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UNIT-IV
INVERTERS
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2. Single-Phase Inverters
Half-Bridge Inverter
One of the simplest types of inverter. Produces a square wave output.
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3. Single-Phase Inverters (cont’d)
Full Bridge (H-bridge) Inverter
Two half-bridge inverters combined.
Allows for four quadrant operation.
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4. Single-Phase Inverters (cont’d)
Quadrant 1: Positive step-down converter
(forward motoring)
Q1-On; Q2 - Chopping; D3,Q1 freewheeling
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5. Single-Phase Inverters (cont’d)
Quadrant 2: Positive step-up converter
(forward regeneration)
Q4 - Chopping; D2,D1 freewheeling
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6. Single-Phase Inverters (cont’d)
Quadrant 3: Negative step-down converter
(reverse motoring)
Q3-On; Q4 - Chopping; D1,Q3 freewheeling
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7. Single-Phase Inverters (cont’d)
Quadrant 4: Negative step-up converter
(reverse regeneration)
Q2 - Chopping; D3,D4 freewheeling
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8. Single-Phase Inverters (cont’d)
Phase-Shift Voltage Control - the output of the H-bridge inverter can be controlled by phase shifting the control of the component half-bridges. See waveforms on next slide.
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9. Single-Phase Inverters (cont’d)
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10. Single-Phase Inverters (cont’d)
The waveform of the output voltage vab is a quasi-square wave of pulse width . The Fourier series of vab is given by:
The value of the fundamental, a1=
The harmonic components as a function of phase angle are shown in the next slide.
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11. Single-Phase Inverters (cont’d)
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12. Three-Phase Bridge Inverters
Three-phase bridge inverters are widely used for ac motor drives. Two modes of operation - square wave and six-step. The topology is basically three half-bridge inverters, each phase-shifted by 2/3, driving each of the phase windings.
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13. Three-Phase Bridge Inverters (cont’d)
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14. Three-Phase Bridge Inverters (cont’d)
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15. Three-Phase Bridge Inverters (cont’d)
The three square-wave phase voltages can be expressed in terms of the dc supply voltage, Vd, by Fourier series as:
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16. Three-Phase Bridge Inverters (cont’d)
The line voltages can then be expressed as:
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17. Three-Phase Bridge Inverters (cont’d)
The line voltages are six-step waveforms and have characteristic harmonics of 6n1, where n is an integer. This type of inverter is referred to as a six-step inverter.
The three-phase fundamental and harmonics are balanced with a mutual phase shift of 2/3.
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18. Three-Phase Bridge Inverters (cont’d)
If the three-phase load neutral n is isolated from the the center tap of the dc voltage supply (as is normally the case in an ac machine) the equivalent circuit is shown below.
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19. Three-Phase Bridge Inverters (cont’d)
In this case the isolated neutral-phase voltages are also six-step waveforms with the fundamental component phase-shifted by /6 from that of the respective line voltage. Also, in this case, the triplen harmonics are suppressed.
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20. Three-Phase Bridge Inverters (cont’d)
For a linear and balanced 3 load, the line currents are also balanced. The individual line current components can be obtained from the Fourier series of the line voltage. The total current can be obtained by addition of the individual currents. A typical line current wave with inductive load is shown below.
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21. Three-Phase Bridge Inverters (cont’d)
The inverter can operate in the usual inverting or motoring mode. If the phase current wave, ia, is assumed to be perfectly filtered and lags the phase voltage by /3 the voltage and current waveforms are as shown below:
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22. Three-Phase Bridge Inverters
The inverter can also operate in rectification or regeneration mode in which power is pushed back to the dc side from the ac side. The waveforms corresponding to this mode of operation with phase angle = 2/3 are shown below:
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23. Three-Phase Bridge Inverters (cont’d)
The phase-shift voltage control principle described earlier for the single-phase inverter can be extended to control the output voltage of a three-phase inverter.
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24. Three-Phase Bridge Inverters (cont’d)
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25. Three-Phase Bridge Inverters (cont’d)
The three waveforms va0,vb0, and vc0 are of amplitude 0.5Vd and are mutually phase-shifted by 2/3.
The three waveforms ve0,vf0, and vg0 are of similar but phase shifted by .
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26. Three-Phase Bridge Inverters (cont’d)
The transformer’s secondary phase voltages, vA0, vB0, and vc0 may be expressed as follows:
where m is the transformer turns ratio
(= Ns/Np). Note that each of these waves is a function of  angle.
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27. Three-Phase Bridge Inverters (cont’d)
The output line voltages are given by:
While the component voltage waves va0, vd0, vA0 … etc. all contain triplen harmonics, they are eliminated from the line voltages because they are co-phasal. Thus the line voltages are six-step waveforms with order of harmonics = 6n1 at a phase angle .
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28. Three-Phase Bridge Inverters (cont’d)
The Fourier series for vA0 and vB0 are given by:
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29. Three-Phase Bridge Inverters (cont’d)
The Fourier series for vAB is given by:
Note that the triplen harmonics are removed in vAB although they are present in vA0 and vB0.
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PWM Technique
While the 3 6-step inverter offers simple control and low switching loss, lower order harmonics are relatively high leading to high distortion of the current wave (unless significant filtering is performed).
PWM inverter offers better harmonic control of the output than 6-step inverter.
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PWM Principle
The dc input to the inverter is “chopped” by switching devices in the inverter. The amplitude and harmonic content of the ac waveform is controlled by the duty cycle of the switches. The fundamental voltage v1 has max. amplitude = 4Vd/ for a square wave output but by creating notches, the amplitude of v1 is reduced (see next slide).
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32. PWM Principle (cont’d)
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PWM Techniques
Various PWM techniques, include:
Sinusoidal PWM (most common)
Selected Harmonic Elimination (SHE) PWM
Space-Vector PWM
Instantaneous current control PWM
Hysteresis band current control PWM
Sigma-delta modulation
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Sinusoidal PWM
The most common PWM approach is sinusoidal PWM. In this method a triangular wave is compared to a sinusoidal wave of the desired frequency and the relative levels of the two waves is used to control the switching of devices in each phase leg of the inverter.
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35. Sinusoidal PWM (cont’d)
Single-Phase (Half-Bridge) Inverter
Implementation
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36. Sinusoidal PWM (cont’d)
when va0> vT T+ on; T- off; va0 = ½Vd
va0 < vT T- on; T+ off; va0 = -½Vd
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37. Sinusoidal PWM (cont’d)
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38. Sinusoidal PWM (cont’d)
Definition of terms:
Triangle waveform switching freq. = fc (also called carrier freq.)
Control signal freq. = f (also called modulation freq.)
Amplitude modulation ratio, m = Vp VT
Frequency modulation ratio,
mf (P)= fc / f
Peak amplitude
of control signal
Peak amplitude
of triangle wave
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39. Multiple Pulse-Width Modulation
In multiple-pulse modulation, all pulses are the same width
Vary the pulse width according to the amplitude of a sine wave evaluated at the center of the same pulse
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40. Generate the gating signal
2 Reference Signals, vr, -vr
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41. Comparing the carrier and reference signals
Generate g1 signal by comparison with vr
Generate g4 signal by comparison with -vr
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42. Comparing the carrier and reference signals
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43. Potential problem if Q1 and Q4 try to turn ON at the same time!
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44. If we prevent the problem
Output voltage is low when g1 and g4 are both high
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45. This composite signal is difficult to generate
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46. Generate the same gate pulses with one sine wave
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Alternate scheme
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rms output voltage
Depends on the modulation index, M
Where δm is the width of the mth pulse
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49. Fourier coefficients of the output voltage
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Harmonic Profile
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51. Compare with multiple-pulse case for p=5
Distortion Factor is considerably less
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52. Series-Resonant Inverter
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Operation
T1 fired, resonant pulse of current flows through the load. The current falls to zero at t = t1m and T1 is “self – commutated”.
T2 fired, reverse resonant current flows through the load and T2 is also “self-commutated”.
The series resonant circuit must be underdamped,
R2 < (4L/C)
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54. Operation in Mode 1 – Fire T1
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To find the time when the current is maximum, set the first derivative = 0
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To find the capacitor voltage, integrate the current
The current i1 becomes = t=t1m
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59. Operation in Mode 2 – T1, T2 Both OFF
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t2m
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61. Operation in Mode 3 – Fire T2
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64. Space Vector Modulation
Space Vector Diagram
Active vectors: to
(stationary, not rotating)
Zero vector:
Six sectors: I to VI
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65. Space Vector Modulation
Space Vectors
Three-phase voltages
(1)
Two-phase voltages
(2)
Space vector representation
(3)
(2)  (3)
(4)
where
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66. Space Vector Modulation
Space Vectors (Example)
Switching state [POO]  S1, S6 and S2 ON
and
(5)
(5)  (4)
(6)
Similarly,
(7)
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67. Space Vector Modulation
Active and Zero Vectors
Active Vector: 6
Zero Vector: 1
Redundant switching
states: [PPP] and [OOO]
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68. Space Vector Modulation
Reference Vector Vref
Definition
Rotating in space at ω
(8)
Angular displacement
(9)
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69. Space Vector Modulation
Relationship Between Vref and VAB
Vref is approximated by two active
and a zero vectors
Vref rotates one revolution,
VAB completes one cycle
Length of Vref corresponds to
magnitude of VAB
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70. Space Vector Modulation
Dwell Time Calculation
Volt-Second Balancing
(10)
Ta, Tb and T0 – dwell times for and
Ts – sampling period
Space vectors
, and
(11)
(11)  (10)
(12)
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71. Space Vector Modulation
Dwell Times
Solve (12)
(13)
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72. Space Vector Modulation
Vref Location versus Dwell Times
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73. Space Vector Modulation
Modulation Index
(15)
(16)
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74. Space Vector Modulation
Modulation Range
Vref,max
(17)
(17)  (16)
ma,max = 
Modulation range: 0  ma  1
(18)
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75. Space Vector Modulation
Switching Sequence Design
Basic Requirement:
Minimize the number of switchings per
sampling period Ts
Implementation:
Transition from one switching state to the next involves only two switches in the same inverter leg.
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76. Space Vector Modulation
Seven-segment Switching Sequence
Selected vectors:
V0, V1 and V2
Dwell times:
Ts = T0 + Ta + Tb
Total number of switchings: 6
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77. Space Vector Modulation
Undesirable Switching Sequence
Vectors V1 and V2 swapped
Total number of switchings: 10
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78. Space Vector Modulation
Switching Sequence Summary (7–segments)
Note: The switching sequences for the odd and ever sectors are different.
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79. Space Vector Modulation
Simulated Waveforms
f1 = 60Hz, fsw = 900Hz, ma = 0.696, Ts = 1.1ms
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80. Space Vector Modulation
Waveforms and FFT
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81. Space Vector Modulation
Waveforms and FFT (Measured)
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82. Space Vector Modulation
Waveforms and FFT (Measured)
( and )
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83. (starts and ends with [OOO]) (starts and ends with [PPP])
Space Vector Modulation
Even-Order Harmonic Elimination
Type-A sequence
(starts and ends with [OOO])
Type-B sequence
(starts and ends with [PPP])
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84. Space Vector Modulation
Even-Order Harmonic Elimination
Space vector Diagram
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85. Space Vector Modulation
Even-Order Harmonic Elimination
Measured waveforms and FFT
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86. Space Vector Modulation
Even-Order Harmonic Elimination
( and )
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87. Space Vector Modulation
Five-segment SVM
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88. Space Vector Modulation
Switching Sequence ( 5-segment)
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89. Space Vector Modulation
Simulated Waveforms ( 5-segment)
f1 = 60Hz, fsw = 600Hz, ma = 0.696, Ts = 1.1ms
No switching for a 120° period per cycle.
Low switching frequency but high harmonic distortion
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