Transformer Phasors details

1. TRANSFORMER
PHASORS

2. Ideal Transformer
Phasor:
 Here we are going to develop the phasor of a
practical transformer first at no load and then under
load. But before that we will have a look on the
phasor of an ideal transformer.
 (a) Ideal transformer at no load (b) Ideal transformer at
load

3. Transformer at No Load
 Now for the no load , the magnetic flux Φ being
common to both primary and secondary is drawn
first. The induced Emf E1 and E2 lags Φ by 90 and
are shown accordingly in the fig.
 The emf -E1 is being replaced by V1’ just for
convenience. Alternatively V1’ may be treated as a
voltage drop in the primary, in the direction of
flow of primary current. The various
imperfections in a real transformer are now
considered one by one.
 The various imperfections are now considered one
by one.

4. a) Effect of Transformer core loss:- The core loss
consist of Hysteresis loss and eddy current loss.
The hysteresis loss in the core is minimized by
using Cold-rolled-grain oriented (CRGO) steel
and eddy current loss is minimized by using thin
laminations for the core.
 The above two figs shows the variation the
exciting current Ie with respect to flux. It also
shows that that the current Ie leads the flux ‘Φ’
by an angle of ‘α’. This angle depends upon the
hysteresis loop.

5.  The No Load primary current ‘Ie’ is called the
exciting current of the transformer and can be
resolved into two components.
 The component ‘Im’ along ‘Φ’ is called the reactive
or magnetizing current, since its function is to
produce the required magnetic flux ‘Φ’.
 The second component is along V1’ which is ‘Ic’
and this component is called as the core-loss
component or the power component of ‘Ie’; since
‘Ic’ when multiplied by V1’ gives total core loss Pc.

7. b) Effect of Transformer resistance:- The effect of
transformer resistance R1 can be accounted for,
by adding to V1’, a voltage drop equal to ‘IeR1’.
Note that ‘IeR1’ is in phase with ‘Ie’ and is drawn
parallel to ‘Ie’ in the phasor diagram

8. c) Effect of Leakage flux:- For the direction of
current ‘Ie’ in the primary the point A is at
higher magnetic potential than point B.
 This magnetic potential difference establishes:
I. The mutual flux Φ linking both the windings.
II. The primary leakage flux ΦL1, which links only
the primary winding.

9.  The mutual flux Φ exist entirely in the
ferromagnetic core and therefore involves
hysteresis loop.
 On the other hand, primary leakage flux ΦL1 exist
largely in the air . Although ΦL1 does passes
through some part of iron core, the reluctance
offered to ΦL1 is mainly due to air. Therefore it can
be taken is phase with the exciting current Ie that
produce it.
 In the primary winding, Φ induces an EMF E1
lagging it by 90, similarly ΦL1 induces an emf Ex1
in the primary winding and lagging it by 90.

10.  Since Ie leads Ex by 90, it is possible to write
Ex1=-JIeX1.
 The total voltage equation
in the primary at no load can be
written as-
V1=V1’+Ie(R1+jx1)

11. Transformer Phasor Under Load
 In this the secondary circuit of the transformer is
considered first and then primary for developing
the phasor diagram under Load.
 When switch ‘S’ is closed, secondary current I2
starts flowing from the terminal ‘n’ to the load as
shown in fig.

12.  Assuming the load to have a lagging power factor
so that I2 lags secondary load voltage V2 by an
angle θ2.
 The secondary resistance drop
Is accounted by drawing I2R2
Parallel to I2.
 The secondary mmf I2N2 give
Rise to leakage flux which
Link only secondary & not
Primary.
 The secondary no load
Voltage E2 must have a
Component equal & opposite
to –JI2X2

13.  Thus the phasor sum of V2, I2R2 and JI2X2 gives
secondary induced emf E2 as shown in fig.
 The voltage equation for the secondary circuit can
now be written as:-
 E2= V2 + I2(R2+jX2)= V2 + I2Z2 -----(a)
 Where Z2 is the secondary leakage impedance of
the transformer.
 Similarly we can also draw the transformer phasor
for the leading load as well.