A multi conductor transmission line model for the evaluation of the rotor shaft voltages in adjustable speed drive motors

The use of switching devices, such as IGBTs, characterised by high switching frequencies and very low switching times in new generation pulse width modulation (PWM) inverters has increased the efficiency and performances of Adjustable Speed Drives (ASDs) for industrial and traction applications. However, such systems may be affected by disadvantages like over voltages at the motor terminals, when long cables are used between the drive, and the generation of rotor shaft voltage, due to the capacitive couplings in the motor (between the windings and the rotor and between the rotor and the stator). The shaft voltage may cause the breakdown of the lubricating film in the bearings. The resulting impulsive currents, by damaging the bearing elements shorten the component life, which in turn seriously affects the ASD reliability. For this reason, it is of great importance to develop numerical models able to predict the shaft voltage so as to estimate the currents flowing through the bearings. Several works, based on either concentrated or distributed circuit models, have been proposed for the evaluation of the shaft voltage magnitudes for several motors sizes. However, the results obtained by such approaches suffer from approximations and simplifications in the considered circuit model. Therefore, in the present paper, a numerical model able to accurately predict the shaft voltage in high power induction motor for traction applications fed by a PWM inverter is presented. The windings of the motor are modelled by a multi conductor transmission line (MTL), whereas the cables between the source and the motor are described by a single transmission line. The effect of wave propagation and reflection and of the frequency-dependent distributed losses is considered by using a time-domain equivalent circuit to represent the MTL. A semi-analytical method, based on the perturbation theory of the spectrum of symmetric matrices, is adopted. The parameters of the MTL are obtained either analytically or numerically by using a commercial software (Maxwell® by Ansoft). The effects of the rise time of the input voltage together with the length of the cables are considered.