ECE 442 1

Three-Phase Power

ECE 442 2

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

ECE 442 3

Phasor Diagram

ECE 442 4

Delta-Connected Sources

VLINE = V

ECE 442 5

Phasor Diagram, VAB as reference

ECE 442 6

Look at the Currents

I = ILINE / 3

ECE 442 7

Y-Connected Sources

ECE 442 8

Phasor Diagram with A as reference

ECE 442 9

Complete Phasor Diagram

VLINE = 3V

ECE 442 10

Look at the Currents

I = ILINE

ECE 442 11

Three-Phase Bridge Rectifier

ECE 442 12

Conduction Sequence

ECE 442 13

Average Output Voltage, Vdc

0

6

0

1 ( )

2 3 cos ( )263 3 1.654

T

dc

dc m

dc m m

V f t dtT

V V td t

V V V

ECE 442 14

rms Output Voltage12

62 2

0

12

2 3 cos ( )26

3 9 32 4

1.6554

rms m

rms m

rms m

V V td t

V V

V V

ECE 442 15

Diode Currents

12

62 2

0

3

4 cos ( )2

0.5518

mm

r m

r m

VI peakR

I I td t

I I

ECE 442 16

Transformer Secondary Current12

62 2

0

12

8 cos ( )2

2 1 2sin6 2 6

0.7804

s m

s m

s m

I I td t

I I

I I

ECE 442 17

Instantaneous Output Voltage

02 2( ) 0.9549 (1 cos(6 ) cos(12 ) ...35 143mv t V t t

ECE 442 18