Sustainable cities and societies through innovative optimization of off-grid biomass/photovoltaic/battery and wind/photovoltaic/battery hybrid systems under diverse climatic conditions

• Enhanced Whale Optimization Algorithm integrates rotational dynamics for efficiency. • Rotation matrix improves exploration, diversifies search, and escapes local optima. • Optimized Biomass/PV/Battery and Wind/PV/Battery systems power remote areas affordably. • Algorithm cuts energy costs by 42% vs PSO, achieving 0.0548 US$/kWh for biomass systems. • Faster convergence and reduced power loss highlight robust optimization for sustainability. Hybrid energy systems, combining multiple renewable resources, require effective optimization to improve efficiency and cost. However, many state-of-the-art metaheuristics suffer from premature convergence and weak exploration in high-dimensional spaces. To address this, this work introduces a Whale Optimization Algorithm with Rotational dynamics (WOAR) that augments the canonical WOA position update with an orthonormal rotation operator. This simple but powerful change diversifies search directions at each iteration, strengthens global exploration without sacrificing local refinement, and reduces the tendency to stall near local optima, advantages that distinguish WOAR from previously published WOA variants that rely solely on scalar encircling/spiral moves. The method’s practical value is demonstrated on real hybrid power-system design problems under two markedly different climates (humid-equatorial and Sahelian), showing that the same optimizer and hyperparameters scale across resource regimes and load profiles. The paper’s contributions are threefold: (i) a mathematically compact rotational update for WOA with clear intuition and low computational overhead; (ii) a rigorous benchmark against established optimizers for sizing biomass/photovoltaic/battery and wind/photovoltaic/battery systems, evaluated on standard metrics, loss of power supply probability, net present cost, and levelized cost of energy; and (iii) evidence of robustness and transferability under heterogeneous climatic conditions, supporting regional energy planning where data, costs, and resource patterns differ. Comparative evaluations against Particle Swarm Optimization and Whale Optimization Algorithm were performed to assess performance. The results show that the enhanced Whale Optimization Algorithm achieves superior convergence speed, solution quality, and computational efficiency. Specifically, WOAR achieves an LCOE of US$ 0.0548/kWh, compared to US$ 0.0957/kWh with WOA and US$ 0.1657/kWh with PSO, which corresponds to 42.7% lower than WOA and 66.9% lower than PSO. For the Wind/Photovoltaic/Battery system, the present technique exhibited the lowest Net Present Cost at US$ 62,000, a significant reduction compared to Particle Swarm Optimization (US$ 100,000) and Whale Optimization Algorithm (US$ 86,000). The Loss of Power Supply Probability was minimized to 0.129, outperforming the benchmarks. Additionally, this method achieved comparable runtime while delivering superior solution quality and faster convergence. These findings underscore the robustness and adaptability of the proposed approach across standard techno-economic criteria in renewable energy systems, making it a promising tool for sustainable energy planning and deployment.