Analysis of power grid operation modes considering the influence of tooth harmonics
Authors: Khomenko Igor , Plakhtii Oleksandr , Shelest Dmytro 
Published: December 2023

A harmonic analysis of the magnetic field of an asynchronous motor was carried out, taking into account bilateral gearing and magnetic asymmetry of the air gap. The spectrum is obtained in the form of infinite series of spatio-temporal harmonic components. Magnetic asymmetry of an asynchronous motor takes into account static and dynamic eccentricity, magnetic asymmetry of steel. 27 different spatial harmonics of the field in the air gap of the induction motor were obtained. The considered spectrum of harmonics of the magnetic field will be induced in the stator windings by the electromotive force with the corresponding frequencies. The fields with γр ± κ pairs of poles rotate asynchronously with the rotor and are damped by the fields created by the currents of the rotor cage. Thus, the magnetic asymmetry affects the spatial harmonics of the magnetic field, changing the angular velocities of their rotation in the air gap. The appearance of magnetic asymmetry causes a redistribution of the spatio-temporal distribution of the harmonics of the magnetic field of the tooth frequency, which leads to a change in the amplitude and phase relationships between the quantities. This leads to the appearance of an asymmetric system of electromotive force of tooth frequency in the stator windings, and, therefore, to a different effect of the asymmetry of the air gap at the level of symmetrical components. In the general case, at the level of symmetric components, the electromotive force of the gear frequency is influenced by two groups of factors that determine asymmetric or different from the nominal operating modes of an asynchronous motor of the same size. An increase in the magnetic asymmetry of the air gap causes a nonlinear, close to parabolic character of the growth of the existing symmetrical components. Symmetric components of the electromotive force of the toothed frequency cause currents of the corresponding components to flow through the closed circuits of the stator windings of the asynchronous motor and the entire power supply system. The calculation scheme for replacing a three-phase network for toothed harmonics of electromotive force is given. The phase resistances of the windings of rotating electric machines for asymmetric three-phase networks are not the same for different sequences. The main method of calculating the considered network is the method of symmetrical components. The calculation is made for one main phase according to the substitution schemes, which corresponds to the symmetrical components of the electromotive force of the tooth frequency. As a result of theoretical studies, functional dependences of the influence of magnetic asymmetry on the level and distribution of phase currents of the toothed frequency were obtained. The nature of the influence at the level of symmetric components is close to parabolic, and the most sensitive to changes in magnetic asymmetry is the minor symmetric component of the zero sequence. The method of calculating the currents and voltages of the toothed frequencies of asynchronous motors in the conditions of power consumption has been developed. Theoretical propositions are confirmed by experimental studies. It has been established that the levels of toothed harmonics in power supply systems, as a rule, do not exceed 10–15 % of the level of the fundamental frequency. This leads to a decrease in the reliability of the operation of electrical networks and a shortening of the service life of the main energy equipment at the enterprise. However, frequency-amplitude resonance at tooth frequencies causes the greatest threat to the power plants of industrial enterprises. This is due to the specific nature of gear harmonics of asynchronous motors (parity, dependence on load and various technological factors). The biggest threat arises when using the same type of asynchronous motors with similar operating modes. Oscillograms of experimental studies are given.