Convex modeling of energy buffers in power control applications

This paper describes modeling steps for presenting energy buffers as convex models in power control applications. Except obtaining the optimal control, the paper also shows how convex optimization can be used to simultaneously size the energy buffer while optimally controlling a trajectory following system. The energy buffers are capacitors and batteries with quadratic power losses, while the resulting convex problem is a semidefinite program. The convex modeling steps are described through a problem of optimal buffer sizing and control of a hybrid electric vehicle. The studied vehicle is a city bus driven along a perfectly known bus line. The paper also shows modeling steps for alternative convex models where power losses and power limits of the energy buffer are approximated. The approximated models show significant decrease in computation time without visible impact on the optimal result.