Off-line and on-line optimization of the energy management strategy in a hybrid electric helicopter for urban air-mobility

This study addresses the optimization of the energy flows in a Hybrid Electric Helicopter for air-taxi operation in order to minimize the fuel consumption on four typical missions (defined in terms of power and altitude profiles) and contemporarily allowing electric back-up operation at any time during the mission. The proposed parallel hybrid electric powertrain includes a turboshaft engine, two electric machines, a lithium ion battery and all necessary control systems. The powertrain is modeled with an empirical but comprehensive approach in order to make possible the combination with numerical optimization algorithms. In particular, the battery is modeled with an electric equivalent circuit model that includes the effect of battery aging. The fuel consumption of the turboshaft engines is calculated with a mathematical function of power request, altitude and Mach number whose coefficients are fitted by means of comparison with the commercial code Gas-turbine Simulation Program (GSP). The optimization of the energy management of the hybrid powertrain is performed in two steps. The first one was the application of Dynamic Programming in order to obtain the optimal usage of the battery for a given mission (target values) and to provide insights into how to develop a suitable on-line optimizer to be applied during the real operation of the rotorcraft. For this second step analysis, the authors developed a version of the Equivalent Consumption Minimization Strategy opportunely adapted to the specific case of an aerial vehicle with turboshaft engine, in particular taking in to account the desired state of charge and the actual state of health of the battery. After an off-line optimization of its parameters with a multi-objective approach, the on-line optimizer guaranteed results similar to the target values and allowed a reduction of the fuel burn ranging between 10% and 22% with respect to using only the thermal engine to power the rotor shaft and without any need to adapt the parameters in case of aged battery.