## 2 Methodology  
### CO\({}_{2}\) Emission of Electricity and Gasoline  
In this work, the well-to-wheel, i.e., well-to-tank plus tank-to-wheel CO\({}_{2}\) emission of CV and EV was predicted. It is worth noting that, while this study accounts for the carbon emission from battery manufacturing and waste recovery, the CO\({}_{2}\) emission of car manufacturing and that is induced by the increased infrastructure for power supply are not considered. In this study, the well-to-wheel CO\({}_{2}\) emission was calculated using a vehicle dynamic model, which incorporates a spark-ignition direct-injection (SIDI) gasoline engine, a motor, battery and transmission system. The SIDI gasoline engine was chosen because it is the mainstream technology due to its improved fuel economy, more precise air-fuel ratio control and improved transient response [26; 27; 28; 29; 30].  
The well-to-tank CO\({}_{2}\) emission of gasoline, i.e., carbon emission during the mining, storage and transportation process, is estimated to be 406.8 g/L [31]. The well-to-wheel CO\({}_{2}\) emission of gasoline vehicle is calculated to be 2.734 kg/L, with the CO\({}_{2}\) emission regulation and fuel consumption assumption of 128 g/km and 5.5 L/100 km, respectively. This emission level will be applied together with the fuel consumption calculated in the next section, to predict the CO\({}_{2}\) emission of gasoline vehicles over the years.  
The CO\({}_{2}\) emission of EV mainly depends on the emission of power, as well as the carbon emission from battery manufacturing and waste recovery. According to [PERSON] and [PERSON] [20], approximately 1510-1870 MJ of primary energy is required during the manufacturing process of 1 kWh of Li-ion battery storage capacity and its materials. Therefore, the average value of 1700 MJ or 10 g CO\({}_{2}\)-eq/km was estimated as the carbon impacts of battery over the vehicle life-cycle from that of lithium-ion battery. The carbon emission of power is determined by the composition of the power grid because different forms of power generation result in different levels of CO\({}_{2}\) emission, as shown in Figure 1[31].  
Based on the life-cycle CO\({}_{2}\) emission of different forms of power generation shown in Figure 1, and the composition of power grid of different countries/regions reported in International Energy Outlook 2017 [7], the CO\({}_{2}\) emission of electricity (g/kWh) for the world average, EU, China and Japan can therefore be estimated, as shown in Figure 2. These countries/regions were chosen in this study as China and the EU are two extreme cases, representing the highest and lowest CO\({}_{2}\) emission per kWh of electricity generated, respectively, while that of Japan and World Average are in the middle. It can be seen from year 2018 to 2040 that the overall CO\({}_{2}\) emission of electricity is projected to decrease over the years for all countries/regions studied, as a result from the anticipated increase in the share of renewables with lower carbon emissions in all power supply chains. Of the individual countries/regions studied, China has the highest CO\({}_{2}\) emission per kWh of electricity generated due to its large share of coal-fired power, while the EU has the lowest over the years. The world average CO\({}_{2}\) emission level is in between the EU and China, whilst Japan has an emission level slightly higher than the world average over the 32-year projection. These data, when combined with the electricity consumption of EVs calculated in the following section, can be used to project the CO\({}_{2}\) emission of EVs for different countries/regions through 2040.  
Figure 1: Life-cycle CO\({}_{2}\) emission from different forms of power generation [31]. BWR and PWR are abbreviations for boiling water reactor and pressurized water reactor, respectively.