A Comparative Study of Harmonic Filtering Strategies for a Shunt
Active Filter
P. S. Sensarma, Student Member, K. R. Padiyar, Senior Member, V. Ramanarayanan
Department of Electrical Engineering,
Indian Institute of Science,
Bangalore: 560 012, India.
Abdmct- In recent years, the issue of harmonic flltering has received considerable attention. Although
various strategies of harmonic filtering have been proposed, there h still some confurion regarding the prefkrable solution. In this paper, a comparative analyal of
the filtering strategies, for a pure shunt active filter, is
carried out. The analysis ia based on frequency-domain
techniques and includes the various non-idealities which
appear in a real system. All analytical arguments are
corroborated with experimental results. f i r exclusive
load compensation purposes, the preferred rolutlon is
indicated.
by a modified high-pass filter function [SI. The significant non-idealities are considered for system modeling
and the filtering characteristic of each method is derived using frequency-domain techniques. Analytical
predictions am experimentally verified on a 2 KW, sixpulse thyristor rectifier load. Harmonic filtering is done
by an IGBT-based STATCOM. Based on the filtering
characteristics and ocperimental results, relevant conclusions are drawn.
11. THECURRENT CONTROLLER
I. INTRODUCTION
Fig. 1shows the circuit schematic ofthe STATCOM.
In the deregulated power market, adherence to Power
Quality (PQ) standards has emerged as a figure-ofmerit for the competing power distribution utilities.
Among the various PQ problems, harmonic distortions
in the line currents and consequently in the voltage at
the Point of Common Coupling (PCC) greatly disturbs
the normal operation of connected loads.
aaditional harmonic filtering solutions using passive
series-tuned filters suffer from dependancy of filtering
characteristics on the component values of the tuned
circuit. Drift of component values also deteriorates
the filtering performance. Moreover, these are prone
to resonance interference with the network. In recent
years, availability of voltage source inverters with fast
switches and good controllability has spurred the development of active filters. The active filters are immune to network resonance effects. Possible active filter topologies include both series [l] and shunt conkurations [2], although unified approaches 131 have also
been reported. In [4], the application areas for pure
series and pure shunt active filters (PSAF) are clearly
demarcated. However, large and medium power industrial rectifiers have smoothing chokes either on the 8~
or dc side. The present focus is on harmonic filtering
for such types of non-linear loads, where using a PSAF
is meaningful.
In this paper, the different harmonic filtering strategies applicable to a PSAF are analyzed and compared.
In all the cases, the Synchronous Reference Rame
(SRF) method [5] is used for harmonic measurement
as the accuracy of this method is independent of dip
tortions in the PCC voltage. The SRF approach is a
two-step procedure which involves convertingthe three
phase currents to their rotating frame (d,q) equhlents. The harmonic components are then extracted
Each of the series inductors has an inductance L and an
internal resistance R. The ac side currents are sensed
through Hall effect sensors and fed back for control.
The current controller is designed on the basis of vector
decoupling of the d and q axis currents [I.The general
form of the control law for either of the axes is
vd/q
(1)
The current error is modulated by the function H i ( . )
which is given by
The controller is realized on a digital platform, which
is based on a DSP processor (TMSF240). As a consequence, a time delay, equal to one computation period,
appears in the current control loop. In addition, the
current sensors also introduce a delay in the feedback
path. For a signal f(t), delayed by a time interval 7 ,
0-7803-6401-5/00/$10.00 0 2000 IEEE
2509
- id/*).
= e d / q f wLiq/d i-Hi(ikq
the s-domain representation is given by
0 ....................
1
L{f(t - 7 ) ) = e - r r f ( s ) N ---T(s)
1+87
(3)
if the frequencies of interest are small in comparison
with 1 / ~ .F(a) ia the Laplace nansform of f(t). If
3
:,. .........
.. .
.. . .
...........;. ........
..) ... I . . ...:. .
. . .. . . . . . . .
j ........... ..i
......................
-10
g
. . . . . . . . . . .:..........i.....................
.
.
..
. . ..
:
i
.
4 .....................................................
.
.
.
.
. . i.....+
i.............1.......
. .:......
.. .
.
: . .
.
the time delay due to the STATCOM current Bensor is
Td and the computation interval is T,,then, using (3),
their input-output relationships in the sdomain are
Using this approximation, the current loop ie configured as shown in fig. 2. The block Gf, shown in fig. 2,
is the phnt t r a d e r function, which is e x p m d below.
10'
Fig. 3. Bode plot for current controller loop gain, Go,.
(5)
"i
-10
,
.
,
.
,.i. ...........................................
F
.
. -
......................
The closed-loop transfer function thus becomes,
:
I :
I 1
.
...
.
. ... ..
.
..
..
. . . . . . . . . . I :. . . . . . . . . . . . . . . . . .. . . . . .. . . . . .. .
-100
.
$ j
8 ;
8
-1 50
10'
-
.
I
O
Fig. 4,
:\I
...............................................................
:
:
1 :
.
.
,..
I
I :'
..
..
.
-16'
For the system data shown in Table I, the bode plot for
the loop transfix function is shown in fig. 3. Since the
phase margin is about Me,the closed-loop current control system, with all non-idealities considered, is stable.
Fig. 4 shows the corresponding plots for the closed
loop system. The vertical dashed line in fig. 4 is drawn
for easy reference, corresponding to a frequency of 300
1'
0
Frequsny ( r r d e c )
:
.
..
.
.
.
..
Flequency ( d - 4
..
10
'
Bode plot for current ccintroller cloeed-loop transfer
function, Gci.
Hz. The phase lag at 300 Hz (1885rad/s) is 20°. The
current control loop forms the innermost loop in the
control hierarchy and is identical for all compensation
strategies which are discussed in this paper.
III. COMPENSATION
STRATEGIES
Of the various strategies for harmonic compensation
that have been reported in litmature [8][9][10],the ones
applicable for a PSAF are mentioned below. The circuit schematic of a PSAF Is &own in fig. 5. All
d i k d o n s in this section refer to this schematic and
the etrategies use terminal qiiantities, available at the
I
Fig. 2. Current control loop with internal del-
ineluded.
TABLE 1
CIRCUXT
AND CONTROL
PARAMETERS
Inverter aeries inductance
Inverter series resistance
Inverter sen-espath time constant
Inverter Bwitching frequency
Current emmr delay
Unit sample delw
High Pase Filter time conetant
Current Control loop
Dc loop gain
PI controller time constant
Rf
9.67 mH
0.206R
fr
36.1 ma
8 KHs
L
q
'&.TA
Tv
TF
K
Tc
2 5 0 ~
1% a
6.3 me
6963
18.1 ms
Fig. 6. STATCOM in the system (current directions shown).
2510
qG}‘““7i-
harmonic components of the PCC voltage by e h and
positive currente to be taken BB shown in fig. 5, the
describing equation for this strategy is
ContFOllcr
Entraction
iz(t) = Kvh
Fig. 6. Method I: Compenaation schematic.
eh(t).
(10)
This method was shown [lo) to be suitable for reducing the overall voltage distortion in an interconnected
system. However, if the active filter is used for load
compensation only, this scheme can lead to overcompensation. This situation arises,for example, when the
PCC voltage has harmonic distortion but the load is
lineat or it is wvitched off.For this reason, this method
is not investigatedfurther.
PCC.
A. Method I: h a d Current Sensing
This method is basically a feedforward scheme. It
involves measurement of the load current and subsequent extraction of ita harmonic content using a high
pass filter scheme. The harmonic components, so extracted, are adjusted for polarity and used as.reference
commands for the current controller. This is explained
Iv.ANALYSISOF FILTERING SCHEMES
A. Load Current Sensing
with the help of fig. 6.
Denoting the harmonic mmponenta of the load current by ilh and positive currents to be taken as shown
in 6g. 5, the describing equation for this strategy is
iT(t) = i l h ( t ) .
*
Denoting the delay in the load current sensor by a
firstorder hg,with time constant Tal, the compensation achematic is shown in fig. 9. GF(B)is the transfer
function for the high pass filter which is expressed as
(8)
B. Method 11: Source Current Sensing
In this strategy, the source current is measured and
its harmonic component extracted. This is scaled by
a suitable controller, usually of the proportional type.
The output of the proportional controller is provided 89
a reference to the current controller. This is schemati-
Also,
i,(t) = i&)
- ir(t).
(12)
cally represented in fig. 7.
Fig. 7. Method 11: Compensation schematic.
The harmonic extraction block u
s
e
s a similar high pass
scheme as in Method I. Denoting the harmonic components of the source current by &h and poaitive currents
to be taken 69 shown in fig. 5, the describing equation
for this strategy is
iE(t) = ‘Kih
e
i,h(t).
(9)
C.Method 111: PCC Voltage Sensing
This method requires measurement of the harmonic
component of the PCC voltage, e(t). The harmonic
component is then used to generate the current reference, after pawing it through a proportional controller.
Schematically, it is represented in fig. 8. Denoting the
the schematic can be reduced to that shown in fig. 10.
It is seen that the control structure comprises two flow
paths in parallel. Since both the individual paths consist of linear eystems, stability of these individual systems guarantee overall stability. One of the paths has
a gain of -1 and is therefore stable. Stability of HI(s),
therefore, ensures total system stability. &om the discussion of the previous section, it is obvious that the
closed-loop poles of the current control system lie in
the left-half of the s-plane. These are also the poles of
Hi(#), along with a left-half pole at s = -1/Tdl. Thus,
all the poles of H&) lie in the left-half of the s-plane.
So, it represents a stable system and the compensation
5
1 +rT&
‘c
+
Fig. 9. Method I. Total system schematic.
Fig. 10. Method I. Equivalent eystem schematic.
Fig. 8. Metbod 111: Compensation schematic.
251 1
Fig. 12. Method 1. Modified system schematic for finite load
impedance.
Fig. 11. Method I: filtering characteristics.
function for the entire
scheme is also stable. " s f e r
scheme is therefore,
Gl(8)=
H lmt
i
p = -1
-IH[(8).
(4
Fig. 11 shows the Bode plots for G[(a). This shows
the filtering characteristics of Method I. It is seen that
there is about 2.5 dB attenuation given to the 300 Hz
component.
The above analysis is applicable t o situations where
the load can be represented by a current source, with
infinite internal impedance. Since this is not practically
available, a portion of the STATCOM current flows into
the load circuit. In this context, a quantity Z h , called
"sharing factor" is introduced.
xh
<
1.
\
3Y8000 -8000
-6000 -4ooo
Real suds
-2dw
0
am0
Fig. 13. Roots of the @stem, Glf(.9), with variation in sharing
factor from 0.1 to 0.9.
The closed-loop poles are plotted in fig. 13, for a
variation of s h from 0.1 to 0.9. S i c e there are no
right-half roots, the system is stable. However,this
conclusion is valid for equal phase angles of the murce
and load impedances, which ia a special case.
where,
Zuh is the internal impedance provided by the murce
network to a harmonic component of h-th order, and
Z[h is the internal impedance provided by the load circuit to the same harmonic component.
The sharing factor indicates the Norton's current in the
source branch, due t o the STATCOM, as a fraction of
i,.It is also clear that in a practical situation,
0 <
+++
(14)
B. Source Current Sensing
The control schematic, with all sensor and computation delays included, is shown in fig. 14. Tdl is the
time constant in the source aurent sensor model. The
system involves a feedback element, as is evident from
the control schematic. The loop gain is given by
(16)
With this consideration, Kirchoff's Law at the PCC
node gives
i, = x h i c i [ O
(17)
where,
i ~ ois the current in the load branch, without STATCOM operation.
The modified schematic is shown in fig. 12. Stability
of the total system is ensured if the positive feedback
system, shown within dotted l i e s in fig. 12, is stable.
The dosed-loop poles of the positive feedback a
m
are obtained below t o investigate stability.
The closed loop transfer function ia
-
Robustness of this system is considered for two diflerent
C89e5.
Case 11-A:K j h = 0.1.
Fig. 15 shows the bode plots of Go,for this w e . Fig.
' ' ~ ~ z t
I+
q,
Fig. 14. Method 11. System schematic.
2512
I1 is unable to provide any filtering &e&.
Thus, harmonic filteringof Method 1I is poorer than
that of Method I.
V. DELAYCOMPENSATION
SC~EME~
Id
10‘
Frequ-Y
Based on the analysis of the previous section, the
load current Bensing method ia adopted here. The
problem in achieving satisfactory compensation is the
phase delay introduced by the cascade combination
(Ht)of the current control loop, high-pass filter and
the load current sensor. Two separate approaches can
be adopted for delay compensation and these are de
acribed and analyzed below.
I 0‘
1-(
A . Method I-A: The ‘Dynamic” Compensation Apm c h
Fig. 15. Case IX-A. Loop gain.
This method of delay compensation can be realized
with both analog and digital controller hardware. Here,
a phaselead filter is provided after the high-psss filter,
as shown in fig. 18. The phaselead filter dynamics is
described by the following t r d e r function.
where,
U,,,is the central frequency where maximum phase lead
v is obtained, and
rd
lo‘
a is the “spread factor” which decides the value of v.
The bode plots of GPLF(S)
are shown in fig. 19 (a)
and (b). F’rom the magnitude plot in fig. 19 (a), it is
Frequency (radlsec)
Fig. 16. Case XI-A. Filtering eharacteristica.
seen that the filter haa high pass characteristics. This
may not be a signiscant problem because of the -40
dB roll-off in the closed-loop transfer function of the
current controller. Since the gain always exceeds unity,
the filter output has to be appropriately scaled down
to generate the current controller reference command.
The phase plot shown in fig. 19 (b) has a sharp peak
at the central frequency.
Fig. 20 shows the bode plot of Ht. Comparison of
the two phase plots reveal that an exact cancellation
of phase delay for an extended frequency range is not
possible. Under this circumstance, the b a t option is to
attempt cancellation of the dominant harmonic component. For a six-pulse rectifier, which is used here,
the dominant harmonics are the 5 t h and 7-th, both
of which appear as 6 t h harmonic components in the
aynchronous1y rotating reference frame.
nom Sg. 20, phase delay given to the 300 Hz component is about 42O. From fig. 19 (b), this can be
cancelled by choosing a = 4.
16 shows the filtering characteristics for this method,
which is the bode plot of the correspondingclosed-loop
system. This system is stable, as the gain plot does
not crws the 0 dB lime. However, the magnitude plot
of 6g. 16 reveals minimal harmonic filtering
Case II-B: Kjh = 8.
Fig. 17 shows the bode plots of Go, for this case. The
magnitude plot of fig. 17 shows that 0 dB ciosaover
occurs at the mavimum point and the phase margin is
about zero. Thus, a PSAF realimtion based on Method
C
3
1
O
-=
-100
U
Fig. 18. Dynamic delaJr compensation approach.
2513
-1.
J
1
I.
0
t
t
......................
...................
....................
......................
.......................
........
.
..:....... ..........
.
.
......................
a
-
.. .. .. . .. . .. . .. . ...
.. . . . .. . . . . .
.
:
. .
... ....
. .
.
.... .... .... ....
. . . .
..
....
. .
........
.......
..............
......
..... .................,.!.
.. . . . .
... . ... . ...
..
...
. . . . . .. . .
.
10'
Frequency (nldlsac)
I
-20'
ld
10'
10'
Fig. 20. Bode pl'ot of H1.
Freqwncy(ad'-el
Fig. 19. Phase lead filter characteristice for 1
magnitude (b) phase.
5
(I
5.10. (a)
.
.
.: . <
.
...
.
.... ...
...
.
-10 ................... .l.i.................................
.
.
1 :
.. . . . .
1 :
0 . . . . . . . . . . . . . . I ..............
Fig. 21 (a) and (b) show the bode plots for the combined system, as shown in fig. 18. It is seen that the
phase shift is zero at the central frequency (300 Ha)
only. Loop gain at the central frequency is approximately 2.3, which has to be scaled down to unity.
B. Method I-B: The 'Steady-state" Compensation Approach
Fig. 22 shows the control schematic for this method.
The phase-lead filter is replaced by a reference genere
tion block, other components remain identical. This
method can be applied only where the controller is
realized on a digital processor platform. Thia allows
for data sampling and storage. The approach is based
on the assumption that the load harmonic current is
strictly periodic.
Consequently,
+
- +
h [ ( k &)Tal= iih[kT, TP nT8]
(21)
where,
n is a positive integer.
This implies that future values of the current can be
predicted from the information obtained from the previous cycles.
To determine the value of n, an audit of the various
phase shifts, at 300 Hz,are given below.
Current Controller
High Pass Filter
: -20"
: 5"
A phase lag of 1S0 at 300 Ha corresponds to a time lag
of 139 ps. Delay introduced by the current sensor can
be considered to be a time-shift, T a . Therefore the
total time advance needed is
T+ = T a + 1 3 9 p
= 3 8 9 ~
For a sampling interval of 125 ps, n is rounded &to 3.
In the following section, experimental results for
Methods I-A, I-B and Method I1 are provided. The
2514
I :
I
I :
.
.
.....
.
.
. .
.. .
..
:.
. . ....i ......
. .
(a)
Fig. 21. Method I-A: Bode plots for closed-loop transfer function
i&)/il(a)
(a)magnitude (b) pbase.
Rdcnnu;
Fig. 22. Steady-state delaJr compensation approach.
current harmonic spectra for each of these casw are
also plotted for comparative appraisal.
VI. EXPERIMENTAL
RESULTS
The experimental results ishow the source current
waveforms for the different control strategiesmentioned
before. Fig. 23 shows the sou1:ce current in the absence
of compensation. The cur,reni; waveform is typical of a
six-pulse rectifier in continuous conduction. The dc
side of the rectifier feeds a resistive load, through a
smoothing choke.
Fig. 24 show the harmctnic spectra of the three
line currents. The first plot on each row shows the
fundamental and the second shows the harmonic components. All graphs are plotted against the hannonic
number and the y-axis is calibrated as a percentage of
the fundamental component,, which remains constant
throughout the experiment. It is seen that the dominant harmonics are the 5 t h (28%, 26%, 25%).,7-th
VII. CONCLUSIONS
(5%, 4%, 4.5%) a d 11-th (8%, 7%, 6.5%) harmonic
components. A slight unbalance in the load currents
can be observed.
F
i
g
.25 shows the source current with Method I-A.
The waveshape shows significantimprovement. Fig. 26
shows the corresponding harmonic spectra. The 5-th
harmonic component is attenuated to 4% of the fund&
mental, but there is no significant improvement in the
11-th harmonic, which remains at 7 %.
Fig. 27 shows the source currents obtained with
Method I-B. Their harmonic spectra are shown in fig.
28. No individual harmonic exceeds 3% of the fun&
mental.
Fig. 29 shows the source current for the three phasea,
obtained with Method 11. The high-frequency compe
nents in the current waveform is to be noted. Fig.
30 shows the harmonic spectra. The 5 t h harmonic
is brought to below 7% in all the phases. But the
source current has a very large 20-th harmonic component which grows in magnitude with increasing Kfi.
This validates the theoretical predictions, derived from
frequency-domain analysis.
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filtering characteristics over the source current sen&
ing method @I), which has a possibility of instability. The PCC voltage sensing method (111) may not
be very suitable for exclusive load compensation purposes. Two delay compensation schemes were analyzed
in connection with Method I. Both the methods show
identical filtering performance at the dominant harmonic frequency. However the "steady-state" method
(EB) was seen to a t e r an extended range of harmonics in comparison with the udynamic" method (I-A),
Reaults from frequency-domain analysis were experimentally validated on a 2 K W thyristor rectifier and
a STATCOM of appropriate rating. Therefore, it is
concluded that method I-B is the preferred harmonic
filtering strategy, if transient performance is not a major concern.
o.m
.
....
......
.
.
........
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-om
and in the absence of any delay compensation, the
load current sensing method (I) has marginally better
.
0.m 0.01
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4.z~
In this paper, a comparative study of the exist-
ing harmonic sltering schemes for a PSAF was performed. For identical current controller parameters
4w
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Fig. 26. Source currents with compensation (Method I-A) (a)
b o @) i a b (c)
Fig. 23. Source currents without compensation (a) ia0
(b) i.6
(c) i,c.
.
..
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..
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....... ...... ........ . .....
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no
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E
DD
HmnmbNmhr
=
Fig. 26*,Harmonic spectra of source currents with compensation
(Method E A ) (a)i.* (b) 6.1 (C) ire.
Fig. 24. Harmonic spectra of source currents without compeneation (a) ia0
(b) idb (c) Le.
25 15
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Fig. 27.
Source currents with compenaation (Method I-B) (a)
Fig. 29. Source currents with compensation (Method 11) (a) i,,
(b) i.b (c) is=.
i.a (b) i,b (c) iac.
,m. .....:........_. .:
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P
RI
.
w
1
.
~
1
..
....... ... ..... .. .....
.
.
.
H.mol*Nunk
Fig. 28. Harmonic spectra of Bource currents with compensation
(Method EB) (a) i,*(b) i,b (c) iaC.
ACKNOWLEDGMENT
Fig. 30. Harmonic spectra of source currents with compensation
(Method II).(a)
(b) ish (c) is,.
[4]
The authors acknowledge the support of Mr.
Chowridass, Mr. RamachGdra, Mr. Sadanand and
Mr. Paul,workshop s t d l Department of Electrical Engineering, IISc, during fabrication of the experimental
hardware.
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IEEE Industry Applications Maigoaine, Septemberf October,
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[5]
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