Three – Phase Power System

Three-Phase Power

Definitions

• 4 wires– 3 “active” phases, A, B, C– 1 “ground”, or “neutral”

• Color Code– Phase A Red– Phase B Black– Phase C Blue– Neutral White or Gray

Balanced Three – Phase System

0 cba VVV

Phasor DiagramPositive Phase Sequence abc

120

120

0

mc

mb

ma

VV

VV

VV

Phasor Diagram Negative Phase Sequence acb

120

120

0

mc

mb

ma

VV

VV

VV

Delta-Connected Sources

Vline = V

Line Voltages Vline

Vab Vbc Vca

Phase Voltages VΦ

Va Vb Vc

Currents for the Delta Connection

Line Current Iline Phase Current IΦ

Iline = √3IΦ

Y-Connected Sources

Line Voltages Vline

Vab Vbc Vca

Phase Voltages VΦ

Va Vb Vc

Vline = √3VΦ

Currents for the Y - Connection

Line Current IlinePhase Current IΦ

Line Current = Phase Current ---- Iline = IΦ

Power in a Balanced Three – Phase System

Total Power is equal to 3 times the power per phase!

cos3

3

cos

IVP

PPPPP

PPPP

IVP

T

CBAT

CBA

Power in a Balanced Three – Phase System

(Continued)

For a Balanced Y – Connected System

cos3

cos3

3

3

cos3

linelineT

lineline

T

line

line

T

IVP

IV

P

II

VV

IVP

For a Balanced Δ – Connected System,

cos3

cos3

3

3

cos3

linelineT

linelineT

line

line

T

IVP

IVP

II

VV

IVP

Three-Phase Bridge Rectifier

Conduction Sequence

Average Output Voltage, Vdc

0

6

0

1( )

23 cos ( )

26

3 31.654

T

dc

dc m

dc m m

V f t dtT

V V td t

V V V

rms Output Voltage1

2

62 2

0

1

2

23 cos ( )

26

3 9 3

2 4

1.6554

rms m

rms m

rms m

V V td t

V V

V V

Diode Currents

1

26

2 2

0

3

4cos ( )

2

0.5518

mm

r m

r m

VI peak

R

I I td t

I I

Transformer Secondary Current1

26

2 2

0

1

2

8cos ( )

2

2 1 2sin

6 2 6

0.7804

s m

s m

s m

I I td t

I I

I I

Instantaneous Output Voltage

0

2 2( ) 0.9549 (1 cos(6 ) cos(12 ) ...

35 143mv t V t t