A Series Active Power Filter Based on a Sinusoidal Current-Controlled Voltage-Source Inverter.pdf
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997
A Series Active Power Filter Based on a Sinusoidal
Current-Controlled Voltage-Source Inverter
Juan W. Dixon,
Senior Member, IEEE,
Gustavo Venegas, and Luis A. Moran,
Senior Member, IEEE
reasons, different solutions are being proposed to improve the
practical utilization of active lters. One of them is the use of
a combined system of shunt passive lters and series active
lters. This solution allows one to design the active lter for
only a fraction of the total load power, reducing costs and
increasing overall system efciency [4].
Series active lters work as isolators, instead of generators
of harmonics and, hence, they use different control strategies.
Until now, series active lters working as controllable voltage
sources have been proposed [5]. With this approach, the
evaluation of the reference voltage for the series lter is
required. This is normally quite complicated, because the
reference voltage is basically composed by harmonics, and
it then has to be evaluated through precise measurements of
voltages and/or current waveforms. Another way to get the
reference voltage for the series lter is through the “ –
theory” [6]. However, this solution has the drawback of
requiring a very complicated control circuit (several analog
multipliers, dividers, and operational ampliers).
To simplify the control strategy for series active lters, a
different approach is presented in this paper, i.e., the series
lter is controlled as a
sinusoidal current source,
instead of a
harmonic voltage source. This approach presents the following
advantages.
1) The control system is simpler, because only a sinusoidal
waveform has to be generated.
2) This sinusoidal waveform to control the current can be
generated in phase with the main supply, allowing unity
power-factor operation.
3) It controls the voltage at the load node, allowing excel-
lent regulation characteristics.
Abstract—
A series active power lter working as a sinusoidal
current source, in phase with the mains voltage, has been devel-
oped and tested. The amplitude of the fundamental current in
the series lter is controlled through the error signal generated
between the load voltage and a preestablished reference. The
control allows an effective correction of power factor, harmonic
distortion, and load voltage regulation. Compared with previous
methods of control developed for series active lters, this method
is simpler to implement, because it is only required to generate a
sinusoidal current, in phase with the mains voltage, the amplitude
of which is controlled through the error in the load voltage. The
proposed system has been studied analytically and tested using
computer simulations and experiments. In the experiments, it
has been veried that the lter keeps the line current almost
sinusoidal and in phase with the line voltage supply. It also
responds very fast under sudden changes in the load conditions,
reaching its steady state in about two cycles of the fundamental.
Index Terms—
Active lters, current control, power electronics,
power lters, pulsewidth-modulated power converters.
I. I
NTRODUCTION
H
ARMONIC contamination, due to the increment of non-
linear loads, such as large thyristor power converters,
rectiers, and arc furnaces, has become a serious problem
in power systems. These problems are partially solved with
the help of
LC
passive lters. However, this kind of lter
cannot solve random variations in the load current waveform.
They also can produce series and parallel resonance with
source impedance. To solve these problems, shunt active
power lters have been developed [1], [2], which are widely
investigated today. These lters work as current sources,
connected in parallel with the nonlinear load, generating the
harmonic currents the load requires. In this form, the mains
only need to supply the fundamental, avoiding contamination
problems along the transmission lines. With an appropriated
control strategy, it is also possible to correct power factor and
unbalanced loads [3] .
However, the cost of shunt active lters is high, and they
are difcult to implement in large scale. Additionally, they also
present lower efciency than shunt passive lters. For these
II. G
ENERAL
D
ESCRIPTION OF THE
S
YSTEM
The circuits of Fig. 1(a) and (b) show the block diagram and
the main components, respectively, of the proposed system: the
shunt passive lter, the series active lter, the current trans-
formers (CT’s), a low-power pulsewidth modulation (PWM)
converter, and the control block to generate the
sinusoidal
template
for the series active lter. The shunt passive
lter, connected in parallel with the load, is tuned to eliminate
the fth and seventh harmonics and presents a low-impedance
path for the other load current harmonics. It also helps to
partially correct the power factor. The series active lter,
working as a sinusoidal current source in phase with the line
voltage supply , keeps “unity power factor,” and presents a
very high impedance for current harmonics. The CT’s allow
Manuscript received April 15, 1996; revised April 7, 1997. This work was
supported by Conicyt under Proyecto Fondecyt 1940997 and 1960572.
J. W. Dixon is with the Department of Electrical Engineering, Ponticia
Universidad Catolica de Chile, Santiago, Chile (e-mail: jdixon@ing.puc.cl).
G. Venegas was with the Department of Electrical Engineering, Ponticia
Universidad Catolica de Chile, Santiago, Chile. He is now with Pangue S.A.,
Santiago, Chile.
L. A. Moran is with the Department of Electrical Engineering, Universidad
de Concepcion, Concepcion, Chile (e-mail: lmoran@renoir.die.udec.cl).
Publisher Item Identier S 0278-0046(97)06534-9.
0278–0046/97$10.00
ã
1997 IEEE
DIXON
et al.
: SERIES ACTIVE POWER FILTER BASED ON VOLTAGE-SOURCE INVERTER
613
(a)
Fig. 2.
Circle diagram of the series lter.
Assuming, for example, a series lter able to generate a
voltage , the magnitude of which is 50% of the funda-
mental amplitude , the maximum phase shift should be
approximately , which poses a limit in the ability to
maintain unity power factor. The larger the value of , the
larger the rating of the series active lter (kvar). From Fig. 2:
(2)
Replacing (1) into (2)
(b)
Fig. 1. Main components of the series active lter. (a) Block diagram. (b)
Components diagram.
(3)
for the isolation of the series lter from the mains and the
matching of the voltage and current rating of the lter with
that of the power system. In Fig. 1, represents the
load
current,
, the current passing through the
shunt passive lter,
and the
source current
. The source current is forced to
be sinusoidal because of the PWM of the series active lter,
which is controlled by . The
sinusoidal waveform
of
comes from the line voltage , which is ltered and kept in
phase with the help of the PLL block [Fig. 1(b)].
By keeping the load voltage constant, and with the
same magnitude of the nominal line voltage , a “zero-
regulation” characteristic at the load node is obtained. This
is accomplished by controlling the magnitude of through
the error signal between the load voltage and a reference
voltage . This error signal goes through a PI controller,
represented by the block
Then, (2) corresponds to the total reactive power required by
the load to keep unity-power-factor operation from the mains
point of view.
It can be observed from the circle diagram of Fig. 2 that, in
order to obtain unity power factor at the line terminals ( ), a
little amount of active power has to go through the series lter.
However, most of this active power is returned to the system
through the low-power PWM converter shown in Fig. 1. The
amount of active power that has to go through the series active
lter, according to Fig. 2, is given by
(4)
.
is adjusted to be equal
can also be obtained through
to the nominal line voltage .
The two aforementioned characteristics of operation (“unity
power factor” and “zero regulation”), produce an automatic
phase shift between
(5)
and
, without changing their mag-
nitudes.
Equations
(4) and (5) are equivalent.
They are related
through (1) and the trigonometric identity
.
For cost considerations, it is important to keep as
low as possible. Otherwise, the power ratings of both the series
lter and the small PWM rectier shown in Fig. 1 become
large. This means that the capability to compensate power
factor of the series lter has to be restricted. The theoretical
kilovoltampere ratings of the series lter and the low-power
A. Power-Factor Compensation
To have an adequate power-factor compensation in the
power system, the series active lter must be able to generate
a voltage the magnitude of which is calculated through
the circle diagram of Fig. 2 according to
(1)
614
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997
PWM converter can be related to the kilovoltampere rating
of the load ( ). The kilovoltampere rating of the series
lter, from Fig. 2 or from (2) and (4), is
voltage drop is related with the
th harmonic impedance of
the lter and the
th harmonic current:
(11)
Assuming a
six-pulse thyristor rectier load,
with a shunt
passive lter like the one shown in Fig. 1, the th harmonic
current can be evaluated in terms of the fundamental
(6)
:
As
it yields
with
(12)
Replacing (10)–(12) into (9) yields
(7)
(13)
On the other hand, the relative kilovoltampere rating of the
low-power PWM converter comes from (5) and is
The impedance , will depend on the parameters of the
lter ( ), and is very small for the fth and seventh
harmonics. On the other hand, takes a constant value for
high-order harmonics (high-pass lter) and, for this reason,
when is large, the terms in the summation in (13)
can be neglected ( ). With these assumptions, the term
represented by the square root in (13), can be as small as
3%–10% of the load base impedance. Then,
(8)
If we again consider , it yields %of
that of the power load. It can be noticed that when no power-
factor compensation is required, both the series lter and the
small PWM converter become theoretically null. However,
the small converter has to supply the power losses of the
series lter (which are very small), and the series lter needs
to compensate the harmonic reactive power. The low-power
PWM converter is a six-pack insulated-gate-bipolar-transistor
(IGBT) module, inserted into the box of the series lter.
(14)
The small size of series lters, compared with the shunt active
lters (30%–60% of ), is one of the main advantages
of this kind of solution. The small size of series lters also
helps to keep the power losses at low values [4].
C. Power Losses
The power losses of the series active lter depend on the
inverter design. In this paper, the series lter was implemented
using a three-phase PWM modulator, based on IGBT switches.
With this type of power switches, efciencies over 96% are
easily reached. Then, 4% power losses can be considered for
the series lter, based on its nominal kilovoltampere. Now,
if the lter works only for harmonic compensation, its rating
power will be between 3%–10% of the nominal load rating
(14). Then, power losses of the series lter represent only
0.12%–0.4% (less than 1%) of that of the kilovoltampere
rating of the load [4]. However, if the series lter is also
designed for power-factor compensation (
or
B. Harmonic Compensation
The
kvar
requirements of the series lter for harmonic
compensation are given by
(9)
where is the rms harmonic voltage at the series lter
terminals and is the fundamental current passing through
the lter. As the series lter is a fundamental current source,
harmonic currents through this lter do not exist.
The harmonic compensation is achieved by blocking the
harmonic currents from the load to the mains. As the series
lter works as a fundamental sinusoidal current source, it
automatically generates a harmonic voltage equal to the
harmonic voltage drop at the shunt passive lter. In this
way, harmonics cannot go through the mains. Then, the rms
value of can be evaluated through the harmonic voltage
drop at the shunt passive lter:
), the relative power losses can be
as high as 2%.
III.
S
TABILITY
A
NALYSIS
A. Harmonic Analysis
The following assumptions will be made to analyze the
stability due to harmonics.
1) The source voltage is a pure fundamental waveform.
2) The load is represented by a harmonic current source,
.
(10)
where represents the rms value of the voltage drop pro-
duced by the
th harmonic in the shunt passive lter. This
DIXON
et al.
: SERIES ACTIVE POWER FILTER BASED ON VOLTAGE-SOURCE INVERTER
615
(a)
(a)
(b)
Fig. 4. Control loops of the series active lter. (a) For the line current
I
S
.
(b) For the load voltage
V
F
.
(b)
Then, the larger the value of (17), the better the series lter.
The relation between the harmonics going through the line
supply ( ) and the harmonics generated by the load ( ) can
be obtained with the help of Fig. 3(b). From this gure, the
transfer function
Fig. 3.
(a) Single-phase equivalent circuit. (b) Harmonics equivalent circuit.
With these assumptions, the equivalent harmonic circuit for
the system is shown in Fig. 3(b), where the series active lter
is represented by the impedance . Ideally, this impedance
should have an innite value to all harmonics, because the
lter is assumed to work as a sinusoidal, fundamental current
source. However, as the lter is made with real components
with limited gains, that is not true and, hence, it is required
to know the amount of impedance the series lter is able to
generate, to attenuate the harmonics going from the load to
the source.
According to Fig. 3(a), the voltage
is
(18)
where
and
generated by the
series lter is given by
Modeling
in a simplied form, just as a proportional
gain “
,” and replacing “
” from (17) into (18), yields
(15)
(19)
where
source current (controlled by the series l-
ter);
current sensor gain;
sinusoidal template, in phase with the mains
supply;
transfer function of series active lter and
CT’s;
where
proportional-integral gain
(PI controller).
The sinusoidal template is controlled to keep only the
in-phase fundamental value of the total load current. Then
, and the harmonic voltage
Applying the Routh–Hurwitz criterion for stability, the
system is stable when all the coefcients of the characteristic
equation have the same sign, or . As this condition
is always satised, the system is stable for the harmonic
components.
can be evaluated
from (15), yielding
(16)
B. Fundamental Analysis
The control implemented for the fundamental has two
control loops, which have to accomplish the following two
well-dened objectives.
1) The line current has to follow the reference, which has
been designed to be a pure sinusoidal (fundamental),
From (16), the impedance the lter is able to generate
operating as a current source is given by
(17)
616
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 44, NO. 5, OCTOBER 1997
(a)
(b)
(c)
Fig. 5. Simulation results for a smooth change in the ring angle
(50 Hz). (a) Line voltage
V
L
[100 V/div] (220 V phase to neutral). (b) Series lter
voltage
V
LF
[100 V/div]. (c) Active power through the small PWM rectier.
in phase with the mains voltage (unity-power-factor
operation) and with variable amplitude.
2) The module of the load voltage
Now, from (21) and (22),
(23)
has to keep the
nominal value of the mains voltage
(zero regulation
and from Fig. 4(b)
operation).
These two control loops are now described.
1) Line Current Control:
The control loop implemented
for the line current is shown in Fig. 4(a). From this gure, the
following equations are obtained:
(24)
Equating (23) and (24) nally yields
(25)
Finally, the equations for the complete control loop are ob-
tained:
(20)
(26)
It can be noticed from (26) that the control loop is strongly
dependent on the load impedance, because it is included in
the term . Then, both the loops have to consider the load
effect in the design of the series active lter.
with
(21)
IV. S
IMULATIONS AND
E
XPERIMENTAL
R
ESULTS
For the simulations and experiments, a shunt passive lter
with a quality factor was used. The high-pass lter
(HPF) shown in Fig. 1 was not connected. That means the
passive lter being used presents a higher impedance to
harmonics than normal industrial lters. The source inductance
1 mH. In simulations, 220-V phase-to-neutral line
supply was used, and the load was a six-pulse thyristor
rectier. In experiments, only 70-V phase-to-neutral supply
was used, and the load was a diode rectier, instead of thyristor
converter. The dc-link voltage at the experimental series lter
was set at 300-V dc (max). As the turns ratio of the TC’s
was 3.4, the maximum generated at the line side was
around 40-V rms. For this reason, only 70 V were used in the
power supply for the experiments. Otherwise, power-factor
compensation could not be shown. Table I shows the values
of
In these equations, is the total equivalent impedance
of the load, which is comprised of the nonlinear load and the
shunt passive lter. Under steady state ( ) and,
hence, . This means that the current follows
the reference template. However, it is important to note that
(21) is strongly dependent on the load, which is included in
the term .
2) Load Voltage Control :
The control loop for the load
voltage is shown in Fig. 4(b), where is the gain of
the voltage sensor and (S) is a PI controller. To get the
complete transfer function of the control loop, it is necessary
to obtain the transfer function of
. Let
(22)
and
used in the shunt passive lter.
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