Optimal energy management in electric vehicles: convex optimization for model predictive control
Keywords: Energy Management
Electric Vehicles
Model Predictive Control
Convex Optimization

Increased electrification of road vehicles has been identified as an important method of mitigating air pollution and climate change, and the past ten years has seen a paradigm shift in the automotive market towards hybrid, plug-in hybrid, and all-electric vehicles. Electric vehicle battery technology currently suffers from several limitations relating to cost, lifespan, and energy density, so a common approach to electric powertrain design is a hybrid system in which an additional power or energy source is included to reduce the battery’s shortcomings. The performance of a hybrid powertrain is strongly dependent on the control system used to determine the power delivered from each source. Therefore the design of control systems that can balance the power demand in a way that is optimal (in the sense of minimizing fuel consumption, for example) is of great interest to both academia and industry. Model predictive control (MPC) is a strong candidate for this problem as it explicitly considers predictions of future driver and vehicle behaviour together with hard constraints on system performance. However MPC requires that a potentially challenging constrained optimization problem is solved repeatedly throughout a given journey. This introduces a trade off between the closed loop performance of the controller and the tractability of the associated MPC optimization problem.
This thesis presents an investigation into the use of convex optimization for model predictive energy management in electric vehicles. The aim is to generate convex formulations that permit more general descriptions of system dynamics than linear quadratic MPC, whilst still ensuring that the resulting optimization problem can be readily solved online using limited hardware. A particular contribution relative to previous work in the area is the development of optimization algorithms that are specifically tailored to the structure of the resulting convex optimization problem. The major part of the thesis is focussed on energy management in plug-in hybrid electric vehicles (where the objective is to minimize fuel consumption over a given journey), although the methods are extended to all-electric vehicles with hybrid energy storage systems consisting of both conventional batteries and supercapacitors (in this case the objective is to minimize energy consumption and battery degradation). The MPC optimization problem for plug-in hybrid electric vehicles is first formulated considering only the terminal constraint on the battery state of charge, then progressively extended to consider the general state-of-charge constraints, optimal engine switching, and driver behaviour uncertainty. In each case, the performance of the MPC formulation and optimization algorithm is demonstrated in numerical studies, and it is shown the the controllers obtain a highly accurate approximation of the globally optimal solution, whilst dramatically reducing the computational requirement relative to the current state-of-the-art.