## 5 Results  
Comparative simulations among the traditional rule-based controller, adaptive rule-based controller, and comprehensive controller considering the traffic information are conducted under the WLTP driving cycle. The traditional rule-based controller is illustrated in Table 7, which possesses a superior economic performance in comparison to other traditional controllers [10]. \(P_{min}\) is the threshold of the output power of the battery. Figure 8: Diagram of fuzzy logic controller. Figure 9: Comprehensive controller considering traffic information. At the termination of the driving cycle, to prevent the comparison error caused by the unequal SOC of the ultra-capacitor in the three controllers, the battery compensates the SOC of the ultra-capacitor to the same standard, as depicted in Equation (12). \[\Delta SOC_{bat}=\frac{\Delta SOC_{uc}\times E_{uc}\times\eta}{SOC_{ batc.max}\times U_{bat}\times Q_{rate}} \tag{12}\]  
where, \(\Delta SOC_{bat}\) denotes the SOC that battery compensates the ultra-capacitor. \(\Delta SOC_{uc}\) presents the difference value of the final SOC to the initial SOC. \(E_{uc}\) represents the total energy of the ultra-capacitor. \(\eta\) is the efficiency of the DC/DC converter and \(U_{bat}\) is the voltage of the battery. The simulation results of the battery SOC and life loss are listed in Table 8. Table 9 illustrates the use of the battery in the three controllers. The details of the simulation results are given in Figures 10-13. It is not hard to discover, from Table 9, that the battery in the traditional rule-based controller possess the most using times and the highest average power, which leads to the great life loss of battery and the large consumption of SOC. As Figures 10 and 11 depict, due to the fixed rules, the traditional rule-based controller cannot adjust its power allocation according to the driving cycle so that its ultra-capacitor always maintains high quantity of electricity. Actually, when the demand power is low, in order to reduce the use of the battery, the ultra-capacitor can consume its electricity and regain energy through regenerative braking. Thus, the adaptive rule-based controller and the comprehensive controller increase the use of the ultra-capacitor by judging the current driving condition and utilizing the general law of optimal power allocation. Moreover, the high electricity constricts of the ultra-capacitor in the traditional rule-based controller ensures that the battery frequently charges the ultra-capacitor, which further increases the battery using times. The frequent electricity transferring from the battery to the ultra-capacitor is detrimental to the system efficiency. It can be observed in Table 8 that compared to the traditional rule-based controller, the adaptive rule-based controller reduces the battery life loss by 3.76% and the SOC consumption by 3.55% by properly using the ultra-capacitor. However, because of the lack of traffic information, the adaptive rule-based controller fails to achieve a further adjustment for the power allocation. In contrast, through the acquirement of the traffic condition and road grade, the comprehensive controller applies the electricity of the ultra-capacitor to the time points with a great power demand, which means that, as described in Figure 12, at many times, the comprehensive controller achieves the lower output power of the battery in comparison with the adaptive rule-based controller. Therefore, as can be seen from Table 8, compared to the adaptive rule-based controller, the comprehensive controller reduces the battery life loss by 2.98% and the SOC consumption of battery by 1.88%. Figure 11: State of change (SOC) of the ultra-capacitor. Figure 12: Output power of battery. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Battery index\textbackslash{} Controllers** & **TRBC** & **ARBC** & **CC** \\ \hline Battery using times & 13,074 & 10,933 & 9564 \\ \hline Average power of battery/kW & 9.31 & 9.05 & 8.87 \\ \hline \hline \end{tabular}
\end{table}