06 Multiphase Rectifier.pdf

EE363 POWER ELECTRONICS Chapter 03 – Rectifiers Lectures 06

Dr. Tauseef Tauqeer

Outline 1. Multiphase Star Rectifier 2. Three Phase Uncontrolled Bridge Rectifier 3. Rectifier Circuit Design 4. Performance Parameters

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Dr. Tauseef Tauqeer

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3.6: Multiphase Star Rectifier (1/5) • The single phase rectifier can

be extended to multiple phases by having multiphase windings on the transformer’s secondary side. • This circuit can be considered as q single phase half wave rectifiers. • The kth diode conducts during the period when the voltage of kth phase is higher than that of other phases. • The conduction period of each diode is 2π/q.

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Dr. Tauseef Tauqeer

3.6: Multiphase Star Rectifier (2/5) • Assuming a cosine wave from π/q to 2π/q, the average

and rms values of the output voltage for a q phase rectifier are given by:  /q Vdc 

2 q  V cos  td (  t )  V sin m m 2 / q 0  q 1/ 2

 2  /q 2  2 Vrms   Vm cos td (t )   2 / q 0 

1/ 2

 q  /q 1   Vm   (1  cos 2t )d (t )  0 2  1/ 2

 /q  q  1  Vm  (t  sin 2t )  2  2 0  

 q  Vm   2

1/ 2

 1 2    sin  q  q 2

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Dr. Tauseef Tauqeer

3.6: Multiphase Star Rectifier (3/5) • If the load is purely resistive, the peak current through the

diode is Im=Vm/R and we can find the rms value of a diode current (or transformer current as)

 2 IS    2

 /q

 0 I cos td (t ) 

 q  Im   2 Vrms  R

2 m

1/ 2

2

 1 2   sin q q 2

  

1/ 2

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Dr. Tauseef Tauqeer

Fourier Series of the Output Voltage (4/5) Example 3.9: a) Express the output voltage of a q-phase rectifier in Fourier series. b) If q=6, Vm=170V, and supply frequency is f=60 Hz, determine the rms value of the dominant harmonic and its frequency.

 

 2 n vo (t )  Vm sin 1   2 cos cos nt   q  n  q , 2 q ,... n  1 q  q

•



For q=6 the output voltage can be expressed as:

2 2 vo (t )  0.9549Vm (1  cos 6t  cos12t  ......) 35 143 •

The sixth harmonic is dominant one. The rms value of the 1 sinusoidal voltage is 2 times its peak magnitude and the rms of the 6th harmonic is v6th  0.9549Vm  2 /(35  2 )  0.0386 Vm (or 6.56 V) and its frequency is f6=6f=360Hz

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Dr. Tauseef Tauqeer

3.6: Multiphase Star Rectifier (5/5) Signle phase full wave 2Vm 2Vm 2Vm vo (t )  0.636Vm (1  cos 2t  cos 4t  cos 6t  .... 3 15 35

Multiphase rectifier vo (t )  0.9549Vm (1 

2 2 cos 6t  cos12t  ......) 35 143

Observations/Advantages of Multiphase Rectifiers: • A multiphase rectifier increases the amount of dc component and lowers the amount of harmonic components. • The output voltage of a q-phase rectifier contains harmonics whose frequencies are multiples of q (q times the supply frequency), qf.

Dr. Tauseef Tauqeer

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3.7: Three Phase Uncontrolled Bridge Rectifier • A three-phase bridge rectifier is commonly used in high power

applications. It’s a full wave rectifier,. It can operate with or without a transformer and gives six pulse ripples on the output voltage. • The diodes are numbered in order of conduction sequences and each one conducts for 120o. • The conduction sequence for diodes is D1-D2, D3-D2, D3-D4, D5-D4, D5-D6, and D1-D6. • The pair of diodes which are connected between that pair of supply lines having the highest amount of instantaneous line-to-line voltage will conduct.

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Dr. Tauseef Tauqeer

3.7: Three Phase Uncontrolled Bridge Rectifier van  Vm sin( t )

1.73 1.5

vbn  Vm sin( t  120o )

Vab

Vac

30

150

vcn  Vm sin( t  240o ) Line Voltage

vab  3Vm sin(t  30) At ωt=30o

3 vab  3Vm sin(60)  Vm 2 At ωt=60o

vab  3Vm sin(90)  3Vm At ωt=90o

3 vab  3Vm sin(120)  Vm 2

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Dr. Tauseef Tauqeer

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3.7: Three Phase Uncontrolled Bridge Rectifier The line to line voltage is 3 times the phase voltage of a three phase Y-connected source. The conduction process is as follows: (i)

a-b----1-6

(ii) a-c----1-2

(iii) b-c----3-2 (iv) b-a----3-4 (v) c-a----5-4 (vi) c-b----5-6

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Dr. Tauseef Tauqeer

3.7: Three Phase Uncontrolled Bridge Rectifier •

•

•

If Vm is the peak value of the phase voltage then the instantaneous phase voltage can be described as: Because the line to line voltage leads the phase voltage by 30o, the instantaneous line to line voltage can be described by: Assuming a cosine wave from /6 to 2/6, the average values of the output voltage for a 3 phase rectifier are given by;

van  Vm sin( t ) vbn  Vm sin( t  120o ) vcn  Vm sin( t  240o ) vab  3Vm sin( t  30o ) vbc  3Vm sin( t  90o ) vca  3Vm sin( t  210o )

Vdc  

2 2



6

(  6

3Vm cos t )d (t )

0

6 1 3 V     1.654Vm m  2

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Dr. Tauseef Tauqeer

3.7: Three Phase Uncontrolled Bridge Rectifier  2 6  2 2 Vrms   3Vm cos (t )d (t )   2 6 0    

•

The rms value of the output voltage is;

•

If the load is purely resistive, the peak current through the diode is Im=√3 Vm/R, and the rms value of the diode current is

 4 Ir    2 



 2 2 I cos (t )d (t ) m 0   6

2   1  1  I m    sin   6 2 6     0.5518I m

1 2

1 2

1 2

 2 6  2 1  3Vm (1  cos 2t )d (t )  2  2 6 0    

 2 1 1  3Vm2 (t  sin 2t ) 2 2  2 6 0

 /6

 2 1  1 2  3Vm2   sin 2 6 2 6  2 6 1/ 2

3 9 3  Vm  1.6554 Vm    2 4   

  

1 2

  

1 2

1 2

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Dr. Tauseef Tauqeer

3.7: Three Phase Uncontrolled Bridge Rectifier •

The rms value of the transformer secondary line current is;

 8 Is    2 



 0 I cos (t )d (t )  6

2 m

2

2   2  1  I m    sin   6 2 6     0.7804 I m

1 2

•

Where Im the peak secondary line current

•

For a three phase rectifier q=6, and Eq (3.38) gives the instantaneous output voltage as

2 2 vo (t )  0.9549Vm (1  cos 6t  cos12t  ......) 35 143

1 2

Dr. Tauseef Tauqeer

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3.10: Rectifier Circuit Design •

The design of uncontrolled rectifier involves determining the ratings of semiconductor diodes. The ratings of diodes are normally specified in terms of:  average current  rms current  peak current, and  peak inverse voltage.

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The output of the rectifier contains harmonics. Filters can be used to smooth out the dc output voltage of the rectifier and these are known as dc filters. These filters are normally L, C, and LC type

Dr. Tauseef Tauqeer

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3.10: Rectifier Circuit Design •

Due to rectification action, the input current of the rectifier also contains harmonics, and an ac filter is used to filter out some of the harmonics from the supply system. The ac filter is normally of LC type.

•

Normally, filter design requires determining the magnitudes and frequencies of the harmonics.

•

The steps involved in the designing rectifiers and filters are explained by examples.

For R load only Circuit Diagram

Voltage and Current waveforms of Diode and load VDC , IDC and PDC Vrms , Irms and Prms Efficiency Form Factor (FF) Ripple Factor (RF) Total Harmonic Distortion (THD) Power Factor (PF) Peak Inverse Voltage (PIV) Output Voltage ripple frequency

Single Phase Half Wave Rectifier

Single Phase Center Tap Full Wave Rectifier

Single Phase Full Wave Rectifier

Six Phase Star Rectifier

Three Phase Bridge Rectifier