Electromagnetic reactors are used to carry out practical tasks of automatic control of power lines operation modes, distribution grids and energy supply systems of the industrial enterprises. The reactors' characteristics significantly depend on the harmonic's manifestation magnetic field saturation, which is different in the magnetization modes of reactors: forced, free and symmetrical. For the purpose of their analysis, a generalized mathematical model of the cross-sectional magnetic circuits of static ferromagnetic devices with rotating magnetic field has been developed on the base of nonlinear magnetic circuits theories. It was found that the best mode is symmetric magnetization, characterized by the following advantages: an increased range of reactive power control, enhanced stabilizing effect on the controlled current, reduced losses in steel, increased speed and the absence of "shaking" vibrations of the reactor magnetic core. It is shown that the free magnetization mode is close in its merits to the symmetric magnetization mode. © Published under licence by IOP Publishing Ltd.