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Power Electronics

Power Electronics. Chapter 3 AC to DC Converters (Rectifiers). Outline. 3.1 Single-phase controlled rectifier 3.2 Three-phase controlled rectifier 3.3 Effect of transformer leakage inductance on rectifier circuits 3.4 Capacitor-filtered uncontrolled rectifier

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Power Electronics

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  1. PowerElectronics Chapter 3 AC to DC Converters (Rectifiers)

  2. Outline 3.1 Single-phase controlled rectifier 3.2 Three-phase controlled rectifier 3.3 Effect of transformer leakage inductance on rectifier circuits 3.4 Capacitor-filtered uncontrolled rectifier 3.5 Harmonics and power factor of rectifier circuits 3.6 High power controlled rectifier 3.7 Inverter mode operation of rectifier circuit 3.8 Realization of phase-control in rectifier circuits

  3. 3.1 Single-phase controlled (controllable) rectifier 3.1.1 Single-phase half-wave controlled rectifier 3.1.2 Single-phase bridge fully-controlled rectifier 3.1.3 Single-phase full-wave controlled rectifier 3.1.4 Single-phase bridge half-controlled rectifier

  4. 3.1.1 Single-phase half-wave controlled rectifier • Half-wave, single-pulse • Triggering delay angle, delay angle, firing angle Resistive load (3-1)

  5. Inductive (resistor-inductor) load 3.1.1 Single-phase half-wave controlled rectifier

  6. 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. (3-2) ωt =a，id= 0 (3-3)

  7. VT i T d i VD R L u VT a) u u u 2 1 d R VD R Single-phase half-wave controlled rectifier with freewheeling diode Inductive load (L is large enough) • Maximum forward voltage, maximum reverse voltage • Disadvantages: • Only single pulse in one line cycle • DC component in the transformer current (3-5) (3-6) (3-7) (3-8)

  8. Resistive load 1 3 i VT VT d i 2 T a u R u u d 1 2 b 2 4 VT VT a) 3.1.2 Single-phase bridge fully-controlled rectifier • For thyristor: maximum forward voltage, maximum reverse voltage • Advantages: • 2 pulses in one line cycle • No DC component in the transformer current

  9. 3.1.2 Single-phase bridge fully- controlled rectifier Resistive load • Average output (rectified) voltage (3-9) • Average output current (3-10) • For thyristor (3-11) (3-12) • For transformer (3-13)

  10. 3.1.2 Single-phase bridge fully-controlled rectifier Inductive load(L is large enough) • Commutation • Thyristor voltages and currents • Transformer current (3-15)

  11. Electro-motive-force (EMF) load • Discontinuous current id With resistor

  12. Electro-motive-force (EMF) load 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 (3-17)

  13. 3.1.3 Single-phase full-wave controlled rectifier • Transformer with center tap • Comparison with single-phase bridge fully-controlled rectifier

  14. 3.1.4 Single-phase bridge half-controlled rectifier • Half-control • Comparison with fully-controlled rectifier • Additional freewheeling diode 1 2 i VT VT i d a 2 T L R u VD u d 2 R b 3 4 VD VD

  15. 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

  16. 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

  17. 3.2 Three-phase controlled (controllable) rectifier 3.2.1 Three-phase half-wave controlled rectifier (the basic circuit among three-phase rectifiers) 3.2.2 Three-phase bridge fully-controlled rectifier (the most widely used circuit among three-phase rectifiers)

  18. 3.2.1 Three-phase half-wave controlled rectifier Resistive load, a = 0º • Common-cathode connection • Natural commutation point

  19. Resistive load, a = 30º

  20. Resistive load, a = 60º

  21. Resistive load, quantitative analysis • When a 30º, load current id is continuous. • When a > 30º, load current id is discontinuous. (3-18) (3-19) • Average load current • Thyristor voltages (3-20) 1- resistor load 2- inductor load 3- resistor-inductor load

  22. (3-23) (3-24) (3-25) Inductive load, L is large enough • Load current id is always continuous. • Thyristor voltage and currents, transformer current (3-18)

  23. 1 VT 1 i i a d T VT VT load a 5 3 u d n b c VT VT VT 2 6 4 d 2 3.2.2 Three-phase bridge fully-controlled rectifier d Circuit diagram • Common-cathode group and common-anode group of thyristors • Numbering of the 6 thyristors indicates the trigger sequence.

  24. Resistive load, a = 0º

  25. Resistive load, a = 30º

  26. Resistive load, a = 60º

  27. Resistive load, a = 90º

  28. Inductive load, a = 0º

  29. Inductive load, a = 30º

  30. Inductive load, a = 90º

  31. Quantitative analysis (3-26) • Average output voltage For resistive load, When a > 60º, load current id is discontinuous. • Average output current (load current) • Transformer current • Thyristor voltage and current • Same as three-phase half-wave rectifier • EMF load, L is large enough • All the same as inductive load except the calculation of average output current Electronics (3-27) (3-20) Power (3-28) (3-29) 31

  32. 3.3 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.

  33. Commutation process analysis • Circulating current ik during commutation • Commutation angle • Output voltage during commutation ub-ua = 2·LB·dia/dt ik: 0 Id ia = Id-ik : Id 0 ib = ik : 0 Id (3-30)

  34. Quantitative calculation • Reduction of average output voltage due to the commutation process • Calculation of commutation angle • Id ,g • XB ,g • For a 90o , a , g (3-31) (3-36)

  35. Single-phase full wave Single-phase bridge Three-phase half-wave Three-phase bridge m-pulse recfifier ① ② Circuits Summary of the effect on rectifier circuits • 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 voltage

  36. 3.4 Capacitor-filtered uncontrolled (uncontrollable) rectifier • Emphasis of previous sections • Controlled rectifier, inductive load • Uncontrolled rectifier: diodes instead of thyristors • Wide applications of capacitor-filtered uncontrolled rectifier • AC-DC-AC frequency converter • Uninterruptible power supply • Switching power supply 3.4.1 Capacitor-filtered single-phase uncontrolled rectifier 3.4.2 Capacitor-filtered three-phase uncontrolled rectifier

  37. Single-phase bridge, RC load 3.4.1 Capacitor-filtered single-phase uncontrolled rectifier

  38. Single-phase bridge, RLC load 3.4.1 Capacitor-filtered single-phase uncontrolled rectifier

  39. Three-phase bridge, RC load 3.4.2 Capacitor-filtered three-phase uncontrolled rectifier

  40. Three-phase bridge, RC load Waveform when wRC1.732 a）wRC=b）wRC< 3.4.2 Capacitor-filtered three-phase uncontrolled rectifier

  41. Three-phase bridge, RLC load 3.4.2 Capacitor-filtered three-phase uncontrolled rectifier

  42. 3.5 Harmonics and power factor of rectifier circuits • Originating of harmonics and power factor issues in rectifier circuits • Harmonics: working in switching states—nonlinear • Power factor: firing delay angle causes phase delay • Harmful effects of harmonics and low power factor • Standards to limit harmonics and power factor 3.5.1 Basic concepts of harmonics and reactive power 3.5.2 AC side harmonics and power factor of controlled rectifiers with inductive load 3.5.3 AC side harmonics and power factor of capacitor-filtered uncontrolled rectifiers 3.5.4 Harmonic analysis of output voltage and current

  43. 3.5.1 Basic concepts of harmonics and reactive power • For pure sinusoidal waveform • For periodic non-sinusoidal waveform or where • Fundamental component • Harmonic components (harmonics) (3-54) (3-55) (3-56)

  44. 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. (3-57) (3-58)

  45. Definition of power and power factor For sinusoidal circuits • Active power • Reactive power Q=U Isinj • Apparent power S=UI • Power factorl =cosj (3-59) (3-61) (3-60) (3-63) (3-62) (3-64)

  46. Definition of power and power factor For non-sinusoidal circuits • Active power P=U I1cosj1 • Power factor • Distortion factor (fundamental-component factor) n =I1 / I • Displacement factor (power factor of fundamental component) l1 = cos1 • Definition of reactive power is still in dispute. (3-65) (3-66)

  47. 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 ¹ 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. Electronics Power 47

  48. 3.5.2 AC side harmonics and power factor of controlled rectifiers with inductive load Single-phase bridge fully-controlled rectifier

  49. n=1,3,5,… AC side current harmonics of single-phase bridge fully-controlled rectifier with inductive load • Conclusions • Only odd order harmonics exist • In 1/n • In / I1 = 1/n (3-72) where (3-73)

  50. Power factor of single-phase bridge fully-controlled rectifier with inductive load • Distortion factor • Displacement factor • Power factor (3-75) (3-76) (3-77)

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