Virtual Energy Storage-Based Charging and Discharging Strategy for Electric Vehicle Clusters

Abstract

In order to address the challenges posed by the integration of regional electric vehicle (EV) clusters into the grid, it is crucial to fully utilize the scheduling capabilities of EVs. In this study, to investigate the energy storage characteristics of EVs, we first established a single EV virtual energy storage (EVVES) model based on the energy storage characteristics of EVs. We then further integrated four types of EVs within the region to form EV clusters (EVCs) and constructed an EVC virtual energy storage (VES) model to obtain the dynamic charging and discharging boundaries of the EVCs. Next, based on the dispatch framework for the participation of renewable energy sources (RESs) and loads in the distribution network, we established a dual-objective optimization dispatch model, with the objectives of minimizing system operating costs and load fluctuations. We solved this model with NSGA-II and TOPSIS, which guided and optimized the charging and discharging of EVCs. Finally, the simulation results show that the system operating cost was reduced by 7.81%, and the peak-to-valley difference of the load was reduced by 3.83% after optimization. The system effectively achieves load peak shaving and valley filling, improving economic efficiency.

1. Introduction

EVs have bi-directional energy storage capabilities, allowing them to provide power to the grid during peak demand periods and store energy during valley periods. This flexible energy exchange function offers potential support for grid peak shaving [1]. However, different types of EVs have varying battery capacities and charging/discharging power ratings, leading to diverse constraints in terms of optimization. This increased complexity poses challenges for the unified optimization of EVCs.

With the continuous development of V2G technology, many studies have focused on user behaviors. This technology optimizes the charging and discharging process of EVs based on the demand response (DR) mechanism to ensure orderly charging behaviors. Liu et al. [2] modeled the power of EVs based on charging preferences and travel characteristics. He optimized the scheduling of EVs to improve the wind power consumption rate while ensuring the interests of multiple parties, such as wind turbines (WTs) and users. Banol et al. [3] proposed a coordinated optimization method for EV charging based on hierarchical optimization and user satisfaction. The method took into account the complexity of the power system, as well as charging demand and user preferences, in an integrated medium/low voltage network. It improved user satisfaction and reduced the burden on the power system. Yao et al. [4] proposed a fast optimization algorithm considering the joint routing and charging problem of multiple EVs. The experimental results show that the algorithm can effectively solve the joint routing and charging problem of multiple EVs. It performed well in terms of time efficiency and solution quality. Sepetanc et al. [5] proposed an EVC model for charging a fleet of EVs in a single car park. The experimental results show that the method can significantly reduce energy costs and improve charging efficiency. Tang et al. [6] proposed an intelligent charging and discharging strategy based on decision functions. It was applied to EVs in smart grids. The strategy can dynamically adjust the charging and discharging time and power of EVs based on factors such as electricity price, grid load, and the charging demand of EVs. It aimed to maximize the benefits for EVs and the grid.

The orderly charging mechanism mentioned for EVs is mainly based on the DR for charging and discharging optimization. The energy storage characteristics and energy management of EVs themselves are neglected. Considering the energy storage characteristics of EVs, such as battery capacity, charging rate, and discharging efficiency, it can make more effective use of the energy storage capacity of EVs to achieve more intelligent and efficient charging strategies. Wang et al. [7] established an effective and fast EV charging and discharging management model in the day-ahead stage. It optimizes EV charging and discharging in generalized energy storage (GES). Zheng et al. [8] proposed a hybrid energy storage system (ESS) consisting of EVs and supercapacitors. Based on Pontryagin’s minimum principle, he proposed an optimal energy management strategy and simulated the energy management strategy and rule-based energy management strategy. Hu et al. [9] optimized a hybrid energy storage system (HESS) consisting of an EV battery and ultracapacitor and proposed an adaptive wavelet transform-fuzzy logic control energy management strategy based on driving pattern recognition to address the high impact of driving cycles on the energy management system. Eseye et al. [10] investigated the optimization of a combination of EVs in the day-ahead and real-time markets by using EVs as a dynamic ESS by considering the flexibility of flexible loads in a building. It aimed to maximize the total profit of the building microgrid. Wang et al. [11] proposed a fuzzy controlled energy management strategy for a hybrid ESS for EVs. It established accurate battery and supercapacitor models and optimized the fuzzy affiliation function with the objective of minimizing energy loss using a genetic algorithm.

EVs can participate in HESSs for power management; however, the current ESSs are expensive and have long investment cycles. The over-allocation of energy storage capacity will lead to both increased investment costs and the under-capacity of the energy storage devices. It cannot guarantee the high consumption rate of clean energy in the integrated energy system. Li et al. [12] established a VES model for EVs and considered EVVES in the optimal scheduling of the local grid. It reduced the volatility of RESs and improved the revenue of the local grid. Wu et al. [13] developed a control model for an EVVES to participate in grid peaking based on the different operating modes of EVs. The model considered the minimum remaining capacity of the battery, the remaining capacity of the standby trip, and the driving range. Han et al. [14] used a two-stage optimal control method for HESSs based on adaptive noise complete ensemble empirical mode decomposition from the perspective of EV lifetime. It achieved energy management of the EVVES and improved the utilization of RESs. Dai et al. [15] considered a joint VES modeling of EVs participating in the Energy Bureau smart grid to construct an EVVES model. Later, for the optimization of VES, he proposed a continuous rolling optimization algorithm to determine the feasible solution of a high-dimensional, complex, and constrained optimization problem to solve the optimization problem. Zhang et al. [16] established a VES model based on the thermal storage characteristics of buildings. He brought in controllable equipment and VES state metrics and determined the target smoothing power of tie lines by filtering to ensure a power fluctuation smoothing effect.

The relevant research on EVVES has been conducted at home and abroad. Among them, the common use of V2G and EVVESs has been more clearly recognized, but EVVESs are still in their infancy in practical application. The research on EVVESs in the United States, Japan, and other countries started earlier. In the USA, William Kempton of the University of Delaware successfully connected an EV to the grid as a peaking generator [17]. Google announced an investment of USD 10 million to develop EVVES technology. In Japan, Nissan installed bi-directional charging posts at the European Technical Center, in addition to powering them with V2G technology in France. While in New Zealand, Madawala et al. integrated EVs into RESs to power family homes [18]. In Germany, Sauer et al. focused on the impact of V2G in energy storage and replacing GES [19]. Denmark’s use of EV battery storage for wind power on an island has become the largest demonstration of an EVVES. The Shanghai World Expo 2010 introduced the V2G concept, which connects distributed mobile energy storage units to the smart grid in China. Therefore, EVVES is a prominent research focus in EVC in-grid control strategies.

In response to the above problems, we take EVCs as the research object. The main contributions of this paper are as follows:

• The EVVES model is established based on the charge-discharge characteristics of EVCs for a day, including mileage, moments of arrival and departure, battery capacity, and power of charging and discharging.
• According to the VES model, this paper proposes an EVVES optimization charging and discharging strategy, considering two objectives: system operation cost and grid net load variance.
• In this paper, the EVVES optimization charging and discharging strategy is simulated for comparison under three types of scenarios, such as comparisons with irregular charging, real energy storage, and single objectives.

This paper is organized as follows: Section 1 introduces the current state of research on EVs and the VES. Section 2 explains the connotation of VESs. Section 3 analyzes and establishes three models of a single EV, EVC, and EVVES. Section 4 establishes the EVVES optimal scheduling strategy on the basis of Section 2. Section 5 conducts an arithmetic example analysis to compare the optimization results of the three models. Section 5 concludes the paper.

2. The Modeling of VES

VES is an indirect method of storing electrical energy by applying advanced communication control and other technologies to aggregate controllable loads (for example, air conditioners, EVs, and industrial production processes). It transfers the electrical energy demand in the form of a DR and balances the energy of the power system to realize an effect similar to that of charging and discharging in physical energy storage.

2.1. The Single EV Model

The travel characteristics of EVs are the key factors for calculating the charging and discharging loads of EVs. They mainly include EV start charging time (the last return moment), end charging time (the start of the trip moment), daily mileage, and remaining battery capacity (state of charge (SOC)) [20].

Table 1. Data on four types of EVs. (Adapted with permission from Ref. [21]).

Type	Types of Vehicles	Travel Time	Charging Power/kW	Battery Capacity/ kWh	Mileage/ km	Unit Power Consumption/ (km/kWh)
A	Electric taxis	Shift handover or residual power drops to a threshold	8.5	50	300	6–8
B	Electric private cars	Long parking time and plenty of charging time	7	80	400	5–8
C	Electric trucks	Intermittently distributed and relatively stable travel time	5	100	200	4–6
D	Electric buses	Relatively regular travel time and mileage	5	150	250	3–5

shows the data related to the four types of EVs. The trips of different types of EVs are strongly randomized and disorganized in time and space. Different EV users have different loads because of the time of use, daily mileage, and remaining battery capacity. Therefore, compared to other types of EVs, this paper first takes the electric private car as the research object.

In this paper, we use statistics from the 2017 NHTS Travel Report [22]. In order to better analyze the charging and driving behavior of EVs, the data of charging start moment, charging end moment, and daily driving mileage are fitted.

A. 

Probability distribution of daily mileage

Considering that EVs are currently a relatively new type of transportation, their sample size is still small compared to traditional fuel vehicles. Therefore, this paper assumes that the use habits of EV users and fuel car users are basically the same. The daily mileage of EVs follows a lognormal distribution, i.e., $L~Log-N\left({\mu }_s,{{\sigma }_s}^2\right)$. The probability density function is shown in Equation (1).

$$f_s(L)={\displaystyle \frac{1}{L{\sigma }_s\sqrt{2\pi }}}\exp \left(-{\displaystyle \frac{{\left(\ln L-{\mu }_s\right)}^2}{2{\sigma }_s^2}}\right)$$

(1)

where s is the daily mileage, ${\mu }_s$ = 3.4, and ${\sigma }_s$ = 0.86.

It is assumed that EVs are fully charged before each trip. After obtaining the probability distribution of the daily mileage, the probability distribution of the SOC at the last return moment can be derived.

B. 

Probability distribution of return and departure moments for EVs

The return moment, $t_s$, of EVs follows a normal distribution [23], i.e., $t~N({\mu }_t,{\sigma }_t^2)$. Its probability density function is shown in Equation (2):

$$f_t\left(t\right)=\{\begin{array}{ll}{\displaystyle \frac{1}{{\sigma }_s\sqrt{2\pi }}}\exp \left(-{\displaystyle \frac{{\left(t-{\mu }_s\right)}^2}{2{\sigma }_s}}\right)\hfill & {\mu }_s-12<x<24\hfill \\ {\displaystyle \frac{1}{{\sigma }_s\sqrt{2\pi }}}\exp \left(-{\displaystyle \frac{{\left(t+24-{\mu }_s\right)}^2}{2{\sigma }_s^2}}\right)\hfill & 0<x<{\mu }_s-12\hfill \end{array}$$

(2)

where t is the starting moment of charging and discharging, ${\mu }_s$ = 7.42, and ${\sigma }_s$ = 3.54.

C. 

Probability distribution of battery capacity

At present, there are many differences in the battery capacity of different EVs. From Table 1, it can be seen that most EV battery capacities are distributed between 60–70 kWh. The probability density function is Equation (3).

$$f_{ϵ}\left(x\right)=\{\begin{array}{ll}{\displaystyle \frac{1}{10}}\hfill & \hspace{1em}60\le x\le 70\hfill \\ 0\hfill & \hspace{1em}\mathrm{others}\hfill \end{array}$$

(3)

In Equation (3), a uniform distribution in the range of 60–70 kWh is selected in this paper to represent different battery capacities for the convenience of subsequent calculations.

D. 

Probability distribution of charging and discharging power

The charging and discharging process of the electric private car studied in this section is conventional slow charging and discharging over a long time. In contrast, the start and end stages of the process can be simply treated. Therefore, the charging and discharging process of a single EV can be simplified as a horizontal straight line under the P-t coordinate axis.

In summary, the electrical load of a single EV is obtained through Monte Carlo simulation, and the charging and discharging process model of the EV is further obtained:

$$\{\begin{array}{l}SO{C}_{\mathrm{EV}}={\displaystyle \frac{L_{\max }-L}{L_{\max }}}\\ W=\rho L={\displaystyle {\int }_{t_s}^{t_e}(P_c+P_{\mathrm{d}})dt}\end{array}$$

(4)

where $L_{\max }$ is the maximum daily mileage of the EV; $\rho$ is the power consumption per unit distance traveled by the EV (KW·h/km), as shown in Table 1; $t_s, t_e$ are the start and end moments of the charging and discharging of the EV, respectively; $P_c, P_d$ are the charging and discharging power of the EV, where, $P_d$ is negative. $W$ is the total energy after charging and discharging.

2.2. The EVC Model

A residential region containing EV charging and discharging and RES power generation is assumed, and we establish the EVC model based on the region. Different types of EVs have different driving behaviors and charging characteristics [24]. EVs cannot be considered as a single charging model solution. Therefore, on the basis of the single model of EVs, the four types of EVs in the region are formed into n EVCs to solve the EVC model.

Firstly, we look at the different types of EVs in a single EVC k (k = 1, 2, …, n):

A. 

EVC charging and discharging power

$$\{\begin{array}{l}{P}_{\mathrm{EVs},k}^{ch}(t)={\displaystyle \sum _{i=1}^t{\displaystyle \sum _{j=A}^D{N}_{EV,j}\cdot P_{EV,j}^{ch}(t)}}\\ P_{\mathrm{EVs},k}^{dis}(t)={\displaystyle \sum _{i=1}^{24-t}{\displaystyle \sum _{j=A}^D{N}_{EV,j}\cdot P_{EV,j}^{dis}(t)}}\end{array}$$

(5)

where $P_{EV\mathrm{s},\mathrm{k}}^{ch}(t), P_{EV\mathrm{s},\mathrm{k}}^{dis}(t)$ are the charging and discharging power of EVC k, respectively; $N_{EV,j}$ is the number of EVs of type j in EVC k; $P_{EV,j}^{ch}(t), P_{EV,j}^{dis}(t)$ are the charging and discharging power of EVs of type j, respectively; A, B, C, and D are four types of EVs; t is the total charging time of EVC k in a day.

B. 

Capacity of EVCs

$$N_{\mathrm{EVs},\mathrm{k}}=N_{\mathrm{EV},A}+N_{\mathrm{EV},B}+N_{\mathrm{EV},C}+N_{\mathrm{EV},D}$$

(6)

$$S_{\mathrm{EVs},\mathrm{k}}(t)={\displaystyle \sum _{j=1}^{N_{\mathrm{EVs},k}}(W_j(t)-W_j^0)}$$

(7)

where $N_{EV\mathrm{s},\mathrm{k}}$ is the total number of EVs in EVC k; $N_{EV,A},N_{EV,B},N_{EV,C}$, and $N_{EV,D}$ are the number of EVs in A, B, C, and D, which are the four types of EVs; $S_{EV\mathrm{s},\mathrm{k}}(t)$ is the charging and discharging capacity of EVC k; $W_j(t)$ is the current residual power of the jth EV; $W_j^0$ is the minimum power required (initially) by the jth EV.

In this paper, it is assumed that n EVCs exist in region i. The total EVC charging and discharging power, capacity, and SOC in region i are obtained by using Equation (8):

$$\{\begin{array}{l}{P}_{\mathrm{EVs}}^{ch}(t)={\displaystyle \sum _{k=1}^n{P}_{\mathrm{EVs},k}^{ch}(t)}\\ P_{\mathrm{EVs}}^{dis}(t)={\displaystyle \sum _{k=1}^n{P}_{\mathrm{EVs},k}^{dis}(t)}\\ S_{\mathrm{EVs}}(t)={\displaystyle \sum _{k=1}^n{S}_{\mathrm{EVs},k}(t)}\\ SO{C}_{\mathrm{EVs}}=S_{\mathrm{EVs}}(t)/S_{\mathrm{EVs}}^N(t)\end{array}$$

(8)

where $P_{EVs}^{ch}(t), P_{EVs}^{dis}(t)$ are the total charging and discharging power of EVCs in region i, respectively; $S_{EVs}(t)$ is the total capacity of the EVCs in region i; $S_{EVs}^N(t)$ is the total rated capacity of the EVCs; $SO{C}_{EVs}$ is the total SOC of the EVCs.

2.3. The EVVES Model

Based on the EVC model and the region, multiple EV batteries are aggregated into an equivalent VES unit for scheduling in a dispatch center. The variables of EVVES charging and discharging are needed for the dispatch optimization calculation, including charging and discharging power and available energy storage capacity. Initially, we need to determine the number of EVs in the area during different time periods. The maximum number of EVs at time t is obtained by maximizing and minimizing the original number.

$$\max N_{\mathrm{EV},i}(t)=N_{EV,i}(t-1)+\max N_{\mathrm{EV},i}^{arrive}(t)-\min N_{\mathrm{EV},i}^{leave}(t)$$

(9)

where $N_{EV,i}(t)$ is the number of EVs in region i at time t; $N_{EV,i}^{arrive}(t)$ is the number of EVs arriving in region i; $N_{EV,i}^{leave}(t)$ is the number of EVs leaving in region i.

The number of EVs at time t is limited to the number of charging piles and the maximum number of EVs in region i. When the number of charging piles is small, the number of EVs is limited to the number of charging piles, $N_{EV,i}(t)=N_{p,i}$. Conversely, when there is a surplus of charging piles, ${\mathrm{N}}_{EV,i}(t)=\max N_{EV,i}(t)$. Therefore, the number of EVs is shown in Equation (10):

$${\mathrm{N}}_{\mathrm{EV},i}(t)=\min \{N_{p,i},\max N_{\mathrm{EV},i}(t)\}$$

(10)

where $N_{p,i}$ is the number of charging piles.

The available energy storage capacity that the EVVES can provide is not only related to the number of EVs but is also related to the EV’s physical condition (starting SOC, battery capacity, power, efficiency, 100 km power consumption, etc.), all-day stopping status, and user driving demand. In this paper, the EVVES model is obtained based on the above considerations, as shown below:

A. 

Capacity of the EVVES

The current charging and discharging capacity of EVs in the region is obtained by subtracting the current remaining power of the EVs from the initial required power.

$$S_{\mathrm{EVVES},i}(t)={\displaystyle \sum _{j=1}^{N_{\mathrm{EV},i}(t)}(W_{j,i}(t)-W_{j,i}^0)}$$

(11)

where $S_{EVVES,i}(t)$ is the energy storage capacity of the EVVES in region i at time t; $W_{j,i}(t)$ is the current remaining power of the jth EV in region i; $W_{j,i}^0$ is the initial minimum power required by the jth EV.

The rated capacity of the EVVES is obtained from the rated capacity of the energy storage of EVs, as shown in Equation (12):

$$S_{\mathrm{EVVES},i}^N(t)={\displaystyle \sum _{j=1}^{N_{\mathrm{EV},i}(t)}(W_{j,i}^N(t)-W_{j,i}^0)}$$

(12)

where $S_{EVVES,i}^N(\mathrm{t})$ is the rated capacity of the EVVES at time t; $W_{j,i}^N(t)$ is the rated capacity of energy storage of the jth EV.

The Charging and discharging sequence of the EVVES is shown in Figure 1. Figure 1 shows the charging and discharging sequence of the EVVES. The time when the EVCs stop in the region can be divided into two parts, where ① is the period when the EVCs are fully charged and ② is the period when the EVCs are alternately charged and discharged.

In Figure 1, EVCs enter region at time t_s, stop to charge and leave at time $t_e$. Based on this situation, we designed the charging and discharging sequence of the EVVES. The EVCs are first sequentially charged in ① until the EVCs are fully charged. They then perform alternating charging and discharging at time $t_c$ until the EVCs finally leave the region. Charging and discharging exist synchronously in ②, so the time slots of ② are generally even. When the time slots of ② are odd, the EVC has charging demands but the remaining time cannot maintain it fully charged. Therefore, the invalid time needs to be removed to ensure that ② is even.

As a result, the total charging capacity $S_{EVVES,i}^C(t)$ and the total discharging capacity $S_{EVVES,i}^D(t)$ of the EVVES at N time periods are obtained based on the rated capacity of charging and discharging and the capacity at time t, as shown in Equations (13) and (14):

$$S_{\mathrm{EVVES},i}^C(t)=\{\begin{array}{ll}{\displaystyle \sum _{j=1}^{N_{EV,i}(t)}(S_{\mathrm{EVVES},i}^N(t)-S_{\mathrm{EVVES},i}(t))}& t_s<t\le t_c\\ {\displaystyle {\sum }_{t=t_c+1,t_c+3,\dots }^{t_{ch}}{\displaystyle \sum _{j=1}^{N_{EV,i}(t)}(S_{\mathrm{EVVES},i}^N(t)-S_{\mathrm{EVVES},i}(t))}}& t_{\mathrm{c}}<t\le t_{\mathrm{e}}\end{array}$$

(13)

$$S_{EVVES,i}^D(t)={\displaystyle {\sum }_{t=t_c,t_c+2,\dots }^{t_{dis}}{\displaystyle \sum _{j=1}^{N_{EV,i}(t)}(S_{EVVES,i}(t)-0) t_{\mathrm{c}}<t\le t_{\mathrm{e}}}}$$

(14)

where $S_{EVVES,i}^C(t)$ is the total charging capacity of the EVVES at time t; $S_{EVVES,i}^D(t)$ is the total discharging capacity of the EVVES at time t; $t_c$ is the time for an EV to be fully charged; $t_{ch}$ and $t_{dis}$ are the end moments of charging and discharging of the EVVES, respectively, with the charging moment $t_{ch}=t_c+2\lfloor {\displaystyle \frac{t_{end}-t_c}{2}}\rfloor -1$ and the discharging moment $t_{dis}=t_c+2\lfloor {\displaystyle \frac{t_{end}-t_c}{2}}\rfloor -2$.

B. 

SOC of the EVVES

It is assumed that the EV batteries in the EVVES are all in constant power operation mode and that every EV can be in continuous service. The SOC of the EVVES is obtained from the available capacity of the EVVES and the rated capacity, as shown in Equation (15):

$$SO{C}_{\mathrm{EVVES},i}(t)=S_{\mathrm{EVVES},i}(t)/S_{\mathrm{EVVES},i}^N(t)$$

(15)

C. 

Charging and discharging power of the EVVES

In this paper, it is assumed that EVs are charged to the rated capacity on the basis of the original capacity for subsequent trips. EV users discharge EVVES with available capacity when they feed the power back to the grid for sale. The charging and discharging power of EVVES is shown in Equation (16):

$$\{\begin{array}{l}{P}_{\mathrm{EVVES}}^{ch}={\displaystyle \frac{S_{\mathrm{EVVES},i}^C(t)}{T}}\\ P_{\mathrm{EVVES}}^{dis}={\displaystyle \frac{S_{\mathrm{EVVES},i}^D(t)}{T}}\end{array}$$

(16)

where $P_{EVVES}^{ch}, P_{EVVES}^{dis}$ are the charging and discharging power of the EVVES, respectively; T is the charging and discharging time period. Therefore, we obtain the EVVES boundary of charging and discharging, which provides the basis for realizing the optimal scheduling strategy of the EVVES.

In the section, Equations (1)–(4) are the energy storage characteristics of a single EV; Equations (5) and (8) are the energy storage characteristics of the EVC; Equations (13)–(16) are the energy storage characteristics of EVVES in this paper. The model provides the basis for the subsequent optimized scheduling strategy for EVVES.

3. EVVES Optimized Scheduling Strategy

3.1. Uncertainty in PV and WT

In a high percentage RES distribution network, there is significant uncertainty in the output power of wind and PV power. It is difficult to accurately model and predict this. However, this uncertainty can be overcome by an approach based on the prediction results [25]. We calculate its uncertainty range to obtain Equation (17):

$$\{\begin{array}{l}{\tilde{P}}_{\mathrm{PV},t}=P_{\mathrm{PV},t}(1+{\eta }_{PV}{\rho }_{PV}){\eta }_{\mathrm{PV}}\in \left[-1,1\right]\\ {\tilde{P}}_{\mathrm{WT},t}=P_{\mathrm{WT},t}(1+{\eta }_{\mathrm{WT}}{\rho }_{\mathrm{WT}}){\eta }_{\mathrm{WT}}\in \left[-1,1\right]\end{array}$$

(17)

where ${\tilde{P}}_{PV,t},{\tilde{P}}_{WT,t}$ are the output power of PV and WT with uncertainty, respectively; ${\eta }_{PV},{\eta }_{WT}$ are the direction coefficients of the power generation prediction errors for PV and WT, respectively, in the range of [−1, 1]; ${\rho }_{PV},{\rho }_{WT}$ are the error coefficients of the power output estimation for PV and WT, respectively.

3.2. Objective Function

In order to promote the motivation of operators and EV users to participate in the consumption of RES, as well as to consider the constraints on the safe operation of the grid, a multi-objective function that minimizes the operating costs in the region and the mean squared deviation of the grid load is established as follows:

A. 

System operating cost objective

For charging operators, the objective is to minimize the cost of V2G modulation. The objective function of the optimization model is as follows:

$$\min C_{total}={\displaystyle \sum _{t=1}^T\left(C_{INV}(t)+C_{grid}(t)+{\displaystyle \sum _{i=1}^M{C}_{\mathrm{EV},i}(t)}\right)}$$

(18)

where $C_{total}$ is the total cost of V2G modulation; $C_{INV}$ is the investment cost in the region; $C_{EV}$ is the EV charging and discharging cost; and M is the total number of EVs in the region.

There are investment costs $C_{INV}$ for the construction of PV and WT in the region and regular investment in maintenance and operation:

$$C_{INV}(t)=f_{\mathrm{WT}}\times S_{\mathrm{WT}}(t)+f_{\mathrm{PV}}\times S_{\mathrm{PV}}(t)$$

(19)

where $f_{PV},f_{WT}$ are the individual investment costs (CNY/kW) of PV and WT, respectively, in the region; $S_{PV}(t)$ is the operation scale (capacity) of PV, $S_{PV}(t)={\displaystyle {\int }_{t_s}^{t_e}{\tilde{P}}_{PV,t}\cdot \Delta t}$; $S_{WT}(t)$ is the capacity of WT, $S_{WT}(t)={\displaystyle {\int }_{t_s}^{t_e}{\tilde{P}}_{WT,t}\cdot \Delta t}$.

$C_{grid}(t)$ is the cost of purchasing electricity from the grid from the microgrid, as shown in Equation (20):

$$C_{grid}(t)=f_{grid}\times S_{grid}(t)$$

(20)

where $f_{grid}$ contains the price of electricity in the time period of time t, which can be a step, peak and valley, time-sharing, or real-time price; $S_{grid}(t)$ is the capacity of the region to purchase from the grid.

Guided by the auxiliary peaking price, the EVVES costs consist of the cost of EV charging, the benefit of EV participation in grid peaking, and the charging and discharging losses in batteries. Thus, there are costs, as shown in Equation (21):

$$C_{\mathrm{EV},i}(t)=f_{ch}-f_{dis}+f_{ess}$$

(21)

$$\{\begin{array}{l}{f}_{dis}={\displaystyle \sum _{j\in {\mathrm{N}}_{EV,i}(t)}(c_{dis,t}+d_{dis,t})}{P}_{EVVES}^{dis}\Delta t\\ f_{ch}={\displaystyle \sum _{j\in {\mathrm{N}}_{EV,i}(t)}(c_{ch,t}+d_{ch,t})}{P}_{EVVES}^{ch}\Delta t\end{array}$$

(22)

where $f_{ch},f_{dis}$ are the EVVES cost of charging and discharging, respectively; C is the cost of charging and discharging losses in batteries; $c_{dis,t},c_{ch,t}$ are the price of discharging and charging EVs, respectively; $d_{dis,t},d_{ch,t}$ are the compensation/penalty price, respectively, for participating in peaking at time t.

B. 

Grid net load variance objective

The access of large-scale distributed uncontrolled WT, PV, and EV charging loads will affect the normal operation of the grid. Therefore, this objective collects daily loads at 1 h intervals and issues dispatch instructions to establish the optimization objective of minimizing the standard deviation of the system net load. The objective function is as follows:

$$\min \delta ={\displaystyle \frac{\sqrt{{\displaystyle \sum _{t=1}^N(P_{NL,t}-}{P}_{ave}{)}^2}}{N}}$$

(23)

where $\delta$ is the net load variance of the grid; $P_{NL,t}$ is the net load of the grid; $P_{ave}$ is the equivalent average load of N time periods per day.

The net load of the grid is jointly composed of traditional load, RES output, and the EVVES proposed in this paper, where the RES includes distributed WT and PV with uncertainty. They are shown in Equations (24) and (25):

$$P_{NL,t}=P_{L,t}+P_{\mathrm{EVVES},t}-P_{RDG,t}$$

(24)

$$P_{RDG,t}={\tilde{P}}_{\mathrm{PV},t}+{\tilde{P}}_{\mathrm{WT},t}$$

(25)

where $P_{L,t}$ is the traditional load of the distribution network at time t, $P_{RDG,t}$ is the RES output at time t; $P_{EVVES,t}$ is the charging and discharging load of the EVVES at time t.

According to Table 1 and Equation (16), there are four types of EVs in region i. The EVVES consists of the charging and discharging power of four people. Where A, B, C, and D are charged, and B and C can be discharged in the EVVES due to abundant charging time and relatively long parking time. Thus, $P_{EVVES,t}$ can be expressed as per Equation (26):

$$P_{\mathrm{EVVES},t}=P_A^{ch}+P_B^{ch}+P_C^{ch}+P_D^{ch}+P_B^{dis}+P_C^{dis}$$

(26)

$P_{ave}$ is the average of equivalent loads (N time periods), as shown in Equation (27):

$$P_{ave}={\displaystyle \frac{{\displaystyle \sum _{t=1}^{96}(P_{L,t}+P_{\mathrm{EVVES},t}-P_{RDG,t})}}{N}}$$

(27)

3.3. Constraints

The EVVES can be regarded as an ESS that dynamically manages and optimizes the allocation of distributed energy resources (DERs). In order to internally ensure stability and minimize the cost of energy consumption for EV users, it is necessary to balance the supply and demand of RESs and loads in the system, and the capacity, charging, and discharging power in the system must meet its own constraints during operation. At the same time, the system capacity and charging and discharging power must meet their own constraints during operation. The above conditions, together, constitute the constraints of system operation, as follows:

A. 

Power balance constraint

$$P_{grid,t}+P_{\mathrm{RDG},t}+P_{\mathrm{EVVES},t}^{dis}=P_{L,t}+P_{\mathrm{EVVES},t}^{ch}$$

(28)

where Equation (28) is the power balance constraint. The left side of the equation is the energy gained, which contains the power purchased from the grid, generated from RES, and discharged from the EVVES. The right side of the equation is the energy consumed, which contains the power loads consumed and charged by the EVVES.

B. 

EVVES charging and discharging constraints

The SOC of the EV battery is affected by charging and discharging efficiency and the state of the battery at the previous moment. The SOC at the current moment is

$$SO{C}_{j,i}(t)=SO{C}_{j,i}(t-1)+{\displaystyle \frac{\left({\eta }_{j,ch}{P}_{j,t}^{ch}-\frac{P_{j,t}^{dis}}{{\eta }_{j,dis}}\right)\Delta \mathrm{t}}{S_{EVVES,i}^N(t)}}$$

(29)

$$SO{C}_{j,i}(t-1)\in \left[SO{C}_{j,i}^{\min },SO{C}_{j,i}^{\max }\right]$$

(30)

where $SO{C}_{j,i}(t)$ is the SOC of the jth EV in region i; $SO{C}_{j,i}^{\min },SO{C}_{j,i}^{\max }$ are the minimum and maximum allowable load states, respectively, of the jth EV battery in region i.

C. 

EV battery current constraint

The EV battery constraint is mainly composed of the current constraint and the capacity constraint. EV users have a wide variety of travel demands. The types of EVs and battery losses also are different. Therefore, the EVVES current constraint should make the charging and discharging power of EVs no higher than the rated charging and discharging power, as shown in (31):

$$\left|P_{j,i}(t)\right|\le P_{bat}^N$$

(31)

where $P_{j,i}(t)$ and $P_{bat}^N$ are the charging and discharging power and rated power of the EVVES, respectively.

D. 

EV battery capacity constraint

When constructing the EVVES in region i, the initial minimum power required for the jth EV needs to be less than the rated charging and discharging capacity of the EV.

$$W_{j,i}^N(t)-W_{j,i}^0>0$$

(32)

Meanwhile, it is assumed that the current charging and discharging capacity of the EVVES is more than 0:

$$S_{\mathrm{EVVES},i}(t)>0$$

(33)

E. 

Users’ satisfaction constraint

Users’ satisfaction is related to the cost of charging $f_{ch}$ and the total cost of EV users $C_{EV,i}(t)$. The more users cost, the lower the satisfaction. Conversely, the lower the users’ cost, the higher the satisfaction.

$$D_{\mathrm{EVVES}}=1+{\displaystyle \frac{f_{ch}-C_{EV,i}(t)}{f_{ch}}}$$

(34)

where $D_{EVVES}$ is the users’ satisfaction with charging.

In Section 3.2 and Section 3.3, Equations (18) and (23) are the objective functions of this paper, which include the minimization of cost and load fluctuation; Equations (28), (29), (31), (32) and (34) are the constraints of this paper, and they provide constraints for Equations (18) and (23) in terms of power, capacity and users’ satisfaction.

3.4. Model Solution

A. 

The NSGA-II algorithm

NSGA-II is an evolutionary algorithm for solving multi-objective optimization problems [26,27]. It utilizes the fitness of individuals within a population to stratify the current population by using fast, non-dominated sorting. In the same layer, there is no dominance relationship between individuals. In order to increase the diversity of the population, NSGA-II introduces the concept of crowding. It is used to measure the denseness of individuals in the neighborhood of the solution and to evaluate the superiority or inferiority of individuals within the same layer. Finally, NSGA-II uses an elite sampling strategy to mix parent and offspring individuals to reduce the loss rate of good individuals. It increases the evolutionary speed of the population and enhances the practicality of the algorithm. The flowchart of the algorithm is shown in Figure 2.

Figure 2 illustrates the flowchart of NSGA-II, which is divided into three main parts:

• The first part is the initial definition. We first initialize the population and determine the number of objective functions and the size of the population. Next, we perform an undominated sorting to determine the number of each individual that is dominated and the set of solutions that dominate the other solutions [28]. Through selection, crossover, and mutation operations, we preserve the diversity of individuals in the population;
• The next part is the elite selection. We evaluate the number of new populations after a parent-children merger and perform a fast, non-dominated sorting of these individuals. Based on the calculated crowding, we select individuals to retain those with higher fitness;
• The final part is iteration. We continuously perform selection, crossover, and mutation until the predetermined number of iterations is reached.

B. 

The Topsis method

The common methods for the comprehensive evaluation of optimization results mainly include the analytic hierarchy process (AHP), fuzzy comprehensive evaluation (FCE), factor analysis (FA), the TOPSIS method, and so on [29]. AHP and FCE belong to the subjective assignment method. It requires a high level of knowledge reserves and judgment from researchers to determine the weights of the indicators. The FA and TOPSIS methods belong to the objective assignment method. FA requires a lot of data, and it is difficult to determine the actual significance of new variables after dimensionality reduction. The TOPSIS method has no specific requirements for data sources or evaluation objects. The method is relatively simple, and the results produced are more objective and scientific.

After comparing and analyzing the above evaluation methods, we selected the TOPSIS method for our comprehensive evaluation. The TOPSIS method evaluates the relative advantages and disadvantages of each observation object by measuring the distance of the observation object relative to the best and the worst. In this paper, the weights of the two objectives were determined first. Then, the TOPSIS method was used to carry out the comprehensive evaluation to obtain the optimal solution.

C. 

Model-solving procedure

The solution flow of the overall optimization scheme is shown in Figure 3 and is detailed as follows:

Step 1: Input the data. The operating costs of RESs and EVVES in the distribution network are calculated to obtain the total system operating cost.

Step 2: Randomly generate the initial population. Based on the cost objective and load fluctuation objective, calculate the individual objective function values that satisfy constraints.

Step 3: Perform fast, non-dominated sorting on the initial population and select high-quality parents for further genetic inheritance based on the layer order and congestion information of individuals to obtain the offspring population.

Step 4: Based on constraints, apply the elite strategy to selecting, crossover, and variations to retain individual diversity in the population and select a new generation of parents of the same size.

Step 5: Determine whether the maximum number of iterations is reached. If so, exit the calculation; otherwise, go back to step (3) to continue iteration.

Step 6: After iterating to the upper limit, input the optimized value into the calculation of EVVES to further realize the optimal cost and net load of regional EV populations. After the strategy satisfies each constraint, output the optimized value of the EVVES and adjust the EVC charging and discharging range.

4. Case Study

4.1. Case Parameters

In order to verify the practical effect of the VES model and optimal scheduling strategy proposed in this paper, an industrial park containing PV, WT, and EV charging piles was taken as an example for calculation and analysis. The industrial park includes one 5 MW PV, named PV1, and one 2 MW WT, named W1. Their actual power and planned power are derived from the actual field station data; EVCs in the region use four types of EVs, as shown in Table 1. Each of them has 1000 EVs to participate in the model construction and optimal scheduling of the EVVES. The number of iterations was 50; the CPU was a 12th Gen Intel(R) Core(TM) i9-12900H with a main frequency of 2.50 GHz; the RAM was 16.0 GB; the simulation environment was Matlab R2018b; and the total running time was 80.78 s. Constants for the EVVES are shown in

Table 2. Constants for the EVVES (Adapted with permission from Ref. [27]).

Constants for EVVES	Meaning	Data
$P_{\max }^{grid}$/$P_{\min }^{grid}$	Upper/lower limit of power purchased and sold	3 MW/1 MW
$f_{peak}^{grid}/f_{flat}^{grid}/f_{valley}^{grid}$	The prices of peak/flat/valley in the microgrid exchange	1.230 CNY/(kW·h)/ 0.820 CNY/(kW·h)/ 0.410 CNY/(kW·h);
$f_{peak}^{PV}/f_{flat}^{PV}/f_{valley}^{PV}$	The prices of peak/flat/valley in PV	1.384 CNY/(kW·h)/ 0.923 CNY/(kW·h)/ 0.461 CNY/(kW·h);
$f_{peak}^{WT}/f_{flat}^{WT}/f_{valley}^{WT}$	The prices of peak/flat/valley in WT	2.153 CNY/(kW·h)/ 1.436 CNY/(kW·h)/ 0.718 CNY/(kW·h);
$c_{ch,t}/$$c_{dis,t}$	Costs and benefits of EVVES charging and discharging	0.8657 CNY/(kW·h)/ 0.7560 CNY/(kW·h);
$SO{C}_{\max }/SO{C}_{\min }$	Upper/lower limit of EVVES state of charge	1/0.4
Type/number of EVs		4/4000

.

4.2. The Boundary of EVVES

According to the EVVES model proposed in this paper, the EVVES charging and discharging power boundary was obtained, as shown in Figure 4. From Figure 4, it can be seen that the charging time of the EVCs is mainly distributed in the time period of 20:00–05:00. Meanwhile, the charging and discharging boundary is larger in this region. Therefore, the EVVES has a boundary of larger values.

The charging and discharging power boundary of Figure 4 were merged with the capacity of the EVVES. We established the relationship between $S_{EVVES}$ and $P_{EVVES}$ to obtain the EVVES model characteristic curve, as shown in Figure 5.

In Figure 5, a is the EVVES charging region, and b is the EVVES discharging region. There exists a zero point of charging power between them. First, the upper and lower limits of the EVVES characteristic curve are determined by the maximum values of the actual charging and discharging power of EVs, $P_{EVVES}^{ch} \mathrm{and} P_{EVVES}^{dis}$. They are the maximum values of the curve shown in Figure 4. The left and right limits in the figure are determined by the upper and lower limits of the regional EVVES’s energy storage. Above $S_{EVVES}^{\min }$, it just stores the current moment energy, and below $S_{EVVES}^{\max }$, it just releases the current moment energy. Finally, ① is the equivalent charging process determined by the EVVES characteristics, which is jointly determined by $P_{EVVES}^{ch}$ and $S_{EVVES}^{ch}$. The symbol ② is the equivalent discharging process determined by the EVVES characteristics, which is jointly determined by $P_{EVVES}^{dis}$ and $S_{EVVES}^{dis}$. The obtained EVVES characteristics provide the basis for the subsequent optimal scheduling.

4.3. Example Analysis of EVVES Optimization

Based on the models in Section 2.2 and Section 3.2, the NSGA-II algorithm was used to solve the dual-objective optimization problem. The population size was set to 300, and the number of iterations was 50. The Pareto optimal solution set obtained from the solution is shown in Figure 6.

It can be concluded from Figure 6 that the minimum cost and minimum net load variance are mutually exclusive objectives. A decrease in one must be accompanied by an increase in the other. Therefore, we applied the TOPSIS method to find the relative optimal solution, as shown by the labeled points in Figure 6. Finally, the minimum cost of CNY 309,689.2 and the minimum net load variance of 113.1558 kW were obtained.

Figure 7 shows the power curve after being optimized by the EVVES optimization model. From the above curve, we can see that the charging of the EVVES is concentrated in the time periods of 20:00–23:00, 01:00–05:00, and 07:00–08:00. In these three time periods, the EVVES can promote the orderly charging of EVs in the region. During four time periods of 15:00–16:00, 20:00–21:00, 22:00–0:00, and 1:00–3:00, the EVVES releases the stored energy and obtains the revenue to minimize the total operating cost and fluctuation in the region. This ensures the normal operation of the EVVES. The power of charging and discharging and the power of purchasing and selling in Figure 7 were combined with the load curve to obtain the load curve optimized by the EVVES, as shown in Figure 8.

The optimization model characteristics of the EVVES were studied for the following three comparison scenarios:

A. 

Comparison of regular and irregular charging with EVVES

First, the regular charging and discharging with the EVVES optimization strategy was compared with the irregular strategy of EVs in the region, as shown in Figure 9.

In Figure 9, we can see that the EVVES optimization strategy proposed in this paper can effectively perform peak shaving and valley filling. The effect of peak shaving and valley filling is especially obvious in four time periods 0:00–8:00, 9:00–12:00, 16:00–17:00, and 19:00–21:00. Thus, the comparison of the two strategies is shown in

Table 3. Comparison of the metrics between the strategy with EVVES and the irregular strategy of EVs.

Strategy	Costs/CNY	Load Fluctuation/kW	Running Time/s	Peak-to-Valley Ratio/%
Strategy of this paper	30,968.92	113.1558	80.787	20.6937
Disorderly strategy	33,593.58	118.9088		24.5211

.

As shown in Table 3, the EVVES proposed in this paper can reduce costs and fluctuations to greatly realize the peak shaving and valley filling of the regional load. It promotes the orderly charging and discharging of EVs and improves the economy and stability of the regional grid.

B. 

Comparison of optimization with GES and with EVVES

Secondly, the regular charging and discharging of the EVVES-containing optimization strategy was compared with the GES-containing strategy, as shown in Figure 10.

In Figure 10, the strategy of this paper is similar to the GES optimization in terms of its overall degree. However, the EVVES has a larger charging and discharging range compared to GES, which is especially obvious in time periods of 1:00–7:00, 9:00–12:00, and 19:00–21:00. Meanwhile, the EVVES-containing strategy can effectively reduce the load curve slope. It distributes regional energy more efficiently and better utilizes regional RESs. A comparison of the two is shown in

Table 4. Comparison of the metrics between the EVVES and GES strategies.

Strategy	Costs/CNY	Load Fluctuation/kW	Running Time/s	Peak-to-Valley Ratio/%
Strategy of this paper	30,968.92	113.1558	80.787	20.6937
Strategy of GES	32,435.43	118.6114	87.305	25.5429

.

As shown in Table 4, the EVVES proposed in this paper can reduce the costs and fluctuations relative to the GES strategies to realize the peak shaving and valley filling of the regional load. In contrast to the fixed boundaries of GES, the storage boundaries of EVVES change over time, so this strategy effectively reduces its running time.

C. 

Comparison of dual-objective optimization and single-objective optimization

Finally, the EVVES dual-objective optimization strategy was compared with the single-objective optimization strategy, as shown in Figure 11.

Figure 11a shows the curves of the fitness values and generations for EVVES single-objective optimization, and Figure 11b shows the Pareto front for dual-objective optimization. A comparative analysis of the single and dual-objective load optimizations based on the result of Figure 11 is shown in Figure 12.

In Figure 12, the difference between the single and dual-objective optimizations is large. The dual-objective load curves are significantly smaller than the single-objective load curves in the four time periods of 3:00–5:00, 9:00–11:00, 17:00–19:00, and 21:00–0:00. It is more capable of achieving peak shaving and valley filling in the region.

According to

Table 5. Comparison of the metrics for single and dual-objective optimization with EVVES.

Strategy	Costs/CNY	Load Fluctuation/kW	Running Time/s	Peak-to-Valley Ratio/%
Strategy of this paper	30,968.92	113.1558	80.787	20.6937
Single-objective optimization	30,967.35		45.117	23.0668

, the EVVES dual-objective optimization strategy proposed in this study is similar to the single-objective optimization strategy in terms of cost, but the peak-to-valley ratio of the strategy in this paper is reduced by 2.37% in comparison. It can effectively realize peak shaving and valley filling to ensure the economy and stability of the regional grid.

Comparing three strategies, it is concluded that the strategy proposed in this paper effectively reduces the operating cost and load fluctuation of the system. However, the data used in this paper is the sample data based on simulation, and it will be validated by applying real grid data in the future.

5. Conclusions

In order to give full play to the scheduling characteristics of large-scale EVC grid connections, this paper proposes an EVVES model by considering EV charging and discharging sequences. We established an optimal scheduling strategy for EV charging and discharging based on VES and obtained the following conclusions based on the simulation results:

• In this paper, we equated EV charging and discharging characteristics to the EVVES model, which effectively realizes the peak shaving and valley filling of loads when large-scale EVCs are connected to the grid. Meanwhile, the EVVES model promotes the orderly charging and discharging of EVCs in the region and improves the solution speed of the algorithm.
• For the constructed EVVES model, we propose an EVVES optimization charging and discharging strategy. It effectively reduces the operating costs and load fluctuations of the system to improve the economy and stability of the grid.

In this paper, the residence time and SOC values of EVs are generated by using the Monte Carlo method. Considering the uncertainty of EV charging time will be the focus of subsequent research. Meanwhile, the available data in this paper are sample data based on simulation model parameters and are not real data. It will be subsequently validated by applying real grid data in future work.