Sinusoidal Pulse Width Modulation
The sinusoidal PWM with third harmonic injection (THSPWM) is a type of sinusoidal
pulse width modulation where a harmonic component is added to the voltage signal
so that the waveform of the modulating signal has its top flattened and one reduces
the period of over modulation.
From: Model Predictive Control for Doubly-Fed Induction Generators and
Three-Phase Power Converters, 2022
Related terms:
Switching Frequency, Amplitudes, Pulse Width Modulation, Pulse-Width-Modulation Technique, Space Vector, Waveform, Electric Potential, Inverter
View all Topics
Pulse width modulation inverters
Sang-Hoon Kim, in Electric Motor Control, 2017
7.2.2 Sinusoidal PWM Technique [2]
Sinusoidal PWM is a typical PWM technique. In this PWM technique, the sinusoidal
AC voltage reference is compared with the high-frequency triangular carrier wave in
real time to determine switching states for each pole in the inverter. After comparing,
the switching states for each pole can be determined based on the following rule:
•
Voltage reference Triangular carrier : upper switch is turned on (pole voltage=)
•
Voltage reference Triangular carrier : lower switch is turned on (pole voltage=)
Here, the peak-to-peak value of the triangular carrier wave is given as the DC-link
voltage . In this PWM technique, the necessary condition for linear modulation is
that the amplitude of the voltage reference must remain below the peak of the
triangular carrier , i.e., . Since this PWM technique utilizes a high-frequency carrier
wave for voltage modulation, this kind of PWM technique is called a carrier-based
PWM technique. Especially, this carrier-based technique is called SPWM since the
reference is given as the shape of a sine wave. This is also called the triangle-com-
parison PWM technique since this uses the carrier of a triangular wave. Fig. 7.29
depicts the sinusoidal PWM technique for one phase.
Figure 7.29. Sinusoidal PWM technique.
Modulating Wave and Carrier Wave
In the carrier-based PWM techniques, the desired voltage reference waveform is
referred to as modulating wave. In addition, a wave which is modulated with the
modulating wave is referred to as carrier wave or carrier. The carrier wave usually
has a much higher frequency than the modulating wave. The triangular waveform is
the most commonly used carrier in the PWM technique for modulating AC voltage.
On the other hand, different forms of modulating wave can be used according
to the PWM technique. Typical SPWM technique uses the sinusoidal modulating
waveform.
Difference Between Pole Voltage and Phase Voltage References
An inverter output determined by comparing a voltage reference with the triangular
carrier wave is the pole voltage. Thus the voltage reference that is compared with the
triangular carrier wave is considered as the pole voltage reference. Typical SPWM
technique uses a phase voltage reference as the pole voltage reference. On the other
hand, different pole voltage reference can be used according to the PWM techniques.
In this PWM based on comparison with the triangular wave, if the ratio of carrier
frequency to fundamental frequency is large enough (greater than 21), then the
fundamental component of the output voltage varies linearly with the reference
voltage for a constant DC-link voltage as
(7.40)
In addition, the fundamental frequency of the output voltage is identical to that of
the reference voltage.
The output voltage of Eq. (7.40) can be rewritten in terms of the modulation index
MI as
(7.41)
Here, since , so .
The range of is called the linear modulation range because, in this range, the inverter
can generate an output voltage linearly proportional to the reference voltage as
shown in Fig. 7.30. In this case, the PWM inverter is considered to be simply a voltage
amplifier with a unit gain.
Figure 7.30. Voltage modulation range for SPWM.
However, when the reference exceeds the peak of the triangular carrier (i.e., ),
the inverter cannot produce an output voltage linearly proportional to the voltage
reference. The range of is called overmodulation region, where the linearity of the
modulation is lost. We will discuss the overmodulation techniques in Section 7.5.
The maximum linear output voltage, , attainable by the SPWM technique corresponds to 78.5% of the maximum output voltage, , by the six-step inverter.
Therefore, when using the PWM technique, the attainable maximum limit of the
linear modulation range is inevitably less than the maximum output voltage of an
inverter.
Fig. 7.31 shows the SPWM technique for a three-phase inverter.
Figure 7.31. SPWM technique for a three-phase inverter.
In the SPWM technique, the switching frequency of an inverter is equal to that of
a carrier wave. From Figs. 7.29 and 7.31, we can see that the switch is turned on/off o
nce every period of the triangular carrier wave. Thus the SPWM technique has an
advantage of having a constant switching frequency. A constant switching frequency
makes it possible to calculate the losses of switching devices, so the thermal design
for them becomes easier. In addition, since the harmonic characteristics will be
well-defined, the design of a low-pass filter to eliminate the harmonics will become
easier.
Now we will evaluate which harmonics are contained in the output voltage generated
by the SPWM technique. First, we will investigate the harmonic components of the
pole voltage as shown in Fig. 7.29. It is widely known that the pole voltage contains
harmonics at the carrier frequency and frequencies of its integer multiples (M),
and the sidebands (N) of all these frequencies [4]. Thus these harmonics, which are
known as switching frequency harmonics, can be expressed as
(7.42)
Here, is the fundamental frequency of the output voltage and is the frequency
modulation index, which denotes the ratio of the carrier frequency to the fundamental
frequency, i.e., . M and N are integers, and M+N is odd. h denotes the phase of
harmonic component. From Eq. (7.42), the orders of harmonics are given as
(7.43)
Among the harmonics, the component of order has the largest magnitude. This
means that the harmonic with the frequency equal to the switching frequency is the
largest one.
As an example, Fig. 7.32 shows the frequency spectrum for the pole voltage of and
. In this case, the harmonic of 1050 Hz(=21×50 Hz), i.e., the switching frequency is
the largest component.
Figure 7.32. Frequency spectrum of the pole voltage for the SPWM.
The higher the switching frequency is, the higher the order of the major harmonic is.
Thus, when a higher switching frequency is used, the quality of the voltage waveform
can be improved and filtering can be made easier. However, this leads to greater
switching losses. Therefore it is important to consider the overall performance of
the system when selecting the switching frequency.
Next we will examine the harmonic components for the line-to-line and phase voltages. Since the line-to-line voltage is the difference between the two pole voltages,
they do not have any harmonic at multiples of three, which exist in the pole voltages.
As mentioned earlier, this is because the harmonics at multiples of three included in
the pole voltages will have no phase difference with each other. Hence, if we select
the value of as multiples of three, then the total harmonics will be reduced in the
line-to-line voltage due to the elimination of the harmonics at multiples of three.
For this reason, the value of is usually selected as multiples of three. Furthermore,
among these values, only the odd values can eliminate the even harmonics for
the symmetry of three-phase PWM patterns. In that case, the harmonic of order
becomes the largest component for the range of MI<0.9, while around MI=1. For
example, Fig. 7.33 depicts the harmonic spectrum for the line-to-line voltage in the
case of and MI=0.8. In this case, unlike that of the pole voltage, the largest harmonic
component becomes the order of . The phase voltages have harmonic components
identical to those of the line-to-line voltages, but their magnitudes are different.
Figure 7.33. Frequency spectrum of the line-to-line voltage for the SPWM (MI=0.8,
mf=21).
The SPWM technique has been widely popular due to the simplicity of its principle
and analog implementation. In the analogue implementation of the SPWM (referred
to as naturally sampled PWM), an analog integrator is used to generate a triangular
carrier wave, and an analog comparator is used to determine the intersection
instants of the triangular carrier wave and modulating signal.
In contrast, its software-based implementation using a digital technique or microprocessor is not easy because this requires solving the transcendental equation,
which defines points of intersection used to determine the switching instants.
Instead, as shown in Fig. 7.34, the so-called regular-sampled PWM is used in which
the sinusoidal reference is held at a constant sampled value for the carrier interval,
and the sampled value is compared with the carrier wave to determine the switching
instants [5]. In the regular-sampled PWM, there are two types of sampling, symmetric and asymmetric. In the symmetrical sampling of Fig. 7.34A, the sinusoidal
reference is sampled once at the peak of the triangular carrier wave, whereas in the
asymmetrical sampling of Fig. 7.34B, it is sampled twice at both the positive and
negative peaks of the triangular carrier wave. Nowadays, its digital implementation
can be easily done by using microcontrollers supporting the dedicated module for
the PWM signal generation.
Figure 7.34. Regular-sampled PWM technique (A) Symmetrically sampling and (B)
asymmetrically sampling.
Since the SPWM technique can perform voltage modulation every sampling interval
with a fixed switching frequency, it exhibits a better dynamic performance than
the programmed PWM. However, this technique has a limited voltage linearity
range (only 78.5% of six-step operation) and a poor waveform quality in the high
modulation range. To overcome these problems, many improved PWM techniques
have been developed. Improvements to extend the voltage linearity range have
been mainly done through the modification of the modulating signal, resulting
in nonsinusoidal modulating signals. As a typical example of the improvement,
the third harmonic injection PWM makes it possible to increase the fundamental
component of the output voltages by 15.5% more than the conventional SPWM
technique. Now we will discuss the third harmonic injection PWM.
> Read full chapter
Conventional Multilevel Inverter
Pradyumn Chaturvedi, in Modeling and Control of Power Electronics Converter
System for Power Quality Improvements, 2018
3.3.2.1 Based on carrier signals
Various SPWM techniques can be derived based on the placement of carrier signals,
their magnitude and frequency, and the amplitude of overlapping signal with each
other.
1.
2.
3.
Phase disposition SPWM (PD SPWM)In this SPWM technique, all the carrier
signals are in phase and level shifted. Fig. 3.11 shows the principle of pulse
generation for five-level PD SPWM. The carrier signals are C1, C2, C3, and C4
while three-phase reference or modulating signals are , , and . Comparison of
these four carrier signals with the corresponding modulating signal generates
the control signal, which has to be given to the corresponding switches of that
phase-leg devices.Figure 3.11. PD SPWM technique for five-level inverter.
Phase opposition disposition SPWM (POD SPWM)The carrier signals above the
reference/zero line are in the same phase and the carrier signals below the zero
line are in the same phase, but the carriers below and above the zero line are
out of phase by 180 degrees as shown in Fig. 3.12.Figure 3.12. POD SPWM
technique for five-level inverter.
Alternate phase opposition disposition SPWM (APOD SPWM)It is similar to PD
SPWM technique; however, the carriers are phase displaced from one another
by 180 degrees alternatively as shown in Fig. 3.13.Figure 3.13. APOD SPWM
technique for five-level inverter.
4.
5.
6.
Phase shift SPWM (PS PWM)All the carriers are phase shifted by appropriate
angle as shown in Fig. 3.14. The performance of the technique depends
on phase-shift angle between carriers.Figure 3.14. PS SPWM technique for
five-level inverter.
Variable frequency carrier bands SPWM (VFCB SPWM)In this technique, the
frequency of all the carriers is not the same. Some carriers have different
frequency than others, as shown in Fig. 3.15. The techniques mentioned above
in (1)–(4) can be modified to achieve VFCB SPWM.Figure 3.15. VFCB SPWM
for five-level inverter.
Carrier overlapping PWM (CO PWM)All the carriers are overlapping each other
by some definite magnitude as shown in Fig. 3.16. The amount of overlapping
magnitude will decide the output performance of inverter.Figure 3.16. CO
PWM for five-level inverter.
> Read full chapter
Neutral-point-clamped and T-type
multilevel inverters
Hasan Komurcugil, Sertac Bayhan, in Multilevel Inverters, 2021
2.1.3.1 Sinusoidal pulse width modulation (SPWM)
The SPWM mainly is employed in industrial applications and based on the comparison of modulation and carrier signals. A sine wave (modulation signal, vm) is
compared with two triangular waveforms (carrier signals, vc1 and vc2) to generate
PWM signals as shown in Fig. 2.4. It should be mentioned that this modulation
scheme is only represented for the phase “a.” To generate switching signals for
the other phases, modulation signals should be shifted 120° according to each
other while using the same carrier signals. The frequency of the modulation signal
determines the output voltage frequency while the frequency of the carrier signals
determines the switching frequency. Furthermore, the amplitude of the output
voltage is determined by the amplitude of the modulation signal.
Fig. 2.4. (A) Block diagram of the SPWM generator scheme; (B) waveforms of the
modulation and carrier signals; and (C) hexagon containing the possible voltage
vectors for SPWM.
Similar to the traditional two-level SPWM, the amplitude of the first harmonic of the
voltage supplied by the inverter is proportional to the amplitude of the modulating
signal only if this latter does not exceed amplitude Vc of the carrier. This limitation
implies that using SPWM, a voltage vector can be realized only if it is inside the inner
hexagon depicted in Fig. 2.4C. Therefore, in the steady-state sinusoidal operation,
the voltage representative vector can assume a maximum value equal to 0.75 Vmax
[10].
> Read full chapter
Induction machine and three-phase
power converter dynamic models
Alfeu J. Sguarezi Filho, in Model Predictive Control for Doubly-Fed Induction Generators and Three-Phase Power Converters, 2022
2.4.1 Sinusoidal PWM
This section introduces the sinusoidal PWM (SPWM) [10–12] theory for the activation of the switches of the converter, as depicted in Fig. 2.3. In this PWM technique,
the carrier is a saw-tooth wave that is compared with a voltage reference signal called
modulating. The result of this comparison will activate the switches on each arm of
the converter so that the switches on the same arm cannot be turned on at the same
time instance. In SPWM, the frequency and amplitude of the fundamental harmonic
component are determined by the frequency of the reference voltage, and the carrier
defines the switching frequency. A comparison of the carrier and the modulating
will result in the following voltage values:
(2.77)
where , or b.
The relationship between the carrier and modulating waves' amplitude values is
known as the amplitude modulation index and it can be represented by
(2.78)
where guarantees the operation in the linear range of the modulation. In this way,
will be the value received by the peak value of the fundamental component of the
voltage.
The block diagram for the SPWM can be seen in Fig. 2.5 in which the reference
voltages , , and (modulating signals), carrier (triangular wave), and other items
necessary for its implementation can be observed. So it is possible to activate the
switches , , and . It is important to mention that the signals , , and have the
complementary value of the signals , , and . Hence, if then , and vice versa.
Figure 2.5. Block diagram for implementation of the SPWM.
The waveform of the carrier (saw-tooth wave), three-phase voltages, , , and for a
three-phase SPWM are depicted in Fig. 2.6. A comparison of the carrier and the
modulating signals is depicted in Fig. 2.6(a), the voltages (Fig. 2.6(b)) and (Fig. 2.6(c))
can be seen using Fig. 2.3, and the line voltage (Fig. 2.6(d)) will be applied to the
load.
Figure 2.6. SPWM curves: (a) comparison of the carrier and the modulating signals,
(b) va0, (c) vb0, and (d) vab.
2.4.1.1 Sinusoidal PWM with third harmonic injection
The sinusoidal PWM with third harmonic injection (THSPWM) is a type of sinusoidal
pulse width modulation where a harmonic component is added to the voltage
signal so that the waveform of the modulating signal has its top flattened and
one reduces the period of over modulation. As a consequence, the fundamental
component of the voltage has greater amplitude with less harmonic distortion. In
the case of this section, the third harmonic component will be employed together
with the fundamental component, as shown in Fig. 2.7. However, the amplitude of
this component must be less than the fundamental component. It is mentioned
that, in such a case, this component cannot be seen in the output voltage. The
fundamental component of the voltage is increased by 1.15 without being in the
overmodulation region in a situation where the amplitude of the third harmonic
component is 1/6 of the amplitude of the fundamental component [11,12]. The
third harmonic component of the voltage can be calculated using the three-phase
voltages, as presented in the following expression [10]:
Figure 2.7. Voltage by using third harmonic component.
(2.79)
The diagram for the THSPWM is shown in Fig. 2.8. It is observed that Eq. (2.79)
is employed for the calculation of the third harmonic component that is added to
the three-phase voltages. Hence, the mentioned voltages will be compared with the
saw-tooth wave, so it is possible to activate the switches , , and . Again, it is important
to mention that the signals , , and have the complementary value of the signals , ,
and . Hence, if then , and vice versa.
Figure 2.8. THSPWM diagram.
> Read full chapter
Conventional H-bridge and recent multilevel inverter topologies
Ilhami Colak, ... Gokhan Keven, in Multilevel Inverters, 2021
3.4.2 Unipolar SPWM
The unipolar SPWM modulation, also known as three-level modulation, is used in
H4 inverters instead of bipolar SPWM for reducing the THD value. The switching
states are complementary in one branch of the H4 inverter. For example, S1 and
S2 are switched in complementary states to each other, and S3 and S4 are also
complementary to each other, as seen in Fig. 3.9. Two sinusoidal signals that are 180°
phase shifted from each other are compared with a triangle carrier signal varying
from “0” to “+ 1” for generating switching signals. If a DC source or a PV panel is
connected as VDC in the inverter input, the output levels of the inverter vary between
+ VDC, 0, and − VDC [15–18]. The advantages of unipolar SPWM include decreased
values for filtering the inverter output, lower core loss, and higher efficiency (up
to 98%) due to reduced losses during the zero voltage state. The disadvantage of
unipolar SPWM is that the EMI and leakage current are very high [18].
Fig. 3.9. Unipolar SPWM modulation strategy switching states.
The generation of unipolar switching states is shown in Fig. 3.9. While the S4 switching signal is at “ON” in the positive half-cycle, S1 and S2 are pulsed as complementary
to each other at the carrier frequency. On the other hand, while the S2 switching
signal is at the “ON” position in the negative half-wave, S3 and S4 are pulsed as
complementary to each other at the carrier frequency. There are four modes in the
unipolar SPWM modulation strategy, as shown in Fig. 3.10. The positive half-cycle
and negative half-cycle are depicted in Fig. 3.10A and B, respectively. Freewheeling
mode-I and freewheeling mode-II are indicated in Fig. 3.10C and D, respectively.
Freewheeling modes achieve zero voltage at the output. Unipolar SPWM is not
suitable for nonisolated grid-tied inverters due to the high leakage current and
variable CMV [15–18].
Fig. 3.10. Unipolar SPWM: (A) positive half-cycle, (B) negative half-cycle, (C) freewheeling mode-I, (D) freewheeling mode-II.
Table 3.3 summarizes the switching states of unipolar SPWM where freewheeling
mode-I and freewheeling mode-II are identical but switching orders of devices
are at different modulation frequencies in these modes. S4 is always in the “ON”
position and S3 is always in the “OFF” position in freewheeling mode-I. S1 and S2
are controlled with complementary PWM signals in carrier frequency. S2 is at the
“ON” position and S1 is at the “OFF” position in freewheeling mode-II. S3 and S4 are
switched with complementary PWM signals in carrier frequency [19].
Table 3.3. Switching states for unipolar SPWM.
Switching State
“ON” state Switches
“OFF” state Switches
Vout
Positive half-cycle
S1-S4
S2-S3
+ VDC
Freewheeling mode-I
S2-S4
S1-S3
0
Freewheeling mode-II
S1-S3
S2-S4
0
Negative half-cycle
S2-S3
S1-S4
− VDC
> Read full chapter
Some questions and answers
Bimal K. Bose, in Power Electronics and Motor Drives (Second Edition), 2021
A15. SVM and SPWM are the two most viable PWM techniques for such a system.
However, if the load neutral is connected for zero sequence current circulation,
only SPWM can be used. Note that both the PWM methods are open-loop carrier
frequency-based, where the carrier frequency can be fixed and free-running (unsynchronized) or synchronized with the fundamental frequency. In free-running mode,
unless the carrier-to-fundamental ratio is high, some amount of subharmonics is
introduced into the load. Most of the three-phase loads including AC motors have
isolated neutral. The general comparison between SVM and SPWM for an isolated
neutral load can be given as follows:
•
•
•
SPWM is simple to implement compared with SVM, which requires complex
computations in real time. SPWM can be implemented by simple hardware or
software.
The linear undermodulation range of SPWM extends up to modulation index
m = 0.785 (where m = 1.0 at square wave). In comparison, SVM has a higher
undermodulation range, i.e., up to m = 0.907. The bus voltage utilization is
better with SVM in this region. However, the sinusoidal modulating wave of
SPWM can be mixed with an appropriate amount of triplen harmonics (zero
sequence components) to achieve the same modulation index.
The harmonic distortion in SPWM and SVM is comparable up to m = 0.4. As
m increases, the distortion on SPWM increases nonlinearly typically as shown
in Fig. 13.6, where d2 is the index for distortion.Figure 13.6. Comparison of
harmonic distortion in sinusoidal pulse-width modulation (SPWM) and space
vector pulse-width modulation (SVM) in the undermodulation region (note •
that triplen harmonics have been added in SPWM to increase ).
In a PWM double-converter drive system, the line-side rectifier must operate
in the undermodulation mode, whereas the load-side inverter can operate in
either undermodulation or overmodulation mode. Higher m in SVM permits
line voltage synthesis with lower DC link voltage (Vd). This is a definite
advantage.
> Read full chapter
The key devices of unified power flow
controller
YIN Jijun, ... LI Peng, in Unified Power Flow Controller Technology and Application,
2017
3.1.3.1 Carrier phase shift sinusoidal pulse width modulation
(CPS-SPWM)
The principle of CPS-SPWM is shown in Fig. 3.11. CPS-SPWM is a modulation
strategy used in multilevel converters. The technical features of CPS-SPWM are:
low SPWM switching frequency in all submodules, frequency modulation ratio of
, amplitude modulation ratio of , common sinusoidal modulation signal generated
to all submodules. The phase of carrier waveform is shifted by a difference of 360/M
degrees.
Figure 3.11. CPS-SPWM schematic diagram.
Owing to the uniform distribution of 2M triangular waves in the whole modulated
wave period, the voltage level of output waveforms is (2M+1). The output voltage
increases M times the linear amplification, and the equivalent switching frequency
also increases 2M times. The harmonic component of the output voltage is greatly
reduced when the switching frequency does not change.
The number of submodules in each bridge arm is set to M, and the reference
modulation waveform in each submodule is given by the following formula.
(3.1)
(3.2)
In these formulas: UA, UB, UC respectively for three-phase AC output RMS voltage;
, , respectively for the reference voltage value of each three-phase up bridge arm
submodule; , , respectively for the reference voltage value of each three phase down
bridge arm submodule.
The carrier phase shifted pulse width modulation carrier is a triangular wave, the
phase shift angle of the triangle wave is related to the submodule position in the
converter bridge arm. The phase shift angle of each up bridge arm submodule is
The phase shift angle of each down bridge arm submodule is
> Read full chapter
Inverters (DC–AC Converters)
Stefanos N. Manias, in Power Electronics and Motor Drive Systems, 2017
6.5.5.3 PSC-SPWM Control Technique Applied to a Single-Phase Five-Level CHBMI
As mentioned before, the PSC-SPWM control technique is applied only to CHBMIs.
In this section the application of the PSC-SPWM control technique to a three-phase
five-level CHBMI will be examined. As explained before, every phase-leg of the
inverter consists of two H-bridge units (Fig. 6.89) and every H-bridge unit consists of
four semiconductor switches Sa1, Sa2, Sa3, and Sa4. Fig. 6.90 presents the definition
and the generated gating signals of the well-known SPWM control technique for
an H-bridge unit. As shown in Fig. 6.90, the gating signals of the first-leg of the
H-bridge are generated from the intersection points between the reference 1 signal
and the carrier and the gating of the second-leg from the intersection points
between the reference 2 signal and the same carrier.
Figure 6.89. One phase-leg of the five-level cascaded H-bridge multilevel inverter.
Figure 6.90. Sinusoidal pulse width modulation (SPWM) control technique for the
H-bridge unit.(a) SPWM definition; (b)–(e) SPWM gating signals.
The rest of the H-bridge units of the same phase-leg are using the same PWM
control technique with the only difference being that the carrier signal is phase
shifted by an angle shift with respect to the carrier of the previous H-bridge. The
reference signals are the same for every H-bridge in the same phase-leg. The phase
displacement between the carrier signals depends on the required number of levels
to be generated by the CHBMI and is given by the following equation:
(6.109)
(6.110)
where i = full-bridge unit number = 1,2,3,…
Also, the following equation holds:
(6.111)
where m = number of levels of the output phase voltage of the CHBMI.
For m-level inverter, the most significant harmonic components are located in
lateral bands around (m − 1)mf, where mf is the frequency modulation factor. For
even values of frequency modulation factor, mf, the output generated voltages
present quarter-wave symmetry, resulting in only even harmonics. Fig. 6.91 shows
the modulation control circuit with the reference and carrier signals of an m-level
CHBMI that employs PSC-SPWM.
Figure 6.91. Modulation circuit with the reference and carrier signals of an m-level
cascaded H-bridge multilevel inverter that employs phase shift carrier-sinusoidal
pulse width modulation.
According to Eqs. (6.109) and (6.111) for the five-level inverter of Fig. 6.89 two carrier
signals with a phase shift of shift = 360°/4 = 90° are needed. Fig. 6.92 shows the
two reference signals and two carrier signals required to generate the gating signals
of the two H-bridge inverters of a single-phase five-level CHBMI. The intersection
points between the carrier 1 and the reference 1 signals define the gating signals
of the top H-bridge, whereas the intersection points between the carrier 2 and
reference 2 signals define the gating signals for the bottom H-bridge.
Figure 6.92. Reference and carrier signals of the first H-bridge of a five-level cascaded H-bridge multilevel inverter that employs phase shift carrier-sinusoidal pulse
width modulation.
Fig. 6.93 presents the frequency spectra of the output voltages of the multilevel
inverter when PSC-SPWM is employed.
Figure 6.93. Frequency spectra of cascaded H-bridge multilevel inverter when
SPC-SPWM is used.(a) Frequency spectrum of vao; (b) frequency spectrum of vab.
As shown in Fig. 6.93(a) and (b), the most significant harmonic components of the
output voltages are located in lateral bands around (m − 1)mf. Also from the Fourier
analysis of the output voltages, the following results are obtained:
(6.112)
(6.113)
(6.114)
(6.115)
(6.116)
(6.117)
In case a three-phase five-level CHBMI with PSC-SPWM needs to be implemented,
two additional phase shifted reference signals are needed to generate with the
same carriers the gating signals of the other two phase-legs. Fig. 6.94 shows the
three-phase definition of PSC-PWM for a three-phase five-level CHBMI.
Figure 6.94. Definition of phase shift carrier-sinusoidal pulse width modulation for
three-phase five-level cascaded H-bridge multilevel inverter.
Fig. 6.95 presents the PSIM simulation results of a single-phase five-level CHBMI
that employs PSC-SPWM technique.
Figure 6.95. Power simulation results for a single-phase five-level cascaded
H-bridge multilevel inverter that employs phase shift carrier-sinusoidal pulse width
modulation (PSC-SPWM) (s = 2, ma = 0.8, mf = 21, Vin = 500 V, fo = 50 Hz, and
R–L load).(a) Simulation circuit; (b) PSC-SPWM definition; (c) output phase voltage,
vao; (d) frequency spectrum of vao; (e) output line-to-line voltage, vab; (f ) frequency
spectrum of vab.
Finally, Fig. 6.96 presents the simulation results of a single-phase seven-level CHBMI that employs PSC-SPWM technique.
Figure 6.96. Power simulation results for a single-phase seven-level cascaded
H-bridge multilevel inverter that employs phase shift carrier-sinusoidal pulse width
modulation (PSC-SPWM) (s = 3, ma = 0.7, mf = 21, Vin = 500 V, fo = 50 Hz, and
R–L load).(a) PSC-SPWM definition; (b) output phase voltage, vao; (c) frequency
spectrum of vao; (d) output line-to-line voltage, vab; (e) frequency spectrum of vab.
Apart from the multicarrier SPWM techniques presented in this section, there are
also the following additional modulation techniques which can be used depending
on the application of the multilevel inverter.
> Read full chapter
Power converter solutions and controls
for green energy
Vijay K. Sood, Haytham Abdelgawad, in Distributed Energy Resources in Microgrids, 2019
Abbreviations
CSI current source inverter
DSP digital signal processor
DSP-digital sinusoidal pulse width modulation
WM
EDPCextended direct power control
FLC feedback linearization control
FPGAfield-programmable gate array
GaN gallium nitride
HC hysteresis controller
hc
harmonic compensator
HER-highly efficient and reliable inverter concept
IC
HF high frequency
IEEEinstitute of electrical and electronics engineers
IGBTinsulated gate bipolar junction transistor
LF
low frequency
LV low voltage
MICsmodule-integrated converters
MOSFET
metal oxide–semiconductor field effect transistor
MPPmaximum power point
MPPTmaximum power point tracking
MV medium voltage
NPCneutral point clamped
OCCone cycle control
PCC point of common coupling
PCSPpower control shifting phase
PI
proportional integral controller
PIC peripheral interface controller
PLL phase-locked loop
PR proportional resonant controller
PV photovoltaic
PVG photovoltaic generator
PWMpulse width modulation
SiC silicon carbide
SICP-super imposed carrier pulse width modulation
WM
SPWM
sinusoidal pulse width modulation
THDtotal harmonic distortion
ZCDzero-crossing detector
ZCS zero current switching
ZVS zero voltage switching
> Read full chapter
Inverters
Nimrod Vázquez, Joaquín Vaquero López, in Power Electronics Handbook (Fourth
Edition), 2018
11.3.2 Square-Wave Operation of Three-phase VSIs
Large values of ma in the SPWM technique lead to full overmodulation. This is
known as square-wave operation as illustrated in Fig. 11.19, where the power semiconductors are on for 180°. In this operation mode, the VSI cannot control the load
voltage except by means of the dc link voltage vi. This is based on the fundamental
ac line-voltage expression
Fig. 11.19. The three-phase VSI. Square-wave operation: (A) switch S1 state, (B) switch
S3 state, (C) ac output voltage, and (D) ac output voltage spectrum.
(11.27)
The ac line output voltage contains the harmonics fh, where (), and they feature
amplitudes that are inversely proportional to their harmonic order (Fig. 11.18D).
Their amplitudes are
(11.28)
> Read full chapter
ScienceDirect is Elsevier’s leading information solution for researchers.
Copyright © 2018 Elsevier B.V. or its licensors or contributors. ScienceDirect ® is a registered trademark of Elsevier B.V. Terms and conditions apply.