Analytical Expression for the No-Load Starting Current of an Induction Machine Under Direct-Online Conditions

Direct-on-line (DOL) starting of induction machines (IMs) is accompanied by pronounced transient phenomena, primarily high inrush currents that may have adverse effects on both the machine itself and the power system. This paper presents a closed-form analytical approach for determining the no-load starting current of an IM as a function of time. The proposed expression is derived by combining an analytical description of slip variation during the start-up process with a Thevenin equivalent circuit. The accuracy and applicability of the developed model are validated on two IMs with different rated powers. The analytically obtained speedtime and current-time characteristics are compared with reference results obtained in the MATLAB/Simulink environment under various operating conditions, including different rotor inertia values and supply voltages. The results demonstrate very good agreement throughout the entire acceleration process, confirming the robustness of the proposed analytical formulation.