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PHASOR DIAGRAM OF TRANSFORMER Prepared By ELECTRICALBABA.COM

TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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Page 1: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR DIAGRAM OF

TRANSFORMER

Prepared By

ELECTRICALBABA.COM

Page 2: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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 .

Page 3: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

IMPORTANT POINTS FOR PHASOR OF

TRANSFORMER

� So under load condition, I 1 = Primary Current, is

phasor Sum of I’ and Excitation Current Ie.

Page 4: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

NO LOAD PHASOR OF A TRANSFORMER

Page 5: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

NO LOAD PHASOR OF A TRANSFORMER

� Working Flux Ø taken as Reference

Flux Ø

Page 6: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

NO LOAD PHASOR OF A TRANSFORMER

� Excitation Current Ie leading Ø by α.

Ie

α

Ie

Ø

Page 7: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

NO LOAD PHASOR OF A TRANSFORMER

� Induced EMF E1 and E2 lagging Flux by 90 degree.

Ie

α

Ie

E1, E2 = V2

Ø

Page 8: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

NO LOAD PHASOR OF A TRANSFORMER

� V1’ = -E1

Ie

V1’ = -E1

α

Ie

E1, E2 = V2

Ic

ImØ

Page 9: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

NO LOAD PHASOR OF A TRANSFORMER

Ie

V1’ = -E1 r1Ie

� Voltage drop r1Ie in Primary.

α

Ie

E1, E2 = V2

Ic

Im

Page 10: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 11: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 12: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 13: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

INDUCTIVE LOAD

Page 14: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 15: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

INDUCTIVE LOAD

� Working Flux Ø is taken as referance.

Ø

Page 16: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

INDUCTIVE LOAD

Ø

Ie

α

Page 17: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

INDUCTIVE LOAD

Ø

Ie

α

E1,E2

Page 18: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

INDUCTIVE LOAD

V1’=-E1

Ø

Ie

α

E1,E2

Page 19: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

INDUCTIVE LOAD

V1’=-E1

Ø

Ie

α

E1,E2

V2

Page 20: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 21: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 22: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 23: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 24: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 25: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 26: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 27: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 28: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

CAPACITIVE LOAD

� As load is capacitive, secondary current will lead

secondary load voltage V2 by some angle.

Page 29: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

CAPACITIVE LOAD

� Working Flux Ø is taken as reference.

Ø

Page 30: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

CAPACITIVE LOAD

Ø

αIe

Page 31: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

CAPACITIVE LOAD

Ø

αIe

E1,E2

Page 32: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

CAPACITIVE LOAD

V1’= -

E1

Ø

αIe

E1,E2

V2

Page 33: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

CAPACITIVE LOAD

V1’= -

E1

Ø

αIe

E1,E2

V2 I2Ɵ2

Page 34: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

CAPACITIVE LOAD

V1’= -

E1I1’

Ø

αIe

E1,E2

V2 I2Ɵ2

Page 35: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

CAPACITIVE LOAD

V1’= -

E1 I1’

I1

Ø

αIe

E1,E2

V2 I2Ɵ2

Page 36: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

CAPACITIVE LOAD

V1’= -

E1

I1’

I1

I1r1

Ø

αIe

E1,E2

V2 I2Ɵ2

Page 37: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

CAPACITIVE LOAD

V1’= -

E1

I1’

I1

I1r1

jI1X

Ø

αIe

E1,E2

V2 I2Ɵ2

Page 38: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 39: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 40: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 41: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 42: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

Page 43: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

� For Resistive Load, load current will be in phase

with the load Voltage V2.

Page 44: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

� Working Flux Ø is taken as reference.

Ø

Page 45: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

Ø

Ie

α

Page 46: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

Ø

Ie

α

E1,E2

Page 47: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

V1’= -E1

Ø

Ie

α

E1,E2

Page 48: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

V1’= -E1

Ø

Ie

α

E1,E2

V2

Page 49: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

V1’= -E1

Ø

Ie

α

E1,E2

V2

I2

Page 50: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

V1’= -E1

I1’

Ø

Ie

α

E1,E2

V2

I2

Page 51: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

V1’= -E1

I1’I1

Ø

Ie

α

E1,E2

V2

I2

Page 52: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

V1’= -E1

I1’I1

I1r1

Ø

Ie

α

E1,E2

V2

I2

Page 53: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

V1’= -E1

I1’I1

I1r1

jI1X1

Ø

Ie

α

E1,E2

V2

I2

Page 54: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 55: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

PHASOR OF A TRANSFORMER FOR

RESISTIVE LOAD

V1’= -E1

I1’I1

I1r1

jI1X1

V1

Ø

Ie

α

E1,E2

V2

I2

I2r2

Page 56: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

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

Page 57: TRANSFORMER PHASOR DIAGRAM...PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD E2 = V2+I2r2+jI2X2, phasor sum V1’=-E1 I1’ I1 I1r1 jI1X1 V1 Ø Ie α E1,E2 V2 2 I2 I2r2 jI2X2 PHASOR OF

COMMENTS? / QUESTIONS???


Qualitative Phasor Analysis - CiteSeerX

Qualitative Phasor Analysis - CiteSeerX

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