Regulation of Transformer

Regulation of a Transformer

1. When a transformer is loaded with a constant primary voltage, the secondary voltage
decreases* because of its internal resistance and leakage reactance.
Let 0V2 = secondary terminal voltage at no-load.

= E2 = EK1 = KV1 because at no-load the impedance drop is negligible.
V2 = secondary terminal voltage on full-load.
The change in secondary terminal voltage from no-load to full-load is = 0V2 ? V2. This change divided
by 0V2 is known as regulation ‘down’. If this change is divided by V2, i.e., full-load secondary terminal
voltage, then it is called regulation ‘up’.
? % regn ‘down’ = 0 2 2
0 2
100
V V
V
?
× and % regn ‘up’ =
0 2 2
2
100
V V
V
?
×
In further treatment, unless stated otherwise, regulation is to be taken as regulation ‘down’.
We have already seen in Art. 32.16 (Fig. 32.35) that the change in secondary terminal voltage from noload
to full-load, expressed as a percentage of no-load secondary voltage is,
= ?r cos ? ± ?x sin ? (approximately)
Or more accurately
= (?r cos ? ± ?x sin ?) +1200
(?x cos ? + ?r sin ?)2
? % regn = ?r cos ? ± ?x sin ? ...approximately.
The lesser this value, the better the transformer, because a good transformer should keep its
secondary terminal voltage as constant as possible under all conditions of load.
(2) The regulation may also be explained in terms of primary values.
In Fig. 32.51 (a) the approximate equivalent circuit of a transformer is shown and in Fig. 32.51 (b), (c)
and (d) the vector diagrams corresponding to different power factors are shown.
The secondary no-load terminal voltage as referred to primary is E?2 = E2/K = E1 = V1 and if the
secondary full-load voltage as referred to primary is V ? 2 (= V2/K) then
% regn =

Losses in a Transformer
In a static
transformer, there
are no friction or
windage losses.
Hence, the only
losses occuring
are :
(i) C o r e
or Iron Loss : It
includes both
hysteresis loss
and eddy current
loss. Because
the core
flux in a transformer
remains
practically constant
for all loads
(its variation being
1 to 3% from no-load to full-load). The core loss is practically the same at all loads.
Hysteresis loss Wh = ? B1.6
max f V watt; eddy current loss We = PB2
max f2t2 watt
These losses are minimized by using steel of high silicon content for the core and by using very thin

laminations. Iron or core loss is found from the O.C. test. The input of the transformer when on noload
measures the core loss.
(ii) Copper loss. This loss is due to the ohmic resistance of the transformer windings. Total Cu loss
= I1
2R1 + I2
2R2 = I1
2R01 + I2
2R02. It is clear that Cu loss is proportional to (current)2 or kVA2. In other
words, Cu loss at half the full-load is one-fourth of that at full-load.
The value of Cu loss is found from the short-circuit test