Induction Motor Equivalent Circuit
273
resistance motor, so its speed holding as the load changes is better and full-load eYciency can be correspondingly higher. As explained in Chapter 6, these widely diVering characteristics indicate the need to match motor to application. For the sake of completeness, full-load conditions have also been shown, based on an arbitrarily chosen speciWcation that the full-load torque is 40% of the pull-out torque, i.e. Tpo =TX ¼ 2:5. With this constraint, the full-load slips and full-load currents can be calculated using equation (7.21), and thus we can draw up a table summarising the comparative performance of the two motors.
Rotor resistance 0
Low (R2 ¼ 0:1XT ) 0
High (R2 ¼ XT )
Full-load eYciency (%)
Ist If $l
Tst Tf $l
Tpo Tf $l
0.021
97.9
4.85
0.5
2.5
0.208
79.2
3.47
2.5
2.5
sf $l
The full-load points are marked on Figure 7.18: the continuous operating region (from no-load to full-load) occupies the comparatively short section of the locus betweens s ¼ 0 (no-load) to the full-load slip in each case. As already observed, the starting and low-speed performance of the high-resistance motor is superior, but its full-load rotor eYciency is very poor and rotor heating would prevent continuous operation at a slip as high as 21% (unless it was a slipring machine where most of the resistance was external). At normal running speeds the low resistance motor is superior, with its much greater rotor eYciency and steep torque–speed curve; but its starting torque is very low and it could only be used for fan-type loads, which do not require high starting torque. As explained in Chapter 6, the double-cage rotor or the deep-bar rotor combines the merits of both high- and low-resistance rotors by having an outer cage with high resistance and relatively low reactance, in which most of the mains frequency starting current Xows, and an inner cage of relatively low resistance and high reactance. The latter comes into eVect as the speed rises and the rotor frequency reduces, so that at normal speed it becomes the dominant cage. The resulting torque–speed curves – shown typically in Figure 6.9 – oVer good performance over the full speed range. Equivalent circuits for double-cage motors come in a variety of guises, all using two parallel rotor branches, with a variety of methods for taking account of the signiWcant mutual inductance between the cages.