This paper presents convex modeling steps for the problem of optimal battery dimensioning and control of a plug-in hybrid electric vehicle with a continuous variable transmission. The power limits of the internal combustion engine and the electric machine are approximated as convex/concave functions in kinetic energy, whereas their losses are approximated as convex in both kinetic energy and power. An example of minimizing the total cost of ownership of a city bus including a battery wear model is presented. The proposed method is also used to obtain optimal charging power from an infrastructure that is to be designed at the same time the bus is dimensioned.
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Murgovski et al. (2014) studied this question.