Optimal Energy Management of Series Hybrid Electric Vehicles with Engine Start-Stop System

Abstract

This paper develops energy management (EM) control for series hybrid electric vehicles (HEVs) that include an engine start-stop system (SSS). The objective of the control is to optimally split the energy between the sources of the powertrain and achieve fuel consumption minimization. In contrast to existing works, a fuel penalty is used to characterize more realistically SSS engine restarts, to enable more realistic design and testing of control algorithms. The paper first derives two important analytic results: a) analytic EM optimal solutions of fundamental and commonly used series HEV frameworks, and b) proof of optimality of charge sustaining operation in series HEVs. It then proposes a novel heuristic control strategy, the hysteresis power threshold strategy (HPTS), by amalgamating simple and effective control rules extracted from the suite of derived analytic EM optimal solutions. The decision parameters of the control strategy are small in number and freely tunable. The overall control performance can be fully optimized for different HEV parameters and driving cycles by a systematic tuning process, while also targeting charge sustaining operation. The performance of HPTS is evaluated and benchmarked against existing methodologies, including dynamic programming (DP) and a recently proposed state-of-the-art heuristic strategy. The results show the effectiveness and robustness of the HPTS and also indicate its potential to be used as the benchmark strategy for high fidelity HEV models, where DP is no longer applicable due to computational complexity.

Figures (20)

• Figure 1: Powertrain architecture of the series HEV.
• Figure 2: Efficiency of the reversible motor/generator (generator = positive torque, motor = negative torque) Evangelou+Shukla/ACC:2012. The torque bounds (due to power limitation) are shown by dotted lines. The rated power of the machine is 95kW.
• Figure 3: Left: map of overall efficiency of the engine branch. The torque-speed operating points for maximum engine branch efficiency at different output power values are shown by a dashed red curve. Right: fuel mass rate with PS power, when the most efficient torque-speed operating point is followed at each power value.
• Figure 4: Sketch of example optimal solution for a vehicle mission when a state (SOC) constraint is reached. Top: Mission shown as $P_{PL}$ power profile results from the WL-L driving cycle. Middle: Optimal SOC trajectories for the unconstrained (red) and constrained (blue) cases. Bottom: Optimal costate, $\lambda$, for the unconstrained (red) and constrained (blue) cases.
• Figure 5: Optimal power-split solutions found by DP for the case without SSS for an example power demand trajectory $P_{PL}$ of 70 s, an $\soc(T)=0.65$ and three different cases of $\soc(0)$. Each $\soc(0)$ case is chosen to respectively actualize the last three of the closed-form solution cases in \ref{['eq:uoptphi']}, associated with $\lambda=-0.2929$ for Case 2, $\lambda=-0.3448$ for Case 4 and $\lambda \in [-0.3361,-0.3097]$ for Case 3 (the control signal does not depend on $\lambda$), with the two $\lambda$ transition points being $-{\alpha_f Q_{\max} V_{oc}}/{\eta_{dc}}\!=\!-0.3361$ and $-\alpha_f Q_{\max} \eta_{dc} V_{oc}\!=\!-0.3097$. Note that in Case 4 for an even lower $\soc(0)$ (more demand on battery charging), during negative $P_{PL}$ the optimal solution may request the engine to contribute to the charging of the battery, and therefore $P_{PS}$ may become positive, instead of $0$, while at the same time $P_{SS}$ may become more negative than $P_{PL}$, instead of being equal to $P_{PL}$.