Research on the Diffusion Model of Electric Vehicle Quantity Considering Individual Choice

Abstract

Regarding the issue of individual purchasing behavior in the rapid growth of electric vehicles, this article studies the diffusion model of electric vehicles considering individual choices and social effects from the perspective of the scale and quantity changes of electric vehicles. First, the neural network was used to predict the charging data of electric vehicles, and the economic effects of purchasing electric vehicles were calculated by combining the purchase cost and government subsidies. Then, the utility function for owners to purchase electric or traditional fuel vehicles was created by considering economic effects, cognitive attitudes, and social effects as factors that individuals need to consider when purchasing electric or traditional fuel vehicles. Finally, the discrete choice model was used to calculate the probability of users choosing to purchase electric or traditional fuel vehicles, and the number of electric vehicles was statistically calculated. Analysis of simulation examples shows that the growth rate of fuel vehicles decreases year by year during the simulation period, and the trend of electric vehicle growth follows an S-curve.

1. Introduction

With the development of electric vehicles (EVs) and energy storage battery technology, electrification of transportation has become a means to alleviate energy crises and the increasing demand for electricity [1]. Electric vehicles not only meet people’s travel needs but also make significant contributions to environmental protection by replacing fuel-based transportation with electric-powered transportation [2]. However, the increase in EV planning and rapid diffusion not only brings tremendous pressure to the transportation system but also presents challenges to the power supply of the grid [3]. Therefore, it is necessary to accurately evaluate and predict the scale evolution of EVs in the future, grasp the inherent rules of their quantity diffusion, and thus make rational use of EV resources [4].

Compared with conventional petrol-driven vehicles (PdVs), EVs employ electric-drive technologies to boost vehicle efficiency through regenerative braking-recapturing energy otherwise lost during braking. Because EVs rely in whole or part on electric power, their fuel economy is measured differently from that of conventional PdVs. Therefore, EVs can reduce fuel costs dramatically because of the high efficiency of electric-drive components. From an environmental perspective, EVs are a major factor in improving air quality and environmental pollution. Even without significant changes in the sources of electricity generation, i.e., coal, natural gas, and renewable energy, an EV can still reduce CO₂ emissions by 60% compared with a traditional PdV. If charging times and locations are carefully planned, EVs could provide additional benefits for owners. Smart charging can schedule EVs to charge when electricity prices are low and stop charging when electricity demand is too high. It means that EV owners can reduce charge costs by avoiding charging during times when electricity prices are high. Additionally, EVs play a crucial role in electric power balance because EV batteries can store surplus electricity and distribute it back to the grid. Therefore, EVs have become a promising option to solve environmental and energy problems, and EV diffusion is also a concern for managers in various industries and EV owners. To sum up, this work mainly focuses on the scale evolution of EVs in the long term.

Currently, there are many researchers in the world who have conducted research on the changes in the number of electric vehicles [5,6,7,8,9,10]. Reference [5] established a multi-agent-based system dynamics model to explore the key role of factors such as license restrictions, charging station construction subsidies, and EV purchase subsidies in the changes and benefits of EV quantities. Reference [6] used spatial analysis and Poisson statistical models to study the role of neighborhood effects and workplace effects on the diffusion of electric vehicles in California, USA. Reference [7] explored the dynamic impact of different policies on the change in the number of EVs using a small-world network model, and the results showed that government subsidies and traffic restriction policies could increase the number of EVs. Reference [8] studied the relationship between the penetration rate of EVs among the population and different factors and analyzed the inherent connection between the quantity changes of EVs and traditional cars using regression analysis. Reference [9] used various innovative diffusion models to simulate and predict the trend of EV ownership changes in 20 major countries around the world in the future. The above methods for studying the changes in the number of EVs can be roughly divided into three categories: multi-agent technology, data regression analysis theory, and spatial prediction analysis. Although these methods can evaluate and predict the changes in the number of electric vehicles from different perspectives, they mainly focus on the EV scale all from a macro perspective to study the trend of EV quantity changes in a certain region. Namely, national or regional level models were established to predict the EV based on local economic, social, environmental, and other conditions. Nevertheless, some significant individual-level elements affecting EV diffusion were ignored in these models. To some extent, consumers’ willingness to buy EVs depends on user’s micro-level choice behavior, e.g., consumers’ cognitive attitudes toward EVs and the impact of EV owners on non-EV consumers. Therefore, this work mainly focuses on EV diffusion based on the individual level compared with other existing methods.

There are also many scholars who have conducted research on the purchasing behavior and choice of electric vehicles [11,12,13]. Reference [11] studied the internal mechanism of consumer electric vehicle purchasing decisions using structural equation modeling. Reference [12] proposed a “reservation/on-demand” charging and discharging service model and analyzed users’ purchasing intentions with the goal of maximizing user benefits. Reference [13] used the planned behavior theory integration model, which includes perceived risks and values, to analyze consumers’ willingness to purchase electric vehicles. The above-mentioned literature studies the changes in the number of EVs from the perspective of micro-level individual users, but still does not consider the influence of neighboring users. In reality, when neighbors near the user make decisions to buy electric vehicles, it will to some extent affect the user’s own purchasing behavior. Therefore, it is necessary to consider the adjacent effect of users when studying the process of changes in the number of electric vehicles.

The article examines a diffusion model for the expansion of electric vehicle (EV) quantities based on individual user choice behavior. Firstly, a neural network was employed to predict the daily charging power sequence of EVs, which allows for measuring consumers’ economic feasibility based on billing data. Logistic regression was used to quantify consumers’ cognitive attitudes toward electric vehicles. The impact of EV owners on non-EV consumers, i.e., social effects, was evaluated by constructing a small-world network. Afterward, discrete choice models were utilized to calculate the probabilities of users choosing to purchase EVs or PdVs, and statistical calculations were performed to estimate the quantity of EVs. Finally, using a specific urban area as the research subject, simulations were conducted to analyze the future changes in the quantities of gasoline-powered cars and EVs. The results indicate that the growth rate of PdV holdings is gradually decreasing, while the quantity of EVs shows an S-shaped curve in its changes.

2. User Choice Behavior Model

Against the backdrop of increasingly scarce fossil fuel resources, EVs powered by electricity have gradually replaced PdVs as a popular choice for people to buy cars. People will evaluate PdVs and EVs comprehensively when buying a car, taking various factors into consideration to make the appropriate purchasing decision. Therefore, this article selects three indicators of the economic effect, cognitive attitude, and social effect of people’s evaluations of EVs and PdVs to establish a user choice behavior model, as shown in Figure 1 below.

The three factors that users need to consider when choosing between purchasing an electric vehicle or a traditional fuel-powered vehicle are economic effects, cognitive attitudes, and social effects. Economic effects encompass the purchase cost, operating cost, and battery replacement cost. Cognitive attitudes include age, household income, family size, and educational level. Social effects consist of the total number of users, interpersonal relationships, and whether the user already owns an electric or fuel-powered vehicle.

The user individual utility function is shown in Equation (1), and the choice behavior of individual users can be studied based on the utility function, thereby deducing the diffusion and scale changes of electric vehicles.

$$U_{\mathrm{ev}}=\alpha \cdot U_{\mathrm{e}}^{\mathrm{ev}}+\beta \cdot U_{\mathrm{att}}^{\mathrm{ev}}+\gamma \cdot U_{\mathrm{ne}}^{\mathrm{ev}}$$

(1)

$$U_{\mathrm{oil}}=\alpha \cdot U_{\mathrm{e}}^{\mathrm{oil}}+\beta \cdot U_{\mathrm{att}}^{\mathrm{oil}}+\gamma \cdot U_{\mathrm{ne}}^{\mathrm{oil}}$$

(2)

In the equation: U_ev and U_oil represent, respectively, the comprehensive utility of individual users purchasing electric vehicles and petrol-driven vehicles; U_e^ev and U_e^oil represent, respectively, the economic effects brought by individual users purchasing electric vehicles and petrol-driven vehicles; U_att^ev and U_att^oil represent, respectively, the cognitive attitudes of individual users toward EVs and PdVs; U_ne^ev and U_ne^oil represent, respectively, the social utility of individual users purchasing electric vehicles and petrol-driven vehicles; α, β, and γ represent, respectively, the inclination of individual users to consider factors when making choices, and they satisfy α, β, γ∈[0,1] and α + β + γ = 1.

It should be noted that since the three indicators selected in the article, economic effect, cognitive attitude, and social effect, have different units of measurement, a normalization method was adopted to process them before calculating the user’s individual utility. Therefore, in Equation (1), U_e^ev, U_e^oil, U_att^ev, U_att^oil, U_ne^ev and U_ne^oil are all the normalized utility values.

2.1. Economic Effect

When purchasing different types of cars, users must consider the economic effects brought by purchasing different cars. As a consumable product, cars themselves do not generate direct benefits, so their economic effects are measured by the comprehensive costs incurred by users when purchasing different cars.

To calculate the user’s economic cost, it is necessary to first obtain the daily charging power sequence Pch.v.t of electric vehicles. A one-dimensional Convolutional Neural Network (CNN) can be used in combination with historical charging data from 1140 EVs in a certain city area over the past five years to predict the data. The CNN model consists of an input layer, convolutional layer, pooling layer, fully connected layer, and output layer. The CNN prediction model is shown in Figure 2 below.

The convolutional layer extracts the features of electric vehicle charging data by performing convolution calculation between the convolution kernel and the data segment:

$$T[n]=(f\ast g)[n]={\displaystyle \sum _{m=0}^{N-1}f(m)g(m)}$$

(3)

In the equation: f(m) is the data segment with a length of N; g(m) is the kernel function sequence of the convolutional layer, which has the same length as the length of the convolution kernel; n is the number of convolutional layers, and T[n] is the feature sequence extracted from f and g after convolution. With the stacking of layers, the generated feature maps can capture increasingly complex global properties in the input signal.

The activation function in machine learning provides a possibility for models to handle high-dimensional nonlinear problems. Among commonly used activation functions, the ReLu activation function has a wide activation range and a simple expression, without any multiplication, division, exponentiation, or power operations, making it computationally efficient with quick output of calculation results. Therefore, selecting the ReLu activation function after the convolutional layer improves the expressive power of CNN:

$$\mathrm{Re}Lu\left(x\right)=\left\{\begin{array}{cc}0,& x<0\\ 1,& x>0\end{array}\right.$$

(4)

To reduce the computational load, a max-pooling layer is added after every two convolutional layers to preserve the main features by selecting the maximum value from the selected fixed-size regions. The fully connected layer outputs the result after stretching all data into one dimension.

During network training, the error is propagated through the network using backpropagation and the gradient descent method is used to train neuron parameters. The mean squared error function is used as the objective function, as shown in the following equation:

$$L=-\frac{1}{n}{\displaystyle \sum _{i=1}^n(y_i-s_i}{)}^2$$

(5)

In the equation: L represents the deviation between the predicted result and the actual result; n is the total number of samples; i represents the i-th sample; y_i is the true label; s is the actual output value after activation by the fully connected layer.

The weight w and bias b update formulas for the convolutional network in each layer are as follows:

$$\left\{\begin{array}{c}{w}_{i+1}=w_i-\alpha \frac{\partial L(w_i,b_i)}{\partial w_i}\\ b_{i+1}=b_i-\alpha \frac{\partial L(w_i,b_i)}{\partial b_i}\end{array}\right.$$

(6)

In the equation: w_i, b_i and w_i+1, b_i+1 represent the weights and biases of the i-th and (i + 1)-th generations, respectively; α is the learning rate. When the loss L gradually decreases with increasing iterations and tends to 0, it indicates that the CNN model has been trained well.

The network structure adopts the classic Lenet-5, which includes an input layer, convolutional layers, pooling layers, fully connected layers, and an output layer. The convolution kernel size is set to 5 × 5, with a stride of 2; the pooling layer has a size of 2 × 2. The optimizer uses the adaptive moment estimation method ADAM [14] and the evaluation metric selected is “accuracy”. The Python version used is 3.7, and the neural network model is built on the Spyder platform in Anaconda.

Equations (7) and (8) represent, respectively, the comprehensive economic costs for users of electric vehicles and fuel-powered vehicles, including car purchase cost, purchase subsidies, operating costs, and battery replacement costs. Due to advancements in battery technology, the selling price of electric vehicles tends to decrease over time. Equation (9) represents the relationship between the selling price of electric vehicles and time. Government support for electric vehicle purchases also gradually decreases as the market size expands. Equation (10) represents the government’s subsidy for users purchasing electric vehicles. The operating cost of electric vehicles is the charging cost, while the operating cost of fuel-powered vehicles is the fuel consumption expense.

$$C_{\mathrm{e}}^{\mathrm{ev}}=(C_{\mathrm{b}}^{\mathrm{ev}}-C_{\mathrm{sub}}^{\mathrm{ev}})\frac{\delta {(1+\delta )}^{Y_{\mathrm{ev}}}}{{(1+\delta )}^{Y_{\mathrm{ev}}}-1}+C_{\mathrm{use}}^{\mathrm{ev}}+C_{\mathrm{batt}}^{\mathrm{ev}}$$

(7)

$$C_{\mathrm{e}}^{\mathrm{oil}}=C_{\mathrm{b}}^{\mathrm{oil}}\cdot \frac{\delta \cdot {(1+\delta )}^{Y_{\mathrm{oil}}}}{{(1+\delta )}^{Y_{\mathrm{oil}}}-1}+C_{\mathrm{use}}^{\mathrm{oil}}$$

(8)

Among:

$$C_{\mathrm{use}}^{\mathrm{ev}}={\displaystyle \sum _{t=1}^T{P}_{\mathrm{ch}.v.t}\cdot s_{\mathrm{ch}}}$$

(9)

$$C_{\mathrm{use}}^{\mathrm{oil}}={\displaystyle \sum _{t=1}^T{s}_{\mathrm{oil}}\cdot L\cdot {\psi }_{\mathrm{oil}}}$$

(10)

In the equation: C_e^ev, C_e^oil are the total costs that users need to spend on purchasing EVs and PdVs, respectively; C_b^ev, C_b^oil are the selling prices of EVs and PdVs; C_use^ev, C_use^oil represent their usage costs; C_sub^ev is the policy subsidy that car owners receive when purchasing EVs; C_batt^ev represents the cost of replacing the battery for car owners; δ represents the discount rate; Y_ev, Y_oil are the service life of EVs and PdVs, respectively; P_ch.v.t is the daily charging power sequence of electric vehicles; s_ch refers to the charging price of EVs; s_oil represents the fuel price; L represents the driving distance that users travel every day; Ψ_oil is the fuel consumption rate, which represents the amount of fuel consumed per kilometer traveled by a gasoline vehicle.

It should be noted that the charging price of electric vehicles is not fixed. Due to changes in the number of electric vehicles, the construction cost and operating income of charging facilities of electric vehicle charging operators also change. Therefore, the charging tariff charged to users will also change, with the expected rate of return and charging tariffs as shown in Equations (11)–(13).

$${\beta }_{\mathrm{ch}}=(C_{\mathrm{use}}^{\mathrm{ev}}-C_{\mathrm{inv}}^{\mathrm{ev}}-C_{\mathrm{opr}}^{\mathrm{ev}})/C_{\mathrm{use}}^{\mathrm{ev}}$$

(11)

$$\Delta s_{\mathrm{ch}}=s_{\mathrm{ch}}{}_{.\mathrm{y}-1}\cdot {\beta }_{\mathrm{ch}}$$

(12)

$$s_{\mathrm{ch}}{}_{.y}=\Delta s_{\mathrm{ch}}+s_{\mathrm{ch}.\mathrm{y}-1}$$

(13)

In the equation: β_ch is the expected rate of return for the power supply company; C_inv^ev and C_opr^ev are the construction and maintenance costs of the charging station, respectively; ΔS_ch is the difference between the charging price S_ch.y−1 in the year y − 1 and the charging price S_ch.y in year y.

Use the following formula to convert the total cost of purchasing different types of cars for users into their economic effects [15]:

$$U_{\mathrm{e}}^{\mathrm{ev}}=1-\frac{1}{(1+e^{-C_{\mathrm{e}}{}^{{}_{\mathrm{ev}}}})}$$

(14)

$$U_{\mathrm{e}}^{\mathrm{oil}}=1-\frac{1}{(1+e^{-C_{\mathrm{e}}{}^{{}_{\mathrm{oil}}}})}$$

(15)

In the equation: C_e^ev and C_e^oil represent the comprehensive expenses that car owners need to incur when choosing to purchase different types of cars.

2.2. Cognitive Attitude

The user’s attitude toward traditional EVs or PdVs depends on their individual characteristics and background. Factors such as age, household income, education level, family size, etc., can cause users to have different cognitive attitudes toward purchasing EVs or PdVs. Therefore, logistic regression was used to quantify the user’s cognitive attitude toward the two types of cars [16,17,18]. The logistic regression model is as follows:

$$y_{\mathrm{ev}}={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_3+{\beta }_4{x}_4$$

(16)

In the equation: x₁, x₂, x₃, and x₄ represent four factors that influence user selection behavior, which are age, household income, family size, and education level, respectively. β₀, β₁, β₂, β₃, and β₄ are the logistic regression coefficients.

$$U_{\mathrm{att}}^{\mathrm{ev}}=\frac{\exp ({\beta }_0+{\displaystyle \sum _{i=1}^4{\beta }_i{x}_i})}{1+\exp ({\beta }_0+{\displaystyle \sum _{i=1}^4{\beta }_i{x}_i})}$$

(17)

$$U_{\mathrm{att}}^{\mathrm{oil}}=1-\frac{\exp ({\beta }_0+{\displaystyle \sum _{i=1}^4{\beta }_i{x}_i})}{1+\exp ({\beta }_0+{\displaystyle \sum _{i=1}^4{\beta }_i{x}_i})}$$

(18)

In the equation, U_att^ev and U_att^oil represent the user’s attitude toward EVs and PdVs, respectively.

2.3. Social Utility

Social effect refers to the “neighborhood effect” in user choice behavior. Each user is closely connected to related groups such as colleagues, relatives, and neighbors through different channels. When making choices, users are influenced by other social members adjacent to them [19,20]. That is to say, for a particular user, when purchasing different types of cars, whether to choose an electric car or a gasoline car will be affected by neighboring social individuals. In fact, in the real world, each user forms a small-world network between completely regular and completely random due to their close connections [21], as shown in the specific diagram in Figure 3:

According to the rules in reference [22], this article randomly generates small-world networks. Regarding the individuals in the network, EVs and PdVs are used as social effects for different choices of individual users, based on their permeability rates throughout the whole population. The specific formula is shown as follows:

$$U_{\mathrm{ne}.i}^{\mathrm{ev}}=\frac{1}{m_i}{\displaystyle \sum _j^N{A}_{ij}\cdot }{x}_{j.\mathrm{ev}}$$

(19)

$$U_{\mathrm{ne}.i}^{\mathrm{oil}}=\frac{1}{m_i}{\displaystyle \sum _j^N{A}_{ij}\cdot }{x}_{j.\mathrm{oil}}$$

(20)

In the equation: U_ne.i^ev and U_ne.i^oil are the social effects of EV and PdV users, respectively; m_i represents the total number of users connected to user i; N is the total number of nodes in the small-world network, that is, the number of users; A_ij represents the connection between user i and user j. When they are connected, A_ij = 1, otherwise A_ij = 0; x_j.ev and x_j.oil are both 0–1 variables. If user j owns an electric vehicle or a gasoline vehicle, x_j.ev = 1 or x_j.oil = 1; otherwise x_j.ev = 0 or x_j.oil = 0.

2.4. Probability Model of Individual Selection Behavior

The discrete choice model is an effective and practical market research technique that can reveal consumers’ choice behavior toward products under different attributes. It is used to estimate consumers’ choice behavior of a product or service with different conditions so it can measure the purchasing behavior of consumers. In the discrete choice model, the user’s choice behavior toward a product or service is reflected through dependent variables and index variables. The dependent variable represents the user’s choice result, and the index variable represents the factors that influence the user’s decision [23,24]. In the article, the user’s behavior of choosing to buy different types of cars based on the utility function is consistent with the discrete choice model. Therefore, the discrete choice model is a promising option to estimate consumers’ willingness to buy EVs and forecast the EV scale. Based on Equation (1), by comprehensively considering the individual’s cognitive attitude, economic effect, and social effect toward choosing different types of cars, the probability of each user choosing to purchase an EV or PdV is calculated through the discrete choice model:

$$P_{\mathrm{ev}}=\frac{e^{U_{\mathrm{ev}}}}{e^{U_{\mathrm{ev}}}+e^{U_{\mathrm{oil}}}}$$

(21)

$$P_{\mathrm{oil}}=\frac{e^{U_{\mathrm{oil}}}}{e^{U_{\mathrm{ev}}}+e^{U_{\mathrm{oil}}}}$$

(22)

In the equation: P_ev and P_oil represent, respectively, the probability of users choosing to purchase an EV or a PdV; U_ev and U_oil represent the overall utility of electric vehicles and gasoline vehicles, respectively, calculated using Equation (1).

3. Scale Evolution Model of Electric Vehicle

The solution process of the EV quantity diffusion model is shown in Figure 4, where “n” represents the nth user and “y” represents the year.

In the algorithm process, first input the relevant parameter information of the user, calculate the economic utility, cognitive attitude, and social utility of each user based on the aforementioned method, and obtain the probability of the user’s purchase of EVs or PdVs through Equations (18) and (19). Then, the number of electric vehicles in the system is counted, and the EV scale evolution model is obtained.

4. Case Study

4.1. Subsection

This article takes a certain city area as the research object. By consulting the statistical data yearbook of the region, we know that there is a total of 53,484 households in the area. There are currently 9752 PdVs and 1140 EVs. The initial charging price is 0.6 yuan/kWh. Other related data are shown in

Table 1. Related parameters of EVs.

Parameter	Number
Purchase price (10,000 yuan (1378 dollars)/vehicle)	20
Government subsidy (10,000 yuan (1378 dollars)/vehicle)	10
Rated on-board capacity (kWh)	30
Maximum charging power (kW)	4
Charging efficiency	95%
Service life (a)	20
Battery life (a)	5
Battery replacement cost (10,000 yuan (1378 dollars)/vehicle)	5

. To simplify the calculation, this article assumes that each household can purchase at most one car, whether it is an electric or gasoline vehicle. In addition, it is assumed that each user’s electric or gasoline vehicle purchased is of the same model.

The parameters of EVs and PdVs are shown in Table 1 and

Table 2. Relevant parameters of PdVs.

Parameter	Number
Purchase price (10,000 yuan (1378 dollars)/vehicle)	10
Fuel consumption rate (L/100 km)	8
Service life (a)	20

, respectively. Due to the longer development time and relatively mature technology of PdVs, and the shorter development time and limitations of battery technology of EVs, a study comparing the sales prices of EVs and PdVs with the same performance level showed that the sales price of EVs was 1.4 to 2.6 times higher than that of PdVs. With the continuous improvement of battery technology, the sales price of electric vehicles will gradually decrease, and the proportion of their sales price will also decrease accordingly. The initial sales price ratio of the two types of cars in this article is set to 2 times. The gasoline price for fuel vehicles is set at 9.2 yuan/L. Due to the increasing energy shortage in recent years, the fuel price will gradually increase slightly over time.

This article divides users’ age into three age groups, namely: youth (20–40 years old), middle-aged (41–65 years old), and elderly (over 65 years old). The individual’s education level is divided into three levels: primary school, secondary school, and university. The size of the household is divided into 1–2, 3–4, 5–6, and more than 6 people. The annual household income is divided into four levels: less than 100,000 yuan (13,777 dollars), 100,000–200,000 yuan (13,777–27,554 dollars), 200,000–500,000 yuan (27,554–68,885 dollars), and more than 500,000 yuan (68,885 dollars). The relevant parameters of users in the region regarding their cognitive attitudes toward purchasing electric cars and fuel gas measurement are shown in

Table 3. Related parameters of cognitive attitude.

		Cognitive Attitude
		Willing to Buy EV	Willing to Buy PdV
Age	Youth	47,436 people	22,015 people
	Middle age	10,854 people	35,621 people
	Old age	3324 people	8236 people
Degree of education	primary school	13,476 people	27,923 people
	middle school	32,684 people	28,304 people
	university	15,876 people	9223 people
Family size	1–2 population	7863 family	6035 family
	3–4 population	9010 family	9857 family
	5–6 population	8425 family	6852 family
	More than 6 people	1743 family	3239 family
Annual household income	Below 100,000 yuan (13,777 dollars)	12,336 family	8358 family
	100,000 to 200,000 yuan (13,777 to 27,554 dollars)	6723 family	12,423 family
	200,000 to 500,000 yuan (27554 to 68,885 dollars)	5247 family	3234 family
	More than 500,000 yuan (68,885 dollars)	3526 family	1637 family

.

According to the analysis of factors affecting the audience of electric vehicles in the “Outlook on Global Electric Vehicles in 2022” released by the International Energy Agency (IEA) [25] and combined with the analysis results of factors affecting user purchase parameters in the references [26,27], this paper sets parameters that represent different degrees of inclination in the user utility function based on the individual characteristic parameters of users in the region. The simulation period is set to 20 years.

4.2. Result Analysis

The variation of the quantity of EVs and PdVs during the simulation period is shown in Figure 5.

From the chart, it can be seen that the number of PdVs increases year by year during the simulated period, but the growth rate gradually decreases. In the 10th year, the number of PdVs basically stops increasing, and it is even speculated that there will be a downward trend in 20 years. This is because the gradually increasing fuel costs have led to a slight increase in the overall cost of PdVs, resulting in a gradual decrease in the number of people buying PdVs and a gradually decreasing growth rate of PdV holdings. The number of EV changes presents an S-shaped curve, with an exponentially rapid growth from 5 to 13 years and a slow growth to saturation from 13 to 20 years during the simulation period. Initially, due to the backward technology level, the high purchase cost of electric vehicles and low user recognition, the comprehensive cost of EVs was higher than that of PdVs. Therefore, the growth of EV holdings was slow in the first few years, and the growth rate was lower than that of PdVs. During this period, government subsidies for EV purchases mainly promoted the slow development of EVs. However, with the advancement of technology, the development of EVs has become more mature, and the cost has gradually decreased. The comprehensive cost of EVs is now lower than that of PdVs, which has led to a rapid rise in EVs, and its growth rate is also higher than that of PdVs. As time goes on, the technology of EVs becomes more mature and its cost remains stable, while the promotion of the government for EVs gradually decreases. The change in the comprehensive cost of EVs is small, which makes the EV market slowly increase and approach stability, and the growth rate also continues to decrease.

To investigate the impact of government subsidies on the change in the number of EVs, medium 50,000 yuan (6889 dollars) and low 20,000 yuan (2755 dollars) subsidies were set up to compare with the high subsidy scenario in this article. The results of EV ownership are shown in Figure 6.

According to Figure 6, under different levels of policy subsidies, the number of EV owners presents an S-shaped curve, starting with a slow increase and then accelerating until it reaches a stable level. The difference lies in that, under moderate and low subsidy conditions, the growth rate of EV ownership is slower, and the time to reach saturation is about 5 years later than that under high subsidy policies. Additionally, the total number of EVs at saturation is also lower by 5000 to 8000 compared to high subsidy policies. In the early stages of slow growth, the growth rate of EV ownership under high subsidies is higher than that under moderate and low subsidies, allowing for faster development and promotion of EVs under the strong support of government subsidies. Moreover, in the later stage where government subsidies continue to decrease, the number of EV ownership also varies.

The changes in charging prices under different policy subsidies are shown in Figure 7.

According to Figure 7, under all three subsidy scenarios, the charging price shows a decrease followed by an increase. Charging prices under high subsidies are 0.1 to 0.2 yuan (1.4 to 2.8 cents) higher than those under medium and low subsidies. The main reason is that the decrease in charging prices in the early stages of slow growth of EVs promotes the development of electric vehicles. Subsequently, due to the rapid increase in the number of EVs, more funds are needed to invest in the construction and operation of charging equipment. Therefore, the charging price keeps increasing to recover the investment in charging equipment and make a profit. In addition, under low policy subsidies, the charging price is the lowest, while under high policy subsidies the charging price is the highest. This is because under high subsidy conditions, there are more EVs, which leads to the need for more charging equipment to be built, thus requiring a higher charging price to recover investment and operational costs.

The sales price can greatly affect the user’s willingness to purchase. In order to analyze the impact of EV sales prices, it is assumed that the EV sales price will not change in the next 20 years due to technological limitations. The comparison results with the scenario in this article are shown in Figure 8 below.

From the figure, it can be seen that the EV increases relatively slowly under the condition of unchanged selling price, and the quantity is also relatively small compared to its continuous decline. The main reason is that when the selling price remains unchanged, users need to spend more cost to purchase EVs, so the increases in quantity and growth rate are both small.

To verify the impact of social effects on the change in EV quantity, the results of the change in EV quantity under scenarios without considering social effects and under the scenario of this paper were compared, as shown in Figure 9.

From the changes in the number of EVs in the graph, it can be seen that the increase in the number of EVs considering social effects is greater than that without considering social effects. The main reason is that social effects can enhance users’ willingness to purchase by neighboring EV users, thereby promoting the increase in their numbers. In addition, the comparison between Figure 7 and Figure 8 shows that under the condition of unchanged sales price, the increase in the number of EVs is less than that without considering social effects, which indicates that users tend to focus more on the sales price when choosing to buy an EV. In other words, the impact of EV sales price on users’ willingness to purchase is greater than the effect of proximity.

To validate the efficiency and effectiveness of the proposed method, we compared CNN to the other three methods, i.e., artificial neural networks (ANN) [28], support vector machine (VSM) [29], and extreme learning machine (ELM) [30]. We compared the deviation between the predicted charging power of consumers by these four methods and its real value, and the calculation time of the four methods. The results are shown in

Table 4. The comparative results of the four methods.

	CNN in the Proposed Method	ANN	VSM	ELM
Deviation (%)	1%	3%	7%	9%
Calculation time (s)	89 s	107 s	153 s	168 s

. Note that the charging power of consumers for comparison is an average of all consumers of EV owners.

It can be noted that the deviation and calculation time calculated by CNN in the proposed method are both minimums compared to other methods. The deviation between the predicted charging power by CNN in the proposed method and the real value is 1%, and the calculation time just is 89 s. The efficiency and effectiveness of the proposed method are the best in these methods.

Additionally, we also compared the predicted scales of EVs and PdVs by the proposed method to other methods, and the real value shown in

Table 5. The predicted scales of EVs and PdVs by the four methods.

	Real Value	CNN in the Proposed Method	ANN	VSM	ELM
EV	1140	1100	1050	1280	1015
PdV	9752	9745	9700	9890	9658

. The predicted results of EVs and PdVs are the scales in the year before the simulation horizon.

It can be noted that 1100 consumers own EVs and 9745 consumers chose to buy PdVs calculated by the proposed method. The quantities of EVs and PdVs predicted by the proposed method are closest to their real data compared to other methods.

5. Conclusions

5.1. Summary

This article proposes a diffusion model for the quantity of electric vehicles based on individual user choice behavior. It utilized neural networks, logistic regression, and small-world networks to calculate the influence of factors such as economic effects, cognitive attitudes, and social effects on users’ decisions to purchase either fuel-powered or electric vehicles. The discrete choice model was employed to calculate the probabilities of users purchasing electric or fuel-powered vehicles and to track the number of electric vehicles. Based on simulation results, it is evident that the growth rate of fuel-powered vehicles declines annually in future time periods, while the quantity of electric vehicles follows an S-shaped curve. Moreover, significant government subsidies are expected to further stimulate the growth and diffusion of electric vehicles.

5.2. Future Work

As residents’ economic levels improve, their diversified travel demands pose higher requirements for vehicle types, including electric and fuel-powered cars. Therefore, considering the impact of users’ diverse travel needs and the influence of different types of electric and fuel-powered vehicles on their scale variations constitutes a key focus for future research.