Modeling the Impact of Different Policies on Electric Vehicle Adoption: An Investigative Study

By inergency On Feb 5, 2024

3.2.1. Model for EV Adoption

An EV adoption model must consider all, if not most, of the factors that influence the decisions of potential EV adopters in their decision-making process. The total number

E V_{t o t a l} (t)

of EVs at time t in the eco-system is the total number of EVs

E V_{t o t a l} (t - 1)

in the previous year i.e., year

(t - 1)

and the number of EVs adopted in the current year

E V_{n e w} (t)

less the number of retired EVs in the current year

E V_{r e t i r e d} (t)

$E V_{t o t a l} (t) = E V_{t o t a l} (t - 1) + E V_{n e w} (t) - E V_{r e t i r e d} (t)$

(1)

Via recursive substitution and taking

t = 1

as the first adoption of EVs considered by the model in the eco-system, Equation (1) can be conveniently expressed as

$E V_{t o t a l} (t) = \sum_{i = 1}^{t} [E V_{n e w} (i) - E V_{r e t i r e d} (i)]$

(2)

The number of EVs adopted in the current year t is a proportion of the number of potential adopters N(t), represented by non-EV users. It is driven by the willingness

W (t)

of the potential adopters to adopt EVs and the attractiveness

A (t)

of EVs at that time.

$E V_{n e w} (t) = N (t) \times W (t) \times A (t)$

(3)

Bass diffusion theory may then be used to represent the willingness

W (t)

to adopt EVs by assuming two groups of potential adopters: (1) Innovators, and (2) Imitators [28]. Innovators are those who are the forerunners in EV adoptions, tend to make their purchasing choices without considering the influence of other consumers, and are primarily driven by advertisements and promotional materials. On the other hand, imitators are those that adopt EVs based on the perceptions of others who have already adopted EVs, and hence, they are primarily influenced by their social circles and word of mouth. Naturally, the larger the proportion of EVs adopted, the larger the number of imitators that can be expected. Based on these, the willingness

W (t)

to adopt EVs can be mathematically represented as

$W (t) = α_{i n n o v a t o r s} + α_{i m m i t a t o r s} \times \frac{E V_{t o t a l} (t - 1)}{N (t)}$

(4)

where $α_{i n n o v a t o r s}$ and $α_{i m m i t a t o r s}$ represent the coefficients of innovation and imitation, respectively.

Substituting Equation (4) into Equation (3), the number of EVs adopted in the current year t can be represented as

$E V_{n e w} (t) = N (t) . A (t) . α_{i n n o v a t o r s} + A (t) . α_{i m m i t a t o r s} . E V_{t o t a l} (t - 1)$

(5)

It can be seen that the innovators are concerned with the attractiveness of EVs $A (t)$ , 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 $A (t)$ , they are very affected by the total number of EVs already in the eco-system; this is particularly relevant during the early introduction of EVs to the market.

EV attractiveness

A (t)

captures the different factors that influence the attractiveness of EVs in comparison to their substitutes, particularly ICEVs, which are more established and the most widely used vehicles in the world. Of importance is the life-cycle cost (LCC) of adopting EVs in comparison to ICEVs. LCC captures the whole life cycle cost of owning an EV, discounted to the present value. Comparative studies between EVs and ICEVs in terms of their financial feasibility have given mixed results, with some research stating that EVs can already financially compete with ICEVs, in contrast to Ref. [42] stating otherwise. Ref. [19] has argued that it is necessary to perform analysis using local parameters to determine economic feasibility due to the complex interactions between the cost components of EVs and ICEVs. Other important parameters that factor into EV attractiveness include the driving range, availability of infrastructure, and charging time of EVs in comparison to ICEVs.

EV attractiveness

A (t)

can be seen as the likelihood of purchasing EVs, with its value normalized between 0 and 1 [30]. This can be calculated as the sum of the product of each factor and its relative importance to the local consumer.

$A (t) = β_{L C C} . F_{L C C} (t) + β_{D R} . F_{D R} (t) + β_{I n f} . F_{I n f} (t) + β_{C T} . F_{C T} (t)$

(6)

where $β_{L C C}$ , $β_{D R}$ , $β_{I n f}$ and $β_{C T}$ 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, $F_{L C C} (t)$ , $F_{D R} (t)$ , $F_{I n f} (t)$ and $F_{C T} (t)$ 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. $F_{L C C} (t)$ , $F_{D R} (t)$ , $F_{I n f} (t)$ and $F_{C T} (t)$ at time t can be determined as,

$F_{L C C} (t) = \frac{1}{2} (\frac{L C C_{I C E V} (t) - L C C_{E V} (t)}{m a x (L C C_{E V} (t), L C C_{I C E V} (t))}) + 0.5$

(7)

$F_{D R} (t) = \frac{1}{2} (\frac{D R_{E V} (t) - D R_{I C E V} (t)}{m a x (D R_{E V} (t), D R_{I C E V} (t))}) + 0.5$

(8)

$F_{I n f} (t) = \frac{1}{2} (\frac{\frac{I n f_{E V} (t)}{I n f_{r a t i o, E V}} - \frac{I n f_{I C E V} (t)}{I n f_{r a t i o, I C E V}}}{m a x (\frac{I n f_{E V} (t)}{I n f_{r a t i o, E V}}, \frac{I n f_{I C E V} (t)}{I n f_{r a t i o, I C E V}})}) + 0.5$

(9)

$F_{C T} (t) = \frac{1}{2} (\frac{{C T}_{I C E V} (t) - {C T}_{E V} (t)}{m a x ({C T}_{I C E V} (t), {C T}_{E V} (t))}) + 0.5$

(10)

where $L C C_{E V}$ , ${D R}_{E V}$ , ${I n f}_{E V}$ , and ${C T}_{E V}$ are LCC, driving range, number of charging infrastructure and charging time for EVs, respectively, whilst $L C C_{I C E V}$ , ${D R}_{I C E V}$ , ${I n f}_{I C E V}$ , and ${C T}_{I C E V}$ 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, $I n f_{r a t i o, E V}$ and refueling infrastructure/ICEV, $I n f_{r a t i o, I C E V}$ .

Relative attractiveness in terms of the different factors considers the disparity between EVs and ICEVs, which are then normalized by dividing by the maximum of either EVs or ICEVs, taking half the values, and adding 0.5 [43], to give values between 0 and 1.

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.

Figure 1 depicts the flowchart of the developed model used to determine EV adoptions. The flowchart outlines the process used to simulate and predict electric vehicle (EV) adoption over time, starting from

t = 0

, the initial point of the simulation. The model operates with the following key steps:

Initial Conditions ( $t = 0$ ): The simulation begins with an input of the total number of EVs in the ecosystem at the start ( $E V_{t o t a l} (0)$ ).
Time Progression ( $t \geq 1$ ): The model aims to predict the number of EV adoptions for any time $t \geq 1$ .
Quantifying Relative Attractiveness ( $F_{L C C} (t)$ , $F_{D R} (t)$ , $F_{I n f} (t)$ and $F_{C T} (t)$ ): At each time $t$ , the model assesses the competitiveness of EVs against ICEVs in terms of life cycle cost ( $F_{L C C} (t)$ ), driving range ( $F_{D R} (t)$ ), infrastructure availability ( $F_{I n f} (t)$ ), and charging time ( $F_{C T} (t)$ ). 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 $A (t)$ , as defined in Equation (6). The relative importance of the LCC ( $β_{L C C})$ , driving range ( $β_{D R}$ ), availability of infrastructure ( $β_{I n f}$ ) and charging time ( $β_{C T}$ ) towards the attractiveness of EVs is determined using a survey to ensure alignment with local relative importance.
Determining Annual EV Adoption ( $E V_{n e w} (t)$ ): Using the calculated EV attractiveness ( $A (t)$ ), along with the coefficients of innovation ( $α_{i n n o v a t o r s}$ ) and imitation ( $α_{i m m i t a t o r s}$ ), the number of potential adopters ( $N (t)$ ), and the total number $E V_{t o t a l} (t - 1)$ of EVs from the previous year $(t - 1)$ in the ecosystem, the model estimates the number of new EV adopters ( $E V_{n e w} (t)$ ) for the current year $t$ .
Accumulating Total number of EVs ( $E V_{t o t a l} (t)$ ) at time $t$ in the Ecosystem: The model updates the total number of EVs ( $E V_{t o t a l} (t)$ )in the ecosystem by adding the newly adopted EVs ( $E V_{n e w} (t)$ ) for the year ( $t$ ) and subtracting the number of EVs retired (( $E V_{r e t i r e d} (t)$ ) 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 user-specific 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

Life Cycle Cost (LCC) encompasses all expenses tied to either EV or ICEV over its lifespan, considering the time-value of money. This includes acquisition (AC), the various operating (OC) and maintenance (MC) costs, and less salvage value (SV) that may be obtained upon disposal of the vehicle or any of its components [44].

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.

The Operating Cost (OC) comprises fuel expenses, either electricity for EVs or gasoline for ICEVs, along with the annual vehicle license fee

V L (t)

and yearly insurance coverage

I C (t)

incurred at year t. Fuel costs vary based on distance traveled and vehicle efficiency, with these expenses assumed to be incurred at the end of each year. Given that the EV has an efficiency of

η_{E V}

and is charged from domestic electric sockets with a charging efficiency of

η_{c h}

, whilst the ICEV has an efficiency of

η_{I C E V}

, cost of fuel for the EV and ICEV can be determined,

$F C_{E V} (t) = η_{E V} \times d (t) \times \frac{C_{e l e c}}{η_{c h}}$

(11)

$F C_{I C E V} (t) = η_{I C E V} \times d (t) \times C_{g a s}$

(12)

where $d (t)$ , $C_{e l e c}$ and $C_{g a s}$ are distance traveled at year t, per unit of cost of electricity and gasoline, respectively.

Typically, the vehicle license fee

V L (t)

is calculated based on the usage category and engine displacement. On the other hand, the insurance coverage cost

I C (t)

is influenced by the type of coverage and the vehicle’s value. Third-party coverage is assumed for both EVs and ICEVs, offering uniform protection and therefore incurring an equal expense. Given an assumed interest rate of r with a vehicle lifetime of n, operating cost (OC) can be represented as,

$O C = \sum_{t = 1}^{n} \frac{F C (t) + V L (t) + I C (t)}{{(1 + r)}^{t}}$

(13)

Maintenance costs considered are service and periodic maintenance

P M (t)

, as well as battery

B R (t)

and tire replacements

T R (t)

. Unscheduled maintenance and repairs are excluded due to uncertainty issues. Period maintenance

P M (t)

is determined by the maintenance rate per distance (MR), which is acquired from the manufacturer and accrued at the end of each year, while battery and tire replacement expenses are accrued in the year when replacements are necessary, as specified by vehicle and tire manufacturers. Maintenance costs (MC) can be represented as:

$M C = \sum_{t = 1}^{n} \frac{(M R \times d (t)) + B R (t) + T R (t)}{{(1 + r)}^{t}}$

(14)

On the other hand, the Salvage Value (SV) encompasses both the scrap worth of batteries

S B (t)

upon replacement and the vehicle

S C

at the end of its lifespan, with the values being disbursed in the year when the vehicle or battery is scrapped.

$S C = \sum_{t = 1}^{n} \frac{S B (t)}{{(1 + r)}^{t}} + \frac{S C}{{(1 + r)}^{n}}$

(15)

Collectively, the life cycle cost (LCC) of an EV or ICEV can be represented as in Equation (15), with a higher LCC indicating a more costly vehicle over its lifetime.

$L C C = A C + \sum_{t = 1}^{n} \frac{F C (t) + V L (t) + I C (t) + (M R \times d (t)) + B R (t) + T R (t) - S B (t)}{{(1 + r)}^{t}} - \frac{S C}{{(1 + r)}^{n}}$

(16)