# Energy Management Scheme for an EV Smart
## 3 Component Modeling and Control
### EV Battery Model  
Since the presence of multiple EVs is studied, an agent-based battery modeling method is utilized. Each EV battery is modeled individually. Parameters of the EVs selected in this study are listed in Table 1.  
The EV batteries are modeled based on the Tremblay Li-ion battery model [40]. The discharge and charge voltage characteristics (\(V_{b}^{D}\) and \(V_{b}^{C}\)) are given by the Li-ion battery Equations (5) and (6), respectively:  
\[V_{b}^{D}=E_{0}-R_{b}i_{b}-K\frac{\varphi}{\varphi-i_{b}t}(i_{b}t+i_{b}^{f})+ Ae^{-Bi_{b}t} \tag{5}\]  
\[V_{b}^{C}=E_{0}-R_{b}i_{b}-K\frac{\varphi}{i_{b}t-0.1\varphi}i_{b}^{f}-K\frac{ \varphi}{\varphi-i_{b}t}i_{b}t+Ae^{-Bi_{b}t} \tag{6}\]  
where \(E_{0}\) is the constant battery voltage, \(R_{b}\) is the internal resistance of the battery, \(K\) is the polarization constant, \(\varphi\) is the ampere-hour battery capacity, \(i_{b}\) is the battery current, \(i_{b}^{f}\) is the filtered current, \(i_{b}t=\int i_{b}dt\) is the battery charge at time \(t\), \(A\) is the exponential zone amplitude and \(B\) is the exponential zone time constant inverse. The battery parameters for both EVs are given in Table 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Label** & **EV Name** & **Vehicle Type** & **Battery Pack (kWh)** & **Range (km)** \\ \hline \(EV_{1}\) & Nissan LEAF [36; 37; 38] & Car & 23.4 [65 Ah, 360 V] & 134 \\ \(EV_{2}\) & ENVYON [39] & Bus & 100.8 [160 Ah, 630 V] & 160 \({}^{*}\) \\ \hline \hline \end{tabular} \({}^{*}\) Assumed range.  
\end{table}
Table 1: EV characteristics.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Nissan LEAF** & **ENVYON** \\ \hline \(E_{0}\) (V) & 390.37 & 683.15 \\ \(K\) & 0.04 & 0.03 \\ \(\varphi\) (Ah) & 65 & 160 \\ \(A\) (V) & 30.23 & 52.91 \\ \(B\) (Ah)\({}^{-1}\) & 0.93 & 0.38 \\ \(R_{b}\) (\(\Omega\)) & 0.06 & 0.04 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Battery parameters.  
Figure 2: DG output power with \(\pm\)50% variance.  
Based on these parameters, and using Equation (5), the discharge voltage characteristics and SoC profiles of both EVs have been established as shown in Figure 3. The discharge curves have been measured at 1C, which is the discharge current that depletes the entire battery capacity in one hour from an SoC of 100% to 0%.  
According to the battery discharge curves shown in Figure 3, the nominal battery operation region lies between the exponential region and the cut-off region, which corresponds to an SoC between 20% and 80%. This fact has been especially standardized by SAESTandard J1772 [41], in which a full charge from 20% to 80% SoC is considered for the higher power levels. The nominal voltage represents the linear zone in the battery discharge curve profile, and operating the battery in this range is favorable to preserve battery life. Only the constant current (CC) strategy is utilized. As mentioned earlier, the full charge for high-power charging is from 20% to 80% SoC, and the usual practice is to switch to a constant voltage (CV) scheme when the SoC reaches 80% to charge the battery to 100%. This aspect is not feasible in the fast-charging scenario and, hence, not considered in this study.