A power allocation strategy for hybrid energy storage systems based on an improved starfish optimization algorithm coupled with variational mode decomposition and secondary correction

Abstract Hybrid energy storage system (HESS) power allocation is constrained by decomposition accuracy, optimization efficiency, and coupled operational limits. This paper proposes a multi-stage strategy integrating improved starfish optimization algorithm-based variational mode decomposition (ISFOA-VMD) and secondary correction. Dynamic-window moving-average filtering first extracts the fluctuating photovoltaic power requiring HESS compensation while satisfying grid-connected fluctuation requirements. ISFOA then improves VMD parameter optimization through nonlinear adaptive GP, elite-guided exploitation, and reflective boundary handling. The decomposed frequency components are allocated using a frequency demarcation point determined by minimizing the equivalent annual cost. Low-frequency components are assigned to the lithium battery, whereas high-frequency components are assigned to the supercapacitor. Secondary correction coordinates state-of-charge (SOC) safety and grid-connected fluctuation constraints while mitigating synchronous power reduction between storage devices. The proposed filtering method reduces cumulative HESS compensation energy by 14.92% compared with conventional fixed window filtering. Under the summer benchmark, the maximum 1 min grid-connected fluctuation rate is limited to 8.85%. The supercapacitor and lithium-battery SOC ranges remain at 32.22%–64.37% and 41.07%–72.73%, respectively, under the same condition. All four seasonal datasets satisfy the prescribed 10% fluctuation limit, while controller hardware-in-the-loop verification confirms real-time closed-loop execution capability.