IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS,VOL. 30, NO. 6, NOVEMBER / DECEMBER 1994
1573
Input Filter Design for PWM
Current-Source Rectifiers
Navid R. Zargari, Student Member, IEEE, Geza Joos, Senior Member, IEEE,
and Phoivos D. Ziogas, Fellow, IEEE
Abstract-Pulse-width modulated (PWM) rectifiers are increasingly used because they allow the elimination of low-order
harmonics, and therefore a reduction in input filter components.
Filtering requirements for PWM current-source rectifiers are
usually satisfied through the use of low-pass LC input filters.
This paper offers a systematic and user-friendly approach to
choosing the filter components. Design of LC filters involves the
positioning of the resonant frequency to meet the harmonic
attenuation requirements (THD), and introducing damping at
the resonant frequency to avoid amplification of residual harmonics. The problem is further complicated by considerations
related to cost., power factor, voltage attenuation, system efficiency, and filter parameter variation. The systematic approach
proposed in this paper focuses on PWM rectifiers, but can easily
be extended to other classes of converters. Practical design
considerations are detailed and design equations derived. Simulated results are presented to validate the design approach.
IIfli i ! i ! i \
.......................................
II
. . . .: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I
...................
OHZ
1m
4m
Fig. 1. Harmonic spectrum of the SPWM switching pattern ( M = 1,
f, = 27pu).
I. INTRODUCTION
S
chronism in the PWM method, switching delays, and
other inaccuracies in implementation, some unwanted
harmonics with small amplitudes exist in the dead-band.
These harmonics can be amplified by the filter, if no
damping is provided. On the other hand, a highly damped
filter will not necessarily meet the harmonics attenuation
requirements 111.
Although filter design and component optimization for
PWM rectifiers have been presented in several papers
[2]-[6], practical considerations have usually not been
addressed systematically. Some of these are as follows.
TATIC power converters, when operated from an ac
power system, generate current harmonics that are
injected back into the ac system. These current harmonics
result in voltage distortions that affect the overall operation of the ac system. The principal method of reducing
the harmonics generated by static converters is provided
by input filters using reactive storage elements. The harmonics generated by a phase-controlled rectifier on the ac
side are of orders (np + / - l),where p is output voltage
pulse number and II = 1,2, .... However, by using PWM
techniques, the frequency spectra of the input waveforms
can be shaped and harmonic components moved to a
higher frequency. This substantially reduces the size of
the filter components. Spectra shaping results in the creation of a “dead-band’’ where no unwanted harmonic
components exist. The break frequency of the LC filter
can therefore be positioned in this dead-band, shown in
Fig. 1. However, in practice, due to the presence of
imperfections such as asymmetry in gating signals, asynPaper IPCSD 94-51, approved by the Industrial Power Converter
Committee of the IEEE Industry Applications Society for presentation
at APEC93. This work was supported in part by the Natural Sciences
and Engineering Research Council of Canada and by the Quebec
Ministry of Education under an FCAR Grant. Manuscript released for
publication June 27, 1994.
N. R. Zargari and G. Joos are with the Department of Electrical and
Computer Engineering, Concordia University, Montreal, P. Q. H3G
1M8, Canada.
P. D. Ziogas was with the Department of Electrical and Computer
Engineering, Concordia University, Montreal, P. Q.
IEEE Log Number 9405050.
0
The existence of uncharacteristic harmonics in the
dead-band region.
The tolerances on the value of the filter components.
The effect of the filter on the converter performance
and on the rating of the converter components.
Considerations related to system efficiency, power
factor, kilovoltampere rating of the filter components
and cost of the filter.
A systematic approach to the design of an input filter
for PWM rectifiers is discussed in this paper taking into
account the above constraints, in particular the problem
of damping at the resonant frequency, which is not discussed in [5], as well as other literature. The proposed
approach is used to design an input filter for a PWM
current-source rectifier. The effects of the filter on the
performance of the rectifier are examined.
0093-9994/94$04.00
0 1994 IEEE
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30, NO. 6, NOVEMBER / DECEMBER 1994
1574
11. PRINCIPLES
OF PWM CURRENT-SOURCE
RECTIFIERS
The complete circuit diagram of a three-phase currentsource-type PWM rectifier is shown in Fig. 2. It consists of
three-phase ac mains, an input LC filter with damping
resistors, a PWM rectifier, an output filter, and a load.
The input rectifier current is given by the following:
where S, , (t ) is line-to-line switching pattern, Z,, is the
output dc current, and i,(t> is the input rectifier current
of phase (a).
Therefore, the harmonic current source of Fig. 3(c)
injects the harmonic contents of the S,,(t) into the ac
mains.
Rf
Fig. 2. Current-source-typePWM rectifier with input filter.
Rs
L,
111. DESCRIPTION
OF THE FILTER
CHARACTERISTICS
A typical connection for a PWM converter to the ac
mains through an input filter is shown in Fig. 3(a). If the
harmonic source has a current-source characteristic, the
preferred choice would be a second-order LC filter, for its
simplicity and the minimum number of components required. The single-line diagram of the ac source, input LC
filter, and PWM converter for the fundamental frequency
and for harmonic frequencies are shown in Fig. 3(b) and
(c). From Fig. 3(c), the transfer function of the filter is
obtained as
'line. h
Ih
(s)
=
L,CJs2
1 + RJCfs
+ (RJ + R s ) C f s+ 1 = G(s)
R,
L,
(2)
where R,, L , are the line impedance (including the added
filter inductance), R f , Cf are the filter components, Zline, h
is the harmonic component of line, and Zh is the harmonic
component of rectifier input currents.
The first step in designing a filter is to identify the
position and amplitude of the harmonics to be attenuated.
If the PWM pattern of the converter is known, the amplitude and order of the harmonics injected can be obtained
(see Fig. 1). Also, the worst operating point in terms of
harmonics (modulation index) can be identified.
The second step is to choose a suitable break frequency
for the filter. This is done based on the following considerations.
(C)
Fig. 3. (a) Typical connection of the input filter. (b) Single-line diagram
for the fundamental frequency. (c) Single-line diagram for harmonic
frequencies.
at the fundamental frequency ( B ) , the filter components
can be obtained from the following set of equations,
which represents the gain of the filter at three different
frequencies:
(3)
(a) To achieve a desired attenuation of the dominant
harmonic, which is at a multiple of the switching frequency, f s w ;
(b) to avoid amplification of the residual harmonics in
the dead-band.
To satisfy the first constraint, the gain of the LC filter
for harmonic components should be obtained. To meet
the second specification, the required damping of the
filter must be designed considering the amplitudes of the
residual harmonics in the dead-band and the maximum
amplification allowed. For a given value of the attenuation
factor ( a ) , the maximum amplification of the residual
harmonics in the dead-band ( A ) and the gain of the filter
(4)
(5)
In order to provide a better representation of the above
procedure, (2) can be rewritten in logarithm as follows:
G(log)
= I,in,,,(log)
- IhOOg).
(6)
From (61, it is seen that the filter transfer function can be
obtained by subtraction in the logarithmic domain. The
design procedure is illustrated in Fig. 4. The frequency
ZARGARI
el
1575
al.: INPUT FILTER FOR PWM CURRENT-SOURCE RECTIFIERS
0
-401
0
-lu'
db 201
-
A
0
4
1Qh
Fig. 5. Flow chart of the filter-design procedure.
1
3(m
3ooh
1-
1.OKb
I
3.0W
frequency
IC
(C)
Fig. 4. (a) Frequency spectrum of the harmonic current source (in
decibels). (b) Desired frequency spectrum of the line current (in decibels). (c) Characteristics of the input filter (A and a are in decibels).
VC
rectifierinputcrrrrent
spectrum of the line current before filtering, Ih(log), is
shown in Fig. 4(a). Since the desired THD of the line
current is specified and since the rectifier switching pattern in known, the desired line current spectrum can be
calculated. This is shown in Fig. 4(b), I,ine.h(log).By subtracting Fig. 4(a) from Fig. 4(b), the values of A and a (in
decibels) are obtained. Knowing the gain of the filter at
three different frequencies ( A , B , and a ) , the filter
characteristics C(1og) are obtained Fig. 4(c).
The design of the filter using (2)-(5) is not complete if
the performance specifications are not met. Also, the
input filter distorts the converter input voltage and modifies the harmonics generated by the converter. Therefore,
this additional distortion should be considered in the
filter-design procedure. The final design is obtained
through an iterative process to meet the desired specifications. The flow chart of the filter design is given in Fig.
5. Since the filter involves the design of two components
( L , and C,), assigning two constraints (THD, and THD,,)
fixes the values of L , and C,. However, one can choose to
include other constraints, such as kilovoltampere or displacement angle minimization. A trade-off has to be made
and the overall specifications can be put together in a
filter optimization program to obtain the optimum filter
design. These factors and other constraints are discussed
later.
CONSIDERATIONS
IV. PRACTICAL
A. Displacement Power Factor
The phasor diagram of the PWM rectifier is shown in
Fig. 6, where it is assumed that the switching pattern is
Fig. 6
rcaificx input voltage
Phasor diagram of PWM rectifier, pattern synchronized with the
capacitor voltages.
synchronized and is in phase with the rectifier input ac
voltage (the capacitor voltage). The input power factor
(PF) is defined as
'<overall)
= 'Fdirtortwn)
* COS 0
(7)
where 0 is the input displacement angle.
Using a filter at the input terminals of the PWM
rectifier increases the input distortion power factor, but it
decreases the input displacement power factor (DPF =
cos 0). Therefore, it may decrease the overall input power
factor. Therefore, it is necessary to limit the displacement
angle ( 0 in Fig. 6). When damping is neglected, the angle
0 is given by the following:
where V, is the rectifier input voltage, I is the amplitude
of the rectifier input current, and X,, X , are the
impedances of the filter components.
The displacement angle 0 is dependent on the modulation index M , since I varies with M . Fig. 7 depicts the
dependency of 0 on the modulation index M with the
break frequency fb as a parameter. It is seen that decreasing M increases 0, hence, resulting in a reduction of the
input DPF. Figs. 8 and 9 show the variation of 0 as a
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30, NO. 6, NOVEMBER / DECEMBER 1994
1576
.
currents generated flow in the capacitor branch, the current and voltage of the capacitor branch are calculated as
-30
MP=
(11)
60
where I, is the hth harmonic component of the rectifier
input current, and Kc is the input ac phase voltage.
The kilovoltampere rating of the capacitor is defined as
0
KVAC
-20
1
XC
10 P
Fig. 9. Displacement angle as a function of filter capacitance X&
5.4 pu.)
=
function of X , and X , with modulation index M as a
parameter. In both of these figures, the filter break frequency is kept constant to obtain similar current harmonic attenuation. As the input inductance increases, the
phase displacement between input current and input voltage decreases and there is a value of X , that provides
unity input DPF. Therefore, the filter can be designed in
such a way that unity DPF at M = 1 is achieved and as M
decreases, the rectifier furnishes leading power factors
(Figs. 7 and 9).
= '~,rmyl/C.,rms
(12)
where Z,,,
is the root mean square value of the capacitor current, and V,,,,, is the root mean square value of
the capacitor voltage.
By equating the derivative of the above equation, the
value of X,, which minimizes KVAC, is obtained as
x, =
1e
h=2
v,,
(;)2
(13)
? , 4 / 4 .
h=-
However, the above value of X , does not guarantee that
the THD,] constraint is met. The variation of KVAC as a
function of X , is depicted in Fig. 11. It is seen that
KVAC does not vary rapidly with the change in C,.
Therefore, it is possible to obtain a value of Cf that
provides a low-kVA rating and achieves a near-unity
ZARGARI et al.: INPUT FILTER FOR PWM CURRENT-SOURCE RECTIFIERS
1577
P
0.0
0.4
M
1.0
€
0.4
Fig. 12. Effect of damping ( 6 ) on the circuit specifications.
Fig. 10. TKVA as a function of modulation index M.
0.9
WAC
0.5
0.0
XC
30.0 pu
Fig. 1 1 . Capacitive KVA as a function of capacitor impedance X,.
displacement power factor. This fact can be used to modify the design flow chart given in Fig. 5.
Fig. 13. Effect of parameter variations on the attenuation factor a.
important, especially if the filter is properly damped.
However, the attenuation factor ( a ) of the filter will
differ from the one predicted for the nominal values. The
change in the attenuation factor ( A a ) as a function of
AL or AC is depicted in Fig. 13.
C. Damping
E. Effect of the Filter on the Converter Pet$omzance
In order to avoid amplification of the residual harmonThe addition of an input filter to the PWM rectifier
ics in the dead-band region, proper damping of the LC distorts the input ac voltages at the rectifier input termifilter is required. Since the amplitude of the residual nals. The output dc voltage is given by
harmonics are expected to be less than one percent, an
v ( ) ( t )= s , , ( t ) E ( t ) + s,,(t>vb(t> + s,,(t>K(t) (14)
amplification of four to seven times can be tolerated. This
gives a criterion for choosing the parameter A in the set where V,(t) is output dc voltage and K,&) are the
of equations (21-6). Damping has three major effects on rectifier input voltages.
the performance of the system:
A distorted input voltage will change the output voltage
harmonics
and this effect must be considered in the
0 it reduces the system efficiency;
design of the output filter. Therefore, input voltage distorit increases the THD,,;
tion must be limited to a reasonable value in order for the
it improves the system response to input transients.
converter to perform as predicted at a particular operatThe latter is done by increaing the overall damping of ing point. Also, it is necessary to ensure capacitive characthe system, hence allowing for less overshoot during the teristics at the rectifier input terminals. These put additransients. Adding damping in the capacitor branch alone tional constraints on the value of the capacitor, which may
is preferred, since the current flowing in this branch is override the kVA consideration.
smaller than that in the inductor branch. The effect of
V. DESIGNEXAMPLE
damping on THD,. and efficiency are shown in Fig. 12.
An input filter is designed for a PWM rectifier. Two
D.Parameter Variation
types of designs are considered.
Variations in the values of the filter components result
in a shifting of the break frequency of the filter. This A. Design A
variation can be critical to the proper operation of a
The filter is designed to achieve the unity displacement
tuned filter. But for a low-pass filter, this effect is not power factor at M = 1. The filter break frequency is given
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 30, NO. 6, NOVEMBER / DECEMBER 1994
1578
TABLE I
FILTERSPECIFICAT~ONS
IN pu, ( M = 0.95, fsw
XL
xc
THD,
THD,
VdC
Idc
2
KVAC
Design (a)
Design (b)
0.17 pu
5.1 pu
0.34 pu
10.2 pu
<5%
19%
1.63 pu
1.48 pu
0.09 pu
-13.8'
0.62 pu
4%
10%
1.69 pu
1.54 pu
0.09 pu
1.10
0.68 pu
Vbue= 120 V, I,
=
I."
=
27 pu)
1
,
.
-L.U
I
J
(a)
70 A.
by the following:
-2.0
ul
(b)
Fig. 14. l)rpical current and voltage waveforms for design A. (a) Rectifier waveforms, (b) Line waveforms (in pu).
For a given attenuation factor ( U ) and rectifier switching
frequency f,, the values of L , and Cf are found using
(81, (1% and (16).
B. Design B
In this case, the cost (TKVA) of the filter is minimized
by minimizing the capacitive kVA, since TKVA is mainly
capacitive. The capacitor value is obtained from (13).
Then L , is calculated for the same break frequency as
design A.
The specifications of the two designs are given in Table
I. From the results, it can be concluded that while the two
designs offer comparable kilovoltampere ratings, design A
yields a higher power factor. Therefore, it is possible to
design a filter by first specifying the range of acceptable
kilovoltampere ratings, and hence, acceptable X , (from
Fig. 11). Then X , can be calculated to obtain unity DPF
at M = 1. These two constraints (limiting the kVA and
achieving unity DPF) can be incorporated in the flow
chart of Fig. 5 according to the designer's preference.
(a)
(b)
t2
-2
AAA
-
(C)
Fig. 15. Frequency spectra of input-output waveforms. (a) Rectifier
input current. (b) Input line current. (c) Output dc voltage.
VI. RESULTS
The simulation results for the filter of design A in
Section V are depicted in Figs. 14 and 15. The input line
current, input ac voltage, and rectifier input current are
shown in Fig. 14. The input displacement power factor is
unity at M = 1. The input line current has a high quality
with THD, less than 5 percent. Frequency spectra of the
line current before and after filtering are shown in Fig. 15.
The frequency spectrum of the line current clearly indicates the effect of the filter and the absence of amplification of the harmonics. Simulation results for design B are
shown in Fig. 16. The filter capacitor is minimized, but the
phase displacement between the input current and voltage
waveforms is increased by about 15".
VII. CONCLUSIONS
A systematic design procedure for a passive LC input
filter for current source PWM rectifiers is proposed. Basic
filtering requirements as well as practical problems such
as filter kilovoltampere rating, efficiency, damping, and
converter input power factor are discussed. It is shown
that with the synchronization scheme used, the input
power factor is affected by both the filter inductor and the
capacitor, while the cost of the filter is decided by the
filter capacitor. The design equations and the design procedure are confirmed by simulation results.
ZARGARl et al.: INPUT FILTER FOR PWM CURRENT-SOURCE RECTIFIERS
2.0
1579
“ i d R Zargari (s’89) received the B.S. degree
in electrical engineering from Tehran University, Tehran, Iran, in 1987 and the M.S. degree
in applied science from Concordia University,
Montreal, P.Q., Canada.
He is currently pursuing the Ph.D. degree at
Concordia University. His research interests include PWM rectifier topologies and control of
power electronic systems.
~
-2.0.
Gem Joos (M’78-SM789) received the M.Eng.
(b)
Fig. 16. Typical current and voltage waveforms for design B. (a) Rectifier waveforms. (b) Line waveforms (in pu).
REFERENCES
[l] E. W. Kimbark, Direct Current Transmission Volume 1. New York:
Wiley-Interscience, 1981, ch. 8, pp. 375-381.
[2] S. B. Dewan, R. S. Segworth, and P. P. Biringer, “Input filter design
with static power converters,” IEEE Trans. Industry, Gen. Applications, vol. IGA-6, pp. 378-383, July/Aug. 1970.
[3] D. A. Gonzales and J. C. McCall, “Design of filters to reduce
harmonic distortion in industrial power systems,” IEEE Industry
Applications Soc. Cor$ Rec., pp. 361-370, Oct. 1985.
[4] S. B. Dewan and E. B. Shahrodi, “Design of an input filter for the
six-pulse bridge rectifier,” IEEE Trans. Industry Applications, vol.
IA-21, pp. 1168-1175, Sep./Oct. 1985.
[5] P. D. Ziogas, Y. G Kang, and V. R. Stefanovic, “PWM control
techniques for rectifier filter minimization,” IEEE Trans. Industry
Applications, vol. IA-21, pp. 1206-1213, Sep./Oct. 1985.
[6] T. G. Habetler and D. M. Divan, “Rectifier/inverter reactive component minimizations,” IEEE Trans. Industry Applications, vol. 25,
pp. 307-315, Mar./Apr. 1989.
and Ph.D. degrees from McGill University,
Montreal, P.Q. Canada, in 1974 and 1987, respectively.
Since 1988, he has been with the Department
of Electrical and Computer Engineering, Concordia University, Montreal, P.Q., Canada,
where he is engaged in teaching and research in
the areas of power converters and electrical
drives. From 1975 to 1988, he was a Design
Engineer with Brown Boveri Canada, and from
1978 to 1988, a Professor-with the Ecole de Technologie Superieur,
Montreal.
Phoivos D. Zioga (SM91-F91) received the
B.Sc., M.S., and Ph.D. degrees from the University of Toronto, Toronto, Ont. Canada, in 1973,
1974, and 1978, respectively.
From 1978 to 1992, he was with the Department of Electrical and Computer Engineering,
Concordia University, Montreal, P.Q., Canada,
where he was engaged in teaching and research
in the area of power converters. He had also
participated as a consultant m several industrial
projects.
Dr. Ziogas died suddenly in September 1992.