This paper describes a methodology and specifics for technical studies on fault-induced delayed voltage recovery (FIDVR) mitigation to ensure power system reliability. Optimal locations of the dynamic volts-ampere-reactive (VAR) sources are determined for addressing the FIDVR issues in the voltage stability analysis and assessment methodology. We propose a voltage stability analysis method for planning dynamic VAR sources for bettering electric power transmission systems under contingency conditions. A time-domain dynamic simulation is performed to assess short-term voltage stability. While conducting dynamic simulations, sensitivity analysis is performed to assess the need for dynamic VAR sources. This study focuses on a reactive power compensation strategy to determine system voltage recovery performance by optimal flexible alternating current transmission system (FACTS) placement in a metropolitan region. The objective of this study is to determine the optimal installation of dynamic VAR sources while satisfying the requirements of voltage stability margin and transient voltage dip under a set of criteria. New insights are presented on the effect of FACTS controls on the reactive power compensation, which supports voltage recovery. The main features of the proposed method are (i) the development based on a load model for FIDVR, (ii) the use of sensitivity analysis of the network to the variations of the IM load, (iii) the establishment of the control function and compensation strategy to maintain the voltage of system within criteria limits, and (iv) the use of the sensitivity analysis based on branch parameterization for unsolvable cases. Case studies on the Korean power system validated the performance of the proposed strategy, showing that it effectively installed FACTS under contingency scenarios.