14 Transformer Phasors

7/31/2019 14 Transformer Phasors

1/13

Click to edit Master subtitle style

8/28/12

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


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


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


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.


6/13

8/28/12


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


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.


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


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


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


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


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.

Documents

14 Transformer Phasors