Optimization scheduling of off-grid hybrid renewable energy systems based on dung beetle optimizer with convergence factor and mathematical spiral

With the rapid development of renewable energy and the increasing modernization demands in remote areas, offgrid hybrid renewable energy systems (HRES) have become a key technology for achieving sustainable development. This paper presents an improved Dung Beetle Optimization (DBO) algorithm that enhances step size by introducing six elementary functions as convergence factors. It combines polar coordinate expressions of three different mathematical spirals, multiplied by a zeroing factor related to the number of iterations, resulting in six distinct mathematical images that optimize the algorithm's dancing path, thereby enhancing global search capability. Experiments on the CEC2022 test functions demonstrate improved optimization performance of the algorithm. Furthermore, the algorithm is applied to the optimization design of off-grid HRES, integrating configurations such as photovoltaic panels, wind turbines, biomass generators and various battery types (Lead Acid battery/Lithium-Ion/Nickel-Iron), with lifecycle cost as the objective function while assessing energy costs. The results indicate that the nickel-iron battery system optimized by the improved DBO algorithm achieves the lowest lifecycle cost ($961,139) and energy cost ($0.3607/kWh), requiring a total of 1329 PV panels, no wind turbines, and 268 nickel-iron battery units.