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This paper presents new methodologies for modeling static VAr compensators (SVCs) in the power flow problem. The proposed formulations utilize sigmoid functions to model the control equations that describe the steady-state behavior of SVCs. The first methodology introduces reactive power injection as a new state variable, while the second methodology utilizes the thyristor firing angle. These steady-state SVC methodologies were applied to the power flow problem using the full Newton formulation, which incorporates the control equations into the system of nonlinear equations. One of the main contributions of these proposed methodologies is that they eliminate the need for alternating adjustments concerning the operational limits of the SVC during the iterative power flow process. The implementation of a power flow program was tested on both small-scale tutorial systems and the medium-scale IEEE Nordic system. The presented results validate and demonstrate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]