# Three-Phase Inverters - UMass D

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 0 t 3 R 3R Req R 2

2 Vs 2Vs i1 Req 3R Q1, Q5, Q6 conduct i1 R Vs van vcn 2

3 2Vs vbn i1 R 3 Summary Table Mode 2 Operation Mode 2 Operation 2

t 3 3 R 3R Req R 2 2 Vs 2Vs i2 Req 3R

Q1, Q2, Q6 conduct 2Vs van i2 R 3 i2 R Vs vbn vcn 2 3

Summary Table Mode 3 Operation Mode 3 Operation 2 t 3 R 3R Req R 2 2

Vs 2Vs i3 Req 3R Q1, Q2, Q3 conduct i3 van vbn 2 2Vs vcn i3 R

3 Phase Voltages for 180 Conduction Fourier Series for Line-to-Line Voltages ao vab (an cos(nt ) bn sin(nt )) 2 n 1 5 56 6

1 bn Vs d (t ) Vs d (t ) 5 6 6 4Vs n n bn

sin( ) sin( ) n 2 3 4Vs n vab sin sin n(t ) 3

6 n 1,3,5,... n For the other Line-to-Line Voltages 4Vs n vbc sin sin n(t ) 3

2 n 1,3,5,... n 4Vs n 7 vca sin sin n(t ) 3

6 n 1,3,5,... n Line-to-Line rms Voltage 2 VL 2 2

3 2 V d ( t ) s

0 2 VL Vs 0.8165Vs 3 1 2

rms value of the nth Component 4Vs n VLn sin 3 2n n 1 Fundamental Component VL1 4Vs sin 60

2 0.7797Vs Line-to-Neutral Voltages 2Vs VL Vp 0.4714Vs 3

3 Phase Voltages (Y-connected load) vaN n 1,3,5,..

vbN n 1,3,5,.. vcN

n 1,3,5,.. 4Vs n sin( ) sin(nt ) 3 3n 4Vs n 2 sin( ) sin n(t )

3 3 3n 4Vs n 4 sin( ) sin n(t ) 3 3 3n

Line Current for an RL load 4Vs n ia sin sin(nt n )

3 n R 2 ( n L) 2 n 1,3,5,... 3 1 n L n tan R

DC Supply Current vs is vab (t )ia (t ) vbc (t )ib (t ) vca (t )ic (t ) .... Vo1 I s 3 I o cos(1 ) Vs Vo1 Is 3 I L cos(1 )

Vs IL=3Io is the rms load line current Vo1= fundamental rms output line voltage Io is the rms load phase current 1 = the load impedance angle at the fundamental Three-Phase Inverter with RL Load

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