Mathematical model of an induction motor for functional diagnostics under supply network voltage unbalance

Abstract

The induction motor is the most widespread device for converting electrical energy into mechanical energy owing to the simplicity of its design. Modern automated technologies, in both industrial and agro-industrial complexes, cannot operate effectively without the use of an induction motor (IM). In both adjustable and non-adjustable electric drives, IMs consume from 60% to 80% of the total electricity consumption of an electrical engineering complex. The annual failure rate of IMs reaches 20–25%, and in some cases up to 30% [1]. Up to 80% of IM failures are caused by insulation damage: frame (ground) insulation failures account for 20–25% of these, while inter-turn insulation failures account for up to 80%. Thus, assessing the technical condition of an IM is a particularly important task for improving the trouble-free operation of an electrical engineering complex. Timely diagnostics of an IM’s condition reduces repair costs and the working-time losses of maintenance personnel associated with unplanned repairs and shutdowns of technological processes. The most promising approach to detecting IM faults is functional diagnostics based on the analysis of phase currents. The aim of the study is to investigate the influence of supply-network voltage asymmetry on the phase current values of an IM, and to obtain an analytical expression for the IM phase current as a function of the voltage asymmetry factor. The paper proves that for a stator winding connected in a “star with isolated neutral” configuration, the effect of supply asymmetry is transmitted exclusively through the negative-sequence component. Importantly, an analytical expression is obtained for calculating the IM phase current as a function of the voltage asymmetry factor, which accounts for the different rotor slip relative to the positive- (s) and negative- (2−s) sequence fields and, consequently, substantially different values of the equivalent-circuit impedances Z1 and Z2; for small- and medium-power IMs, the negative-sequence impedance Z2 is 5–8 times smaller than the positive-sequence impedance Z1, causing the negative-sequence current to grow disproportionately fast with the degree of voltage asymmetry — this effect is the physical cause of increased machine heating even at normatively permissible values of. A numerical example for the 4A80A2U3 induction motor showed that already at= 2% (the normative limit under DSTU EN 50160) the current in the most loaded phase increases by 11.9%, while at= 4% (the limiting value under GOST 13109-97) it increases by 23.9% — an order of magnitude comparable to the typical current change at the initial stage of an inter-turn short circuit. The obtained result substantiates the necessity of mandatorily accounting for the current value of the supply-network voltage asymmetry factor in the calculation (model) component of functional diagnostic methods for detecting inter-turn short circuits in IM stator windings based on phase current magnitudes, specifically in the method for detecting the initial moment of inter-turn short circuit occurrence.Recieved: 12.06.2025. Recieved: 08.08.2026. Accepted: 20.08.2026