Description

A higher order passive power ﬁlter (LLCL ﬁlter)
for the grid-tied inverter is becoming attractive for industrial
applications due to the possibility to reduce the cost of the copper
and the magnetic material. However, similar to the conventional
LCL ﬁlter, the grid-tied inverter is facing control challenges. An
active or a passive damping measure can be adopted to suppress
the possible resonances between the grid and the inverter.

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See discussions, stats, and author proﬁles for this publication at: https://www.researchgate.net/publication/260626478
A New Design Method for the Passive Damped LCL and LLCL Filter-BasedSingle-Phase Grid-Tied Inverter
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in
IEEE Transactions on Industrial Electronics · October 2013
DOI: 10.1109/TIE.2012.2217725
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 10, OCTOBER 2013 4339
A New Design Method for the Passive Damped LCLand LLCL Filter-Based Single-PhaseGrid-Tied Inverter
Weimin Wu, Yuanbin He, Tianhao Tang,
Senior Member, IEEE
, and Frede Blaabjerg,
Fellow, IEEE
Abstract
—A higher order passive power ﬁlter (LLCL ﬁlter)for the grid-tied inverter is becoming attractive for industrialapplications due to the possibility to reduce the cost of the copperand the magnetic material. However, similar to the conventionalLCL ﬁlter, the grid-tied inverter is facing control challenges. Anactive or a passive damping measure can be adopted to suppressthe possible resonances between the grid and the inverter. For anapplication with a stiff grid, a passive damping method is oftenpreferred for its simpleness and low cost. This paper introduces anew passive damping scheme with low power loss for the LLCLﬁlter. Also, a simple engineering design criterion is proposed toﬁnd the optimized damping resistor value, which is both effectivefor the LCL ﬁlter and the LLCL ﬁlter. The control analysis andthe power loss comparison for different ﬁlter cases are given.All these are veriﬁed through the experiments on a 2-kW single-phase grid-tied inverter prototype using proportional resonantcontrollers. It is concluded that, compared with the LCL ﬁlter, theproposed passive damped LLCL ﬁlter can not only save the totalﬁlterinductanceandreducethevolumeoftheﬁlterbutalsoreducethe damping power losses for a stiff grid application.
Index Terms
—Characteristic resonance frequency, dampingpower loss, impedance feature, LCL ﬁlter, LLCL ﬁlter, passivedamping, PR controller, Q-factor.
I. I
NTRODUCTION
T
HE RENEWABLE energy generation catches more andmore impact, and the grid-tied voltage-sourced invertershown in Fig. 1 has been widely adopted [1]–[3] in a largepower range. A low-pass passive power ﬁlter (typical LCLﬁlter) is often inserted between a voltage-source inverter (VSI)and the grid to limit the excessive current harmonics, whichis caused by the sine-wave pulsewidth modulation (PWM),injected into the point of common coupling.
Manuscript received June 19, 2012; revised August 3, 2012; acceptedAugust22,2012.DateofpublicationSeptember7,2012;dateofcurrentversionMay 16, 2013. This work was supported in part by the Leading AcademicDiscipline Project of Shanghai Municipal Education Commission under AwardJ50602andinpartbytheProjectofShanghaiNaturalScienceFoundationunderAward 12ZR1412400.W. Wu and T. Tang are with the Department of Electrical Engineering,Shanghai Maritime University, Shanghai 200135, China (e-mail: wmwu@cle.shmtu.edu.cn; thtang@shmtu.edu.cn).Y. He is with FSP-Powerland Technology Inc., Nanjing 210042, China(e-mail: heyuanbin123@yahoo.com.cn).F. Blaabjerg is with the Department of Energy Technology, Aalborg Univer-sity, 9220 Aalborg, Denmark (e-mail: fbl@et.aau.dk).Color versions of one or more of the ﬁgures in this paper are available onlineat http://ieeexplore.ieee.org.Digital Object Identiﬁer 10.1109/TIE.2012.2217725Fig. 1. VSI connected to the grid through an LCL ﬁlter.
Compared with a ﬁrst-order L ﬁlter, an LCL ﬁlter can bet-ter meet the grid interconnection standards with signiﬁcantlysmaller size and cost, particularly for applications above severalkilowatts. However, it brings extra control difﬁculties like caus-ing the closed-loop control system to be unstable, and it mayalso trigger the resonance between the inverter and the grid.To suppress the possible resonances of an LCL ﬁlter, activedamping [4]–[13] or passive damping [14]–[17] measures maybe adopted. If the power system is “weak” and its impedancechanges widely under the different situations, an active damp-ing method might be preferred, although at the risk of highercost of sensors and more control complexity. For a stiff grid ap-plication, a passive damping strategy is more attractive, owingto its simpleness and low cost.A straightforward passive damping method is often adoptedby inserting a resistor in series with the capacitor in the ﬁlter.It is simple, effective, and reliable, yet the damping resistorwill inevitably give rise to extra power loss and weaken thehigh-frequency harmonic attenuation ability of an LCL ﬁlter.To overcome its demerit, many improved measures have beenintroduced in recent years. One effective solution is to insert anadditional
R
d
–
C
d
circuit branch in parallel with the capacitorof an LCL ﬁlter. Channegowda and John [17] analyze therelationship of power losses, the damping resistor selection,and the damping effect of this method in detail. However,since the capacitor in the damping branch is split from theﬁltering capacitor, the high-frequency harmonic attenuation of the passively damped LCL ﬁlter is then weakened, compared tonot using any damping LCL ﬁlter.Bloemink and Green [18] proposed a method to decreasethe total inductance of the conventional ﬁlter with multitunedtraps.However,itmayexciteaparallelresonancebetweenthesetuned traps. To decrease the total inductance of the conventionalLCL ﬁlter and, also, to avoid the possible parallel resonancebetween the multituned traps, a new LLCL ﬁlter with only onetuned trap was proposed in [19].
0278-0046/$31.00 © 2012 IEEE
4340 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 10, OCTOBER 2013
Fig. 2. Schematic diagrams of (a) LCL ﬁlter and (b) LLCL ﬁlter [19] used ingrid-tied inverters.
Since the LLCL ﬁlter is also a kind of high-order powerﬁlters, a passive or active damper is still needed. Accordingto Channegowda and John [17], an
R
d
–
C
d
passive dampermay be favorable, but due to the extra inductor, the parameterdesign process may turn very complicated and hard for applica-tions. Therefore, an engineering design method for the passivedamped high-order power ﬁlter-based single-phase grid-tiedinverter is desired, particularly for the LLCL ﬁlter-based one.In this paper, the principle of an LCL ﬁlter and an LLCLﬁlter is ﬁrst presented for a single-phase power converter. Then,a new engineering design method to determine the optimizedpassive damping resistor through analyzing the impedance fea-ture of the capacitor circuit is introduced and continued with amethod to set up design criterions for the passive damped LCLand LLCL ﬁlters. The power losses of different methods areanalyzed and compared. Finally, comparative experiments ona 2-kW single-phase prototype using a proportional resonant(PR) plus harmonics compensation (HC) controller are used toverify the theoretical analysis.II. F
ILTER FOR
P
OWER
C
ONVERTER
In power converter systems, the switching-frequency har-monic attenuation is an important performance index in orderto fulﬁll the standards of the IEEE 1547.2-2008 and 519-1992[20], [21]. High-frequency component currents will also resultinhigh-frequency conducted emissionswhichshouldbelimitedin the range of standards [22]. The electromagnetic interference(EMI) noise (150 kHz
∼
30 MHz) depends much on the circuitlayout, and the measurements are often worse than simulations[23]–[27], mainly due to the parasitic components affecting thebehavior at high frequencies. For the sake of simplicity andproper length, EMI effects concerned with the LCL or LLCLﬁlter are not analyzed in depth in this paper.Compared with an L ﬁlter, an LCL ﬁlter [see Fig. 2(a)]can bypass the high-frequency harmonics through an additionalcapacitor branch and then reduce the total ﬁlter inductance andvolume. The selection of parameters is mainly determined bythe dominant harmonic around the switching frequency. If alower impedance of the capacitor branch appears at the switch-ing frequency, then the inductance of the grid-side inductor of an LCL ﬁlter can be continued to be scaled down, which bene-ﬁts of a smaller ﬁlter volume. As shown in Fig. 2(b), the
L
f
–
C
f
series resonant circuit, bypassing completely the current at theswitching frequency, inserted in the existing capacitor branchof the LCL ﬁlter may perform well. Thus, a novel high-orderﬁlter, named LLCL ﬁlter, was proposed in [19].
Fig. 3. Transfer functions
i
g
(
s
)
/u
i
(
s
)
in the case of LCL and LLCL ﬁltersas a function of frequency.
Because the resonant frequency of the
L
f
–
C
f
series resonantcircuit is at the switching frequency, the value of the inductor
L
f
is generally much smaller than that of
L
1
or
L
2
in Fig. 2(b).Assuming initially that the grid is an ideal voltage source, thetransfer function
i
g
(
s
)
/u
i
(
s
)
of the LLCL ﬁlter can be derivedas shown in
G
u
i
→
i
g
(
s
)=
i
g
(
s
)
u
i
(
s
)
u
g
(
s
)=0
=
L
f
C
f
s
2
+ 1(
L
1
L
2
C
f
+ (
L
1
+
L
2
)
L
f
C
f
)
s
3
+ (
L
1
+
L
2
)
s.
(1)If the inductance of
L
f
is set to zero, then the transferfunction of the LCL ﬁlter can be obtained.Fig. 3 shows the transfer functions
i
g
(
s
)
/u
i
(
s
)
of both theLLCL ﬁlter and the LCL ﬁlter while all the other parametersare the same except for the
L
f
. It can be seen that, withinhalf of the switching-frequency range which determines the lowharmonics of the grid current, the LLCL ﬁlter-based grid-tiedVSI has almost the same frequency-response characteristic asthe LCL ﬁlter, and comparing with the LCL ﬁlter, the additionalinductor
L
f
of the LLCL ﬁlter should not bring any extracontrol difﬁculties. Furthermore, an LLCL ﬁlter has nearly zeroimpedance around the switching frequency
ω
s
, and the grid-side inductance is only limited by the harmonics around thedouble of the switching frequency. Therefore, the grid-sideinductor of an LLCL ﬁlter can be scaled down compared tothat of an LCL ﬁlter as the amplitude of the dominant harmonicof the single-phase inverter output voltage around the switchingfrequency is generally higher than that around the double of theswitching frequency.III. P
ROPOSED
D
ESIGN
M
ETHOD FOR
P
ASSIVE
D
AMPING
To attenuate the possible resonance caused by the high-order power ﬁlter, whether an LCL ﬁlter or an LLCL ﬁlter isused, and to improve the stability of the closed-loop invertersystem, passive damping or active damping schemes should beadopted [28]. In view of the simpleness and the cost, the passivedamping method is more attractive than the active dampingmethod. However, it is a challenge to balance the power losses,
WU
et al.
: NEW DESIGN METHOD FOR LCL AND LLCL FILTER-BASED SINGLE-PHASE GRID-TIED INVERTER 4341
Fig. 4. Characteristics of the passive damping method with an
R
d
damperfor an LCL ﬁlter. (a) Schematic diagram of an
R
d
damped LCL ﬁlter.(b) Impedance feature of the capacitor branch (dotted line: without dampingresistor).
the satisfactory damping effect, and the harmonic attenuation insome cases, when selecting the damping parameters for a high-order power ﬁlter [17]. In this section, a simple engineeringdamping design method is proposed.
A. Principle of Passive Damping Scheme of LCL Filter
The aim of the damping is to reduce the Q-factor at thecharacteristic resonance frequency, as shown in Fig. 3. It isoften easy to achieve by inserting a resistor in series withthe capacitor as shown in Fig. 4(a) (named as
R
d
dampedLCL ﬁlter). Its characteristic resonance frequency,
ω
r
, can becalculated as
ω
r
=
L
1
+
L
2
L
1
L
2
C
f
.
(2)In this case, the inserted damping resistor does not affect thevalue of
ω
r
.Itisobvious that,to obtain a proper damping effect,
ω
r
has to be limited in the shadowed areas of Fig. 4(b) (whichshows the impedance feature of the
R
d
–
C
f
circuit), where thecapacitor branch represents the resistive feature and a smallQ-factor can be achieved. This damping method is simple andeffective, and the resistance
R
d
can be optimized by calculatingtheQ-factoroftheﬁlter[29],[30].Nevertheless,boththepowerloss and the high-frequency harmonic attenuation turn out to bedisappointing by using this method.To reduce the damping power loss and to maintain the high-frequency harmonic attenuation, an improved low-loss passivedamping scheme [17] was introduced and shown in Fig. 5(a)(named as
R
d
–
C
d
damped LCL ﬁlter).
Fig. 5. Characteristics of an improved passive damping method with an
R
d
–
C
d
damper for an LCL ﬁlter. (a) Schematic diagram of an
R
d
–
C
d
dampedLCL ﬁlter. (b) Impedance feature of
C
f
and
R
d
–
C
d
damper (dotted line:without damping resistor).
It is assumed that the grid is an ideal voltage source, and thetransfer function
i
g
(
s
)
/u
i
(
s
)
can be calculated as (3) shown atthe bottom of the page.Compared with the former method, the merit of this methodis that the damping branch does not harm the high harmonicsuppression of the LCL ﬁlter [10]–[13]. Unfortunately, un-like the characteristic resonance frequency,
ω
r
, of the formermethod, its characteristic resonance frequency is changeablewith different
R
d
and
C
d
. For example, if
R
d
= 0
, then
ω
r
_
down
=
L
1
+
L
2
L
1
L
2
(
C
f
+
C
d
)
(4)where
ω
r
_
down
is the possible minimum characteristic reso-nance frequency, while if
R
d
=
∞
, then
ω
r
_
up
=
L
1
+
L
2
L
1
L
2
C
f
(5)where
ω
r
_
up
is the possible maximum characteristic resonancefrequency.To ﬁnd out the optimized Q-factor, the exact characteristicresonance frequency should be obtained by calculating thecomplex conjugate solutions of a third-order equation of thetransfer function
i
g
(
s
)
/u
i
(
s
)
, with given
R
d
and
C
d
before-hand. Therefore, it seems difﬁcult to select reasonable dampingparameters directly.In this paper, the design criteria of an LCL ﬁlter except forthe damping branch are almost the same as those presentedin [19]. Since the damping branch is aimed to decrease theQ-factor at the characteristic resonance frequency, in theory,
G
u
i
→
i
g
(LCL)
(
s
) =
i
g
(
s
)
u
i
(
s
)
u
g
(
s
)=0
=
R
d
C
d
s
+ 1
s
(
L
1
L
2
R
d
C
d
C
f
s
3
+
L
1
L
2
(
C
d
+
C
f
)
s
2
+
R
d
C
d
(
L
1
+
L
2
)
s
+
L
1
+
L
2
)
(3)

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