Comparison of supervisory control strategies for series plug-in hybrid electric vehicle powertrains through dynamic programming

This paper compares the optimal fuel and electricity costs associated with two supervisory control strategies for a series plug-in hybrid electric vehicle (PHEV) using dynamic programming. One strategy has no restrictions on engine fuel usage and the second is restricted to fuel usage only after the battery is depleted below a certain threshold. Both strategies are optimized using deterministic dynamic programming (DDP) to ensure a fair comparison. The DDP algorithm is implemented using a backward-looking powertrain model. Such an approach resolves the computational issues arising because of: 1) the interpolations required to obtain value function estimates and 2) the characterization of constraints through penalty functions. The primary conclusion is that there is no significant difference in the optimal performance of the two control strategies for the series PHEV except when gasoline is unreasonably cheap <1/gal. This result contrasts sharply with previous controller performance results for parallel and power-split PHEVs where the two strategies' performance is shown to differ for any gasoline price and driving distance. The reason for the contrast is the flexibility of engine operation in a series PHEV. The results are examined for different relative fuel and electricity prices and trip lengths.