Computationally efficient assessment of fuel economy of multi-modes and multi-gears hybrid electric vehicles: A hyper rapid dynamic programming approach

The powertrain configuration, sizing, and control are multi-dimensional intertwined. Synergy optimization of these three dimensions can yield the greatest benefits. However, the huge computational load limits its implementation. Especially for multi-modes and multi-gears (MMMG) transmissions. Thus, a more efficient optimization method with acceptable accuracy is urgently required. In this study, a near-global optimal method, called Hyper-Rapid Dynamic Programming (HR-DP), is proposed and discussed. The computation time is significantly reduced by optimization of candidate state and control domains, identification of optimal efficiency operating points, and parallel computation approaches. Subsequently, a thorough comparison of the HR-DP, Rapid-DP and DP methods was performed across various driving cycles. Compared to the DP algorithm, the computational efficiency is boosted by a factor of about 100,000, while the fuel consumption error is limited to 1.5 % in Real-world driving cycle (RWDC). Moreover, the HR-DP, in conjunction with particle swarm optimization (PSO), is employed for the first time to optimize essential sizing for MMMG configuration. The MMMG configuration with optimal sizing is demonstrated to be most energy-efficient, with 7.70%–10.6 % fuel-savings achieved, compared to the Toyota Prius. Therefore, HR-DP is well-suited for the design and optimization of HEV transmission configurations and sizing, significantly accelerating the development progress.