Dynamic optimization of an operation strategy for a nested powertrain system design approach

To reduce the CO₂ emissions of the new car fleet, the car manufacturer increase the releases of hybrid and battery electric vehicles. The system design for those vehicles is difficult since the topology, the size of the components and the operation strategy influences the energy consumption, the performance, the comfort and the costs. In this paper a method is presented to optimize the operation strategy regarding the minimum energy consumption of a specific vehicle, for a specific driving cycle. The developed method is valid for a P2/P4 hybrid electric vehicle and its derivatives as P2, P4 hybrid electric vehicles, four wheel and rear wheel drive battery electric vehicles as well as conventional vehicles. A modular vehicle model is developed, adaptable to each considered topology. For hybrid electric vehicles the energy consumption has to be minimized while obtaining a balanced charge of the high voltage battery. The optimization variables are the power distribution between the power sources and power sinks, the gear trajectory as well as the engine state trajectory. The properties of the optimization variables lead to a Mixed Integer - Optimal Control Problem (MI-OCP), which is solved by combining a direct and an indirect optimization method. This method is extended to solve singularities of the indirect method, caused by linear look-up table interpolation or switching decisions. Furthermore, the method is extended such that the indirect method is able to handle state constraints. Additionally, due to comfort reasons, the engine state should not be changed at high frequency and therefore time dependent state constraints are respected by the optimization method. The developed optimization method is applied on an operation strategy for a parallel hybrid electric vehicle. Compared to a reference strategy the optimized strategy reduces the CO₂ emissions by 7.8%.