The equivalent circuit is valuable for designing an induction machine and its driving system, and its parameters are essential for analyzing the electromagnetic performance and establishing the driving model, especially the magnetizing inductance that characterizes the main flux distribution in the machine. The finite element analysis can precisely determine the magnetizing inductance. However, it is unsuitable for the initial design stage when the design parameters need frequent adjustment. Traditional analytical calculations like the flux linkage method neglect the influence factors, such as core saturation, tooth-slot effect, and rotor movement in the actual operation, causing accuracy issues. The improved analytical calculation method can significantly enhance the accuracy. However, the magnetic circuit in each core segment still needs to be more accurate, and the local saturation points are easily ignored. Besides, the solving process contains nonlinear iterations of multi-segment of the magnetic circuit, which has repeating calculations under different slips.

This paper proposes an elementary layer method based on the main and leakage magnetic circuits to calculate the magnetizing inductance. Firstly, the magnetic voltage drop of each pole of the main magnetic circuit under different air-gap flux densities is calculated, and the magnetic voltage drop and the air-gap flux density are converted into the electromotive force and the magnetizing current to obtain the objective function. Secondly, the distribution of the leakage flux in the stator slot and the current induced in the rotor bar is analyzed to calculate the slot leakage inductance of the stator and rotor, together with the rotor AC resistance. The stator terminal voltage expression is constructed as the constraint condition. Finally, each set of the electromotive force and the magnetizing current on the objective function are substituted into the constraint condition to make the results equal to the rated phase voltage of the stator. The ratio of the set is the value of the magnetizing reactance, and therefore, the magnetizing inductance is obtained. In the main and leakage flux circuits, the irregular and nonlinear magnetic and electric circuits are regularized and linearized using the thin layer elements to substitute theoretical integral. Hence, the tooth-slot structure and the nonlinear material properties can be considered more accurately when calculating the magnetic voltage drop and leakage inductance.

A wet submersible induction machine is an example of the analytical calculation of the magnetizing inductance using the proposed elementary layer method and the traditional flux leakage method. Besides, the steady-state outputs of the equivalent circuit are obtained. The prototype test and the finite element simulation under the magnetic saturation of the stator teeth are conducted. The results show that the elementary layer method considers the distribution of the magnetic voltage drop in the core segment, which is more effective than the flux linkage method when the tooth magnetic circuit is saturated. Therefore, the calculation of the magnetizing inductance is more accurate, and in the steady-state outputs of the equivalent circuit, the stator current, input power, and power factor curves are consistent with the finite element analysis. The error is less than 0.5% when the finite element results are used as the reference. The proposed method links the design parameters and the magnetizing inductance, providing convenience for the initial design and optimization of the submersible induction machine and other types of machines.