Multi-Stage Probabilistic Transmission Expansion Planning Under Generation Uncertainty and N-1 Security Using the Pack-Based Grey Wolf Optimizer

Multi-Stage Transmission Network Expansion Planning (MS-TNEP) is critical for adapting power grids to long-term renewable integration. However, the simultaneous incorporation of N-1 security, active power losses, and uncertainties regarding the spatial and temporal growth of power generation capacity imposes prohibitive computational complexity. This paper proposes a probabilistic MS-TNEP model evaluated over a 20-year horizon. To overcome this computational intractability, a hybrid decomposition framework is employed. The investment subproblem determines the discrete decisions for network investment via a metaheuristic, while the probabilistic operation subproblem utilizes linear programming to assess the operational feasibility of these decisions under multiple spatial and temporal growth of power generation capacity scenarios, active power losses, and N-1 contingencies. Furthermore, a novel Pack-Based Grey Wolf Optimizer (PBGWO) is introduced. The approach is validated on the Garver and the Southern Brazilian equivalent systems under multiple scenarios for the growth of both wind and conventional power generation capacity. Comparative analysis against the Genetic Algorithm, the standard Grey Wolf Optimizer, and the Whale Optimization Algorithm reveals that PBGWO is a highly competitive approach for MS-TNEP problems, consistently identifying the most cost-effective expansion plan.