Pricing Strategies for Distribution Network Electric Vehicle Operators Considering the Uncertainty of Renewable Energy

Abstract

In the future, the active load of the distribution network side will be dominated by electric vehicles (EVs), showing that the charging power demand of electric vehicles will change with the change in charging electricity price. With the popularity of electric vehicles in the distribution network, their aggregation operators will play a more prominent role in pricing management and charging behavior, and setting an appropriate charging price can achieve a win–win situation for operators and electric vehicle users. At the same time, the proportion of scenery in the distribution network is relatively high, and the uncertainty of self-output has a certain impact on the pricing strategy of operators and the charging behavior of electric vehicle users, which has become an important research topic. Based on the above background, an EV operator pricing strategy considering the landscape uncertainty is proposed, a Stackelberg game model is established to maximize the respective benefits of operators and EV users, and the two-layer model is further transformed into a single-layer model through the Karush–Kuhn–Tucker (KKT) condition and duality theorem. Finally, the IEEE 33 system is simulated with the CPLEX solver, and the global optimal pricing strategy is obtained. Simulation results prove that electric vehicle operators experience a maximum profit increase of 2.6% due to the impact of maximum capacity of energy storage equipment and the uncertainty of renewable energy output can result in electric vehicle operators losing approximately 20% of their profits at most.

1. Introduction

1.1. Background

The number of electric vehicles has greatly increased in recent years. However, charging behavior is random in time and space, which will affect the operation of the distribution network when large-scale EVs charge un-coordinately. Ref. [1] analyzes the elasticity of a power system from the perspective of the grid and from the perspective of a review. Therefore, it is urgent for an electric vehicle operator to guide EV charging. The schedulable potential of electric vehicles can be reached by setting reasonable charging prices.

1.2. Literature Survey of EVs

The charging behavior of EVs has drawn wide attention at present. In [2], a recharging scheme for EVs is proposed, which considers load, electricity pricing, and renewable energy generation uncertainties. It can be used for peak load shifting and benefit both users and operators. Deep reinforcement learning is applied in [3]. The EV charging scheduling problem is formulated as a Markov Decision Process to find the optimal charging strategy that can balance the charging cost and users’ anxiety. Ref. [4] considers the random arrival of EVs in a residential distribution network. The objective function is to minimize power loss and voltage deviation. EVs charging orderly can participate in the auxiliary service market, so a real-time controller is proposed in [5]. Results show that the controller improves regulation capacity and battery cycling. The charging strategy based on transactive control is divided into two time scales including the day-ahead electricity procurement and the real-time charging management in [6]. There is a conflict between capacity configuration and economic dispatch. Therefore, a cooperative optimization method is proposed to minimize the total cost in [7]. Ref. [8] further considered EV diffusion. It is first modeled and an adaptive fast charging strategy is presented to cope with it. Ref. [9] not only considers minimizing operation costs but also minimizing carbon emissions. Hence, a multi-objective function is proposed to balance the economy and environmental friendliness.

1.3. Literature Survey of Game Theory

At the same time, the EV operator and EV users belong to different owners of interests. The aims of EV operators and EV users are to maximize profits and minimize charging costs, respectively. Obviously, there is a conflict of interest between them. And the pricing strategy of an EV operator is a Stackelberg primary–secondary game process. Ref. [10] studies the charging problem in heterogeneous networks and confirms the effectiveness of the model. The Stackelberg game model has also been used in other aspects of the research. A Stackelberg market strategy is proposed in [11]. Two sides in this game are a distribution market operator and virtual power plants. A multi-timescale algorithm is proposed to solve the allocation problem of available energy and power, which can reduce the power imbalance [12]. To achieve low-carbon economic goals, ref. [13] establishes an energy management method based on the Stackelberg game. In this model, the energy service provider is the leader and prosumers are the followers. Ref. [14] uses the Stackelberg game model to study the interaction between generators and microgrids. Entities on two sides aim to maximize their profits. The Stackelberg game is combined with the distributionally robust optimization in [15]. An energy hub is the leader while EVs are followers in the Stackelberg game model. And the robust model is used to cope with the uncertainty of renewable generation. An optimal operation strategy for a multi-energy microgrid participating in an auxiliary service market is proposed in [16]. The Stackelberg game model is proposed to achieve the peak load shifting in an industrial park [17]. The leaders are unit owners, while the followers are a group of industrial users.

1.4. Literature Survey of New Energy Uncertainty

The analysis of distribution network elasticity has been mentioned in [18,19]. As the penetration of wind and solar power increases in the distribution network, it is necessary to consider the uncertainty. And the chance constraint is a way to deal with it. An online optimal control strategy for power flow management in microgrids with EVs is proposed in [20]. The chance constraint is used to deal with uncertainties of the EV state of charge and connection times. Ref. [21] proposes a two-stage energy management system for power grids with EVs. Results show that the chance constraint can capture the forecast uncertainties, effectively. The total storage power and energy constraints are presented as chance constraints because the renewable generation output or the load power cannot be acquired accurately [22]. To meet future stochastic power and natural gas demands, a chance-constrained programming approach is proposed in [23]. Short-time uncertainties managed by the natural gas storage are also considered in developing a long-term expansion plan for the integrated system. A chance-constrained optimal power flow model is established in [24]. The chance constraints can also be combined with a distributionally robust optimal model, which is used to solve the economic dispatch problem in [25,26,27].

1.5. Motivations

With this background, most existing research aims to maximize the benefits of EV operators or minimize the costs of EV users. Few studies consider the relationship between them, which is meaningful to explore. Then, the topology and power flow of distribution networks are rarely considered. It will affect the EV users’ electricity consumption behavior and further affect the pricing strategy of EV operators. From an environmental point of view, the impact of wind and solar uncertainty on power system operation cannot be ignored. And the distribution network takes the responsibility of new energy accommodation. Thus, there is a correlation between the pricing strategy and the uncertainty of new energy. In summary, it is significant to study the pricing strategy for EV operators considering the above factors.

1.6. Contributions

In this paper, a pricing strategy for EV operators considering wind and solar uncertainty is proposed. First, three kinds of EVs are modeled in this paper. And a two-layer Stackelberg game model is established since the charging behaviors of EV users are influenced by the charging price in the real-time market. The objective function of the upper layer is to maximize the profits of EV operators, while the lower layer aims to minimize the charging costs of EV users. In this model, the wind and solar uncertainty is considered. This is because it can influence the charging price in the real-time market. The typical operation scenes are obtained by Monte Carlo sampling. Then, the uncertainty can be represented by the chance constraints. This two-layer model is converted into a mixed-integer linear programing model using the Karush–Kuhn–Tucker optimality conditions and the strong duality theory. Finally, a revised IEEE 33-bus distribution system is used to verify the feasibility and effectiveness of the proposed model.

1.7. Comparison with Existing Research

Ref. [28] proposes a new distributed algorithm for port microgrids to solve the economic dispatch model, which has the advantage of not only converging quickly to obtain the optimal solution but also protecting the ship’s private information. In the two-tier model we construct, the upper-tier EV operator transmits charging tariff information to the lower-tier EV user, and the lower-tier EV user transmits the demanded power to the upper-tier EV operator; a new reinforcement learning framework is proposed in [29] to determine the optimal charging schedule for EVs, so as to maximize the profitability of charging stations. We adopt a primary–secondary game approach to maximize the profitability of the EV operator while minimizing the charging cost of the EV users, which takes care of the interests of both subjects; ref. [30] ensures the existence of a unique equilibrium solution in pricing-based demand–response by using the proposed pricing conditions, and proposes an energy control strategy capable of eliminating the peak loads and matching the supply with the demand. We use the KKT algorithm to solve the proposed two-tier model, which transforms the lower constrained optimization problem into the upper constraints by introducing the Lagrange multipliers and the duality theory, thus guaranteeing a unique optimal solution, and at the same time strictly guaranteeing the matching of supply and demand.

2. A Stackelberg Model for Electric Vehicle Operator Pricing in Distribution Network

The energy supply sources of the entire system include the wind turbine (WT), photovoltaic (PV), and power supply of the large grid. The load includes the fixed load of each node and the load of EVs. At the same time, electric vehicle operators store and release energy through a battery energy storage system (BESS). The electricity supplied by renewable energy and the power grid is consumed in real-time by users and electric vehicles, or stored by energy storage devices to achieve a balance between supply and demand of electricity. The flow chart of system energy supply and demand is shown in Figure 1.

As an intermediate link between the distribution network and EV users, EV operators set charging prices that meet the needs of the grid and EV users by aggregating an EV bus in the distribution network and collecting information on grid electricity price and user charging time. Electric vehicle operators need to set the electricity price for each period of the next day, but the users make the operator raise or lower the price for a certain period of time due to the consideration of their own charging cost, which constitutes the Stackelberg game relationship between electric vehicle users and operators. The upper decision-maker of the two-layer model is the operator of electric vehicles, and the lower decision-maker is the owner of electric vehicles. The specific game structure is shown in Figure 2.

The flow chart of the solution is also described in Figure 2: the upper layer establishes the objective function with the maximum profit of the electric vehicle operator, and the lower layer establishes the objective function with the minimum charging cost of the electric vehicle. The lower layer is written as the optimal condition of KKT and the strong duality theorem is used to transform the two-layer model into a single-layer model, and finally the Stackelberg game model composed of upper and lower layers is solved.

2.1. Upper Model

2.1.1. Upper Objective Function: Maximize Profits for Electric Vehicle Operators

At the upper level, the profit of electric vehicle operators is the maximum objective function, and the profit of operators is composed of four parts: income from selling electricity, income from selling electricity in the real-time market, cost of contract electricity purchased in the day-before market, and cost of purchasing electricity in the real-time market. The specific expression is as follows:

$$\max {\displaystyle \sum _t^T{\displaystyle \sum _i^I{\displaystyle \sum _n^{N_{EV}}{c}_t{P}_{n,i,t}}}}+{\displaystyle \sum _t^T{\displaystyle \sum _n^{N_{EV}}(c_t^{sell}{D}_{n,t}^{sell}-c_t^d{D}_{n,t}-c_t^{buy}{D}_{n,t}^{buy})}}$$

(1)

where $P_{n,i,t}$ is the charging power of the i electric vehicle at bus n of the distribution network during the period t; $c_t^{buy}$ and $c_t^{sell}$ are, respectively, the purchase and sale prices of electricity in the real-time market at time t; and $c_t^d$ is the contract purchase price from the day-ahead market at time t.

2.1.2. Constraints for Electric Vehicle Operators

Electric vehicle operators have range and scope constraints in pricing and the specific relationship is as follows:

$$\begin{array}{l}{c}_t^L\le c_t\le c_t^U,\forall t\\ {\displaystyle \sum _{t=1}^T{c}_t/T=c_{av}}\end{array}$$

(2)

where $c_t$ is the charging price specified by the operator during the t period; $c_t^L$, $c_t^U$, and $c_{av}$ are, respectively, the lowest, highest, and daily average electricity prices in time period t; and $T$ is the total number of periods.

The constraints on the operator’s energy transaction state and the state of the energy storage device are as follows:

$$\begin{array}{l}{D}_{n,t}\ge 0,0\le D_{n,t}^{buy}\le M{\kappa }_{n,t}\\ 0\le D_{n,t}^{sell}\le P_{n,t}^{dis}(1-{\kappa }_{n,t})\\ {\displaystyle \sum _i^I{\displaystyle \sum _n^N{P}_{n,i,t}}}+P_{n,t}^{cha}-P_{n,t}^{dis}=D_{n,t}+D_{n,t}^{buy}-D_{n,t}^{sell}\\ \hfill \forall n\in N_{EV},t\end{array}$$

(3)

$$\begin{array}{l}{E}_{n,1}=E_{n,T}=E_{n,0}\\ 0\le P_{n,t}^{cha}\le {\mu }_{n,t}{P}_{\max }^{cha},0\le P_{n,t}^{dis}\le (1-{\mu }_{n,t})P_{\max }^{dis}\\ E_{n,t}=E_{n,t-1}+{\eta }^{cha}{P}_{n,t}^{cha}-{\eta }^{dis}{P}_{n,t}^{dis},0\le E_{n,t}\le E_{n,\max }\\ \hfill \forall n\in N_{EV},t\end{array}$$

(4)

where $D_{n,t}^{buy}$ and $D_{n,t}^{sell}$ are the electricity purchased and sold from the n bus of the distribution network during the t period; $D_{n,t}$ is the contract electricity quantity at bus n of the distribution network during the day-ahead market time t; $P_{n,t}^{cha}$ and $P_{n,t}^{dis}$ are the charge and discharge of energy storage devices on bus n of the distribution network during period t; ${\kappa }_{n,t}$ and ${\mu }_{n,t}$ are Boolean variables, indicating the state of energy transaction and the state of energy storage equipment on bus n of the distribution network; $P_{\max }^{cha}$ and $P_{\max }^{dis}$ are the maximum charge and discharge power of the energy storage device, respectively; ${\eta }^{cha}$ and ${\eta }^{dis}$ are charging and discharging efficiency, respectively; $E_{n,\max }$ and $E_{n,0}$ are the maximum and initial capacities of energy storage devices on bus n of the distribution network; $M$ is a large-enough positive number; and $N_{EV}$ indicates the number of buses where the electric vehicle resides.

2.1.3. Distribution Network Constraints

$$\begin{array}{l}{P}_{m,t}^{wind-e}+P_{m,t}^{pv-e}+P_{m,t}^G+{\displaystyle \sum _{j<n}{P}_{jm,t}}={\displaystyle \sum _{k>n}{P}_{mk,t}}+{\displaystyle \sum _i^I{P}_{n,i,t}}+P_{m,t}^{Load}\\ Q_{m,t}^G+{\displaystyle \sum _{j<n}{Q}_{jm,t}}={\displaystyle \sum _{k>n}{Q}_{mk,t}}+Q_{m,t}^{Load}\\ U_{m,t}^2-U_{j,t}^2=2(r_{mj}{P}_{mj,t}+x_{mj}{Q}_{mk,t})\\ U_{m,\min }^2\le U_{m,t}^2\le U_{m,\max }^2\\ -S_l\le P_{mj,t}\le S_l\\ -S_l\le Q_{mj,t}\le S_l\\ -\sqrt{2}{S}_l\le P_{mj,t}+Q_{mj,t}\le \sqrt{2}{S}_l\\ -\sqrt{2}{S}_l\le P_{mj,t}-Q_{mj,t}\le \sqrt{2}{S}_l\\ \hfill \forall n\in N_{EV},m\in N,\forall j,t\end{array}$$

(5)

where $P_{m,t}^{wind-e}$ and $P_{m,t}^{pv-e}$ are the actual injected power of wind power and solar output at m bus of the distribution network at time t, respectively; $P_{m,t}^G$ and $Q_{m,t}^G$ are active and reactive power injected into m bus of the distribution network at time t; ${\displaystyle \sum _{j<n}{P}_{jm,t}}$, ${\displaystyle \sum _{k>n}{P}_{mk,t}}$, ${\displaystyle \sum _{j<n}{Q}_{jm,t}}$, and ${\displaystyle \sum _{k>n}{Q}_{mk,t}}$ are the sum of the active and reactive power of the branches of bus mj injected and discharged, respectively; $P_{m,t}^{Load}$ and $Q_{m,t}^{Load}$ are the active and reactive loads of m bus of the distribution network at time t, respectively; ${\displaystyle \sum _i^I{P}_{n,i,t}}$ is the total charging power of electric vehicles on bus n of the distribution network at time t; $P_{mj,t}$ and $Q_{mj,t}$ are the active power and reactive power flowing on line mj, respectively; $U_{m,t}$ is the bus m voltage at time t; $r_{mj}$ and $x_{mj}$ are the resistance and reactance of line mj, respectively; $U_{m,\max }$ and $U_{m,\min }$ are the maximum and minimum voltages of bus m, respectively; and $S_l$ is the apparent power of the line l.

2.1.4. Chance Constraints on the Uncertainty of Wind Power and Solar Output

The difference in uncertainty between solar and wind energy is not examined in depth, and it is assumed that the uncertainties in wind power output and solar power output are approximate. The opportunity constraint equation can be expressed as

$$\mathrm{Pr}\left\{\begin{array}{l}\alpha {\displaystyle \sum _{t\in T}{\displaystyle \sum _{wind\in W}\widetilde{P_{t,s}^{wind}}}}\le {\displaystyle \sum _{t\in T}{\displaystyle \sum _{wind\in W}{P}_t^{wind-e}}}\\ \widetilde{P_{t,s}^{wind}}\ge P_t^{wind-e},\forall s,t,wind\end{array}\right\}\ge 1-\beta$$

(6)

where Pr{.} is the probability of inequality being established in {}, $\widetilde{P_{t,s}^{wind}}$ is the random wind power output of sample s at time t obtained by the Monte Carlo method, α is the percentage of wind power utilization, and W is the sampling set of wind power. This formula indicates that the probability of wind power satisfying a certain range is 1 − β.

Monte Carlo sampling is performed on the above expression to transform the random problem into a deterministic chance constraint problem. The specific expression is as follows:

$$\begin{array}{l}{\displaystyle \sum _{s\in S}{\sigma }_s}\le \beta \cdot \left|S\right|\\ {\sigma }_s\in \{0,1\},\forall s\\ \widetilde{P_{t,s}^{wind}}+M\cdot {\sigma }_s\ge P_t^{wind-e},\forall s,t,wind\\ \alpha {\displaystyle \sum _{wind\in W}{\displaystyle \sum _{t\in T}\widetilde{P_{t,s}^{wind}}}}\le M\cdot {\sigma }_s+{\displaystyle \sum _{wind\in W}{\displaystyle \sum _{t\in T}{P}_t^{wind-e}}},\forall s\end{array}$$

(7)

where ${\sigma }_s$ is the number of wind power 0/1 variables that meet the requirements, $\beta$ represents the forecast probability of wind power, and $\left|S\right|$ represents the total number of samples; solar power is treated in the same way.

2.2. Lower Model

2.2.1. Lower Objective Function: Minimize Charging Costs for Electric Vehicles

In this paper, the objective function is to minimize the total cost of the system:

$$\min {\displaystyle \sum _t^T{\displaystyle \sum _i^I{\displaystyle \sum _n^{N_{EV}}{c}_t{P}_{n,i,t}}}}$$

(8)

The lower objective function is the minimum objective function of electric vehicle users’ electricity purchase cost based on the interests for electric vehicles themselves.

2.2.2. Constraints for Electric Vehicles

The constraints of the lower-level EV model can be expressed as

$$\begin{array}{l} {\displaystyle \sum _{t\in T_a}^T{P}_{n,i,t}=0.9V_{n,i,\max }-V_{n,i}^0,}\forall n\in N_{EV},\forall i:{\lambda }_{n,i,t}\\ 0\le P_{n,i,t}\le P_{n,i,\max },\forall n\in N_{EV},t\in T_a,\forall i:{\pi }_{n,i,t}^{-},{\pi }_{n,i,t}^{+}\\ P_{n,i,t}=0,\forall n\in N_{EV},t\notin T_a,\forall i:{\delta }_{n,i,t}=0\end{array}$$

(9)

where $V_{n,i,\max }$ is the battery capacity of the i electric vehicle on bus n of the distribution network, $V_{n,i}^0$ is the initial battery capacity of the i electric vehicle on bus n of the distribution network, $P_{n,i,\max }$ is the maximum charging power of the i electric vehicle on bus n of the distribution network, $T_a$ is the charging period for electric vehicles, ${\lambda }_{n,i,t}$ is the dual variable constrained by the charging power balance equation, ${\pi }_{n,i,t}^{-}$ and ${\pi }_{n,i,t}^{+}$ are the dual variables of the inequality constraint on the upper and lower limits of charging power, and ${\delta }_{n,i,t}$ is the dual variable of the charging period equation constraint.

3. Equivalent Nonlinear Programming Transformation of Stackelberg Game Model

The flow chart of the transformed problem is shown in Figure 3.

For two-layer problems, a common solution is to write the lower problem as the KKT condition, whose Lagrange function is as follows:

$$\begin{array}{ll}L=& {\displaystyle \sum _t^T{\displaystyle \sum _i^I{\displaystyle \sum _n^{N_{EV}}{c}_t{P}_{n,i,t}}}}-{\lambda }_{n,i,t}({\displaystyle \sum _{t\in T_a}^T{P}_{n,i,t}-0.9V_{n,i,\max }+V_{n,i}^0})\hfill \\ & -{\pi }_{n,i,t}^{+}(P_{n,i,t}-P_{n,i,\max })-{\pi }_{n,i,t}^{-}{P}_{n,i,t}-{\delta }_{n,i,t}{P}_{n,i,t}\hfill \\ \mathrm{s}.\mathrm{t}.& {\displaystyle \sum _{t\in T_a}^T{P}_{n,i,t}=0.9V_{n,i,\max }-V_{n,i}^0}:{\lambda }_{n,i,t}\hfill \\ & 0\le P_{n,i,t}\le P_{n,i,\max }:{\pi }_{n,i,t}^{-},{\pi }_{n,i,t}^{+}\hfill \\ & P_{n,i,t}=0:{\delta }_{n,i,t}\hfill \end{array}$$

(10)

The Lagrange stationarity constraint and complementary relaxation conditions are as follows:

$$\begin{array}{l}\frac{\partial L}{\partial P_{n,i,t}}=c_t-{\lambda }_{n,i,t}-{\pi }_{n,i,t}^{+}-{\pi }_{n,i,t}^{-}-{\delta }_{n,i,t}=0,\forall n,i,t\\ {\displaystyle \sum _{t\in T_a}^T{P}_{n,i,t}=0.9V_{n,i,\max }-V_{n,i}^0,}\forall n\in N_{EV},\forall i\\ 0\le {\pi }_{n,i,t}^{-}\perp P_{n,i,t}\ge 0,\forall n\in N_{EV},t\in T_a,\forall i\\ 0\ge {\pi }_{n,i,t}^{+}\perp (P_{n,i,t}-P_{n,i,\max })\le 0,\forall n\in N_{EV},t\in T_a,\forall i\\ P_{n,i,t}=0,\forall n\in N_{EV},\forall i,t\notin T_a,{\delta }_{n,i,t}=0,\forall n\in N_{EV},\forall i,t\in T_a\end{array}$$

(11)

The symbol $\perp$ indicates that the product of two expressions is equal to 0, which can be obtained by the equivalence condition:

$$\begin{array}{l}0\le {\pi }_{n,i,t}^{-}\le M{z}_{n,i,t}^{-},\forall n\in N_{EV},t\in T_a,\forall i\\ 0\le P_{n,i,t}\le M(1-z_{n,i,t}^{-}),\forall n\in N_{EV},t\in T_a,\forall i\\ 0\le P_{n,i,\max }-P_{n,i,t}\le M{z}_{n,i,t}^{+},\forall n\in N_{EV},t\in T_a,\forall i\\ M(z_{n,i,t}^{+}-1)\le {\pi }_{n,i,t}^{+}\le 0,\forall n\in N_{EV},t\in T_a,\forall i\end{array}$$

(12)

where $z_{n,i,t}^{+}$ and $z_{n,i,t}^{-}$ are Boolean variables. In Equation (8), there is a nonlinear term $c_t{P}_{n,i,t}$ in the objective function, and the equation can be obtained by using the strong duality theorem:

$${\displaystyle \sum _t^T{\displaystyle \sum _i^I{\displaystyle \sum _n^{N_{EV}}{c}_t{P}_{n,i,t}}}}={\displaystyle \sum _i^I{\displaystyle \sum _n^{N_{EV}}{\lambda }_{n,i,t}(0.9V_{n,i,\max }-V_{n,i}^0)}}+{\displaystyle \sum _t^T{\displaystyle \sum _i^I{\displaystyle \sum _n^{N_{EV}}{\pi }_{n,i,t}^{+}{P}_{n,i,\max }}}}$$

(13)

After equality substitution, the upper objective function is transformed into

$$\begin{array}{ll}\max & {\displaystyle \sum _i^I{\displaystyle \sum _n^{N_{EV}}{\lambda }_{n,i,t}(0.9V_{n,i,\max }-V_{n,i}^0)}}+{\displaystyle \sum _t^T{\displaystyle \sum _i^I{\displaystyle \sum _n^{N_{EV}}{\pi }_{n,i,t}^{+}{P}_{n,i,\max }}}}+\hfill \\ & {\displaystyle \sum _t^T{\displaystyle \sum _n^{N_{EV}}(c_t^{sell}{D}_{n,t}^{sell}-c_t^d{D}_{n,t}-c_t^{buy}{D}_{n,t}^{buy})}}\hfill \end{array}$$

(14)

4. Case Study

4.1. Case Setting

Based on the research of charging and pricing management in the distribution network of electric vehicle operators under wind–PV uncertainty, this paper adopts the IEEE33-bus power system as an example. Among them, bus 1 purchases electricity from the large power grid, bus 18 and bus 22 are connected to the wind turbine, bus 25 and bus 33 are connected to the solar unit, and bus 10, bus 15, and bus 30 are connected to the electric vehicle and thus constitute an electric vehicle operator. The specific system can be seen in Figure 4.

4.2. Simulation Results and Analysis

In the distribution network, the trading strategy of electric vehicle operators is affected by the uncertainty of wind power–solar output, which directly affects the operators’ contract purchase of electricity in the day-ahead market and sales of electricity in the real-time market. The day-ahead market is a market in which transactions take place one or more days in advance of actual electricity consumption. Transactions take place in advance of actual electricity consumption to determine the price at which electricity will be traded for a future period of time, usually one day. The real-time market is a market in which transactions take place within the day of actual electricity consumption. Trading occurs when electricity is actually used in response to real-time electricity demand and market changes. For specific impacts, see

Table 1. Optimal trading strategy without considering the uncertainty of wind and PV output.

Electricity Purchased in the Day-Ahead Market/kwh	bus10	bus15	bus30	Real-Time Market to Sell Electricity/kwh	bus10	bus15	bus30
1	210	210	210	1	49.7	0	0
2	210	210	210	2	54.5	0	0
3	1193.5	526.8	773.3	3	0	0	0
4	210	210	0	4	0	0	41.9
5	30	0	0	5	0	0	35.2
6	0	0	0	6	0.4	0	0
7	0	0	0	7	0.6	0	0
8	0	0	0	8	44.8	0	0
9	0	0	0	9	60.9	0	0
10	0	0	0	10	0	0	69.9
11	0	0	0	11	75.6	0	0
12	0	0	0	12	73.1	0	0
13	0	0	0	13	0	0	42.9
14	0	0	0	14	45.9	0	0
15	0	0	0	15	70.9	0	0
16	0	0	0	16	73.9	0	0
17	0	0	0	17	78.3	0	0
18	0	0	0	18	0	0	0
19	0	0	0	19	31.5	0	0
20	0	0	0	20	1.9	0	0
21	0	0	0	21	0	0	0
22	0	0	0	22	43.9	0	0
23	0	0	0	23	0	0	0
24	0	0	150	24	0	0	0

and

Table 2. Optimal trading strategy after considering the uncertainty of wind power and PV output.

Electricity Purchased in the Day-Ahead Market/kwh	bus10	bus15	bus30	Real-Time Market to Sell Electricity/kwh	bus10	bus15	bus30
1	210	210	210	1	0	73.7	0
2	210	210	210	2	72.5	0	0
3	1082.7	666.4	1210	3	0	0	0
4	210	210	0	4	8.3	0	54.5
5	300	0	0	5	52.2	0	0
6	0	0	0	6	5.4	0	0
7	0	0	0	7	0	0	5.6
8	0	0	0	8	61.8	0	0
9	0	0	0	9	75.9	0	0
10	0	0	0	10	85.9	0	0
11	0	0	0	11	0	0	91.6
12	0	0	0	12	0	0	93.2
13	0	0	0	13	0	86.9	0
14	0	0	0	14	92.9	0	0
15	0	0	0	15	0	88.9	0
16	0	0	0	16	0	0	88.9
17	0	0	0	17	0	0	94.3
18	0	0	0	18	79.6	0	0
19	0	0	0	19	0	0	48.5
20	0	0	0	20	16	0	0
21	0	0	0	21	0	0	40.4
22	0	0	0	22	66	0	0
23	0	0	0	23	0	0	77.7
24	0	0	210	24	0	0	94.9

.

Table 1 shows the data of electricity purchases by distribution network electric vehicle operators in the day-ahead market and real-time market when the uncertainty of wind-driven output is ignored, and Table 2 shows the data of electricity purchases by distribution network electric vehicle operators in the day-ahead market and real-time market when the uncertainty of wind-driven output is considered. It can be seen from Table 1 and Table 2 that before and after considering the uncertainty of wind power output, the electricity purchased by operators in the real-time market has a large change, while the electricity purchased in the day-ahead market has a small change. This is mainly reflected in the relative decrease in the output of wind power and solar power after considering the uncertainty of the scenery, which makes the operator need to purchase more electricity from the day-ahead market. According to the statistical data in the table, the total electricity purchased in the day-ahead market during the whole period considering the uncertainty of the scenery is 5149.1 kwh. Compared with the total purchased power of 4353.6 kwh when the uncertainty of wind–wind output is ignored, the total purchased power is 795.5 kwh higher. Similarly, due to the consideration of the uncertainty of the wind and the wind, the purchase of electricity in the full time of the large grid increased from 805 kwh to 818 kwh, which enabled the operator to sell more electricity in the real-time market, and the total amount of electricity sold in the full time increased from 895.8 kwh to 1555.6 kwh, increasing by 659.8 kwh. Figure 5 shows the wind power–PV output before and after considering opportunity constraints.

The Sbus curve represents the bus output after considering the uncertainty of the scenery. It can be seen from the figure that the output of wind power and solar power decreased before and after considering the uncertainty of the scenery. This is because after the opportunity constraint condition was adopted, the output of wind power units meeting the requirements was selected by sampling and the results were obtained by simulation under different scenarios. This results in a decrease in the average sample of the expected scenery and a decrease in the output of the scenery due to the probability method compared with the case without considering the uncertainty of the scenery.

4.3. Influence of Number of Electric Vehicles on Operation Results

The electric vehicle group is divided into three categories: the first category represents the “early emergence and late return type”; the second category represents the “normal rest type”; and Category 3 represents the “night shift type”. Take N = [50 20 10] vehicles, N = [80 40 25] vehicles, and N = [120 80 40] vehicles, and give the operator operation and charging power of electric vehicles under different numbers, as shown in

Table 3. Economic impact of the number of electric vehicles on operations.

Scenario	Profits for Electric Vehicle Operators/USD	Charging Costs for Electric Vehicles/USD
[50 20 10]	81.61	162.12
[80 40 25]	106.75	297.05
[120 80 40]	141.55	490.80

and Figure 6 below, respectively.

It can be seen from the table that with the overall increase in the number of electric vehicles, both the operator’s profit and the charging cost of electric vehicles are increasing, which is because the increase in the charging amount of electric vehicles causes changes in the number combination of electric vehicles on each bus. The charging conditions of electric vehicles under the conditions of [50 20 10], [80 40 25], and [120 80 40] are analyzed, respectively, and the specific analysis is as follows: It can be seen from the figure above that the change in the number of electric vehicles has little impact on the charging behavior of type 1 electric vehicles, which increases linearly with the increase in the number of electric vehicles, because the type 1 electric vehicles play a dominant role in the selection of quantity combination. Although the number of different types of electric vehicles changes, the proportion of type 1 electric vehicles in the total number of types is the largest. This makes the charging behavior change trend of class 1 load consistent. In comparison, because the proportion of class 2 and class 3 is relatively small, the change trend and change amount of their charging behavior change significantly with the number of differences. It can be seen that the dominant type of EV has an important impact on its charging behavior. For bus 30, the original distribution load of the distribution network is large, which makes the total charging amount of EVs in the whole period under the management of the node operator the least, only 360 kwh, while bus 10 and bus 15, which have a small electric load, have a larger total charging amount in the whole period. It can be seen that in the process of the game, the charging behavior of electric vehicles in the distribution network is affected by the power load of the original distribution network.

4.4. Influence of Wind Power and Solar Output Randomness on Real-Time Electricity Price

In the process of the game, the uncertainty of wind power–PV output has an impact on the pricing strategy of electric vehicle operators, and the specific results are shown in Figure 7.

The blue curve represents the day-ahead market price, the value of which is determined by the day-ahead market and is both known and used as a standard for real-time price adjustment. The orange curve represents the real-time market price without considering the uncertainty of the scenery, and its value is generated by the game between the electric vehicle operator and the electric vehicle power buyer, which is an optimization variable. The black curve represents the real-time market price when the wind and landscape uncertainty is considered, and its value is generated in the same way as the orange curve, which is also an optimization variable. First of all, comparing the blue and orange curves, we can see that as the game between the electric vehicle operator and the electric vehicle power buyer goes on, for the power buyer, the reduction in the electricity price during peak hours is in line with their own interests; for the power seller, although the electricity price decreases during peak hours, the increase in the electricity price during low hours is also in line with their own interests. Secondly, the orange curve and the black curve are compared. It can be seen from Figure 4 that after considering the uncertainty of the scenery, the charging power of Class III electric vehicles at bus 10 increases at the 6th and 21st moments, which changes the electricity price at or near the corresponding period in the black curve.

4.5. Influence of Energy Storage Device Capacity and β on Electric Vehicle Operators

Assuming that a varies from 3000 kwh to 10,000 kwh, and β varies from 0.2 to 1, the impact of the maximum capacity of energy storage equipment and uncertainty of wind power on operators’ profits is analyzed, respectively, and the specific results are shown in Figure 8.

As can be seen from the figure above, with the increase in the maximum capacity of energy storage equipment, the profit of operators first increases rapidly and then tends to be stable. This is because at the beginning of the maximum capacity increase, the operator can choose to purchase electricity for storage in the low-price period of the market, which reduces the purchase of electricity in the high-price period and reduces the cost of an electricity purchase in the day-ahead market, while the operator can sell electricity in the high-price period of the real-time market, and its profits are increasing rapidly. However, as the capacity increases to a certain extent, limited by the charge and discharge rate of the energy storage itself and the capacity constraints of the distribution network line, the charging behavior of electric vehicles no longer changes, so the profits of operators no longer increase. It can be seen from the figure that with the increase in β, the profits of electric vehicle operators are increasing. β represents the probability of meeting the conditions of wind power. The greater the value, the lower the accuracy of meeting the requirements of wind power as a decision-maker, which directly leads to the increase in wind power output, while for an operator, providing more electric energy to the electric vehicle’s own profit increases. When β is 1, it indicates that decision-makers ignore the uncertainty of wind power output, and the power injected into the distribution network is the largest. Operators also have the most to gain.

5. Discussion

The development of electric vehicles makes clean travel possible, and due to how their own charging power can be adjusted, it is expected to become the construction trend of the active load direction of the grid in the future. As more and more electric vehicles are put into the distribution network, it is urgent for the corresponding aggregator operators to manage their charging behavior and overall pricing strategy. At the same time, the world fossil energy crisis has made more and more countries increase the proportion of new energy power generation in the grid, among which wind power and photovoltaic supply as the main forms of new energy power generation have been widely of concern, and with the development of electric vehicles, the output of wind power and photovoltaic supply is bound to have a certain impact on operator pricing and electric vehicle charging power. This is a problem that must be faced in the future development of energy and electric vehicles.

6. Conclusions

This paper proposes a primary–secondary game model for pricing of EV operators in the distribution network, discusses the EV charging strategy under the uncertain conditions of wind power–PV, and verifies that the win–win situation of both operators and EV users can be achieved through optimal pricing under this strategy.

The influence of the three types of electric vehicles in the distribution network on their respective quantity factors is analyzed, and the conclusion is drawn that the dominant electric vehicle type changes little and the charging behavior of electric vehicles in the distribution network is affected by the original load of the distribution network.

A numerical example verifies the effectiveness of the strategy proposed in this paper. The results show that, within a certain range, operators’ profits increase with the increase in the capacity of energy storage equipment, but due to the constraints of the line capacity and charging rate, a further increase in capacity cannot continue to improve operators’ earnings. Electric vehicle operators experience a maximum profit increase of 2.6% due to the impact of maximum capacity of energy storage equipment.

The real-time electricity price is affected by the uncertainty of wind and solar power, and the electricity price fluctuates within 10% of the original real-time electricity price. When β = 1, that is, when the uncertainty of wind power output is not considered, the power injected into the grid by wind power–photovoltaic supply is the most, and the profit for electric vehicle operators is also the largest. The uncertainty of renewable energy output can result in electric vehicle operators losing approximately 20% of their profits at most. Therefore, increasing the forecast output of wind power–PV supply is an effective way to increase operators’ earnings.