Dual-Stage MPC for SoC Balancing in Second-Life Battery Energy Storage Systems Based on Delta-Connected Cascaded H-Bridge Converters

Using second-life batteries (SLBs) to build battery energy storage systems (BESSs) yields substantial environmental and economic benefits. The cascaded H-Bridge (CHB) converter has emerged as an attractive candidate to integrate SLBs into the electrical grid, allowing the unbalanced power distribution among its sub-modules (SMs) with high efficiency and a low estimated cost. However, capacity differences among SLBs pose further challenges for the control system in meeting the BESS power constraints, while balancing the state-of-charge (SoC) of SLBs. This work proposes a dual-stage model predictive control (DS-MPC) strategy to balance the SoC of SLBs using a delta-connected CHB (DCHB) converter. The formulation of the proposed DS-MPC strategy is based on a discrete-time SoC dynamic model, which considers the SM modulating signals and the DCHB circulating current reference in the rotating synchronous $dq$-frame as control inputs. In this way, the proposed DS-MPC strategy obtains optimal charging and discharging currents for each SLB-SM by solving two sequential optimizations, which include maximum current ratings and converter modulation constraints, ensuring the safe operation of the BESS. Experimental results that verify the effectiveness of the proposed DS-MPC strategy are provided for a DCHB converter with nine SMs connected to Lithium-ion SLB packs of different capacities.