发表机构
The Pennsylvania State University（宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种解析的Koopman谱降阶模型用于锂离子电池单粒子模型，无需训练数据，相比有限体积模型大幅提升计算速度并保持高精度。
AI 中文摘要
基于物理的电池模型为估计和控制提供内部电化学状态，但求解控制固体扩散的偏微分方程可能计算成本高昂。因此，本文针对单粒子模型开发了一种解析的Koopman谱降阶模型。Koopman特征泛函和特征值直接从自伴零通量扩散算子的特征函数推导得出。零模态表示体积平均浓度，非零模态描述衰减的径向梯度，而电流相关表面通量的投影产生一个线性状态空间模型，该模型可重构平均浓度、表面浓度和完整径向浓度。与数据驱动的Koopman模型不同，所提出的公式既不需要训练数据，也不需要经验提升函数。与400控制体积有限体积模型（FVM）在恒定1C放电期间相比，80个Koopman模态的模型实现了负和正表面浓度均方根误差（RMSE）分别为$1.26\times10^{-5}\\,\mathrm{mol/m^{3}}$和$4.10\times10^{-6}\\,\mathrm{mol/m^{3}}$，端电压RMSE为$8.42\times10^{-4}\\,\mathrm{V}$。具有5个和80个Koopman模态的模型分别比FVM模型快约225倍和31倍。这些结果表明了一种物理可解释且计算高效的电池扩散动力学表示方法。
英文摘要
Physics-based battery models provide internal electrochemical states for estimation and control, but solving the partial differential equations governing solid diffusion can be computationally expensive. This paper therefore develops an analytical Koopman spectral reduced-order model for the single particle model. The Koopman eigenfunctionals and eigenvalues are derived directly from the eigenfunctions of the self-adjoint zero-flux diffusion operator. The zero mode represents the volume average concentration, the nonzero modes describe decaying radial gradients, and projection of the current dependent surface flux yields a linear state-space model that reconstructs the average, surface, and full radial concentrations. Unlike data-driven Koopman models, the proposed formulation requires neither training data nor empirical lifting functions. Compared with a 400 control volume finite volume model (FVM) during a constant 1C discharge, the 80 Koopman mode model achieves negative and positive surface concentration RMSE values of $1.26\times10^{-5}\,\mathrm{mol/m^{3}}$ and $4.10\times10^{-6}\,\mathrm{mol/m^{3}}$, a terminal voltage RMSE of $8.42\times10^{-4}\,\mathrm{V}$. The models with 5 and 80 Koopman modes were approximately 225 and 31 times faster than the FVM model, respectively. These results demonstrate a physically interpretable and computationally efficient representation of battery diffusion dynamics.
