377275109-Ch-2-Uncontrolled-Rectifiers-Autosaved.pptx

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1. Power Electronics & Drives College of Engineering and Technology Adigrat University Electrical & Computer Engineering Department ECEg4222/4312: Power Electronics G/Tsadik Teklay (M.Sc. Electrical Power Engineering) Chapter 2 Uncontrolled Rectifiers

2. Contents Basic rectifier concepts and AC to DC Converters Types of Uncontrolled Rectifiers Single-Phase Half-Wave Rectifiers Single-Phase Full-Wave Rectifiers Three-Phase Rectifiers (Half-Wave and Full-Wave) Effect of source inductance on rectifier operation

3. Objectives Understand operation of half-wave and full-wave rectifier circuits Determination of dc output voltages and currents for single phase and three phase rectifiers. Analyze the performance of a single phase and three phase uncontrolled rectifiers. Analyze the operation of rectifier circuit with capacitor filter Calculation of peak inverse voltage for rectifier circuits Define the problem occurs when connecting inductive load to single phase half wave rectifier and how to solve it using freewheeling diode. Analyze the effect of source inductance on rectification process.

4. Introduction to Rectifiers (AC to DC Converters) For nearly a century, rectifier circuits have been the most common power electronic circuits used to convert a c to dc. The word rectification is used not because these circuits produce dc, but rather because the current flows in one direction ; only the average output signal (voltage or current) has a dc component. Moreover, since these circuits allow power to flow only from the source to load, the are often termed unidirectional converters . As will be seen shortly, when rectifier circuits are used solely, their outputs consist of dc along with high-ripple ac components. To significantly reduce or eliminate the output ripple, additional filtering circuitry is added at the output.

5. Basic rectifier concepts Several types of rectifier circuits are available: single-phase and three-phase half-wave and full-wave, controlled and uncontrolled, etc. For a given application, the type used is determined by the requirements of that application. In general the types of rectifiers are: 1. Uncontrolled Rectifier Provide a fixed d.c. output voltage for a given a.c . supply where diodes are used only . 2. Controlled Rectifier Provide an adjustable d.c. output voltage by controlling the phase at which the devices are turned on, where thyristors and diodes are used .

6. Cont’d Controlled Rectifiers A. Half-controlled allows electrical power flow from a.c . to d.c. (i.e. rectification only ) Fully-controlled allow power flow in both directions (i.e. rectification and inversion )

7. Uncontrolled Rectifiers The diode rectifiers are referred to as uncontrolled rectifiers, which make use of power semiconductor diodes to carry the load current. The diode rectifiers give a fixed dc output voltage (fixed average output voltage) and each diode rectifying element conducts for one half cycle duration (T/2 seconds), that is the diode conduction angle = 1800 or π radians. We cannot control (we cannot vary) the dc output voltage or the average dc load current in a diode rectifier circuit. Controlled SCR rectifiers are line-commutated ac to dc power converters that are used to convert a fixed voltage, fixed frequency ac power supply into variable dc output voltage.

8. Cont’d Applications of Rectifier Circuits : DC welder DC motor drive (Variable speed DC drives) Battery charger DC power supply HVDC Power rating of a single-phase rectifier tends to be lower than 10 kW. Three-phase bridge rectifiers are used for delivering higher power output, up to 500 kW at 500 V dc or even more.

9. Definitions

10. Single-phase Half-Wave Uncontrolled Rectifier with resistive load A single-phase half-wave rectifier consists of a single diode connected This is the simplest of the rectifier circuits. It produces an output waveform that is half of the incoming AC voltage waveform.

11. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Cont’d Resistive load

12. Cont’d

13. Rectifier Performance Parameters Output d.c. power (Average output power) Pdc = Vdc Idc Output ac power P ac = V rms I rms Efficiency of a rectifier,

14. Cont’d  

15.   or,

18. Analysis of Single-phase Half-Wave Uncontrolled Rectifier with resistive load Average (dc) value of output voltage:

19. With R-L Load An increase in the conduction period of the load current can be achieved by adding inductor in series with the load resistance. Due to the inductive load, the conduction period of the diode will extend beyond 180 o until the current becomes zero, This means the load current flows not only during Vs <0, but also for a portion of Vs<0. the diode is kept in the on state by inductor’s voltage, which offsets the negative voltage of Vs(t). The load current is present between T/2 and T, but never for the entire period, regardless of the inductor size. This can be easily explained by assuming that the diode conducts for the entire period. Consequently, the output voltage V0 must equal Vs, since the diode voltage is zero. This can occur only when the load current is alternating. This is clearly a contradiction, and there must be a time in which the diode stops conducting.

20. A Simple Circuit ( R-L Load) Current continues to flows for a while even after the input voltage has gone negative

21. A Simple Circuit ( R-L Load)

22. Cont’d

23. Cont’d During diode conduction, The solution of this differential equation is : At This is a transcendental equation and can be solved by iterative techniques . The extinction angle can be determined for a given load impedance angle  .

24. Cont’d Equation of the current: The equation for the current through R-L load can be found from the solution of the differential equation (3.16) which can be re-written as: This is a first order differential equation. The solution of this equation has two parts: Force response or particular response (has the same form as the input) Natural response or homogeneous response (due to the behavior the circuit itself)

27. Cont’d The average output voltage is The average output current is

28. Peak Inverse Voltage The maximum amount of reverse bias that a diode will be exposed to is called the peak inverse voltage or PIV. For the half wave rectifier, the value of PIV is: The reasoning for the above equation is that when the diode is reverse biased, there is no voltage across the load. Therefore, all of the secondary voltage (Vm) appears across the diode. The PIV is important because it determines the minimum allowable value of reverse voltage for any diode used in the circuit.

29. With free-wheeling Diode Without free-wheeling, as the previous diode, the circuit is characterized by discontinuous and high ripple current. Continuous load current can result when a diode D m , called free-wheeling diode, is added across the load. D m prevents the voltage across the load (output voltage) from reversing during the - ve half-cycle of the supply voltage. When diode D 1 ceases to conduct at zero volts, D m provides an alternative free-wheeling path. That means when D1 is off, Dm allows energy in the circuit to maintain continuity by providing a path through which the inductor current can “ free wheel ”.

31. Half-wave Rectifier with Capacitor Filter The capacitor is the most basic filter type and is the most commonly used. The half-wave rectifier for power supply application is shown below. A capacitor filter is connected in parallel with the load. The rectifier circuit is supplied from a transformer . Circuit operation The operation of this circuit during positive half cycle of the source voltage is shown in figure 8. During the positive half cycle, diode D1 will conduct, and the capacitor charges rapidly. As the input starts to go negative, D1 turns off, and the capacitor will slowly discharge through the load (figure 9 ). Figure 8: Half wave rectifier with capacitor filter – positive half cycle Figure 9: Half wave rectifier with capacitor filter – negative half cycle

32. Using the previous half wave rectifier as an example, figure 10 examines what is happening with our filter. (a) Unfiltered output from the half wave rectifier (b) When the next pulse does arrive, it charges the capacitor back to full charge as shown on the right. The thick line shows the charge – discharge waveform at the capacitor. (c) The load sees a reasonably constant DC voltage now, with a ripple voltage on top of it.

33. A Simple Circuit (Load has a dc back-emf) Current begins to flow when the input voltage exceeds the dc back-emf Current continues to flows for a while even after the input voltage has gone below the dc back-emf

34. Effect of source inductance on rectifier operation Ideal VS real rectifier with source inductance The output DC voltages of the rectifier circuits discussed so far have been found by assuming that diode currents transfer (commutate) from one diode to another instantaneously (rectification in previous reciter was insensitive to the location of L). However this can not happen when the AC source has some inductance Ls . (Change of current through any inductance must take some time!). The presence of inductance on the ac side as well as on the dc side creates a third topological state of network: both diodes are on simultaneously. This state is known as commutation state because the load current is transferred, or commutated, from one diode to the other during this state. This source inductance is associated with the leakage inductance of the supply transformer and the inductance of the AC supply network to the input transformer. The commutation process (or the overlap process) forces more than one diode or a pair of diodes (in a bridge rectifier) to conduct simultaneously, resulting in a drop voltage from the output terminals which is proportional to the load current.

35. Commutation Process In the following analysis, we will assume that L/R >>T/2 so that the load current io is constant. This assumption is valid since in many applications the load inductance is very much larger than the ac-side inductance. The behavior of the circuit can easily be analyzed by assuming that one of the diodes, D1, is conducting for some time during the positive half cycle of the source Vs (t), while D2 is off. Since the current in D1 is constant, then the voltage across Ls is zero and the voltage across D2 or Vo is positive and is forced to equal the source voltage. During this mode, we have the following current and voltage values:

36. Cont’d At t=T/2, Vs (t) starts to become negative, causing D1 to stop conducting. However, since the current in D1 is the same as the inductance current, which is not allowed to change instantaneously, D2 turns on in order to maintain the inductor current’s continuity. During this overlapping time, when both diodes are conducting, is(t) changes from +I0 to zero, while iD2(t) changes from zero to +I0. the time during which both D1 and D2 are is known as the commutation period, and has a duration in electrical degrees. This is why the ac-side inductance, Ls , is know as the commutation inductance. This circuit mode of operation is referred to as commutation mode. During mode, the following equations hod :  

37. Cont’d The initial condition for for is(t) at t=T/2 is I0. using the above VLs equation with the given initial condition, we obtain the following input current integration: Substituting for VLs(t)= Vs in the integral and solving for is(t), we obtain  

38. Cont’d At the end of the commutation period, ; is(t) becomes zero, forcing D1 to turn off at zero current; and D2 remains forward biased, carrying the load current as shown in the circuit mode 3: In this mode we have the following current and voltage equations”  

39. Cont’d Let us assume that the load current Id is smooth and ripple-free (i.e., of constant, due to the highly inductive load).Assume also that for ωt > 0, the load current flows through the rectifier diode and that for ωt > π, it commutates to the free-wheeling diode Df . This transfer of the load current between the rectifier and the freewheeling diodes can not however be instantaneous, because of the source inductance Ls . This transfer takes place over a small commutation or overlap angle µ, during which time, the current gradually falls to zero in one circuit and it rises to Id in the other circuit at the same rate. Clearly, the two diodes simultaneously conduct during the commutation process (µ).

40. Cont’d

41. Single-phase full-wave rectifier Full Bridge Rectifier – Simple R Load Full-wave Rectifier with Center tap Transformer

42. Full-Wave Rectifiers with R load Center-tapped D 1 i s + v s _ - v o + i D1 i D2 i o + v s1 _ + v s2 _ D 2 + v D1 - + v D2 - Center-tapped (CT) rectifier requires center-tap transformer. Full Bridge (FB) does not. CT: 2 diodes FB: 4 diodes. Hence, CT experienced only one diode volt-drop per half-cycle Conduction losses for CT is half. Diodes ratings for CT is twice than FB + v s _ i s i D1 + v o _ i o Full Bridge D 1 D 2 D 4 D 3

43. Cont’d

44. 46 Bridge waveforms p 2p 3p 4p V m V m -V m -V m v s v o v D1 v D2 v D3 v D4 i o i D1 i D2 i D3 i D4 i s + v s _ i s i D1 + v o _ i o Full Bridge D 1 D 2 D 4 D 3

45. 47 Center-tapped waveforms p 2p 3p 4p V m V m -2V m -2V m v s v o v D1 v D2 i o i D1 i D2 i s Center-tapped D 1 i s + v s _ - v o + i D1 i D2 i o + v s1 _ + v s2 _ D 2 + v D1 - + v D2 -

46. Full wave bridge, R-L load

47. Full wave bridge, R-L load + v s _ i s i D1 + v o _ i o + v R _ + v L _ v o v s i o i D1 , i D2 i D3 ,i D4 i s w t p 2p

48. 50 Approximation with large L

49. 51 R-L load approximation v o v s i o i D1 , i D2 i D3 ,i D4 i s w t p 2p with a large L (i.e. L → ∞) is used in the filter, io becomes a constant DC current

50. Cont’d Average output rectified voltage is : Input power factor calculations The input real power is defined by : Vs is the RMS value of the input voltage ( vs ); Is1 is the RMS current of the fundamental component of is ; θ represents the phase difference between vs and is1 Since the input current (is) is now a square waveform, using Fourier series, is can be expressed as:

51. Cont’d

52. Cont’d

53. Cont’d Full Bridge Rectifier – Simple Constant Load Current ( Idealized case with a purely dc output current THD=48.43%

54. Three-phase rectifiers Many industrial applications require high power that a single-phase system is unable to provide. Three-phase diode rectifier circuits are used widely in high-power applications with low output ripple. In this section, we will cover both half- and full-wave rectifier circuits under resistive and high inductive loads.

55. Cont’d Figure below shows the general configuration for an m-phase half-wave rectifier connected to a single load. The explanation of the circuit is quite simple since all diode cathodes are connected to the same point, creating diode-OR arrangement. At any given time, the highest anode voltage will cause its corresponding diode to conduct, with all other diodes in the reverse-bias state . In other words, the output voltage will ride on the peak voltage at all times. Fig 2 shows four random sine functions and the output voltage.

56. Cont’d The half-wave three-phase resistive-load rectifier circuit is shown. We assume that the three-phase voltage source is configuration with the three balanced voltages given by Figure (b) shows the output waveform. This circuit is also known as a three-pulse recti fier circuit. Here, the number of pulses refers to the number of voltage peaks in a given cycle.  

57. A diode will turn-on when its voltage is higher than the other two diodes, i.e., the diode connected to the highest of the three voltages will conduct. The resulting output is shown in Fig. 2.30b; notice that the diode conduction starts and ends when two of the three voltages are equal. Also, each diode conducts for an angle of 120 , and the output voltage has 3 pulses, during one cycle of the input . Therefore, the fundamental frequency of the output voltage is three times the frequency of the input voltage. The DC component of the output of each of them can be calculated by the average over its period as: The DC voltage is higher than the output voltage of a single-phase full-wave rectifier. Of course, the drawback is the need of a three-phase source, which is most common for industrial applications.

58. Cont’d Fig (a) and (b) show the equivalent circuit for a half-wave circuit under a highly inductive load and waveforms, respectively.

59. Three-phase Full-Wave rectifiers Two groups with three diodes each The full-bridge rectifier is more common since it provides a high output voltage and less ripple . If two 3-pulse rectifiers are connected the resulting topology is shown in Fig.. This circuit is known as a 6-pulse rectifier , and it is the building block for all high power multiple-pulse rectifier circuits.

60. Cont’d

61. Three-phase rectifiers 63 D 1 v o =v p - v n + v o _ v pn v nn i o D 3 D 2 D 6 + v cn - n + v bn - + v an - D 5 D 4 p 2p 4p V m V m v an v bn v cn v n v p v o = v p - v n 3p

62. Cont’d Top group: diode with its anode at the highest potential will conduct. The other two will be reversed. Bottom group: diode with the its cathode at the lowest potential will conduct. The other two will be reversed. For example, if D 1 (of the top group) conducts, v p is connected to v an . . If D 6 (of the bottom group) conducts, v n connects to v bn . All other diodes are off. The resulting output waveform is given as: v o = v p -v n For peak of the output voltage is equal to the peak of the line to line voltage v ab .

63. Cont’d

64. Cont’d The 6-pulse rectifier is the building block for all high power multiple-pulse rectifier circuits . Two 6-pulse rectifier circuits can be connected through the use of Y-Y and Δ Y transformers for building 12-pulse rectifiers. If the two rectifiers are connected in series, the resulting circuit is shown in Fig. 2.32a and is suitable for high voltage , whereas the converter is connected in parallel as shown in Fig. 2.32b, the circuit is suitable for high current.

65. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Single-Phase Diode Rectifier Bridge Large capacitor at the dc output for filtering and energy storage

66. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Diode-Rectifier Bridge Analysis Two simple (idealized) cases to begin with: (a) R load (b) current load R load I load

67. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Waveforms with a purely resistive load at the output

68. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Diode-Rectifier Bridge Input Current Idealized case with a purely dc output current THD=48.43% DPF =1.0 PF=DPF x I s1 / Is = 0.9

69. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Diode-Rectifier Analysis with AC-Side Inductance Output current is assumed to be purely dc

70. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Understanding Current Commutation Assuming inductance to be zero

71. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Understanding Current Commutation #2 Assuming inductance to be zero

72. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Understanding Current Commutation #3 Assuming inductance to be zero

73. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Understanding Current Commutation #4 Inductance is included

74. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Current Commutation Waveforms v d v L i s u I d

75. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Current Commutation Waveforms

76. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Average voltage < V d > When L=0 With finite L Reduction in average output voltage

77. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Current Commutation in Full-Bridge Rectifier

78. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Current Commutation in Full-Bridge Rectifier

79. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Current Commutation Waveforms

80. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Average voltage < V d > When L=0 With finite L Reduction in average output voltage

81. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Conclusions Average output voltage drops with increased current increased frequency Increased L Load Regulation is a major consideration in most rectifier systems because voltage changes with load ( I L )

82. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Diode-Rectifier with a Capacitor Filter Power electronics load is represented by an equivalent load resistance

83. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Diode-Bridge Rectifier: Waveforms Analysis using PSpice

84. Copyright © 2008 by Jose Bastos Chapter 5 Line-Frequency Diode Rectifiers Voltage Doubler Rectifier In 115-V position, one capacitor at-a-time is charged from the input. input input