7/31/2019 14 Transformer Phasors
1/13
Click to edit Master subtitle style
8/28/12
TRANSFORMER
PHASORS
7/31/2019 14 Transformer Phasors
2/13
8/28/12
ea rans ormerPhasor:Here we are going to develop the phasor of apractical transformer first at no load and thenunder load. But before that we will have a lookon the phasor of an ideal transformer.
(a) Ideal transformer at no load (b) Ideal
7/31/2019 14 Transformer Phasors
3/13
8/28/12
Transformer at No
LoadNow for the no load , the magnetic flux being common to both primary andsecondary is drawn first. The induced EmfE1 and E2 lags by 90 and are shown
accordingly in the fig.
The emf -E1 is being replaced by V1 justfor convenience. Alternatively V1 may betreated as a voltage drop in the primary,
in the direction of flow of primary current.The various imperfections in a realtransformer are now considered one byone.
The various imperfections are now
7/31/2019 14 Transformer Phasors
4/13
8/28/12
a) Effect of Transformer core loss:-The coreloss consist of Hysteresis loss and eddycurrent loss. The hysteresis loss in the
core is minimized by using Cold-rolled-grain oriented (CRGO) steel and eddycurrent loss is minimized by using thinlaminations for the core.
) The above two figs shows the variationthe exciting current Ie with respect to
flux. It also shows that that the current Ieleads the flux b an an le of . his
7/31/2019 14 Transformer Phasors
5/13
8/28/12
The No Load primary current Ie is calledthe exciting current of the transformer andcan be resolved into two components.
The component Im along is called thereactive or magnetizing current, since its
function is to produce the requiredmagnetic flux .
The second component is along V1 whichis Ic and this component is called as thecore-loss component or the powercomponent of Ie; since Ic when
multiplied by V1 gives total core loss Pc.
7/31/2019 14 Transformer Phasors
6/13
8/28/12
7/31/2019 14 Transformer Phasors
7/13
8/28/12
b) Effect of Transformer resistance:- Theeffect of transformer resistance R1 canbe accounted for, by adding to V1, a
voltage drop equal to IeR1. Note thatIeR1 is in phase with Ie and is drawnparallel to Ie in the phasor diagram
7/31/2019 14 Transformer Phasors
8/13
8/28/12
c) Effect of Leakage flux:- For the directionof current Ie in the primary the point Ais at higher magnetic potential than point
B.
This magnetic potential differenceestablishes:
I. The mutual flux linking both thewindings.
II. The primary leakage flux L1, which linksonly the primary winding.
7/31/2019 14 Transformer Phasors
9/13
8/28/12
The mutual flux exist entirely in theferromagnetic core and therefore involveshysteresis loop.
On the other hand, primary leakage flux
L1 exist largely in the air . Although L1
does passes through some part of ironcore, the reluctance offered to L1 ismainly due to air. Therefore it can betaken is phase with the exciting current Ie
that produce it.
In the primary winding, induces an EMFE1 lagging it by 90, similarly L1 inducesan emf Ex1 in the primary winding and
7/31/2019 14 Transformer Phasors
10/13
8/28/12
Since Ie leads Ex by 90, it is possible towrite Ex1=-JIeX1.
The total voltage equation
in the primary at no load can be
written as-
V1=V1+Ie(R1+jx1)
T f Ph U d
7/31/2019 14 Transformer Phasors
11/13
8/28/12
Transformer Phasor UnderLoadIn this the secondary circuit of the
transformer is considered first and thenprimary for developing the phasordiagram under Load.
When switch S is closed, secondary
7/31/2019 14 Transformer Phasors
12/13
8/28/12
Assuming the load to have a laggingpower factor so that I2 lags secondaryload voltage V2 by an angle 2.
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
7/31/2019 14 Transformer Phasors
13/13
8/28/12
Thus the phasor sum of V2, I2R2 and JI2X2gives secondary induced emf E2 as shownin fig.
The voltage equation for the secondarycircuit can now be written as:-
E2= V2 + I2(R2+jX2)= V2 + I2Z2-----(a)
Where Z2 is the secondary leakageimpedance of the transformer.
Similarly we can also draw the transformerphasor for the leading load as well.