The increasing penetration of renewable resources, particularly wind generation, introduces considerable stochasticity into modern transmission networks, thereby complicating system monitoring, fault diagnosis, and post-disturbance restoration. Sudden fluctuations in wind power injections can distort network states, reduce observability, and hinder the accuracy of conventional protection schemes. As a result, the ability to accurately locate faults and minimize restoration time has become a critical requirement for achieving resilient power system operation. Motivated by these evolving challenges, this paper proposes a comprehensive multi-objective optimization framework for simultaneous fault location and restoration time minimization in a modified IEEE 39-Bus transmission system that incorporates both thermal generating units and probabilistic wind-energy resources.
The proposed methodology extends the OPF-embedded fault-location paradigm established in earlier research by formulating fault resistance, faulted-bus index, and corrective operational decisions as optimization variables. Wind uncertainty is represented using probabilistic forecast distributions, ensuring that the model realistically captures variability in renewable injections. The multi-objective problem is solved using a hybrid MOABC–NSGA-II metaheuristic, chosen for its complementary strengths: the Multi-Objective Artificial Bee Colony (MOABC) algorithm contributes strong global exploration and adaptability under non-convex OPF landscapes, while NSGA-II provides efficient non-dominated sorting, diversity preservation, and convergence control. Together, these capabilities allow the hybrid framework to effectively navigate the intricate solution space induced by fault scenarios and renewable variability. The optimization simultaneously minimizes two conflicting objectives: (i) fault-location mismatch, defined as the error between the measured system quantities and the OPF-estimated post-fault responses; and (ii) restoration time, expressed as a composite of switching, feeder reconfiguration, generator rescheduling, and ramping delays.
The resulting Pareto front reveals the trade-offs inherent in achieving high diagnostic accuracy while reducing operational downtime. Simulation studies were carried out across multiple wind-power uncertainty cases, enabling a robust performance assessment under realistic stochastic operating conditions. Results indicate that the hybrid MOABC–NSGA-II approach consistently outperforms standalone MOABC and NSGA-II algorithms across all tested scenarios. The hybrid formulation achieves smoother, denser Pareto fronts with enhanced convergence behavior and improved solution diversity. Notably, the method demonstrates superior robustness under large wind-power fluctuations, maintaining both accurate fault localization and minimal restoration times even in the presence of significant uncertainty. In addition, the framework exhibits computational scalability suitable for real-world transmission-level applications.
Overall, the proposed hybrid multi-objective OPF-based strategy advances the state of the art in fault management for renewable-integrated grids. By unifying fault localization and restoration optimization within a probabilistically informed decision-support mechanism, the framework provides power system operators with a powerful tool for improving situational awareness and accelerating service recovery. The results underscore the potential of metaheuristic hybridization and uncertainty-aware OPF modeling to strengthen grid resilience and operational reliability in an emerging era of high renewable penetration.
