An adaptive modified Newton–Raphson-based optimizer for efficient optimal power flow performance under multiple operating conditions

The optimal power flow (OPF) problem is essentially about finding the cheapest and safest way to operate a power system without breaking any of the operational limits that govern it. In this paper, we introduce a new Modified Newton-Raphson-Based Optimizer (MNRBO) specifically designed to tackle real-world OPF problems, integrating renewable photovoltaic sources. The NRBO integrates gradient-inspired search using the NR search rule and the trap avoidance strategy. Our MNRBO extends this framework by adding two adaptive components. An Adaptive Crossover Mechanism (ACM) is added that lets solutions dynamically exchange useful information with each other, keeping the population diverse and preventing everyone from getting stuck in the same mediocre spot too soon. Also, a Sigmoid decay mode that smoothly and gradually shifts the algorithm from broad exploration (looking around the whole search space) in the early stages to careful fine-tuning (exploitation) toward the end. This gives much steadier and more predictable convergence than the original abrupt or polynomial decay. The resulting MNRBO algorithm forms a self-evolving optimization framework that automatically adjusts its learning strategy as the search progresses. We thoroughly tested MNRBO on the standard IEEE 30-bus system across a wide range of realistic scenarios: minimizing fuel costs (with smooth quadratic models, valve-point ripples, and multi-fuel options), handling generators with prohibited operating zones, and minimizing transmission losses under normal, peak, and light-load conditions. In every single case, MNRBO delivered better solutions, faster and more consistent convergence, and dramatically lower variation across multiple runs compared to the original NRBO and several other state-of-the-art algorithms. The results clearly show that MNRBO is not only more accurate but also far more robust and dependable, exactly what operators need when solving OPF in real power systems where reliability really matters. To further validate the applicability of the proposed approach under renewable energy uncertainty, a probabilistic OPF framework incorporating photovoltaic renewable generation is developed. In this case study, the integration of renewable solar photovoltaic energy in conditions of variable irradiance is examined using the Point Estimate Method (PEM) with lognormal irradiance modeling. In addition, an ablation study is conducted to quantify the individual contributions of the ACM and sigmoid decay strategy in the presence of renewable photovoltaic sources, demonstrating their significant impact on convergence stability, robustness, and optimization accuracy.