3rd The International Conference on Renewable Energy Research and Applications
19-22 Oct 2014 Milwakuee-USA
LCL Filter Resonance Mitigation Technique for
Voltage Source Converters
Yogesh P. Patel and Lixiang Wei
Adel Nasiri
Rockwell Automation
Mequon, WI, USA
yppatel@ra.rockwell.com
lwei@ra.rockwell.com
University of Wisconsin - Milwaukee
Milwaukee, WI, USA
nasiri@uwm.edu
ABSTRACT
This paper investigates the control technique to mitigate the
LCL filter resonance issue for voltage source converters. Two level
voltage source converter with and without passive damping of LCL
filter are selected for the comparative study. Control algorithm is
discussed to estimate the source impedance based on variable
carrier PWM. Estimated source impedance is used to tune the
control of the VSC to avoid the resonance of LCL filter has been
presented. There have been scenarios when LCL resonance can’t
be avoided just by tuning the control parameter. In these cases
energy efficient technique has been discussed which allows
running voltage source converter with minimum performance
difference. Simulation studies have been performed to evaluate the
above techniques and verified with the experimental results.
Keywords- LCL filter, voltage source inverter, resoanace.
I.
INTRODUCTION
Voltage source converters (VSC) are extensively used in
applications like wind, solar, fuel cell and motor drives etc.
The advantages of the VSC are to achieve variable power
factor, controllable DC link voltage and bidirectional power
flow. Depending up on the rating of the unit the switching
frequency of the power device is varying from 3-8 kHz.
When VSC is used in conjunction with LCL filter, the overall
system provides low harmonic solution and can easy to meet
the IEEE 519 standard. In addition it helps reduce the EMI of
the system. LCL filter design guidelines and its inherent
resonance characteristic are provided in references [1]-[2].
In this paper mathematical model of the LCL with and
without passive damping are presented. The importance of the
grid impedance estimation is discussed in detail. There are
multiple off-line and online methods available to estimate the
grid impedance. The pros and cons of each method will be
described and compare with the proposed novel method to
detect the grid impedance estimation. The proposed method
use the variable carrier PWM technique to actuate the
resonance in the LCL. Frequency spectrum analysis is used to
identify the resonance peak and estimate the source
impedance. The effect of the source impedance on the LCL
resonance characteristic can be used to define the VSC control
loop gain parameter, which alleviates potential resonance
issue. In some applications, this technique may not necessary
helps and requires additional step to avoid resonance. This
ICRERA 2014
paper also describes the propose technique to reduce the LCL
resonance in above mention case. Simulation analysis will be
discussed in section IV and will be verified using experimental
results.
II.
MATHAMATICAL MODEL OF LCL FILTER
Per phase LCL filter with and without passive damping is
show in figure 1(a) and 1(b). Where Lg, and Lc are grid side
and converter side inductance, Cf is filter capacitor and Rf is
damping resistor. Transfer function for LCL with and without
damping is given by equation (1) and (2) [2]-[3]. The
resonance frequency can be evaluated using equation (3). For
300kW rated VSC with 3% grid side, 9% converter side
inductors and 5% filter capacitor, the resonance frequency of
the system is 1.8 kHz. Stiff source is consider for this analysis.
Bode plot of LCL with and without damping is shown in
figure 2. Without damping the admittance is 137dB, whereas
with 0.1 ohm damping resistor its drop down to 3.5dB.
S 2 Lg C f + 1
i( s )
=
2
v( S ) S [ S Lg LcC f + ( Lg + Lc )]
(1)
S 2 Lg C f + SC f R f + 1
i( s )
=
2
v( S ) S[ S Lg LcC f + SC f R f ( Lg + Lc ) + ( Lg + Lc )]
(2)
f res
Lg + Lc
1
=
2π
Lg LcC f
(3)
ig
Lg
Lc
i
e
Cf
v
Figure 1(a): LCL filter without passive damping
3rd The International Conference on Renewable Energy Research and Applications
19-22 Oct 2014 Milwakuee-USA
Figure 1(b): LCL filter with passive damping
III.
ALGORITHM TO ESTIMATE SOURCE IMPEDANCE
The source impedance significantly affects the behavior of
the LCL filter response. This will be identify by the bode plot
of the LCL filter transfer function with different source
impedance as shown in figure 3. In figure 3, Lg includes the
source impedance as well as grid side inductance (3% L) of
the LCL filter. One can observe that as the source impedance
increase, the resonance frequency reduces [4]. If source is
more than 20 times the rating of VSC then source impedance
is negligible compare to the grid side inductance and has
minimum effect on the resonance frequency.
Figure 2 : Bode plot of the LCL filter W/WO passive damping
For the stiff source, the resonance frequency is 1.8 kHz. In
contrary, if VSC is connected to generator, in this case the
source impedance is almost 5 times the grid side inductor of
the LCL filter. The resonance frequency may drop to 1.1 kHz
and the effective bandwidth of the control loop reduces
significantly. If the control loop parameter is tuned based on
just LCL filter without considering the source impedance, for
any step change in load VSC goes to the unstable mode. It is
obvious that as source impedance increase, the attenuation of
the switching frequency component also increase. This
additional attenuation won’t really help the converter because
LCL is already designed to provide enough attenuation with
stiff source to meet IEEE 519 low harmonic requirement. For
better turning of the control loop of the VSC required the
information about source impedance [5]-[8].
ICRERA 2014
Figure 3: LCL filter with different source impedance
The different approaches to estimate the grid impedance
are classified in to offline and online approaches. In offline
approach, the grid impedance is measured while inverter is not
connected, where as in online approach the inverter is always
connected to the grid. The offline grid estimation method
discussed in [13] requires additional instrumentation to
measure the grid impedance. This method provides accurate
measurement but it is not practically possible for grid tie
inverter as grid impedance is dynamically changing. The
different online approaches are discussed in [4] and [14]. The
drawback of these methods are low accuracy and frequent
introduction of the disturbance to the system. The proposed
variable frequency triangular carrier based PWM technique is
simple to implement and used once at installation of the unit to
estimate the source impedance. The carrier frequency is sweep
from the standard switching frequency of the VSC which is 4
kHz in this case to 1 kHz while VSC is running in close loop
mode or in open loop mode based on the control
implementation. When the carrier frequency sweeps though
the resonance frequency of the LCL unit which now includes
source, it starts resonating. Save the input current and voltage
waveform at point of common coupling (PCC) with sampling
rate at least 5 times standard switching frequency of the VSC
unit to memory. As resonance leads to change in characteristic
of the VSC parameters like DC bus pump up and increase in
input current, the unit can be shut down with either bus over
voltage or input over current in event of uncontrolled
resonance. Fast Fourier Transform (FFT) analysis can be
performed on either input current data or voltage data which
provides the information about resonance frequency. This
resonance frequency can be used to calculate the source
impedance using equation (4) as values of Lg, Lc and Cf are
known.
Lg =
Lc
2
LcC f (2πf res ) − 1
(4)
The above measure grid impedance is used for control of
the active converter, resonance evaluation, weak grid stability
margin analysis and short circuit current level evaluation.
Even after considering the source impedance and tune the
control loop of the VSC, there are some cases where VSC
control cannot avoid resonance. One of the scenarios is shown
3rd The International Conference on Renewable Energy Research and Applications
19-22 Oct 2014 Milwakuee-USA
in figure 4 where two drives are connected to same PCC.
One drives switching frequency is overlapping to other drives
LCL resonance frequency leads to resonance.
Figure 4: Two VSC’s connected at same PCC
Another scenario where the source impedance is very high
approximately 10-15%, which results in distorted input
voltage waveform as shown in figure 5 without any load on
the inverter. The inverter current in figure 6 shows the
significant resonance. The FFT analysis is performed on the
line current, which gives total harmonic distortion around
26.33%. The 13th, 14th, 17th and 18th order harmonics are
dominating as shown in figure 7. The inverter current control
loop turning did not help to prevent this low order resonance.
Active or passive damping techniques will require to eliminate
the resonance. The active damping control techniques are
discussed in references [9]-[12]. The control of the active
damping requires higher control bandwidth and sampling rate.
For better active damping performance requires higher
bandwidth and higher accuracy sensors, low propagation delay
and minimum phase shift of the signal. This leads to increase
the control complexity and higher cost to the end product.
The only easy way to alleviate this problem is by adding
passive damping circuit to the unit which is resonating. The
passive damping also helps to reduce core loss in converter
side inductor.
Figure 6: Input current waveform with inverter modulating and no
load condition
Figure 7: Input phase R current and its FFT analysis
General perspective of the passive damping is an
additional watt loss and low efficiency of the product. This
problem can be solved as shown in figure 8. The damping
resistor is in series with the filter capacitor. The contactor or
switch is in parallel to the damping resistor. The SW1 is in
normally ON position when there is no resonance, which
bypass the damping resistor and increase the efficiency of the
product. When control system detects the resonance, SW1 will
be turn off, which allows putting the resistor in series with
filter capacitor to help damping the LCL resonance. The watt
loss in resistors occur only if there is resonance.
LCL
Lg
Figure 5: Input voltage waveform of inverter without loading
Lc
Cf
C
SW1
VSC
Figure 8: LCL damping resistor switching circuit
ICRERA 2014
3rd The International Conference on Renewable Energy Research and Applications
IV.
19-22 Oct 2014 Milwakuee-USA
SIMULATION AND EXPERIMENTAL RESULTS
The Simulation study has been performed in Matlab
Simulink environment. Simulation results are shown in figure
9 for 300kW VSC with LCL filter (Lc=180uH, Cf=172uF,
Lg=60uH) and an additional source impedance of 60uH.
Without considering source impedance, the resonance
frequency of the LCL filter is about 1.8 kHz. The variable
carrier PWM is used to actuate the resonance started with 4
kHz frequency. For simulation purpose the carrier frequency
changes in steps but can be varied gradually. When the carrier
frequency reduces to 1.65 kHz the resonance is gradually
increases and reaches to highest level at 1.3 kHz. The
equivalent distortion can be observed on the phase to ground
voltage. Frequency analysis is performed on the voltage
waveform gives exact frequency of the resonance. This
information is used to predict the source impedance. Figure 10
shows the FFT analysis of the voltage waveform.
The
resonance frequency component is 1.36 kHz. When calculate
the source impedance using equation (4), it turn out to be
60uH, which match the source impedance values used for the
simulation purpose. When two VSC based drive connected to
same PCC, equivalent scenario can be simulated with adding
1.6kHz noise to the source. For simulation purpose, source
impedance is ignored. Figure 11 shows that when noise
introduce to the source, drive start resonating. When damping
resistor is placed in series with filter capacitor by turning off
the switch SW1 at time 0.55sec reduce the resonance
significantly. FFT analysis of the current waveform is
performed on resonance current with and without damping.
The THD reduced from 128% to 18% as shown in figure 12.
Figure 10: FFT of voltage waveform
Figure 11: Waveform W/WO resonance damping
Figure 9: Resonance using variable carrier frequency PWM
Figure 12: FFT W/WO resonance damping
In order to evaluate the effect of the soft source on the
converter, experiment is performed using 300kW converter
connected to grid using isolating transformer. The isolation
transformer is choose such that it provide soft line condition to
the converter. Significant resonance is observed as shown in
figure 13. By adding damping resistor in series with the
capacitor reduce the resonance as shown in figure 14.
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3rd The International Conference on Renewable Energy Research and Applications
[3]
[4]
[5]
[6]
[7]
[8]
Figure 13: Experimental result: Resonance of the LCL filter
[9]
[10]
[11]
[12]
[13]
[14]
Figure 14: Experimental result: LCL filter with passive damping
V.
CONCLUSION
In this paper, an algorithm is proposed to estimate the
source impedance and deliver the resonance mitigation
technique to eliminate the resonance. The main advantage of
the proposed algorithm is to estimate the source impedance
accurately and use it to tune the control loop to avoid
resonance. In some cases if control cannot avoid the resonance
then propose resonance mitigation technique is used which
switch the damping resistance circuit in series with the filter
capacitor. It alleviate the resonance issue and allow VSC to run
with reduce performance. It is energy efficient solution because
resistor is only in circuit if control cannot avoid the resonance.
Simulation results support the propose claim in this paper. In
addition the experimental results validate the simulation
analysis.
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19-22 Oct 2014 Milwakuee-USA
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