Post on 21-Apr-2017
TRANSFORMER PHASOR DIAGRAM
Prepared ByETRICAL.BLOGSPOT.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 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’ = N2I2 where 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.
α
Ie
Ø
NO LOAD PHASOR OF A TRANSFORMER
Induced EMF E1 and E2 lagging Flux by 90 degree.
α
Ie
E1, E2 = V2
Ø
NO LOAD PHASOR OF A TRANSFORMER V1’ = -E1
α
Ie
E1, E2 = V2
V1’ = -E1
Ic
Im Ø
NO LOAD PHASOR OF A TRANSFORMER
α
Ie
E1, E2 = V2
V1’ = -E1
Ic
Im
r1Ie
Voltage drop r1Ie in Primary.
NO LOAD PHASOR OF A TRANSFORMER
α
Ie
E1, E2 = V2
V1’ = -E1
Ic
Im
r1Ie
jIeX1
Ø
Voltage drop IeX1 in Primary due to reactance.
NO LOAD PHASOR OF A TRANSFORMER Sourec Voltage V1 = V1’+r1Ie +jIeX1, phasor sum.
α
Ie
E1, E2 = V2
V1’ = -E1
Ic
Im
r1Ie
jIeX1V1
Ø
NO LOAD PHASOR OF A TRANSFORMER No load Power Factor = CosƟ
α
Ie
E1, E2 = V2
V1’ = -E1
Ic
Im
r1Ie
jIeX1V1
Ø
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 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 Working Flux Ø is taken as referance.
Ø
Ieα
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.
Ø
Ieα
E1,E2
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.
Ø
Ieα
E1,E2
V1’=-E1
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.
Ø
Ieα
E1,E2
V1’=-E1
V2
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.
Ø
Ieα
E1,E2
V1’=-E1
V2
Ɵ2
I1’
I2
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.
Ø
Ieα
E1,E2
V1’=-E1
V2
Ɵ2
I1’
I2
I1
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.
Ø
Ieα
E1,E2
V1’=-E1
V2
Ɵ2
I1’
I2
I1
I1r1
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.
Ø
Ieα
E1,E2
V1’=-E1
V2
Ɵ2
I1’
I2
I1
I1r1
jI1X1
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.
Ø
Ieα
E1,E2
V1’=-E1
V2
Ɵ2
I1’
I2
I1
I1r1
jI1X1V1
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.
Ø
Ieα
E1,E2
V1’=-E1
V2
Ɵ2
I1’
I2
I1
I1r1
jI1X1V1
I2r2
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Load Voltage V2 = E2+I2r2+jI2X2, phasor sum
Ø
Ieα
E1,E2
V1’=-E1
V2
Ɵ2
I1’
I2
I1
I1r1
jI1X1V1
I2r2
jI2X2
PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Primary Power Factor= Cos Ɵ1
Ø
Ieα
E1,E2
V1’=-E1
V2
Ɵ2
I1’
I2
I1
I1r1
jI1X1V1
I2r2
jI2X2
Ɵ1
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD As load is inductive, secondary current will lag
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
Øα
Ie
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
V1’= -E1
V2
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
V1’= -E1
V2 I2Ɵ2
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
V1’= -E1
V2 I2Ɵ2
I1’
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
V1’= -E1
V2 I2Ɵ2
I1’I1
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
V1’= -E1
V2 I2Ɵ2
I1’I1
I1r1
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
V1’= -E1
V2 I2Ɵ2
I1’I1
I1r1jI1X
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
V1’= -E1
V2 I2Ɵ2
I1’I1
I1r1jI1X
V1 V1=V1’+I1r1+jI1X1, phasor sum
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
V1’= -E1
V2 I2Ɵ2
I1’I1
I1r1jI1X
V1 V1=V1’+I1r1+jI1X1, phasor sum
I2r2
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
V1’= -E1
V2 I2Ɵ2
I1’I1
I1r1jI1X
V1 E2=V2+I2r2+jI2X2, phasor sum
I2r2jI2X2
PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD
Øα
Ie
E1,E2
V1’= -E1
V2 I2Ɵ2
I1’I1
I1r1jI1X
V1 E2=V2+I2r2+jI2X2, phasor sum
I2r2jI2X2
Ɵ1
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
Ieα
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
V1’= -E1
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
V1’= -E1
V2
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
V1’= -E1
V2
I2
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
V1’= -E1
V2
I2
I1’
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
V1’= -E1
V2
I2
I1’ I1
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
V1’= -E1
V2
I2
I1’ I1
I1r1
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
V1’= -E1
V2
I2
I1’ I1
I1r1jI1X
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
V1’= -E1
V2
I2
I1’ I1
I1r1jI1X1
V1 V1=V1’+I1r1+jI1X1, phasor sum
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
V1’= -E1
V2
I2
I1’ I1
I1r1jI1X1
V1
I2r2
PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD
Ø
Ieα
E1,E2
V1’= -E1
V2
I2
I1’ I1
I1r1jI1X1
V1
I2r2
jI2X2
E2=V2+I2r2+jI2X2, phasor sum
COMMENTS? / QUESTIONS???