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This article describes a detailed analytical method for obtaining the capacitance matrix elements in variable capacitance synchronous machines (VCSMs). The analytical modelling approach is performed by introducing a decentralized sinusoidal distribution of the stator/rotor electrodes and involves obtaining the capacitance matrix elements based on the electro motive force distribution in the air gap and calculating the induced electric charge in the stator/rotor electrode surfaces. The proposed analytical formulas are valid for both radial-field and axial-field VCSM structures. The analytical model is evaluated and well verified through analysing a multi-stack axial-field VCSM using 3D finite element simulation. Furthermore, a prototype of the VCSM is manufactured and tested to validate the results obtained from the proposed analytical model and finite element method simulations. Based on the results, the proposed model and analytical formulas are able to accurately estimate the capacitance matrix elements of the VCSMs. Ahmad Darabi is the co-author of this study. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Doubly fed induction machines (DFIMs) are less commonly used as motors in the industry. DFIMs are more commonly designed as doubly fed induction generators (DFIGs) and used as variable speed generators in wind turbines. In this paper, a large‐scale DFIM is studied in steady‐state operation. In this study, using the steady‐state models and equivalent circuits, a comprehensive analysis of the DFIM performance in motor operation mode is performed. Using the simulation results, the behaviour of the motor in all three synchronous, super‐synchronous, and sub‐synchronous modes is analyzed and evaluated in detail. Adjusting and controlling the rotor voltage in DFIMs is very essential. Therefore, a simple method for optimally adjusting the amplitude and angle of the rotor voltage in steady state is proposed for three different optimization scenarios that maximize output power, efficiency, and power factor, respectively. The results show that by properly determining the rotor voltage, the DFIM can perform optimally in a wide range of speed variations.