Two-Stage Energy Dispatch for Microgrids Based on CVaR-Dynamic Cooperative Game Theory Considering EV Dispatch Potential and Travel Risks

Abstract

With the rapid development of microgrids (MGs) and electric vehicles (EVs), leveraging the flexibility of EVs in MG optimization scheduling has attracted significant attention. However, existing research does not consider the impact of EV scheduling potential on MG uncertainty or the avoidance of conflicts in EV users’ mobility needs and their charging/discharging activities. Therefore, this paper proposes a two-stage microgrid energy scheduling model integrated with the conditional value-at-risk (CVaR) and dynamic cooperative game theory. In addition, the aforementioned issues are specifically addressed by considering both EV scheduling potential and travel risk. The day-ahead model minimizes the MG’s operational costs, where a CVaR-based uncertainty model for MG net load is established to quantify risks from both renewable energy generation and load. The EV dispatchable potential is calculated using Minkowski summation theory. In the real-time stage, the adjustment of participating EVs and optimal incentive compensation costs are determined through the proposed EV travel risk model and dynamic cooperative game, aiming to minimizing the MG’s real-time adjustment costs. The simulation results validate the effectiveness of the proposed method, which can help to reduce the operational costs of MGs by 4%, reduce real-time adjustment costs by about 85%, and decrease load variability by 3%. For the main grid, the proposed method can avoid the “peak-on-peak” phenomenon. For EV users, travel demands can be fully satisfied, charging costs can be reduced for 34% of users, and 2.4% of users gain profits.

1. Introduction

1.1. Background

Faced with the deterioration of the global ecological environment, the worsening crisis of fossil fuel scarcity, and increasing societal calls for low-carbon and sustainable development, there is an imperative for the power system to transition towards low-carbon and green energy solutions. Renewable energy sources (RESs) will play an important role in the process of power system energy transition by virtue of their environmental friendliness and renewability [1]. As a new type of power system, microgrids (MGs) can reduce the impact of renewable energy uncertainty on the power grid, and at the same time become one of the key research areas for power system transformation with its high proportion of renewable energy generation, high degree of power automation, and customizable personalized power services [2]. However, the volatility, intermittency, and uncertainty of RES power generation may negatively affect the stable operation of the power grid [3]. With the growing development of electric vehicles (EVs) and their increased penetration in the grid, an effective means to address this issue is to apply vehicle-to-grid (V2G) technology for EVs to provide auxiliary services for the coordinated charging and discharging of MGs [4] and to realize the stable operation of microgrids. Therefore, realizing the positive interaction between EVs and MGs and increasing the motivation of EV users to participate in the provision of auxiliary services will play an important role in the future power system industry and energy sector.

1.2. Literature Review

Due to the rapid development of MGs and EVs, energy management for the EVs involved in MGs has become the focus of many scholars’ research [5]. To date, a large number of studies have been carried out on various aspects of MGs and obtained fruitful research results. Therefore, this section centers on some of the current advances in research on MGs and EVs, and introduces the relevant research methods and techniques used with MGs and EVs.

The uncertainty of RESs and loads poses significant challenges to the operational stability and reliability of MGs [6]. Therefore, to address the uncertainty issues in MGs, previous research proposed the use of several methods, such as robust optimization (RO), stochastic optimization (SO), and risk aversion methods [7]. SO relies on accurate probability distributions of uncertain variables, which are hard to precisely characterize using existing mathematical models. Additionally, in scenarios with high complexity and large data volumes, the SO method cannot sufficiently meet engineering requirements due to assumptions of uncertainty distributions. Static RO methods typically involve one-time decision-making, preventing subsequent variable adjustments and leading to conservative results [8]. Thus, dynamic RO methods are proposed to enable self-correction based on control actions after initial decisions, enhancing the system’s disturbance resilience. For instance, Ref. [9] proposes a two-stage optimal energy management model: the first stage determines possible uncertain energy sources and reserve dispatch energy, while the second stage involves optimal dispatch based on discrepancies between real-time and forecasting data. Ref. [10] proposed a two-stage distributed RO model using the Wasserstein metric to extract fuzzy sets representing the probability distribution of uncertainties in wind and solar outputs of MGs. The first stage minimized system energy consumption costs and penalties for curtailed wind and solar power. The second stage adjusted the day-ahead plan to minimize real-time adjustment costs under optimized extreme scenarios. However, though the aforementioned modeling approaches effectively characterize uncertainty through probabilistic constraints, they fail to precisely reflect the risk preferences of MG operators [11] and lack detailed characterization and modeling of the potential risks associated with breaching confidence intervals [12].

To solve the above problems, the conditional value-at-risk (CVaR), which is a risk assessment method applied in the financial field, is adopted in many studies to measure the impact of risks from uncertainty on optimal scheduling. Ref. [13] built a risk assessment model for integrated energy system planning at the campus level, using CVaR as a risk metric to quantify the impact of energy price change uncertainty on the planning problem. Ref. [14] used CVaR metrics to measure the impacts of uncertainty in RESs, real-time power markets, load variations, and the driving behaviors of EV users on the scheduling of MGs and EVs for optimal energy management. Ref. [15] proposed a CVaR-based model to address the impact of uncertainty in the operating parameters of each agent in the resource scheduling of MGs. Ref. [16] proposed a power system day-ahead optimal scheduling model, which utilized the CVaR index to measure the risk of wind output, to reduce wind abandonment, and to make full use of dispatchable resources. However, the above works (Refs. [13,14,15,16]) neglected the impact of EV dispatchability potential and EV charging flexibility on the risks posed by MG uncertainty. In this work, an EV dispatchability potential model is introduced into the day-ahead scheduling framework combined with CVaR to perform MG day-ahead scheduling. The proposed approach comprehensively addresses the uncertainties in RESs, EVs, and load.

Considering that certain errors between the predicted and actual values cannot be fully avoided, it is necessary to involve distributed resources in an MG’s real-time adjustment to enhance the energy resilience and operational stability of the MG. For example, EVs are equipped with quick response ability and great flexibility, which can provide auxiliary services to MGs through V2G (vehicle-to-grid) technology [17]. Nevertheless, the spatial and temporal distribution of large-scale EVs and uncertainty in EV users’ driving behavior make it difficult to realize the optimal charging strategy by customizing personalized services for each EV [18]. Such a problem leads to a decrease in the motivation of EVs to participate in the provision of ancillary services. Therefore, the EV aggregator (EVA) has emerged as a means to address EV uncertainty and unlock the scheduling potential of large-scale EVs [19]. In [20], an improved EVA model for ancillary services was developed by considering the energy and power coupling of EVs, and the joint chance constrained planning (JCCP) model was used to describe the EV uncertainty. Ref. [21] proposed a hybrid incentive scheme combining static incentives and dynamic control to improve EV charging flexibility utilization. Ref. [22] proposed a two-tier coordinated operation method that embedded an integrated EV model considering driver response willingness. It can effectively verify the dispatch potential of EVs and reduce the cost for both the integrated energy system and EV users. Ref. [23] proposed an EVA model considering EV charging and discharging stresses using RO to deal with the uncertainty of RES generation and industrial loads. Ref. [24] proposed a multi-timescale energy scheduling model embedded with differentiated billing management strategies. Ref. [25] developed a new mechanism that combined the financial modeling of V2G services and incentive participation schemes into the decision making of different types of chargers to achieve optimal pricing of each service relative to the invested capital. Refs. [20,21,22,23,24,25] proposed models for EV user uncertainty to reduce adjustment costs during the real-time phase. In addition, the diversity of EV users is considered by establishing personalized expected incentives to encourage EV user participation in MG scheduling. However, optimal EVA scheduling often compromises EV user charging satisfaction by neglecting future mobility needs and associated risks, thereby dampening participation motivation. To this end, this work introduces an EV mobility risk model with a dynamic game theory framework into the real-time scheduling stage. This approach can comprehensively balance overall benefits and enhance scheduling participation enthusiasm.

Most studies focus on EV users who remain parked during working hours, assuming that they will not leave during the scheduling period and will fully comply with the schedule. However, such an assumption overlooks the normal vehicle mobility of EV users and parking lots, and may fail to address the optimization of scheduling for EV users who stay parked for extended periods or overnight. Simultaneously, to address multiple uncertainties and achieve the dual objectives of enhancing participant benefits and reducing system operating costs, it is necessary to establish a comprehensive optimization model that enables positive interactions among the distribution grid, microgrids, and EV users [26,27].

1.3. Paper Contributions and Organization

To address the challenges in the above research areas, this paper proposes a two-stage conditional value-at-risk (CVaR)-based and dynamic cooperative game two-stage energy dispatch model for MGs considering EV travel risk, and establishes a two-stage dispatch model enabling MG operators to participate in the day-ahead market and real-time market for purchasing the required energy. Meanwhile, a CVaR-based day-ahead energy dispatch model is designed, where MG operators rely on RES generation and the orderly charging of EVs to reduce the total power purchase cost. A dynamic game real-time correction strategy considering EV travel risk is proposed to maximize the benefits of energy regulation participants.

The major contributions of the study are as follows:

• In this paper, an uncertainty model based on CVaR is designed considering photovoltaic (PV), wind turbine (WT), load, and EV charging uncertainty. In the day-ahead stage, an EV aggregation model is established based on predicting EV users’ driving behavior, and the dispatchable potential calculation is realized. The day-ahead energy scheduling plan was designed based on EV dispatchable potential and CVaR to reduce the power purchase cost for MG operators as well as the charging cost for EV users.
• Based on EV users’ travel information, an EV travel risk function is designed, and then an EV demand–response energy management strategy based on incentives is designed to satisfy EV users’ travel demand and reduce the real-time charging cost by considering travel risk, charging cost, and EV battery loss.
• In the real-time stage, a real-time correction strategy based on the dynamic cooperative game is proposed. By means of compensation incentives, EV users are stimulated to form cooperative alliances, and their charging and discharging power is adjusted through EV cooperative alliances to compensate for dynamic power deviations caused by various types of uncertainties and reduce real-time adjustment costs for MG operators.

The article is organized as follows. Section 2 introduces the MG system and day-ahead market, and focuses on CVaR-based uncertainty modeling to model and solve the day-ahead energy dispatch optimization problem. Section 3 focuses on EV travel risk modeling and the energy dispatch strategy based on a dynamic cooperative game, and Section 4 presents the dispatch results and analyzes the case study. Finally, the conclusions are given in Section 5.

2. Day-Ahead Energy Scheduling Method Based on CVaR Risk Assessment Considering Schedulable Potential Capacity of EVs

This paper focuses on the energy scheduling and management methods for grid-connected MGs in industrial parks. Thus, this paper proposes a two-stage microgrid energy scheduling model based on CVaR and a dynamic cooperative game considering EV travel risk. The microgrid system designed in this paper consists of distributed PVs, WTs, V2G charging stations, and EVs. The overall architecture of the MG system and the framework of the modeling methodology are shown in Figure 1.

Among them, EV users are divided into two categories: regular users and temporary users. Regular users are characterized by predictable driving behavior and can participate in MG regulation; temporary users are characterized by charging on arrival and leaving at the end of charging and do not participate in MG regulation, and are regarded as a part of the MG’s load. Meanwhile, the MG system participates in the day-ahead power purchase market; i.e., in the day-ahead stage, the MG signs a next-day power purchase plan with the distribution grid operator, which is used to obtain a cheaper power purchase price through a more accurate power purchase plan. However, at the same time, the amount of electricity exceeding or falling below the power purchase plan in the real-time stage is also subject to more severe penalties.

2.1. Uncertainty Model for Payload Based on CVaR

Due to the uncertainty inherent in wind turbines, photovoltaic generation, and user loads, microgrid systems exhibit certain risk characteristics. Therefore, to balance the risks arising from uncertainty, this paper introduces a net load uncertainty model based on CVaR into the day-ahead energy scheduling of microgrids. Extreme tail risks are primarily measured in such a model, which can better reflect risk characteristics beyond threshold values compared with traditional methods. Thus, the robustness of microgrid resource allocation portfolio solutions can be enhanced by comprehensively considering the uncertainties in both renewable energy output and user loads (including electric vehicle charging and daily user electricity consumption) incorporated with risk characteristics beyond thresholds. In addition, the prediction error of the model is also analyzed using the historical data in this paper. Moreover, more advanced forecasting techniques can be introduced in the proposed model to further improve the performance of the model, which is not the focus of this paper. A brief explanation of CVaR and net load definitions are explained as follows.

The assumptions $x,y$ are the decision variables and random variables, respectively. The continuous probability density of random variable $y$ is $\theta (y)$ and the loss function is $L(x,y)$. If the decision variable $x$ is determined with the threshold $\delta$, the cumulative distribution function of the loss function $L(x,y)$ is as follows:

$$\phi (x,\delta )\triangleq {\displaystyle \underset{H(x,y)\le \delta }{\int }\theta (y)}dy$$

(1)

Therefore, the expression of the $VaR$ (value-at-risk) function for a determined decision variable $x$ at confidence level $\alpha \in (0,1)$ is as follows:

$$VaR(x)\triangleq \min \{\delta \in R:\phi (x,\delta )\ge \alpha \}$$

(2)

where the confidence level $\alpha$ is determined by the decision maker based on the internal resources of the system and the scheduling ability of the resources, and $R$ is the set of real numbers.

The $CVaR$ function expression can be derived from the $VaR$ function as follows:

$$CVaR(x)={\displaystyle \frac{1}{1-\alpha }}{\displaystyle \underset{H(x,y)\ge Va{R}_{\alpha }(x)}{\int }L(x,y)\theta (y)dy}$$

(3)

However, it is too complicated to solve the above expression exactly in the process of solving real problems, so we construct auxiliary functions to simplify the expression:

$$F_{\alpha }(x,\delta )=\delta +{\displaystyle \frac{1}{1-\alpha }}{\displaystyle \underset{y\in R}{\int }\max \{L(x,y)-\delta ,0\}\theta (y)dy}$$

(4)

Thus, the $CVaR$ function can be transformed into

$$CVaR(x)=\underset{\alpha \in R}{\min }{F}_{\alpha }(x,\delta )$$

(5)

By sampling points instead of integrals and adding an auxiliary function, Equation (6) can be further simplified to obtain

$$CVaR=\min \left\{\delta +{\displaystyle \frac{1}{N(1-\alpha )}}{\displaystyle \sum _{i=1}^N\max \{L(x,y)-\delta ,0\}}\right\}$$

(6)

where $N$ is the total number of samples, and threshold $\delta$ is an auxiliary variable with an optimal value of $VaR$.

In this paper, the net load uncertainty model based on CVaR is used to develop a reasonable power purchase plan and power tolerance interval, where the net load and net load error of the system are modeled as follows:

$$\left\{\begin{array}{l}{P}_t^N=P_t^{Load}-P_t^{PV}-P_t^{WT}\\ E{r}_t={\displaystyle \frac{({\tilde{P}}_t^N-P_t^N)}{{\tilde{P}}_t^N}}\end{array}\right.\forall t\in T$$

(7)

where $P_t^N$, $P_t^{Load}$, $P_t^{PV}$, $P_t^{WT}$ are the system payload, total system load, PV output power, and wind power output at time $t$; $E{r}_t$ is the payload error; ${\tilde{P}}_t^N$ is the actual payload at time $t$; and $T$ is the total operating time.

The net payload tolerance interval is the interval within which the distribution grid can accept net load disturbances. Within this interval, the MG can dissipate the net payload power fluctuations caused by any reason without risk and without being penalized by the distribution network. At the same time, the tolerance interval is proportional to the contracted tariff, i.e., the more the tolerance interval the more the contracted tariff is higher. In this paper, $\pm VaR$ is used as the boundary condition for the power tolerance interval, and the penalty function $H(E{r}_t)$ for exceeding the power tolerance interval is as follows:

$$\begin{array}{l}H(P_t^N,E{r}_t)={\displaystyle \sum _{i=1}^{h-1}{P}_t^N\times \left(\frac{i+D}{100}\right)}\times {\rho }_{sell,t}^{EM}+\\ \hspace{1em}\hspace{1em}\hspace{1em}(\left|E{r}_t\right|-Va{R}_t-h*\Delta Er)\times P_t^N\times (h+D)\times {\rho }_{sell,t}^{EM}\\ h={[{\displaystyle \frac{\left|E{r}_t\right|-Va{R}_t}{\Delta Er}}]}^{+}\end{array}$$

(8)

where $E{r}_t$ is the $t$ moment net payload error, $P_t^N$ is the $t$ moment power tolerance interval boundary, 5 is th $t$ moment MG net load, ${\rho }_{sell,t}^{EM}$ is the $t$ moment grid power sale price, $\Delta Er$ is the leapfrog degree, $D$ is the base penalty multiplier, and ${\left[x\right]}^{+}$ is the upward rounding function.

2.2. Model of Schedulable Potential Capacity of EVs

At the day-ahead stage, the number of EVs participating in scheduling in the campus MG is large, and if all EV user data are directly reported to participate in the scheduling of the MG, a large number of high-dimensional variables will be generated in the scheduling process. However, a large amount of high-dimensional data will increase the computational complexity in the optimization solution process, which is prone to cause dimensional disasters; at the same time, it is difficult for the capacity of EV individuals to meet the demand of regulation as well as to safeguard the privacy and security of EV users. Therefore, in this section, EV individuals are modeled, while the EV groups of park charging stations are aggregated using EVA through Minkowski summation theory, and upper and lower limits of the schedulable potential capacity of EVs of park charging stations are calculated.

2.2.1. Model of EVs

For regular EVs entering the charging station in the park, the charging pile will obtain the initial SoC (state of charge), arrival time, departure time, and expected SoC of EVs, and the load model corresponding to individual EVs will be established by the above information, as follows in Equation (9):

$$\left\{\begin{array}{l}0\le P_{ch,x,t}^{EV}\le P_{ch,x,\max }^{EV}\times {\lambda }_{ch,x,t}^{EV}\\ 0\le P_{dis,x,t}^{EV}\le P_{dis,x,\max }^{EV}\times {\lambda }_{dis,x,t}^{EV}\\ 0\le {\lambda }_{ch,x,t}^{EV}+{\lambda }_{dis,x,t}^{EV}\le {\lambda }_{x,t}^{EV}\\ So{C}_{x,\min }\le So{C}_{x,t}^{EV}\le So{C}_{x,\max }\\ So{C}_{x,t}=So{C}_{x,t-1}+({\eta }_{ch}^{EV}\times P_{i,t}^{ch}-{\displaystyle \frac{P_{i,t}^{dis}}{{\eta }_{dis}^{EV}}})\Delta t\end{array}\right.t\in [t_{ar},t_{le}]$$

(9)

where $P_{ch,x,t}^{EV}$, $P_{dis,x,t}^{EV}$ are the charging and discharging charging rates of EVs at time $t$; $P_{ch,x,\max }^{EV}$, $P_{dis,x,\max }^{EV}$ are the upper limit of the charging and discharging power of EVs; ${\lambda }_{ch,x,t}^{EV}$, ${\lambda }_{dis,x,t}^{EV}$ are the Boolean variables of the EV charging and discharging state, i.e., the charging and discharging of a single EV can not be carried out at the same time; ${\lambda }_{x,t}^{EV}$ is the Boolean variable of the EV arrival state, and the EVs can be charged and discharged when ${\lambda }_{x,t}^{EV}=1$; $So{C}_{x,t}^{EV}$ is the charge state of the EVs at time $t$, and $So{C}_{x,\min }$, $So{C}_{x,\max }$ are the upper and lower limit of the charge state of the EVs; ${\eta }_{ch}^{EV}$, ${\eta }_{dis}^{EV}$ are the charging and discharging efficiency of EVs; $\Delta t$ is the time period of EV charging and discharging; $t_{ar}$, $t_{le}$ are the arrival time and departure time of EVs; and $x$ is the type of EV.

2.2.2. Schedulable Potential Capacity of EVs

To address the fact that the arrival and departure time have variability among EV individuals, in this paper, the Boolean variable ${\lambda }_{x,t}^{EV}$ is considered in the calculation of charging and discharging power, through which the MG connection times of all EVs are unified into the same domain of definition. As a result, the individual EVs have Minkowski additivity [28], and then the power–capacity model of the charging station EVA (CSEVA) is as follows:

$$\left\{\begin{array}{l}0\le {\displaystyle \sum _{x\in X^{EV}}{P}_{ch,x,t}^{EV}}\le {\displaystyle \sum _{x\in X^{EV}}{P}_{ch,x,\max }^{EV}\times {\lambda }_{ch,x,t}^{EV}}\\ 0\le {\displaystyle \sum _{x\in X^{EV}}{P}_{dis,x,t}^{EV}}\le {\displaystyle \sum _{x\in X^{EV}}{P}_{dis,x,\max }^{EV}\times {\lambda }_{dis,x,t}^{EV}}\\ {\displaystyle \sum _{x\in X^{EV}}So{C}_{x,\min }\times {\lambda }_{x,t}^{EV}}\le {\displaystyle \sum _{x\in X^{EV}}So{C}_{x,t}^{EV}}\le {\displaystyle \sum _{x\in X^{EV}}So{C}_{x,\max }\times {\lambda }_{x,t}^{EV}}\\ {\displaystyle \sum _{x\in X^{EV}}So{C}_{x,t}={\displaystyle \sum _{x\in X^{EV}}So{C}_{x,t-1}}+{\displaystyle \sum _{x\in X^{EV}}(P_{ch,x,t}^{EV}-P_{dis,x,t}^{EV})\times \Delta t}+}\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\displaystyle \sum _{x\in X^{EV}}So{C}_{n,ar}\times {\lambda }_{x,t}^{EV}\times ({\lambda }_{x,t}^{EV}-{\lambda }_{x,t-1}^{EV})}-\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\displaystyle \sum _{x\in X^{EV}}So{C}_{n,le}\times {\lambda }_{x,t-1}^{EV}\times ({\lambda }_{x,t-1}^{EV}-{\lambda }_{x,t}^{EV})}\end{array}\right.\hspace{1em}\hspace{1em}t\in [t_{ar},t_{le}]$$

(10)

where $So{C}_{n,ar}$, $So{C}_{n,le}$ are the battery charge states at the arrival and departure time of EVs; $X^{EV}$ is the set of EV types.

In summary, the variables, parameters, and schedulable potential z for CSEVA are as follows:

$$\left\{\begin{array}{l}{P}_{ch,t}^{EVs}={\displaystyle \sum _{x\in X^{EV}}{P}_{ch,x,t}^{EV}}\\ P_{dis,t}^{EVs}={\displaystyle \sum _{x\in X^{EV}}{P}_{dis,x,t}^{EV}}\\ P_{ch,\max }^{EVs}={\displaystyle \sum _{x\in X^{EV}}{P}_{ch,x,\max }^{EV}\times {\lambda }_{ch,x,t}^{EV}}\\ P_{dis,\max }^{EVs}={\displaystyle \sum _{x\in X^{EV}}{P}_{dis,x,\max }^{EV}\times {\lambda }_{dis,x,t}^{EV}}\\ So{C}_t^{EVs}={\displaystyle \sum _{x\in X^{EV}}So{C}_{x,t}}\\ So{C}_{\max }^{EVs}={\displaystyle \sum _{x\in X^{EV}}So{C}_{x,\max }\times {\lambda }_{x,t}^{EV}},\hspace{1em}So{C}_{\min }^{EVs}={\displaystyle \sum _{x\in X^{EV}}So{C}_{x,\mathrm{m}\min }\times {\lambda }_{x,t}^{EV}}\\ \Delta So{C}_t={\displaystyle \sum _{x\in X^{EV}}So{C}_{n,ar}\times {\lambda }_{x,t}^{EV}\times ({\lambda }_{x,t}^{EV}-{\lambda }_{x,t-1}^{EV})}-\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{\displaystyle \sum _{x\in X^{EV}}So{C}_{n,le}\times {\lambda }_{x,t-1}^{EV}\times ({\lambda }_{x,t-1}^{EV}-{\lambda }_{x,t}^{EV})}\end{array}\right.$$

(11)

$${\mathsf{\Omega }}_{EV}=\{P_{ch,\max }^{EVs},P_{dis,\max }^{EVs},\Delta So{C}_t,So{C}_{\max }^{EVs},So{C}_{\min }^{EVs}\}$$

(12)

where $P_{ch,t}^{EVs}$, $P_{ch,t}^{EVs}$, $So{C}_t^{EVs}$ are the charging and discharging power of the CSEVA and the power of the CSEVA at time $t$; $P_{ch,\max }^{EVs}$, $P_{dis,\max }^{EVs}$ are the upper limit of the charging and discharging of the CSEVA at time $t$; $So{C}_{\max }^{EVs}$, $So{C}_{\min }^{EVs}$ are the upper and lower limits of the power of the CSEVA at time t, respectively; and $\Delta So{C}_t$ is the change in the power of the CSEVA at time $t$ due to the driving behavior of the EV users.

2.3. Day-Ahead CVaR-Based Scheduling Model Considering Schedulable Potential Capacity of EVs

In the day-ahead stage, this study uses a CVaR-based day-ahead scheduling model for MGs that considers the schedulable potential capacity of EVs. With the optimization objective of minimizing the system power cost, the model considers the risk cost of CVaR and the schedulable potential capacity of EVs, solves the intraday optimal EV charging power curve, and generates the power purchase plan between MGs and the grid. This section briefly describes the day-ahead model objective function, constraints, and solution method.

2.3.1. Objective Function

In order to reasonably balance the uncertainty risk and system cost of optimizing renewable energy and load, this paper brings the conditional value-at-risk-based net payload uncertainty model into the MG’s day-ahead energy management to obtain the microgrid day-ahead scheduling model based on CVaR risk assessment. Its objective function is to minimize the system cost by adding the expected cost and risk cost for the MG system. Therefore, in order to quantitatively analyze the microgrid revenue risk, based on the CVaR risk theory in Section 2.1, with the actual net payload ${\tilde{P}}_t^N$ as the decision variable, the net payload prediction $P_t^N$ as the random variable, and the net payload error function $E{r}_t$ as the loss function $L(x,y)$, the objective function established in this paper is as follows:

$$\min F_{ahaed}=F_1+F_{CVaR}$$

(13)

$$\left\{\begin{array}{l}{F}_1={\displaystyle \sum _{t=1}^T(C_{buy,t}^{EM}+C_t^{PV}+C_t^{WT})}\\ C_{buy}^{EM}={\displaystyle \sum _{t=1}^T{\rho }_{sell,t}^{EM}\times P_t^N}\\ CVa{R}_t=\min \left\{Va{R}_t+{\displaystyle \frac{1}{N(1-Va{R}_t)}}{\displaystyle \sum _{i=1}^N\max \{E{r}_t-Va{R}_t,0\}}\right\}\\ F_{CVaR}={\displaystyle \sum _t^{T}H(P_t^N,CVa{R}_t)}\end{array}\right.$$

(14)

In Equations (13) and (14), $F_1$ is the cost of MG operation; ${\tilde{F}}_{\alpha }(x,\xi )$ is the cost of conditional risk caused by the uncertainty of the payload; $C_{buy,i}^{EM}$, $C_t^{PV}$, $C_t^{WT}$ are the cost of power purchase from the grid, the cost of PV operation, and the cost of wind turbine operation at time $t$; $P_t^N$ is the net power of the MG at time $t$; and ${\rho }_{sell,t}^{EM}$ is the price of power sold from the grid at time $t$.

2.3.2. Constraints

(1)

Power balance

$$\left\{\begin{array}{c}{P}_t^{WT}+P_t^{PV}+P_t^N=P_t^{Load}\\ P_t^N=P_t^{else}+P_{ch,t}^{EVs}\end{array}\right.\hspace{1em}\forall t\in T$$

(15)

$$\begin{array}{c}\Delta P_{MG}=P_{\max }^{Load}-P_{\min }^{Load}\\ \Delta P_{MG}\ge \Delta {\overline{P}}_{MG}\end{array}$$

(16)

where $P_t^{else}$ is the power of MG loads other than regular EVs at the time $t$, $P_{ch,t}^{EVs}$ is the charging load of regular EV users at the time $t$, $P_t^N$ is the payload which is also the purchased power of MG, $\Delta P_{MG}$ the peak to valley difference of MG loads before optimization, and $\Delta {\overline{P}}_{MG}$ the peak–valley difference of MG loads by optimization.

(2)

Grid constraints

$$P_{\min ,t}^{grid}\le P_t^N\le P_{\max ,t}^{grid}\hspace{1em}\forall t\in T$$

(17)

where $P_{\max ,t}^{grid}$, $P_{\min ,t}^{grid}$ are the upper and lower limits of power purchases with the grid.

(3)

EV constraints

In the day-ahead scheduling, only the charging flexibility of EVs available for dispatch is considered, and EV discharging is not considered. Currently, the common process of scientific charging of lithium-ion batteries can be divided into three stages: pre-stabilized charging, constant current charging, and constant voltage charging [29]. Therefore, in order to protect the charging life and charging safety and improve the charging efficiency of EV batteries, the EVs battery charging process and the number of charging times are constrained as follows:

$$0\le nu{m}_{ch}^{EV}\le nu{m}_{ch,\max }^{EV}\hspace{1em}\hspace{1em}\hspace{1em}nu{m}_{ch}^{EV}\in {\mathbb{N}}^{+}$$

(18)

$$P_{ch,x}^{EV}=\left\{\begin{array}{ll}{P}_{x,\max }^{ESS}& \hspace{1em}20\%\le So{C}_x\le 80\%\\ P_{x,\min }^{ESS}& \hspace{1em}So{C}_x<20\% or So{C}_x>80\%\end{array}\right.$$

(19)

$$So{C}_{x,le}=So{C}_{x,end}$$

(20)

In Equations (18)–(20), $nu{m}_{ch}^{EV}$ is the number of charging times—reducing the number of charging times to increase the charging continuity can protect the battery life. $P_{ch,x,\max }^{EV}$ is the maximum charging power of the battery, which will be changed with the change in SoC so that it matches the three-stage charging. When $20\%\le So{C}_x\le 80\%$, the constant current charging state can use high current charging, so the charging power is $P_{x,\max }^{ESS}$. When $So{C}_x<20\% \mathrm{or} So{C}_x>80\%$, in the pre-stabilized and constant voltage charging state, the charging current is small in order to protect the battery life, so the charging power is $P_{x,\min }^{ESS}$. In the actual charging process, $P_{ch,x}^{EV}$ varies with the change in the charging current.

2.3.3. Approach

In this paper, the EV charging process is simplified into three constant-power charging stages for computational convenience. A binary variable matrix is used to represent the EV charging and discharging states, and the number of EV charging and discharging cycles as well as their schedulable potential are calculated. The day-ahead planning problem is transformed into a mixed-integer linear programming and solved using the Gurobi solver to obtain the day-ahead EV charging power as well as the day-ahead power purchase curve. In the day-ahead stage, the day-ahead power purchase plan is formed using the solved power purchase curve as a benchmark and the day-ahead average VaR as the power allowance range.

3. Real-Time Correction Approach Based on Dynamic Game Considering EV Travel Risk

In the real-time stage, it is expected that the actual power purchases observe the day-ahead scheduling results. However, there is inevitably a prediction error in the output power of PV and WT as well as the load demand power during the actual operation. At the same time, the actual driving behavior of EV users also has a certain deviation from the prediction result. These factors make it difficult for the actual power purchase plan to accurately match the daily scheduling plan. Therefore, in this paper, we propose a real-time correction approach based on dynamic game considering EV travel risk to reduce the adjustment cost and deviation in the real-time stage.

3.1. Model of EV Travel Risks

In this paper, aggregated EVs are utilized as an energy storage system to adjust real-time power purchases. However, while using EV charging and discharging to adjust the intraday power purchase curve, the system needs to guarantee the regular user travel demand and protect the predictability of regular users’ driving behavior. Therefore, this paper proposes an EV travel risk model, which is utilized to quantify the impact of current time charging and discharging on the expected SoC at the departure time. Due to the variability of regular users’ driving behavior and the different sensitivity of travel demand, this paper takes the current SoC, the expected SoC at the departure time, the stop time, and the current required charging time as the parameters, and obtains the travel risk model by modeling with the generalized bell shaped membership function, as follows:

$$\left\{\begin{array}{l}{R}_{x,t}^{EV}={\displaystyle \frac{1}{1+{\left|\frac{So{C}_{x,t}-10}{100\times \sigma }\right|}^{\mathsf{\partial }\times So{C}_x^{end}}}}\\ \sigma ={\displaystyle \frac{T_{ch}}{T_{stop}}}\end{array}\right. \hspace{1em}\hspace{1em}\hspace{1em}t\in [t_{ar},t_{le}],x\in X^{EV}$$

(21)

where $R_{x,t}^{EV}$, $So{C}_{x,t}$ are the EV travel risk and state of charge at time $t$; $So{C}_x^{end}$ is the desired SoC when the EV leaves; $\mathsf{\partial }$ is an adjustment coefficient reflecting EV users’ sensitivity to $So{C}_x^{end}$; and $\sigma$ is the ratio of the current required charging time $T_{ch}$ to the stop time $T_{stop}$. After experiments with actual EV travel data, $\mathsf{\partial }$ is recommended to be set as 4. Meanwhile, it can be reasonably adjusted according to the sensitivity of EV users to the expected SoC.

In order to give full play to the flexibility of EVs and to actively motivate EV users to participate more in the dispatch of MGs, this paper sets up incentives to encourage EV users to sell charging flexibility and EV power. In this paper, an incentive-based approach is adopted, i.e., EV users are awarded compensation when they sell charging flexibility and EV power. Considering that EV selling power causes battery power decay, in order to quantify the degree of battery attenuation, Ref. [30] proposed the following battery attenuation function:

$$D(e_{t,x})={\displaystyle \frac{\left|e_{t,x}\right|}{C{L}_{nom}\times (Do{D}_{nom}/100\%)\times 2\times E_x}}$$

(22)

where $C{L}_{nom}$, $Do{D}_{nom}$ are the cycle life and depth of discharge of the EV battery under nominal conditions, $e_{t,x}$ is the current discharge, and $E_x$ is the maximum EV battery charge.

As a result, the risk cost of an EV selling one charge of flexibility and power is as follows:

$$C_{x,t}^{EV}=P_{out,x,t}^{EV}\times {\rho }_{sell,t}^{MG}+D(e_{t,x})\times (V_x^{buy}-V_x^{\mathrm{recovery}})$$

(23)

where $P_{out,i,t}^{EV}$ is the power of EVs participating in dispatch at time $t$; ${\rho }_{\max }^{MG}$ is the maximum charging tariff of MGs; $V_x^{buy}$ is the price of purchasing an EV battery; and $V_x^{\mathrm{recovery}}$ is the price of the end-of-life recycling of an EV battery.

3.2. Decision Model Based on Dynamic Cooperative Game Considering EV Travel Risk

In the real-time stage, this paper adopts a decision-making model based on a dynamic cooperative game. This decision model does not take the global optimum as the decision-making objective in the decision-making process; it takes a single time point as the cross-section, and makes decisions at each time point with the objectives of minimizing the current adjustment cost and maximizing the EV union’s profit, taking into considering the EV travel risk. Meanwhile, the numbers of both union members and users will change at different time points. The core of this decision problem is how to distribute benefits while minimizing the MG adjustment cost, and how to ensure profitability for each individual participating in the discharge EVs while maximizing the benefits of the EV coalition. The objective function and constraints of this model are explained in detail in this section, and the third section of this chapter focuses on the problem-solving process.

3.2.1. A Brief Overview of Cooperative Game Theory

Cooperative games, an important branch of game theory, can be used to describe the ways in which multiple subjects cooperate with one another. Cooperative game problems need to satisfy the following axioms [31,32].

(1)

Validity: For all individuals participating in the coalition, the benefits gained from participating in the system scheduling in the coalition should be greater than the benefits of individual participation, otherwise individuals will not participate in the coalition; at the same time, the sum of the benefits of all individuals in the coalition is equal to the coalition’s benefits.

(2)

Symmetry: If the gamers in the coalition are exchangeable with each other, then their benefits or allocations should also be the same.

(3)

Additivity: If two independent cooperative games are combined into a new game, then the solution of the new game is equal to the sum of the solutions of the two original games [33].

According to the above axioms, it can be found that the cooperative game ensures that the benefits gained by individual EVs participating in the cooperative union are greater than the benefits gained by their freely formed small coalitions or by participating in scheduling alone; thus, EVs can be mobilized to participate more in cooperative union scheduling. In the MG real-time scheduling process, the participants are individual EVs and all participants spontaneously form a cooperative union with realization constraint contracts.

3.2.2. Objective Function

(1)

EV Union Objective Function

In the real-time stage, although EVs are unified and aggregated by CSEVA to participate in the scheduling of MGs, there is a conflict of interest among EV individuals. Therefore, the whole MG is still a multi-subject system, each EV individual is still independent when making decisions, and no EV individual will give up their own interests to participate in the system scheduling. Therefore, EVs participating in the cooperative union should not only increase their own profits, but also pay attention to the reasonable distribution of profits. EVs should be encouraged to participate more in the real-time scheduling of the system, and at the same time to ensure the travel demand of EV users and consider the cost of charging and the cost of battery degradation.

Therefore, the objective function of an EV union is

$$\max F_{union,t}^{EVs}=C_{incentive,t}^{EV}-{\displaystyle \sum _{i=1}^Z{C}_{i,t}^{EV}}$$

(24)

where $C_{incentive,t}^{EV}$ is the total union revenue; $C_{i,t}^{EV}$ is the cost of the risk of EV selling charging flexibility and power once, i.e., the benefit of participating in scheduling individually; and $Z$ is the number of members of the cooperative union.

(2)

MG objective function

The objective of the MG scheduling plan in the real-time stage is to achieve compensation for deviations from the day-ahead power purchase plan with minimized adjustment costs. In order to guarantee the day-ahead power purchase plan, the energy exchange between the modification and the grid is reduced. In case of deviation from the real-time power purchase, the virtual energy storage aggregated by EVs is prioritized for regulation and correction.

The MG objective function for the real-time stage is as follows:

$$\min F_{real,t}=C_{\mathrm{incentive},\mathrm{t}}^{EV}+C_{punish,t}^{grid}$$

(25)

$$C_{punish.t}^{grid}=H(P_t^N,\tilde{E}{r}_t)\hspace{1em}\hspace{1em}\left|\tilde{E}{r}_t\right|\in (VaR,+\infty ]$$

(26)

In Equations (25) and (26), $C_{\mathrm{incentive},\mathrm{t}}^{EV}$ is the cost of incentive compensation that an MG needs to give to the EV union, $C_{punish,t}^{grid}$ is the cost of extra punishment that an MG needs to give to the grid, and $\tilde{E}{r}_t$ is the actual payload error.

3.2.3. Constraints

(1)

Real-time power balance constraints

$$\left\{\begin{array}{l}{\tilde{P}}_t^{PV}+{\tilde{P}}_t^{WT}+{\tilde{P}}_t^N={\tilde{P}}_t^{Load}\\ {\tilde{P}}_t^{else}+{\tilde{P}}_{ch,t}^{EVs}-{\tilde{P}}_{dis,t}^{EVs}={\tilde{P}}_t^N\end{array}\right.\hspace{1em}\forall t\in T$$

(27)

where ${\tilde{P}}_t^{Load}$, ${\tilde{P}}_t^N$, ${\tilde{P}}_t^{PV}$, ${\tilde{P}}_t^{WT}$ are the actual total system load, the actual payload (i.e., the actual purchased power), the actual PV output power, and the actual wind power output power; and ${\tilde{P}}_{dis,t}^{EVs}$, ${\tilde{P}}_{ch,t}^{EVs}$ are the actual discharge power and the actual charging power of the CSEVA.

(2)

Grid constraints

$$P_{\min ,t}^{grid}\le {\tilde{P}}_t^N\le P_{\max ,t}^{grid}\hspace{1em}\hspace{1em}\hspace{1em}\forall t\in T$$

(28)

$$\left|{\widetilde{Er}}_t\right|\le VaR$$

(29)

In Equations (28) and (29), $\left|{\widetilde{Er}}_t\right|\ge VaR$ means that the MG is over (or under) the power purchase required by the power purchase plan, and will be subject to power purchase punishment for power over the upper and lower limits.

(3)

EV constraints

In the real-time scheduling process, in order to ensure that EV individuals do not leave the cooperative union, it is necessary to ensure that the travel demand of EV individuals and profitability are considered, so the specific constraints are as follows:

$$C_{share,i}^{EV}-C_{i,t}^{EV}\ge 0$$

(30)

$$\left\{\begin{array}{l}So{C}_{x,le}={\widetilde{SoC}}_{x,end}\\ Equations (9)~(11)\&(19)~(20)\end{array}\right.$$

(31)

where ${\widetilde{SoC}}_{x,end}$ is the actual expected SoC at the time of the EV’s departure, and $C_{share,i}^{EV}$ is the EV’s profit from distribution in the cooperative union.

3.3. Approach

In the real-time stage, this paper adopts the dynamic cooperative game model for decision making in order to minimize the MG system real-time adjustment cost. However, the problem of union benefit allocation in the cooperative game process is the core problem of solving the cooperative game. Therefore, this section describes the union benefit allocation and the model solving process in detail.

In solving the cooperative game problem, we can split the solution of the model into two mutually affecting sub-problems: sub-problem 1 focuses on maximizing the interests of the main subjects of the cooperative union, and reasonably allocates the benefits of the individual EVs participating in the cooperative union in order to satisfy the interests of all parties as well as the fairness of the cooperative game; and sub-problem 2 focuses on minimizing the cost of the real-time adjustment of the MG system, and ensures that the cost of the adjustment process is minimized by reasonably allocating the MG system’s internal resources to achieve real-time adjustment cost minimization and ensure the maximization of MG real-time benefits.

Therefore, this paper adopts a bilevel optimal model to solve the cooperative game model: the upper-level model optimization problem is sub-problem 1, its optimization objective is Equation (24), and the decision variable of the upper-level model is the number of cooperative union EVs participating in real-time adjustment. The lower-level model optimization problem is sub-problem 2, whose optimization objective is Equation (25). The decision variables of the lower level are the cost of MG real-time adjustment and the total benefit of cooperative union, calculated according to the optimization of the number of cooperative unions in the upper level, and will be returned to the upper-level model optimization. The flow of the solution algorithm is shown in Figure 2.

The upper-level model optimization calculation is based on an iterative algorithm, which is solved iteratively by setting upper and lower limits for the number of EVs of cooperative unions, solving through different numbers of EVs, passing the optimized number of EVs and the total power of EV response into the lower-level model, and ending the iteration when all EVs in a cooperative union are profitable and no longer increase or reach the upper and lower limits of the number of EVs. At the initial iteration, the cooperative union did not participate in the real-time adjustment; so, by setting an initial value, the initial value is passed into the lower-level model, and the lower-level model carries out the subsequent optimization based on the initial value.

The upper-level model cooperative union EV quantity is passed in from the upper-level model, and Gurobi optimization is used to solve the real-time adjustment cost based on the parameters of the EV quantity passed in from the upper-level model and the cooperative union incentive cost is calculated. At the end of optimization, the cooperative union incentive cost is passed into the upper-level model, the upper-level model calculates and solves the EV individuals’ benefits, and then continues to pass the number of EVs into the upper-level model based on whether all EVs should be profitable or not.

The upper level cooperative union benefit distribution mechanism process is as follows. In Section 3.2.1, the validity of the cooperative gaming union’s achievements is described, i.e., the benefits generated by the cooperative union should be greater than the sum of the benefits of each participant in the union in the separate participation mode. The validity should be

$$C_{\mathrm{incentive},\mathrm{t}}^{EV}>{\displaystyle \sum _{i=1}^Z{C}_{i,t}^{EV}}$$

(32)

For union-based cooperative games, the Shapley value method is commonly used to allocate the benefits of multiple subjects. The Shapley value allocation method is based on the amount of the marginal contribution of the union members to the total benefits of the union to allocate the benefits [34]. Its expression is as follows:

$$C_i^{profit}={\displaystyle \sum _i^N\frac{[(\left|S\right|-1)!(N-\left|S\right|)!]}{N!}}\times [V(S)-V(S/\{i\})]$$

(33)

where $i=1,2,\cdots N$; set $L$ contains the set of cooperative union of all members of the cooperative union; $S$ denotes the set of set $L$ containing member $i$; $V(S)$ is the set of gains generated by the cooperative game played by all contained members $i$ in set $L$; $V(S/\{i\})$ is the gains generated by the game played by set $S$ after removing member $i$; $\left|S\right|$ is the number of members in set $S$; $N$ is the total number of members participating in the cooperative game; and $C_i^{profit}$ is the profit of member $i$, obtained from participating in the cooperative game.

Therefore, to achieve efficient benefit distribution within the cooperative alliance, a special contribution calculation method for individual EVs is designed based on a nonlinear energy mapping function in this work [35]. In detail, this benefit allocation function combines travel risk and energy contribution to determine an EV’s contribution within the alliance. Unlike traditional benefit allocation methods such as the Shapley value method, which requires calculating numerous marginal contribution values, the proposed approach significantly reduces the computational burden. The specific formula is as follows:

$$\begin{array}{l}{\phi }_i^{EV}=F({\displaystyle \frac{P_{dis,t,i}^{EV}}{P_{dis,t,\max }^{EV}}})\times F(R_{i,t}^{EV})\\ {\gamma }_i={\displaystyle \frac{F_i({\phi }_i^{EV})}{{\displaystyle \sum _i^Z{F}_i({\phi }_i^{EV})}}}F(x)\\ C_i^{profit}={\gamma }_i\times C_{\mathrm{incentive},\mathrm{t}}^{EV}\end{array}$$

(34)

where $P_{dis,t,i}^{EV}$, $P_{dis,t,\max }^{EV}$ are the output power of member $i$ and the maximum output power of the members in the union; $R_{i,t}^{EV}$ is the risk factor of member $i$; ${\phi }_i^{EV}$ is the nonlinear energy contribution value of member $i$; $F(x)$ is the nonlinear mapping function, and, in this paper, we use the exponential function of the natural logarithm; and ${\gamma }_i$ is the global contribution of member $i$.

The specific steps for solving the cooperative game using the bilevel optimal model are as follows:

(1)

Initialize the parameters related to MGs, EVs, and cooperative alliances at time t, including parameters such as MG power shortfall, tariff, EV travel risk, and benefits gained from EV participation in scheduling.

(2)

Set the initial number of cooperative union EVs to

$$\mathrm{M}={\displaystyle \frac{\Delta P_{del}}{P_{dis,\max }^{EV}}},$$

(35)

where $\Delta P_{del}$ is the MG power gap and $P_{dis,\min }^{EV}$ is the minimum non-zero discharge power.

(3)

Calculate the total EV response power from the number of participating EVs and pass it to the lower-level model.

(4)

The lower-level model calculates the real-time adjustment cost without EV participation. Then, the EVs that meet the requirements are extracted based on the total EV response power and the number of EVs, and the real-time adjustment cost of the cooperative union’s participation and the cooperative union’s benefits are optimally solved based on the Gurobi solver, and passed into the upper-level model.

(5)

The upper-level model calculates the benefits gained from the EVs’ participation in the cooperative union according to Equation (34).

(6)

Judge whether all EVs participating in the cooperative union are profitable according to Equation (30). If all of them are profitable, output the real-time adjustment cost and EV profitability; otherwise, execute (7).

(7)

Judge whether the number of EVs reaches the upper and lower limits. If so, stop the iteration and output the real-time adjustment cost and EV profitability; otherwise, adjust the number of EVs and execute (3).

4. Simulation and Case Study Results

In this section, the simulation data and the simulation results are given to demonstrate the method proposed above for the applicability of the MG system in the park. The study period lasted for 24 h with a time separation rate of 15 min. For the RESs in the park’s MG system, two small wind turbines rated at 2.5 MW and distributed photovoltaics with a total rated power of 10 MW are considered. It is assumed that all of the charging piles at the charging station in the park MG, which is open to the public and has a maximum capacity of 600 EVs, are V2G charging piles, which means that a maximum of 600 vehicles can participate in the energy scheduling. In order to efficiently dispatch and model EVs, it is therefore assumed that the battery characteristics of EVs of the same type are the same. Additionally, two typical days were selected for analysis in the simulation to demonstrate the applicability of the proposed method. The total number of EVs within the overall timeframe does not equal the maximum capacity for EVs, as EVs continuously flow through the charging station during MG operations. Most EV users are park employees who require extended charging periods. The EV users sign a contract with the industrial park operator to obtain additional benefits. The simulation parameters of the EVs are shown in

Table 1. Parameters of different types of EVs.

Parameter	EV1	EV2
Battery capacity (KW/h)	75	75
Charge/discharge power limit (KW)	60/30	60/30
Charge/discharge power efficiency	0.97/0.97	0.97/0.97
SoC upper/lower limits	1/0	1/0
Battery cycle life (cycles)	1500	2000
Maximum discharge depth	0.8	0.8
Purchase/Recycling Price (USD)	10,350/1400	8300/1400

. The electricity purchase/sale price was derived from market research and may be adjusted based on local actual purchasing and selling market conditions.

The U.S. Federal Highway Administration released the results of the National Household Travel Survey in 2017, and the travel statistics from the survey were normalized and analyzed using maximum likelihood estimation. An EV’s arrival time and departure time were fitted to a normal distribution function [36]. Therefore, in order to take into account the “two-shift” production mode in industrial parks and the impact of nearby residential users on the commuting of EVs, as well as the stochastic nature of the driving behavior of EV users, the bimodal normal distribution model was assumed in this study to be the probability distribution of arrival and departure moments. Due to the uncertainty of EV users’ commuting time, this paper takes the average arrival moment and average departure moment as the expected normal distribution, and randomly generates the arrival and departure times for all EVs. In the industrial park scenario, this paper assumes that the mean arrival times are 8:00 and 18:00 with a standard deviation of 3.5 h. The average departure times are 7:00 and 19:00, and the standard deviation is also 3.5 h. Meanwhile, the SoC of EV users arriving at the park charging station is also randomly generated, and in this paper, it is assumed that the SoC of arriving at the park follows a normal distribution with a mean of 0.3 and a standard deviation of 0.1. The resulting distribution is shown in Figure 3 below.

Figure 4a,b show the predicted output power of PV, WT, and load power curves of MG predicted days ahead. Figure 4c shows the payload error data for 2020–2023. The PV, WT, and load forecast data were obtained from the publicly available dataset at https://transparency.entsoe.eu/ (accessed on 14 September 2024).

In the case of this study, the MG selling and purchase power is calculated using the time-of-use tariffs [37] shown in Figure 5. The park’s ability to become tolerant to risk is set by the decision maker, and this parameter will affect the stability evaluation and robustness of the park.

The software tools used for model building and for solving the proposed model in this paper were Gurobi 11.0.0 and Python 3.10, and the hardware parameters for the implementation were 3.20 GHz AMD Ryzen 7 5800H 64-Core Processor CPU, NVIDIA GeForce GTX 1650 GPU, and 16.00 RAM.

4.1. EV Travel Risk Analysis

In this section, the travel risk coefficient is analyzed based on EV charging behavior and corresponding influencing factors to validate its effectiveness. EV users are assumed to start charging upon arrival and report their desired SoC and departure time. Meanwhile, the charging stations will update the EV’s current SoC in a real-time manner during the charging process.

Figure 6 illustrates the relationship between the current SoC and travel risk. The travel risk of EV users decreases with the increase in SoC. This suggests that a larger current SoC leads to a shorter required charging time and lower travel risk, and vice versa. Thus, EV users are more inclined to discharge for greater benefits.

Meanwhile, different EVs have different SoC expectations at the moment of departure, and the travel risk curves are also different. Users with high SoC expectations have greater travel demand and are more sensitive to changes in SoC. In addition, their travel risk is greater, increasing with the rate of change in SoC. In addition, their choices change at different stages. At the high-SoC stage, these users focus on their own profitability, while at the low-SoC stage, they pay more attention to their own travel demands. In contrast, users with low SoC expectations have lower travel demands and are less sensitive to SoC changes, and their travel risk has a relatively small rate of change with SoC. Their choices at different stages are more consistent, and their discharge flexibility is lower than that of users with high SoC expectations.

The time required for EV charging and stopping time are also major factors affecting travel risk. In order to obtain a better representation of the current impact of the time required for EV charging and stopping time on travel risk, this paper incorporates the ratio of the two into the travel risk model. As shown in Figure 7a, as the ratio of time required for charging and dwell time (referred to as charging-to-stopping ratio) is larger, the slope of travel risk variation with SoC is smaller. Therefore, the larger the charge–stop ratio is, the richer the choices of EV rechargeable time slots are, and EV users are more inclined to discharge at that time slot to obtain greater benefits. However, as shown in Figure 7b, with the same SoC of EVs and the same time required for charging, as the stopping time is shortened, i.e., the closer to the moment of departure, the EV user’s willingness to charge is stronger, and thus the risk of traveling increases accordingly and the EV user is more inclined to charge in that time period to satisfy his or her traveling needs. In the case of the same stopping time and the same SoC, as shown in Figure 7c, the shorter the charging time is, the more charging time slots are available for EVs; then, EV users’ willingness to charge is lower, and they are more willing to discharge to obtain a greater benefit.

In summary, the travel risk model can well describe the willingness of EV users to charge and discharge, can help in planning and decision-making regarding the charging and discharging behaviors of EVs, and assist in scheduling EVs to participate in intra-day energy management.

4.2. Analysis of the Results of the Day-Ahead Scheduling Stage

This subsection analyzes the dispatch results in the day-ahead stage. In the day-ahead stage, the system utilizes the average VaR as the power allowance range and signs a power purchase plan with the grid based on the day-ahead dispatch results; the smaller the system error of the power purchase plan signed in the day-ahead market, the smaller the tariff received. Since VaR is positively correlated with the confidence level, it can be seen from

Table 2. System cost and risk cost at different confidence levels.

Confidence Level	0.9	0.95	0.99
RES operating costs (USD)	50,967.51	50,967.51	50,967.51
Power purchase costs (USD)	566,328.27	573,865.38	596,476.69
Penalty costs (USD)	263,093.27	253,128.39	231,744.28
Total system cost (USD)	880,389.05	877,961.28	879,188.48

that under the same system configuration, the system cost tends to increase as the confidence level continues to rise. In contrast, the cost of risk shows a monotonically decreasing trend as the confidence level continues to rise. This is because the higher the confidence level, the greater the uncertainty of the system’s dispatchable resources, the more conservative the day-ahead scheduling plan, and the smaller the penalty risk borne by the system during the day. When the system bears more cost, the risk cost decreases. The day-ahead scheduling results reported in this paper were derived at a confidence level of 0.95.

The results of the day-ahead MG scheduling in the park are shown in Figure 8. It can be seen that after optimal scheduling, the peak-time electricity consumption periods (11:00–13:00 and 18:00–20:00) shift to valley-time periods (16:00–18:00) by means of scheduling the EV. Consequently, the maximum peak–valley difference in the park is reduced by about 3%. At the same time, it avoids EV charging in the two peak hours of the distribution network, which helps alleviate the phenomenon of “peak-on-peak” in the distribution network. In addition, after day-ahead, the day-ahead load curve is smoother, reducing the volatility of the park’s load curve.

The result for the schedulable potential capacity of EVs is shown in Figure 9. The schedulable potential is calculated by the scheduling load of CSEVA. In Figure 9a,b,e,f, it can be seen that MG plans the CSEVA charging at low electricity price periods for EV charging. During high electricity price periods, the CSEVA performs EV-dispatchable discharging. The planning of EVs’ orderly charging reduces the electricity purchase cost. The day-ahead dispatchable potential power and electricity results are shown in Figure 9c,d,g,h, which show that the dispatchable potential has high downward regulated power during charging time periods and low upward regulated power. Meanwhile, the schedulable potential capacity of EVs increases as the number of EVs increases. During charging periods, as the number of charging EVs increases, the SoC of EVs and the regulated capacity of CSEVA keeps rising, but the holdable capacity decreases. When the SoC of EVs decreases, the regulated capacity decreases, and the holdable capacity rises.

Figure 10 shows the charging curves of all regular EVs before the day. It can be seen that the number of EV charging times in the day-ahead stage is not greater than two. Therefore, the continuity of EV charging is increased and frequent EV charging is avoided, which protects the service life of the individual EV batteries.

4.3. Analysis of the Results of the Real-Time Correction Stage

Figure 11 shows the actual and predicted data for PV, WT, and load in the real-time scheduling stage.

The real-time scheduling results are demonstrated in Figure 12. In Figure 12, it can be seen that the real-time correction strategy used in this paper can achieve better tracking performance and ensure that the intra-day dispatch results do not overly deviate from the day-ahead schedule plan.

The intra-day power purchase results are shown in Figure 13, which shows that the intra-day power purchases from the same distribution network are all within the power day-ahead purchase plan, and there is no penalty due to large deviations.

Table 3. Comparison of intra-day system operating costs and adjustment costs.

Cost Type	With EV Participation	Without EV Participation
Intra-day system operational costs (USD)	53,429.12	53,429.12
Intra-day adjustment costs (USD)	2655.09	32,335.81
Intra-day power purchase costs (USD)	574,084.98	574,084.98
Total intra-day costs (USD)	630,169.19	659,849.91

shows the total system operating costs and total real-time adjustment costs for the real-time phases before and after EV participation at the 0.95 confidence level, where the intra-day system operating costs and intra-day power purchase costs do not change, but the intra-day adjustment costs for EV participation do not change. The day adjustment costs are reduced by about 90%.

In addition, the real-time adjustment cost is shown in Figure 14. It can be seen that in the real-time stage, the real-time adjustment cost paid by EVs’ participation in the scheduling is much smaller than that paid by EVs’ non-participation.

In the real-time stage, the overall benefit of the coalition is used as the final evaluation standard in the decision-making process, based on the solution algorithm for the bilevel optimization model proposed in Section 3.3. Figure 15 demonstrates the trend of incentive cost and penalty cost, where the number of EVs of the initial EV coalition EVs is set as M and the upper limit of the EV number is set as $M_{\max }={\displaystyle \frac{\Delta P_{del}}{P_{dis,\min }^{EV}}}$. From Figure 15, it can be seen that as the number of EVs increases, the penalty cost decreases and the incentive cost gradually increases. However, the incentive cost increase speed is much smaller than the decrease speed of the penalty cost. As the penalty cost decreases to 0, the total cost reaches its minimum. The total cost increases as the number of EVs increases. Therefore, when the penalty cost reaches 0, the EV number obtains the optimal solution.

By combining the cost and the number of EVs shown in Figure 15, the EV benefit curve in the upper optimization model can be derived. In Figure 16, when the number of EVs is M, i.e., the penalty cost is 0, the total coalition benefit has an inflection point and reaches the maximum benefit. Subsequently, the number of EVs is increased. As the MG is not granting the subsidy, the total coalition benefit is no longer increasing, and all EVs participating in the cooperative union are profitable according to the calculation. Therefore, for the decision-making process of this algorithm, the coalition benefit can be maximized when the penalty cost is the lowest.

The CSEVA real-time dispatch results are shown in Figure 17 and Figure 18. It can be seen that the CSEVA charging power is more dispersive and not just concentrated in the low price periods. CSEVA needs to deal with the power fluctuation in the real-time stage due to the uncertainty of PV, WT, and load. When the load is exceeded during peak times, EVs spontaneously form a coalition to discharge to meet the power demands of the MG. In addition, EVs that participate in the response regulation are also compensated for by incentives. During periods when the power consumption is low, the park MGs utilize the reduction in charging tariffs through price incentives to encourage EV users to consume more electricity.

The real-time charging cost of EV users is shown in Figure 19 and

Table 4. Comparison of charging costs for EVs participating in real-time correction.

Type of EV (Initial SoC = 40%)	Average Charging Cost on Day#1 (USD)	Average Charging Cost on Day#2 (USD)
Best-case EV user	−5.11	−6.21
Regular EV user	16.96	18.74
Temporary EV user	35.98	35.98

. It can be seen that the users who participate in discharging can reduce the charging cost in the real-time stage, and some EVs not only realize 0-cost charging at the real-time stage, but also obtain the revenue. As shown in Table 4, the cost of electricity consumption for the users who participate in regulation is much lower than that of the users who do not participate in regulation.

The EVs’ SoC at the departure time slot in the real-time stage is shown in Figure 20. The SoC of all of the EVs participating in regulation achieve their desired values, while only 2.3% of them are not fully charged. Therefore, the proposed travel risk model can effectively quantify the effect of current charging and discharging on the desired departure SoC. Consequently, EVs in the regulation process gain benefits while satisfying their own travel needs.

It should be noted that the nonlinear energy mapping function and two-layer optimization model proposed in this paper achieve millisecond-level solution speeds for cooperative game problems in the simulation process. Given that the decision time interval in this method is 15 min, there exists a significant order-of-magnitude difference between the decision cycle and computational response time. This discrepancy does not substantially impact the decision process or outcomes. Therefore, this approach effectively reduces computational burden when the number of EVs in the cooperative alliance increases exponentially, enabling problem resolution. Furthermore, the proposed two-stage microgrid energy scheduling—based on CVaR and dynamic cooperative games while accounting for EV travel risks—effectively manages energy and resources for the campus microgrid during both day-ahead and real-time planning phases. This reduces operational costs and ensures the stable operation of the campus microgrid.

4.4. Comparative Experiments and Analysis

In order to verify the feasibility and superiority of the proposed method, a traditional two-stage energy management strategy for MGs was conducted for comparison. Descriptions of three methods are provided as follows:

Method #1: The energy dispatch method based on traditional forecasting is used in the day-ahead stage, and the energy management strategy considering economic dispatch is used in the real-time stage.

Method #2: The day-ahead stage is consistent with method #1, and the energy management strategy considering economic objectives based on the psychological model of EV users is used in the real-time stage.

Method #3 (proposed): The day-ahead dispatch model is based on CVaR and EV dispatchable potential. The real-time stage adopts the EV travel risk model and a dynamic cooperative game.

In addition, the three methods are consistent in the configurations of PV, wind turbines, and EVs. The results of the comparison experiments are shown in

Table 5. Comparison of energy management strategy for the park microgrid with day-ahead forecasting and real-time dispatch strategy.

Indicator		Method #1	Method #2	Method #3
Economic indicators	Operational costs (USD)	53,429.12	53,429.12	53,429.12
	Adjustment costs (USD)	7272.73	6153.84	2655.09
	Penalties (USD)	0	112,867.13	0
	Purchased electricity cost (USD)	609,230.76	608,811.19	574,084.98
	Total cost (USD)	669,932.61	781,261.06	630,169.19
EV user satisfaction indicators	Travel demand satisfaction rate	78.8	90.2	100
	Average SoC	93.1	97.7	99.9

and Figure 21.

The following analysis focuses on the economy and EV user satisfaction. Compared with method #1, the proposed method exhibits more economic benefits, reducing the total cost by 6%, the adjustment cost by 63%, and the power purchasing cost by 5.7%. As can be seen in Figure 21, though the real-time power purchase curve and day-ahead forecast consistency of method #1 is better, the two have no penalty costs because the adjustment result of method #3 is within the tolerance interval. In terms of EV user satisfaction, the travel demand satisfaction rate of method #3 is 100% (method #1—78.8%), and the satisfaction of the average SoC at departure time is 99.9% (method #1—93.1%). Thus, it can be verified that the travel risk model in this paper effectively realizes the scheduling of EVs and guarantees the travel demand of EVs. In addition, under the proposed energy management strategy, a certain amount of power purchase curve consistency is sacrificed, but the operational cost is reduced and the travel demand of EV users are met, which can improve satisfaction and willingness to participate in the scheduling of EVs.

Compared with method #2, the proposed energy management method fully considers the EV dispatch potential and the uncertainty of renewable energy, EVs, and loads in the day-ahead phase, and does not incur penalty costs in the real-time phase through the effective scheduling of EVs.

For method #2, these factors are not effectively considered in the day-ahead stage, leading to large penalty costs and an increase in the total costs of 19.3%. Thus, the proposed method reduces the park microgrid operation costs, avoids high penalty costs, and achieves the economic operation of the MG through the calculation of CvaR and EV dispatchable potential. The EV user satisfaction indicators of method #3 are higher than for method #2. Through the travel model and the full consideration of EV dispatchable potential in the day-ahead stage, it comprehensively enhances the service experience of EV users, and lays a good foundation for the promotion of users’ participation in grid scheduling. This double enhancement of economy and user satisfaction fully verifies the superiority and practical value of the energy management strategy in this paper.

To validate the impact of EV penetration rates on the methodology proposed in this paper, experiments were conducted for a typical day under different EV penetration scenarios with 100% penetration as a baseline. The statistical analysis of metrics including real-time adjustment costs and EV charging fulfillment rates yielded the results shown in

Table 6. Comparison of method results based on different electric vehicle penetration rates.

Method	Permeability	Real-Time Adjustment Costs (USD)		EV Charging Achievement Rate (%)
		Adjustment Cost	Electricity Purchase Cost	Travel Demand Satisfaction Rate	Average SoC
Method #3	80%	2920.599	574,084.98	95.6	94.2
Method #3	100%	2655.09	574,084.98	100	99.9
Method #1	100%	7272.73	669,932.61	93.1	78.8

. In Table 6, higher EV penetration rates yield greater dispatchable EV potential. Although real-time adjustment costs exhibit no significant change, the increased number of dispatchable EVs leads to higher EV charging success rates. Consequently, the proportion of EVs reaching the desired SoC levels notably increases, and average charging costs decrease. However, compared to other methods, the proposed approach maintains substantially lower real-time adjustment costs and electricity procurement costs even at reduced penetration rates, while achieving significantly superior EV-related metrics.

In summary, the proposed two-phase microgrid energy scheduling method can effectively utilize the EV’s dispatchable potentials and reduce total operational costs due to the introduction of CVaR and a dynamic cooperative game. In addition, the stable operation of the MG can be guaranteed.

5. Summary and Prospects

5.1. Summary

In this paper, a two-stage microgrid energy schedule based on CVaR and a dynamic cooperative game considering EV dispatchable potential and travel risk is proposed for an industrial park MG. In this model, the uncertainty of MGs and schedulable potential capacity of EVs are modeled using CVaR and Minkowski additivity in the day-ahead phase, and this mixed-integer optimization problem is solved using Gurobi. In the real-time stage, the EV travel risk function is established based on the generalized bell-shaped affiliation function for EV user travel demand variability, which is integrated into the cooperative game model in the real-time stage, and then solved using the bilevel optimal model.

In addition, a simulation validation was carried out using the case of an industrial park, and the conclusions are as follows:

• The method proposed in this paper verifies that EVs’ charging demand is concentrated in the valley of electricity consumption in the park, avoiding the “peak-on-peak” phenomenon; moreover, the method ensures the continuity of EV charging and protects the service life of EV batteries while reducing the load volatility of the MG.
• In the real-time phase, the EV scheduling model for travel risk proposed in this paper rationally arranges the charging and discharging demand of EVs according to their travel demand, thus significantly reducing the charging cost for EV users by 50% on average. In the best case, it not only meets the travel demand of EV users, but also ensures that EV users achieve profitability.
• The real-time phase of the real-time dynamic cooperative game decision-making model proposed in this paper not only reduced the cost of the real-time adjustment of the system, but also reduced the deviation from the previous day’s real-time plan while meeting the travel demands of all EV users, achieving a win–win situation for the system participants.

In terms of the uncertainties of load, EVs, and RESs, the model proposed in this paper is limited, as these uncertainties are based on a large amount of historical data and do not consider EV user privacy and V2G technology information security issues. In future research, we are committed to the study of MG and EV energy management strategies based on a distributed robust framework to achieve the secure and stable operation of EVs and MGs under fusion privacy protection.

5.2. Real-World Applications

The proposed model can be applied in real-world industrial, residential, or commercial parks with the following conditions: (1) the EVs in these scenarios should remain parked for extended periods in one day. (2) The park must be equipped with V2G chargers and exhibit a certain level of vehicle mobility characteristics. (3) The uncertainty of RES and load is derived from extensive historical data, which suggests that the model’s scheduling accuracy is influenced by the reliability of the historical data. (4) EV users sign a contract with the operator of the park or MG; thus, their EVs should be fully dispatchable when connecting to the charger. Furthermore, EV user privacy and V2G technology information security issues need to be considered in real-world scenarios due to their impact on the willingness to be scheduled, which is not the main focus of this work.

5.3. Future Work

In future research, the authors are committed to developing energy management strategies for MGs and EVs within a distributed robust optimization framework. By leveraging such models, the authors aim to enhance the system’s adaptability and robustness. Simultaneously, tailored scheduling strategies for EV users with distinct characteristics will be considered to enable a “customized” scheduling approach. This approach will balance EV privacy protection while improving the safety, robustness, and stability of MG operations.