Convex modeling of energy buffers in power control applications

Abstract

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.

Convex relaxations in the optimal control of electrified vehicles

“…However, it is not obvious that the solution of the relaxed problem (27) returns the global optimum of problem (23). Indeed, there is an incentive for (27b) to hold with inequality, since larger y t may decrease battery losses in (27c).…”

“…More details on the convexity of these functions can be found in [12], [23], [24], [4], [13], [15]. A convex and nondecreasing EGU model has been proposed by [12], based on the EGU models of [25].…”

“…A convex and nondecreasing EGU model has been proposed by [12], based on the EGU models of [25]. The convexity of buffer losses and power limits have been established by [23], [16] and hold both for supercapacitors and batteries modeled with linear relationship between open circuit voltage and state of charge. Quadratic EM model, convex in P M , has been widely used in literature; see, e.g., [4] and references therein.…”

Least costly energy management for Electric Vehicles with plug-in Range Extenders

“…The battery model defined above is not readily usable in a disciplined convex programming approach [18]. Letting aside the aging model, a convex reformulation of the remainder of this model is proposed in [14], [19]. The energy level E corresponding to a given SoC is given by…”

Convex Optimization for the Energy Management of Hybrid Electric Vehicles Considering Engine Start and Gearshift Costs

“…In order to apply the concepts presented in Section 4 below, the generic, nonlinear vehicle model has to be approximated by a convex model, see [27] for a general introduction to convex optimization, and [29,45] for an introduction to convex modeling and optimization of HEVs.…”