A numerical method for solving for the current and field distributions inside devices containing type II superconductors is described. The two-dimensional solution technique accommodates the effects of surrounding media including iron and can handle systems with an arbitrary number of type II superconductors and conventional materials. The technique is based on the finite element method, the method of moments and the critical state model. The impetus behind this work is the study of rotating electrical machines which contain superconducting artefacts placed alongside magnetic materials and current sources. In this paper, a reluctance machine consisting of an iron rotor flanked with two HTS pieces is chosen to demonstrate the method.
A mathematical model of the critical state based on averaged fluxon motion has been implemented to solve for the current and field distributions inside a high temperature superconducting hysteresis machine. The machine consists of a rotor made from a solid cylindrical single domain HTS placed in a perpendicular rotating field. The solution technique uses the finite difference approximation for a two-dimensional domain, discretized in cylindrical polar co-ordinates. The torque generated or equivalently the hysteresis loss in such a machine has been investigated using the model. It was found that to maximize the efficiency, the field needs to penetrate the rotor such that B 0 /µ 0 J c R = 0.56, where B 0 is the applied field amplitude, J c is the critical current density and R is the rotor radius. This corresponds to a penetration that is 27% greater than that which reaches the centre of the rotor. An examination of the torque density distributions across the rotor reveal that for situations where the field is less than optimal, a significant increase in the performance can be achieved by removing an inner cylinder from the rotor.
The use of high temperature superconducting material in its bulk form for engineering applications is attractive due to the large power densities that can be achieved. In brushless electrical machines, there are essentially four properties that can be exploited; their hysteretic nature, their flux shielding properties, their ability to trap large flux densities and their ability to produce levitation. These properties translate to hysteresis machines, reluctance machines, trapped-field synchronous machines and linear motors respectively. Each one of these machines is addressed separately and computer simulations that reveal the current and field distributions within the machines are used to explain their operation.
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