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PHASOR DIAGRAM OF
TRANSFORMER
Prepared By
ELECTRICALBABA.COM
IMPORTANT POINTS FOR PHASOR OF
TRANSFORMER
� Transformer when excited at no load, only takes
excitation current which leads the working Flux by
Hysteretic angle α.
� Excitation current is made up of two components, one
in phase with the applied Voltage V is called Core Loss in phase with the applied Voltage V is called Core Loss
component (Ic) and another in phase with the working
Flux Ø called Magnetizing Current (Im).
� Electromotive Force (EMF) created by working Flux
Ø lags behind it by 90 degree.
� When Transformer is connected with a Load, it takes
extra current I’ from the Source so that N1I’ = N2I2where I’ is called load componete of Primary Current I
1 .
IMPORTANT POINTS FOR PHASOR OF
TRANSFORMER
� So under load condition, I 1 = Primary Current, is
phasor Sum of I’ and Excitation Current Ie.
NO LOAD PHASOR OF A TRANSFORMER
NO LOAD PHASOR OF A TRANSFORMER
� Working Flux Ø taken as Reference
Flux Ø
NO LOAD PHASOR OF A TRANSFORMER
� Excitation Current Ie leading Ø by α.
Ie
α
Ie
Ø
NO LOAD PHASOR OF A TRANSFORMER
� Induced EMF E1 and E2 lagging Flux by 90 degree.
Ie
α
Ie
E1, E2 = V2
Ø
NO LOAD PHASOR OF A TRANSFORMER
� V1’ = -E1
Ie
V1’ = -E1
α
Ie
E1, E2 = V2
Ic
ImØ
NO LOAD PHASOR OF A TRANSFORMER
Ie
V1’ = -E1 r1Ie
� Voltage drop r1Ie in Primary.
α
Ie
E1, E2 = V2
Ic
Im
NO LOAD PHASOR OF A TRANSFORMER
Ie
V1’ = -E1 r1Ie
jIeX1
Voltage drop IeX1 in Primary due to reactance.
α
Ie
E1, E2 = V2
Ic
ImØ
NO LOAD PHASOR OF A TRANSFORMER
Sourec Voltage V1 = V1’+r1Ie +jIeX1, phasor sum.
Ie
V1’ = -E1
r1Ie
jIeX1
V1
α
Ie
E1, E2 = V2
Ic
ImØ
NO LOAD PHASOR OF A TRANSFORMER
No load Power Factor = CosƟ
Ie
V1’ = -E1
r1Ie
jIeX1
V1
Ɵ
α
Ie
E1, E2 = V2
Ic
ImØ
Ɵ
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
� As load is inductive, secondary current will lag
secondary load voltage V2 by some angle.
� r1 = Primary winding Resistance
� X1 = Primary winding leakage Reactance
r2 = Secondary winding Resistance� r2 = Secondary winding Resistance
� X2 = Secondary winding leakage Reactance
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
� Working Flux Ø is taken as referance.
Ø
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
Ø
Ie
α
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
Ø
Ie
α
E1,E2
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
V1’=-E1
Ø
Ie
α
E1,E2
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
V1’=-E1
Ø
Ie
α
E1,E2
V2
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
� Working Flux Ø is taken as referance.
V1’=-E1
I1’
Ø
Ie
α
E1,E2
V2
Ɵ2
I1’
I2
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
� Working Flux Ø is taken as referance.
V1’=-E1
I1’ I1
Ø
Ie
α
E1,E2
V2
Ɵ2
I1’
I2
I1
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
� Working Flux Ø is taken as referance.
V1’=-E1
I1’ I1
I1r1
Ø
Ie
α
E1,E2
V2
Ɵ2
I1’
I2
I1
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
� Working Flux Ø is taken as referance.
V1’=-E1
I1’ I1
I1r1
jI1X1
Ø
Ie
α
E1,E2
V2
Ɵ2
I1’
I2
I1
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
� Working Flux Ø is taken as referance.
V1’=-E1I1’ I1
I1r1
jI1X1
V1
Ø
Ie
α
E1,E2
V2
Ɵ2
I1’
I2
I1
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
� Working Flux Ø is taken as referance.
V1’=-E1I1’ I1
I1r1
jI1X1
V1
Ø
Ie
α
E1,E2
V2
Ɵ2
I1’
I2
I1
I2r2
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD� E2 = V2+I2r2+jI2X2, phasor sum
V1’=-E1I1’ I1
I1r1
jI1X1
V1
Ø
Ie
α
E1,E2
V2
Ɵ2
I1’
I2
I1
I2r2
jI2X2
PHASOR OF A TRANSFORMER FOR
INDUCTIVE LOAD
� Primary Power Factor= Cos Ɵ1, angle between V1 &
I1.
V1’=-E1I1’ I1
I1r1
jI1X1
V1
Ø
Ie
α
E1,E2
V2
Ɵ2
I1’
I2
I1
I2r2
jI2X2
Ɵ1
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
� As load is capacitive, secondary current will lead
secondary load voltage V2 by some angle.
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
� Working Flux Ø is taken as reference.
Ø
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
Ø
αIe
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
Ø
αIe
E1,E2
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
V1’= -
E1
Ø
αIe
E1,E2
V2
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
V1’= -
E1
Ø
αIe
E1,E2
V2 I2Ɵ2
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
V1’= -
E1I1’
Ø
αIe
E1,E2
V2 I2Ɵ2
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
V1’= -
E1 I1’
I1
Ø
αIe
E1,E2
V2 I2Ɵ2
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
V1’= -
E1
I1’
I1
I1r1
Ø
αIe
E1,E2
V2 I2Ɵ2
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
V1’= -
E1
I1’
I1
I1r1
jI1X
Ø
αIe
E1,E2
V2 I2Ɵ2
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
V1’= -
E1
I1’
I1
I1r1
jI1X
V1V1=V1’+I1r1+jI1X1, phasor
sum
Ø
αIe
E1,E2
V2 I2Ɵ2
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
V1’= -
E1
I1’
I1
I1r1
jI1X
V1V1=V1’+I1r1+jI1X1, phasor
sum
Ø
αIe
E1,E2
V2 I2Ɵ2
I2r2
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
V1’= -
E1
I1’
I1
I1r1
jI1X
V1E2=V2+I2r2+jI2X2, phasor
sum
Ø
αIe
E1,E2
V2 I2Ɵ2
I2r2
jI2X2
PHASOR OF A TRANSFORMER FOR
CAPACITIVE LOAD
V1’= -
E1
I1’
I1
I1r1
jI1X
V1E2=V2+I2r2+jI2X2, phasor
sum
Ɵ1
Ø
αIe
E1,E2
V2 I2Ɵ2
I2r2
jI2X2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
� For Resistive Load, load current will be in phase
with the load Voltage V2.
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
� Working Flux Ø is taken as reference.
Ø
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
Ø
Ie
α
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
Ø
Ie
α
E1,E2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
V1’= -E1
Ø
Ie
α
E1,E2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
V1’= -E1
Ø
Ie
α
E1,E2
V2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
V1’= -E1
Ø
Ie
α
E1,E2
V2
I2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
V1’= -E1
I1’
Ø
Ie
α
E1,E2
V2
I2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
V1’= -E1
I1’I1
Ø
Ie
α
E1,E2
V2
I2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
V1’= -E1
I1’I1
I1r1
Ø
Ie
α
E1,E2
V2
I2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
V1’= -E1
I1’I1
I1r1
jI1X1
Ø
Ie
α
E1,E2
V2
I2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
V1’= -E1
I1’I1
I1r1
jI1X1
V1 V1=V1’+I1r1+jI1X1, phasor
sum
Ø
Ie
α
E1,E2
V2
I2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
V1’= -E1
I1’I1
I1r1
jI1X1
V1
Ø
Ie
α
E1,E2
V2
I2
I2r2
PHASOR OF A TRANSFORMER FOR
RESISTIVE LOAD
V1’= -E1
I1’I1
I1r1
jI1X1
V1 E2=V2+I2r2+jI2X2, phasor sum
Ø
Ie
α
E1,E2
V2
I2
I2r2
jI2X2
COMMENTS? / QUESTIONS???
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