Optimal Charging of an Electric Vehicle Battery Pack: A Real-Time Sensitivity-Based MPC approach

Lithium-ion battery packs are usually composed of hundreds of cells arranged in series and parallel connections. The proper functioning of these complex devices requires suitable Battery Management Systems (BMSs). Advanced BMSs rely on mathematical models to assure safety and high performance. While many approaches have been proposed for the management of single cells, the control of multiple cells has been less investigated and usually relies on simplified models such as equivalent circuit models. This paper addresses the management of a battery pack in which each cell is explicitly modelled as the Single Particle Model with electrolyte and thermal dynamics. A nonlinear Model Predictive Control (MPC) is presented for optimally charging the battery pack while taking voltage and temperature limits on each cell into account. Since the computational cost of nonlinear MPC grows significantly with the complexity of the underlying model, a sensitivity-based MPC (sMPC) is proposed, in which the model adopted is obtained by linearizing the dynamics along a nominal trajectory that is updated over time. The resulting sMPC optimizations are quadratic programs which can be solved in real-time even for large battery packs (e.g. fully electric motorbike with 156 cells) while achieving the same performance of the nonlinear MPC.