On Modeling and Optimal Control of Modular Batteries: Thermal and State-of-Charge Balancing

Doctoral thesis, 2016

There has in recent years been an increasing interest in battery-powered electrified vehicles (xEVs) to reduce carbon footprint of transportation and the dependence on fossil fuels. Since the battery pack of xEVs is one of the most expensive but a key component in the powertrain, the battery lifetime is an important factor for the success of xEVs. Thermal and state-of-charge (SOC) imbalance is well known to cause non-uniform ageing in batteries. This thesis formalizes the simultaneous balancing of temperature and SOC, which are two conflicting objectives, using load sharing concept. This concept is realized using a cascaded converter based air-cooled modular battery, which allows cell-level control including cell-shunting. It can be operated using unipolar (UPC) and bipolar (BPC) control modes i.e., two- and four-quadrant module operation. The optimal control problem is to decide the power distribution among battery modules such that the total power/voltage demand is satisfied, all modules remain fairly balanced in terms of SOC and temperature, and physical limits are not violated. In addition to control design, the particular investigations include the requirements on battery control mode and the load intensity/prediction for the problem feasibility, the controller's structural and functional properties to understand and characterize its internal working, and control robustness under parametric variations. The control problem is formulated offline as a constrained convex quadratic program, which uses the averaged battery electro-thermal model and the full future load information to generate global optimal load distribution as a benchmark for other suboptimal controllers. For online applications with limited future information, a model predictive control (MPC) scheme is proposed for load management under both UPC and BPC modes. It is based on a novel idea of orthogonal decomposition of controller into two additive components namely voltage and balancing controls. The performance is thoroughly evaluated through simulations under various driving situations, prediction horizons, and modeling uncertainty. Using the structural insight offered by the orthogonal control decomposition, two simple computationally efficient control algorithms (so-called projected LQ and gain-scheduled proportional control) are proposed for real-time implementation. These control simplifications reveal two dominant modes of the balancing controller and completely unfold its internal working, allowing its simple rule-based implementation. This study concludes that the UPC mode using one-step state prediction is sufficient to achieve robust balancing performance under most driving situations, which do not demand continuously high load current.