Chaos oscillator differential search combined with Pontryagin’s minimum principle for simultaneous power management and component sizing of PHEVs

Abstract

Over the past decade, plug-in hybrid electric vehicles (PHEVs) have found a good reputation in the automotive industry due to the fact that they neatly satisfy the existing tight environmental regulations and fuel economy requirements. Recently, there has been more interest in the design optimization of the PHEV powertrains to improve their operational characteristics to the maximum possible extent. The PHEV powertrains are complicated systems and include different controllers and components which should operate corporately to guarantee the acceptable performance of the vehicle. The reported investigations indicate that improving the performance of PHEVs is a very arduous task because both control strategies and component sizes should be optimized in tandem; however, in most of the previous studies, the focus has been on improving one of the above-mentioned aspects, which does not result in the most efficient design. The main goal of the current study is to take advantage of a bi-level optimization framework which combines the optimizations of both powertrain component sizes and power management controller for a specific PHEV, namely 2012 Toyota plug-in Prius. The bi-level optimizer comprises a chaos-enhanced differential evolutionary algorithm, which is in charge of the component sizing, and a classical optimal control approach based on the Pontryagin’s minimum principle, which optimizes the vehicle power management strategy. A high-fidelity model of the vehicle is developed in the Autonomie software. This high-fidelity model is used to identify the parameters of a reduced model representing the vehicle dynamics by means of the homotopy analysis method, and the resulting model is then employed for the optimization procedure. The results of the numerical experiments indicate that by considering both component sizing and control strategy optimization, a very powerful tool is developed which can significantly improve the total fuel cost (F C ), acceleration time (T acc ), and battery state of charge (SOC) trajectory of the vehicle.