Optimal Allocation of Synchronous Condensers in Weak Grids with Variable Search Spaces

Synchronous condensers (SCs) are among the leading solutions to maintain grid strength in power systems increasingly dominated by inverter-based resources (IBRs). When grid strength issues affect large network areas, determining the optimal size and location of SCs becomes a large-scale optimization (LSO) problem, and its computational cost increases significantly with the number of candidate buses for SC placement. This paper presents a novel methodology that enhances current practices by solving the optimization problem with reliable performance across variable search space sizes. The proposed nonlinear optimization model incorporates the effective short-circuit ratio to ensure compliance with minimum grid strength requirements. Case studies based on a modified IEEE 39-bus benchmark system validate the proposed approach and demonstrate its effectiveness to find the global optimum solution. The results highlight the importance of algorithm selection, since single-solution-based methods fail to identify feasible solutions in large search spaces.