19 CHAPTER 2 CONTROL TECHNIQUES FOR MULTILEVEL VOLTAGE SOURCE INVERTERS 2.1 INTRODUCTION Pulse Width Modulation (PWM) techniques for two level inverters have been studied extensively during the past decades. Many different PWM methods have been developed to achieve the following aims; wide linear modulation range, reduced switching loss, lesser total harmonic distortion in the spectrum of switching waveform, easy implementation, less memory space and computation time on implementing in digital processors for the proposed work. The two most widely used PWM schemes for multi-level inverters are the carrier based PWM (sine-triangle PWM or SPWM) techniques and the space vector based PWM techniques. These modulation techniques are extensively studied and compared for the performance parameters with two level inverters. The SPWM schemes are more flexible and simple to implement, but the maximum peak of the fundamental component in the output voltage is limited to 50% of the DC link voltage and the extension of the SPWM schemes into over-modulation range is difficult. In SVPWM schemes, a reference space vector is sampled at regular intervals for determination of the inverter switching vectors and their time durations, in a sampling interval. A space phasor based PWM scheme for multi-level inverters use only the instantaneous amplitudes of reference phase voltages. The SVPWM scheme
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19
CHAPTER 2
CONTROL TECHNIQUES FOR MULTILEVEL
VOLTAGE SOURCE INVERTERS
2.1 INTRODUCTION
Pulse Width Modulation (PWM) techniques for two level inverters
have been studied extensively during the past decades. Many different PWM
methods have been developed to achieve the following aims; wide linear
modulation range, reduced switching loss, lesser total harmonic distortion in
the spectrum of switching waveform, easy implementation, less memory
space and computation time on implementing in digital processors for the
proposed work. The two most widely used PWM schemes for multi-level
inverters are the carrier based PWM (sine-triangle PWM or SPWM)
techniques and the space vector based PWM techniques. These modulation
techniques are extensively studied and compared for the performance
parameters with two level inverters.
The SPWM schemes are more flexible and simple to implement, but
the maximum peak of the fundamental component in the output voltage is
limited to 50% of the DC link voltage and the extension of the SPWM
schemes into over-modulation range is difficult. In SVPWM schemes, a
reference space vector is sampled at regular intervals for determination of the
inverter switching vectors and their time durations, in a sampling interval. A
space phasor based PWM scheme for multi-level inverters use only the
instantaneous amplitudes of reference phase voltages. The SVPWM scheme
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presented for multi-level inverters can also work in the over-modulation
range, using only the instantaneous amplitudes of reference phase voltages.
In the recent past the multilevel power converters have drawn a
tremendous interest in the field of high voltage and high power applications
field in industries. The multilevel inverter approach allows the use of high
power and high voltage electric motor drive systems. Using the multilevel
inverter concept, a divide and conquer approach allows more flexibility and
control over the discrete components that makeup the system. In the
researches on multilevel inverters, their corresponding PWM control
strategies are the emerging research areas.
In high power and high voltage applications, the two level inverters,
however, have some limitations in operating at high frequency mainly due to
switching losses, dv/dt and di/dt stresses in power semiconductor devices and
constraint of the semiconductor power device ratings. For high voltage
applications two or more power devices can be connected in series to achieve
the desired voltage ratings and in parallel to achieve the current ratings.
Multilevel inverters can increase the power by (m-1) times than that of two
level inverter through the series connection of power semiconductor devices.
This research focuses on the different control strategies and a suitable
modulation strategy is selected based on the outputs obtained through the
simulations on the MATLAB SIMULINK software environment.
2.2 OPEN LOOP MODULATION
The control techniques for the multilevel voltage source inverter are
classified into three basic types as PWM, Selective Harmonics Elimination
Pulse Width Modulation (SHEPWM) and Optimized Harmonics Stepped
Waveform (OHSW). PWM can be classified into open and closed loop as
discussed by Carrara et al (1992).
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The Sinusoidal Pulse Width Modulation (SPWM) has got a
few different supplementary names in relation with the triangular carrier
waveforms and are as shown in Figure 2.1. Symmetrical SPWM, when
triangular carrier was symmetric, as shown in Figure 2.1 (a). Leading edge
SPWM, when the initial slope of triangular carrier signal was infinite, as
shown in Figure 2.1 (b). Trailing edges SPWM, when the trailing edge
slope of triangular carrier signal was infinite, as shown in
Figure 2.1 (c).
(a) (b) (c)
Figure 2.1 a) Symmetrical SPWM carrier, b) Leading edge SPWM
carrier, c) Trailing edge SPWM carrier
Generally SPWM have got a few different supplementary names in
relationship with the position of the carrier signal to the modulation wave.
Synchronous SPWM, both signals were synchronous with each other if the
carrier frequency is a multiple of the sine wave frequency (fs = k*fm).
Asynchronous SPWM, both signals were asynchronous, when the carrier
frequency is not a multiple of the sine wave frequency (fs ≠ k*fm)
Based on the applications of PWM signals to multilevel inverters,
the multilevel sinusoidal PWM can be classified according to carrier and
modulating signals as shown in Figure 2.2.
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Figure 2.2 Classification of SPWM
2.3 MULTICARRIER PWM TECHNIQUES
Multicarrier PWM techniques entail the natural sampling of a single
modulating or reference waveform typically being sinusoidal same as that of
output frequency of the inversion system, through several carrier signals
typically being triangular waveforms of higher frequencies of several kilo
Hertz discussed by McGrath et al (2002) and Samir Kouro et al (2008). They
can be categorized as follows
Sinusoidal Pulse
Width Modulation
Modulating Signal Carrier Signal
Phase Disposition
Super Imposed
Carrier
Phase Opposition
Disposition (POD)
Alternate POD
Hybrid (H)
Phase Shift (PS)
Other Techniques
Dead Band
Third Harmonic
Injection
Pure Sinusoidal
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2.3.1 Alterative Phase Opposition Disposition (APOD)
This technique requires each of the (m – 1) carrier waveforms, for
an m-level phase waveform, to be phase displaced from each other by 1800
alternately as shown in Figure 2.3. The most significant harmonics are
centered as sidebands around the carrier frequency fc and therefore no
harmonics occur at fc.
Time (Seconds)
Mag
nit
ud
e (p
u)
Figure 2.3 APOD carrier technique
2.3.2 Phase Opposition Dispositions (POD)
The carrier waveforms are all in phase above and below the zero
reference value however, there is 1800 phase shift between the ones above and
below zero respectively as shown in Figure 2.4. The significant harmonics,
once again, are located around the carrier frequency fc for both the phase and
line voltage waveforms. The three disposition PWM techniques that are
APOD, PD and POD generate similar phase and line voltage waveforms.
Furthermore, for all of them, the decision signals have average frequency
much lower than the carrier frequency.
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[
Mag
nit
ud
e (p
u)
Time (Seconds)
Figure 2.4 POD carrier technique
2.3.3 Hybrid (H)
This technique, as mentioned earlier, combines the previously
presented ones (disposition) and the well known phase shifted multicarrier
technique. The bands used for modulation are only two, however, each time
the level of the power converter is increased, and more triangular carriers are
introduced and phase shifted accordingly. The two carriers above zero have
the same peak to peak value and the same frequency fc. However, there is an
1800 phase shift between them. The same applies for the two carriers below
zero. In the case that the number of converter levels is higher, the carriers are
phase shifted accordingly, that is 1200 for a 7 level system and 90
0 for a 9
level system and so on and so forth.
It is important to note that the significant harmonics are
concentrated around multiples of (m - 1)/2 of the carrier frequency fc. For
instance, for a 5-level converter, the harmonics are located around 2fc, for a 7
level around 3fc
and for a 9 level around 4fc. The gap between the
fundamental and the first significant harmonics increases accordingly as
shown in Figure 2.5.
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Figure 2.5 H carrier technique
2.4 MODULATING SIGNAL
Sinusoidal PWM can be classified according to the modulating
signal into, Pure Sinusoidal PWM (PSPWM), Third Harmonic Injection
PWM (THIPWM) and Dead Band PWM (DBPWM) by Salmon et al (2008),
Zhong Du et al (2008) and Zhou and Wang (2002). Sinusoidal PWM is the
most widely accepted PWM technique, where a triangular wave is compared
with a sinusoidal reference known as the modulating signal, shown in
Figure 2.6.
Figure 2.6 Pure sinusoidal modulating signal control technique
Mag
nit
ud
e (p
u)
Time (Seconds)
Time (Seconds)
Mag
nit
ud
e (p
u)
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2.4.1 Third Harmonic Injection PWM (THIPWM)
A method to improve the gain of the pulse width modulator in a
multilevel inverter is to inject a third harmonic. This technique is derived
from conventional sinusoidal PWM with the addition of a 17% third harmonic
component to the sine reference waveform as shown in Figure 2.7. The
hardware implementation of this technique is straightforward. It should be
noted that the 15% increase in gain over the SPWM technique is achieved at
the expense of introducing third harmonics on the line to neutral waveforms.
However for a balanced load with a floating neutral point, third harmonic
current cannot flow and therefore third harmonic voltages are not present on
the line to line waveforms. Although, the above mentioned switching patterns
for PWM converters provide increased gain compared with the conventional
SPWM technique, they also imply the reference or modulating waveforms
have to be continuous regardless of their shape.
As a result they do not provide any reduction in switching frequency
compared with the SPWM. For third harmonic injection PWM, the reference
waveform is defined as f(ω,t) = 1.15Ma sin(ωot)+0.19 Ma sin(3ωot); 0 ≤ ωot ≤
2π Where, Ma is the modulation index ratio. The zero sequence voltage can