This paper studies convex optimization and modelling for component sizing and optimal energy management control of hybrid electric vehicles. The novelty in the paper is the modeling steps required to include a battery wear model into the convex optimization problem. The convex modeling steps are described for the example of battery sizing and simultaneous optimal control of a series hybrid electric bus driving along a perfectly known bus line. Using the proposed convex optimization method and battery wear model, the city bus example is used to study a relevant question: is it better to choose one large battery that is sized to survive the entire lifespan of the bus, or is it beneficial with several smaller replaceable batteries which could be operated at higher c-rates?