328
IEEE TRANSACTIONS ON POWER ELECTRONICS. VOL
3. NO 3. J U L Y 1988
PWM Technique for Power MOSFET Inverter
KATSUNORI TANIGUCHI,
MEMBER, IEEE,
Abstract-A new sinusoidal PWM inverter suitable for use with
power MOSFETs is described. The output waveforms in the proposed
PWM inverter are investigated both theoretically and experimentally.
A modulating signal for the three-phase PWM inverter is obtained by
adding the harmonic components of integer multiples of 3 to the threephase sine waves. By using the new modulating signal, the amplitude
of the fundamental component is increased about 15 percent more than
that of a conventional sine wave inverter and the commutation number
of the inverter is decreased to two-thirds of a conventional one.
INTRODUCTION
HE PULSEWIDTH modulation (PWM) method can
move unwanted frequency components to a higher
frequency region, i.e., the sidebands of a carrier frequency. Thus the output waveform of a PWM inverter is
generally improved by using a high ratio between the carrier frequency and the output fundamental frequency.
Since solving the noise problem of a PWM inverter requires raising the switching frequency to above the audible range, the carrier-to-output fundamental frequency ratio becomes extremely high. Recent power devices have
very small switching losses. However, when an auxiliary
circuit for limiting surges, such as a snubber circuit, is
connected in parallel with each device, the switching energy loss is increased. Heat generated inside of the devices must be dissipated. If an inverter has an interval
where the switching operation stops during a part of one
period, the heat generated in the devices is reduced and
the size of the inverter system is minimized because of
the reduction in the heat-dissipating equipment.
The fundamental amplitude in the PWM output waveform is smaller than for the rectangular waveform. The
ratio of fundamental voltage in the output waveform to
the direct supply voltage must be higher. The conventional technique which generates three-phase PWM waveforms in an inverter uses a triangular carrier wave and a
three-phase sinusoidal modulating wave. In this case, the
ratio of the fundamental component of the maximum lineto-line voltage to the direct supply voltage is 0.87. This
value indicates poor utilization of the dc power supply. A
modulation technique to increase the amplitude of the
fundamental component was proposed in [ 11, where a
third harmonic wave is added to the three-phase sinu-
T
Manuscript received August 28, 1987; revised April 18, 1988.
K . Taniguchi and Y . Ogino are with the Osaka Institute of Technology,
5-16-1 Omiya, Asahi-ku, Osaka. 535 Japan.
H. Irie is with the University of Osaka Prefecture, Mozu Umemachi 4408, Sakai, Osaka, Japan.
IEEE Log Number 8822136.
YASUMASA OGINO,
AND
HISAICHI IRIE
al modulating wave. Some new techniques have also been
developed in [7]-[ 101.
This paper deals with new sinusoidal PWM inverter for
the use of power metal-oxide semiconductor field effect
transistors (MOSFETs) which has a high carrier-to-fundamental output frequency ratio. The fundamental component of the three-phase line-to-line voltage is increased
by about 15 percent above than that of the conventional
sine-wave inverter. The heating of the devices is reduced
because the inverter stops the switching operation during
one-third of the period.
EQUIVALENT
CIRCUITOF THE PWM INVERTER
Fig. 1 shows a three-phase bridge inverter using power
MOSFETs. In a balanced three-phase PWM inverter,
average phase voltages ( V u , V,,, V,) and currents ( I , , I , , ,
I , ) are expressed as follows:
V, =
Jz Vsin ( q t )
V,, =
h Vsin ( q t - 2 ~ / 3 )
I,
=
d21sin ( w s r - 4 )
I,
=
I,
42 I sin ( q f- 2 a / 3
= J ~ sinI (uSr- 4w/3
-
4)
-
4)
(2)
where V and I are the effective value of the phase voltage
and current, 0, is the fundamental output angular frequency, and C#I is the load angle. The duty factors ( d u ,d,,,
d,) which are required to obtain the average phase voltage in each arm of the inverter are given by
du = do
+
V U B d
+ V,,/Ed
= do + V,,./E,
d,. = do
d,.
(3)
where the duty factor do corresponds to the neutral point
voltage of the three-phases and E(, is the direct supply
voltage. When do is included in each phase, the value of
do does not need to be a constant. From (1)-(3), the direct
current Id is derived as
Id
duZu + d,,l,, + d,,.Z,,
=
3 VI
COS
~
Ed
4.
(4)
By using (3) and (4), the equivalent circuit of the threephase PWM inverter of Fig. 1 can be obtained as shown
in Fig. 2. P, is the loss which is caused by the pulsating
0885-8993/88/0700-0328$01.OO @ 1988 IEEE
Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on January 26,2022 at 19:04:28 UTC from IEEE Xplore. Restrictions apply.
329
TANIGlJCHl ef a l . : P W M TECHNIQUE FOR POWER MOSFET INVERTER
Fig. I . Three-phase P W M inverter using power MOSFETs
Fig. 2 . Equivalent circuit of three-phase PWM inverter.
current flowing through load resistance r . In a reactive
load, such as an induction motor, this pulse current loss
can be decreased remarkably by increasing the pulse frequency. P,. is the switching loss of the inverter devices.
This loss is reduced on account of recent progress in making switching devices and can also be decreased by the
PWM technique.
Ed
THEORETICAL
ANALYSIS
A conventional technique for producing a three-phase
PWM waveform is illustrated in Fig. 3. A triangular carrier wave of a fixed frequency is compared with a threephase sine wave of variable frequency. The camer signal
eh has an amplitude Eh and angular frequency U,,.The sine
waves e,, e , , , and e,? are called the modulating signal.
They are balanced three-phase voltages which have amplitude E, and angular frequency U,. Since the ratio of two
frequencies wh / U, is generally incommensurable, the
PWM wave becomes a nonperiodic function. A harmonic
analysis of such a wave can be made by using the double
The PWM waveform E,, shown in
Fourier series [11-[7].
.~~~
Fig. 3(b) is expressed by the double Fourie; series in
complex form as
f m
Euq(Ubt,~ . ~=t )C
(a)
0
(b)
Ed
yEvq
0
un
inn
Ed
0
(d)
Ed
0
i m
C K,,
m=O n = O
exp [ j ( m w h t + n ~ , t ) ]
-Ed
(e)
(5)
Fig. 3 . Conventional three-phase PWM inverter waveforms
Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on January 26,2022 at 19:04:28 UTC from IEEE Xplore. Restrictions apply.
IEEE TRANSACTIONS ON POWER ELECTRONICS. VOL 3. NO 3. J U L Y 1088
330
. exp [-j(mwbr
+ nwsr)]
(6)
where K,,,, is the complex Fourier coefficient, m = 0, f 1,
f 2 , * * - , n = 0, f 1 , + 2 , * . . Waveform E,,, illustrated in Fig. 3(c) can be expressed in the same way. The
PWM line-to-line voltage Vu,,shown in Fig. 3(e) appears
across point U and U as the difference voltage between Eu,
and E,,,. In the general polyphase case such a waveform
also becomes the difference voltage. Thus the line-to-line
voltage waveforms Vut,(wbr,w,r) for the balanced P,phase modulating signal is given by
*03
Vu,.(whr,w,r) =
(bl
Ed
-0
*m
C C
m=O n=O
K,,A, exp [ j { m w h r + nw,r>]
Ed
0
(7)
A = 1 -
,y12~n/Pn
(8)
where P, is the phase number. Therefore, the PWM lineto-line voltage waveform is obtained by multiplying the
right side of ( 5 ) by coefficient A, of (8). The Fourier coefficient K,,,, can be derived from the sampling phase angle
which is obtained from the intersection of the carrier and
modulating waves. As a result of the analysis for the threephase modulating signal shown in Fig. 3 , the fundamental
output waveform
in the conventional PWM line-toline voltage is given by
Vu,,l = (&/2) ME, sin ( w s t
+~/6)
-Ed
(d)
Fig. 4. Illustrating reduction of commutating number for single-phase
PWM inverter.
0
(9)
where M = E.y/Ebis the modulation degree. The maximum value of the fundamental component is 0.87Ed at M
= 1 [7].
REDUCTIONOF COMMUTATION
NUMBER
If the carrier frequency is high, the pulse current loss
P, shown in Fig. 2 is decreased because the sidebands are
distributed in the high-frequency region. To decrease the
switching loss P,, it is necessary to reduce the commutation number of the inverter.
To make a sinusoidal line-to-line voltage with a PWM
inverter, each phase voltage does not need to keep a sinusoidal waveform. That is, the modulating signal may add
the same voltage to the polyphase sine wave. The coefficient A, of (8) can be applied to reduce the commutation
number and still produce a sinusoidal line-to-line voltage.
Coefficient A, for single-phase inverter substitutes 2 for
P, in (8) and obtains
A,
=
1 - (-l),.
( 10)
Equation (10) becomes zero when n is an even number.
In other words, even-number harmonic components may
be added to a sine wave as the modulating signal for a
single-phase inverter. This principle is shown in Fig. 4.
Although each inverter arm stops its switching action during a half-period as seen in Fig. 4, the output waveform
of the inverter becomes a sinusoidal PWM wave.
(e)
Fig. 5 . Illustrating new strategy for three-phase sinuwidal PWM inverter.
Coefficient A, for a three-phase inverter is given as
A,
=
[ { 1 - (-1)")
COS
( n ~ / 6 -) j { 1
sin (n.rr/6)]exp [ j ( n ~ / 6 ) ] .
+ (-I),)
(11)
This equation is obtained by substituting 3 for P,, in (8).
Equation (1 1) becomes zero at n = 3 N , where N is an
integer. Therefore, the modulating signal for the three-
Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on January 26,2022 at 19:04:28 UTC from IEEE Xplore. Restrictions apply.
33 1
TANIGUCHI er a l . PWM TECHNIQUE FOR POWER MOSFET I N V E R T k R
phase PWM inverter can add 3Nth harmonic components
to the three-phase sine wave. The new three-phase modulating signals ( e , , e,, e , ) are shown in Fig. 5. The lineto-line voltage of the inverter becomes a sinusoidal PWM
waveform. As seen in Fig. 5, each PWM voltage El,,, E,,,,
and Eh,, has an interval where it is zero. That is, each
inverter arm is switched off for one-third of the period.
This fact implies that the heat generated in the switching
devices is reduced.
SPECTRUM
ANALYSIS
When one cycle of the modulating signal e , shown in
Fig. 5(a) is divided into the following three intervals, the
sampling phase angles in each interval are given by the
following:
eJh"lb
where U = mMx. These values give the amplitude of the
frequency components included in the PWM voltages
( El,,, El,,, E,,(,) in each inverter arm. Multiplying these
values by coefficient A,, of (1 l ) , substituting them into (7),
and expanding VI,,,(w,,t, w, t ) into a real-valued Fourier
series gives the PWM line-to-line voltage as
m
I/l,,.(Whr,
w s t ) / E c , = M sin w , t
+
If1
=
+m
-
I
c
I1 =
iI
A,,,,,
. sin (mwhr + n w , t )
(12)
A,,,, = 2 ( - 1 ) f " [ {1 - ( - I ) ~ ' } / ~ ~ ] J , , ( u )
- x ( M s i n y - 1)
. {1
+ 1)
x(Msiny
=
k
- nl
where
1) interval [0, 2 x / 3 ]
cyaI =
. sin (kx/6) k -
+ cos ( n / 3 ) a )
-
( -1)f'+ff1(4/x2m)
2) interval [2x/3, 4x/3]
aU2=
- x { ~ s i n( y
x/3)
-
-
1)
sin ( y - x / 3 ) + 1 )
(Yb2 =
3 ) interval [4x/3, 2 x 1
(Yu3
= (Yb3 =
T.
Then the Fourier coefficient K,,, is derived as
1
K",,
=
[
2
(2x1
so
(2/3)T
J
ahl
a<,I
e(x, Y > dX dY
where
Carrying out the integration of K,,,, we obtain the values
of Fourier coefficient as follows:
K,
=
(3/2x) ME,
Kol = - j ( M E , / 2
h ) e pJ"/b
KO,, = [ M E , / { 2 x ( 1
-
n 2 ) ) ]( 1
+ e-J2na/3+ e-J4na/3>
+W
k
The line-to-line voltages Vt,,,,and V,,.,,are obtained when
the phase angle of w,t in (12) is delayed by 2 x / 3 and
4x/3, respectively. Equation (12) indicates that the PWM
line-to-line voltage is composed of fundamental component w, and the unwanted frequency components mwb 5
nu., and that harmonic components of the modulating signal are not included. The unwanted frequency components distribute around the integer multiple of the carrier
frequency. They are sidebands of the carrier frequency.
The sidebands are concentrated in the high-frequency region apart from the fundamental component when wh >>
U,. That is, in the proposed method, adding the 3Nth harmonics to the sine wave modulating signal yields 100percent utilization of the dc supply voltage and brings a
one-third reduction of the commutation number.
RESULTS
EXPERIMENTAL
A block diagram for PWM control signal generation
using a microprocessor is shown in Fig. 6. Data for the
modulation are stored in a read-only memory (ROM) table, and a modulating signal having arbitrary amplitudes
is rewritten into a random access memory (RAM) table in
accordance with an amplitude control signal V I , .The frequency, according to signal V f , is obtained by controlling
an interrupt signal to the CPU. The modulating signals
( e , , e , , e ; ) become the balanced three-phase voltages because the data of the RAM are converted from digital to
analog. Comparators derive the PWM pulse by comparing the modulating signal with the triangular carrier signal.
Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on January 26,2022 at 19:04:28 UTC from IEEE Xplore. Restrictions apply.
IEEE TRANSACTIONS ON POWER ELECTRONICS. VOL. 3, NO. 3 , JULY 19x8
332
D IG I T U .
Ly$
ANALOG
CONVERTER
MICROCOMPIITFR
ANALOG
COMPARATOR
I
CPU
I
Fig. 6 . Block circuit diagram for three-phase P W M pulse signal generator
Modulation degree M
0
0
-C a l c u l a t e d
Measured
-10
-
m
m
6b
I
I
2k
F r e q u e n c y [Hzl
4k
(a)
80
bJs
I
I
Fig. 7 . Amplitudes of major line-to-line voltage components as function
of modulation degree M.
Fig. 7 shows amplitude variations of the w , ~and the
Wb
k nu, components for modulation degree M . Theoretical
curves were calculated from (12). The marked points indicate the measured values. These values were obtained
for the case of direct supply voltage Ed = 100 V , output
frequency f, = u,/2a = 60 Hz, and carrier frequency fb
= u b / 2 a = 2 kHz. An example of the output voltage
frequency spectrum at M = 0.8 is shown in Fig. 8(a).
Fig. 8(b) shows the frequency spectrum at M = 0.8 for
the conventional PWM method (see Fig. 3). In Fig. 8 the
spectra have the same commutation number in the inverter. Thus the carrier frequency of the conventional
method is 1.33 kHz. The carrier frequency of Fig. 8(a) is
2 kHz in spite of the intervals when the component signals
are zero. The sidebands appear 1.5 times higher than the
Frequency [Hz]
(b)
Fig. 8. Frequency spectra of three-phase P W M inverters. (a) Proposed
method. (b) Conventional method.
frequency region of the conventional carrier frequency.
Although the width of the sidebands is increased, the fundamental component is not influenced very much because
these sidebands exist in the high-frequency region away
from the fundamental frequency. The amplitude of the
fundamental component is increased by about 15 percent
compared to that of a conventional one as seen from Fig.
8.
Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on January 26,2022 at 19:04:28 UTC from IEEE Xplore. Restrictions apply.
TANIGUCHI er
U/.:
333
PWM T E C H N I Q U E FOR POWER MOSFET INVERTER
60
20k
Frequency [ H z ]
40k
Fig. 10. Frequency spectrum for M O S F E T inverter
PH 1...PH4;PHOTO-COUPLER
FET1,FETZ;POWERMOSFET(BU7.211)
LG=imH Cf=20pF
~,=,01;~,~,=502
Fig. 9 . Driving circuit for M O S F E T inverter.
MOSFET PWM INVERTER
An inverter taking into account the noise problem requires a carrier frequency of over 20 kHz. As a high-speed
device, the recent progress of the power MOSFET is remarkable. The proposed method has advantages for PWM
inverters using power MOSFETs. In a low-noise inverter
using the power MOSFETs, the spread of the sidebands
has no effect on the fundamental component because the
carrier-to-output fundamental frequency ratio becomes
very high. High carrier frequency increases the switching
loss. Even if switching loss is small compared with the
total loss in the inverter system, the heat generated inside
the devices must be dissipated. The proposed method has
an interval when the switching operation stops during onethird of each period. Thus the size of the inverter system
is minimized because of the resulting reduction in the heat
dissipating equipment.
Fig. 9 shows a driving circuit for a MOSFET inverter
and illustrates one arm of a three-phase inverter. In the
operation of the inverter the upper and lower MOSFETs
must not create a short circuit and also the period in which
a pair of devices are off simultaneously has to be as short
as possible. The circuit shown in Fig. 9 prevents the short
circuit that would be caused by turning on a pair of MOSFETs at the same time. The upper and lower MOSFETs
turn on alternately after the delay time of a photocoupler.
This delay time is very short compared with the period of
the 20-kHz carrier frequency.
Fig. 10 shows an example of the frequency spectrum of
a MOSFET inverter. Experimental values in the subsequent figures are obtained for the case of Ed = 100 V, f,
= 60 H z , =
~ 20 kHz, and M = 0.8. The sidebands are
concentrated in the ranges of integer multiples of the carrier frequency as seen in Fig. 10. Therefore, the fundamental wave in this MOSFET inverter can easily be separated from the sidebands by using a simple low-pass
(b)
Fig. 11. Filter output waveforms of three-phase PWM inverter. ( a ) Waveforms of inverter arm and line-to-line voltages. (h) Filter output of threephase PWM inverter.
filter. Fig. 1 l(a) gives the phase voltages and the line-toline voltage waveforms of the filter outputs. The filter was
made with a series inductance of 7 mH and a parallel capacitance of 20 pF. The oscillograms of Fig. 1 l(b) show
three-phase output voltage waveforms appearing across a
wye-resistance of 10 Q . In this case, the noise of the carrier frequency is not heard.
CONCLUSION
A new sinusoidal PWM inverter suitable for use with
power MOSFETs has been described, and the output
waveform of the proposed PWM inverter has been investigated both theoretically and experimentally. The equivalent circuit of this three-phase PWM inverter is shown.
To make the line-to-line voltage sinusoidal, each phase
voltage of the PWM inverter does not need to be a sinusoidal waveform. The modulating signal for a three-phase
PWM inverter can add 3Nth harmonics to the conven-
Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on January 26,2022 at 19:04:28 UTC from IEEE Xplore. Restrictions apply.
tional three-phase sine waLe By using a new modulating
signal, the line-to-line voltages of the inverter become
sinusoidal PWM waveforms. the amplitude of the fundamental component is about 15 percent more than that
of a conventional sine wave inverter, and the coinmutation number of the inverter becomes two-thirds that of a
conventional one. These facts imply that the direct supply
voltage is utilized effectively and that the heating of the
devices is reduced.
REFER E N c M
D . A . Grant. J . A . Houldsuorth. and K . N . Lower. " A new highqualit) PWM ac drive." / E E E /run\. /rid. A p p / . . \ o l . 1.4-19. pp.
21 1-216. M a r . / A p r . 1983.
K . Taniguchi. H . Irie. and T . I s h u a h i . "Pulsew idth-modulated power
amplifier consisting of thyristor-bridge inverter." 7-rari\ /!I\/ E l c j c , .
Cifi. Jupciri, bol. 93-B. n o . 9. pp. 385-390. Sept. 1973. Also in Elrc..
Gig. J c ~ p r i .scripta. \ o l . 93. no. 5 . pp. 15-SO. Sept. 'Oct. 1973.
M . Mazrucchelli, L . Pugli\i. and G . Sciutto. "PWM systenir in power
converters' An exten\ion of the 'subharmonic' iiiethotl." /EEE Trilric.
/ r i d Elecrrori. Corirr. /m/riirri. . \,ol. IECI-28. pp. 3 15-322. N o \
lY8l.
K. Taniguchi. S . Kaku. and H . Irie. " A three-phaw \inusoidal PWM
inverter." in / E E L / r i d . A p p l . Soc. Cr1ri.f Rrc.. . Oct. 1985. pp. 126')1173.
S. R . Bowes and B . M Bird. "Kovel approach to the analhsis a n d
aynthejis o f niodulation process in power conberter." P r i r //I\/ E / K .
Etig., vol. 122. n o . 5 . pp. 507-513. May 1975.
K Taniguchi and H . Irie. "A modulating signal for three-phaw \ i n usoidal P W M inverter." Tr-uris / r i . \ ~ . Elec. Erig. ./upori. \oI 105-5.
no. I O . pp. 880-885. Oct. 1985.
-. "Trapezoidal modulating signal for thrcc-phaw P W M inverter." l E E E Trtrm. /rid. E/c~crrr>ri.,
vol. 1E-33. n o . 2 . pp. 193-200.
May 1986.
T . Ohnishi and H . Okitu. " A novel P W M technique for three-phase
voltage source inverter." /PEC ToL>o Corif: K c t . . . 1983. pp. 381395.
T . H . Chin. M . Nakano. and Y . F u h a . "New PWM technique u \ i n g
a triangular carrier w a \ e o f saturable amplitude," / E E E Truri.\. / r i d .
A p p l . . vol. IA-20. no. 3. pp. 643-6.50. M a y / J u n e 1981.
W . McMurray. "Modulation o l the chopping frcqucnc) in dc choppers and PWM inberters having current-hysteresis controller\." I t
Trfiric. /rid. A p p l . . vol. 1A-20. no 4. pp. 763-768. J u l y i A u g l Y X 4 .
hat\unori lariiguchi ( M 75) w i i \ boin
i n h'tg'i
\dhi J,ip,in o n April 7 1 1943 He r e i e i \ c d t h i
B S degree in clcitriiitl engineering trtiiii O \ , i h , i
In\titute 0 1 Technoloz\ O d d Jan'iii i n lYh6
.incl the M S .ind Ph I) degree\ I i o i i i the L n i \ e t
\ i t \ of O \ d h , i Prctecturc Os,ih,i Jap'tn i n I Y 7 0
,ind 1971 re\peiti\el\
S i n i c 1966 he h,i\ been u i t h the Dep.iitnient
of Eleitriidl Engincciing C h C i h c i I n \ t i t u t e i)l
Teihnolog! where he I\ itirreiitl\ P i o l e \ ~ i ) t H e
I\ eng'igcd in rc\cdrih o i i the PM U in\erter .tnd
its appliidtion
t o motor control
..
Dr Taniguchi i \ a member of the Institute o f Electrical Engineer\ oi
Japan. the Societ) of In\truiiientation and Control Engineer\. and the Japan
Society f o r P o u c r Electronic\.
--
Since l Y 5 Y . he h a \ been \ k i t h the 1)epartiiicnt
of Electrical Engineering. O \ a h n In\tirute of
Technolog). where he i \ currcntl! a n -\\sociate
Profe\sor. At prc\ent he i \ engaged i n research o n
linear motor\ and rohoric\
M r . Ogino i \ a member of the In\titute o f Electrical Engineers o f Japan.
the Robotic\ Societ) of J a p a n . the Societ) of In\trunientntion and Control
Engineers. a n d the Japan Society for P o u e r Electronics.
Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on January 26,2022 at 19:04:28 UTC from IEEE Xplore. Restrictions apply.
