Optimizing torque distribution for enhanced energy efficiency in battery electric vehicles

Doctoral thesis, 2025

This thesis addresses the energy management problem (EMP) in battery electric vehicles (BEVs), focusing on the optimization of velocity trajectories and torque distribution in vehicles equipped with multiple electric motors. Optimization-based control allocation is a widely used method for coordinating motor redundancy to enhance energy efficiency. It is based on the simplifying assumption that vehicle motion control and actuator coordination can be addressed independently. In other words, it assumes that the two subproblems constituting the EMP, i.e., finding the energy-optimal velocity trajectory and torque distribution, can be solved sequentially, as opposed to simultaneously. However, it is found in this thesis that the two subproblems are inherently coupled, as the optimal velocity trajectory depends on the efficient regions of the motors.
The first part of this thesis investigates the energy consequences of solving the EMP sequentially versus jointly in a BEV with two electric motors, one per axle. Two optimization architectures are evaluated: a centralized architecture (CA) and de-centralized architecture (DCA). CA jointly optimizes the velocity trajectory and torque distribution for minimal energy consumption in a predictive framework, while DCA solves these subproblems hierarchically: velocity trajectory optimization is performed predictively, and torque distribution is computed instantaneously. This decoupling leads to an increase in energy consumption of 3.5% at low velocities, 2.2% in an urban city cycle, and up to 8.2% at high peak road grades compared to CA. To mitigate the energy consequences, the objective function in the predictive layer of DCA is augmented with an aggregated power loss map (APLM), which achieves energy savings close to CA.
The second part of the thesis explores torque allocation strategies in a BEV with four identical permanent magnet synchronous motors (PMSMs) to minimize motor and tire power losses during moderate driving. Due to the significant idle losses of PMSMs, mechanical decoupling is crucial and identified as the main source of energy savings. A quadratic programming (QP) algorithm is developed to optimize torque distribution and manage couplings, reducing energy consumption by 3.9% compared to equal torque distribution; without couplings, the reduction drops to 0.2%. Tire losses, including lateral slip losses during cornering, are found to have minimal impact on energy consumption compared to motor losses during moderate driving. In addition, the single-speed transmission ratios of the front and rear motors are optimized for minimal energy consumption, alongside torque distribution. When coordinated optimally, the optimal ratios result in one axle configured for low-speed and the other for high-speed efficiency. This leads to a reduction in energy consumption by 8.4% compared to a setup with equal torque distribution and equal transmission ratios.
In summary, during moderate driving, knowledge of motor losses is found to be the most significant contributor to reducing energy consumption in BEVs by optimizing the speed profile and torque distribution.