  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.
