IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 2005
1281
Design and Control of an LCL-Filter-Based
Three-Phase Active Rectifier
Marco Liserre, Member, IEEE, Frede Blaabjerg, Fellow, IEEE, and Steffan Hansen, Member, IEEE
Abstract—This paper proposes a step-by-step procedure for
designing the LCL filter of a front-end three-phase active rectifier.
The primary goal is to reduce the switching frequency ripple at a
reasonable cost, while at the same time achieving a high-performance front-end rectifier (as characterized by a rapid dynamic
response and good stability margin). An example LCL filter design
is reported and a filter has been built and tested using the values
obtained from this design. The experimental results demonstrate
the performance of the design procedure both for the LCL filter
and for the rectifier controller. The system is stable and the grid
current harmonic content is low both in the low- and high-frequency ranges. Moreover, the good agreement that was obtained
between simulation and experimental results validates the proposed approach. Hence, the design procedure and the simulation
model provide a powerful tool to design an LCL-filter-based active
rectifier while avoiding trial-and-error procedures that can result
in having to build several filter prototypes.
Index Terms—Cascade control, LCL filter, rectifier, stability,
voltage-source converter (VSC).
I. INTRODUCTION
T
HE voltage-source converter (VSC) may be used as an
active rectifier, with the advantages of its potential for
full control of both dc-link voltage and power factor, and its
ability to work in rectifying and regenerating mode [1]. Moreover, the use of pulsewdith modulation (PWM) in conjunction
with closed-loop current control allows a sinusoidal input
current to be achieved with a total harmonic distortion (THD)
below 5%, even if grid voltage or current sensors are not used
[2]–[5]. However, typical power device switching frequencies
of between 2–15 kHz can cause high-order harmonics that can
disturb other sensitive loads/equipment on the grid, and can
also produce losses [6].
To reduce the current harmonics around the switching frequency a high value of input inductance should be used. However, for applications above several kilowatts, it becomes quite
expensive to realize higher value filter reactors. Moreover, the
system dynamic response may become poorer.
Paper IPCSD-05-045, presented at the 2001 Industry Applications Society
Annual Meeting, Chicago, IL, September 30–October 5, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Power Converter Committee of the IEEE Industry Applications Society.
Manuscript submitted for review July 1, 2003 and released for publication June
2, 2005.
M. Liserre is with the Dipartimento di Elettrotecnica ed Elettronica, Politecnico di Bari, 70125 Bari, Italy (e-mail: liserre@ieee.org; liserre@poliba.it).
F. Blaabjerg is with the Institute of Energy Technology, Aalborg University,
DK-9220 Aalborg East, Denmark (e-mail: fbl@iet.auc.dk).
S. Hansen is with Danfoss Drives A/S, DK-6300 Graasten, Denmark (e-mail:
s_hansen@danfoss.com).
Digital Object Identifier 10.1109/TIA.2005.853373
An alternative and attractive solution to this problem is to use
an LCL filter as shown in Fig. 1. With this solution, optimum
results can be obtained in the range of power levels up to hundreds of kilovoltamperes, still using quite small values of inductors and capacitors [6], [7].
A further issue for a VSC is high-frequency electromagnetic
interference (EMI) (differential mode and common mode) [8],
which needs specific filters (passive [9], [10] or active [11])
in frequency ranges above 150 kHz and rated at lower power
levels. Of course, an LCL filter that is effective in the reduction of switching frequency harmonics may also be effective
for differential mode EMI if the filter inductors are built using
chokes that can mitigate high frequency (using ferrite cores,
for example). Similarly, for common-mode EMI, a commonmode inductor could be included in the differential-mode filter
as suggested in [12]. However, conducted EMI is a very complex problem: depending on the frequency range it needs different solutions and specifically designed filters. Hence, even if
filter integration is feasible in some cases, the use of one filter
over a wide frequency range is often too expensive since the
same reactive element must be designed to work over different
frequency ranges and at different power levels.
It should be noted that European standards in the frequency
range 2–150 kHz are incomplete and still under discussion and,
hence, grid filters are often designed to work at frequencies
higher than 150 kHz [13]. However, IEEE 519-1992 recommends that harmonics higher than the 35th should be limited
and switching current ripple reduction is also explicitly required
for equipment with high safety issues (such as cranes and elevators). Hence, the design of an LCL filter to limit switching
frequency ripple injection into the grid in the range of 2–150
kHz is often specifically required.
A good criterion to choose LCL filter parameters is to limit the
size of the installed reactive elements (these can result in a poor
power factor [14]) and the LCL filter power losses (due to the
passive damping required to avoid resonance). Some issues have
been explored in the literature: criteria for parameter choices
[15], [16], active damping of the filter [7], [17], and state feedback control using state observers [15], [16], [18]–[21]. Techniques for current control have also been compared taking into
account the LCL filter design [22]. However, the design of an
LCL filter, and how it might be optimized, has not been analytically studied to date.
This paper presents a design procedure for an LCL filter together with consideration of the control of an active rectifier
employing an LCL filter using proportional-plus-integral (PI)based control strategies for the dc voltage and the ac current.
These current regulators are typically designed in a rotating
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Fig. 1.
Three-phase active rectifier with LCL filter.
Fig. 2.
Single-phase equivalent of the active rectifier with LCL filter.
frame but the use of the LCL filter requires additional investigation to determine correct orientation of the frame [23]. Furthermore, stability problems should be correctly addressed by
considering zero/pole placements in the -plane. Finally, the
dynamic performance of the controlled system should be verified. All these topics are addressed in this paper, to provide a
detailed and practical guideline both for the design and for the
control of an LCL-filter-based three-phase active rectifier.
II. MODEL AND CONTROL OF THE SYSTEM
The LCL-filter-based active rectifier has been previously
modeled in the rotating frame [7] and state feedback controls
have been presented to guarantee the stability of the system.
However, these approaches require either an increased number
of sensors or increased complexity in the control algorithm
[15], [16], [18]–[21].
The purpose of this paper is to present a simple and low-cost
(both in hardware and in software) LCL-filter-based active rectifier. The system is shown in Fig. 2. The VSC is connected to the
grid through an LCL filter and an isolation transformer (used in
the test setup for security purposes). Note that the transformer
and resistance
have to be taken into acinductance
count in the design of the filter and the controllers. The LCL
filter is made up of three reactors with resistance and inductance on the converter side, three reactors with resistance
and inductance
on the grid side, and three capacitors
(each of them damped with a resistor
). Fig. 2 also shows a
common-mode filter that may or may not be included in the LCL
filter [12]. The design of this filter is not treated in this paper.
The system proposed has no additional sensors compared to
a conventional L filter configuration. It should be noted that the
current sensors are on the converter side because in an industrial
inverter they are also used to protect the power converter and are,
therefore, integrated in it.
The main aim is to achieve decreased switching ripple with
only a small increase in filter hardware, and by only adapting
the parameters of the PI-based controller that is already used for
the L filter configuration. This is expected because the LC part
of the LCL filter aims to primarily reduce the high-frequency
current ripple, and the capacitor’s influence can be neglected in
the current controller design if its value is low. In fact, current
control, because of its bandwidth, primarily influences only the
low-order current harmonics. Thus, the upgrade to an LCL filter
is easy and effective with a little increase in overall system cost
and no new sensors required.
Overall, a designer needs to model the system in the rotating
frame of the L-filter-based active rectifier (for the control), and
consider the transfer function of the overall filter with damping
for stability and dynamic purposes.
A. Controller Design
From Fig. 2, the system can be defined using the following
equation, neglecting the filter capacitor
:
(1)
,
,
is
where
is the converter current space
the grid voltage space vector,
is the converter-side voltage space vector.
vector, and
Current control is developed in a frame that rotates at an
angular speed (note that can be zero). In this frame, two
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LISERRE et al.: DESIGN AND CONTROL OF AN LCL-FILTER-BASED THREE-PHASE ACTIVE RECTIFIER
Fig. 3.
1283
Vector diagram for the active rectifier.
voltage equations can be written to identify the
components
and
current
(2)
These
currents are controlled by the correct choice of the
voltages generated by the converter. Two PI regulators command a space-vector modulator to generate the voltages that
should control these currents. The design of the PI controllers
is done using zero/pole placement in the -domain, where as
a design criterion the “technical optimum” is used with both
current control having the same time conplants for the
stant
[7]. All processing and modulation delays
should be taken into account [23], [24].
For dc voltage control, once the dc load current , the dc
load voltage , and the converter-side current are defined,
the following equation can be written:
(3)
The dc voltage is controlled using the converter-side dc current. The PI controller is synthesized using zero/pole placement
in the -domain with the objective of obtaining the best possible
compromise between rapid dynamic control of the dc output
voltage and reduction of the ac current overshoot. All processing
and filtering delays must be considered.
B. Rotating Frame Orientation
A rotating frame is often chosen in order to obtain current
control with rapid dynamic response [2]. However, similar results can be obtained using resonant controllers in the stationary
frame [2], [25]. For the active rectifier, the frequency of rotation
of the frame is the line frequency. If the axis is oriented on
the grid voltage vector
, the grid current vector
should
have a zero component to obtain unity power factor while the
component regulates the dc voltage (Fig. 3). However, probframe: firstly
lems can arise from wrong orientation of the
it can be difficult to obtain unity power factor, and then the efficiency of the control loops may be compromised. Two issues
must be considered.
1) Since current control is performed on the converter current rather than the grid current , it should be controlled
with the goal of zero displacement between the grid current and the grid voltage. This implies a nonzero -com-
Fig. 4. Input filter model for active rectifier.
ponent reference for the converter current, to take the filter
capacitor into account [24].
2) The voltage used for the -frame orientation is not the
grid voltage
, if a transformer is present (such as the
isolation transformer used in this setup) or if the capacitor
voltage is sensed instead of the grid voltage for active
damping purposes [7]. Thus, the voltage drop between
the grid voltage and the sensed voltage creates an angle
displacement that should be taken into account. This also
results in a nonzero -reference current.
Thus the component of the reference current is used for dc
voltage control and the component of the reference is used for
correct orientation of the
frame.
C. LC Filter Influence
The selection of the parameters of the filter will be explained
in the next section, but the configuration of the filter should be
taken into account when the stability of the system is investigated. So far, the current controller design has neglected the zero
and poles introduced by the capacitor presence. If the whole
LCL filter is considered as in Fig. 4, its transfer function becomes in case
(4)
and
. Hence, the LCL filter has two more zeros and two
more poles compared to a simple L filter.
If the transfer function expressed by (4) is discretized, and the
closed-loop root locus is considered with the PI controller tuned
using the previously identified criteria (i.e., considering only the
), these additional zeros and poles can make the
inductance
system unstable without proper damping. Damping is achieved
by connecting a resistor in series with the filter capacitor, as
shown in Fig. 1, Fig. 2, and the model of the input filter of Fig. 4.
This moves the unstable poles more inside the stability region,
as will be shown by analyzing the -domain zeros and poles of
the closed-loop system in Section VI.
where
III. CONSTRAINTS ON THE LCL FILTER DESIGN
The LCL filter aims to reduce high-order harmonics on the
grid side, but a poor filter design can cause lower attenuation
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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 2005
,
,
(
is the switching frequency), and
is the switching frequency harmonic order.
The attenuation introduced by the LCL filter is effective only
if the filter is properly damped. Otherwise, the resonance of the
filter produces a higher ripple. One damping method is to connect a resistor in series with the filter capacitor. The plant of the
current-controlled system as expressed by (4) then becomes
where
Fig. 5. Equivalent single-phase LCL filter at the h harmonic.
compared to what is expected, or can even cause a distortion increase because of oscillation effects. In fact, the rectifier current
harmonics may cause saturation of the inductors or filter resonance. Therefore, the inductors should be correctly designed
considering current ripple, and the filter should be damped to
avoid resonances. However, the damping level is limited by cost,
the value of the inductors, losses, and degradation of the filter
performance.
The procedure for choosing the LCL filter parameters uses
the power rating of the converter, the line frequency, and the
switching frequency as inputs. The process to calculate the
switching ripple attenuation is based on a frequency-domain
approach rather than on a time-domain approach.
In the following development, the filter values are reported as
a percentage of the base values, given by
(5)
(6)
where
is the line-to-line rms voltage,
is the grid frequency, and
is the active power absorbed by the converter
in rated conditions. The resonant frequency is referred to the
switching frequency value by
(7)
where the factor expresses how far the switching frequency
is from the resonant frequency
.
The equivalent single-phase LCL filter configuration for the
harmonic is shown in Fig. 5, neglecting the resistors , , and
(Fig. 2).
and
indicate the harmonic of the curis the order of the switching
rent and of the voltage, while
frequency harmonic. The current ripple attenuation is computed
by considering that at high frequencies, the converter is a harmonic generator, while the grid can be considered as a short circuit. Therefore, the converter voltage harmonic, at the switching
and the grid voltage harmonic, at the
frequency, is
.
switching frequency, is
The ripple attenuation, passing from the converter side to the
grid side, can be calculated with the following steps:
(8)
(9)
(10)
(11)
and the losses can be calculated as
(12)
where the skin effect is neglected.
The main terms of the sum in (12) are for the index near
(previously defined) and its multiples. In fact, damping absorbs a part of the switching frequency ripple to avoid the resonance. The losses decrease as the damping resistor value increases but at the same time this reduces its effectiveness (11).
Furthermore, the required damping cannot be calculated without
considering the current control strategy because the LCL filter
is connected to a closed-loop-controlled rectifier. Also, a disturbance can trigger a reaction from the closed-loop current controller (e.g., caused by a PWM modulator with a wide spectrum
spread between the fundamental and the switching frequency
harmonics, by an A/D characterized by poor resolution, by inadequate filters on the measured grid voltage [14], [26], or by an
external disturbance such as a load connected to the same point
of common coupling (PCC) [17]). If the closed-loop control is
not properly damped, a resonance can occur.
Having established (10) and (12) to design the filter, some
limits on the parameter values should be introduced.
a) The capacitor value is limited by the decrease of the power
factor at rated power (generally less than 5%). The power
factor decrease can also be a function of the ac sensor
position as discussed in [14].
b) The total value of inductance should be less than 0.1 pu
to limit the ac voltage drop during operation. Otherwise a
higher dc-link voltage will be required to guarantee current controllability, which will result in higher switching
losses [14]. Moreover, the maximum overall inductance
of the LCL filter is strongly dependent on the power
level and on the application. A standard mass-produced
product (low power) should integrate the LCL filter into
its hardware and, as a consequence, a more stringent
overall inductance limit (perhaps less than 5%) should
be adopted to avoid packaging problems. On the other
hand, for higher power levels (at present power levels of
interest by industry for active rectifier applications are
above tens of kilowatts) and in the absence of clearly
defined standards on the switching ripple, the LCL filter
will probably not be integrated in the converter. In this
case the main aim is to avoid saturation in the inductors,
with consequent higher losses.
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LISERRE et al.: DESIGN AND CONTROL OF AN LCL-FILTER-BASED THREE-PHASE ACTIVE RECTIFIER
c) The resonant frequency should be in a range between ten
times the line frequency and one-half of the switching
frequency, to avoid resonance problems in the lower and
upper parts of the harmonic spectrum.
d) Passive damping must be sufficient to avoid oscillation,
but losses cannot be so high as to reduce efficiency [7].
Finally, depending on the desired application, the designer
should impose some constraints: on the filter efficiency at low
frequency (first 50 harmonics) and high frequency (around the
switching frequency), and on the current tracking capability
(which can be compromised by the reactive power absorbed by
the input capacitors).
The following performance factors are used to verify the filter
effectiveness (the first three are low-frequency indicators and
the last two are high-frequency indicators):
• THD of the current
•
•
•
•
power factor
;
;
average of the absolute dc voltage error
largest of the sideband current harmonics around the
(this is because of the freswitching frequency
quency-domain approach used to study the switching
ripple reduction);
rms value of the high-frequency (2.5–20 kHz) harmonic
as a
content of the current
;
percentage of the fundamental harmonic
where is the overall rms value of the current and
is the
rms value of the current harmonic and is the angle between
the fundamental current and fundamental voltage.
IV. LCL FILTER DESIGN PROCEDURE
The LCL filter can be designed using the following step-bystep procedure.
1) Select the required current ripple on the converter side
design the inner inductor . The outer inductor value can
then be determined as a function of , using the index
for the relation between the two inductances
(13)
2) Select the reactive power absorbed at rated conditions
determine the capacitor value. Take as a percentage of
the reactive power absorbed under rated conditions
(14)
The capacitor value is limited by condition a) above.
knowledge
3) Select the desired current ripple reduction
of and then design the outer inductor . The ripple attenuation, calculated neglecting losses and damping of the
filter, is defined by (10) and can be rewritten, considering
(13) and (14), as
(15)
1285
is a constant. Before using (15) to calwhere
culate , the desired attenuation should be multiplied by a
factor that takes into account the losses and the damping.
If the sum of the two inductances does not respect condition (b), another attenuation level should be chosen, or
another value for the absorbed reactive power should be
selected as per step 2).
4) Verify the resonant frequency obtained
(16)
which can be written, considering (7), (13), and (14), as
(17)
where
is a constant. The resonant frequency is limited by condition (c). If this is not correct the
absorbed reactive power returned in step 2) or the attenuation returned in step 3) should be changed.
5) Set the damping according to condition d) above. At the
resonant frequency the impedance of the filter is zero. The
aim of the damping is to insert an impedance at this frequency to avoid oscillation. Hence, the damping value is
set to a similar order of magnitude as the series capacitor
impedance at the resonant frequency [26].
If the filter attenuation is not adequate, the design procedure returns to step 3) to increase the multiplication coefficient that takes into account the decrease of the filtering action due to losses. If this is not sufficient the
design procedure should go back to step 2) and select a
higher value of the reactive power.
6) Verify the filter attenuation under other load conditions
and with other switching frequencies.
V. LCL FILTER DESIGN EXAMPLE
The step-by-step procedure has been applied to a system with
(line to line) and rated power of
a rated voltage of 380 V
4.1 kW (maximum test power for the laboratory prototype). The
base impedance is approximately 35 , and the base capacitance
V and
W in (5) and (6).
is 90 F, taking
The lower rectifier switching frequency was chosen as 5 kHz,
but tests were also done up to 8 kHz because these frequencies
are suitable for the chosen power level. The procedure of Section IV is as follows.
1) Adopting a 2.7% impedance for the converter side, a 10%
current ripple is obtained. Adding the LC part the aim is
selected to reduce the current ripple to 2%.
2) The maximum capacitor value is 4.7 F under the limits
of condition 1. However, if too low a capacitor value is
selected, too high a value of inductance could be necessary. Hence, it is better to start with about one-half of this
value (2.2 F) and then, if some of the constraints cannot
be respected, increase it up to the maximum limit.
3) Selecting a current ripple attenuation of 20% with respect
is calto the ripple on the converter side, a value of
culated using (15) (see Fig. 6). The isolation transformer
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1286
Fig. 6.
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 2005
Relation between the harmonic attenuation at the switching frequency and the ratio r between grid and converter inductors.
TABLE I
LCL FILTER PARAMETERS
for the experimental setup provides a 2.7% inductance.
With a 1.8% inductor, the resultant 4.6% grid inductance
gives an value of 1.6, which takes into account the reduction in filter effectiveness caused by damping. It is
commented also that to obtain a ripple attenuation of less
than 20%, the value of increases too much (as shown in
Fig. 6) and the filter may become too expensive.
4) The consequent resonant frequency is 2.5 kHz, which is
exactly one-half of the switching frequency.
5) The impedance of the filter capacitor at the resonant frequency is 29 . The damping value is chosen as one-third,
i.e., 10 . The losses are 0.8% of rated power (under rated
conditions). Even with this damping the filter gives good
results and the objective of a ripple reduction to 20% is
fulfilled.
6) Simulation and experimental tests, using the designed
LCL filter (Table I), show the ripple reduction achieved
over a wide range of working conditions.
VI. ANALYSIS AND SIMULATION OF THE SYSTEM
Simulation models have been built using Matlab and
Simulink. The rated rms line-to-line voltage is 380 V and the
rated power of the system is 4.1 kW, the switching frequency
of the rectifier is in the range 5–8 kHz, and the modulation
strategy adopted is the sinusoidal modulation with centered
pulses, with the sampling frequency equal to the switching
frequency. The dc-voltage reference is 700 V and the rated load
current is 5.5 A.
The stability and dynamic response of the system will now
be analyzed, and then the designed filter effectiveness will be
evaluated to validate the reported procedure.
A. Stability and Dynamic Response
The stability and dynamic response of the overall system is
analyzed in the plane using the poles of the closed-loop current
controller. It should be noted that there is one sample delay in
the system for the digital processing, plus one-half sample delay
caused by the double-edge PWM because the modulator cannot
Fig. 7. Zeros and poles of the closed-loop current control 1 without and 2 with
damping (5-kHz sampling frequency).
respond for this period after the duty cycle has been determined
by the control algorithm [7]. This half-period delay is implicitly
introduced by discretization of the system plant using a zerothorder hold, as is commonly used to describe continuous systems
controlled by PWM.
From the analysis of the left side of the plane it is clear that
the system is close to the border of the stability region without
damping (zeros and poles numbered with 1 in Fig. 7). If a 10damping resistor is used then the system becomes more stable
(zeros and poles numbered with 2 in Fig. 7). It is commented
that stability analysis relating to resonance dynamics becomes
less reliable as the sampling frequency approaches twice the resonant frequency [26]. For this example, the resonant frequency
is just below 2.5 kHz and, hence, a stability analysis at a 5-kHz
sampling frequency is still possible.
From the analysis of the right side of the plane in Fig. 7, it
is clear that the dynamic response remains unchanged with the
introduction of damping, because the two complex poles shift
only slightly. Further proof comes from frequency analysis of
the filter using the Bode diagram shown in Fig. 8, where it can
be seen that at low frequency the damped LCL filter behaves like
.
an L filter of value
It is also useful to study the evolution of the zeros and poles
as the sampling frequency changes (with the consequent change
of the parameters in the current controller) but with the same
damping. With respect to stability, as the sampling frequency
increases the poles move toward the stability borders and so the
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LISERRE et al.: DESIGN AND CONTROL OF AN LCL-FILTER-BASED THREE-PHASE ACTIVE RECTIFIER
1287
Fig. 10. Simulation of d-axis reference and feedback currents for a step change
from 33% to 100% rated load (5-kHz sampling and switching frequency).
Fig. 8. Bode plot of the transfer function of the L filter and of the damped
LCL filter (bold).
Fig. 9. Zeros and poles of the closed-loop current varying the sampling
frequency from 5 to 8 kHz with 1-kHz step variation (the arrows show the
evolution of the zeros and poles).
damping becomes less effective (Fig. 9). In particular, for an
8-kHz switching frequency, the poles cross the border of the stability region. However, around the resonant frequency the passive elements of the system have extra resistance due to skin
effect and iron losses, and this does offer some extra damping.
As the sampling frequency increases, the bandwidth of the
current controller varies from 200 to 400 Hz. Its dynamic response can be tested in simulation with a step load change.
Using a step from 33% to 100% of rated load it is possible to
confirm whether the active rectifier with LCL filter is stable and
if the controllers have been well tuned. The result of this test
is shown in Fig. 10 and it is satisfactory. It should be noted that
this result has been obtained simply by adjusting the parameters
of the PI controllers without any change in their structure.
B. Filter Effectiveness
Fig. 11 shows the simulated converter and grid currents
and their associated high-frequency spectra obtained with the
Fig. 11. (a) Simulated steady-state converter current, (b) grid current, and (c)
their spectra (black for the grid current and white for the converter one) at high
frequency with LCL filter (rated conditions).
LCL filter, operating under rated conditions. The largest near
switching frequency current harmonic component is 0.48 A
on the converter side and 0.07 A
on the grid side. Thus, it
has been reduced to 15%.
Table II compares the performance factors identified in Secfilter configuration and the LCL filter. The
tion III, for the
results show that the high-frequency current ripple has been reduced by one-half using the filter capacitors, while at low frequency the two filters have an equivalent performance.
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L
TABLE II
FILTER VERSUS LCL FILTER
TABLE III
ELECTRICAL PARAMETERS OF THE VSC
Fig. 13. Measured grid voltage (86 V/div), grid current, converter current,
and input filter capacitor current (5 A/div) at rated conditions (5-kHz switching
frequency).
Fig. 12.
Controller setup for active rectifier with LCL filter.
VII. EXPERIMENTAL RESULTS
The experimental setup used in the laboratory of the Institute of Energy Technology at Aalborg University, Aalborg, Denmark, consists of a three-phase 30-kVA programmable power
supply, a commercial Danfoss inverter VLT 3008 (ratings shown
in Table III), with the control card removed and a resistor used
to load the dc link. The control is implemented using an Analog
Devices ADSP-21 062 SHARC floating-point digital signal processor, while the timing of the system and the PWM generation
is managed by a Siemens microcontroller SAB80C167 [27], as
shown in Fig. 12.
A. Validation of the Model
The first use of the experimental system was to validate the
simulation model for both the low- and the high-frequency
ranges.
In the low-frequency range, the simulated grid current fed
from a sinusoidal grid voltage had a THD of 1.4%. In contrast,
the experimental system had a grid current THD of 3%, but
the grid voltage had a THD of 1%, (waveforms are shown in
Fig. 13). However, the measured grid current has some low-frequency harmonics, with about a 1% amplitude relative to the
fundamental. The odd harmonics come from system unbalances
that also cause slight even harmonics in the dc-link voltage as
Fig. 14. Measured grid currents (5 A/div) and dc voltage (14 V/div, only ac
component) at rated conditions (5-kHz switching frequency).
shown in Fig. 14 [28]. The even harmonics come from dead
time, some delays, suppression of pulses, and the fact that the
grid voltage is measured after a dominant reactance [23].These
harmonics have less influence as the switching and sampling
frequency increase (Fig. 15 shows the grid currents and the dc
voltage in the case of 8 kHz).
The high-frequency range is more effective to verify the
filter’s performance. It has already been shown in simulation
that with a ripple-free grid voltage, the largest near switching
on the converter
frequency harmonic currents are 0.48 A
on the grid side. The comparable experside and 0.07 A
imental results are, respectively, 0.41 A
and 0.07 A .
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LISERRE et al.: DESIGN AND CONTROL OF AN LCL-FILTER-BASED THREE-PHASE ACTIVE RECTIFIER
1289
TABLE V
GRID CURRENT HIGH-FREQUENCY HARMONIC CONTENT VARYING THE LOAD
AND THE SAMPLING/SWITCHING FREQUENCY
TABLE VI
DAMPING LOSSES VARYING THE SAMPLING/SWITCHING FREQUENCY
Fig. 15. Measured grid currents (5 A/div) and dc voltage (14 V/div only ac
component) at rated conditions (8-kHz switching frequency).
TABLE IV
GRID CURRENT THD VARYING THE LOAD AND
SAMPLING/SWITCHINGFREQUENCY
THE
Also, the total rms high-frequency harmonic current ripple
(as defined in Section III) is 16% of the fundamental on the
converter side and 1.2% on the grid side.
B. Performance Evaluation of the Overall System
A performance analysis of the system on the grid side, shows
that the low-frequency distortion is well below 5% at rated load
and the high-frequency ripple is properly reduced. However, it is
useful to analyze the system performance under different load
conditions and for different switching frequencies as stated in
step 6) of the design procedure.
In the low-frequency range, grid current THD (defined in Section III) is the significant parameter. Table IV shows this parameter for different switching frequencies and for three different
load conditions. The high THD at low power occurs because the
harmonics caused by the system unbalance have more weight
when the fundamental current value is low.
In the high-frequency range, the harmonic content of the current (defined in Section III) is the significant parameter: Table V
shows that, as would be expected, higher switching frequencies
lead to a more effective filter.
The next step in the system performance analysis is to consider the damping losses. Since load variation has little effect
Fig. 16. Measured grid currents (5 A/div) and dc voltage (28 V/div, only ac
component) for a step change from 33% to 100% rated load (5-kHz switching
frequency).
on the damping losses, Table VI shows the effect of varying
switching frequency for the same value of damping resistor (10
). It can be seen that damping losses decrease as the switching
frequency increases. However, as identified in Section VI-A the
system is also less damped, and at 8 kHz reaches the limit of the
stability region.
Finally, the dynamic response of the system has been tested
by step changing the load from 33% to 100% of rated power, as
shown in Fig. 16. It can be seen that the dc voltage dynamic
response is slowed down compared to simulation because of
the dc filter that is used to reduce measurement ripple to avoid
problems in the control loops [14].
VIII. CONCLUSION
This paper has analyzed both the design and control of an
active rectifier employing an LCL filter to reduce the switching
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1290
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 41, NO. 5, SEPTEMBER/OCTOBER 2005
frequency current ripple. The main aim is to provide a design
procedure for the filter and study the stability and the dynamic
response of the overall system. The design procedure has been
tested in simulation and with an experimental system, and the
desired current ripple attenuation has been achieved for the test
system parameters. In fact, compared to a simple L filter with an
inductance equal to the sum of all inductances in the LCL filter,
the current ripple magnitude has been halved. Stability and a
rapid dynamic response have also been confirmed. Moreover,
all the results have been obtained using a simple control method
and no additional sensors. Thus, the system can be implemented
using a standard industrial inverter.
A further research topic in this field is the development of
a more embedded design procedure taking into account conducted EMI disturbances. However, this will be strongly dependent on the ongoing standards in the field and on the limits they
will impose on the switching ripple injection in the grid, and is
left for future investigations.
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1992.
Marco Liserre (S’00-M’03) received the M.Sc. and
Ph.D. degrees in electrical engineering from the Politecnico di Bari, Bari, Italy, in 1998 and 2002, respectively.
He is currently an Assistant Professor at the
Politecnico di Bari. He spent one year as an Invited
Researcher and two months as an Invited Associate
Professor at the Institute of Energy Technology,
Aalborg University, in 2001 and 2004, respectively.
Since 1999, he has been carrying out a collaboration
with the Università dell’Aquila. His research interests are in power converters and drives, namely, in the control of converters, in
power quality, and in distributed generation. He has coauthored more than 70
technical papers, ten of them published in IEEE TRANSACTIONS.
Dr. Liserre is a Member of the IEEE Industry Applications, IEEE Industrial
Electronics, and IEEE Power Electronics Societies. In the IEEE Industrial Electronics Society, he has been an AdCom Member for the period 2003–2004, Chair
for Student Activities for the period 2002–2004, Chair for Region 8 Membership Activities since 2004, and Newsletter Editor since 2005. He has served
as a Student Forum Co-Chair of ISIE 2002, ISIE 2003, ISIE 2004, ISIE 2005,
Mechatronics and Robotics 2004, and ICIT 2004.
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LISERRE et al.: DESIGN AND CONTROL OF AN LCL-FILTER-BASED THREE-PHASE ACTIVE RECTIFIER
Frede Blaabjerg (S’86–M’88–SM’97–F’03) was
born in Erslev, Denmark, in 1963. He received the
M.Sc.E.E. degree from Aalborg University, Aalborg
East, Denmark, in 1987, and the Ph.D. degree
from the Institute of Energy Technology, Aalborg
University, in 1995.
He was with ABB-Scandia, Randers, Denmark,
from 1987 to 1988. During 1988–1992 he was a
Ph.D. student at Aalborg University. He became an
Assistant Professor in 1992, an Associate Professor
in 1996, and a Full Professor of power electronics
and drives in 1998 at Aalborg University. In 2000, he was a Visiting Professor
at the University of Padova, Padova, Italy, as well as becoming a part-time
Programme Research Leader at the Research Center Risoe, working with wind
turbines. In 2002, he was a Visiting Professor at Curtin University of Technology, Perth, Australia. His research areas are power electronics, static power
converters, ac drives, switched reluctance drives, modeling, characterization of
power semiconductor devices and simulation, wind turbines, and green power
inverters. He is involved in more than ten research projects with industry.
Among them is the Danfoss Professor Programme in Power Electronics
and Drives. He is the author or coauthor of more than 300 publications in
his research fields including the book including the book Control in Power
Electronics (New York: Academic, 2002).
Dr. Blaabjerg is a Member of the European Power Electronics and Drives
Association and of the Industrial Drives, Industrial Power Converter, and
Power Electronics Devices and Components Committee Committees of the
IEEE Industry Applications Society. He is an Associate Editor of the IEEE
TRANSACTIONS ON INDUSTRY APPLICATIONS, IEEE TRANSACTIONS ON POWER
ELECTRONICS, Journal of Power Electronics, and the Danish journal Elteknik.
He has been active in the Danish Research Policy for many years. He became
a member of the Danish Academy of Technical Science in 2001. He served as
a Member of the Danish Technical Research Council during 1997–2003, and
from 2001–2003 he was its Chairman. He received the 1995 Angelos Award
for his contribution to modulation technique and control of electric drives and
an Annual Teacher Prize from Aalborg University, also in 1995. In 1998, he
received the Outstanding Young Power Electronics Engineer Award from the
IEEE Power Electronics Society. He has received four IEEE Prize Paper Awards
during the last five years. In 2002, he received the C. Y. O’Connor Fellowship
from Perth, Australia, and in 2003, the Statoil Prize for his contributions to
power electronics. He also received the Grundfos Prize in 2004.
1291
Steffan Hansen (S’95–A’96–M’99) was born in
Sonderborg, Denmark, in 1971. He recieved the
M.Sc.E.E . and the Ph.D. degrees through an industrial fellowship supported by Danfoss Drives A/S
and the Danish Academy of Technical Sciences from
Aalborg University, Aalborg East, Denmark, in 1996
and 2001, respectively.
Since 1996, he has been with Danfoss Drives
A/S, Graasten, Denmark, where his main research
activities are focused on solutions to reduce line-side
harmonics from adjustable-speed drives. He is currently Product Manager responsible for high-performance drives and products
reducing secondary effects.
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