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CH.4 Full-wave and Three- phase rectifiers (Converting AC to DC)

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Presentation on theme: "CH.4 Full-wave and Three- phase rectifiers (Converting AC to DC)"— Presentation transcript:

1 CH.4 Full-wave and Three- phase rectifiers (Converting AC to DC)
4-1 Introduction The average current in AC source is zero  in the  full-wave rectifier, thus avoiding  problems associated with nonzero average  source currents, particularly in transformers. The output of the full-wave rectifier has  inherently less ripple than the half-wave  rectifier. Uncontrolled and controlled single-phase and three-phase full-wave converters used as  rectifiers are analyzed.

2 4-2 Single-phase full-wave rectifiers
Fig. 4-1 Bridge rectifier: The lower peak diode voltage make it more suitable for high-voltage applications.


4 Fig. 4-2 center-tapped transformer rectifier 
  With electrical isolation, only one diode voltage drop between the source and load, suitable for low-voltage, high-current applications

5 Resistive load: power absorbed by the load resistor:
 power factor :Pf=1

6 R-L load: Fig.4-3

7 If L is relatively large, the load current is essentially dc. ( )
Source harmonics are rich in the odd-numbered harmonics. Filters:reducing the harmonics.

8 R-L source load: Fig.4-5

9 Discontinuous current is analyzed like section 3-5.
 For continuous current operation, the only modification to the analysis that was done for R-L load is in the dc term of the Fourier series .The dc component of current in this circuit is.  The sinusoidal terms in the Fourier analysis are unchanged by the dc source, provided that the current is continuous.    Discontinuous current is analyzed like  section 3-5.

10  Capacitance output filter: Fig.  4-6

11 =? solved numerically for
Assuming ideal diodes :the angle where the diodes become reverse biased, which is the same as for the half-wave rectifier  and is =?  solved numerically for   Peak-to-peak variation(ripple):

12 minimal output voltage occurs at
 In practical circuits where ωRC , minimal output voltage occurs at   is half that of the half-wave rectifier.

13 voltage doubler(sw. closed)
Fig. 4-7 (a) Voltage doubler Fig. 4-7 (b) Dual voltage rectifier        =full-wave rectifier(sw. open)+         voltage doubler(sw. closed)

14 L-C filtered output: Fig.4-8
C holds the output voltage at a constant level, and the L smoothes the current from rectifier and reduces the peak current in diodes.

15 =0 , full-wave rectified Continuous Current:
 The variation in  can be estimate from the first  Ac term (n=2)  in the Fourier series.  The amplitude of the inductor current for n=2 is  where   For Continuous current,  

16 Discontinuous current: When is positive ( at )

17  Procedure for determining Vo:
Estimate a Value for Vo slightly below Vm, and solve    (2) Solve  numerically, (3) Solve  (4) Slove Vo= (5) Repeat step (1)~(4)  until the computed Vo in step(4)   equals the estimated Vo in step(1) Output Voltage for discontinuous current is larger than  for continuous current.(see Fig4-8(d))

18 4-3 controlled full-wave rectifiers
Resistive load:  Fig.4-10

19 The rms current in source is the same as the rms current in the load.
 The power delivered to the load  The rms current in source is the same as the rms current in  the load.

20 R-L load : Fig.4-11

21 For discontinuous current
 Analysis of the controlled full-wave rectifier operating in the discontinuous current mode is identical to that of the controlled half-wave rectifier, except that the period for the output current is  .

22 continuous current

23  Fig 4-12


25 R-L Source load : Fig.4-14  The SCRS may be turned on at any time that they are forward biased, which is at an angle

26 average load current is
  For continuous current case, the average bridge output voltage is average load current is   The ac voltage terms are unchanged from the controlled rectifier with an R-L load.  The ac current terms are determined from circuit.  Power absorbed by the dc voltage is Power absorbed by resistor in the load is

27 Controlled Single-phase converter operating as an inverter:
seeing  Fig 4-14.  4-15 .

28  Vdc and Vo must be negative
For inverter operation, power is supplied by the dc source, and power is absorbed by the bridge and is transferred to the ac system.   Vdc and Vo must be negative    rectifier operation              inverter operation

29 4-4 Three-phase rectifiers
Resistive load : Fig 4-16  


31 A transition of the highest line-to-line voltage must take place every
 上、下半部Diode,每次僅一個ON;同相上、下Diode不可同時ON;Diode ON由瞬間最大線電壓決定。  A transition of the highest line-to-line voltage must take place every  .  Because of the six transitions that occur for each period of the source voltage, the circuit is called a six-pulse rectifier.  vo(t)之基頻為 電源頻率之6倍  Diode turn on in the sequence 1,2,3,4,5,6,1,..

32 Each diode conducts one-third of the time, resulting in
 Apparent power from the three-phase source is

33 Since the output voltage is periodic with period 1/6 of the ac supply voltage, the harmonics in the output are of order 6kω, k=1,2,3,… Adevantage:output is inherently like a dc voltage, and the high-frequency low-amplitude harmonics enable filters to be effective.

34  For a dc load current (constant I0) --- Fig4.17

35 which consists of terms at fundamental frequency of the ac system and harmonics of order 6k
 Filters(Fig.4-18)  are frequently necessary to prevent harmonic currents to enter the ac system.  Resonant filters for 5th and 7th harmonics.  High-pass filters for higher order harmonics.

36 4-5 Controlled three-phase rectifiers

37  Harmonics for output voltage remain of order 6k, but amplitude are functions of 
.  seeing  Fig. 4-20


39 Twelve-pulse rectifiers:using two six-pulse bridges

40 This results in inputs to two bridges which are
 The purpose of the   transformer connection is to introduce phase  shift between the source and bridge. This results in inputs to two bridges which are   apart. The two bridge outputs are similar, but also shifted by .  The delay angles for the bridge are typically the same.  The peak output of the twelve-pulse converter occurs midway between alternate peaks of the six-pulse converters. Adding the voltages at that point for gives 

41  Since a transition between conducting SCRs every 
, there are a total of 12 such transitions for each period of the ac source.  The output has harmonic frequencies which are multiple of 12 times the source fre. (12k  k=1,2,…) Cancellation of harmonics 6(2n-1) , n=1, 2, … has resulted from this transformer and converter configuration.

42  This principle can be expanded to arrangements of higher pulse number by incorporating increased number of six-pulse converters with transformers which have the appropriate phase shifts.  The characteristic ac harmonics of a p-pulse converter will be  pk   ,  k=1,2,3…  More expense for producing high-voltage transformers with the appropriate phase shifts.

43 Three-phase converter operating as a inverter:
 seeing 4-22. 

44  The bridge output voltage Vo must be negative.

45 4-6 DC power transmission
․ By using controlled twelve-pulse converter (generally). ․ Used for very long distances of transmission lines. Advantages:(1)   ,  voltage drop↓ in lines (2)   ,  line loss  ( ) (3) Two conductors required rather than three (4) Transmission towers are smaller. (5 ) Power flow in a dc transmission line is controllable  by adjustment of delay angles at the terminals. (6) Power flow can be modulated during disturbances on    one of the ac system.  System stability increased. (7) The two ac systems that are connected by the dc line  do not need to be in synchronization. Disadvantages:costly ac-dc converter, filter, and control system required at each end of the line to interface with the ac system.

46 Fig.4-23  using six-pulse converter

47 For current being ripple free 
 Power supplied by the converter at terminal 1 is   Power supplied by the converter at terminal 2 is 

48 Fig.4-24 using twelve-pulse converter
      (a bipolar scheme)

49 One of the lines is energized at and the other is energized at -
 One of the lines is energized at   and the other is energized at In emergency situations, one pole of the line can operate without the other pole, with current returning through the ground path.

50 4-7 commutation :effect of source inductance ( )
  Single-phase bridge  rectifier: Fig.4-25

51 Commutation interval starts at ωt=
 Assume that the load current is constant Io. Commutation interval starts at ωt= Commutation is completed at ωt= +u => Commutation angle:

52 Average load voltage is
  Source inductance lowers the average output voltage of full-wave rectifier.

53 Three-phase rectifier:  Fig.4-26

54  During Commutation from   , The voltage across La is
 Current in  starts at I0 and decreases zero in the   commutation interval

55 During the commutation interval from , the converter output voltage is
Average output Voltage:  類似 Single-phase rectifier  Source inductance lowers the average output voltage of three-phase rectifiers.

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