Optimal Cell-to-Cell Balancing Topology Design for Serially Connected Lithium-Ion Battery Packs

A battery pack can see energy imbalance among its cells resulting from cell-to-cell variation in capacity, internal resistance, and other parameters. Its successful and safe operation thus necessitates dynamic energy equalizing to adjust each cell's state-of-charge to the same level. The cell equalizing system for a serially connected battery pack is modeled as a multiagent system here. A consensus-based state-of-charge equalizing algorithm is proposed with its convergence proved through theoretical analysis. Following this development, an interesting and important problem is investigated: how to add extra individual cell equalizers or edges to the original cell equalizing system's topology to maximally accelerate the equalizing process. It is found that the balancing time depends on the algebraic connectivity of the topology graph, which is measured by the second smallest eigenvalue of the graph's Laplacian matrix. Then, a combinatorial 0-1 optimization problem is formulated and addressed to optimally choose added edges that lead to the maximum increase in the algebraic connectivity. The proposed results are validated through simulation and experiments, which demonstrate that the balancing time can be significantly reduced by just adding one optimal individual cell equalizer to the original cell equalizing system.