Some characteristics of a class of parametric reluctance machines

This paper deals with a class of brushless a.c. reluctance machines capable of operating over a wide speed range when fed from a source of constant voltage and frequency. The principle of operation depends upon the exploitation of the properties of a series RLC circuit in which the stator-winding inductance is a function of both current and rotor position. The system is described by nonlinear differential equations having periodic coefficients. An approximate analytical solution for the flux and current, comprising a series of upper and lower sidebands based on the fundamental supply frequency and shifted by multiples of the shaft speed, permits the calculation of the total average torque in terms of the contribution from individual sideband components. Those sidebands, the frequency of which is closest to the system´s large-signal natural frequency, dominate the solution, and consequently, it has been shown that the efficiency of these machines will be less than 50%. However, the fall in the rotor conversion efficiency with speed is compensated by the increase in effective pole number at slower speeds. The reasonable agreement between measured and theoretical torque/speed characteristics suggests that the model and the approximate solution represent at least the major effects within such machines.