Co-Optimization of Design and Control of Energy Efficient Hybrid Electric Vehicles Using Coordination Schemes

Design and control co-optimization studies for hybrid vehicles have been proposed in the past. However, such works suffer from difficulties arising due to (a) diverse real- and integer-valued variables, (b) complex nonlinear powertrain dynamics and design interconnections, (c) conflicting objective functions with path constraints, and (d) high computational resources requirements. To meet these challenges, this study presents an efficient co-optimization framework for hybrid electric vehicles (HEVs) which is built using existing algorithms and coordination schemes. Particular emphasis is given to the simultaneous scheme and the decomposition-based scheme. The decomposition-based scheme with the problem decomposition proposed in this work can efficiently handle multitime scale state variables and both integer- and real-valued design and control optimization variables. This is demonstrated by solving the mixed-integer optimal design and control problem of a series hybrid vehicle over a 1-h long drive cycle with time discretization of 1 s. The problem complexity is elevated by using an increasing number of state variables (including battery state of charge, battery energy, and after-treatment system temperature), control variables (such as the engine power and engine on/off), and design parameters (such as the number of battery cells and the type and size of the engine). In addition, a multi-objective cost function is used to find a tradeoff solution between fuel consumption and emissions minimization. The results show that in terms of optimality of the solution, the decomposition-based scheme is comparable with the simultaneous but can give a 14% improvement in computational performance. The effectiveness of the proposed framework is demonstrated by comparing the co-optimization results against a baseline case in which only the optimal control problem is solved. The co-optimized solution yields up to 3.7% average genset efficiency improvement and a fuel consumption reduction to 1.6 kg from 2.5 kg, which is further reduced to 1.5 kg by adding the engine on-off control. Finally, a decision matrix is developed to provide guidance on the selection of the optimization algorithm and coordination scheme for any problem at hand.