0195136047.pdf

494 MAGNETIC CIRCUITS AND TRANSFORMERS

VHIH

1000

=

2640 × 208. 33

1000

=550 kVA

or

VXIX

1000

=

2400 × 229. 16

1000

=550 kVA

which is 11 times that of the two-winding transformer. The transformer must boost the

currentIHof 208.33 A through a potential rise of 240 V. Thus the kVA transformed by

electromagnetic induction is given by

240 × 208. 33

1000

=50 kVA

The remaining 500 kVA is the conducted kVA.

(c) With the currents and voltages shown for the autotransformer connections, the losses

at full load will be 823 W, the same as in Example 11.4.2. However, the output as an

autotransformer at 0.8 power factor is given by

550 × 1000 × 0. 8 = 440 ,000 W

The efficiency of the autotransformer is then calculated as

η=

440,000

440,823

= 0. 9981 ,or 99.81%

whereas that of the two-winding transformer was calculated as 0.98 in Example 11.4.2.

Because the only losses are those due to transforming 50 kVA, higher efficiency results

for the autotransformer configuration compared to that of the two-winding transformer.

11.7 LEARNING OBJECTIVES

Thelearning objectivesof this chapter are summarized here, so that the student can check whether

he or she has accomplished each of the following.

• Analysis and design of simple magnetic circuits.


• Equivalent circuits of transformers.


• Predicting transformer performance from equivalent circuits.


• Basic notions of three-phase transformers.


• Elementary autotransformer calculations and performance.

11.8 PRACTICAL APPLICATION: A CASE STUDY

Magnetic Bearings for Space Technology

The high magnetic energy stored in rare-earth-cobalt permanent magnets allows the design of

lightweight motors and magnetic bearings for high-speed rotors. Magnetic bearings are not subject

to wear, and with the ability to operate under high vacuum conditions, they appear to be ideal for

applications requiring high rotational speeds, such as 100,000 r/min. Important applications are

for turbomolecular pumps, laser scanners, centrifuges, momentum rings for satellite stabilizations,

and other uses in space technology.