<p>In battery management systems, the health status of lithium batteries constantly affects the accurate estimation of their charging status and energy status, making the health status particularly important. However, in energy storage systems, rapidly and accurately estimating the health status of lithium batteries, as well as estimating it at an appropriate proportion, has always been a challenge. Therefore, to improve the stable operation of energy storage systems, this paper proposes a model that optimizes a hybrid kernel extreme learning machine using the circle mapping chaotic method and particle swarm optimization algorithm to improve the gray wolf algorithm. First, to address the issues of initialization instability and slow convergence speed in the gray wolf optimization algorithm, the ideas of circle mapping chaos and particle swarm optimization are proposed to replace the position update formula of the gray wolf optimization algorithm, thereby enhancing the algorithm’s stability and convergence speed. Second, to address the limitation of the single learning capability of the kernel extreme learning machine model, a hybrid kernel extreme learning machine model is employed. The generalization and learning capabilities of the entire model are verified through simulation experiments. Finally, simulation predictions are conducted again under different data-splitting proportions to obtain an optimal training proportion, providing additional reference directions for practical application. Experimental results demonstrate that the proposed model maintains a fit above 0.99 for four sets of batteries, and ensures the reliability and reasonableness of the model when using a 50% training set proportion.</p> Graphical Abstract <p></p>