## 6 Conclusions  
This contribution described a model-based analysis of different ECMS implementations for a plug-in hybrid electric powertrain, which can be operated in different operation modes and each of them operating at two speeds. A corresponding powertrain model was \begin{table}
\begin{tabular}{|p{113.8 pt}|p{113.8 pt}|p{113.8 pt}|} \hline
**Operating Strategy** & **Prediction Method** & **Input Information** & **Deviation to Minimal Fuel Consumption 1 (\(\blacktriangle\))** \\ \hline ECMS based on the Hamilton-Jacobi-Bell-mann equation & Optimization results from DP (map) & Averaged driving cycle of the real driving behavior & 0.6\% (\(\blacktriangle\)) \\ \hline  & \begin{tabular}{c} Optimization results from DP 2 \\ (Optimized characteristic _SoC_*) \\ \end{tabular} & \begin{tabular}{c} Averaged driving cycle of the real driving behavior \\ (Optimized characteristic _SoC_*) \\ \end{tabular} & 6.9\% (\(\blacktriangle\)) \\ \hline ECMS with control-based method & \
\begin{tabular}{c} Linear characteristic with adaption to the current _SoC_ \\ \end{tabular} & Distance of the intended route & 8.7\% (\(\blacktriangle\)) \\ \hline  &
\begin{tabular}{c} Linear characteristic \\ - \\ \end{tabular} & - & 10.1\% (\(\blacktriangle\)) \\ \hline CD-CS-Operation & - & - & 17.4\% (\(\blacktriangle\)) \\ \hline \end{tabular}  
* Mean percental increase of the fuel consumptions obtained with each operating strategy related to the theoretically minimal fuel consumptions obtained with the DP. 2 Not necessarily DP, as the optimized characteristic can also be obtained by means of other optimization methods.  
\end{table} 
Table 1: Overview of the considered operating strategies and summary of the simulation results shown in Figure 10.  
developed based on the backward simulation approach. This model neglects the system dynamics except for the vehicle mass and describes the fuel and energy consumptions by means of maps. The powertrain model is part of the ECMS algorithm, which is an optimization-based operating strategy based on PMP. In order to apply the ECMS on the considered powertrain, an appropriate description of the Lagrange multiplier is required. Two methods for the determination of this description were presented: the Hamilton-Jacobi-Bellmann equation, which requires a predefined driving cycle and a corresponding optimization with DP in advance, and a control-based method, where the state of charge is controlled based on a predefined characteristic for the controller's setpoints. Both methods require a prediction of the future driving behavior. Either a driving cycle or the distance to be driven must be predicted. The analysis of the ECMS and its prediction methods was carried out based on various driving cycles, which were measured for the same route. For the predictions, either the mean driving cycle obtained from the measurements, the corresponding navigation data, or the distance to be driven was considered. As it turned out, the ECMS based the Hamilton-Jacobi-Bellmann equation enabled the best results. However, this method requires a driving cycle, which is usually unknown, and time-consuming optimization in advance. For the ECMS with the control-based approach, it is sufficient to know the distance to be driven. The fuel consumptions obtained with this method were higher compared with the ECMS based on the Hamilton-Jacobi-Bellmann equation but were still lower compared with a simple CD-CS operating strategy. The results of the analysis show that the ECMS enabled significant improvements in fuel consumption compared with a non-optimization-based method. It was found that, in general, the more information about the future driving behavior was available, the lower the fuel consumptions were. The application of the ECMS is not limited to plug-in hybrid electric powertrains. It can also be applied to any other hybrid powertrain configuration which has one or more degrees of freedom regarding the control of the power distribution. Likewise, configurations without the capability of external recharging can be considered.