## 2 Methodology
### Vehicle Characteristics, Powertrain, and Energy Management Strategy  
A vehicle with the characteristics listed in the table below is used for the analysis of the multiple converter configuration [5]. The vehicle equations are taken from [PERSON] and [PERSON] [3] and [PERSON], [PERSON], and [PERSON] [5] with the characteristics shown in Table 1.  
Table 2 shows the parameters of the vehicle powertrain system consisting of a B pack, a UC bank, converters (C), and motor (M). Each of the parameters is detailed in the modeling section of the multiple converter configuration.  
To analyze the C-MC, in addition to the powertrain and vehicle characteristics, an energy management strategy is needed to distribute power between the energy sources and the load. The EMS used in this work has the following characteristics (see Table 3): (i) the batteries have the capacity to meet the load demand; (ii) the UCs have the capacity to meet the load demand; (iii) regenerative braking is considered for recharging Bs and UCs; (iv) Bs and UCs work together when required and  
Figure 4: Multiple converter configuration (C-MC) [7].  
have the capacity to meet the load demand; (v) the battery considers a minimum and maximum state of charge; (vi) the UC considers a minimum and maximum state of charge; (vii) the B and UC consider a minimum and maximum current. The variables and parameters shown in Table 3 are described in more detail in Section 2.6.  
EMS restrictions improve vehicle performance. In addition to the above, the analyzed configuration in this work was subjected to different terrain conditions: city and semi-urban. These terrain conditions were met through driving cycles or driving patterns. Different patterns represent various energy demand conditions which may arise during the trip of a vehicle. Driving patterns are speed versus time profiles under different traffic scenarios (urban, semi-urban, road); there are standard driving patterns that are used in the automotive industry to assess vehicle performance [3; 21].  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Air density & \(1.18\frac{K_{\rm G}}{m^{3}}\) \\ Rolling resistance coefficient & \(0.014\) \\ Transmission ratio & \(3\) \\ Crag coefficient & \(0.5\) \\ Frontal area & \(3.225\ m^{2}\) \\ Gravity & \(9.8\ \frac{m}{s^{2}}\) \\ Tire radius & \(0.2651\ m\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Vehicle parameters.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Battery: Valence Model U1–12 xp** & **UC: BMOD0165–Maxwell Model** \\ \hline \(R_{\rm bs}=2.2\ {\rm m}\Omega\) & \(SOC_{b\ max}=1\) & \(SOC_{uc\ max}=1\) & \(V_{nom}=48\ {\rm V}\) \\ \(R_{bp}=2.5\ {\rm m}\Omega\) & \(I_{b\ min}=-80\)A & \(I_{uc\ min}=-130\)A & \(R_{\rm us}=6.3\ {\rm m}\Omega\) \\ \(C_{bc}=20\)kF & \(I_{b\ max}=80\)A & \(I_{uc\ max}=130\)A & \(C_{uc}=165\)F \\ SOCB\({}_{min}=0.2\) & \(I_{bc}=-20\)A & \(I_{bc}=-20\)A & \(SOC_{uc\ min}=0.5\) \\ \(c_{1}=10\) & \(c_{2}=3\) & \(V_{max}=51\)V & \(n_{\rm prec}=4\) \\ \(V_{nom}=12.8{\rm V}\) & \(n_{pb}=5\) & \(n_{\rm isc}=2\) & \(SOC_{uc}({\rm t}0)=0.8858\) \\ \(n_{sb}=5\) & \(P_{b,c}=-3024W\) & & \\  & **Load: Curtis Motor 1236-6501 (72 V, 550 A)** & & \\  & \(V_{\rm load}=V_{moder}=96V\) & & \\  & **Converter** & & \\  & \(\eta_{b,com}=\eta_{uc,com}=0.9\) & & \\  & \(V_{b,com}=V_{uc,com}=96V\) & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Powertrain parameters.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Conditions** & **Power Delivered by the Battery Converter** & **Power Delivered by the UC Converter** \\ \hline \(P_{\rm last}=0\ SOC_{b}>SOC_{c,\min}\) & \(P_{b,com}=0\) & \(P_{uc,com}=0\) \\ \(SOC_{b}>SOC_{c,\min}\) & & \(P_{b,com}=P_{\rm load}-P_{uc,com}\) & \(P_{uc,com}=-P_{uc,com}\) \\ \(SOC_{uc}<SOC_{c,\min}\) & & \(P_{b,com}=P_{\rm load}-P_{uc,com}\) & \(P_{uc,com}=