This study covers completely the modeling and simulation methods needed for a detailed study of the steady-state operation of electrical power systems containing a power electronic controller: the series connected matrix converter. The matrix converter has a link with the transmission line between two transformers. Such a compensator controls the phase-angle and magnitude of voltage node. The chief aim of this study was to show how the appropriately modified Jacobian matrixes are augmented to the conventional power flow Jacobian. Three models of matrix converter for analysis of power flow are proposed which can be employed in steady state control of one of the ensuing variables: (1) the nodal voltage; (2) the real power flowing through the line and (3) both of the nodal voltage and the active power flowing through the line. Jacobian matrixes for any feasible operation of the device are derived. MATLAB/mfile codes are used to evaluate the numerical results for 6-bus system, IEEE 14-bus, 57-bus and 118-bus systems. Numerical examples on these standard power test systems are employed to show the models viability in Newton-Raphson power flow algorithm.