Hybrid electric vehicles are seen as a solution to improving fuel economy and reducing pollution emissions from automobiles. By recovering kinetic energy during braking and optimizing the engine operation to reduce fuel consumption and emissions, a hybrid vehicle can outperform a traditional vehicle. In designing a hybrid vehicle, the task of finding optimal component sizes and an appropriate control strategy is key to achieving maximum fuel economy.
In this paper we introduce the application of convex optimization to hybrid vehicle optimization. This technique allows analysis of the propulsion system's capabilities independent of any specific control law. To illustrate this, we pose the problem of finding optimal engine operation in a pure series hybrid vehicle over a fixed drive cycle subject to a number of practical constraints including:
nonlinear fuel/power maps
min and max battery charge
battery efficiency
nonlinear vehicle dynamics and losses
drive train efficiency
engine slew rate limits
We formulate the problem of optimizing fuel efficiency as a nonlinear convex optimization problem. This convex problem is then accurately approximated as a large linear program. As a result, we compute the globally minimum fuel consumption over the given drive cycle. This optimal solution is the lower limit of fuel consumption that any control law can achieve for the given drive cycle and vehicle. In fact, this result provides a means to evaluate a realizable control law's performance.
We carry out a practical example using a spark ignition engine with lead acid (PbA) batteries. We close by discussing a number of extensions that can be done to improve the accuracy and versatility of these methods. Among these extensions are improvements in accuracy, optimization of emissions and extensions to other hybrid vehicle architectures.