A first-order lumped-parameter model for the prediction of thermal behavior of a single-cylinder gasoline engine for Hybrid Electric Vehicles (HEVs) has been implemented. The model is coupled with a zero-dimension in-cylinder model that evaluates the working cycle of the engine according to the actual operating conditions and calculates the temperature of the exhaust gases, the overall efficiency of the engine and the exhaust gases flow rate. The model takes into account the possibility of using exhaust gas heat recirculation in order to enhance engine warm-up during cold start which improves its efficiency. The supervisory strategy takes into account not only predicted speed and ambient and road conditions along a future time window but also actual battery state of the charge and engine temperature to select the optimal power split between the ICE-generator group and the batteries. The proposed model represents an improvement with respect to a previous investigation of the authors where the temperature of the engine were assumed to increase/decrease of on Celsius degree in each seconds according to the state of the engine (ON/OFF).

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