标题： 一种用于主动电池均衡系统的统一模型 显示英文标题

标题： A Unified Model for Active Battery Equalization Systems

摘要： 锂离子电池组需要有效的主动均衡系统来提高其可用容量和寿命。 尽管文献中提出了许多拓扑结构和控制方案，但由于缺乏统一的电池组级数学模型，进行定量分析、全面比较和系统优化仍然具有挑战性。 为解决这一差距，我们引入了一种基于超图的新方法，建立第一个统一的模型，用于各种主动电池均衡系统。 该模型通过将电池单元和均衡器分别表示为超图的顶点和超边，揭示了它们之间的内在关系。 利用所开发的模型，我们通过可控制性分析确定了所有均衡系统实现平衡的必要条件，为选择均衡器数量提供了有价值的见解。 此外，我们证明了电池均衡时间与每个均衡系统的超图拉普拉斯矩阵的第二小特征值成反比。 这显著简化了均衡系统的选取和优化设计，无需进行大量实验或仿真即可得出均衡时间。 示例结果展示了所提出模型的效率，并验证了我们的发现。 显示英文摘要

摘要： Lithium-ion battery packs demand effective active equalization systems to enhance their usable capacity and lifetime. Despite numerous topologies and control schemes proposed in the literature, conducting quantitative analyses, comprehensive comparisons, and systematic optimization of their performance remains challenging due to the absence of a unified mathematical model at the pack level. To address this gap, we introduce a novel, hypergraph-based approach to establish the first unified model for various active battery equalization systems. This model reveals the intrinsic relationship between battery cells and equalizers by representing them as the vertices and hyperedges of hypergraphs, respectively. With the developed model, we identify the necessary condition for all equalization systems to achieve balance through controllability analysis, offering valuable insights for selecting the number of equalizers. Moreover, we prove that the battery equalization time is inversely correlated with the second smallest eigenvalue of the hypergraph's Laplacian matrix of each equalization system. This significantly simplifies the selection and optimized design of equalization systems, obviating the need for extensive experiments or simulations to derive the equalization time. Illustrative results demonstrate the efficiency of the proposed model and validate our findings.