Transformer phasor diagram

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TRANSFORMER PHASOR DIAGRAM Prepared By ETRICAL.BLOGSPOT.COM

Transcript of Transformer phasor diagram

Page 1: Transformer phasor diagram

TRANSFORMER PHASOR DIAGRAM

Prepared ByETRICAL.BLOGSPOT.COM

Page 2: Transformer phasor diagram

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 .

Page 3: Transformer phasor diagram

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

NO LOAD PHASOR OF A TRANSFORMER

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NO LOAD PHASOR OF A TRANSFORMER

Working Flux Ø  taken as Reference

Flux Ø 

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NO LOAD PHASOR OF A TRANSFORMER

Excitation Current Ie leading Ø by α.

α

Ie

Ø 

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NO LOAD PHASOR OF A TRANSFORMER

Induced EMF E1 and E2 lagging Flux by 90 degree.

α

Ie

E1, E2 = V2

Ø 

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NO LOAD PHASOR OF A TRANSFORMER V1’ = -E1

α

Ie

E1, E2 = V2

V1’ = -E1

Ic

Im Ø 

Page 9: Transformer phasor diagram

NO LOAD PHASOR OF A TRANSFORMER

α

Ie

E1, E2 = V2

V1’ = -E1

Ic

Im

r1Ie

Voltage drop r1Ie in Primary.

Page 10: Transformer phasor diagram

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.

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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

Page 12: Transformer phasor diagram

NO LOAD PHASOR OF A TRANSFORMER No load Power Factor = CosƟ

α

Ie

E1, E2 = V2

V1’ = -E1

Ic

Im

r1Ie

jIeX1V1

Ø

Ɵ

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PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD

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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

Page 15: Transformer phasor diagram

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 Working Flux Ø is taken as referance.

Ø

Ieα

Page 17: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.

Ø

Ieα

E1,E2

Page 18: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.

Ø

Ieα

E1,E2

V1’=-E1

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PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.

Ø

Ieα

E1,E2

V1’=-E1

V2

Page 20: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR INDUCTIVE LOAD Working Flux Ø is taken as referance.

Ø

Ieα

E1,E2

V1’=-E1

V2

Ɵ2

I1’

I2

Page 21: Transformer phasor diagram

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

Page 22: Transformer phasor diagram

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

Page 23: Transformer phasor diagram

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

Page 24: Transformer phasor diagram

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

Page 25: Transformer phasor diagram

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

Page 26: Transformer phasor diagram

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

Page 27: Transformer phasor diagram

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

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PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD As load is inductive, secondary current will lag

secondary load voltage V2 by some angle.

Page 29: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD Working Flux Ø is taken as reference.

Ø

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PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD

Øα

Ie

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PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD

Øα

Ie

E1,E2

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PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD

Øα

Ie

E1,E2

V1’= -E1

V2

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PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD

Øα

Ie

E1,E2

V1’= -E1

V2 I2Ɵ2

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PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD

Øα

Ie

E1,E2

V1’= -E1

V2 I2Ɵ2

I1’

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PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD

Øα

Ie

E1,E2

V1’= -E1

V2 I2Ɵ2

I1’I1

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PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD

Øα

Ie

E1,E2

V1’= -E1

V2 I2Ɵ2

I1’I1

I1r1

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PHASOR OF A TRANSFORMER FOR CAPACITIVE LOAD

Øα

Ie

E1,E2

V1’= -E1

V2 I2Ɵ2

I1’I1

I1r1jI1X

Page 38: Transformer phasor diagram

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

Page 39: Transformer phasor diagram

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

Page 40: Transformer phasor diagram

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

Page 41: Transformer phasor diagram

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

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PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

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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 RESISTIVE LOAD Working Flux Ø is taken as reference.

Ø

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PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

Ø

Ieα

Page 46: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

Ø

Ieα

E1,E2

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PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

Ø

Ieα

E1,E2

V1’= -E1

Page 48: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

Ø

Ieα

E1,E2

V1’= -E1

V2

Page 49: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

Ø

Ieα

E1,E2

V1’= -E1

V2

I2

Page 50: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

Ø

Ieα

E1,E2

V1’= -E1

V2

I2

I1’

Page 51: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

Ø

Ieα

E1,E2

V1’= -E1

V2

I2

I1’ I1

Page 52: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

Ø

Ieα

E1,E2

V1’= -E1

V2

I2

I1’ I1

I1r1

Page 53: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

Ø

Ieα

E1,E2

V1’= -E1

V2

I2

I1’ I1

I1r1jI1X

Page 54: Transformer phasor diagram

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

Page 55: Transformer phasor diagram

PHASOR OF A TRANSFORMER FOR RESISTIVE LOAD

Ø

Ieα

E1,E2

V1’= -E1

V2

I2

I1’ I1

I1r1jI1X1

V1

I2r2

Page 56: Transformer phasor diagram

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

Page 57: Transformer phasor diagram

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