Hybrid power-split powertrains are getting more attention as they present great efficiency and performance. These powertrains connect components by planetary gear sets. Energy management strategy of the powertrain determines the power flow through each component. This paper presents a framework to address the problem of the fuel-optimal control strategy for an energy management strategy of power-split powertrains using convex optimization. To do this, we present a novel model for the power unit

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... and other components using convex equations and constraints. We then use numerical solvers for the convex problems to efficiently solve the optimal control problem. Convex solver shows better performance in considerably less amount of time for the tested driving cycles, compared to the dynamic programming. This makes it suitable for design cases which need to iteratively solve the optimal control problem for different initiations in the design space. Another application is using the presented optimization-based approach to obtain the control input of the powertrain in the real-time applications. INDEX TERMS Convex optimization, energy management, fuel-optimal, hybrid powertrains, optimal control, power-split.