Optimizing Electric Vehicle Integration with Vehicle-to-Grid Technology: The Influence of Price Difference and Battery Costs on Adoption, Profits, and Green Energy Utilization

Abstract

Over the past decade, the widespread adoption of global green energy has emerged as a predominant trend. However, renewable energy sources, such as wind and solar power, face significant wastage due to challenges in energy storage. Electric vehicles (EVs) are considered an effective solution to address the energy storage dilemma. “Vehicle-to-grid” (V2G) technology, allowing vehicles to feed electricity into the grid, enhances the efficiency of renewable energy utilization. This paper proposes an electric vehicle game model that comprehensively considers user choices, corporate profits, and green energy utilization. The model, based on difference in prices, electricity rates, and fuel prices, establishes user utility models to determine optimal driving distances and driving decisions. It separately formulates the maximum profit functions for selling conventional electric cars and V2G electric cars, deriving optimal pricing for enterprises and user adoption rates. The research findings indicate that when price difference can offset V2G battery costs, increasing price difference and reducing battery costs effectively enhance electric vehicle adoption rates, increase corporate profits, and improve green energy utilization. Moreover, compared to conventional electric vehicles, V2G electric vehicles demonstrate a comparative advantage, with the implementation of V2G expanding corporate profits and green energy utilization. Validation using Chinese data reveals that when price difference can offset V2G battery costs, drivers are more inclined to choose V2G electric vehicles. Both battery electric vehicles (BEVs) and V2G electric vehicles exhibit adoption rates that can increase by over 35%. This study provides theoretical and model support for the future development of V2G and policy formulation, underscoring the comparative advantages of V2G in enhancing green energy utilization efficiency. Additionally, this study offers valuable insights as a reference for business models in the V2G electric vehicle industry.

1. Introduction

Over the past few centuries, renewable energy has been increasingly recognized as a means to alleviate energy shortages [1]. According to the planning by the International Renewable Energy Agency (IRENA), by the year 2050, over two-thirds of energy production will be derived from renewable sources, with contributions from renewable sources such as wind and solar energy reaching 60% [2]. However, both wind and solar energy face significant waste due to energy storage challenges. As the world’s largest producer of wind and solar power, China experienced an average wind curtailment rate of 3.2% and a discarded wind power quantity of approximately 6 billion kilowatt-hours in the first quarter of 2022. The solar curtailment rate was 2.8%, with a discarded solar power quantity of around 2.4 billion kilowatt-hours [3]. Countries worldwide are also grappling to varying extents with energy storage issues leading to wastage of green energy. The prevailing viewpoint suggests that managing the surplus of wind and solar power is more challenging than addressing their deficiencies [4]. This is attributed to the intricate nature of storing wind and solar energy, where surplus electricity can result in an increased burden on the power grid. Therefore, optimizing electrical energy storage and promptly integrating excess electricity into the grid are crucial measures to enhance the utilization of green energy and achieve sustainable development.

EVs are considered a key solution to address energy storage challenges. V2G power technology is one of several storage technologies, enabling vehicles to feed electricity into the grid. Through unified demand control in the power system, V2G can better utilize fluctuating renewable energy. For power companies, V2G offers benefits such as backup power, load balancing, peak load reduction [5,6], and reduced uncertainty in daily and hourly power load forecasts [7]. Importantly, numerous studies suggest that V2G can effectively enhance the energy efficiency of wind and solar power [3,8]. Conventional EVs (BEVs and PHEVs) can contribute to peak shaving by charging in an orderly manner at night, but they cannot feed power back to the grid during the day, offering only limited peak load reduction for fluctuating grids [9]. In contrast, V2G EVs not only contribute to peak shaving at night but can also provide power back to the grid during peak demand hours in the daytime [10], making their advantages more apparent in terms of green energy utilization [11].

Numerous studies have demonstrated that V2G strengthens green energy utilization. Current research primarily focuses on mathematically modeling ways to efficiently integrate electric vehicles into the grid, optimizing the peak shaving effect of V2G. Many studies model from an electrical energy perspective, relying on energy dispatch strategies for efficient operation [12,13]. Some research models from the perspective of charging station allocation, utilizing more efficient charging station layout strategies to ensure network efficiency [14]. Another common model focuses on the user perspective, aiming to minimize user costs [15]. Yuxin Wen et al. [16] proposed an optimal scheduling strategy for EV microgrids based on deep Q-learning, utilizing a reinforcement learning model to adapt to the non-linear effects of periodic EV mobility and user behavior. These studies suggest positive expectations for V2G in terms of user costs, grid stability, and green energy utilization.

However, most of these mathematical models largely overlook user preferences, considering only the interaction between vehicles and the grid without accounting for the users as the primary actors in V2G behavior. Many studies on user preferences and V2G adoption use survey methods [17,18], lacking a model to systematically simulate user choices. Adoption rate is a robust indicator reflecting user preferences; Le Wen et al. [19] introduced the concept of adoption rate in V2G research, stating that the adoption rate of EVs directly reflects the effectiveness of policy formulation [20,21] or indicates the direction specified by the policy [22,23]. This article utilizes adoption rates to accurately reflect user choices, thereby addressing this gap.

Research on V2G is a complex issue that requires consideration of the interests of users, electric vehicle manufacturers, and societal benefits. However, current studies predominantly focus on whether electric vehicle owners can profit from V2G services, neglecting the comprehensive analysis of all stakeholders involved in V2G services [15]. The innovation of this paper lies in two aspects. Firstly, it takes into account user choices, using the adoption rate as an intuitive measure to reflect the actual preferences of users and demonstrate changes after parameter variations. Secondly, this study innovatively incorporates electric vehicle manufacturers into the discussion. Prior research primarily concentrated on the profitability of charging station operators. However, in practical business models, electric vehicle manufacturers are often deeply involved in V2G, sometimes even participating directly as charging station operators in subsequent business activities. Therefore, investigating the profitability of electric vehicle manufacturers is crucial.

In summary, this paper proposes an electric vehicle game model with the following main contributions:

• The proposition of a model based on price difference, electricity prices, and fuel prices. By establishing user utility models to determine optimal driving distances and driving decisions, it subsequently formulates the maximum profit functions for enterprises selling conventional electric cars and V2G electric cars, obtaining optimal pricing for enterprises and user adoption rates.
• Analysis of the impact of price difference and battery costs on users, enterprises, and society after the integration of electric vehicles into V2G, and comparison of the changes in benefits for users, enterprises, and society after the integration of electric vehicles into V2G, demonstrating the comparative advantages of V2G.
• Calibration of the model using data from China.

2. Game Model Construction of Electric Vehicles

2.1. Introduction to the Model

We propose both BEV and V2G models. The BEV model simulates the driver’s choice between a gasoline car and a conventional electric car based on utility, while the V2G model simulates the driver’s choice between a gasoline car and a V2G-enabled electric car based on utility. We calculate the adoption rates, company profits, and green energy utility at equilibrium for both models and then compare them.

We assume that the main difference between gasoline cars and electric cars lies in the battery. In the BEV model, drivers have utilities for driving gasoline cars and conventional electric cars. The utility of driving a gasoline car depends on the gasoline price and mileage, while the utility of driving a conventional electric car depends on the electricity price, battery cost, and mileage. Drivers are rational and choose the optimal mileage to maximize the utility of both gasoline and electric cars. When the utility of driving a gasoline car is higher, drivers choose gasoline cars, and vice versa. After determining the optimal mileage and substituting the values, the optimal utility of driving a gasoline car is determined by the gasoline price, and the optimal utility of driving a conventional electric car is determined by the electricity price and battery cost.

Next is the interaction between companies and drivers. The battery cost, i.e., the pricing of the battery, is decided by the electric vehicle manufacturer. Electric vehicle manufacturers are rational and aim to maximize profits by ensuring the product of the number (or ratio) of electric car drivers and the pricing is maximized through a balanced interaction. Therefore, the pricing of the battery is the result of an interaction between drivers and electric vehicle manufacturers. Ultimately, the proportion of drivers choosing electric cars after equilibrium is the adoption rate.

The distinction between the V2G model and the BEV model lies in the additional utility that drivers gain after choosing an electric vehicle, specifically through participation in V2G activities. After purchasing a V2G electric vehicle, drivers engage in V2G behavior to generate additional benefits. More specifically, this involves discharging during high electricity prices (peak hours) and charging during low electricity prices (off-peak hours), aiming to make a profit through buying low and selling high. In this buy-low, sell-high process, the price difference plays a crucial role, representing the price gap between peak and off-peak electricity, directly determining the income generated by V2G. As the utility of V2G electric vehicles differs from that of regular electric vehicles, the equilibrium pricing and adoption rates will undergo changes.

To simplify our model, we assume that electric vehicle suppliers can only operate either conventional electric cars or V2G-enabled electric cars.

2.1.1. Driver Utility Description

We divide the driver’s utility of owning a vehicle into several components:

Mileage Utility: This represents the utility generated by the driver due to daily driving distance. This utility increases with the increase in driving distance, and the marginal benefit decreases. Following the research by Farahat et al. [24], this paper adopts $u(X)=\frac{1}{\mathsf{\omega }}\left(\lambda X-\frac{X^2}{2}\right)$ as the mileage utility function. In this function, $X$ represents the driving distance covered, $\lambda$ denotes the average satisfaction level of the driver, and $\mathsf{\omega }$ serves as the proportionality factor measuring driving utility.

Green Utility: This represents the additional utility gained by the driver due to owning an electric vehicle. Following the research by Hidrue et al. [25], we assume that green utility, ${\tilde{\mathrm{U}}}_{gr}$, is uniformly distributed within a certain interval $[0,d]$, where $d$ represents the driver’s daily willingness to pay for green utility.

Operating Costs: The driver incurs various expenses related to vehicle ownership and operation. These expenses include the purchase price of the vehicle, fuel, electricity, battery costs, taxes, and maintenance fees. Specific costs vary based on the type of vehicle and mode of operation. We standardize the initial purchase price of fossil fuel vehicles and electric vehicles without batteries to zero and assume that all vehicles have the same life cycle.

Additionally, we assume that the driver’s daily driving can be divided into two parts: planned and unplanned. The planned portion is determined based on the driver’s driving needs and cost information at the time of purchase, representing the daily average driving distance expected or planned by the driver. The unplanned portion includes additional driving due to factors such as life situations, driving needs, driving costs, unexpected circumstances, and traffic.

Drivers need to consider various costs associated with vehicle purchase and operation, which may vary depending on the vehicle model and driving mode. The daily driving distance can be divided into planned and unplanned parts, where the planned part is based on information at the time of purchase, and the unplanned part is influenced by various random factors. We use a random variable, $\gamma$, to represent the unplanned mileage, where the variable follows a density function drawn from a finite variance distribution, $g(\cdot )$, with a mean of zero and an inverse cumulative distribution function of $G(\cdot )$.

2.1.2. Driver’s Utility for Purchasing a Gasoline Vehicle

The driver’s perceived utility of purchasing a gasoline vehicle consists of two components: mileage utility and operating costs. Therefore, the driver’s perceived utility of purchasing a gasoline vehicle is given by

$$U_g=E_{\gamma }[u({\zeta }_g+\gamma )]-c_g{\zeta }_g.$$

(1)

In this equation, ${\zeta }_g$ and $\gamma$ denote the planned and unplanned driving distances for the gasoline vehicle, $E_{\gamma }[u({\zeta }_g+\gamma )]$ constitutes the mileage utility obtained by the driver due to the distance traveled, $c_g$ represents the fuel price per mile for the gasoline vehicle, and $c_g{\zeta }_g$ comprises the operating costs.

2.2. BEV Model

The BEV model serves as a benchmark model for comparison with the BEV-V2G model. The BEV model represents the traditional purchasing model, simulating the driver’s choice between a conventional vehicle and a BEV based on their utility.

For the BEV model, the driver’s behavior is divided into pre-purchase and post-purchase phases. Firstly, in the pre-purchase phase, the supplier provides the selling price, i.e., the price premium of the electric vehicle over the gasoline vehicle. Subsequently, the driver makes a choice between the gasoline vehicle and the electric vehicle based on the expected utility, considering the price premium. Then, the driver determines the planned driving distance based on the relevant marginal costs and benefits. Finally, in the post-purchase phase, the driver adds unplanned travel variables to the planned distance, constituting the driver’s final utility. The game process is illustrated in Figure 1 below:

The driver’s perceived utility of purchasing an EV consists of four components: mileage utility, green utility, battery purchase price, and operating costs. Therefore, the driver’s perceived utility of purchasing an electric vehicle is given by

$$U_{ev}=E_{\gamma }[u({\zeta }_{ev}+\gamma )]-c_{ev}{\zeta }_{ev}-F_{ev}+{\tilde{U}}_{gr},$$

(2)

in this equation, $c_{ev}$ represents the cost of electricity per mile for EVs, while $F_{ev}$ denotes the purchase price of the battery. For drivers, the selection of a commuting vehicle is contingent upon maximizing utility, prompting electric vehicle suppliers to determine the optimal battery purchase price. To achieve maximum profitability, enterprises must address the following issues:

$$\underset{P_{ev}}{\max }{E}_{{\tilde{U}}_{gr}}[I\{U_{ev}>U_g\}·(F_{ev}-c)],$$

(3)

where $I\{U_{ev}>U_g\}$ represents the total number of eligible electric vehicles, and $c$ is the normalization of electric vehicle battery costs on a daily basis. Due to

$$E_{{\tilde{U}}_{gr}}[I\{U_{ev}>U_g\}]=P({\tilde{U}}_{gr}>U_g-E_{\gamma }[u({\zeta }_{ev}+\gamma )]+c_{ev}{\zeta }_{ev}+F_{ev}),$$

(4)

and the green utility following uniform distribution within the interval $[0,d]$, we obtain

$$E_{{\tilde{U}}_{gr}}[I\{U_{ev}>U_g\}]=\frac{d-U_g+E_{\gamma }[u({\zeta }_{ev}+\gamma )]-c_{ev}{\zeta }_{ev}-F_{ev}}{d}$$

(5)

Substituting Equation (5) into Equation (3) and taking its derivative, then setting it equal to zero, we obtain

$$F_{ev}=\frac{1}{2}(d-U_g+E_{\gamma }[u({\zeta }_{ev}+\gamma )]-c_{ev}{\zeta }_{ev}+c).$$

(6)

We take the second derivative of Equation (3) and find that it is less than zero, indicating that (6) is the optimal pricing strategy.

Lemma 1.

(a) In order to maximize their utility, drivers have an optimal mileage of ${\zeta }_{ev}^{*}$, where ${\zeta }_{ev}^{*}$ satisfies the following conditions:

$$E_{\gamma }[u^{\prime }({{\zeta }_{ev}}^{*}+\gamma )]=c_{ev}.$$

(7)

(b) To maximize profit, enterprises set battery prices, thereby deriving the adoption rate function of electric vehicles:

$${P_{ev}}^{*}=\frac{d+E_{\gamma }[u({{\zeta }_{ev}}^{*}+\gamma )]-c_{ev}{{\zeta }_{ev}}^{*}-U_g-c}{2d}.$$

(8)

(c) At this equilibrium state, the maximum profit that the enterprise can obtain is

$${{\Pi }_{ev}}^{*}=\frac{1}{4d}{(d+E_{\gamma }[u({{\zeta }_{ev}}^{*}+\gamma )]-c_{ev}{{\zeta }_{ev}}^{*}-U_g-c)}^2.$$

(9)

Proof of Lemma 1.

Detailed proofs are provided in Appendix A. □

We evaluate the value of electric vehicles to the electrical grid and society from the perspective of green energy utilization. In the case of battery electric vehicles (BEVs), drivers engage in nighttime charging during off-peak hours. Given the lower electricity demand on the grid during these off-peak hours, renewable energy sources (such as wind power) may go unused, resulting in wasted potential. Consequently, BEVs charging during off-peak hours effectively channel green energy utilization into the batteries, thereby significantly enhancing nocturnal green energy utilization. Due to the conservation of electrical energy in electric vehicles (i.e., the charging quantity equals the discharging quantity), we employ the utilization rate coupled with the integral of energy consumption by daytime drivers to quantify the green energy utilization of conventional electric vehicles:

$${\varpi }_{ev}=E_{\gamma }({{\zeta }_{ev}}^{*}+\gamma ){P_{ev}}^{*}\omega ,$$

(10)

where $\omega$ represents the electric energy consumption per mile for electric vehicles.

2.3. V2G Model

For V2G electric vehicles, the driver’s behavior can also be divided into two phases: pre-purchase and post-purchase. Firstly, in the pre-purchase phase, the supplier offers a selling price, which includes a price premium for V2G electric vehicles compared to conventional gasoline vehicles. Subsequently, the driver makes a choice between gasoline vehicles and V2G electric vehicles based on their expected utility and then decides on the planned driving distance based on relevant marginal costs and benefits. Finally, in the post-purchase phase, the driver adds variables for unplanned trips to the planned mileage and includes the V2G discharging revenue they can participate in. These factors together constitute the driver’s ultimate utility. Therefore, for V2G electric vehicles, in addition to meeting the sequence of traditional vehicles, owners need to discharge when electricity prices are high in order to obtain revenue, which typically results in higher overall utility for V2G electric vehicle owners. The process is illustrated in Figure 2:

Owners of V2G electric vehicles generate daily income by discharging their vehicles. Specifically, they charge their vehicles during off-peak nighttime hours while absorbing renewable energy, commute as usual during the day, and discharge during peak hours. This strategy is employed to achieve peak load management and generate income. The specific process is illustrated in Figure 3.

The utility of a driver purchasing a V2G electric vehicle consists of five components: mileage utility, green utility, battery purchase price, operating costs, and V2G utility.

V2G Utility: This is the utility drivers derive from participating in V2G activities. The utility from V2G can be divided into two parts: one part is the profit gained from V2G, and the other part is the additional battery costs incurred due to V2G. Both components of V2G utility are associated with the daily discharge rate of the driver’s vehicle. We use $v$ to represent the discharge rate and $t$ to represent the discharge duration, where $t$ follows a uniform distribution in the interval $[0,t_0]$. The daily V2G discharge quantity for the driver can be represented by $vt$. The driver’s V2G utility can be expressed as follows:

$${\tilde{U}}_{v2g}=p_{d}vt-p_{b}vt,$$

(11)

in which $p_d$ represents the price difference per unit of electricity for drivers when participating in V2G, and $p_b$ represents the additional battery cost incurred per unit of electricity generated by drivers participating in V2G.

Therefore, the utility of a driver purchasing a V2G electric vehicle is

$$U_{v2g}=E_{\gamma }[u({\zeta }_{v2g}+\gamma )]-c_{v2g}{\zeta }_{v2g}-F_{v2g}+{\tilde{U}}_{gr}+{\tilde{U}}_{v2g}.$$

(12)

Similar to the game process with electric vehicles, we derive the optimal mileage, adoption rate, and maximum profit through equilibrium.

Lemma 2.

(a) In order to maximize their utility, drivers have an optimal mileage of ${\zeta }_{v2g}^{*}$, where ${\zeta }_{v2g}^{*}$ satisfies the following conditions:

$$E_{\gamma }[u^{\prime }({{\zeta }_{v2g}}^{*}+\gamma )]=c_{v2g},$$

(13)

where $c_{v2g}$ represents the electric cost per mile for V2G electric vehicles.

(b) To maximize profit, enterprises set battery prices, thereby obtaining the adoption rate function of V2G electric vehicles:

$${P_{v2g}}^{*}=\frac{d+E_{\gamma }[u({{\zeta }_{v2g}}^{*}+\gamma )]-c_{v2g}{{\zeta }_{v2g}}^{*}+{\tilde{U}}_{v2g}-U_g-c}{2d}.$$

(14)

(c) At this equilibrium state, the maximum profit that the enterprise can obtain is

$${{\Pi }_{v2g}}^{*}=\frac{1}{4d}{(d-E_{\gamma }[u({{\zeta }_{v2g}}^{*}+\gamma )]+c_{v2g}{{\zeta }_{v2g}}^{*}-{\tilde{U}}_{v2g}+U_g-c)}^2.$$

(15)

Proof of Lemma 2.

The proof procedure is the same as that in Lemma 1. □

For V2G electric vehicles, in addition to charging during off-peak nighttime hours to increase storage of renewable energy, discharging during daytime peak hours also directly expands green energy utilization. Discharging not only helps stabilize the electrical grid load but also means that the electricity that would otherwise be wasted from off-peak renewable sources is transferred back to the grid during peak hours. Therefore, the green energy utilization of V2G electric vehicles can be expressed as follows:

$${\varpi }_{v2g}=E_{\gamma }({{\zeta }_{v2g}}^{*}+\gamma ){P_{v2g}}^{*}\omega +E_t(vt){P_{v2g}}^{*}.$$

(16)

2.4. The Impact of Difference in Electricity Prices

First, let us discuss the impact of price difference on V2G. Price difference refers to the difference in electricity prices during peak and off-peak hours. With the increasing adoption of V2G electric vehicles in the future, the price difference at which drivers buy and sell electricity will directly influence their choices, consequently affecting corporate profits and green energy utilization. So, how does price difference affect user choices? The following results will provide an answer to this question.

Theorem 1.

There exists a threshold price difference, denoted ${p_d}^{*}$, such that when the price difference can offset the battery cost incurred by drivers participating in V2G, the utility of purchasing V2G electric vehicles becomes higher than that of purchasing regular electric vehicles. In this scenario, the adoption rate of electric vehicles increases, leading to higher corporate profits and enhanced green energy utilization.

Proof of Theorem 1.

Detailed proofs are provided in the Appendix A. □

Theorem 1 explains that price difference is the foundation of V2G, and when price difference can offset V2G battery costs, it signifies the most basic environment for V2G development. Moreover, increasing the price difference can effectively boost V2G adoption. When the price difference is above a certain threshold, promoting V2G can drive the widespread adoption of electric vehicles and significantly increase green energy utilization.

2.5. The Impact of Difference in Electricity Prices

Reducing battery costs has long been a shared goal of both businesses and governments. As battery costs decrease, the cost of purchasing V2G electric vehicles becomes lower for users, making them more inclined to buy electric vehicles instead of conventional gas-powered cars. This increase in adoption rates leads to higher sales for businesses and, as a result, increased profits. Additionally, higher adoption rates mean that more electric vehicles participate in grid balancing, resulting in a greater capacity for green energy utilization.

Theorem 2.

With the reduction in battery costs, the adoption of V2G electric vehicles, corporate profits, and green energy utilization will all increase.

Proof of Theorem 2.

Detailed proofs are provided in the Appendix A. □

Theorem 2 proves the effectiveness of reducing battery costs in promoting V2G electric vehicles, establishing the economic sustainability of developing V2G electric vehicles, and enhancing the utilization of green energy.

Theorem 2 suggests that governments can encourage the development of the electric vehicle industry by investing in battery research and providing battery cost subsidies. Specifically, doing so can increase user willingness, improve the electric vehicle business environment, and enhance the utilization of green energy and grid stability. Simultaneously, for businesses, it is advisable to prioritize iterative improvements in V2G electric vehicle battery technology to increase profits.

3. Effectiveness of BEV-V2G Model

3.1. Adoption

As mentioned earlier, price difference forms the basis for the superiority of V2G. When the price difference exceeds the cost savings provided by V2G, the utility perceived by V2G users will be higher than that perceived by BEV users. This means that users are more likely to choose V2G electric vehicles over BEVs.

Theorem 3.

The adoption of V2G electric vehicles is higher compared to BEVs when $p_d>{p_d}^{*}.$

Proof of Theorem 3.

Detailed proofs are provided in Appendix A. □

Theorem 3 suggests that with a favorable business environment, V2G is more effective than BEV in promoting electric vehicles. Therefore, the government should prioritize the promotion of V2G electric vehicles when price differences are high.

3.2. Profits

When the price difference exceeds the cost savings provided by V2G, it indicates that the basic business environment for V2G is already in place. As we previously demonstrated, the adoption rate of V2G electric vehicles is higher. Therefore, businesses operating V2G electric vehicles will have higher sales, resulting in increased profits.

Theorem 4.

Businesses operating V2G electric vehicles tend to have higher profits compared to those dealing with BEVs when the price difference exceeds the cost savings provided by V2G when $p_d>{p_d}^{*}$.

Proof of Theorem 4.

Detailed proofs are provided in Appendix A. □

When battery costs decrease, the change in adoption rates for both V2G and BEV companies is linear. However, business profits are expressed as a quadratic function of adoption rates, making them nonlinear. Therefore, when the price difference exceeds the cost savings provided by V2G, V2G electric vehicles naturally have higher adoption rates, thus amplifying the increase in business profits resulting from reduced battery costs.

Theorem 5.

As battery costs decrease, businesses operating V2G electric vehicles will experience a faster rate of profit increase compared to BEV businesses when $p_d>{p_d}^{*}$.

Proof of Theorem 5.

Detailed proofs are provided in Appendix A. □

Theorems 4 and 5 demonstrate that price difference is the basis for the superiority of V2G electric vehicles over BEVs, and a reduction in battery costs can enhance the advantage of V2G electric vehicles.

3.3. Green Energy Utilization

V2G electric vehicles naturally have a higher renewable energy storage capacity than BEVs because they can discharge power back to the grid during the day. Therefore, at the same adoption rate, V2G electric vehicles will have a higher green energy utilization compared to BEVs.

Theorem 6.

V2G electric vehicles have a higher green energy utilization compared to BEVs when $p_d>{p_d}^{*}$.

Proof of Theorem 6.

Detailed proofs are provided in Appendix A. □

The reduction in battery costs leads to an increase in adoption rates. Since V2G electric vehicles have a higher green energy utilization than BEVs, at the same adoption rate, the rate of change in green energy utilization for V2G electric vehicles is higher. Therefore, the decrease in battery costs results in additional green energy utilization.

Theorem 7.

As battery costs decrease, the rate of increase in green energy utilization for V2G electric vehicles is higher compared to BEVs when $p_d>{p_d}^{*}$.

Proof of Theorem 7.

Detailed proofs are provided in Appendix A. □

Theorems 6 and 7 indicate that V2G has a significant advantage in green energy utilization, and the reduction in battery costs further amplifies this advantage. The government should promote V2G when price difference are appropriate and invest in research and development to lower battery costs, thereby fostering grid stability and enhancing the utilization of green energy.

4. Scenario Analysis

We have chosen China as the research country to evaluate our model. China is one of the world’s largest automobile markets, and the size of the Chinese market significantly influences the adoption rates and profitability of electric vehicles. In 2021, China’s National Development and Reform Commission (NDRC) explicitly expressed the need to accelerate the promotion of V2G pilot projects and operations, highlighting the enormous potential demand for V2G electric vehicles.

Furthermore, China has implemented a series of government policies to promote the development of electric vehicles, including subsidies, emission reduction targets, fuel economy standards, and more [26]. These policies may have varying effects on the adoption rates and profitability of V2G electric vehicles, making them worth studying.

For the sake of research convenience, we assume a vehicle and battery lifespan of 8 years, with the ability to undergo 2000 charging cycles. The parameters and sources in the scenario analysis are shown blow.

Table 1. Battery technology parameters.

Parameter	Estimated Value	Estimation Method/Sources
Battery cost	$c=\mathrm{USD} 3.93/\mathrm{day}$	According to the price range of lithium-ion batteries at 153 US dollars/kWh [27], as well as the mileage and battery capacity of a Tesla Model 3 Performance, we can determine that the daily battery cost of an EV in 2021 is USD 3.93/day.
Battery cost in V2G	$p_b=\mathrm{USD} 0.099/\mathrm{kwh}$	According to a lithium-ion battery price of USD 153/kWh [27] and 2000 battery charge cycles, a 30% profit can be made on the battery cost.
Electricity consumption per mile	$\omega =0.1807 \mathrm{kwh}/\mathrm{mile}$	Calculated according to the battery capacity and actual mileage of a Model 3 Performance.
Green utility—maximum willingness to pay	$d=\mathrm{USD} 5.30/\mathrm{day}$	According to Hidrue et al.’s [25] research, the willingness of value holders to pay for green utility was estimated. We estimated it to be equivalent to 8 years, calculated at a fixed annuity ratio of 11.03%, equivalent to USD 5.30/day.

lists the various parameters of batteries and driver’s willingness to pay, while

Table 2. Energy price parameters.

Parameter	Estimated Value	Estimation Method/Sources
Electricity price	$c_{ev}=2.08 ¢/\mathrm{mile}$	The unit electricity cost per mile for EVs in China is 2.08 cents/mile; this is based on 2021 electricity prices [28] and the mileage and battery capacity of a Tesla Model 3 Performance. The electricity price of the V2G vehicle is the same as that of the ordinary vehicle.
Fuel price	$c_g=10.837 ¢/\mathrm{mile}$	The unit fuel cost per mile for fuel vehicles in China is calculated as 10.837 cents/mile, using the 2021 average fuel consumption of 4.99 liters per 100 kilometers for fuel vehicles in China and a fuel price of USD 1354.47/ton [29].
Difference in electricity prices	$p_d=12.73 ¢/\mathrm{kwh}$	The electricity price difference per kilowatt hour in China is 12.73 cents/kwh, respectively, using Beijing electricity price data for 2023 [28,30].

lists the prices of various energy sources.

We determined the distribution of unplanned mileage and the parameters of mileage utility based on research by Avci et al. [31] and others on electric vehicle battery swapping stations, as presented in

Table 3. Driving utility parameters.

Parameter	Estimated Value
Distribution	$g()\equiv$ Shifted gamma
Gamma shape	$k=1.0876$
Gamma scale	$m=34.147$
Gamma location	$p=37.14$
Satiation level	$\lambda =58.54$
Scaling factor	$b=277.74$

.

In order to calibrate the model and discuss the impact of changes in various parameters on the utility of purchasing electric vehicles, the adoption rate of electric vehicles, corporate profits, and green energy utilization, we used the data in the table above to calibrate the model.

4.1. Difference in Electricity Prices

Figure 4 illustrates the impact of the price difference on the adoption rate, corporate profits, and green energy utilization. Figure 4a shows that as the price difference increases, the adoption rate of V2G shows a linear increase and gradually surpasses that of charging only electric vehicles (BEVs) and Figure 4b shows that the profits of V2G enterprises also gradually increase, with the same critical point as a1. And then, Figure 4c shows that the green energy utilization of V2G electric vehicles has always been higher than that of ordinary electric vehicles. It is evident that when the price difference can offset the cost of V2G batteries (USD 0.099/kWh), users are more inclined to choose V2G electric vehicles. Corporate profits and green energy utilization also increase as the price difference rises, aligning with the conclusions of Theorem 1. Compared to BEVs, when the price difference can cover V2G costs, businesses can achieve higher profits than when operating BEVs. The grid can also attain greater green energy utilization, confirming the findings of Theorems 3, 4, and 6 and supporting V2G being superior to BEVs. Therefore, companies need to dynamically adjust their business strategies based on the price difference to ensure profitability, and governments can expand the price difference through subsidies and other means to adjust the development goals of electric vehicles.

4.2. Battery Costs

Figure 5 demonstrates the impact of battery costs when the price difference can cover V2G costs. Figure 5a shows that when battery costs decrease, the adoption rates of V2G and charging only electric vehicles both increase linearly and Figure 5b shows that the profit growth rate of V2G enterprises is greater than that of ordinary electric vehicles. Figure 5c shows that the green energy utilization of V2G electric vehicles is once again much greater than that of ordinary electric vehicles. As battery costs decrease, adoption rates, corporate profits, and green energy utilization all see improvement, aligning with the conclusions of Theorem 2. Compared to BEVs, under the condition that the price difference can cover V2G costs, the reduction in battery costs leads to greater incremental profits for V2G and increased green energy utilization, consistent with Theorems 5 and 7.

Figure 5 indicates that when battery costs decrease from USD 5.93 per day to USD 1.93 per day, both BEVs and V2G electric vehicles experience an adoption rate increase of over 35%, highlighting the significant impact of lower battery costs on consumer purchase intent. Lowering battery costs is a long-term investment goal shared by both businesses and governments. Reducing battery costs can bring substantial profits to businesses, while governments can enhance green energy utilization. Therefore, both governments and businesses should increase research and development investments to lower battery costs. For V2G electric vehicles, the advantages of lower battery costs are much more pronounced, particularly in the context of green energy utilization. This suggests that government incentives for battery technology are more applicable to V2G electric vehicles.

By comparing Figure 4 and Figure 5, it becomes evident that an increase in the price difference and a decrease in battery costs significantly enhance electric vehicle adoption, corporate profits, and green energy utilization, with these effects being more pronounced for V2G electric vehicles. These results provide important modeling references for the sustainable development and business models of electric vehicles. Companies can dynamically adjust their business strategies based on factors such as the price difference and battery levels. Governments can formulate corresponding policies and incentives based on this model, directing investments in battery research and price difference, to achieve the goal of expanding green energy utilization and developing the new electric vehicle industry.

In conclusion, our scenario analysis suggests that as long as the price difference exceeds V2G battery costs, V2G electric vehicles are a better choice for consumers, businesses, and governments. The adoption of V2G electric vehicles can further enhance corporate profits and green energy utilization.

5. Discussion

This study constructed two models, the BEV model and V2G model. The BEV model simulates users’ choices between gasoline vehicles and regular electric vehicles, while the V2G model simulates users’ choices between gasoline vehicles and V2G-enabled electric vehicles. The equilibrium optimal adoption rate, corporate profit, and green energy utilization were calculated to demonstrate the superiority of V2G electric vehicles.

The research findings regarding price differentials indicate that the price difference forms the basis for the superiority of V2G electric vehicles over regular electric vehicles. When the price difference can offset the costs associated with V2G, V2G electric vehicles exhibit higher adoption rates, corporate profits, and green energy utilization compared to regular electric vehicles. The importance of price differentials in V2G behavior aligns with the views of Datta et al. [32] and others. Using Chinese data, Xinzhou Li et al. [33] and others discovered that when the peak electricity price in Shanghai exceeds three times the off-peak price, electric vehicle users experience a positive net income. Calibrating with data from December 2023 in Shanghai [34], where the peak-to-off-peak electricity price difference is USD 0.0954/kWh, the only 3.6% difference from the USD 0.099/kWh derived in this study’s scenario analysis confirms the precision of the price difference characterization. The V2G model demonstrates significant advantages in green energy utilization, especially in its peak shaving and valley filling capabilities, as mentioned in various articles [35,36,37]. In the scenario analysis, even with a price difference of zero, V2G electric vehicles exhibit higher green energy utilization compared to regular electric vehicles. The study also reveals substantial differences in battery costs, emphasizing the peak shaving and valley filling capabilities of V2G.

Research on battery costs indicates that reducing battery costs can enhance the adoption rate, corporate profit, and green energy utilization of both regular electric vehicles and V2G electric vehicles. Furthermore, V2G electric vehicles show comparative advantages in corporate profit and green energy utilization, with a greater increase in profit and green energy utilization increments as battery costs decrease. While many studies advocate government subsidies for V2G electric vehicles [38,39,40], our research suggests that the government can not only provide subsidies but also incentivize battery technology for the development of V2G electric vehicles. The advantages brought about by the reduction in battery costs for V2G electric vehicles far exceed those for BEVs, particularly in terms of significant improvements in green energy utilization.

Our model focuses on the interaction between users and automakers, but it inevitably sacrifices other considerations. Firstly, electric vehicle adoption is a dynamic process, and our model struggles to simulate this dynamic process, relying on a one-time calculation. Secondly, electric vehicle adoption is a complex process, with users having access to various green transportation modes (such as walking, cycling, public transport, etc.). Users who purchase V2G electric vehicles may choose not to participate in V2G activities. In future research, attempting to establish adoption models for multi-mode transportation patterns could be explored. Lastly, as a study modeling from a business perspective, we avoid addressing power-related issues, such as the potential for electric vehicles to exchange batteries and the degradation of battery capacity over usage.

6. Conclusions

This study presents, for the first time, an accurate depiction of the impact of V2G electric vehicle price differences and battery costs on car owners, businesses, and society, particularly concerning the utilization of green energy. We introduced a game model based on price difference, electricity prices, and oil prices, establishing a user utility model to determine optimal mileage and driving decisions. Then, the maximum profit function for the company’s sales of ordinary trams and V2G trams was established, and the company’s optimal pricing user adoption rate were obtained. This model comprehensively considers user choices, taking into account users, electric vehicle manufacturers and social benefits, thus providing a new reference for subsequent research.

Further more, the study focuses on the analysis of the impact of price difference and battery costs on users, enterprises, and society after electric vehicles join V2G, and compares the changes in the benefits to users, enterprises and society after electric vehicles join V2G, proving the comparative advantages of V2G. Our research indicates that when the price difference can offset the cost, increasing the price difference and reducing battery costs can effectively increase the adoption rate of electric vehicles, thereby increasing corporate profits and improving green energy utilization. Compared with ordinary electric vehicles, V2G can expand corporate profits and green energy utilization, and increase user enthusiasm. The government should give priority to subsidies to V2G users rather than ordinary vehicle users. We also made additional findings, indicating that reducing battery costs for operating V2G electric vehicles is more economically advantageous for businesses. This is because companies can thereby increase their profits significantly. This result provides important theoretical and model support for the future development of V2G and the formulation of relevant policies.

Finally, we used Chinese data for verification, and the results showed that when the price difference can offset the cost of V2G batteries (USD 0.099/kwh), users are more willing to choose V2G electric vehicles; when the battery cost drops from USD 5.93 to USD 1.93 per day, the user adoption rate of BEV and V2G electric vehicles will increase by more than 35%. Additionally, we compared our research with existing models, using data from Shanghai, China, as the benchmark. Our study shows a difference of only 3.6% from the critical price difference for V2G derived by Xinzhou Li et al. [33] and others. This result affirms the high credibility of the model proposed in this paper.

Our study identified several limitations that should be considered in future research. Firstly, the charging and discharging behavior of V2G users needs more accurate description and optimization, especially when sufficient V2G pilot data become available. Secondly, our research did not highlight the impact of range anxiety on users, acknowledging that despite advanced battery technology, this still affects electric vehicle adoption. Finally, we did not consider the diversified needs of car companies. We believe that in the future, car companies should operate both V2G electric vehicles and ordinary electric vehicles. Therefore, we encourage further research to explore these scenarios more deeply.