A Planning Method for Synchronous Condensers in Weak Grids Using Semi-Definite Optimization

Synchronous Condensers (SynCons) offer voltage regulation, inertia, and fault current contribution to solve the challenges of voltage and frequency instability introduced by the high penetration of renewable energy resources (RERs). However, the cost of installation and operation of a SynCon is noticeable. Furthermore, the SynCons installation can take more than a year, which means the number, size, and placement of the SynCons must be selected optimally. This paper proposes a method to formulate the optimal sizing and allocation of the SynCons via mixed-integer convex optimization. The optimization procedure aims to minimize the cost of SynCons installation, maintenance, and operation while maintaining a certain Short Circuit Ratio (SCR) at points of connection (PoCs). To ensure the SCR at the PoCs is greater than a certain threshold, the SCRs are formulated as constraints in the proposed optimization procedure. The modified IEEE 39-bus system is used to evaluate the proposed optimization method. The performance of the system with optimal SynCons is verified by electromagnetic transient time-domain simulation using PSCAD/EMTDC software. The simulation results show that the system with the optimal installation of SynCons performs better than the system without the SynCons or with a non-optimal installation of SynCons. With the optimized system, all renewable energy resources are stable after contingencies.