Method and/or apparatus for controlling the motor speed of an electric AC motor and/or a method of determining torque

DETAILED DESCRIPTION OF THE INVENTION In this specification the units p.
u.
used refer to proportions of the rated value of that unit.
Considering the terminal voltage and current of a squirrel-cage induction motor producing torque M but constrained to operate with constant slip-frequency .
omega.
.
sub.
s.
Then using the per-phase equivalent circuit shown in FIG.
1 the torque M is given by the well known expression: ##EQU3## where p=the number of pole pairs in the machine and the other symbols are as shown in FIG.
1.
Note that the machine has been assumed to be three phase, but this purely for convenience as the technique is applicable to motors with any number of phases.
Re-arranging equation (1) leaves ##EQU4## The input current I.
sub.
1 is given by ##EQU5## With typical machine parameters and noting that operation is at constant slip so that the minimum possible value for .
omega.
is .
omega.
.
sub.
s the magnitude of V.
sub.
1 may be approximated within 1-2% by ##EQU6## while the magnitude of the terminal current I.
sub.
1 is, from equation (5) ##EQU7## At any frequency .
omega.
with rated slip .
omega.
.
sub.
s and torque M the terminal voltage and current are therefore ##EQU8## We define the 1 p.
u.
value of .
vertline.
I.
sub.
1 .
vertline.
(i.
e.
the rated machine current) to be given by equation (11) when rated torque occurs with rated slip independent of the frequency.
The 1 p.
u.
value of .
vertline.
V.
sub.
1 .
vertline.
we take to be frequency dependent at rated torque according to the expression ##EQU9## where M.
sub.
r is the rated machine torque.
Then, in the general case at frequency .
omega.
with torque M we have ##EQU10## Also from equation (3) the air gap voltage in the machine V varies with frequency and the load torque.
Thus the machine's air-gap flux, which is proportional to V/.
omega.
, is exactly proportional to the square root of the load torque for this control strategy.
In per unit terms, therefore the machine flux is also .
sqroot.
M/M.
sub.
r pu.
In practice however the flux cannot be simply determined so that a controller based on voltage measurements is a more practical device especially considering that the 1 pu voltage expression is from equation (12) a linear function of the frequency