Synthesis of Optimal Battery State-of-Charge Trajectory for Blended Regime of Plug-in Hybrid Electric Vehicles in the Presence of Low-Emission Zones and Varying Road Grades

Abstract

The powertrain efficiency for plug-in hybrid electric vehicles (PHEV) can be maximized by gradually discharging the battery in a blended regime, where the engine is regularly used all over the driving cycle. A key step in designing an optimal PHEV control strategy for the blended regime corresponds to synthesis of battery state-of-charge (SoC) reference trajectory. The paper first demonstrates that the optimal SoC trajectory can significantly differ from a typical linear-like shape in the case of varying road grade and presence of low-emission zones (LEZ). Next, dynamic programming (DP)-based optimizations of PHEV control variables are conducted for the purpose of extracting and analyzing optimal SoC trajectory patterns. It is shown that the optimality is closely related to the minimization of SoC trajectory length with respect to travelled distance. This finding is used for SoC reference trajectory synthesis in the presence of LEZ and varying road grades. Finally, the overall PHEV control strategy is applied to a PHEV-type city bus and verified by means of computer simulations in comparison with the DP optimization benchmark.

Online Synthesis of an Optimal Battery State-of-Charge Reference Trajectory for a Plug-in Hybrid Electric City Bus

“…The optimal SoC trajectory expressed with respect to the travelled distance (Figure 5a) has a linear trend in the case of a zero road grade. However, in the presence of a road grade the optimal SoC trajectory deviates from the linear trend, particularly in the case of low-frequency (LF) and mid-frequency (MF) grade variations [9]. To gain a deeper insight into the optimal SoC trajectory behaviour, the rate of change of the optimal SoC trajectory was analysed with respect to the power demand P d defined by Equation (4) [9].…”

“…The PHEV powertrain backward-looking model and the corresponding energy management control strategy are outlined based on the previous publications [9,18], respectively.…”

“…where the terminal cost J f penalizes SoC deviation from the prescribed final value SoC f = SoC(t f ), while the second right-hand term relates to fuel consumption and reads [9]:…”

“…For instance, the authors in [6,7] describe a linear SoC reference trajectory that is determined at the beginning of the driving cycle and incorporated into an adaptive Pontryagin's minimum principle (PMP)-based energy management strategy. However, the optimal SoC trajectories can significantly deviate from the linear-like trend in different real-world driving conditions, e.g., in the presence of lowemission zones (LEZ; where electric-only driving is preferred) [8], significantly varying road grade [5,9], and mixed driving patterns (e.g., city driving followed by highway driving) [10]. To account for these effects, a piecewise-linear SoC reference trajectory can be synthesized based on a principle of minimizing battery losses and dynamic programming (DP) optimization results [8,9].…”

“…To this end, this paper proposes an online, computationally efficient, heuristics-based SoC reference trajectory synthesis method for a general class of driving cycles including the presence of LEZs and varying road grades. The first step towards the online strategy is based on an improvement of the authors' previous work presented in [9], in terms of designing an offline synthesis method that does not require a preview of the whole driving cycle, but only predictions of the mean vehicle velocity and the mean demanded power. This is a particularly proper assumption for the considered application in city buses, as they operate on fixed routes.…”