## 5 Analysis of Different ECMS  
For the analysis of the ECMS, the fuel consumptions obtained by applying the different prediction methods described in Section 4 were compared to each other. The powertrain model was parametrized according to Figure 4, while the evaluation of the fuel consumptions was carried out according to the ECMS algorithm shown in Figure 5. In the simulation, the vehicle braked by means of recuperation, which was limited to a maximal electrical power of 35 kW. Furthermore, the battery's initial state of charge was defined to be 80%, and the lower boundary was set to 30%. In order to consider the difference between the predictions and the real driving behavior, various driving cycles of the same route were simulated. For this purpose, a daily commute in both directions was measured 39 times, including sections on a German inter-state. Each of these driving cycles had a distance of 80 km and was unique due to varying driving behavior and traffic. Figure 9 shows the minimal, maximal, and mean vehicle speeds resulting from the measured driving cycles. Additionally, a driving cycle of the same route obtained from the navigation data is shown. This driving cycle as well as the mean driving cycle was used for the predictions, while the measured driving cycles were used to evaluate the fuel consumptions. Figure 10 shows the simulation results obtained from the ECMS for all considered prediction methods and driving cycles. For comparison, the results of an offline optimization with DP (black marker) are shown, representing the theoretically minimal fuel consumption for each of the measured driving cycles. Furthermore, the results of a simple CD-CS operating strategy (charge depleting-charge sustaining) are shown, too (grey marker). It was first driven with the electric motor until the battery reached its lower boundary of the state of  
Figure 8: Prediction of \(SoC^{\text{SP}}\): (**a**) linear characteristic, (**b**) linear characteristic with adaptation to the recuperated braking energy, and (**c**) optimized characteristic obtained from DP for a predicted driving cycle. Figure 9: Minimal, maximal, and mean value of 39 measured driving cycles of the same route and the route’s driving cycle obtained from navigation data [45]. charge. Then, it was mainly driven by the ICE, keeping the state of charge constant. The CD-CS strategy was applied by means of the control-based approach, where \(SoC^{\text{SP}}=30\%\) was a constant setpoint. The results of the 39 driving cycles were arranged in ascending order of energy for propulsion so that the fuel consumptions on the left corresponded to a conservative driving style and those on the right corresponded to an agile driving style. The lowest fuel consumptions were obtained by the ECMS based on the Hamilton-Jacobi-Bellmann equation (red marker), where the mean driving cycle was used for parametrization. However, since such a driving cycle is generally unknown, it can only be determined when the driving behavior of frequently driven routes is measured (e.g., daily commute). More common is the parametrization according to the navigation data (green marker), which does not need any measurements and causes slightly higher fuel consumptions. For the application of both ECMS variants, a representative driving cycle must be determined, and in particular, a time-consuming optimization needs to be carried out in advance. Therefore, it is rather appropriate for trips, which can be scheduled in advance. The fuel consumptions obtained by applying the control-based methods were generally higher compared with the consumptions obtained with the method based on the Hamilton-Jacobi-Bellmann equation. As expected, the best results were obtained with an optimized state of charge characteristic for the setpoints of the controller (purple marker). This variant also required a predefined driving cycle and optimization in advance, which was carried out here by means of DP.