An MILP Model for Optimal Placement and Sizing of Synchronous Condensers in a Weak Grid

With the increasing proliferation of inverter-based resources (IBR), the strength (measured by short-circuit ratio [SCR]) and inertia of the power system are decreasing. This is because IBRs do not have the rotational inertia of conventional synchronous generators (SG), and they do not contribute to short-circuit fault currents as much as SGs do. As a result, the IBRs may not have sufficient fault ride-through (FRT) capability in a weak grid. Installing synchronous condensers (SC) is a solution to compensate for reduced strength and inertia because SCs can provide rotational inertia and voltage support by injecting reactive power. However, SCs are expensive, and their capital, operational, and maintenance costs need to be minimized by determining the optimal size and location of newly installed SCs. This paper proposes a mixed-integer linear programming (MILP) model for optimal placement and sizing of SCs, aiming to minimize the total cost of SCs and maintain the SCR above a desired value at the point of connection of all IBRs. By taking into account the fault current contribution from IBRs, the proposed method reduces the total size of SCs by 6.25%–51.08% and the associated costs by 3.2%–34.2% compared to previously proposed methods. The MILP formulation efficiently achieves near-optimal solutions, enabling rapid scenario analysis for grid planners. The results of electromagnetic transient simulation in the PSCAD/EMTDC software confirm that installing the optimally sized and placed SCs provides rotational inertia and voltage support, thus enabling the IBRs to ride through faults.