Modeling the Impact of Different Policies on Electric Vehicle Adoption: An Investigative Study
3.2.1. Model for EV Adoption
$$E{V}_{total}\left(t\right)=E{V}_{total}\left(t1\right)+E{V}_{new}\left(t\right)E{V}_{retired}\left(t\right)$$
$$E{V}_{total}\left(t\right)=$$
$$E{V}_{new}\left(t\right)=N\left(t\right)\times W\left(t\right)\times A\left(t\right)$$
$$W\left(t\right)={\alpha}_{innovators}+{\alpha}_{immitators}\times \frac{E{V}_{total}\left(t1\right)}{N\left(t\right)}$$
where ${\alpha}_{innovators}$ and ${\alpha}_{immitators}$ represent the coefficients of innovation and imitation, respectively.
$$E{V}_{new}\left(t\right)=N\left(t\right).A\left(t\right).{\alpha}_{innovators}+A\left(t\right).{\alpha}_{immitators}.E{V}_{total}\left(t1\right)$$
It can be seen that the innovators are concerned with the attractiveness of EVs $A\left(t\right)$, particularly in comparison to their substitutes, i.e., ICEVs. The coefficient of innovation can be increased by more effective promotion and advertisement of EVs. While the imitators are also concerned with the attractiveness of EVs $A\left(t\right)$, they are very affected by the total number of EVs already in the ecosystem; this is particularly relevant during the early introduction of EVs to the market.
$$A\left(t\right)={\beta}_{LCC}.{F}_{LCC}\left(t\right)+{\beta}_{DR}.{F}_{DR}\left(t\right)+{\beta}_{Inf}.{F}_{Inf}\left(t\right)+{\beta}_{CT}.{F}_{CT}\left(t\right)$$
where ${\beta}_{LCC}$, ${\beta}_{DR}$, ${\beta}_{Inf}$ and ${\beta}_{CT}$ represent the relative importance of the LCC, driving range, availability of infrastructure, and charging time towards the attractiveness of EVs. Again, it is important to account for the relative importance of each factor within the local context, and for this study, the relative importance of the 4 factors was extracted from survey data. On the other hand, ${F}_{LCC}\left(t\right)$, ${F}_{DR}\left(t\right)$, ${F}_{Inf}\left(t\right)$ and ${F}_{CT}\left(t\right)$ represent the relative attractiveness of EVs relative to ICEVs in terms of LCCs, driving range, availability of infrastructure, and charging time. Generally, lower LCCs, shorter charging times, a higher number of charging infrastructures, and a longer driving range before the need for recharging are advantageous for the adoption of EVs. ${F}_{LCC}\left(t\right)$, ${F}_{DR}\left(t\right)$, ${F}_{Inf}\left(t\right)$ and ${F}_{CT}\left(t\right)$ at time t can be determined as,
$${F}_{LCC}\left(t\right)=\frac{1}{2}\left(\frac{LC{C}_{ICEV}\left(t\right)LC{C}_{EV}\left(t\right)}{max\left(LC{C}_{EV}\left(t\right),LC{C}_{ICEV}\left(t\right)\right)}\right)+0.5$$
$${F}_{DR}\left(t\right)=\frac{1}{2}\left(\frac{D{R}_{EV}\left(t\right)D{R}_{ICEV}\left(t\right)}{max\left(D{R}_{EV}\left(t\right),D{R}_{ICEV}\left(t\right)\right)}\right)+0.5$$
$${F}_{Inf}\left(t\right)=\frac{1}{2}\left(\frac{\frac{In{f}_{EV}\left(t\right)}{In{f}_{ratio,EV}}\frac{In{f}_{ICEV}\left(t\right)}{In{f}_{ratio,ICEV}}}{max\left(\frac{In{f}_{EV}\left(t\right)}{In{f}_{ratio,EV}},\frac{In{f}_{ICEV}\left(t\right)}{In{f}_{ratio,ICEV}}\right)}\right)+0.5$$
$${F}_{CT}\left(t\right)=\frac{1}{2}\left(\frac{{CT}_{ICEV}\left(t\right){CT}_{EV}\left(t\right)}{max\left({CT}_{ICEV}\left(t\right),{CT}_{EV}\left(t\right)\right)}\right)+0.5$$
where $LC{C}_{EV}$, ${DR}_{EV}$, ${Inf}_{EV}$, and ${CT}_{EV}$ are LCC, driving range, number of charging infrastructure and charging time for EVs, respectively, whilst $LC{C}_{ICEV}$, ${DR}_{ICEV}$, ${Inf}_{ICEV}$, and ${CT}_{ICEV}$ are LCC, driving range, number of refueling infrastructure and charging time for ICEVs, respectively. For relative attractiveness in terms of infrastructure, the number of charging infrastructure and refueling infrastructure is divided by the ideal ratio of recharging infrastructure/EV, $In{f}_{ratio,EV}$ and refueling infrastructure/ICEV, $In{f}_{ratio,ICEV}$.
Driving range, number of charging/refueling infrastructures, and charging/refueling times for EVs and ICEVs can be obtained directly from the available local data. However, LCC requires consideration of the overall cost over the lifespan of the vehicles, with the methodology adopted to determine LCCs described in the following section.

Initial Conditions ($t=0$): The simulation begins with an input of the total number of EVs in the ecosystem at the start ($E{V}_{total}\left(0\right)$).

Time Progression ($t\ge 1$): The model aims to predict the number of EV adoptions for any time $t\ge 1$.

Quantifying Relative Attractiveness (${F}_{LCC}\left(t\right)$, ${F}_{DR}\left(t\right)$, ${F}_{Inf}\left(t\right)$ and ${F}_{CT}\left(t\right)$): At each time $t$, the model assesses the competitiveness of EVs against ICEVs in terms of life cycle cost (${F}_{LCC}\left(t\right)$), driving range (${F}_{DR}\left(t\right)$), infrastructure availability (${F}_{Inf}\left(t\right)$), and charging time (${F}_{CT}\left(t\right)$). These factors are calculated using Equation (7) through Equation (10), as detailed in Section 3.2.2. The model assigns a relative attractiveness score between 0 and 1, where a score of 0.5 indicates that EVs and ICEVs are equally competitive. A score above 0.5 suggests that EVs are more competitive than ICEVs, while a score below 0.5 points to EVs being less competitive compared to ICEVs.

Consideration of Relative Importance: Different users assign varying importance to the aspects of relative attractiveness. Therefore, the model incorporates relative importance factors to derive an overall EV attractiveness score $A\left(t\right)$, as defined in Equation (6). The relative importance of the LCC (${\beta}_{LCC})$, driving range (${\beta}_{DR}$), availability of infrastructure (${\beta}_{Inf}$) and charging time (${\beta}_{CT}$) towards the attractiveness of EVs is determined using a survey to ensure alignment with local relative importance.

Determining Annual EV Adoption ($E{V}_{new}\left(t\right)$): Using the calculated EV attractiveness ($A\left(t\right)$), along with the coefficients of innovation (${\alpha}_{innovators}$) and imitation (${\alpha}_{immitators}$), the number of potential adopters ($N\left(t\right)$), and the total number $E{V}_{total}\left(t1\right)$ of EVs from the previous year $\left(t1\right)$ in the ecosystem, the model estimates the number of new EV adopters ($E{V}_{new}\left(t\right)$) for the current year $t$.

Accumulating Total number of EVs ($E{V}_{total}\left(t\right)$) at time $t$ in the Ecosystem: The model updates the total number of EVs ($E{V}_{total}\left(t\right)$)in the ecosystem by adding the newly adopted EVs ($E{V}_{new}\left(t\right)$) for the year ($t$) and subtracting the number of EVs retired (($E{V}_{retired}\left(t\right)$) in the same year.
This methodology provides a comprehensive framework for understanding and predicting EV adoption dynamics, considering both the comparative advantages of EVs over ICEVs and userspecific preferences. The model’s adaptability to various local conditions and its ability to integrate a broad range of factors make it a valuable tool for policymakers and stakeholders in the EV industry.
3.2.2. Life Cycle Cost
The acquisition cost (AC) of a vehicle only considers the Manufacturer Suggested Retail Price (MSRP) without any added import tax. As electric vehicles (EVs) are relatively new, no tax rate has been decided by the government yet, and since EVs operate differently from ICEVs and do not rely on internal combustion engines, the usual vehicle import tax rates based on engine capacity are not applicable. Additionally, the assumption is that the vehicles are bought outright without loans, freeing the acquisition costs from fluctuating interest rates. These acquisition costs are incurred solely at the start of the first year and hence are not affected by the present value calculations.
$$F{C}_{EV}\left(t\right)={\eta}_{EV}\times d\left(t\right)\times \frac{{C}_{elec}}{{\eta}_{ch}}$$
$$F{C}_{ICEV}\left(t\right)={\eta}_{ICEV}\times d\left(t\right)\times {C}_{gas}$$
where $d\left(t\right)$, ${C}_{elec}$ and ${C}_{gas}$ are distance traveled at year t, per unit of cost of electricity and gasoline, respectively.
$$OC=$$
$$MC=$$
$$SC=$$
$$LCC=AC+$$
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