## 3 Torque and Battery Distribution Strategy
### Torque and Battery Distribution (TBD) Strategy  
Figure 4 shows the flowchart for the torque and battery distribution (TBD) strategy. Before the EV started from rest, the SOC of the front, rear right, and rear left battery packs was respectively measured as \(SOC_{F}\), \(SOC_{L}\), and \(SOC_{R}\). The SOC gap and SOC ratio were calculated:  
1. SOC gap (\(SOC_{g}\)): The SOC gap was defined as the difference between the SOC of the front battery pack and the lower SOC of the two rear battery packs. It was negative when the front battery had less power remaining than the rear batteries, and it was positive when the front battery had more \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Strategy**} & \multicolumn{4}{c}{**Battery Energy Consumption [Wh]**} \\ \cline{2-6}  & & **Front** & **Rear Right** & **Rear Left** & **Total** \\ \hline \multicolumn{6}{c}{**UDC on a Straight Road**} \\ \hline \multirow{6}{*}{PTR} & PSO & 223.2 & 37.76 & 37.76 & 298.72 \\  & \(P_{r}=0\) & 44.00 & 158.4 & 158.4 & 361.16 \\  & \(P_{r}=0.25\) & 55.20 & 150.8 & 150.4 & 356.68 \\  & \(P_{r}=0.5\) & 91.60 & 123.2 & 123.2 & 338.44 \\  & \(P_{r}=0.75\) & 338.8 & \(-\)11.88 & \(-\)11.88 & 315.12 \\  & \(P_{r}=1\) & 351.2 & \(-\)19.72 & \(-\)19.72 & 311.92 \\ \hline \multicolumn{6}{c}{UDC Clockwise along a Circular Path (Radius 100 m)} \\ \hline \multirow{6}{*}{PTR} & PSO & 285.6 & 96.00 & 35.36 & 417.08 \\  & \(P_{r}=0\) & 93.20 & 216.8 & 158.0 & 467.92 \\  & \(P_{r}=0.25\) & 113.2 & 205.2 & 146.0 & 464.28 \\  & \(P_{r}=0.5\) & 179.2 & 166.4 & 107.6 & 453.44 \\  & \(P_{r}=0.75\) & 429.2 & 32.32 & \(-\)14.28 & 447.36 \\  & \(P_{r}=1\) & 447.2 & 22.20 & \(-\)16.08 & 453.40 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Energy consumption of battery packs. power than the rear batteries. In applications, a default value \(SOC_{g}<-\kappa\%\) (\(0<\kappa<2\)) can be assigned to determine the torque distribution mode (Figure 4). 2. SOC ratio (\(SOC_{r}\)): The SOC ratio was defined as the ratio of energy consumption in terms of the SOC between the front battery pack and the two rear battery packs. On the basis of the simulation of straight road driving under the PSO strategy, as indicated in Table 2, the \(SOC_{r}\) converged to 2.94 for the long-term operation of the UDCs. In applications, a default value, \(\rho\) (\(<\) 2.94), was assigned to determine the torque distribution mode under the TBD strategy. Through the use of \(SOC_{g}\), the state of balance (SOB) of the three battery packs was investigated. The three states of battery balance are described:  
1. State 1: The SOC of the front battery pack was higher than that of any of the rear battery packs. 2. State 2: The SOC of the front battery pack was equal to that of any of the two rear battery packs. 3. State 3: The SOC of the front battery pack was lower than that of the rear battery pack. Three torque distribution modes were then determined by the SOC gap (\(SOC_{g}\)):  
1. Mode 1: \(P_{r}=1\) was proposed when the front motor had the first priority for delivering the torque under the condition of \(SOC_{g}>0\) and \(SOC_{r}\geq\rho\). At Mode 1, the SOC of the front battery pack was much higher than that of the rear battery packs. When the \(SOC_{r}\) was larger than 2.94, the \(SOC_{g}\) could increase continuously, and the battery balance could worsen even though the PSO strategy was executed. It was better for the front battery pack to reach a balance between the front and rear batteries. 2. Mode 2: The PSO strategy was prescribed when there was not much difference in the SOC of the three battery packs under the following conditions: \(SOC_{g}=0\) or (\(SOC_{g}>0\) and \(SOC_{r}<\rho\)) or (\(0>SOC_{g}\geq-\kappa\%\) and \(|SOC_{g}|\) was increasing). Because the PSO strategy is superior to the PTR strategy for distributing the torque among the traction motors, it should be used whenever the difference in the SOC of the battery packs is negligible.