Efficient Powertrain Design -- A Mixed-Integer Geometric Programming Approach

TL;DR

This paper introduces a novel convex mixed-integer nonlinear programming approach combining geometric programming and Benders decomposition to optimize electric vehicle powertrain design efficiently, with fast solutions and global convergence.

Contribution

The paper presents a new systematic optimization method that transforms a non-convex problem into a convex one, enabling faster and more reliable powertrain design optimization.

Findings

Fast solution times for complete driving cycles

Global convergence of the optimization process

Ability to compute local sensitivities at the optimal design point

Abstract

The powertrain of battery electric vehicles can be optimized to maximize the travel distance for a given amount of stored energy in the traction battery. To achieve this, a combined control and design problem has to be solved which results in a non-convex Mixed-Integer Nonlinear Program. To solve this design task more efficiently, we present a new systematic optimization approach that leads to a convex Mixed-Integer Nonlinear Program. The solution process is based on a combination of Geometric Programming and a Benders decomposition. The benefits of this approach are a fast solution time, a global convergence, and the ability to derive local sensitivities in the optimal design point with no extra cost, as they are computed in the optimization procedure by solving a dual problem. The presented approach is suitable for the evaluation of a complete driving cycle, as this is commonly done in powertrain system design, or for usage in a stochastic approach, where multiple scenarios are sampled from a given probability density function. The latter is useful, to account for the uncertainty in the driving behavior to generate solutions that are optimal in an average sense for a high variety of vehicles and drive conditions. For the powertrain model we use a transmission model with up to two selectable transmission ratios and an electric motor model that is based on a scaled efficiency map representation. Furthermore, the shown model can also be used to model a continuously variable transmission to show beneficial energy savings based on this additional degree of freedom. The presented design approach is also applicable to a wide variety of design tasks for technical systems besides the shown use case.