Open Science Repository Engineering
LCL Filter for 3-Ø Stable Inverter Using Active Damping Method (Genetic Algorithm)
Rajendra Aparnathi , Ved Vyas Dwivedi 
 Faculty of Technology and Engineering, Maharaja Sayajirao University of Baroda, Gujarat, India
 Noble Group of Institutions, Junagadh, Gujarat, India
The use of an LCL-filter mitigates the switching ripple injected in the grid by a three-phase active rectifier or three-phase voltage source inverter. However stability problems arise in the current control loop. In order to overcome them a damping resistor can be inserted, at the cost of efficiency. On the contrary, the use of the active damping seems really attractive but it is often limited by the use of more sensors with respect to the standard control and by the complex tuning procedure. This research paper introduces a novel active damping method that does not need the use of more sensors and that can be tuned using Genetic Algorithms (GA) for optimized performance. It consists of adding a filter on the reference voltage for the converter/inverter modulator. The tuning process of this filter is easily done, for a wide range of sampling frequencies using GAs.
Keywords: LCL filter, direct power control (DPC), voltage source inverter (VSI), voltage oriented control (VOC), pulse with modulation (PWM).
Citation: Aparnathi, R., & Dwivedi, V. V. (2013). LCL Filter for 3-Ø Stable Inverter Using Active Damping Method. Open Science Repository Engineering, Online(open-access), e70081934. doi:10.7392/Engineering.70081934
Received: January 24, 2013
Published: February 28, 2013
Copyright: © 2013 Aparnathi, R., & Dwivedi, V. V. Creative Commons Attribution 3.0 Unported License.
The front-end stage of a power
converter is not a mass produced product. In fact, it should be specifically
designed for the application it is used for, such as chemical, electrolysis,
aluminium, graphitizing furnace, zinc electrolysis, copper refining, traction
substation, AC and DC drive system. If the attention is focused to applications
that can take advantage from dc voltage regulation, the diode bridge with
on-load tap changers or with saturable core reactors and the thyristor-bridge are still the
preferred design solutions in respect to diode-bridge plus
chopper systems . For historical reasons, the diode-bridge plus chopper have
been considered as the “new” solution in the rectifier field. In fact the
chopper has been successfully experimented in traction system over the past
three decades. Hence, it was quite natural to consider the chopper as the next
step also for other rectifier applications. However, the use of a chopper stage
increases the number of switching devices, which results in a higher failure
rate and mean time to repair [1 - 2].
In this scenario, active rectifiers,
employing the VSIs are valid competitors both for traditional solutions, such as
thyristor, and for newer ones, as chopper, due to the
reduced number of power devices and the enhanced capability of grid current
and power factor control. Particularly VSIs, employing PWM techniques, are the
widest used power converters for applications such as industrial motor drives,
robotics, air conditioning and ventilation, uninterruptible power supplies and
electric vehicles ,. Thus they are considered as prime candidates for
interfacing high-power electronic equipment to power supply lines.
Over the last few years an interesting
emerging control technique, the direct power control (DPC), has been developed
analogously with the well-known direct torque control used for adjustable speed
drives. In DPCs, there are no internal current loops . PWM
modulator blocks, because of the converter/inverter switching states, are
appropriately selected by a switching table based on the instantaneous errors
between the commanded and estimated values of active and reactive power. The
principal drawbacks are the need for a high sampling frequency required to
obtain satisfactory performance and the variable switching frequency. However,
this can be solved by the combination of a modulator and the DPC-technique ,,.
Adjustable speed drives in hoisting applications
(cranes and elevators), in high inertia applications (centrifuges) and in the
end stage of wind turbines have highly demanding safety issues but cannot adopt
high inductance values. Thus the use of an LCL-filter on the ac side is an
interesting solution: reduced values of the inductance can be used and the grid
current is almost ripple free. In this way, a low THD
of the current is obtained. The design of the LCL-filter has already been
investigated. Attention has also been
paid to the possible instability of the system caused by the zero impedance
that the LCL-filter offers at its resonance frequency [7 – 10]. Some passive
damping solutions of the filter have already been studied, tested and
industrially used in the switching converter field.
The use of a damping resistor increases the
encumbrances, the losses could result in need for more cooling (e.g., forced)
and efficiency decrease becomes a key point. Thus, it seems very attractive to
use an active damping method by means of control in order to avoid system
instability without increasing the losses. This solution has already been
partially studied. A proposal is made to add a derivative action based on the
line side current in the current control loop; thus new sensors are needed. The
LCL-filter capacitor voltage is controlled with a lead-lag network; the tuning
of the network is described. Moreover an interesting approach to perform active
damping is proposed: a virtual resistor is added. The virtual resistor is an
additional control algorithm that makes the filter behaves as if it had a real
resistor connected to it. This approach is attractive because it can be related
to a “real” physical component. In this case, an additional current sensor is
needed if the virtual resistor is connected in series to the filter inductor or
capacitor and an additional voltage sensor is needed if it is connected in
parallel , .
All the previous active damping methods
require additional sensors and they do not mention the influence of the damping
on the dynamics and on the susceptibility of the system. In this paper a new
damping method is introduced. It does not need the use of additional sensors
and the tuning can be done with the help of genetic algorithms. Soft computing,
such as genetic algorithm, has been successfully applied both to drive control
and to the design of a single-phase rectifier system. Genetic algorithms are
used to optimize the poles. Placement of an observer using a cost function that
takes into account the system dynamics. A single-ended boost PFC converter is
optimized to fulfill the PFC and EMI standards. In short, the genetic
algorithms have been considered particularly suitable to optimize nonlinear
trade-off problems involving multiple parameters. The proposed active damping
is based on the use of a filter on the reference voltage for the modulator. The
tuning process of this filter is easily done, for a wide range of sampling
frequencies, with the use of genetic algorithms. This method is used only for
the optimum choice of the parameters of the filter and an on-line
implementation is not needed .
The analysis is validated with three design
cases characterized by different requirements in terms of stability and dynamic
performance. Section II of this paper describes the modeling of an LCL filter
based active rectifier, while the controller modeling is explained in section
III. The current control loop analysis has been presented in section IV, and
section V discusses about the active damping methods. The stability analysis is
highlighted in the section VI of this paper which leads to discussions on the
results followed by a good potential references.
2. Modelling the LCL filter based active
The LCL-filter based VSI active rectifier is modelled in
 is reproduced here in Fig. 1:
Fig. 1: Three-phase LCL-filter based active rectifier 
The differential equations for the LCL-filter in the
stationary reference frame are expressed in (1)-(3).
For rotating frame,
the (1)-(3) can be rearranged as in (4)-(9) in the dq
are grid currents; and ia2
inverter/converter currents; io
is total o/p current; iC
is the o/p
current passing through the o/p balancing capacitor(C) being used as a filter; iL
is the o/p load current. ea
is the voltage observed at
filter capacitor (Cf
are i/p inverter voltages; Vo
is grid inductance while R2
is inverter/converter inductance; and S represents the inverter/converter
Also in this case, the (4)-(9) show how both
the currents and the capacitor voltages are dependent on the cross-coupling
(t) and ωiq
Low and high frequency
models, as well as the use of coordinate transformation and small-signal
linearization for control purposes, are needed in order to design the basic
controls such as phase control and current control of the active rectifier
A. AC current controller
The entire ac
current control (CC) is more suitable because the current controlled converter
exhibits, in general, better safety, better stability and faster response. This
solution ensures several additional advantages. The feedback loop also results
in some limitations, such as that fast-response voltage modulation techniques
must be employed, like PWM. Optimal techniques, which use pre calculated
switching patterns within the ac period, cannot be used, as they are not
oriented to ensure current waveform control ,,, .The CC has been
applied to active rectifier in order to ensure dc-link voltage regulation. The
current controlled rectifier has been applied to front-end operation in ac
drives with dc-link voltage regulation. The use of an LCL-filter claims for a
deep dynamic and stability analysis of the current control loop , .
axis-based current control
The most used control
technique is the two axis-based Voltage Oriented Control
(VOC) as shown in fig 2. Rectifier is based on the use of a rotating dq
-frame oriented technique such as the d-axis is
aligned on the grid voltage vector.
The space-vector of the fundamental has
constant components in the dq
-frame while the
other harmonic’s space vectors have pulsating components. The main purpose of
the active rectifier is to generate or to absorb sinusoidal currents. The
components of the reference current in the dq
are dc quantities. The reference current d-component
) is controlled to perform the dc voltage
regulation, while the reference current q-component
) is controlled to obtain a unity power factor. To have the grid current
vector in phase with the grid voltage vector, i*q
should be zero. The dc-link
voltage control is achieved
through the control of the power exchanged by the converter. The dc-link
voltage loop is the outer loop and the current loops are the inner loops. These
internal loops are designed to achieve short settling times and unity gain. On
the other hand, the main goals of the outer loop are optimum regulation and
stability, thus the voltage loop could be designed to be 5-29 times slower .
Therefore, the internal and the external
loops can be considered decoupled, and there by the actual grid current
components can be considered equal to their references when designing the outer
dc-link controller .However some instability in the dc-loop can arise when
the rectifier is working in the re-generative operation. This kind of approach
can be easily used to design more advanced control methods such as Lyapunov-based and sliding mode controllers have been
adopted aiming to system stability and the absence of steady state errors
C. Emerging control techniques
Fig. 2: Voltage Oriented Control based on the use of a rotating
No amongst the different emerging control techniques the Direct Power
Control (DPC) is gaining interest for its simple implementation while Fuzzy
Logic and Genetic Algorithm for their capability to optimize the system
performance, if current sensors are not adopted, or
if active damping has to be implemented , .
Level-1 Direct power control
: A level-1 in the last years the most
interesting emerging technique has been the direct power control developed in
analogy to the well-known direct torque control used for drives. In DPC there
are no internal current loops and no PWM modulator block because the converter
switching states are appropriately selected by a switching table based on the
instantaneous errors between the commanded and estimated values of active and
reactive power shown in Fig 6. The main advantage of the DPC is in its simple
algorithm instead the main disadvantage is in the need for high sampling
frequency required to obtain satisfactory performances , .
Level-2 Genetic algorithm:
Fig. 3: DPC based on the active and reactive power calculation
A level-2Soft computing, such as genetic algorithm, can be
used to optimise the design of rectifier systems ,  or to adapt the
parameters of advanced controls such as active damping. Particularly introduces
a new active damping method that does not need the use of more sensors and that
can be tuned using genetic algorithms. It consists of adding a filter on the
reference voltage for the converter’s modulator. The tuning process of this
filter is easily done, for a wide range of sampling frequencies, with the use
of genetic algorithms. This method is used only for the optimum choice of the
parameters of the filter and an on-line implementation is not needed. Thus the resulting
active damping solution does not need new sensors or complex calculations 
4. Current loop analysis
AC current control (CC) is considered particularly suitable for active
rectifiers due to its safety, stability performance and fast response. Usually
the CC is implemented in a dq-rotating frame that has
the d-axis oriented on the grid voltage .
Thus the controller structure is cascaded,
because the dc voltage controller calculates the reference value for the d-axis
current controller shown in Fig. 4. Typically, the inner current loops are at
least ten times faster than the outer loop controlling the dc voltage .
Fig. 4: ARC structure with dq-axis oriented cascaded control
It is demonstrated that in the low frequency
filter behaves like an inductor where
. Thus the low frequency model used to set the controllers
(frequencies approximately lower than one half of the resonance frequency), should
be written neglecting the filter capacitor Cf
is the switching
is the space-vector of
the rectifier input voltages,
is the space-vector of
the controlled currents,
is the space-vector of
the input line voltages.
The space-vector of the fundamental harmonic
has constant components in the dq
the other harmonic space vectors have pulsating components. The main purpose of
the active rectifier is to generate or to absorb sinusoidal currents which
represent active and reactive power; thus the reference current components in
-frame are dc quantities . The
reference current component
is controlled to perform the dc voltage regulation while the
reference current component
is typically controlled to obtain a unity power factor. In fig
4 the grid voltage and dq
compensations are adopted; as such, both the d-axis or q–axis have the plant
model equation (12) that can be used to tune the PI-controllers.
Where the time constant is
The design is made using the zero/pole-placement in the
z-plane and with the “technical optimum” as a criterion all the processing and modulation
delays have been taken into account. As such, the parameters are expressed in
is the sampling time. The filter capacitor Cf
previously neglected, only influences the current loops. In fact, the capacitor
introduces zero and poles around the resonance frequency that do not modify the
slow dc voltage loop. The d- and q-current loops are equivalent in the
stability and dynamic analysis because once the compensations of the grid
of the cross-coupling
are made, they have the same system plant behavior. If the
converter side current is sensed, the system plant for control is [1, 3]
If the grid side current is sensed, the plant
for control is
. The un-damped closed loop transfer function
(Z) can be expressed as in (16).
G(z) being the zero order hold (ZOH) equivalent
of G(s) and D(z) the controller usually designed on the basis of the “technical
optimum.” In the following paragraphs, the stability and dynamic of the overall
system are analyzed through the zeros and poles of the closed loop system in
the z-plane and with the Bode plot .
Active damping of the current loops
current controlled system can be made stable by changing the control algorithm,
thus using so called “active damping.” In this case the active damping is
obtained with a filter on the voltage reference for the modulator as shown in
Fig. 5. The basic idea can be explained in the frequency domain by introducing
a negative peak with the filter that compensates for the resonant peak due to
the LCL-filter as shown in Fig.6. However, even if the solution seems simple,
an optimization process for the choice of filter must be done in order to have
the desired stability of the system and to preserve dynamics performance [11,12]. A GA is well suited to solve this optimization problem
A. Genetic algorithm
Fig.5: Active damping using a filter on the voltage reference for the modulator
The GA attempts to simulate Darwin’s theory
on natural selection and Mendel’s work in genetics on inheritance: the stronger
individuals are likely to survive in a competing environment. The GA uses a
direct analogy of such a natural evolution. By evaluating many solutions of an
assigned problem and combining them, the best one can be found. This method,
also called derivative free optimization, does not need functional derivative
information to search for a set of parameters that minimizes (or maximizes) a
given objective function. Derivative freedom also relieves the requirement for
differentiable functions, so an objective function can be used which, despite
its complexity, avoids sacrificing too much computation time in extra coding.
The GA considers the optimal solution of a problem as an individual , .
Fig. 6: Active damping action and the resulting transfer function of the stable system
The characteristics of the individual are due
to the genes of his chromosomes in much the same way that the characteristics
of a possible solution are due to its parameters. Thus, as the desired
individual can be created through an evolutionary. Process starting from a
random choice of individuals forming a population, the optimal solution can be
found through a combination of a random set of solutions. In the following, the
term “individual” indicates the possible solution, the term “gene” indicates
one of the digits of the parameter of the solution and the “fitness value”
indicates the degree of goodness of the individual [20-21]. The GA is both
flexible and strong. Although it is a stochastic method, the fitness function
and the encoding scheme give the search a solid and rational structure.
Initialization of the GA is done by choosing the representation to be used and
the size of the population. Subsequently, one needs to specify the crossover
and mutation probabilities and a stop criterion . The GA process is
performed through the following iterative steps:
the individuals are selected on the basis of their fitness value to reproduce
in the mating pool;
each new individual is generated by two that are reproducing. This process is
performed using part of the genes characterizing each individual;
the way to randomly produce new characters in the new individual of the
population by changing one of its genes.
These genetic operations, if correctly
implemented, can solve different kinds of problems.
B. Use of genetic algorithm for active damping optimization
A generic solution “i”
of the problem is characterized by the following parameters: the coefficients
of active damping filter
and proportionality constant
of the PI current
mathematically expressed in (17-18):
The GA only needs a small amount of
information from the overall system to solve, for example, stability problems
or dynamic specification. This flexibility facilitates both structure and
parameter identification in complex models such as the LCL-filter active
rectifier. The active damping optimization algorithm is organized with a GA
sub-routine for each coefficient
. The aim of each
routine is to find the best individual the current controlled system can be
made the best
the best proportional
constant of the PI, current controller
in order to have the desired damping of the high frequency
poles and the desired bandwidth of the current loop .
The first step is to decide on the desired
position of the two pairs of complex-conjugate poles and how important it is
for the algorithm to find a solution that minimizes the distance
in respect to the first pair and the distance
in respect to the second pair. This is mathematically
expressed through the so called fitness value f(i) of each individual ‘I’ in (19).
are the weights used to give more or less importance. to the desired damping of the high frequency poles or of the
bandwidth of the current controller. If
, the main aim is to obtain the desired damping of the high
frequency poles, while if
the main aim is to have the desired dynamic performance. The
flow chart of the optimization algorithm is shown in Fig.7. Initially, the
dimension of the population should be chosen (i.e., the starting number of
possible solutions): too many individuals are not a good choice as the method
becomes a random search and the convergence may not be reached. The number of
individuals chosen to be 20 and will be constant during the evolution. This
means that the new individuals will replace the old ones. Subsequently, the
system-closed loop transfer function in the Z-domain is used to determine the
position of the conjugate complex poles in the Z-plane in order to evaluate the
fitness value. The f(i) of
each individual i. “Elitism” is used to prevent the
best individuals from being eliminated. This operation is used to avoid having
all the genes modified by crossover and mutation in a way that no good solution
will ever exist. Moreover, it increases the convergence speed of the algorithm
Fig. 7: Algorithm used to search for optimum parameters of active damping on the basis of the genetic algorithm
Genetic operations of selection, crossover
and mutation are used to produce the next generation of solutions suitable for
the problem. The selection operation determines which individuals participate
in producing the next generation. These members enter the mating pool with a
selection probability proportional to their fitness values. After this step, a
“two-point crossover” scheme is used. Crossover cannot reach the best solution
if the population does not contain all the encoded information needed to solve
the problem. Mutation allows other possible solutions to be generated and
uniform mutation is adopted so that each bit has the same probability of
mutation. This operation provides random excursions into new parts of the
search space. There are many ways to terminate a GA, many of them similar to
termination conditions used for conventional optimization algorithms ,
C. Using the
genetic algorithm for active damping optimization
The individuals are generated randomly by the
MATLAB algorithm “rand.” The elitism is then applied using the MATLAB algorithm
“sort”: the vector composed by the fitness function a value of a generation is
rearranged in such a way that the best fitness values are ranked last in the
vector and they will not participate in crossover and mutation, i.e., they will
continue to survive in the next generation. The individuals which are not part
of the elite group will reproduce in the mating pool. The individuals have been
encoded using the MATLAB “num2str.” In this way, each digit of the coefficient,
representing a gene, is part of a string and it can be exchanged with another
individual (crossover) or randomly changed (mutation). The “crossover” is
implemented, randomly choosing where to cut each individual string. The string
is divided into three parts and the “two point crossover” is adopted as the
increase of the cutting points reduces the algorithm performance , .
The crossover is performed with a
probability of 100% which means it is executed at every cycle. The “mutation”
is implemented randomly changing. One gene on chromosome stands for one digit.
The “mutation” is performed with a probability of 1%,
otherwise the genetic algorithm could result in a random search. The number of
individuals chosen for elitism is determined by the need to find the best
solution with a reduced number of attempts. The elitism is chosen equal to 6
(30% of the population) and is a good trade-off between the need to find the
best possible solution and the convergence of the genetic algorithm search. The
relation between the two weights adopted for the cost function, one for the
“dynamic” poles and the other for the “stability” poles, depends on which aim
is considered more important. If the pole position indicated is reasonable. A
good strategy in choosing reasonable aims is to individuate the passive damping
needed to have the desired position of the high frequency poles and the
proportional coefficient needed to have the desired bandwidth. Then the genetic
algorithm tuning can be used to reach both the stability and dynamics of the
overall system, thus finding a good trade-off oriented in a preferred direction
with a small number of attempts in comparison with complex optimization
algorithms that usually work well in the neighborhood of the initial state.
Since the initial state is often unknown in the tuning of the active damping
network and the number of constraints can differ from the number of
coefficients to be optimized, the genetic algorithm can also guarantee a sensible
reduction of the hours needed for the tuning .
6. Stability analysis
the damping of the system is chosen in a qualitative manner, resulting in a
decrease of efficiency and unknown dynamic of the system. Design guidelines for
both passive and active damping are given and with different approaches.
However, the possible variants in the system configuration, due to the position
of the current sensors, presence of delays, tuning of the PI parameters and
switching frequency are many. Thus passive and active damping have sometimes
opposite effects in different systems. The un-damped system is always unstable
if the current sensors are on the converter side, can be stable if the grid
sensors are on the grid side. It is worth to highlight that these results as
shown in Fig.8 (a) and (b) are strongly dependent on the parameters of the LCL
filter. Thus it is very important to clearly fix the constraints both on the
damping of the two high frequency poles and on the dynamic of the system (thus
on the damping of the right plane poles). It is difficult to comply with them
using a simple design method; thence it is very attractive to use soft
computing optimizing methods such as genetic algorithm in shown in Fig.8 (a)&(b) .
Discussion on results
The LCL filter consists of
an LC filter 3.5mH, and on the grid side, the transformer’s inductance as
2.7mH. The setup consists
• Inverter/converter rated power: 1KVA
• Rated input LCL filter frequency: 50-60 Hz
• Rated output voltage: 3x230 V
• Rated output frequency:50-55Hz
• Rated output current: 4.6/4.8 A(max)
• 2 series connected Delta Electronica DC power supplies
• Type: SM300 D10
• Rated power: 3KW
• Rated current: 10A
• Rated voltage: 330V as shown in Fig.9, and result
output waveform shown in Fig.10 to Fig.15.
Fig 8(a) shows in position of poles and
zeros without optimization and fig 8(b) uses GA optimization method stable
position of poles and zeros. Research project set-up in laboratory circuit diagram
using inverter, microcontroller for PI controller using PWM modular, LCL filter
with connected grid system in shown Fig.9.Using Psim
software and design model of 3-Ø inverter using 8KHz PWM frequency and LCL
filter though connected 3-Ø grid system shown in Fig.10 and Psim
research model result o/p voltage, current LCL filter waveform and o/p grid
voltage, current waveform system is stable some second shown in Fig.11. Using
MATLAB software and design research model using value of different parameter in
Fig.12 and o/p 3-Ø voltage, current waveform and filter waveform fuel cell
waveform and after some second system will be stable shown in Fig.13. Now
research model design and on line implement using this parameter and switching
frequency shown wave form o/p inverter voltage and though LCL filter connected
in 3-Ø grid in Fig.14 and Fig.15.
Fig. 8: Closed loop current root locus with GA optimized active damping (a) starting population (b) final results
Fig. 9: Experimental set up
Fig. 11: Output waveforms of the Psim model shown in Fig. 10
Fig. 12: MATLAB proposed model
Fig. 13: Output Vo, Io & fuel cell
(MATLAB results for the research)
Fig. 14: Output result waveform
Fig. 15: Output waveform with LCL-filter
This research work focuses on the design of the active
damping for three-phase active rectifiers as a three-phase inverter using a
genetic algorithm. It is not possible to define an ideal classic design method
for active damping that could be valid for the position of the current sensors,
the voltage sensors, the presence of delays, the tuning of the PI parameters
and the sampling frequency. Thus the genetic algorithms are good solution to
find the best parameters of the active damping methods. In particular, they
have proved to be particularly suitable in reducing the susceptibility of the
system in a high polluting environment. Moreover it is possible to define the
desired bandwidth of the current control and the desired damping of the high
frequency poles and make them have different weights in the GA-based
optimization process. Genetic algorithms are used only for the optimum choice
of the parameters of the active damping method using off-line application and
it is not used in on-line implementation.
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Cite this paper
Aparnathi, R., & Dwivedi, V. V. (2013). LCL Filter for 3-Ø Stable Inverter Using Active Damping Method. Open Science Repository Engineering, Online(open-access), e70081934. doi:10.7392/Engineering.70081934
Aparnathi, Rajendra, and Ved Vyas Dwivedi. “LCL Filter for 3-Ø Stable Inverter Using Active Damping Method.” Open Science Repository Engineering Online.open-access (2013): e70081934. Web. 28 Feb. 2013.
Aparnathi, Rajendra, and Ved Vyas Dwivedi. “LCL Filter for 3-Ø Stable Inverter Using Active Damping Method.” Open Science Repository Engineering Online, no. open-access (February 28, 2013): e70081934. http://www.open-science-repository.com/engineering-70081934.html.
Aparnathi, R. & Dwivedi, V.V., 2013. LCL Filter for 3-Ø Stable Inverter Using Active Damping Method. Open Science Repository Engineering, Online(open-access), p.e70081934. Available at: http://www.open-science-repository.com/engineering-70081934.html.
1. R. Aparnathi, V. V. Dwivedi, LCL Filter for 3-Ø Stable Inverter Using Active Damping Method, Open Science Repository Engineering Online, e70081934 (2013).
1. Aparnathi, R. & Dwivedi, V. V. LCL Filter for 3-Ø Stable Inverter Using Active Damping Method. Open Science Repository Engineering Online, e70081934 (2013).
Research registered in the DOI resolution system as: 10.7392/Engineering.70081934.
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