# Investigating Market Diffusion of Electric Vehicles with Experimental Design of Agent-Based Modeling Simulation

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## Abstract

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## 1. Introduction

_{2}) emissions [3]. Hence, both climate change and the scarcity of energy resources require a transition to an energy-efficient transportation system. Electric vehicles (EVs) that can operate either partially or fully on electric power are a promising alternative to conventional internal combustion engine vehicles (ICEVs). The use of such vehicles may significantly reduce both air and noise pollution from passenger and freight vehicles. There are different types of EVs; the four common types are hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEVs), battery electric vehicles (BEVs), and fuel cell electric vehicles (FCEVs); readers may refer to [4] for more detailed descriptions of each type. Overall, HEV and PHEV can be categorized as hybrid vehicles (HVs) that have reduced emission levels compared to conventional ICEVs that use diesel or gasoline, whereas BEVs and FCEVs are zero-emission vehicles (ZEVs) that can be considered a viable step toward zero-carbon transportation.

## 2. Model Development

_{2}emissions. These attributes were selected for this study because they correspond to the most common vehicle characteristics applied in the literature and are the most important vehicle features affecting the car purchase decision-making process of customers. A multinomial logit function was employed to represent the utility of individuals, as the most common way to mathematically model technology diffusion processes involves exponential functions. Thus, the utility of each vehicle type is generally assumed to be an exponential linear combination of all the attributes of each vehicle type multiplied by a preference parameter that denotes the weight of the attribute.

_{2}emissions are expressed in percentages relative to conventional ICEVs. All the baseline values can be adjusted as per the actual values of the vehicle market contexts based on stated preference survey data, although data from the current literature are used for demonstration purposes in this study. The ABM simulation was constructed using NetLogo software version 6.2.0. Each iteration (called a ‘tick’ in NetLogo) in the simulation corresponds to a month, and all simulations were run for ten years. For each iteration, a random sample of $N$ individuals was generated from a Poisson distribution with a mean of 500, which formed the market of newly purchased vehicles. Then, the potential utility for each type of vehicle was calculated for individual customers. As mentioned earlier, the utility function was constructed as a multinomial logit model, and is thus expressed as a linear combination of different factors, which are listed in Table 1.

Algorithm 1 Pseudo-Code for ABM Simulation |

1: for $t=1$ to $120$ do2: $N~Poisson\left(500\right)\leftarrow $ Generate $N$ customers from a Poisson distribution with mean 500; 3: for $i=1$ to $N$ do4: for $k$=1 to $6$ do5: ${U}_{i}^{k}={\displaystyle \sum}_{j=1}^{J}{\beta}_{j}^{k}{X}_{ij}^{k}+{\epsilon}_{i}\leftarrow $ Calculate utility for vehicle type $k$; 6: end7: ${U}_{i}=\left({U}_{i}^{1},{U}_{i}^{2},{U}_{i}^{3},{U}_{i}^{4},{U}_{i}^{5},{U}_{i}^{6}\right)\leftarrow $ Utility vector for customer $i$; 8: ${p}_{i}=\left({p}_{i}^{1},{p}_{i}^{2},{p}_{i}^{3},{p}_{i}^{4},{p}_{i}^{5},{p}_{i}^{6}\right)\leftarrow $ Utility-based choice probability vector for customer $i$; 9: ${p}_{i}~U\left(0,1\right)\leftarrow $ Generate a random probability from a Uniform distribution (0,1); 10: Choose vehicle type $k$it $\sum}_{v\le \left(k-1\right)}{p}_{i}^{v}<{p}_{i}\le {\displaystyle \sum}_{v\le k}{p}_{i}^{v};$ 11: end12: ${n}_{t}=\left({n}_{t}^{1},{n}_{t}^{2},{n}_{t}^{3},{n}_{t}^{4},{n}_{t}^{5},{n}_{t}^{6}\right)\leftarrow $ Count each type of vehicles purchased before or at time $t$; 13: Determine the cumulative market share of each vehicle type. 14: end |

## 3. Experimental Design and Simulation Results

## 4. Statistical Analysis of SVM and RSM

#### 4.1. Feature Selection with SVM

#### 4.2. Statistical Analysis with RSM

## 5. Concluding Remarks

_{2}emissions. Then, a series of simulation experiments was designed including six different factors with three levels for each factor to yield a full factorial design. The simulated data were analyzed with a support vector machine and response surface methodology to further examine the statistical significance of individual factor effects and their interactions. Under the specified circumstances, the market diffusion of EVs was more affected by policy measures such as subsidies and tax benefits than by other measures, which is consistent with the results for the U.S. market as investigated by [17]. It should be noted that the significant interactions among individual factors observed imply that individual policy measures need to be carefully designed with a holistic perspective. In other words, the magnitude of effects from the combined implementation of different policy interventions is far greater than the simple sum of the individual main effects, which concurs with the results obtained by [19].

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Market shares of different types of vehicles in baseline scenario: (

**a**) comparison of market share of ICEVs and EVs; (

**b**) market share by individual vehicle type.

**Figure 2.**Market shares of different types of vehicles in alternative scenario: (

**a**) comparison of market share of ICEVs and EVs; (

**b**) market share by individual vehicle type.

**Figure 4.**Box plots for relative importance of factors on diffusion of each type of EVs: (

**a**) factors affecting the diffusion of HEVs; (

**b**) factors affecting the diffusion of PHEVs; (

**c**) factors affecting the diffusion of BEVs; (

**d**) factors affecting the diffusion of FCEVs.

**Figure 6.**Residual analysis of second-order response surface model: (

**a**) residual plot; (

**b**) Q-Q plot.

Description of Attributes | Gasoline | Diesel | HEV | PHEV | BEV | FCEV |
---|---|---|---|---|---|---|

Fuel Cost ($/100 km) ^{1} | 9.3 | 6.1 | 5.6 | 6.1 | 2.5 | 8.8 |

Purchase Price ($) ^{2} | 31,426 | 31,426 | 33,694 | 34,641 | 40,922 | 34,463 |

Mileage Per Full Tank/Charge (km) ^{3} | 1000 | 1000 | 1000 | 750 | 175 | 750 |

Refueling Time (min) ^{3} | 5 | 5 | 5 | 5 | - | 5 |

Recharging Time (min) ^{3} | - | - | - | 240 | 480 | - |

Fuel/Charging Station Availability (%) ^{1,3} | 100 | 100 | 100 | 43.3 | 14.1 | 0.2 |

CO_{2} Emission (%) ^{3} | 100 | 100 | 77 | 31 | 0 | 0 |

Factors | Levels | Values | ||
---|---|---|---|---|

A: Purchase Tax on ICEVs (% Purchase Price) | 3 | 5%, | 10%, | 15% |

B: Fuel Cost (% Increase) | 3 | 0%, | 15%, | 30% |

C: Purchase Subsidy for EVs (% Purchase Price) | 3 | 0%, | 10%, | 20% |

D: Driving Mileage Per Full Charge (% Improvement) | 3 | 0%, | 50%, | 100% |

E: Battery Charging Time (% Reduction) | 3 | 0%, | 25%, | 50% |

F: Charging Station Availability (% Increase) | 3 | 0%, | 50%, | 100% |

Factors | HEV | PHEV | BEV | FCEV | All EVs | |||||
---|---|---|---|---|---|---|---|---|---|---|

Mean | Rank | Mean | Rank | Mean | Rank | Mean | Rank | Mean | Rank | |

A | 11.24 | 5 | 12.31 | 5 | 7.74 | 5 | 13.15 | 4 | 92.46 | 3 |

B | 140.14 | 2 | 131.80 | 2 | 166.49 | 3 | 229.27 | 1 | 146.55 | 2 |

C | 143.82 | 1 | 158.72 | 1 | 268.44 | 1 | 202.70 | 2 | 391.45 | 1 |

D | 20.53 | 4 | −0.69 | 6 | 20.17 | 4 | 3.26 | 5 | 4.19 | 5 |

E | 47.20 | 3 | 20.91 | 4 | 167.24 | 2 | 59.57 | 3 | 19.92 | 4 |

F | −1.01 | 6 | 31.44 | 3 | −2.47 | 6 | 3.74 | 6 | −1.89 | 6 |

$\mathbf{Model}\text{}({\mathit{R}}_{\mathit{a}\mathit{d}\mathit{j}}^{2})$ | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Squares | F-Statistic | p-Value |
---|---|---|---|---|---|---|

First-Order (0.899) | Model | 52,270 | 5 | 10,454.0 | 12,934.76 | <0.001 * |

Residuals | 5887 | 7284 | 0.8082 | |||

Lack of fit | 716 | 237 | 3.0211 | 4.1171 | <0.001 * | |

Pure Error | 5171 | 7047 | 0.7338 | |||

Total | 58,157 | 7289 | ||||

Two-Way Interaction (0.902) | Model | 52,489 | 15 | 3499.20 | 4490.68 | <0.001 * |

Residuals | 5668 | 7274 | 0.7792 | |||

Lack of fit | 497 | 227 | 2.1894 | 2.9837 | <0.001 * | |

Pure Error | 5171 | 7047 | 0.7338 | |||

Total | 58,157 | 7289 | ||||

Pure Quadratic (0.904) | Model | 52,587 | 10 | 5258.70 | 6872.19 | <0.001 * |

Residuals | 5570 | 7279 | 0.7652 | |||

Lack of fit | 399 | 232 | 1.7198 | 2.3438 | <0.001 * | |

Pure Error | 5171 | 7047 | 0.7338 | |||

Total | 58,157 | 7289 | ||||

Second-Order (0.908) | Model | 52,805 | 20 | 2640.25 | 3585.95 | <0.001 * |

Residuals | 5352 | 7269 | 0.7362 | |||

Lack of fit | 181 | 222 | 0.8153 | 1.1111 | 0.131 | |

Pure Error | 5171 | 7047 | 0.7338 | |||

Total | 58,157 | 7289 |

Effects | Estimate | Standard Error | p-Value |
---|---|---|---|

Purchase Tax | 0.5266 | 0.0123 | <0.001 * |

Fuel Cost | 0.7066 | 0.0123 | <0.001 * |

Purchase Subsidy | 3.1480 | 0.0123 | <0.001 * |

Driving Mileage | 0.1130 | 0.0123 | <0.001 * |

Charging Time | 0.2369 | 0.0123 | <0.001 * |

Purchase Tax: Fuel Cost | −0.0669 | 0.0151 | <0.001 * |

Purchase Tax: Purchase Subsidy | −0.1412 | 0.0151 | <0.001 * |

Purchase Tax: Driving Mileage | −0.0140 | 0.0151 | 0.3522 |

Purchase Tax: Charging Time | −0.0261 | 0.0151 | 0.0839 |

Fuel Cost: Purchase Subsidy | −0.1909 | 0.0151 | <0.001 * |

Fuel Cost: Driving Mileage | 0.0014 | 0.0151 | 0.9245 |

Fuel Cost: Charging Time | 0.0026 | 0.0151 | 0.8618 |

Purchase Subsidy: Driving Mileage | −0.0434 | 0.0151 | 0.0040 * |

Purchase Subsidy: Charging Time | −0.0612 | 0.0151 | <0.001 * |

Driving Mileage: Charging Time | −0.0051 | 0.0151 | 0.7339 |

Purchase Tax^{2} | 0.0026 | 0.0213 | 0.9039 |

Fuel Cost^{2} | −0.0095 | 0.0213 | 0.6568 |

Purchase Subsidy^{2} | −0.4419 | 0.0213 | <0.001 * |

Driving Mileage^{2} | −0.0096 | 0.0213 | 0.6518 |

Charging Time^{2} | −0.0073 | 0.0213 | 0.7336 |

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**MDPI and ACS Style**

Ebrie, A.S.; Kim, Y.J. Investigating Market Diffusion of Electric Vehicles with Experimental Design of Agent-Based Modeling Simulation. *Systems* **2022**, *10*, 28.
https://doi.org/10.3390/systems10020028

**AMA Style**

Ebrie AS, Kim YJ. Investigating Market Diffusion of Electric Vehicles with Experimental Design of Agent-Based Modeling Simulation. *Systems*. 2022; 10(2):28.
https://doi.org/10.3390/systems10020028

**Chicago/Turabian Style**

Ebrie, Awol Seid, and Young Jin Kim. 2022. "Investigating Market Diffusion of Electric Vehicles with Experimental Design of Agent-Based Modeling Simulation" *Systems* 10, no. 2: 28.
https://doi.org/10.3390/systems10020028