The influence of mode change penalties on the comparison of hybrid drivetrain topologies

Hybrid drivetrains are systems with complex behavior of which finding the optimal design is a problem with a large design space. To assess a design on efficiency over a driving cycle, a control strategy is needed. Introducing mode change and engine start penalties in the optimization of the control increases the accuracy of the results at the cost of increased computation time. Yet, due to the large design space of the design problem, computation time is critical. In this work, an extensive case study is presented to analyze the influence of penalizing mode changes and engine starts on the comparison of hybrid drivetrain topologies. Eight different drivetrain topologies are considered, including parallel, series-parallel, and multimode powersplit topologies. For these topologies, the control is optimized over two driving cycles using dynamic programming with and without penalties. The introduction of mode change and engine start penalties reduces the number of mode changes by a factor of three to five, and the number of engine starts by approximately a factor of three. Yet, the influence on the fuel consumption comparison between the topologies is small: the largest change in relative fuel consumption is 0.36 percentage points, with the average absolute change over both cycles being 0.15 percentage points. The computation time is increased by approximately a factor of 26 due to the introduction of the penalties. Therefore, in the context of the system level design of hybrid drivetrains, it can be argued that the additional computation time outweighs the minor increase in accuracy provided by mode change penalties.