Optimizing regenerative braking -- a variational calculus approach

TL;DR

This paper models and optimizes regenerative braking using variational calculus to determine the most efficient velocity profile for maximizing battery charge recovery, considering physics and efficiency constraints.

Contribution

It introduces a variational calculus framework to optimize regenerative braking profiles, incorporating constraints and simplifying assumptions for energy recovery.

Findings

Derived the optimal braking velocity profile using Euler-Lagrange equations.

Analyzed conditions under which regenerative braking is energetically advantageous.

Explored the impact of fixed-displacement constraints on braking strategies.

Abstract

We examine some basic physics surrounding regenerative braking and air drag. First, we analyze under what conditions it becomes energetically favorable to use aggressive regenerative braking to reach a lower speed over ``coasting'' where one relies solely on air drag to slow down. We then proceed to reformulate the question as an optimization problem to find the velocity-profile that maximizes battery charge. Making a simplifying assumption on battery-charging efficiency, we formulate the recovered energy as an integral quantity and solve the associated Euler-Lagrange equation to find the optimal braking curve. Using Lagrange-multipliers, we also explore the effect of adding a fixed-displacement constraint.