Conceptual method for the detailed analytical calculation of capacitance matrix elements in variable capacitance synchronous machines

Abstract 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.