Bilinear models of electric power systems (EPS) are used to analyze small-signal and transient stability, evaluate states and parameters, and also reduce the order of large-scale models. In particular, they allow the analysis of various bilinear effects in power systems and nonlinear characteristics of phase measurement units. However, it is not easy to find sufficiently accurate bilinear test models of EPS in the literature. In this study we derive a set of equations for nonlinear model of two-area four-generators power system with six-order generator model. We obtain the Taylor series expansion of this model to quadratic terms. These formulas are the basis for a bilinear test model. In particular, they allow one to perform the Carleman bilinearization procedure and explore the application of various modal analysis methods to the essentially nonlinear system like EPS.