V2G Scheduling of Electric Vehicles Considering Wind Power Consumption

Abstract

The wind power (WP) has strong random volatility and is not coordinated with the load in time and space, resulting in serious wind abandonment. Based on this, an orderly charging and discharging strategy for electric vehicles (EVs) considering WP consumption is proposed in this paper. The strategy uses the vehicle-to-grid (V2G) technology to establish the maximum consumption of WP in the region, minimizes the peak–valley difference of the power grid and maximizes the electricity sales efficiency of the power company in the mountainous city. The dynamic electricity prices are set according to the predicted values and the true values of WP output, and the improved adaptive particle swarm optimization (APSO) and CVX toolbox are used to solve the problems. When the user responsiveness is 30%, 60% and 100%, the WP consumption is 72.1%, 81.04% and 92.69%, respectively. Meanwhile, the peak shaving and valley filling of the power grid are realized, and the power sales benefit of the power company is guaranteed.

1. Introduction

At present, wind power (WP) has developed rapidly due to its clean and pollution-free characteristics, gradually replacing traditional thermal power generation. However, because of the random volatility of WP, large-scale integration into the power grid may cause the grid frequency to be separated from the safety red line, affecting the normal operation of the power grid [1]. The WP output and load consumption are not coordinated in time and space, leading to the phenomenon of abandoning WP, thus resulting in the waste of resources [2]. In addition, due to the unreasonable planning of distributed generation (DG), a large number of WP sources cannot be connected to the power grid [3]. Therefore, in the case of ensuring the safety of the power grid, how to consume the WP as much as possible is a pressing problem to be solved. Under the V2G architecture, EVs can store the excess electric energy generated by WP sources [4] to reverse the incoordination between WP and load. When the power grid is in a high-load state, the electric energy can be transmitted back to the grid, benefiting both the grid side and the user side [5].

Many scholars have studied the practicability of EV orderly charging and discharging in the consumption of WP. In reference [6], an improved PSO is proposed to optimize the strategy of EV to absorb WP. This strategy reduces the amount of abandoned WP and the fluctuation of WP output. To solve the influence of WP output fluctuation, a timely control measure for aggregating EV is proposed in the literature [7]. The strategy can smooth the output WP and also reduce the peak and decrease the valley to drop the fluctuation of load. Reference [8] proposed an orderly charging method for micro-grid EVs. This strategy can optimize the EV charging plan according to the current micro-grid load status, EV charging and discharging requirements and other real-time data, effectively avoiding the load spike problem caused by plenty of EVs entering the network. Aiming at the problem of mismatch between WP and load, a scheduling model of interaction between the power generator and users is proposed in the literature [9]. The model improves the interests of power generation measurement and user side, and it also enhances the consumption rate of WP. Relying on the V2G technology of EVs and considering the collaboration between a WP generator and EV integrators, the literature [10] effectively reduces the adverse effect of WP’s reverse peak shaving performance, making both sides profitable to each other. The literature [11] proposed a tracking absorption strategy of new energy with interaction between supply and demand, adjusting the charging process of an EV to achieve the absorption of renewable energy power. Reference [12] established a multi-objective scheduling model considering the V2G characteristics of EVs, and they abandoned the wind volume, charging cost, etc., so that thermal power units, wind turbines and EVs can be collaboratively optimized. Reference [13] proposed an intelligent management measure for charging and discharging an EV, which makes the load curve smoother, reduces the randomness of WP, improves the consumption rate of WP, and reduces carbon emissions. On the basis of decreasing power grid fluctuation and accommodating new energy, reference [14] further considers the economy of a load aggregator (LA) by using wind–solar complementation. Reference [15] fully considers the power generation structure and establishes the goal of minimizing operating costs, carbon emissions, grid variance and user costs under the V2G architecture. In reference [16], a timely optimization model based on WP prediction error and EV prediction information was established. The improved alternating direction multiplier method (ADMM) was used to solve the model, and the goals of peak load shifting, WP consumption and operating cost reduction were achieved. The literature [17] constructs an energy management system composed of micro-grid and demand response. With the minimum operating cost, pollutant treatment cost and carbon emission cost as the goals, PSO and artificial bee colony algorithm (ABC) are used to solve the problem, which makes full use of renewable energy. On the basis of WP consumption, most of the above studies only considered the grid side and the user side, but it did not take into account the electricity sales benefits of the power company.

At the same time, 24% of the world’s areas are mountains, and 10% of people live in mountainous cities. Due to the terrain, the mountainous cities will affect the user’s travel mode, resulting in a certain amount of random charging load, and the non-linear and non-planar extension of the road will increase the travel distance, aggravate the EV travel dependence, and increase the power consumption. Although the regenerative braking function can recover part of the energy during the braking process, this technology has not been popularized, and the recovered energy is far from enough to compensate for the consumed energy. Therefore, it is also essential to study the orderly charging of EVs in mountainous cities. Reference [18] studied the orderly charging method of EV in mountainous cities, considered the two charging methods of centralized charging and decentralized charging, proposed the concept of EV access probability, and optimized the economic benefits of EV aggregators by using the Lagrange relaxation method. Reference [19] planned the charging infrastructure in mountainous cities. Using the improved Floyd shortest-path algorithm, the self-sufficiency rate coefficient, climbing coefficient and traffic congestion coefficient were proposed. The characteristics of mountainous urban roads were quantified, which provided ideas for the charging facilities in mountainous cities. At present, there are few studies on the orderly charging of EVs in mountainous cities, and the problem of EVs helping to absorb WP in this case is not considered.

Based on these, under the background of mountainous cities, this paper establishes an EV orderly charging and discharging strategy that maximizes the consumption of WP, minimizes the peak–valley difference of power grid load and maximizes the sales benefits of the power company. Firstly, the charging model of an EV in mountainous cities is established. The daily mileage of an EV, the amount of charging required after the end of a day’s travel, the time of entering the network, and the time of leaving the network are modeled. The orderly charging and discharging strategy of EVs in mountainous cities is proposed, and the process is sorted out. Secondly, according to the road characteristics of mountainous cities, the ‘non-linear coefficient’ is used to simulate and model the road selected by EV users as a constraint condition for solving the objective functions, 10% random load is left in the residential district for charge and discharge scheduling; using the WP output data, variational mode decomposition (VMD) and bi-directional long short-term memory (Bi-LSTM) are used to predict the WP, and the time-of-use price is formulated according to the predicted and true WP output value as well as the basic load value. Finally, taking a community in Chongqing, China, as an example, the simulation verification is carried out.

2. Orderly Charging and Discharging of EVs in Mountainous Cities

The areas with relative height greater than 200 m are collectively referred to as mountains. Mountainous cities refer to cities where most of the land is distributed in mountainous areas, such as Chongqing in China, San Francisco in the United States, Casares in Spain, Seoul in South Korea, and Rio de Janeiro in Brazil. Their roads and terrain have the following characteristics: the non-linear factor of traffic travel is large. On the one hand, because of the speedy shift of height differences, there will be lots of curves passing round, increasing the actual distance; on the other hand, because of the restriction of terrain, the road network is generally freely arranged in according to the terrain, resulting in more proximal roads, poor connectivity of the road network, increased detour distance and the actual distance. In recent years, with the continuous increase of car ownership, traffic congestion is becoming more and more serious. In addition, the characteristics of mountainous cities have increased the power consumption of EVs, and EV users are charging more frequently. Secondly, considering the characteristics of the terrain, people in mountainous cities will choose to use public transportation, so it will generate stranded vehicles and increase the random charging load.

The Monte Carlo method is used to simulate the daily mileage of EV, the daily required charging capacity and the charging start time [20], as shown below.

(1) Daily mileage

According to Reference [18], the daily mileage of EVs in mountainous cities meets the lognormal distribution, as shown in Equation (1):

$$f_s\left(x\right)=\frac{1}{x{\sigma }_s\sqrt{2\pi }}exp[-\frac{{(lnx-{\mu }_s)}^2}{{\left(2{\sigma }_s\right)}^2}]$$

(1)

In the formula, ${\mu }_s$ = 3.31, ${\sigma }_s$ = 0.87. Figure 1 shows the daily mileage of EVs.

(2) The daily required charging capacity

According to the mileage, the daily charging amount of EV users can be calculated. This paper takes 200 BYD e6 EVs as an example and uses the Monte Carlo method to simulate the daily charging capacity of EVs, as shown in Figure 2.

It can be seen from Figure 2 that most EVs require about 5 kWh of electricity per day; that is, EVs have a lot of time and excess electricity to charge and discharge in an orderly manner, acting as energy storage equipment for peak shaving and valley filling. However, EVs can not discharge endlessly as an energy storage element but only as an auxiliary way of load regulation, and the number of EVs in a certain area has an upper limit; otherwise, the excessive number will destroy the safety of the power system. Therefore, this paper assumes that when $SO{C}_{min}$ < 0.2, EVs will be prevented from continuing to discharge.

(3) Charging start time

According to Reference [18], the charging starting time of an EV satisfies Equation (2):

$$f_t\left(s\right)=\left\{\begin{array}{cc}\frac{1}{{\sigma }_t\sqrt{2\pi }}exp[-\frac{{(x+24-{\mu }_t)}^2}{{\left(2{\sigma }_t\right)}^2}],\hfill & 0<x<{\mu }_t-12\hfill \\ \frac{1}{{\sigma }_t\sqrt{2\pi }}exp[-\frac{{(x-{\mu }_t)}^2}{{\left(2{\sigma }_t\right)}^2}],\hfill & {\mu }_t-12<x<24\hfill \end{array}\right.$$

(2)

where, ${\mu }_t$ = 17.8, ${\sigma }_t$ = 3.2. Figure 3 is the charging start time of an EV and the probability distribution of the EV charging start time.

It is shown in Figure 3 that most EV users will charge at about 18:00, which is exactly the peak load period, and each EV still has most of the power left after completing a day’s trip. The energy storage characteristics of an EV can be used for orderly discharge to avoid excessive peak load, and orderly charging at about 0:00 to avoid too low valley load, and it can make full use of night WP generation to absorb it.

The choice of EV charging and discharging has the following three factors: charging and discharging price, battery state of charge (SOC) and parking time. The day every 15 min for a period of time, divided into 96 periods, refreshing the network EV situation after the end of each period. [21]. The user independently decides whether to carry out disorderly charging, orderly charging or orderly charging and discharging. After the user makes a choice, the charging pile determines the charging and discharging flexibility according to the SOC, the time-of-use prices and the basic load, then updates the current schedulable capacity of the charging station. If the user chooses to charge in a disorderly manner, the EV is charged immediately at constant power. If the user chooses to charge in an orderly manner, it arranges the user to charge during a large period of WP output and consume as much WP as possible. At the same time, it is essential to pay attention to the maximum load to be borne by the transformer to avoid overload. If the user chooses to charge and discharge in an orderly manner, the charging pile schedules according to the initial $SO{C}_0$. If the initial $SO{C}_0$ is greater than the allowable minimum $SO{C}_{min}$, the EV can be arranged to discharge to the grid during the peak load period and charge during the normal load period and the valley period. If the $SO{C}_0$ is less than the allowable minimum $SO{C}_{min}$, the EV does not discharge, and the EV is arranged to charge during the normal period or the valley period. The charge–discharge flow chart is shown in Figure 4.

As shown in Figure 4, after the EV is connected to the power grid, the intelligent charging pile refreshes the number of EVs entering the network, and it reads the initial $SO{C}_0$, expected SOC, charging time and other information while waiting for the user to select the charging and discharging mode. If the user chooses disorderly charging, the charging pile immediately charges the EV according to the constant power regardless of other factors, and the final charging cost is calculated according to the conventional electricity price. If the user chooses to charge in an orderly manner, the charging pile schedules EV charging when the electricity price is low according to the wind power output and the basic load power consumption until the expected power is reached. If the user chooses to charge and discharge in an orderly manner, the charging pile first detects whether its initial $SO{C}_0$ is greater than the minimum discharge capacity $SO{C}_{min}$. After meeting the discharge requirements, the EV will be arranged to discharge during the peak load period and charge during the valley period or the normal period. Otherwise, the discharge will not be carried out, and the EV will be charged only during the valley period or the normal period.

3. Charging and Discharging Model of EV in Mountainous Cities

3.1. Objective Function

Under the background of mountainous cities, to consume WP as much as possible in the region, this paper establishes the maximization of WP consumption rate, the minimization of peak–valley difference of the power grid and the maximization of power sales efficiency of the power company as the goals, and it sets the time-of-use prices according to the WP output and the basic load to ensure the full consumption of WP.

(1) Maximize the WP consumption rate.

The electricity generated by WP is preferentially consumed by EV charging, and the remaining electricity is used for basic load in the area. Therefore, the actual consumption value of WP generation is the total value of basic load and EV consumption minus the value of both’s consumption from a large power grid.

$$max{f}_1=\frac{{\sum }_{t=1}^T[P_{EV}\left(t\right)+P_L\left(t\right)-P_G\left(t\right)]}{{\sum }_{t=1}^T{P}_{WT}\left(t\right)}$$

(3)

In the formula, $P_{EV}\left(t\right)$ is the EV charging power value, $P_L\left(t\right)$ is the basic load power value, $P_G\left(t\right)$ is the load consumption grid power value, and $P_{WT}\left(t\right)$ is the total WP output value.

(2) Minimum peak–valley difference of grid load.

To guarantee the safety and stability of the power grid and save energy consumption, the peak–valley difference of the power grid must be as small as possible.

$$\begin{array}{cc}\hfill min{f}_2& =maxP\left(t\right)-minP\left(t\right)\hfill \\ \hfill P\left(t\right)& =P_L\left(t\right)+P_{EV.ch}\left(t\right)\hfill \end{array}$$

(4)

where, $P_{EV.ch}\left(t\right)$ is the EV charging load.

(3) Maximize the electricity sales benefit of power company.

The power company purchases electricity from the power grid for basic load and EV charging in the region. To ensure the sustainable income of the power company, it should obtain the maximum electricity sales benefit. The power company purchases electricity from the power grid at a prices below the market price and sells it to the user at the market price so as to make a profit.

$$\begin{array}{cc}\hfill max{f}_3& =P_L\left(t\right)(C_L\left(t\right)-C_b\left(t\right))\Delta T+{\alpha }_t^i{\sum }_{t=1}^T{\sum }_i^N{P}_{EV.i.ch}\left(t\right)(C_{ch}\left(t\right)-C_b\left(t\right))\Delta T_{ch}\hfill \\ \hfill & -{\beta }_t^i{\sum }_{t=1}^T{\sum }_i^N{P}_{EV.i.dch}\left(t\right)C_{dch}\left(t\right)\Delta T_{dch}\hfill \end{array}$$

(5)

where, $C_L\left(t\right)$ is the price of the basic load at time t.

Table 1. Basic load price in different periods.

Time Interval	C${}_{\mathit{L}}$ (Yuan/kWh)	C${}_{\mathit{b}}$ (Yuan/kWh)
Peak period (11:00–14:00, 17:00–21:00)	1.2	1.0
Flat period (7:00–11:00, 14:00–17:00, 21:00–24:00)	0.8	0.7
Valley period (0:00–7:00)	0.4	0.3

lists the basic load prices of the electricity selling company in different peak and valley periods. $P_{EV.i.ch}\left(t\right)$ is the power value of the EV charging load at time t, $C_{ch}\left(t\right)$ is the charging price at time t, $C_b\left(t\right)$ is the purchasing price from the power grid at time t, and $C_{dch}\left(t\right)$ is the discharging price at time t. $\Delta T_{ch}$ is the charging time, and $\Delta T_{dch}$ is the discharging time. ${\alpha }_t^i$ and ${\beta }_t^i$ represent the charging and discharging flag of the ith EV, respectively. The relationship between the two is as follows:

$$\left\{\begin{array}{c}\alpha =0,\beta =0\hfill \\ \alpha =1,\beta =0\hfill \\ \alpha =0,\beta =1\hfill \end{array}\right.$$

(6)

In the formula, $\alpha$/$\beta$ = 1 means that it is charging/discharging, and $\alpha$/$\beta$ = 0 means that it is neither charging nor discharging.

3.2. Constraint Conditions

(1) Power constraint

The grid power, WP output and EV through V2G discharging power should be equal to EV through G2V charging power and basic load consumption power.

$$P_G\left(t\right)+P_{WT}\left(t\right)+P_{V2G}\left(t\right)=P_{G2V}\left(t\right)+P_L\left(t\right)$$

(7)

where, $P_G\left(t\right)$ is the power of the grid, $P_{WT}\left(t\right)$ is the power of the WP, $P_{V2G}\left(t\right)$ is the V2G discharge power of the EV, $P_{G2V}\left(t\right)$ is the G2V charging power of the EV, and $P_L\left(t\right)$ is the basic load consumption power.

(2) Transformer capacity constraint

The basic load and EV charging load should be less than the maximum load capacity of the transformer.

$$P_L\left(t\right)+P_{G2V}\left(t\right)\le P_{max}$$

(8)

where, $P_{max}$ is the maximum power of the transformer.

(3) SOC constraint

The excessive charging and discharging of EVs results in battery characteristics loss, so the SOC has upper and lower limits to prevent overcharging and discharging.

$$SO{C}_{min}<SO{C}_{i,j}<SO{C}_{max}$$

(9)

where, $SO{C}_{min}$ is the lower limit of EV charging and discharging, $SO{C}_{i,j}$ is the SOC of the ith EV during period j, and $SO{C}_{max}$ is the upper limit of EV charging and discharging. Among them, $SO{C}_{min}=0.2$, $SO{C}_{max}$ = 1.

(4) WP output constraint

Considering the randomness and disorder of WP output, to ensure the safety of the power system, it is usually thought that the WP output value has an upper limit and a lower limit.

$$P_{WT}^{min}\left(t\right)<P_{WT}\left(t\right)<P_{WT}^{max}\left(t\right)$$

(10)

where, $P_{WT}\left(t\right)$ is the actual output value of WP at time t, $P_{WT}^{max}\left(t\right)$ and $P_{WT}^{min}\left(t\right)$ are the upper and lower limits of WP output at time t, respectively.

(5) Road selection constraint

Mountainous cities are different from plain cities. Their roads are steep and curved, which makes it difficult to travel. Therefore, a non-linear coefficient r is introduced to quantify the detour distance. The non-linear coefficient is the ratio of the actual distance of the line to the spatial distance between the initial and final points of the trip. The larger the value, the longer the line bypass distance.

$$r=\frac{S}{X}$$

(11)

where, S is the actual distance between the initial and final points, and X is the straight distance between the initial and final points. The latitude and longitude coordinates of the first and last positions are known, and the distance between the two points can be calculated by Equation (12) [22]:

$$X_{i,j}=111\times \sqrt{{(y_j-y_i)}^2+{(x_j-x_i)}^2{\left(\cos \frac{y_i+y_j}{2}\right)}^2}$$

(12)

where, $X_{ij}$ is the linear distance between two points, ($x_i$, $y_i$) and ($x_j$, $y_j$) are the latitude and longitude coordinates of two points, respectively. When users choose the travel route, they will be more inclined to choose the route with a small non-linear coefficient to save time and electricity. Therefore, when optimizing, the road with a non-linear coefficient less than 1.4 is preferred.

$$r<1.4$$

(13)

4. Model Solution

4.1. WP Prediction Model

The WP output values vary greatly in different seasons and moments, so the typical days in four seasons are selected to analyze the WP output to predict in different seasons. The WP output fluctuates greatly and is susceptible to seasonal changes. Therefore, the influence of seasons is especially considered in this paper when predicting WP.

In terms of prediction methods, methods based on artificial intelligence algorithms are more accurate, less difficult to predict, and have faster prediction time. Deep learning algorithms are commonly used in predicting time-series problems [23,24,25,26,27]. Before prediction, using VMD to decompose the original data can obtain effective decomposition components of the data and remove noise. In terms of deep learning algorithm selection, LSTM is mainly used to solve the problems of gradient vanishing and gradient explosion during long sequence training, and Bi-LSTM has better performance than LSTM. Therefore, VMD-Bi-LSTM is chosen to predict wind power output [28,29]. Figure 5 is the WP data graph decomposed by VMD.

Figure 6 shows the comparison between the daily WP output predicted by VMD-Bi-LSTM and the true value in summer and the error analysis. The root mean square error (RMSE) of the prediction results is 5.9422 kW, and the coefficient of determination R² is 0.9864.

Taking a typical day in summer as an example, the WP output is predicted according to the historical data, and the average output value is calculated. The actual output value is compared with the average output value. When the actual output value is greater than 125% of the average output value, it is considered that this time is a high output period [30]. In order to avoid wind curtailment, the charging price should be reduced at this time, and the EV connected to the power grid should be charged as much as possible. When the actual output value is less than 75% of the average output value, it is considered to be the low output stage at this time [31], and the basic load power consumption in the region is preferentially satisfied. The formulation of electricity prices should also consider the basic load. If it happens to be the peak load period, users should be encouraged to discharge, so the discharging price should be as high as possible at this time. If it happens to be during the low load period and during the normal WP output period at the same time, the charging price should not be too high. To prevent the rapid change of electricity price from causing users to respond in time, this paper sets the charging and discharging electricity price at an hour interval, as shown in Figure 7.

4.2. Particle Swarm Optimization Algorithm Solution

PSO has the advantages of strong universality, easy implementation, and fast convergence speed, so we choose PSO as model solution algorithm and choose adaptive PSO to achieve the optimal solution result as much as possible.

In PSO, the velocity and position of the particle are two important parameters. The velocity is the direction and distance of the particle moving in the next iteration, and the position is the solution of the problem. Particles adjust their velocity and position according to the current individual extremum they find and the current global optimal solution shared by the whole particle swarm. x is the final solution, and when the maximum number of iterations is reached, the value of $x_i$ is the final solution. The t + 1 generation particle velocity update and position update rules are as follows [32]:

$$\begin{array}{cc}\hfill v_i^{t+1}& =\omega v_i^t+c_1{r}_1(P_{ibest}^t-x_i^t)+c_2{r}_2(G_{ibest}-x_i^t)\hfill \\ \hfill x_i^{t+1}& =x_i^t+v_i^{t+1}\hfill \end{array}$$

(14)

where, $\omega$ is the inertia weight, $c_1$ and $c_2$ are the learning factors, $r_1$ and $r_2$ are the random values between [0,1], $P_{ibest}^t$ is the individual optimum of the i particle in the t generation, and $G_{ibest}^t$ is the global optimum of the collective in the t generation.

In traditional PSO, due to fixed inertia weights and learning factors, they are prone to local minimization and lack the ability to adjust the relationship between local and global searches [33]. The larger $\omega$ is, the easier it is for the particles to find the global optimization, and the easier it is to break away from the local minimum without falling into the local optimum. The smaller the $\omega$ value is, the more conducive to the local search of the particles and the faster convergence to the optimal solution [34]. Therefore, in practical problems, we should have a $\omega$ value as large as possible at first to find a suitable solution and a smaller value subsequently to improve the convergence speed [35], so the $\omega$ should be dynamically adjusted.

The PSO solution flow chart is shown in Figure 8, and the solution steps are as follows:

• Initialize particle swarm parameters, such as particle swarm size, particle dimension, number of iterations, etc.
• Initialize the position and velocity of each particle.
• Determine whether the end condition is satisfied. If the end condition is satisfied, the algorithm ends and the optimal solution is obtained. If the conditions are not met, the following steps will continue.
• Update the position and velocity of the particle, and calculate the fitness value of the particle.
• Then, the individual optimal fitness value and position of each particle and the optimal fitness value and position of the group particles are updated.
• Update other parameters such as inertia weight and learning factor.
• Obtain the final result.

4.2.1. Dynamic Weight Setting

In the initial search stage, the fitness of the particles is larger, and the linear change of $\omega$ with a smaller initial value is adopted to weaken the role of the particles in the update, so that the PSO has a strong global search ability at this stage and can quickly enter the local search. When the particle fitness is small in the later stage of optimization, the non-linear inertia weight is used to increase the role of a single particle in the update so that the algorithm can converge quickly [36].

$${\omega }_i=\left\{\begin{array}{cc}{\omega }_{min}+({\omega }_{max}-{\omega }_{min})\frac{f_{ij}-f_{jmin}}{f_{javg}-f_{jmin}},\hfill & f_{ij}\le f_{javg}\hfill \\ {\omega }_{max}-({\omega }_{max}-{\omega }_{min})\frac{t_i}{t_{max}},\hfill & f_{ij}>f_{javg}\hfill \end{array}\right.$$

(15)

In the formula, j = 1,2,3, respectively. ${\omega }_{min}$ is the minimum value of the inertia weight, taken as 0.4, ${\omega }_{max}$ is the maximum value of the inertia weight, taken as 0.9, $f_{ij}$ is the particle fitness function, which is the result value of the jth objective function after the ith iteration. $f_{jmin}$ is the particle minimum fitness. $f_{javg}$ is the particle average fitness, $t_i$ is the current iteration number, and $t_{max}$ is the maximum iteration number.

4.2.2. Dynamic Learning Factors Settings

$c_1$ and $c_2$ are the learning factors. They decide the influence of information learned by each individual particle and other particles on the optimization performance, reflecting the information exchange between particles. Setting a larger $c_1$ value will make the particles converge too much in the local search; on the contrary, the larger $c_2$ value will let the particles converge to the local optimization prematurely [37]. Therefore, in the early stage of the algorithm search, a larger $c_1$ value and a smaller $c_2$ value are used to make the particles diverge into the search space as far as possible, that is, to emphasize the ‘individual independent consciousness’, and be less affected by other particles in the population, that is, the ‘social consciousness part’, to increase the diversity of particles. As the number of generations selected increases, $c_1$ decreases linearly and $c_2$ increases linearly, thus strengthening the convergence ability of the particles to the global optimum [38].

$$\begin{array}{cc}\hfill c_1^i& =c_1^{start}-(c_1^{start}-c_1^{end})\frac{t_i}{t_{max}}\hfill \\ \hfill c_2^i& =c_2^{start}+(c_2^{end}-c_2^{start})\frac{t_i}{t_{max}}\hfill \end{array}$$

(16)

In the formula, $c_1^{start}$ is the incipient value of the individual learning factor, taken as 2.5, $c_1^{end}$ is the final value of the individual learning factor, taken as 0.5, $c_2^{start}$ is the incipient value of the social learning factor, taken as 1, and $c_2^{end}$ is the final value of the social learning factor, taken as 2.25.

5. Example Analysis

The strategy proposed in this paper is simulated and verified, and the following settings are made for the scene:

• Taking a residential area in Chongqing, China, as an example, it is set that there are 200 EVs in the area, the model is BYD e6, the battery capacity is 82 kWh, the charging mode is conventional slow charging, the power is 7 kW, and the battery charging and discharging efficiency is 0.9. The maximum load capacity of the transformer in the residential area is 5087 kW. Through Monte Carlo simulation analysis of user travel patterns, it is basically selected to go home to charge after work and finish charging before going to work the next day. In this paper, 10% random loads are set; that is, 20 EVs are arranged to carry out orderly charging and discharging scheduling during the working hours of the community.
• After the charging mode is selected for the EV connected to the power grid, the charging station will dispatch the EV according to the dynamic electric price. When the expected SOC set by the user is reached, the charging will stop.
• EV participates in V2G voluntarily, and the users who are willing to respond to the scheduling sign an agreement with the grid to implement the scheduling arrangement. This paper analyzes the objective functions with 30%, 60%, and 100% responsiveness.

5.1. Do Not Participate in V2G Scheduling

EV disorderly charging means that when the user selects the charging mode of disorderly charging after the end of a day’s journey, the charging pile will immediately charge at a constant power of 7 kW until the expected power is reached. When 200 vehicles choose to charge in a disorderly manner, it will lead to a sharp increase in load during the peak load period in the afternoon, and when the WP output is high at night, there will be no or few vehicles to use, resulting in severe peak load and wind abandonment. The basic load and EV disorderly charging accumulation curves are shown in Figure 9.

In Figure 9, we can see that in the case of disorderly charging, the user will charge at about 17:00, and the load reaches a peak at about 19:45. At this time, it is also the peak period of residential electricity load, leading to a peak on the peak. The peak load increased by 11.3%, and the peak–valley difference increased by 12.6%. In this case, the electricity sales benefit of the power company comes from the basic load power consumption and EV charging. Compared with only benefiting from the basic load, the EV charging makes the electricity sales benefit increase by 41.8%. Figure 10 shows the distribution of basic load, disorderly charging and orderly charging load.

Under the condition of orderly charging, the intelligent charging pile dynamically changes the electricity price considered by the WP output value and basic load value in each period, guides users to charge during the periods of high WP output and low basic load power, effectively consumes excess WP, controls peak load, and the peak load decreases by 7.13%. The peak–valley difference decreases by 37.0%, making great contributions to the economic and security benefits of the grid. The electricity sales efficiency of the power company has increased by 18.8% compared to disorderly charging. The WP has a large output during the peak load period from 17:00 to 21:00, resulting in the charging price being lower than the purchasing price. However, this is the peak load period. To avoid load overload, the intelligent charging pile will schedule most EVs to charge during the valley period at night, the WP output at night is larger, and the charging price is much higher than the purchasing price, making the selling efficiency of orderly charging higher than that of disorderly charging.

Table 2. Comparison of basic load, disorderly charging and orderly charging.

	Peak Value/(kW)	Valley Value/(kW)	Peak–Valley Difference/(kW)	WP Consumption Rate/(%)	Electricity Sales Benefit Value/Dollar	Growth Rate/(%)
Basic load	3062.6	1932.0	1130.6	40.62%	4173.17	–
Disorderly charging	3454.7	2161.6	1293.1	41.37%	7108.04	41.8%
Orderly charging	3208.5	2394.0	814.5	68.49%	8752.70	18.8%

compares the peak and valley value, peak–valley difference, WP consumption rate, and sales profit value of the power company for these three scenarios.

Compared with the case where only the basic load is used to absorb WP, the disorderly charging makes the WP consumption rate increase by only 1.25%, there is almost no effective WP consumption, and the condition of wind abandonment is still serious. In the case of orderly charging, the WP consumption rate increased from 41.37% to 68.49%. Although the utilization rate of WP was improved, most of the WP was still wasted. Figure 11 is the distribution of WP consumption in three cases.

5.2. V2G Different Responsiveness Scheduling

Considering the different scheduling intentions and abilities of different individuals, this section sets 30%, 60%, and 100% user V2G responsiveness, and it uses the CVX toolbox to optimize for different user responsiveness, as shown in Figure 12.

As shown in Figure 12, the EVs left in the community are scheduled to discharge during the period from 11:00 to 14:00 in the afternoon, and the EVs that end the day’s journey are scheduled to discharge during the period from 17:00 to 21:00 in the afternoon, resulting in a decrease in peak load. From 21:00 at night to 8:00 the next day, EVs are scheduled to charge in an orderly manner, reaching the expected level and ending the charging process, resulting in an increase in load during the night valley period. As the responsiveness increases, the peak–valley difference is smaller, and the outcome of peak shaving and valley filling is better. The results are shown in

Table 3. Optimization results of V2G under different responsiveness.

User Responsiveness	Peak Value/(kW)	Valley Value/(kW)	Peak–Valley Difference/(kW)	WP Consumption Rate/(%)	Growth Rate/(%)	Electricity Sales Benefit Value/Dollar
30%	2886.2	2002.7	883.5	72.10%	1.05%	7291.26
60%	2868.2	2102.7	765.5	81.04%	9.94%	6264.77
100%	2853.6	2214.7	638.9	92.69%	11.65%	4895.98

.

Compared with disorderly charging and orderly charging, the orderly charging and discharging scheduling of different user responsiveness makes the power company’s electricity sales benefit decrease by different degrees, and the value of electricity sales efficiency decreases with the increase of responsiveness. This is because in order to schedule more EVs for discharge, the discharging price set by the power company will be much higher than the charging price and the selling price, especially during the peak load periods of 11:00–14:00 and 17:00–21:00. Figure 13 shows the WP consumption under three kinds of responsiveness. With the higher user responsiveness, more EVs will discharge during peak hours, further increasing the charging capacity of EVs so as to absorb more WP at night. The WP consumption rate gradually increases. As can be seen from Table 3, when all EVs respond to orderly charging and discharging, the WP accommodation rate reaches 92.69%, effectively realizing the goal of maximizing the consumption of WP.

6. Conclusions

Aiming at the phenomenon of the low utilization rate of WP and serious wind abandonment, a three-objective orderly charging and discharging strategy is proposed to maximize the consumption of WP, minimize the peak–valley difference of load, and maximize the electricity sales benefit of power companies. Considering the terrain characteristics of mountainous cities, 10% random loads and non-linear coefficient are set to quantify the detour distance. The improved adaptive PSO and CVX toolbox are used to optimize the objective function so as to realize the multi-objective functions.

The strategy proposed in this paper aims to fully absorb wind power generation. The electricity generated by WP is prioritized for EV charging. When the electricity generated cannot meet EV charging requirements, other electrical energy will be used. When there is excess electrical energy emitted and there is still some remaining after EV charging, the excess electrical energy is used for the basic load.

The strategy has a positive effect on the consumption of WP, but the power company’s electricity sales benefit gradually decreases with the increase of the user’s discharge responsiveness, which will reduce the enthusiasm of the power company to respond to V2G to a certain extent. Furthermore, this paper only considers the WP prediction situation in clear weather but does not consider the situation during cloudy or rainy days, which cannot be ignored in practical applications. In the follow-up, this paper will make a more detailed division of the electricity prices and fully consider other weather conditions so as to ensure the power company’s electricity sales benefit and be more in line with reality.