output. For example, a transformer having a full-load

is low and the primary current is limited principally by

rating of 100 kVA can supply a 100-kW load at a unity

the counter emf in the winding, the transformer primary

power factor, but only an 80-kW load at a lagging power

current increases when the counter emf in the primary

factor of 80 percent.

is reduced.

Many transformers are rated in terms of the kVA

The increase in primary current continues until the

load that they can safely carry continuously without

primary ampere-turns are equal to the secondary

exceeding a temperature rise of 80°C when maintaining

ampere-turns, neglecting losses. For example, in the

rated secondary voltage at rated frequency and when

transformer being considered, the magnetizing current,

operating with an ambient (surrounding atmosphere)

Ia, is assumed to be negligible in comparison with the

temperature of 40°C. The actual temperature rise of any

total primary current, I1 + Ia, under load conditions

part of the transformers the difference between the total

because Ia is small in relation to I1 and lags it by an angle

temperature of that part and the temperature of the

of 60°. Hence, the primary and secondary ampere-turns

surrounding air.

are equal and opposite; that is,

It is possible to operate transformers on a higher

frequency than that for which they are designed, but it

In this example,

is not permissible to operate them at more than 10

percent below their rated frequency because they will

overheat. The exciting current in the primary varies

directly with the applied voltage and, like any

impedance containing inductive reactance, the exciting

Neglecting losses, the power delivered to the primary is

current varies inversely with the frequency. Thus, at

equal to the power supplied b the secondary to the load.

reduced frequency, the exciting current becomes

If the load power is P2 = E21 2 cos

and cosine

excessively large, and the accompanying heating may

2

equals cosine 30° (0.866), then P = 120 x 6 x 0.866=

damage the insulation and the windings.

624 watts.

The load component of primary current, 11,

increases with secondary load and maintains the

transformer core flux at nearly its initial value. This

The efficiency of a transformer is the ratio of the

action enables the transformer primary to take power

output power at the secondary terminals to the input

from the source in proportion to the load demand, and

power at the primary terminals. It is also equal to the

to maintain the terminal voltage approximately

ratio of the output to the output plus losses. That is,

constant. The lagging power-factor load vectors are

shown in figure 4-31, view D. Note that the load power

factor is transferred through the transformer to the

primary and that

is approximately equal to

the

is slightly larger than

only difference being that

because of the presence of the exciting current, which

The ordinary power transformer has an efficiency

flows in the primary winding but not in the secondary.

of 97 to 99 percent. The losses are due to the copper

The copper loss of a transformer varies as the square

losses in both windings and the hysteresis and

of the load current; whereas the core loss depends on the

eddy-current losses in the iron core.

terminal voltage applied to the primary and on the

The copper losses vary as the square of the current

frequency of operation. The core loss of a

in the windings and as the winding resistance. In the

constant-potential transformer is constant from no load

transformer being considered, if the primary has l,200

to full load because the frequency is constant and the

turns of number 23 copper wire, having a length of 1,320

effective values of the applied voltage, exciting current,

feet, the resistance of the primary winding is 26.9 ohms.

and flux density are constant.

If the load current in the primary is 0.5 ampere, the

primary copper loss is (0.5)2 x 26.9 = 6.725 watts.

If the load supplied by a transformer has a unity

power factor, the kilowatt (true power) output is the

Similarly, if the secondary winding contains 120

turns of number 13 copper wire, having a length

same as the kilovolt-ampere (apparent power) output.

If the load has a lagging power factor, the kilowatt

of approximately 132 feet, the secondary resistance will

output is proportionally less than the kilovolt-ampere

be 0.269 ohm. The secondary copper loss is I2R2, or