Hybrid energy storage systems for photovoltaic storage microgrids power allocation and capacity determination based on adaptive Savitzky-Golay filtering and VMD-DTW

• Adaptive SG filtering achieves a balance between smoothing effect and cost. • The SG parameter optimization model solved by improved DBO enables flexible PV fluctuation adaptation. • VMD-DTW method achieves reasonable hybrid storage energy power allocation. • Models for SOC dynamics and capacity costs are established to determine the most economical storage capacity. In the photovoltaic storage microgrid, fluctuations in PV power generation are mitigated by the Hybrid Energy Storage System (HESS). However, excessive smoothing exacerbates storage burdens while meeting grid-connection standards, and improper power allocation within the storage system escalates costs. To address these challenges, an optimization model for Savitzky–Golay (SG) filtering parameters is formulated. An enhanced dung beetle optimization algorithm is employed to optimize this model, enabling adaptive parameter adjustments in SG filtering. This approach reduces energy storage burdens by trading off smoothing effects while adhering to grid-connection requirements. Upon obtaining the compensated power from HESS, a power allocation method based on Variational Modal Decomposition (VMD) and Dynamic Time Warping (DTW) is proposed. Additionally, a State of Charge (SOC) dynamic transformation model and a full life cycle-based HESS cost model are constructed to quantitatively assess the method’s efficacy and advantages. Simulations using PV power generation data from different seasons in a demonstration project in Hebei Province, China, confirm that this strategy effectively alleviates energy storage burdens and reduces system costs.