The influence of engine active engagement and battery heating behavior in plug-in hybrid electric vehicles (PHEVs) under low-temperature conditions when high battery state of charge (SOC) is investigated. Considering that thermal inertia and cold start processes require long-term condition estimation, which is difficult to accurately predict, average speed, driving distance, and ambient temperature are selected as rough variables, while accounting for the impact of fluctuating charging grid price. The objective is minimization of sum cost including fuel, equivalent electricity consumption, and battery life degradation. Findings indicate that rough parameters for long-term conditions in low-temperature environments can more accurately predict engine activation and battery heating. (1) Typical optimized modes performance reveals that the reasons improved economic performance are earlier engine activation and reduced high-power battery output at low temperatures. The average total cost reduction achieved exceeds 6%, with high-speed conditions surpassing 20%. (2) Mode distribution reveals that average speed influences decisions on electricity/fuel usage, while driving distance affects battery heating behavior and engine pre-activation. Grid price and temperature influence the mode boundary movement. (3) Spearman correlation between influence and strategy parameters reveals that battery heating is disabled in pure engine mode. These behaviors indicate that under low-temperature conditions, engine engagement timing and battery heating decisions require rough condition prediction at the beginning rather than relying only on battery temperature.
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