Download The Relationship Between Space-Vector Modulation and Regular

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997
The Relationship Between Space-Vector Modulation
and Regular-Sampled PWM
Sidney R. Bowes, Fellow, IEEE, and Yen-Shin Lai, Member, IEEE
Abstract— The relationship between regular-sampled pulsewidth modulation (PWM) and space-vector modulation is defined,
and it is shown that, under certain circumstances, the two
approaches are equivalent. The various possibilities of adding
a zero-sequence component to the regular-sampled sinusoidal
modulating wave are explored, and these effects are quantified. It
is shown that this leads to “equal-null” pulse times, which extend
the linear modulation range and simplify the microprocessor
implementation.
FR
Index Terms—PWM control techniques.
p.u.
NOMENCLATURE
,
,
,
Active vector times allocated to the switching
states (100), (010), or (001) and (110), (011), or
(101), respectively.
Null vector times allocated to the switching states
(000) and (111), respectively.
Sampling period.
Polar angle of reference vector referring to
.
Inverter switching states
.
Inverter switching states, either (100), (010), or
(001).
Inverter switching states, either (110), (011), or
(101).
Voltage vector related to the switching state
.
Voltage vector related to switching states
, and
.
Reference space vector.
,
,
Active pulse times allocated to the switching
states (100), (010), or (001) and (110), (011),
or (101), respectively.
Null pulse times allocated to the switching states
(000) and (111), respectively.
Sampling position (angle).
Carrier period.
Manuscript received May 5, 1995; revised November 15, 1996. This work
was supported by the U.K. Science and Engineering Research Council.
S. R. Bowes is with the Department of Electrical and Electronic Engineering, Faculty of Engineering, University of Bristol, Bristol BS8 1TR, U.K.
Y.-S. Lai was with the Department of Electrical and Electronic Engineering,
Faculty of Engineering, University of Bristol, Bristol BS8 1TR, U.K. He is
now with the Department of Electrical Engineering, National Taipei Institute
of Technology, Taipei, Taiwan, R.O.C.
Publisher Item Identifier S 0278-0046(97)06527-1.
Angular frequency of modulating wave.
Modulation index.
Sampled modulating values at .
Prepulse and postpulse switching angles, respectively.
Prepulse and postpulse switching times, respectively, with respect to sampled position.
Pulsewidth of PWM pulse.
Frequency ratio (ratio of carrier/modulating frequencies).
Per unit (1 p.u. corresponds to maximum fundamental voltage produced by sinusoidal PWM
before overmodulation).
I. INTRODUCTION
R
EGULAR-SAMPLED pulsewidth modulation (PWM)
[1], [2] and space-vector modulation [3] are two popular
techniques for providing PWM control of inverter drives.
Although both PWM techniques have been developed from
different “points of view,” they have certain similarities and,
under special circumstances, can be shown to be identical.
Attempts have been made to show this equivalence [3],
[4], although these attempts have been made starting from
the space-vector point of view and have not fully highlighted
many important features.
In contrast, this paper is concerned with deriving the many
important relationships between regular-sampled PWM and
space-vector modulation starting from the “per-phase” point
of view in a form which highlights this equivalence. This is
done by developing a particular form of regular-sampled PWM
based upon adding a particular form of zero-sequence component to the sinusoidal modulating wave. It is shown that this
has the effect of making the “inactive” or “null pulse” times
equal, which results in an extended linear modulation range.
The equations defining the regular-sampled “equal-null”
pulse time PWM process are derived and shown to be equivalent to those derived for space-vector modulation, thus proving
the equivalence of the two approaches.
All the concepts, techniques and derivation of equations
associated with regular-sampled PWM will be shown to be
based on the “per-phase” three-phase viewpoint, without
invoking any concepts of “space-vector” theory. This approach
allows the essential features and characteristics of the two
approaches to be clearly identified and distinguished, as shown
in this paper.
It is shown that the effect of using an “equal-null” pulse time
in the “per-phase” regular-sampled PWM case is to extend
0278–0046/97$10.00  1997 IEEE
BOWES AND LAI: SPACE-VECTOR MODULATION AND REGULAR-SAMPLED PWM
671
the linear voltage range up to
, while its use
in space-vector modulation does not affect the linear voltage
range.
II. THEORY
A. Per-Phase Sinusoidal Regular-Sampled PWM
It is well known that the natural sampling [1]–[2], [5]
switching angle equations are transcendental and, therefore,
not suitable for microprocessor software implementation.
These difficulties led to the development of regular sampling
techniques in the early 1970’s [1]. The principles of regularsampled PWM techniques are shown in Fig. 1 for asymmetric
regular-sampled PWM. Regular-sampling is a digital process
of sampling a modulating wave “ ” at regularly spaced
intervals to produce sinusoidally weighted digital samples
of the modulating wave, represented by “ ” in Fig. 1.
As shown in Fig. 1, two samples “ ” per carrier cycle are
generated. The first sample in the carrier cycle is used to
sinusoidally modulate the “leading-edge” of the PWM pulse
“ ,” and the second sample is used to sinusoidally modulate
the “trailing edge” of the PWM pulse. Thus, each edge of the
PWM pulse is modulated by a different amount with respect
to the regularly spaced pulse centers; hence, the terminology
“asymmetric” regular-sampled PWM.
The derivation of the switching equations describing asymmetric regular-sampled PWM have been given earlier [1], [2],
and the main results are given in the following equations:
prepulse angle defining the leading edge—
(1)
postpulse angle defining the trailing edge—
(2)
These equations are executed in a software algorithm which
simulates the modulation processes shown in Fig. 1, using
switching angles
and
defined in (1) and (2). For sinusoidal modulation, phase uses a modulating wave
, and phases
and
use
and
, respectively [6], [7].
B. Per-Phase Nonsinusoidal Regular-Sampled PWM
The research [8] has shown that using nonsinusoidal modulation can considerably improve the harmonic spectrum. In
particular, it has been shown [8] that by adding 25% third
harmonic (or zero-sequence component) to the sinusoidal
modulating wave, the resulting harmonics could be minimized. This resulted from assuming an arbitrary nonsinusoidal
modulating wave as part of the regular-sampled modulating
process, then numerically minimizing the “total harmonic
current distortion” (THD).
In addition, it was shown [8] that the linear relationship
between fundamental voltage and modulation index
could
be extended beyond the usual pure sinusoidal limit
p.u.
to approximately
p.u. before overmodulation and
pulse dropping occurred.
Fig. 1. Asymmetric regular-sampled PWM.
It is important to note that the addition of 25% third
harmonic derives specifically from the minimization of the
THD, whereas the alternative suggested by others [9], [10] of
1/6 third harmonic addition is based solely on maximizing the
fundamental voltage. Indeed, the analysis [10] which produces
the 1/6 third harmonic addition is based on adding a third
harmonic to a pure sinewave phase voltage and choosing
the magnitude of the added third harmonic to maximize the
sinusoidal line voltage amplitude. Therefore, as a result of
considering only sinusoidal voltages, the harmonics of the
PWM voltages are not considered in the analysis, thereby
producing an inferior harmonic performance compared with
adding 25% third harmonic, as will be confirmed later in
Section III and Fig. 6.
C. Conditions for “Equal-Null” Pulse Times
of Per-Phase PWM
The three-phase width-modulated pulse configuration for a
typical sample period (half carrier cycle) is shown in Fig. 2.
With reference to Fig. 2, the prepulse angles defining the
leading edge can be described as follows:
(3)
and
are the three-phase modulating
where
waves with maximum, middle, and minimum amplitude at the
sampling instant, respectively. Similarly, the postpulse angles
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997
determining the trailing edge shown in Fig. 2 are defined as:
(4)
and , shown in Fig. 2,
The switching times,
represent the sequential switching times of the edges of all
the pulses. As illustrated in the figure, the switching times at
the beginning and end of the sample period (half carrier cycle)
and , respectively, where
refers
are defined by times
to a period when all three inverter phases are connected to the
lower voltage rail corresponding to a PWM output represented
. Similarly, corresponds to
by a switching state
all three inverter phases being connected to the high-voltage
. These
rail, corresponding to a switching state
“null” states represent nonswitching or “inactive” inverter
and
correspond to one of
states. In a similar manner,
.
the six possible inverter switching or “active” states,
These switching times can be derived directly from (3) and
(4) and inspection of Fig. 2 as:
prepulse times—
Fig. 2. Pulse pattern and pulse times using per-phase regular-sampling
PWM.
the zero-sequence components. Thus, the pulse positions are
affected by the additional zero-sequence component, and this
affects the PWM harmonic content. The additional influence
of the zero-sequence component on the position and extension
of the linear modulation range will be explained later in the
case of the per-phase “equal-null” pulse modulation. Equations
(5) and (6) can be used to implement an efficient single-timer
implementation to produce harmonic minimized PWM [15].
It is of interest to briefly consider what form the modulating
wave
would need to be to produce equal null pulse
times
. One possibility is to add a third harmonic to the
three-phase sinusoidal modulating waves to give modulating
functions of the form
(5)
postpulse times—
(7)
(6)
It is important to note that the added zero-sequence component
and , as shown
does not exist in the active pulse times
in (5) and (6) and, therefore, the mean value of the voltage in
, is not
the half carrier cycle, which depends upon
affected by the additional zero-sequence component. However,
and , which
from (5) and (6), the null pulse times
decide the pulse positions in the “per-phase” PWM, includes
where “ ” is the amplitude of the third harmonic to be defined
later.
The conditions for “equal-null” pulse times can be derived
from (5) and (6) and stated as follows:
(8)
Using (7) and (8) provides the equations for the amplitude
of the third harmonic “ ” in the form of (9), at the bottom
of the page. Equation (9) shows the amplitude of the added
harmonics to be a complicated time-varying function, varying
between amplitude limits of 1/4 and 1/6, as illustrated in
(9)
BOWES AND LAI: SPACE-VECTOR MODULATION AND REGULAR-SAMPLED PWM
673
(a)
(b)
(c)
(d)
Fig. 3. Added zero-sequence component and composed modulating waves. (a) Amplitude of third harmonic added for equal-null pulse times. (b) Zero-sequence
t7 ; M
1 p.u. (c) Harmonic spectrum of sinewave segments shown in Fig. 4(b).
component (bold line) added to sinusoidal modulating wave for t0
(d) Modulating waves for t0 = t7 modulation, M = 1 p.u.
=
Fig. 3(a). While it is not suggested that this function should be
used in practice, nevertheless, it does provide confirmation of
the complexity of the added harmonics which would be needed
to produce equal-null pulse times. This result has confirmed
that, in general, there is no simple constant amplitude third
harmonic which can be added to the sinusoidal modulating
wave to give
. The only exception to this occurs
for the case of 25% third harmonic addition PWM when
. Under this condition, the sampled values
and
, which depend on samples of the three-phase modulating
waves, have the same sample values (with opposite signs)
; this point will be explained in more
resulting in
detail later in Section III.
=
In view of this result, it is of interest to enquire what zerosequence component would have to be added to the sinusoidal
modulating signal to produce equal-null pulse times. Rewriting
(7) to include a zero-sequence component (or common mode
signal), “ ” gives
(10)
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997
From (8) and (10), the required zero-sequence component
can be defined as
(11)
Equation (11) shows that the zero-sequence component “ ”
is composed of “segments” of sinewaves, as illustrated in
Fig. 3(b). The corresponding modulating signals are illustrated
in Fig. 3(d), using
p.u. as an example. The harmonic spectrum of the sinewave segments defined in (11) and
illustrated in Fig. 3(b) are shown in Fig. 3(c). As shown, this
spectrum consists of only triple harmonics,
with a third
harmonic of 20.67%. Note that it is possible to show that the
sinewave segment very closely approximates a triangular wave
with an amplitude of 25%. Therefore, as shown in Fig. 3(b),
the zero-sequence component “ ” consists of the smallest
absolute reference modulating signal at any instant in time,
such that
. As will be shown later, this result has
interesting implications in the explanation of the reasons for
adding zero-sequence components. Substituting (11) into (10)
gives the modulating wave for phase , with the zero-sequence
component added as
(a)
(b)
Fig. 4. PWM waveforms for various PWM strategies. (a) PWM waveform
0:9—(a)(c) PWM pulses and (d) nVs0 n; 1/2 denotes
of SPWM, M
null vector (pulse) period; 1/6 means active vector (pulse) period. (b) Active
pulses in a carrier cycle, FR = 6—(a) SPWM, M = 1:0, (b) t0 = t7
PWM, M = 1:0, (c) t0 = t7 PWM, M = 1:1547, (d) sampled points.
=
(12)
and
Noting that similar equations can be derived for
.
These modulated signals can be stored in a lookup table
(LUT) to generate equal-null pulse PWM using the same
approach used previously for conventional regular-sampled sinusoidal PWM. Alternatively, the reference modulating signal
can be computed in “real time” by adding half the demand
voltage of that phase with the smallest absolute value, as
illustrated in Fig. 3(b).
III. EFFECT OF ADDING ZERO-SEQUENCE COMPONENT
The effect of adding the zero-sequence component of (12)
is to flatten the peaks of the modulating wave shown in
Fig. 3(d). As a result of this, the modulation index
and,
thus, fundamental voltage, can be increased beyond
to
before overmodulating and pulse dropping occurs.
This extends the linear voltage control range and thereby
increases the maximum output voltage. Note, of course, that
a similar effect is produced when adding 1/6 third harmonic
[9], [10] or 25% third harmonic [8].
It is of interest to consider in more detail the reasons for
this extension of the linear voltage range in terms of what is
happening to the PWM pulsewidths and positions. Fig. 4(a)
shows the sinusoidal modulated three-phase PWM two-level
voltages
– (line-to-inverter center-tap voltages), together
with the absolute value of the zero-sequence voltage
(starto-inverter center-tap voltage, assuming an isolated star point
at the load).
As illustrated in Fig. 4(a), line “ ,” the zero sequence
voltage assumes the larger of its two magnitudes (1/2) at the
beginning and end of each sample period (1/2 carrier period),
as delineated by the dotted lines. Also shown in the figure are
the “null” pulse times, corresponding to the inactive switching
states designated by
(state 000) and
(state 111) and, as
shown, these are not necessarily equal.
As the modulation index
increases, one of the “null”
pulse times
or
will become zero and limit the linear
voltage range. This is illustrated in Fig. 4(b), where “ ” is for
sinusoidal modulated PWM (SPWM) where
for
. If, however, the active pulse
is centered in the 1/2
sample period using
, as shown in Fig. 4(b), line “ ,”
then the modulation index can be increased beyond
up to a maximum modulation
before
, as shown in Fig. 4(b), line “ .” The above has
provided a clear explanation of how adding a third harmonic
BOWES AND LAI: SPACE-VECTOR MODULATION AND REGULAR-SAMPLED PWM
675
(a)
Fig. 6. THD for four PWM strategies, FR = 9.
(b)
0
Fig. 5. Errors in (t7 t0 ) for various PWM strategies. (a) Maximum error
of (t7 t0 )=T for various additional zero-sequence component. (b) Error of
(t7
t0 ) for various additional zero-sequence component M = 1 p.u.
0
0
(or zero-sequence component) to the sinusoidal modulating
wave affects the positioning of the PWM pulses and thereby
extends the linear voltage range to give an increased maximum
voltage.
In light of the above explanation, it is clear that the effect
of adding the sinewave segment (zero-sequence component),
derived earlier in (11) and shown in Fig. 3(a), is to shift the
to the center of half the carrier period to
active pulse
. In contrast, in SPWM, when either
or
make
, the linear modulation range ends and overmodulation
occurs for further increases of modulation index. However, the
PWM will not finish until
linear modulation range for
. The conclusion can be confirmed by comparing
Fig. 4(b), lines “ ”–“ .”
involved
The maximum pulse-time error
in using the various third harmonic additions as a function of
frequency ratio (FR) is shown in Fig. 5(a). As shown in this
figure, whichever harmonic addition is used, the maximum
error is less than 4%. Increasing the added triple harmonics
shown in Fig. 3(b) can dramatically reduce the error. It is of
interest to consider what error exists between and for each
of the various third harmonic component addition strategies.
Fig. 5(b) shows the errors in a 1/3 fundamental period. As
illustrated in the figure for 1/4 third harmonic addition, at
, the error is zero.
sampling points
This explains why the two PWM strategies,
and 1/4
third harmonic addition, result in the same PWM waveform
for
, as stated earlier.
It is, however, important to note that while all the cases considered in Fig. 5(a) extend the linear modulation range, these
are not all necessarily optimum with regard to minimizing
harmonic distortion. This can be seen in Fig. 6, which shows
the THD for the four main PWM strategies and, as illustrated,
the equal-null pulse time strategies are better than adding a
1/6 third harmonic, but not as good as the 25% third harmonic
addition. This is to be expected, since the 25% third harmonic
addition PWM strategy was specially designed to minimize
the THD by optimally positioning the pulses to give the “best”
harmonic spectrum. In contrast, the other two strategies were
only designed to extend the linear voltage range without regard
to harmonic minimization, thereby giving an inferior harmonic
performance, as shown in Fig. 6.
The above results and discussion of the “zero-sequence
addition” concept and techniques, leading to the “equal-null”
pulse time concept, has been developed using only the “perphase” concepts of the three-phase PWM techniques without
recourse to any “space-vector” concepts or techniques. It is,
however, of considerable interest to compare this “per-phase”
PWM development with the parallel space-vector techniques
in the context of regular-sampling PWM techniques.
IV. COMPARISON
WITH
SPACE-VECTOR TECHNIQUES
Space-vector modulation (SVM) techniques have become
very popular over the past few years, particularly for vector drive control applications. It is, therefore, of interest to
compare SVM with regular-sampled PWM and identify the
relationship between the two approaches to PWM inverter
control. It will be shown that the regular-sampled “equal-null”
pulse time PWM presented in the previous section is exactly
equivalent to SVM, although the two approaches have been
developed from entirely different “viewpoints.”
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997
(a)
(b)
(c)
(d)
=
=
Fig. 7. Simulation and experimental results for t0
t7 PWM, M
0:8 p.u. FR = 15. (a) PWM voltage and current waveforms. (b) PWM voltage
spectrum, simulation. (c) Current spectrum. (d) PWM voltage spectrum, experiment.
The basic concepts, theory, and development of SVM is well
known [3] and, therefore, only those SVM results necessary
to appreciate the comparison with regular-sampled PWM will
be considered.
SVM is based on time-averaging techniques over a sampling
period
and can be expressed in Sector 1 (0 –60 ) by the
following equations [3]:
PWM, the active pulse times for the leading edge can be
derived as
(14)
Similar equations exist for the trailing edge of the pulse by
the same procedure.
Since
, (14) can be rewritten as
(13)
(15)
To make a direct comparison between the two approaches
on the basis of active pulse times
and
(for SVM)
and
(for regular-sampled PWM) is necessary to
and
consider a sampling instant
corresponding
to
. From (2), (5), and (12) for regular-sampled
Comparing (13) for SVM with (15) for regular-sampled PWM
shows that the active pulse times
and
providing the SVM sample time
equals half the carriercycle period
and
.
The same relationship holds for other sectors. Also, since
equals
in both SVM and regular-sampled PWM,
then all the pulse times are equal, confirming that both approaches are exactly equivalent with regard to these switching
where
dc link voltage, and
BOWES AND LAI: SPACE-VECTOR MODULATION AND REGULAR-SAMPLED PWM
(a)
(c)
677
(b)
(d)
Fig. 8. Simulation and experimental results for 25% third harmonic added PWM. (a) PWM voltage and current waveforms. (b) PWM voltage spectrum,
simulation. (c) Current spectrum. (d) PWM voltage spectrum, experiment.
times. It is also possible to show that the switching pattern
is the same in both approaches. For example, in Sector
and for
1, the switching pattern for
, therefore, the switching pattern for the
. For
first sample period is
asymmetric regular-sampled PWM, as shown in Fig. 3(d)
which is plotted according to (10) and (11), the maximum
in this sector is phase , and
modulating wave
is phase . Therefore, from Fig. 2, the switching
for the leading
pattern will be
for the trailing edge.
edge and
Note that, as shown, only one inverter leg switches between
each transition, resulting in minimum switching frequency in
the three-phase modulation case. Thus, the switching patterns
for both SVM and asymmetric regular-sampled PWM are
exactly equivalent, and this equivalence can be confirmed for
all sectors.
The above results have proved that both the switching
times and switching patterns are exactly equivalent in both
approaches and, therefore, will produce the same three-phase
PWM voltage waveforms and harmonic spectra. It is important
to note that, while the equal-null pulse times in the SVM
approach considered have improved the THD, as compared
to sinusoidal PWM, it is not optimum and, as shown in an
earlier section, harmonic minimization with minimum THD
results from adding 25% third harmonic, as shown in Fig. 6.
It has been common practice in SVM [3] to allocate the
and
switching states equally and to
null pulse times to
locate them at the beginning and end of each sample period.
However, this was not done to extend the linear voltage range,
as was the case in regular-sampled PWM described earlier,
and
in SVM does not limit the
since the distribution of
maximum voltage range.
This can be shown to be the case by considering the process
of calculating the various pulse times in SVM. For example,
determines the
in SVM, the reference (or demand) vector
. Thus,
active vector times and
and
provides an additional degree of
the distribution of
freedom which can be arbitrarily chosen and, therefore, does
not contribute to the restriction of the maximum voltage range.
Therefore, the range of linear modulation and voltage in SVM
,
is only decided by the active pulse times
.
which are determined from a given reference vector
and
only determine the positioning of
Consequently,
the pulses and switching patterns which, in turn, influence the
THD and commutation frequency. In contrast, in SPWM, the
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997
range of linear modulation is determined by the modulating
signals and is, therefore, influenced by both the active pulse
times and, also, the null pulse times, as discussed earlier.
V. EXPERIMENTAL RESULTS
Which approach and form of PWM implementation is
adopted in a particular application will depend largely upon
the form of the control strategy used. For example, if the
reference voltage is given in terms of two-axis quantities, for
example, in a vector control system, then using space-vector
modulation has some advantages, since the 2/3 transformation
is not necessary. However, if the reference voltage is given in
terms of three phase voltages, for example, in a feedforward
control system, then the “per-phase” implementation will have
some advantage, since the intensive computation required for
locating the position (sector) of the reference vector and
3/2 transformation are not necessary. In this case, the fourtimer [11]–[14] implementation will be superior to one-timer
implementation [15], [16]. The authors hope to report in more
detail on the implementation of each approach in a future
paper.
The experimental drive system used a TMS 320 C26 digital
signal processor (DSP), and the PWM control software was
programmed using the four-timer approach [11]–[13], [15],
[16] in assembly language. Figs. 7 and 8 show the simulation
and experimental results for a PWM waveform voltage harmonic spectrum. Noting that these voltage harmonic spectra
correspond to the line-to-center-tap voltage and, therefore, the
triple harmonics shown in Figs. 7 and 8 will not appear in
the phase-voltage and the line-voltage spectrum, due to the
three-phase connection with isolated star point. Figs. 7 and 8
show the PWM and current waveform and current harmonic
spectrum, which clearly confirm that the triple harmonics
have been eliminated in the current spectrum. The simulation
results are included to show clearly the harmonics present
in the voltage spectrum and as a basis of comparison and
confirmation with the experimental results. As clearly shown
in these figures, the experimental results agree very well
with simulation results and confirm the results of the analysis
presented earlier in this paper. In particular, Figs. 7 and 8 show
that the voltage harmonic spectrum for 25% third harmonic
addition is slightly better than
PWM (or, equivalently,
SVM), confirming the THD results shown in Fig. 6.
VI. CONCLUSION
This paper has shown the relationship between asymmetric regular-sampled PWM and space-vector modulation techniques.
This comparison was based upon showing the various developments leading to the regular-sampled “equal-null” pulse
time PWM techniques. It was shown how these developments
only involved three-phase concepts and considerations based
on well-established regular-sampling techniques. It was also
illustrated how the
PWM strategy evolved naturally
from these three-phase regular-sampled considerations without
invoking any of the concepts, theory, or techniques normally
associated with “space vectors.”
It has been shown that the “equal-null” pulse time regularsampled PWM is derived by adding a zero-sequence component, in the form of sinewave segments, to the modulating
wave of SPWM. Detailed considerations on the reasons for
adding this zero-sequence component to extend the linear
modulating range wave were also presented. It has also been
confirmed that the use of the “equal-null” pulse times does
not give minimized THD and that adding 25% third harmonic
does provide minimized THD.
It has been shown that the equations used to calculate the
pulse times are the same in both SVM and regular-sampled
PWM and, therefore, the SVM presented in this paper can be
viewed as a particular form of asymmetric regular-sampled
PWM. However, the reasons for using “equal-null” pulse
times has been shown to be different in each approach and
has, therefore, highlighted the significant differences between
SPWM and SVM.
ACKNOWLEDGMENT
The authors gratefully acknowledge the University of Bristol for providing excellent computing and experimental facilities.
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BOWES AND LAI: SPACE-VECTOR MODULATION AND REGULAR-SAMPLED PWM
[16] S. R. Bowes, “Advanced regular-sampled PWM control techniques for
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pp. 367–373, Aug. 1995.
Sidney R. Bowes (M’89–SM’89–F’96) received the
B.Sc., Ph.D., and D.Sc. degrees from the University
of Leeds, Leeds, U.K.
He was with the Chief Mechanical and Electrical Engineer’s Department, British Rail, for six
years before joining the Reluctance Motor Drive
Research Group, University of Leeds, as a Research
Fellow. He subsequently became a Lecturer, Reader,
and Professor at the University of Bristol, Bristol,
U.K. He has been engaged in the research and
development of PWM-controlled drives and power
electronic systems for over 25 years. He has also been a consultant to
numerous international companies.
Dr. Bowes is a Fellow of the Institution of Mechanical Engineers, the
Institution of Electrical Engineers (IEE), U.K., and the Royal Society of Arts.
He has been awarded three IEE Premiums, the F. W. Carter Prize, and the
European Globe Award. He has also served on several IEE committees.
679
Yen-Shin Lai (M’96) received the M.S. degree
from the National Taiwan Institute of Technology,
Taipei, Taiwan, R.O.C., and the Ph.D. degree from
the University of Bristol, Bristol, U.K., both in
electronic engineering.
In 1987, he joined the National Taipei Institute of
Technology, Taipei, Taiwan, R.O.C., as a Lecturer.
He became an Associate Professor in 1996. His
research interests include design of microprocessorbased systems, development of PWM techniques,
and drives and converter control.