Applying Dynamic Programming Algorithms to the Energy Management of Hybrid Electric Aircraft

Abstract

To explore the application of dynamic programming (DP) to the energy management strategies of hybrid electric aircraft, a hybrid powertrain for a lightweight rotorcraft is introduced and its dynamic control model is designed. The model is conceived for the Agusta-Westland A109 helicopter, a twin-engine rotorcraft used in various roles, such as light transport, search-and-rescue and military roles. The turboshaft single spool engines are modeled with the use of performance maps that allow part load specific fuel consumption to be calculated as a function of actual power request and flight conditions. The state-of-the-art lithium polymer batteries are used for the hybridization and their behavior is evaluated by the Sheperd-Peukert model. The control problem is modeled through a graph structure where a node is obtained from the intersection between a time value, representing the starting of a phase of flight, and a splitting factor, representing the percentage of propulsive power required to the battery in such a phase. The edge connecting two nodes concerns with the state transition and the weight of the edge refers to the transition cost. The goal is to find an optimal splitting sequence to minimize the total cost over the whole mission, that is given with regard to speed and altitude. The Dijkstra algorithm, which allows the shortest energy path to be found between nodes in a graph, is used to look for the optimum. A local optimum is achieved when the cost is defined as the fuel consumption whereas the global optimum can be attained when the model is enhanced to include the effect of the battery usage into the cost. The results are compared with the original non-hybrid case and the engine efficiency was suitable evaluated. The applicability to other mission data is suitably evaluated so as to deduce the concept of similarity of mission.