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This paper presents a simplified, yet realistic, model of a hybrid electric powertrain and derives the explicit solution of the optimal energy management. The explicit solution of this optimal control problem consists of simple rules that rely on powertrain parameters only. The simplified model is validated on a more complex model relying on measured data. Finally, a causal, real-time control strategy including anti-windup is presented. This strategy relies on the optimal control of the simplified model and is successfully evaluated on the complex model that relies on measured data.