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Lithium-ion battery packs are usually composed of hundreds of cells arrangedin series and parallel connections. The proper functioning of these complexdevices requires suitable Battery Management Systems (BMSs). Advanced BMSs relyon mathematical models to assure safety and high performance. While manyapproaches have been proposed for the management of single cells, the controlof multiple cells has been less investigated and usually relies on simplifiedmodels such as equivalent circuit models. This paper addresses the managementof a battery pack in which each cell is explicitly modelled as the SingleParticle Model with electrolyte and thermal dynamics. A nonlinear ModelPredictive Control (MPC) is presented for optimally charging the battery packwhile taking voltage and temperature limits on each cell into account. Sincethe computational cost of nonlinear MPC grows significantly with the complexityof the underlying model, a sensitivity-based MPC (sMPC) is proposed, in whichthe model adopted is obtained by linearizing the dynamics along a nominaltrajectory that is updated over time. The resulting sMPC optimizations arequadratic programs which can be solved in real-time even for large batterypacks (e.g. fully electric motorbike with 156 cells) while achieving the sameperformance of the nonlinear MPC.

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