Optimal sizing of a series PHEV : comparison between convex optimization and particle Swarm optimization

Building a plug-in hybrid electric vehicle that has a low fuel consumption at low hybridization cost requires detailed design optimization studies. This paper investigates optimization of a PHEV with a series powertrain configuration, where plant and control parameters are found concurrently. In this work two of ten used methods are implemented to find optimal energy management with component sizes. In the first method, the optimal energy management is found simultaneously with the optimal design of the vehicle by using convex optimization to minimize the sum of operational and component costs over a given driving cycle. To find the integer variable, i.e., engine on-off, dynamic programming and heuristics are used. In the second method, particle swarm optimization is used to find the optimal component sizing, together with dynamic programming to find the optimal energy management. The results show that both methods converge to the same optimal design, achieving a 10.4% fuel reduction from the initial powertrain design. Additionally, it is highlighted that the usage of each of the method poses challenges, such as computational time (where convex optimization outperforms particle swarm optimization by a factor of 20) and the tuning effort for the particle swarm optimization and the ability to handle integer variables of convex optimization.