The need to transition to renewable energy sources (RESs) including wind, solar photovoltaic (PV), and hydro is highlighted by the accelerated depletion of fossil fuel reserves and the increasing need for sustainable power generation. In this regard, the present study explores the use of a probabilistic optimal power flow (POPF) framework that addresses the inherent uncertainties related to the power outputs of various RES technologies. The artificial hummingbird algorithm (AHA), inspired by hummingbirds adaptive foraging behavior, is used to solve the ensuing highly nonlinear, multi-modal problem. Several IEEE 57-bus test systems are used to thoroughly validate the efficacy of the suggested AHA-based POPF model. Comparative studies indicate that the AHA consistently provides notable cost and emission reductions, outperforming advanced metaheuristic approaches in all cases. When compared to coral reef optimization and gray wolf optimizer, the AHA reduces emissions by 1. 74%–3. 08% and costs by 0. 27%–0. 33% in the traditional IEEE 57-bus system. Additional gains are shown with cost reductions of up to 0. 148% and emission reductions of up to 2. 40% when RES units are integrated. AHA achieves the greatest results in the most complicated Test System 3, with an ideal generating cost of 4949 / h and emissions of 1. 0299 t/h. The development of a comprehensive POPF system that concurrently incorporates wind, solar, and hydro power with precise uncertainty modeling and related cost penalties is what makes the study new. The superiority of the suggested solution over sophisticated modern approaches is further shown by extensive statistical assessment of 24-hour dynamic load tests across both IEEE 57-bus system as well as IEEE 118-bus system.
Paul et al. (2026) studied this question.