Some operating conditions of compensated networks are investigated, taking into account nonlinearity of transformers. The load and idle stroke operating conditions of a transformer are considered. Using the example of investigation of the stability of periodic operating conditions in a nonlinear electric circuit, the degree of influence of the type of approximating polynomials, the size of the determinant for the calculation of numerical determinants, and the set values of the amplitude of the flux linkage on the results obtained are clarified. A series of practical and methodical guidance points, facilitating the utilization of the spectrum method of investigation employed in the article, are presented.