Method for calculating the main and differential leakage inductances of the stator winding using the energy method in machines with a uniform air gap

Abstract

Relevance: the accurate determination of the main and differential leakage inductances of the stator winding remains a critical task in the design of alternating current electrical machines. These parameters significantly influence the machine's dynamics, stability, and energy efficiency. In modern designs featuring fractional slot numbers, magnetic core saturation, and complex winding structures, standard calculation methods often lack sufficient accuracy. The energy-based method proposed in this work accounts for both the fundamental and higher harmonic components of the magnetic field in the air gap. This makes it an effective analytical tool for conditions close to real-world operation. The relevance of the method is confirmed by its applicability to synchronous generators with a wide range of design parameters.

Aim: to develop and substantiate an energy-based method for calculating the main and differential leakage inductances of the stator winding in electrical machines with a uniform air gap, taking into account the structural features of the windings and the influence of higher-order harmonics of the magnetic field.

Methods: the work employs an energy-based method grounded in the calculation of electromagnetic energy stored in the machine’s air gap. For magnetic field analysis, harmonic decomposition and numerical methods for summing spatial harmonics were used. The calculations were carried out using a computational model implemented on a computer, taking into account the winding’s structural parameters, magnetic core saturation, and current distribution in the slots.

Results: A calculation methodology for the main and differential leakage inductances of the stator winding was developed and implemented based on the energy method. A numerical analysis was performed for a synchronous generator of type MSA 72/4, demonstrating the high accuracy of the method. It was established that under three-phase supply, the differential inductance is weakly dependent on magnetic saturation, whereas the main inductance changes significantly. It was also found that under single-phase supply, the influence of higher-order harmonics becomes more pronounced, leading to an increase in differential inductance.