1. AC to DC Converters Outline 2.1 Single-phase controlled rectifier
2.2 Three-phase controlled rectifier
2.3 Effect of transformer leakage inductance on rectifier circuits
2.4 Capacitor-filtered uncontrolled rectifier
2.5 Harmonics and power factor of rectifier circuits
2.6 High power controlled rectifier
2.7 Inverter mode operation of rectifier circuit
2.8 Thyristor-DC motor system
2.9 Realization of phase-control in rectifier

2. 2. 1 Single- phase controlled (controllable) rectifier 2. 1
2.1 Single- phase controlled (controllable) rectifier Single-phase half-wave controlled rectifier

3. Inductive (resistor-inductor) load

4. Basic thought process of time-domain analysis for power electronic circuits
The time- domain behavior of a power electronic circuit is actually the combination of consecutive transients of the different linear circuits when the power semiconductor devices are in different states.

5. Single- phase half- wave controlled rectifier with freewheeling diode
load (L is large enough) Inductive

6. Maximum forward voltage, maximum reverse voltage
Disadvantages:
–Only single pulse in one line cycle
–DC component in the transformer current

7. 2.1.2 Single- phase bridge fully-controlled rectifier
Resistive load

8. Average output (rectified) voltage:
Average output current:
For thyristor:
For transformer:

9. Inductive load (L is large enough)

10. Electro- motive-force (EMF) load With resistor

11. With resistor and inductor
When L is large enough, the output voltage and current waveforms are the same as ordinary inductive load.
When L is at a critical value

12. 2.1.3 Single- phase full- wave controlled rectifier

13. 2.1.4 Single- phase bridge half-controlled rectifier

14. Another single- phase bridge half-controlled rectifier
Comparison with previous circuit:
–No need for additional freewheeling diode
–Isolation is necessary between the drive circuits of the two thyristors

15. Summary of some important points in analysis
When analyzing a thyristor circuit, start from a diode circuit with the same topology. The behavior of the diode circuit is exactly the same as the thyristor circuit when firing angle is 0.
A power electronic circuit can be considered as different linear circuits when the power semiconductor devices are in different states. The time- domain behavior of the power electronic circuit is actually the combination of consecutive transients of the different linear circuits.
Take different principle when dealing with different load
– For resistive load: current waveform of a resistor is the same as the voltage waveform
–For inductive load with a large inductor: the inductor current can
be considered constant

16. 2.2 Three- phase controlled (controllable) rectifier
2.2.1 Three- phase half- wave controlled rectifier
Resistive load, α= 0º

17. Resistive load, α= 30º

18. Resistive load, α= 60º

19. Resistive load, quantitative analysis
When α≤ 30º , load current id is continuous.
When α > 30º , load current id is discontinuous.
Average load current
Thyristor voltages

20. Inductive load, L is large enough

21. Thyristor voltage and currents, transformer current :

22. 2.2.2 Three- phase bridge fully-controlled rectifier
Circuit diagram
Common- cathode group and common- anode group of thyristors
Numbering of the 6 thyristors indicates the trigger sequence.

23. Resistive load, α= 0º

25. Resistive load, α= 30º

27. Resistive load, α= 60º

29. Resistive load, α= 90º

31. Inductive load, α= 0º

33. Inductive load, α= 30º

35. Inductive load, α= 90º

37. Quantitative analysis
Average output voltage:
For resistive load, When a > 60º, load current id is discontinuous.
everage output current (load current):
Transformer current:

38. 2.3 Effect of transformer leakage inductance on rectifier circuits
In practical, the transformer leakage inductance has to be taken into account.
Commutation between thyristors, thus can not happen instantly,but with a commutation process.

39. Commutation process analysis
Circulating current ik during commutation
Output voltage during commutation

40. Quantitative calculation
Reduction of average output voltage due to the commutation process
Calculation of commutation angle
– Id ↑,γ↑
– XB↑, γ↑
– For α ≤ 90۫ , α↓, γ↑

41. Summary of the effect on rectifier circuits

42. Conclusions
–Commutation process actually provides additional working states of the circuit.
–di/dt of the thyristor current is reduced.
–The average output voltage is reduced.
–Positive du/dt
– Notching in the AC side voltag

43. 2.4 Capacitor- filtered uncontrolled (uncontrollable) rectifier
2.4.1 Capacitor- filtered single- phase uncontrolled rectifier
Single-phase bridge, RC load:

44. Single-phase bridge, RLC load

45. 2.4.2 Capacitor- filtered three- phase uncontrolled rectifier
Three-phase bridge, RC load

46. Three- phase bridge, RC load Waveform when ωRC≤1.732

47. Three- phase bridge, RLC load

48. 2.5 Harmonics and power factor of rectifier circuits
2.5.1 Basic concepts of harmonics and reactive power
For pure sinusoidal waveform
For periodic non-sinusoidal waveform
where

49. Harmonics-related specifications
Take current harmonics as examples
Content of nth harmonics
In is the effective (RMS) value of nth harmonics.
I1 is the effective (RMS) value of fundamental component.
Total harmonic distortion
Ih is the total effective (RMS) value of all the harmonic components.

50. Definition of power and power factor for sinusoidal circuits
Active power
Reactive power
Apparent power
Power factor

51. Definition of power and power factor For non- sinusoidal circuit
Active power:
Power factor:
Distortion factor (fundamental- component factor):
Displacement factor (power factor of fundamental component):
Definition of reactive power is still in dispute

52. Review of the reactive power concept
The reactive power Q does not lead to net transmission of energy between the source and load. When Q ≠ 0, the rms current and apparent power are greater than the minimum amount necessary to transmit the average power P.
Inductor: current lags voltage by 90°, hence displacement factor is zero. The alternate storing and releasing of energy in an inductor leads to current flow and nonzero apparent power, but P = 0. Just as resistors consume real (average) power P, inductors can be viewed as consumers of reactive power Q.
Capacitor: current leads voltage by 90°, hence displacement factor is zero. Capacitors supply reactive power Q. They are often placed in the utility power distribution system near inductive loads. If Q supplied by capacitor is equal to Q consumed by inductor, then the net current (flowing from the source into the capacitor- inductive- load combination) is in phase with the voltage, leading to unity power factor and minimum rms current magnitude.

53. 2.5.2 AC side harmonics and power factor of controlled rectifiers with inductive load
Single- phase bridge fully-controlled rectifier

54. AC side current harmonics of single- phase bridge fully-controlled rectifier with inductive load
Where
Conclusions
–Only odd order harmonics exist
– In∝1/n
– In / I1 = 1/n

55. A typical gate triggering control circuit

56. Three- phase bridge fully-controlled rectifier

58. AC side current harmonics of three- phase bridge fully- controlled rectifier with inductive load
where

59. 2.5.3 AC side harmonics and power factor of capacitor- filtered uncontrolled rectifiers
Situation is a little complicated than rectifiers with inductive load.
Some conclusions that are easy to remember:
–Only odd order harmonics exist in single- phase circuit, and only 6k±1 (k is positive integer) order harmonics exist in three- phase circuit.
–Magnitude of harmonics decreases as harmonic order increases.
–Harmonics increases and power factor decreases as capacitor increases.
–Harmonics decreases and power factor increases as inductor increases.

60. 2.5.4 Harmonic analysis of output voltage and current

61. Ripple factor in the output voltage
Output voltage ripple factor
where UR is the total RMS value of all the harmonic components in the output voltage
and U is the total RMS value of the output voltage

62. Harmonics in the output current
where

63. Conclusions
for α = 0º
Only mk (k is positive integer) order harmonics exist in the output voltage and current of m- pulse rectifiers
Magnitude of harmonics decreases as harmonic order increases when m is constant.
The order number of the lowest harmonics increases as m increases. The corresponding magnitude of the lowest harmonics decreases accordingly.
For α ≠ 0º
Quantitative harmonic analysis of output voltage and current is very
complicated for α ≠ 0º.
As an example,for 3- phase bridge fully- controlled rectifie

64. 2.6 High power controlled rectifier
2.6.1 Double- star controlled rectifier
Circuit Waveforms When α= 0º

65. Effect of interphase reactor(inductor, transformer)

66. Quantitative analysis when α = 0º

67. Waveforms when α > 0º

68. 2.6.2 Connection of multiple rectifiers

69. Phase-shift connection of multiple rectifiers
Parallel connection

70. Series connection

71. Sequential control of multiple series-connected rectifiers

72. 2.7 Inverter mode operationof rectifiers
Review of DC generator- motor system

73. Inverter mode operation of rectifiers
Rectifier and inverter mode operation of single- phase full- wave converter

74. Necessary conditions for the inverter mode operation of controlled rectifiers
There must be DC EMF in the load and the direction of the DC EMF must be enabling current flow in
thyristors. (In other word EM must be negative if taking the ordinary output voltage direction as positive.)
α > 90º so that the output voltage Ud is also negative.

75. Inverter mode operation of 3- phase bridge rectifier

76. Inversion angle (extinction angle) β
α+ β=180º
Inversion failure and minimum inversion angle
Possible reasons of inversion failures
–Malfunction of triggering circuit
–Failure in thyristors
–Sudden dropout of AC source voltage
–Insufficient margin for commutation of thyristors
Minimum inversion angle (extinction angle)
βmin= δ + γ+ θ′（2-109）

78. 2.8 Thyristor- DC motor system
2.8.1 Rectifier mode of operation

79. Speed- torque (mechanic) characteristic when load current is continuous

80. Speed- torque (mechanic) characteristic when load current is discontinuous
EMF at no load (taking 3- phase half-wave as example)

81. 2.8.2 Inverter mode of operation

82. 2.8.3 Reversible DC motor drive system(4-quadrant operation)

84. 2.9 Gate triggering control circuit for thyristor rectifiers
A typical gate triggering control circuit