ie It is usual to treat DC motors either as field-excited or armature-excited. It is assumed that the mechanical load is composed of a lumped inertia, which has to be driven, together with the inertia of th~ armature of the DC motor, and of friction effects, both load and machine, which are regarded as being entirely linear. This brief summary gives an account of the most common, simplified, mathematical models of electrical machines used in control engineering. No account has been taken of the geometrical dimensionality of the machines, or of the mode of driving them, although these matters are important. They were omitted because they are, to a marked degree, problemdependent. The intention, in producing these simple models, is that they will provide a starting point: no more.

Mathematical Models of Electrical Machines

The objective of the study was the derivation of an algorithm for the selection of a
numerical simulation method for the direct-on-line starting of induction motors from
power supplies whose voltage and frequency may vary during the simulation period.
A major part of the work consisted of an evaluation of methods for treating the
variation of motor parameters under different conditions and the relative effect of
these variations on predicted output. Two new methods were introduced for
predicting the variation of leakage reactance with current and a new method was
developed for deriving the rotor parameter variation with slip for bars of arbitrary, but
known, cross-section.
An existing method was modified to derive model parameters from manufacturer's
quoted performance data. The results are given of an investigation into the effect on
the derived parameters and consequently on the predicted performance, of allowing
the quoted performance data to vary within the tolerances permitted by Australian
Standard 1359.
A set of descriptive measures for simulation output were defined. This enabled the
motor's starting performance to be quantified in terms of a small number of variables.
The factorial method of experimental design was used to calculate relative coefficients
of performance. These related the effect of changes in program input data to the
resultant variation in program output and thus allowed numerical measures to be
placed on the significance of data uncertainty and model complexity as they affected
the simulated performance.
PC-based data acquisition and processing techniques were used to take measurements
from two laboratory motors which confirmed the results of numerical simulation
work.
The broad general conclusion of the thesis was that in most situations, the total
system data needs to be included in the model if the uncertainty is to be improved
beyond that obtainable with simple non-recursive calculations. An expert system shell
was used to present an algorithm for the selection of a method of modelling
appropriate to the quality of the data, the type of system, the purpose of the study and
the availability of computational tools.

An algorithm for the selection of a method for the modelling of direct-on-line starting of cage induction motors from finite supplies

A form of controller/compensator is suggested for the speed control of small induction motors. This controller uses pairs of thyristors in each supply line, incorporated into a resistance/capacitance network. Smooth speed control may be realized over a wide speed range, and the motor current remains substantially sinusoidal. For a small laboratory type motor, the current was reduced by up to 30 percent, and high power factor was maintained over the whole speed range. The overall efficiency of the compensated system increased by about three percent over that of the uncompensated motor.

A Speed and Power Factor Controller for Small Three-Phase Induction Motors

The aim of this work is to investigate the possibility of detecting faults in a 3 phase Induction motor by monitoring and analysing the transient line current waveform during the starting period. This is a particularly onerous time for the machine and the inter-relationships between parameters such as current, torque, speed and time are very complex. As a result two parallel paths of investigation have been followed, by methods of experimentation and computer simulation. Transient line current signals have been obtained from purpose built test rigs and these signals have been analysed in both the time and frequency domains. In order to assist with the comprehension of this data a sophisticated computer simulation of the induction motor during the starting period has also been developed. Computer simulation of the induction motor has been developed initially using the two and then three phase induction motor voltage equations which are solved by numerical integration. Using these techniques it has been possible to detect small degrees of fault level for both wound and cage rotor machines by analysing the line current waveform during the starting period. Good agreement has been found between the real and simulated data. A range of Digital Signal Processing techniques have been utilised to extract the components indicative of rotor faults. These techniques were at first wideband and highly numerically intensive, some originating from Speech Processing. The final processing techniques were far simpler and selected by analysis of the results from experimental data, both real and simulated.

The monitoring of induction motor starting transients with a view to early fault detection.

The meatgrinder is a high-efficiency inductive energy storage
and transfer circuit which may be used to supply high-current
pulsed power requirements in applications such as
electromagnetic propulsion. It overcomes the inherent 25%
efficiency limit when transferring energy between uncoupled
inductors and simultaneously provides current multiplication.
An unloaded six-step demonstration circuit has been used to
multiply current from 7A to 76A at an efficiency of 44%, and a
single-step demonstration circuit has been used to multiply the
current in an uncoupled load induct or from lOA to 30A, the
efficiency of energy transfer being 31%. Both circuits use
power MOSFETs for switching.
These circuits have been used in conjunction with theoretical
analysis and computer simulation to study the design and
performance of the meatgrinder. Investigations have been
carried out in order to confirm the basic theory, to clarify the
details of circuit operation, and to provide the information
necessary for future feasibility studies.

The meatgrinder : an efficient current-multiplying inductive energy storage and transfer circuit

Previous work on the transient performance of induction motors has paid little attention to the effect of variations in winding parameters from some assumed stator/rotor allocation. This paper shows that, based on factorialdesign considerations, a response equation may be derived that expresses the severity of the transient current or torque, or the runup time, in terms of a nominal response, together with contributions derived from the parameter variations. The coefficients of the response expressions for the transients that follow several switching and reswitching operations of a 5.6 kW motor are given. The errors introduced by the use of a fractional factorialdesign plan are shown to be small, and mention is made of typical situations in which the technique described may be useful.

B. Hamill

Papers

Effect of parameter variations on induction-motor transients