Synchronous Condenser Placement for Multiple HVDC Power Systems Considering Short-Circuit Ratio Requirements

High voltage direct current (HVDC) power injections decrease power systems' short-circuit ratio (SCR) and the grid strength. They may cause voltage stability problems, especially in systems with a high share of renewable. The synchronous condenser (SynCon) is a promising solution for increasing the SCR. However, planning SynCons to meet the SCR requirements is challenging since the SCR requirement is a set of nonlinear eigenvalue inequality constraints that are not friendly to solvers. Based on generalized spectral decomposition, this paper proposes a Rayleigh cut method to equivalently transform eigenvalue inequality constraints into a set of linear constraints. Then, a mixed-integer linear programming model is built to solve the SCR-constrained SynCon placement problem. The proposed approach's convergence, complexity, and error analysis are all analyzed theoretically. Also, numerical comparisons with the other seven models suggest the proposed model is effective and efficient, outperforming the other models in terms of solution quality and computation time.