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On the AC Side Interface Filter in Three Phase Shunt Active Power

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On the AC Side Interface Filter in Three Phase Shunt Active Power Powered By Docstoc
					                                           World Academy of Science, Engineering and Technology 70 2010




           On the AC-Side Interface Filter in Three-Phase
                Shunt Active Power Filter Systems
                                    Mihaela Popescu, Alexandru Bitoleanu, and Mircea Dobriceanu


                                                                                     The active filtering performance in terms of harmonic
  Abstract—The proper selection of the AC-side passive filter
interconnecting the voltage source converter to the power supply is                distortion factor of the supply current is substantial influenced
essential to obtain satisfactory performances of an active power filter            by the passive components associated with the VSC structure,
system. The use of the LCL-type filter has the advantage of                        i.e. the interface filter to interconnect the converter to the
eliminating the high frequency switching harmonics in the current
                                                                                   power supply and the DC capacitor.
injected into the power supply. This paper is mainly focused on
analyzing the influence of the interface filter parameters on the active
                                                                                      The main goal of the interface filter is to reduce the
filtering performances. Some design aspects are pointed out. Thus,                 switching harmonic distortion of the injected current as much
the design of the AC interface filter starts from transfer functions by            as possible to prevent the switching harmonics from
imposing the filter performance which refers to the significant current            propagating into the power supply. On the other hand, the flow
attenuation of the switching harmonics without affecting the                       of harmonics to be compensated must be allowed.
harmonics to be compensated. A Matlab/Simulink model of the entire                    Typically, the passive interface filter is either of first-order
active filtering system including a concrete nonlinear load has been               L type or of third-order LCL (inductor-capacitor-inductor)
developed to examine the system performances. It is shown that a                   type.
gamma LC filter could accomplish the attenuation requirement of the
                                                                                      In practice, the simple L filter is not able to ensure the
current provided by converter. Moreover, the existence of an optimal
value of the grid-side inductance which minimizes the total harmonic               active filter dynamics nor to provide sufficient attenuation of
distortion factor of the power supply current is pointed out.                      the current ripple due to the converter switching. An efficient
Nevertheless, a small converter-side inductance and a damping                      alternative is to connect the active filter to the power supply
resistance in series with the filter capacitance are absolutely needed             through an LCL filter as shown in Fig. 1.
in order to keep the ripple and oscillations of the current at the                    As both high and low frequency characteristics of the LCL-
converter side within acceptable limits. The effect of change in the               type filters are superior compared to those of L type, the third
LCL-filter parameters is evaluated. It is concluded that good active               order filters have been increased in popularity in recent years.
filtering performances can be achieved with small values of the
                                                                                      The proper design of the LCL filter is a sensitive action
capacitance and converter-side inductance.
                                                                                   especially when the VSC control is based on hysteresis
                                                                                   controllers which lead to a variable switching frequency.
  Keywords—Active power filter, LCL filter, Matlab/Simulink
modeling, Passive filters, Transfer function.                                         There are a lot of approaches to tuning a LCL filter, most of
                                                                                   them related to interconnecting the VSC to the power network
                              I.   INTRODUCTION                                    in an active rectification structure. In [1], the LCL filter design
                                                                                   is achieved together with the control of the active rectifier
C    ERTAINLY  , the superior performances of the shunt active
    power filters (SAPF) based on voltage source converters
                                                                                   using proportional-plus-integral based control strategies for the
                                                                                   DC voltage and the AC current. In accordance with [2], the
(VSCs) made them the most adopted solution in improving                            total inductance of the filter should be selected at first to meet
power quality of nonlinear loads at the point of common                            the requirement of current ripple and the converter-side
coupling to the power supply.                                                      inductance should be much higher than the grid-side
                                                                                   inductance. Some methods using the resonance frequency and
                                                                                   the attenuation of the line current amplitude at the switching
   Mihaela Popescu is with Faculty of Electromechanical, Environmental and
Industrial Informatics Engineering, University of Craiova, 200440 Craiova          frequency as the main design parameters are presented in
Romania (phone: +40 251 435 255; fax: +40 251 435 255; e-mail:                     literature [3], [4], [5]. To avoid stability problems, passive
mpopescu@em.ucv.ro).                                                               additional damping resistors or active damping solutions have
   A. Bitoleanu is with Faculty of Electromechanical, Environmental and
                                                                                   already been studied and tested [1], [4]. The current control of
Industrial Informatics Engineering, University of Craiova, 200440 Craiova
Romania (phone: +40 251 435 255; fax: +40 251 435 255; e-mail:                     the voltage source inverter connected to the power supply
abitoleanu@em.ucv.ro)..                                                            through an LCL-filter based on state estimators has been
   M. Dobriceanu is with Faculty of Electromechanical, Environmental and           presented in [6].
Industrial Informatics Engineering, University of Craiova, 200440 Craiova
Romania (phone: +40 251 435 255; fax: +40 251 435 255; e-mail:
mdobriceanu@em.ucv.ro).
   This work was supported by Romanian Ministry of Education and
Research, Grant 21-010/2007.




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                                                  World Academy of Science, Engineering and Technology 70 2010




                                                                                      allows expressing the following equations in the domain of
  ua ia               iLa
                                                                                      Laplace transform.
  ub ib               iLb                                          Nonlinear
  uc ic               iLc
                                                                     load             I 1 (s ) = I 2 (s ) + I c (s ) ,                                        (1)

                             Current           Reference current                      U 1 (s ) − U c (s ) = sL1 I 1 (s ) ,                                    (2)
                            controller            calculation

                                                   Voltage         u*DC               U c (s ) − U 2 (s ) = sL2 I 2 (s ) ,                                    (3)
                                                  controller

    ica                     Inverter                                                  I c (s ) = sC f U c (s ) ,                                              (4)
                            control
          icb

                                                                                           Power supply                                           Converter
                icc                                                                           side
                                                                                                                         L2             L1
                       L2                 L1                                                                                                        side

                                                                   C      uDC                                 i2                             i1
                                                                                                        u2                         ic             u1
                                         Cf                                                                                   Cf


Fig. 1 Structure of a three phase shunt active power filter system with
                          LCL interface filter                                          Fig. 2 Equivalent single phase diagram of the idealized LCL filter

    Design considerations on the LCL interface filter between                            As the design process of the passive filter depends on the
the active power filter and the power supply have been very                           attenuation needed to reduce the high switching frequency
little treated in literature.                                                         components of the currents provided by SVC, the transfer
    Different strategies to generate the reference currents for the                   function between converter-side current and grid-side current
current controllers have been analyzed in [7] and the                                 is expressed on the basis of (1)-(4).
advantages of the Fourier method have been pointed out for
imposed values of the LCL filter.
    Contribution [8] had the practical goal to replace the                                    I (s )
                                                                                                              1−
                                                                                                                  U 2 (s)
                                                                                                                              (
                                                                                                                           1 + s 2 L1C f)
                                                                                      H (s ) = 2
                                                                                                                  U 1 (s)
                                                                                                        =                                .                    (5)
                                                                                               I 1 (s )
existing L type interface filter of a four-wire active power filter
                                                                                                                                U ( s)
with an LCL filter in order to diminish the ripple of the current                                              1 + s 2 L2 C f − 2
                                                                                                                                 U 1 (s)
injected into power network. Small inductors in parallel with
damping resistors were selected on the supply- side while the
capacitors selection took into consideration the desired                                Assuming the harmonic frequencies domain, then U2(s)=0
resonant frequency.                                                                   and the transfer function becomes:
    Reference [9] proves that the performances of a passively
                                                                                      H (s ) =
damped LCL filter can be close to those of an active damped                                              1
                                                                                                                    .                                         (6)
LCL filter and that the additional losses are not significant.                                   L2 C f s 2 + 1
    Some transfer functions from the output voltage of a single-
phase inverter to the currents and condenser voltage of the                              The previous expression shows that the attenuation of
LCL filter have been expressed and interpreted in [10]. The                           harmonic currents does not depend on the converter side
total inductance of the passive filter has been chosen                                inductance of the interface filter.
respecting the rated values of DC voltage and maximal current                            The Bode plot in Fig. 3 illustrates the maximum magnitude
through inverter. Then, the effect of distribution of the total                       at natural frequency
inductance over the grid-side and converter-side are analyzed,
while the capacitance is adjusted to maintain an imposed value
                                                                                                    1
of the resonance frequency.                                                            fn =                                                                   (7)
    This paper investigates the influence of the LCL filter                                   2π L2 C
parameters on the active filtering performance based on
Matlab/Simulink time-domain simulations.
                                                                                      and an attenuation of -40dB/decade over the cutoff frequency,
           II. INTERFACE FILTER TRANSFER FUNCTIONS
   The equivalent single phase of the idealized LCL filter (Fig.                       f cutoff = 2 f n .                                                     (8)
2), where the series resistances of the inductors are neglected,




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                                                                    World Academy of Science, Engineering and Technology 70 2010
  Magnitude (dB)




                                                                                                          Magnitude (dB)
                                                  Frequency (Hz)                                                                                      Frequency (Hz)

                   Fig. 3 Frequency response from converter-side current to                               Fig. 4 Frequency responses from VSC output voltage to grid-side
                                       grid-side current                                                     current for LCL-filter (solid line) and L-filter (dashed line)


   Additional transfer functions of the LCL-type filter are
addressed and interpreted in literature, such as I1(s)/U1(s),                                                                           III. INTERFACE FILTER PARAMETERS
I2(s)/U1(s), Ic(s)/U1(s), Uc(s)/U1(s) [1], [8], [10].                                                      In designing the inductors and capacitor values, the
   Among these transfer functions, the admittance transfer ratio                                        harmonic filtering requirements must particularly be taken into
Y21(s)= I2(s)/U1(s) gives information on the advantages of the                                          consideration, i.e. the interfacing filter has to reject the
LCL filter compared to the ordinary first order L filter                                                switching harmonics without affecting the harmonics to be
configuration and can be taken into consideration in LCL filter                                         compensated. For this reason, the cutoff frequency must be
design. It is expressed as                                                                              below the switching frequency in order to obtain a rejection
                                                                                                        current slope of -40dB/decade. Thus, the following condition

                        I 2 (s )
                                                  1−
                                                       U 2 (s)
                                                                (
                                                                1 + s 2 L1C f   )                       is obtained:

Y21 (s ) =
                                                       U 1 ( s)
                                 = sC f
                        U 1 (s )             (                )(
                                        1 + s 2 L1C f 1 + s 2 L2 C f − 1
                                                                         .
                                                                                )           (9)
                                                                                                        fs ≥ 2 fn =
                                                                                                                                             1
                                                                                                                                                      ,                    (11)
                                                                                                                                        π ⋅ 2 L2 C
  In the harmonic frequencies domain, where U2(s)=0, the
expression (9) becomes:                                                                                 where fs is the switching frequency.
                                                                                                           Besides, the minimum frequency which determinates the
                                                                                                        filter pass band must exceed the highest harmonic frequency to
                                           sC f
Y21 (s ) =                                                           =
                        (1 + s             )(                )
                                                                                                        be compensated. Hence, taking into account the superior pass
                                 2
                                     L1C f 1 + s 2 L2 C f − 1
                                                                                           (10)         band limit of f n 2 which has no influence on the input
                                         1
                    =                                                                                   signal, the second condition is expressed:
                        L1 L2 C f s 3 + (L1 + L2 )s
                                                                                                                                    1
                                                                                                        fN ≤                                 ,                             (12)
   The associated frequency response is shown in Fig. 4                                                                     2π ⋅ 2 L2 C
compared to L filter frequency characteristic. It is shown that,                                        where fN is the lowest frequency among the harmonic
if the total inductance is the same, both filters have the same                                         frequencies to be rejected by the interface filter.
behaviour at low frequencies, while the LCL-filter is better at                                            Conditions (11) and (12) can be written together as follows:
high frequencies area since the harmonic admittance decreases
by 60 dB/decade for the LCL-filter compared to 20 dB/decade                                                          1                           1
for the L-filter.                                                                                                                 ≤ L2 C ≤                .                (13)
                                                                                                        2π           2
                                                                                                                           f s2              8π f N
                                                                                                                                                 22



                                                                                                          For instance, by imposing fs = 10 kHz and fN = 2 kHz,
                                                                                                        expression (13) becomes:

                                                                                                        0.51 ⋅ 10 −9 (rad s )−2 ≤ L2 C ≤ 3.17 ⋅ 10 −9 (rad s )−2 .         (14)

                                                                                                          Since the product L2C domain is large and several
                                                                                                        combinations of L2 and C values fulfil the previously




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                                     World Academy of Science, Engineering and Technology 70 2010




expressed conditions, a detailed analysis of the whole active                                   100
filtering system is essential to find an optimal solution.




                                                                           ua /4 (V); iLa (A)
   In addition, although a gamma filter composed of L2 and C                                     50
should be enough to accomplish the current supply ripple
attenuation, the practical implementation of this solution                                        0
makes evident unacceptable high current spike and excessive
rate of current change at the VSC-side, as shown in section IV.                                  -50
Consequently, the converter-side inductance is indispensable
and a damping solution is required.                                                             -100
                                                                                                   0.04   0.045   0.05   0.055   0.06   0.065   0.07   0.075   0.08

     IV. ANALYSIS OF ACTIVE FILTERING PERFORMANCES                                                                        Time (seconds)

   Several computer simulations have been carried out under               Fig. 6 Waveforms of supply voltage (thin line) and distorted load
Matlab/Simulink environment in order to examine the                                     current (thick line) of THD =44%
influence of the interface filter parameters on the active
filtering performances. Thus, the system in Fig. 1 has been                In order to avoid the superposition effect of the DC-bus
implemented into the Simulink model shown in Fig. 5.                    voltage control on the system performances, the assumption of
   The nonlinear load taken into consideration is an                    an ideal DC voltage regulator has been made, so that the DC
uncontrolled rectifier supplying a PWM inverter. The distorted          voltage can be considered constant. A value of 710V has been
load current of THD = 44% and the supply voltage are shown              taken into consideration for this case study.
in Fig. 6.                                                                 The shunt active power filter is charged to compensate both
   The control strategy to generate compensation commands is            the load current harmonics and the reactive power.
based on the Fourier analysis of the distorted load current to             The filtering performances have been appreciated in terms
extract its fundamental component.                                      of tracking of the compensating currents compared to the
   To generate gating signals for the switching devices of the          desired values, the total harmonic distortion factor of the
active power filter the hysteresis-based current (1 A) control          supply current, the ripple current at the converter-side as well
has been implemented.                                                   as of the active filtering effectiveness factor defined as:




                                       Fig. 5 Matlab/Simulink model of the active filtering system

                                                                                                THD L
                                                                        AFE =                         100 ,                                                           (15)
                                                                                                THD S




                                                                  991
                                                               World Academy of Science, Engineering and Technology 70 2010




where THDL and THDS denote the total harmonic distortion                                                                      100

factor of the supply current without and with the APF system.




                                                                                                          ua /4 (V); ia (A)
   Since the attenuation of the converter side current ripple                                                                  50
through the interface filter is essential, the influence of
parameters L2 and Cf has been examined at the beginning.                                                                           0
Thus, as illustrated in Fig. 7, keeping a constant value of filter
capacitance, there is an optimal inductance which minimizes                                                                    -50
the power supply harmonic distortion. Moreover, for both
Cf=0.6µF and Cf= 3µF taken into consideration, the optimal                                                                    -100
                                                                                                                                 0.06         0.065          0.07          0.075               0.08
value of L2 is of about 4mH and the corresponding minimum
                                                                                                                                                       Time (seconds)
THD is of about 6.4%.
                                                                                                                                   Fig. 9 Waveforms of supply voltage and current
                                                                                                                                            for L2= 4mΗ and Cf = 0.6µF
  Supply current THD (%)




                           15                                                                                            600

                                                                                                                         500

                                                                                                                         400




                                                                                                      iDC (A)
                           10
                                                                                                                         300

                                                                                                                         200
                           5
                                                                                                                         100

                                                                                                                               0

                           0                                                                                         -100
                                1    2    3         4      5         6           7   8                                  0.06                 0.065         0.07         0.075           0.08
                                                                                                                     600
                                                 Inductance (mH)
                                                                                                                      400
Fig. 7 Supply current THD versus inductance L2 for Cf = 0.6µF (solid
                                                                                                      i1 (A)




                  line) and Cf = 3µF (dashed line)                                                                    200

                                                                                                                               0
   The current injected into the power supply by the gamma
                                                                                                                  -200
L2C filter tracks the reference current provided by the current
control loop (Fig. 8). As a result, the compensation task is                                                      -400

accomplished, i.e. the supply current is almost sinusoidal and                                                    -600
                                                                                                                     0.06                   0.065         0.07          0.075           0.08
its fundamental is in phase with the voltage supply (Fig. 9).
                                                                                                                                                       Time (seconds)
                                30
                                                                                                                                   Fig. 10 DC-side current and VSC output current
                                20                                                                                                          for L2= 4mΗ and Cf = 0.6µF
                                                                                                                               400
                                10
          i2, iref (A)




                                0                                                                                              200

                            -10
                                                                                                         i1, i2 (A)




                                                                                                                                   0
                            -20

                            -30                                                                                               -200
                              0.06       0.065          0.07             0.075       0.08
                                                   Time (seconds)
                                                                                                                              -400
         Fig. 8 Waveforms of current to be compensated (in black) and                                                            0.04          0.045             0.05           0.055           0.06
                current i2 (in gray) for L2= 4mΗ and Cf = 0.6µF                                                                                         Time (seconds)
                                                                                                  Fig. 11 Input (in gray) and output (in black) currents of the LCL filter
  Although the active filtering effectiveness factor introduced                                                  for L2= 4mΗ, Cf = 0.6µF and L1= 0.1mΗ
by (15) is high (of about 6.8), the lack of converter-side
inductance leads to unacceptable spikes in both VSC input and                                        To reduce the current ripple and oscillations to acceptable
output currents (Fig. 10).                                                                        values, damping resistances are placed in series with the filter
  As it can be seen in Fig. 11, the simple addition of the                                        capacitors (Fig. 12). Thus for instance, by inserting a damping
inductance L1 is not satisfactory due to the significant                                          resistance of 5Ω an important diminution of current
oscillations of the current at the converter-side.                                                oscillations is obtained as illustrated in Fig. 13. The price is
                                                                                                  however the increasing of system losses and a little decreasing
                                                                                                  of AFE factor value to about 6.




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                                                                               World Academy of Science, Engineering and Technology 70 2010




                                                                                                                                                         V. CONCLUSIONS
                                               i2      L2                       L1
   Power supply                                                                            i1         Converter
      side
                                                                                                                               The use of the LCL-type filter to interface the three phase
                                                                                                        side
                                                                                                                            SAPFs based on VSCs to the power supply is an efficient
                                                                                                                            solution due the ability of eliminating high order switching
                                                            Rd                                                              current harmonics. As the tuning process based on transfer
                                                                                                                            functions is rather flexible, time-domain simulations have been
                                                            Cf
                                                                                                                            carried out to find optimal parameters of the interface filter in
                                                                                                                            order to improve the active filtering performances. Although
                                 Fig. 12 LCL interface filter with damping resistors
                                                                                                                            the lack of converter-side inductance seems to have no
                                100
                                                                                                                            influence on the current tracking performance, a small
                                                                                                                            converter-side inductance and a damping resistance in series
                                 50
                                                                                                                            with the filter capacitance are absolutely needed in order to
                                                                                                                            keep the ripple and oscillations of the current at the converter-
    i1, i2 (A)




                                     0                                                                                      side within acceptable limits.
                                                                                                                               The existence of an optimal power supply-side inductance
                                 -50                                                                                        which minimizes the total harmonic distortion factor of power
                                                                                                                            supply current is pointed out.
                                -100                                                                                           It is concluded that good active filtering performances can
                                   0.04              0.045              0.05               0.055               0.06
                                                                 Time (seconds)
                                                                                                                            be achieved with a smaller capacitance and smaller converter-
                                                                                                                            side inductance compared to the corresponding values in
Fig. 13 Input (in gray) and output (in black) currents of the LCL filter
                                                                                                                            literature [8], [9], [10].
          for L2= 4mΗ, Cf = 0.6µF, L1= 0.1mH and Rd= 5Ω

  The harmonic spectra of the current through inductances L1                                                                                               REFERENCES
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                                                                                                                            [3] P. Peltoniemi, R. Pollanen, M. Niemela, and J. Pyrhonen, “Comparison
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                                10
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over 150th order (Fig. 14b).




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