load prediction error.Increasing the energy-storage capacity can reduce the wind curtailment,but increases the investment cost.3) The discharging benefit has significant economic advantages.The total discharge income of the ESS in the whole lifecycle is 3,946,090 yuan,which can be recovered in 4-5 years.Thus,the proposed model can reduce the amount of wind curtailment in the distribution network and achieve a high economic value.

Fig.7 Comparison of wind curtailment before and after configuration of the ESS

Fig.8 presents the typical daily load curve of the system whose energy storage is configured according to Table4.As shown,the proposed configuration method can reduce peakto-valley difference,reducing the effect of the EV charging load on the power grid.

Fig.8 Daily load curves before and after configuration of the ESS

3.4 Effect of DG Penetration

The ESS configuration results are different for the different wind-power penetration rates.As shown in Table6,as the wind-power penetration rate increases,the net income of the ESS decreases gradually.The investment cost and discharging benefit of the ESS decrease,while the wind curtailment cost increases.Because of the increase in the wind-power penetration,which offsets the peak load and reduces the discharge benefits,the discharging benefits of the ESS decrease constantly.With an increase in the wind-power penetration rate,the required ESS capacity in the distribution network decreases,which also leads to the investment and construction cost of the ESS decreasing.When the penetration rate increases,the net income gradually decreases with the increase in the wind curtailment cost.

Table6 Configuration results of the ESS under different wind-power penetration rates

Wind-power penetration CINV(103 yuan)TB(103 yuan) CAW (yuan) Net income(103 yuan)10.0% 1462.834 4017.86 51832.6 2648.07 20.0% 1382.287 3953.17 86420.9 2593.23 26.5% 1206.871 3946.09 116388.4 2538.92 30.0% 1149.250 3735.76 785277.8 2438.09 40.0% 1096.679 3527.94 2639840.7 2195.75 50.0% 1013.841 3254.07 3275681.5 1738.56

For satisfying the load demand when the wind-power penetration rate decreases,the ESS capacity required by the distribution network increases.Although the discharging benefit increases slowly,the ESS investment costs increases gradually.The wind curtailment cost decreases.When the penetration rate is ＞50%,the curtailment cost increases rapidly,and the net income decreases sharply.

3.5 Comparative Analysis of Different EV and Wind-Power Models

The proposed configuration,EV deterministic models,and wind-power deterministic models are analyzed and compared [37].Table7 presents the configuration scheme.As discussed in Section 1.2,two typical scenarios (working days and weekends) are considered for calculating the charge power demand of an EV fast charging station.Additionally,the uncertainty scenario of the wind power is considered.

Table7 Configuration results of the ESS under different wind-power penetration rates

Proposed model Deterministic model EV confirmed Wind power confirmed CINV (103 yuan) 1206.87 1465.37 1409.54 TB (103 yuan) 3946.09 3136.47 4271,18 CAW (103 yuan) 11.64 56.37 23.43 Net income(yuan) 2538.92 1739.74 2771.23

Table7 indicates the following.1) The wind-abandoning phenomenon exists in the proposed configuration model.Although the proposed configuration method considers the volatility of the wind power to the greatest extent possible,it cannot solve the problem of wind-power absorption completely,which leads to a certain degree of conservatism.2) Because the proposed model considering EV charging station charging demand,the net income of the proposed model exceeds that of the EV deterministic model.ES plays a role in alleviating the impact of the charging load of the EV,leading to a significant discharge benefit.3) The wind-curtailment cost and net income of the proposed model are low compared with the model whose wind power is determined.The investment and construction costs of the proposed model are more conservative,because the uncertainty fluctuation of the wind power is considered during the configuration process.Thus,the investment and construction costs of ES are small,as are the charging and discharging benefits.

4 Conclusion

This paper proposed an optimized ES configuration method for EV fast charging stations in the distribution network with wind power and EV charging load scenarios.This general configuration method can be applied to EV charging stations with different distributed generation scenarios and different EV charging requirements.First,the EV charging station load-demand model is established,and the wind-power fluctuation is extracted using the scenario method.Then,considering the EV charging load demand and the effects of DG power fluctuations in the fast charging station,the optimal configuration model is proposed.For solving the nonlinear problem,a linearization method is adopted.A simulation using the improved IEEE-69 bus system verified the feasibility and economic benefits of the ES configuration for EV fast charging stations.The analysis results indicate the following.

1) Different types of ESSs differ with regard to economic performance.Thus,investors should conduct comprehensive configuration of the ES for EV fast charging stations with consideration of different characteristics of ES.

2) The proposed method can yield significant economic benefits and reduce the amount of wind curtailment in the distribution system compared with the traditional fast charging station for EVs.It can also substantially reduce the effect of the EV charging load.

3) Owing to the high unit cost of ES and the limitations on the development of ES technology,the proposed method has broad application prospects.

Declaration of Competing Interest

We declare that we have no conflict of interest.