Three-Phase Inverters

Consider three single-phase inverters in parallel, driven 120° apart.

Three-Phase Inverter (continued)Three single-phase full bridge inverters

12 transistors, 12 diodes, 3 transformers

Could it be simpler?

Alternative (Preferred) Configuration

6 transistors, 6 diodes conduction for 120° or 180°

180° Conduction

• Three transistors ON at a time

Summary Table

Waveforms for 180 Conduction

Phase Voltages for 180 Conduction

Waveforms for 180 Conduction

Summary Table

Mode 1 Operation

Mode 1 Operation

1

1

1

32 223

2 323

eq

s s

eq

san cn

sbn

R RR R

V ViR R

Vi Rv v

Vv i R

03

t

Q1, Q5, Q6 conduct

Summary Table

Mode 2 Operation

Mode 2 Operation

2

2

2

32 223

23

2 3

eq

s s

eq

san

sbn cn

R RR R

V Vi

R R

Vv i R

Vi Rv v

23 3

t

Q1, Q2, Q6 conduct

Summary Table

Mode 3 Operation

Mode 3 Operation

23

t

3

3

3

32 223

223

eq

s s

eq

an bn

scn

R RR R

V ViR R

iv v

Vv i R

Q1, Q2, Q3 conduct

Phase Voltages for 180 Conduction

Fourier Series for Line-to-Line Voltages

1

5 56 6

56 6

1,3,5,...

( cos( ) sin( ))2

1 ( ) ( )

4 sin( )sin( )2 34 sin sin ( )

3 6

oab n n

n

n s s

sn

sab

n

av a n t b n t

b V d t V d t

V n nbn

V nv n tn

For the other Line-to-Line Voltages

1,3,5,...

1,3,5,...

4 sin sin ( )3 2

4 7sin sin ( )3 6

sbc

n

sca

n

V nv n tnV nv n tn

Line-to-Line rms Voltage

12 23

2

0

2 ( )2

2 0.81653

L s

L s s

V V d t

V V V

rms value of the nth Component

1

4 sin32

14 sin 60 0.7797

2

sLn

sL s

V nVn

nVV V

Fundamental Component

Line-to-Neutral Voltages

2 0.471433

sLp s

VVV V

Phase Voltages (Y-connected load)

1,3,5,..

1,3,5,..

1,3,5,..

4 sin( )sin( )33

4 2sin( )sin ( )3 33

4 4sin( )sin ( )3 33

saN

n

sbN

n

scN

n

V nv n tnV nv n tnV nv n tn

Line Current for an RL load

2 21,3,5,...

1

4 sin sin( )33 ( )

tan

sa n

n

n

V ni n tn R n L

n LR

DC Supply Current

IL=√3Io is the rms load line current

Vo1= fundamental rms output line voltage

Io is the rms load phase current

Θ1 = the load impedance angle at the fundamental frequency

11

11

( ) ( ) ( ) ( ) ( ) ( )....

3 cos( )

3 cos( )

s s ab a bc b ca c

os o

s

os L

s

v i v t i t v t i t v t i t

VI IVVI IV

Three-Phase Inverter with RL Load