0195136047.pdf

486 MAGNETIC CIRCUITS AND TRANSFORMERS

11.4 Transformer Performance

The characteristics of most interest to power engineers arevoltage regulationandefficiency. The

voltage regulation of a transformer is a measure of the change in the magnitude of the secondary

voltage as the current changes from no load to full load while the primary voltage is held fixed.

This is defined as

% voltage regulation =

V2NL−V2FL

V2FL

× 100 (11.4.1a)

which may also be expressed as

V 1 −aV 2

aV 2

× 100 (11.4.1b)

or

(V 1 /a)−V 2

V 2

× 100 (11.4.1c)

Thepower efficiency(generally known asefficiency)of a transformer is defined as

η=

real power output

real power input

×100% (11.4.2a)

=

real power output

real power output+losses

×100% (11.4.2b)

=

real power output

real power output+core loss+copper(I^2 R)loss

×100% (11.4.2c)

in which theI^2 Rloss is obviously load-dependent, whereas the core loss is considered to be

constant and independent of the load. It can be shown that the core loss should be equal to the

copper loss for maximum operating efficiency at a given load.

The rated core loss can be approximated by the power input in theopen-circuit testin which

one winding is open-circuited and rated voltage at rated frequency is applied to the other winding.

The rated copper loss (at full load) can be approximated by the power input in theshort-circuit

test, in which one winding is short-circuited and a reduced voltage at rated frequency is applied

to the other winding such that the rated current results.

Theenergy efficiencygenerally taken over a 24-hour period, known asall-day efficiency,is

also of interest. It is given by

ηAD=

energy output over 24 hours

energy input over 24 hours

×100% (11.4.3)

EXAMPLE 11.4.1

The transformer of Example 11.3.1 is supplying full load (i.e., rated load of 50 kVA) at a rated

secondary voltage of 240 V and 0.8 power factor lagging. Neglecting the exciting current of the

transformer,

(a) Determine the percent voltage regulation of the transformer.

(b) Sketch the corresponding phasor diagram.

(c) If the transformer is used as a step-down transformer at the load end of a feeder whose

impedance is 0. 5 +j 2. 0 , find the voltageVSand the power factor at the sending end

of the feeder.