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An electrical power system (EPS) is subject to unexpected events that might cause the outage of elements such as transformers, generators, and transmission lines. For this reason, the EPS should be able to withstand the failure of one of these elements without changing its operational characteristics; this operativity functionality is called N − 1 contingency. This paper proposes a methodology for the optimal location and sizing of a parallel static Var compensator (SVC) in an EPS to reestablish the stability conditions of the system before N − 1 contingencies take place. The system's stability is analyzed using the fast voltage stability index (FVSI) criterion, and the optimal SVC is determined by also considering the lowest possible cost. This research considers N − 1 contingencies involving the disconnection of transmission lines. Then, the methodology analyzes every scenario in which a transmission line is disconnected. For every one of them, the algorithm finds the weakest transmission line by comparing FVSI values (the higher the FVSI, the closer the transmission line is to instability); afterward, when the weakest line is selected, by brute force, an SVC with values of 5 Mvar to 100 Mvars in steps of 5 Mvar is applied to the sending bus bar of this transmission line. Then, the SVC value capable of reestablishing each line's FVSI to its pre-contingency value while also reestablishing each bus-bar's voltage profile and having the lowest cost is selected as the optimal solution. The proposed methodology was tested on IEEE 14, 30, and 118 bus bars as case studies and was capable of reestablishing the FVSI in each contingency to its value prior to the outage, which indicates that the algorithm performs with 100% accuracy. Additionally, voltage profiles were also reestablished to their pre-contingency values, and in some cases, they were even higher than the original values. Finally, these results were achieved with a single solution for a unique SVC located in one bus bar that is capable of reestablishing operational conditions under all possible contingency scenarios. [ABSTRACT FROM AUTHOR]