This paper reviews and assesses the main methodologies for representing static var compensators (SVCs) steady-state behavior in the power flow problem. Different control approaches are considered in each of the models presented, which results in the adoption of the following other state variables: (\textit{i}) reactive power injected; (\textit{ii}) current injected; and (\textit{iii}) thyristor firing-angle. Despite their differences, a \textit{full} Newton method is considered for all methodologies by means of incorporating the respective control equation into the power flow system of nonlinear equations. All propositions were simulated on two different test systems: a 4-bus tutorial system and the IEEE benchmark Nordic system. A Python-based program was developed, and the result simulations were validated by CEPEL’s (Electric Energy Research Center) production-grade academic version software.