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, simultaneously incorporating N-1 security, active power losses, and spatial generation uncertainties imposes prohibitive computational complexity. This paper proposes a probabilistic MS-TNEP model evaluated over a 20-year horizon. To overcome intractability, a hybrid decomposition framework is employed, delegating discrete combinatorial investment decisions to an upper-level metaheuristic while resolving operational feasibility, power losses via fictitious nodal demand, and N-1 contingencies through lower-level linear programming. Furthermore, a novel Pack-Based Grey Wolf Optimizer (PBGWO) is introduced to enhance convergence in this constrained domain. The approach is validated on the modified Garver and the 46-bus Southern-Brazilian systems under multiple wind and conventional generation scenarios. Comparative analysis against the Genetic Algorithm, standard GWO, and Whale Optimization Algorithm reveals that PBGWO consistently identifies the optimal expansion schedules.