## 4 Design Case
### Evaluation of Energy Efficiency Performance  
In the final stage, the energy efficiency of the MLTD system, \(\eta_{sys}\), is evaluated when driving straight with neutral operation, or turning left and right with optimal torque vectoring. Next, a battery model is included to compute the energy consumption of the designed vehicle at cruise speed. In the end, the trade-off between cornering performance and energy efficiency by reducing vehicle mass with or without lateral torque vectoring is investigated. The definition of \(\eta_{sys}\) is expressed as  
\[\eta_{sys}=\frac{P_{w}}{P_{m}+P_{dm}} \tag{49}\]  
where \(P_{w}\) is the power output of two front wheels in W, and equal to \(T_{wil}\omega_{wl}+T_{wil}\omega_{wir}\); \(P_{m}\) and \(P_{dm}\) are the power input of M and DM, respectively, and expressed as \(T_{m}\omega_{m}/\eta_{m}\) and  
Figure 21: Operating points of M with \(v\) in the range of 20 to 120 km/h. Figure 22: Operating points of DM with \(v\) in the range of 20 to 120 km/h. \(T_{dm}\omega_{dm}/\eta_{dm}\). Here, \(\eta_{m}\) and \(\eta_{dm}\) which are both functions of torque and rotational speed, can be obtained by looking up the performance map of M and DM shown in Figures 17 and 22. Consequently, Figure 23 shows the variations in \(\eta_{sys}\) with \(v\) at straight driving (i.e., in neutral mode) or at right and left turn (i.e., in optimal torque vectoring mode). The values of \(\eta_{sys}\) at straight driving vary from the lowest one of 0.781 at \(v=\) 20 km/h to the highest one of 0.837 at \(v=\) 115 km/h with a percentage difference of only 6.7%. As for right or left turn, even though their values show similar trend with those at straight driving, the corresponding lowest values at \(v=\) 20 km/h are much lower, i.e., \(\eta_{sys}=\) 0.560 at left turn and \(\eta_{sys}=\) 0.539 at right turn with a percentage difference of 33% and 32%, respectively. The values of \(\eta_{sys}\) at left turn increase as \(v\) increases and approach those at straight driving as \(v\) is beyond 60 km/h. Furthermore, it can be observed that the highest value of \(\eta_{sys}\) at right turn is still dropped by 5%, since DM is operated in generator mode, rather than motor mode, at right turn, resulting in an undesirable loss of power recirculation. In order to assess the driving range as well as energy consumption of the designed vehicle, the simulation program is incorporated with a tested battery model obtained from ADVISOR 2002 software [21] with the battery type named 'Shaft 6 Ah Li-Ion' for simulating the charging and discharging processes. Arranging 12 cells in series and 18 cells in parallel for a module and 8 modules in series for a pack makes up the capacity of 40.4 kWh and the total voltage of 374.4 V for simulation. The internal resistances, i.e., \(R_{b}\), of charge and discharge, and open-circuit voltage, i.e., \(V_{oc}\), as functions of state of charge, i.e., \(SOC\), are expressed in Figure 24a and b, respectively, at temperature = 25 \({}^{\circ}\)C. Accordingly, the instant current flowing out of the battery, i.e., \(I_{b}\), can be calculated by  
\[I_{b}=\frac{V_{oc}-\sqrt{{V_{oc}}^{2}-4\left(R_{b}+R_{mg}\right)P_{mg}}}{2R_{b}} \tag{50}\]  
where \(R_{mg}\) is the resistance in motor or generator in \(\Omega\); \(P_{mg}\) is the input power of motor or generator in W, positive for motor and negative for generator. Here, \(R_{mg}\) is set to be a constant value of 0.002 \(\Omega\). The power output of the battery, \(P_{b}\), is expressed as  
\[P_{b}=P_{mg}+\left(R_{b}+R_{mg}\right)I_{b}^{2} \tag{51}\]  
Moreover, the corresponding \(SOC\) is estimated by accumulating the electric charge from charging or discharging process through operation time as shown below:  
\[SOC=1-\frac{\int_{0}^{t}I_{b}dt}{Q_{t}} \tag{52}\]  
Figure 23: Variations in \(\eta_{sys}\) with \(v\) at straight driving or at right and left turn.