Improving Computational Efficiency for Energy Management Systems in Plug-in Hybrid Electric Vehicles Using Dynamic Programming based Controllers

Reducing computational time has become a critical issue in recent years, particularly in the transportation field, where the complexity of scenarios demands lightweight controllers to run large simulations and gather results to study different behaviors. This study proposes two novel formulations of the Optimal Control Problem (OCP) for the Energy Management System of a Plug-in Hybrid Electric Vehicle (PHEV) and compares their performance with a benchmark found in the literature. Dynamic Programming was chosen as the optimization algorithm to solve the OCP in a Matlab environment, using the DynaProg toolbox. The objective is to address the optimality of the fuel economy solution and computational time. In order to improve the computational efficiency of the algorithm, an existing formulation from the literature was modified, which originally utilized three control inputs. The approach involves leveraging the unique equations that describe the Input-Split Hybrid powertrain, resulting in a reduction of control inputs firstly to two and finally to one in the proposed solutions. The aforementioned formulations are referred to as 2-Controls and a 1-Control. Virtual tests were conducted to evaluate the performance of the two formulations. The simulations were carried out in various scenarios, including urban and highway driving, to ensure the versatility of the controllers. The results demonstrate that both proposed formulations achieve a reduction in computational time compared to the benchmark. The 2-Controls formulation achieved a reduction in computational time of approximately 40 times, while the 1-Control formulation achieved a remarkable reduction of approximately 850 times. These reductions in computational time were achieved while obtaining a maximum difference in fuel economy of approximately 1.5% for the 1-Control formulation with respect to the benchmark solution. Overall, this study provides valuable insights into the development of efficient and optimal controllers for PHEVs, which can be applied to various transportation scenarios. The proposed formulations reduce computational time without sacrificing the optimality of the fuel economy solution, making them a promising approach for future research in this area.