A Three-Phase Three-Level T-Type Converter for Three-Phase Four-Wire (3P4W) Active Power Filter

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A Three-Phase Three-Level T-Type Converter for Three-Phase Four-Wire (3P4W) Active Power Filter

Bisrat Gezahegn Lemma1, Minfu Laio2*, Duan Xiongying 3

1,2,3, Institute of Electrical and electronics: a school of Electrical Engineering,

Dalian University of Technology Dalian, China

AbstractThree-phase four-wire system is commonly used in residential, commercial and educational centers. However, the three-phase four-wire system has suffered from harmonic, reactive, excessive neutral current and imbalanced loads. In the proposed control, a modified sensitivity function based RC controller was investigated for a three-phase three-level T-type converter to mitigate harmonics, reactive and neutral current caused by the ever-increasing nonlinear loads. The results were analyzed and presented in collaboration with the MATLAB/Simulink environment and the TMS320F28335 board. The proposed control achieved a harmonic compensation, reactive power correction, reduction of neutral current and balancing loads. Therefore, the three-phase three- level T-type converter active power filter can be taken as a good candidate for load harmonics, reactive, and neutral current compensation.

Keywords Three-level; T-type converter; Active power filters; power quality.

  1. INTRODUCTION

    Three-phase four-wire (3P4W) distribution feeders have been used for low voltage systems. The power feeder is taken from the secondary side of the Y distribution transformer to deliver power for residential, commercial, manufacturing- offices and educational centers of single/ three-phase loads. In the present day, single-phase nonlinear loads have been increasing into the low voltage distribution systems. This is due to the attractive features of the appliances from the customers point of view for the ever-increasing requirements of information technology [1] and electric traction [2], [3] [4]. The nonlinear and traction loads have known with an imbalance in the grids. In the case of non-sinusoidal source or unbalanced nonlinear load, the neutral current problem will be serious in the three-phase four-wire system. In the three-phase four-wire distribution cases, the third harmonic current contributed by each single-phase nonlinear load will add up together and results in three times the zero-sequence components of phase current. Moreover, the three-phase four- wire system is exposed to unbalanced loads due to single- phasing and abnormal phase change in the industry.

    The distribution engineers are tried to distribute loads at the design stage equally among the phases to maintained low neutral-line current and better efficiency. However, this is not possible for large loads moreover single-phase loads switched on/off from the system in an unpredicted manner. Moreover, even the balanced single-phase nonlinear loads contribute a significant neutral current. Therefore, in today's three-phase

    four-wire distribution systems excess neutral current, load unbalances and high total harmonic distortion (THD) is a challenging practice.

    The harmonic currents on the three-phase four-wire system have negative effects on phase line(s), /Y distribution transformer and neutral conductor. The harmonic effects on the phase line(s) increase harmonic distortion and power losses. Similarly, harmonic increases the circulation of zero sequences harmonic current on the neutral line and delta winding of distribution transformer. The neutral current depends upon the type and condition of the load in the system. In many cases, the neutral-line current exceeds the phase line- current. An excessive neutral-line current causes overloading of distribution transformer and feeder, rise common mode noise, flat topping voltage waveform. The excessive neutral- line current may raise the potential of the neutral line to cause an accident. It's flat-topping voltage waveform also affects the normal function of precision devices.

    Different researchers have investigated different configurations using the passive filter, star-delta transformer, zigzag-transformer, single/three-phase active power filter, and a combination of the above [5],[6],[7],[8],[9]. The passive filter has been proposed in [FBD] with resonance LC filter branches for dominant positive/negative sequence and zero sequences. The passive filter has low cost and simple to implement with the system. However, the passive filter might losses its tuning performance to the target frequency due to component aging, and creates a series/parallel resonance with the system inductance [10]. The Zigzag transformer is a low cost, high-reliability option to create a low-impedance path for zero-sequence current and open circuit for positive-sequence or negative-sequence current. However, the zig-zag transformer may not be a good option for a system with an unbalanced utility voltage. Because its low-impedance path for zero-sequence source voltage may aggravate the problem of neutral current and even may burn-down the Zig-Zag transformer, the neutral conductor and the distribution power transformer [11]. Moreover, its neutral line current attenuation level determined by the source side to the zig-zag transformer impedance ratio [8, 12]. The DY transformer connected in series with a reduced switched three-phase active has been proposed in [12] to achieve a reduction of neutral current. However delta-star transformer is expensive and its filtering performance depends upon its installation location.

    The multilevel pulse-width-modulation has advantages on its higher efficiency up to medium switching frequency range,

    better harmonic characteristics and smaller output voltage steps as compared to the two-level VSIs [13, 14]. Among the multilevel converter, the T-type topology is much preferred for its reduced number of switching semiconductors than neutral point clamped (NPC). Thus the T-type converter has lower power losses as compared to the NPC [15]. The authors proposed a sensitivity function based repetitive controller (RC) for a three-phase three-level T-type converter [16] to mitigate dominant load harmonic frequency, reactive power, and reduced neutral current. Therefore, the research has significant importance for harmonic and reactive compensation in low voltage applications to improve power quality. In many works of literature, the repetitive controller (RC) is preferred for the active power filter controller due to its good tracking ability and high gain for the desired frequencies [17]. The instability of the RC control is limited by applying a modified squaring sensitivity function [18], [19]. This provides a wide and deep notch at the selected frequencies. The rest of the paper is organized as follows: Section 2 describes a three-phase four-wire three-level T-type converter configuration, section 3 explains the repetitive controller for inner controller section 4 presents simulation and experimental results, and finally, the conclusion is drowned in section 5.

  2. MODEL OF THE SYSTEM

    Fig.1 presents the three-phase four-wire three-level T-type converter with the mixed linear and nonlinear load. The

    converter. The state-space model of the T-type converter is defined as [16]:

    = +

    1 1 + 2

    =

    1 1

    2 1 + 2

    =

    1 2

    (2)

    = +

    1 1 + 2

    =

    1 1

    2 1 + 2

    =

    1 2

    (2)

    Wherethe converter output voltage, vinvxO = Tx1vC1 Tx2vC2 , converter current, ip = Ta1ica + Tb1icb + Tc1icc and in = Ta2ica + Tb2icb + Tc2icc , and the capacitor voltage v1 and v2 respectively. The neutral load current, io = Ta3ica + Tb3icb + Tc3icc.

  3. REPETITIVE CONTROLLER FOR INNER

    CURRENT LOOPS.

    The dynamic of the inner current controller GI(s) is design using the transfer function as:

    () 1/

    () = () = / + 1

    , = 2 ( + 0)

    2

    = 2 (

    (3)

    , = 2 ( + 0)

    2

    = 2 (

    (3)

    The inner controller is discretized with the zero-order hold (ZOH) discretization method. The source voltages are defined as:

    )

    converter has two mono-directional switches (Tx1, Tx2) and

    ,

    3

    4

    Tx1 + Tx2 + Tx3 = 1

    (1)

    Tx1 + Tx2 + Tx3 = 1

    (1)

    one bidirectional switch (Tx3) per phase. Three-phase four- wire active filter is applied to guarantee a unity power factor and to set a balanced three-phase current in the network. The PI controllers are used to regulate the dc-bus voltage variation and the voltage difference between the capacitor. The RC controller is used to compensate for the harmonics and reactive power for the nonlinear loads. The main objective of this controller is to achieve a unity power factor using the proper operation of two power switches and one ac power switch in each leg of the active power filter. The switching states in each leg to generate a unipolar voltage pattern are given as :

    Where Txi = 1 if switch Txi is switched on and Txi = 0 if switch Txi is switched off and i = 1, 2, 3 stands for the upper, bottom and inner legs respectively. Similarly, x = a, b, c stands for the three-phase. The power switch Tx1is turned on to generate a positive ac-side voltage, vx0 which is equal to,

    Vdc. This effect reduces the compensation phase current, i as

    vs,c = Vs2 sin (r 3 )

    In the Fourier series, the steady-state load current of the

    three-phase four-wire system is usually a periodic signal with only odd harmonics. The current in each phase can be written as:

    il,x = an.x sin(r(2n + 1)t + x)

    n

    + bn.x cos (r(2n + 1)t + x)

    (4)

    where an.x, an.x R is the real Fourier series coefficients of the x-phase current. The load currents of the three-phase nonlinear loads are composed of the fundamental active current, fundamental reactive current, and harmonic current.

    il,x = il,x,p() + il,x,q() + il,x,h()

    (5)

    The active nonlinear load current and the active current of the converter are supplied by the ac source:

    isx,p = ic,x,p() + il,x,p()

    (6)

    When the SAPF control meets its goal, the load can be

    2

    sx

    sx

    the boost inductor voltage is negative,L dicx = v

    dt

    Ia = 2 Im cos(t)

    2

    Ib = 2 Imcos(t 3 )

    2

    Ic = 2 Im cos(t + 3 )

    (7)

    Ia = 2 Im cos(t)

    2

    Ib = 2 Imcos(t 3 )

    2

    Ic = 2 Im cos(t + 3 )

    (7)

    vxo

    cx

    . If the

    seen as a resistive for the supply. Taking the Im as the phase RMS current, the corresponding three-phase current can be

    compensation current icx needs to be increased Tx2 is switched

    on. As a result of this, the boost inductor voltage is positive

    written as:

    sx

    sx

    L dicx = v

    dt

    • vxo

      and the ac side voltage vx0

      is changed to

      • Vdc . On the other hand, zero voltage on the ac side is

        2

        achieved with switching on Tx3. Following this switching effect, the compensation current increases for positive phase voltage and decrease for negative phase voltage, vsx . As a result of this switching effect on any phase, a unipolar voltage is obtained on the respective phase of the ac side of the T-type

        The asymmetrical linear and/or nonlinear harmonic in symmetrical nonlinear load causes the imbalance phase current. The imbalance phase current in any phase causes the

        neutral-point current and further aggravates the neutral-point imbalance.

        The system reference and disturbance signals are usually an odd harmonic frequency of the power system. Therefore, the repetitive control is the best choice to introduce an infinite gain at a submultiple of these harmonics below the half of the sampling frequency, i.e. /Ts. The basic block is formed from

        Root Locus Editor for Open Loop 1(OL1) 1

        0.8

        0.6

        0.4

        Imag Axis

        Imag Axis

        0.2

        0

        -0.2

        Open-Loop Bode Editor for Open Loop 1(OL1) 50

        40

        Magnitude (dB)

        Magnitude (dB)

        30

        20

        10

        0 G.M.: 14.6 dB

        -10 Freq: 6.28e+04 rad/s Stable loop

        -20

        45

        0

        the feedback a delay of N N sampling periods, where N =

        T/Ts, T is the period of the signal to be tracked or rejected, and Ts is the sampling period.

        L

        -0.4

        -0.6

        -0.8

        -1

        -1 -0.5 0 0.5 1

        Real Axis

        -45

        Phase (deg)

        Phase (deg)

        -90

        -135

        -180 P.M.: 74.7 deg

        Freq: 7.94e+03 rad/s

        -225

        0 5

        10 10

        Frequency (rad/s)

        Vsa

        Vsb Vsc

        sa

        Lsb Lsc

        nonliner Load

        Fig. 3. Open-loop design for the RC controller.

        Lfa

        P

        1

        = O S_ = 1 + () ()

        1 ()()

        1 ()()(1 ()())

        (9)

        1

        = O S_ = 1 + () ()

        1 ()()

        1 ()()(1 ()())

        (9)

        Lfb

        Lfc

        Assuming that Gx(z)Gx(z) 1, and = 1 for odd RC and = 1 for conventional RC controller, the modified RC

        P

        1 V

        C 2 DC T

        U

        U

        ip Ta1

        T

        Tb1

        Tb1

        sensitivity function can be written as (10):

        • a 2

          Z

          io Tb 2

          a3

          Tb3

          Lf

          a

          Vab

          b

          ica

          1 W(z)H(z)

          SMod_rc = 1 W(z)H(z)(1 G (z)G (z))

          x o

          1 W(z)H(z)

          1 W(z)H(z)

          (10)

          1 W(z)H(z)

          SMod_rc = 1 W(z)H(z)(1 G (z)G (z))

          x o

          1 W(z)H(z)

          1 W(z)H(z)

          (10)

          icb

          icc

          1 V b

          Taking the square of the sensitivity function,

          2

          2

          DC

          CB

          N

          Tb 2

          T

          T

          n

          n

          i b

          b 4

          Tb 4

          Tb1

          2 (1 ()())2

          _

          Bode Diagram

          (11)

          2 (1 ()())2

          _

          Bode Diagram

          (11)

          300

          Fig. 1. Three-phase four-wire active power filter with a three-phase three-

          level T-type converter.

          zl

          200

          Magnitude (dB)

          Magnitude (dB)

          100

          0

          -100

          4

          z N

          Q(z)

          4-.620080 x 10

          Phase (deg)

          Phase (deg)

          0

          Open Loop Conventional function

          r e

          Q(z)

          2

          kr z G (z) G (z)

          r z G (z) G (z)

          z

          z

          • N l m

          c I

          -4.608

          -9.216

          Open Loop of Modified function

          Fig. 2. Robust modified RC structure.

          ()()

          O = 1 + () ()

          (8)

          ()()

          O = 1 + () ()

          (8)

          The inner controller is designed for a phase margin of 74.7 degrees and bandwidth of 6280 rad/sec as depicted in Fig. 3. The closed-loop system without the repetitive controller Go(z) is stable, where (8):

          The sensitivity function of the closed-loop system with RC expressed as (9):

          101 102 103 104

          Frequency (Hz)

          Fig. 4. Comparison of open-loop bode-plot for conventional and modified

          RC controller.

          As one observed from Fig. 4. Comparison of open-loop bode-plot for conventional and modified RC controller and Fig. 5. Comparison of sensitivity function for convectional and modified function the modified sensitivity function based RC controller has higher open-loop gains and deep notches at targeted harmonic frequencies. This provides better performance for the RC controller as compared to the convention one [18].

          Bode Diagram

          Magnitude (dB)

          Magnitude (dB)

          0

          -100

          -200

          Phase (deg)

          Phase (deg)

          2.304

          0

          x 104

          Sensitivity of Conventional function Sensitivity of Modified function

          -2.304

          101 102 103 104

          Frequency (rad/s)

          Fig. 5. Comparison of sensitivity function for convectional and modified

          function.

  4. SIMULATION RESULTS AND DISCUSSION The various MATLAB/Simulink toolboxes are used to

    simulate and design the proposed system of three-phase four- wire with three-level T-type inverter. The six outer IGBTs form the three-phase converter and the other six IGBT form the inner circuits. The simulation incorporates various balanced and unbalanced loads such as three-phase as well as single-phase non-linear loads. The investigation also includes unbalancing source voltage and unbalanced three-phase four- wire nonlinear load.

    1. Balanced three-phase nonlinear loads

      A balanced three-phase nonlinear RL load is applied to the system to evaluate the proposed controller against harmonic compensation. The system harmonic before and after compensation are presented in fig. 1 and 3 respectively.

      6

      4

      2

      is(A)

      is(A)

      0

      -2

      -4

      -6

      0.4 0.405 0.41 0.415 0.42 0.425 0.43 0.435 0.44 0.445 0.45

      Fig. 6. Uncompensated source current waveform for balanced three-phase nonlinear load with rectifier RL loads of R = 100 and L = 10 mH.

      5

      Fig. 9. The load current THD for uncompensated balanced three-phase nonlinear load with rectifier RL loads of R = 100 and L = 10 mH.

    2. Unbalanced nonlinear loads

      Three single-phase nonlinear loads with rectifier RC loads are connected to the system to evaluate its compensation for unbalanced nonlinear loads.

      isa

      isb isc isn

      isa

      isb isc isn

      6

      4

      is(A)

      is(A)

      2

      0

      -2

      -4

      -6

      0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.2

      Fig. 10. Current waveform of the unbalanced three single-phase rectifier with RC loads of phase A = 2 kW, phase B = 1.2 kW, phase C = 0.8 kW.

      20

      0

      -20

      0.05 0.1 0.15 0.2

      6

      isource (A)

      isource (A)

      Mag

      Mag

      4 Fundamental (50Hz) = 17 , THD= 35.52%

      0

      -5

      0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87

      a)

      Fig. 7. Compensated source Current waveform for balanced three-phase nonlinear load with rectifier RL loads of R = 100 and L = 10 mH.

      2

      0 0 5 10 15 2

      iaload

      ibload

      icload

      inload

      iaload

      ibload

      icload

      inload

      Fig. 11. The FFT analysis for phase A.

      15

      10

      i (A)

      i (A)

      5

      Load

      Load

      0

      0

      0.8 0.81 0.82 0.83 0.84 0.85

      -5

      -10

      -15

      0.33 0.335 0.34

      a)

      0.345 0.35

      Fig. 12. Uncompensated load current.

      Mag (% of Fundamental)

      Mag (% of Fundamental)

      20

      15

      Fundamental (50Hz) = 5 , THD= 3.83%

      10

      5

      0 0 10 20 30 40 50

      Fig. 8 . Phase current FFT after compensation for three-phase four-wire system rectifier with RL loads of R = 100 and L = 10 mH.

      isa isb isc isn

      isa isb isc isn

      4

      isa

      15 isb 3

      isc

      10

      (A)

      (A)

      5

      source

      source

      0

      i

      i

      -5

      -10

      -15

      isn

      0.36 0.365 0.37 0.375 0.38 0.385 0.39 0.395 0.4 0.405 0.41

      2

      1

      is(A)

      is(A)

      0

      -1

      -2

      -3

      -4

      0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24

      a)

      a)

      Fig. 13. The current waveforms for compensated source current for

      Fig. 14. Compensated source current for unbalanced source voltage of

      phase A, vsa = 198 2 sin (r 0) phase B, vs,b = 220

      three-phase four-wire active power filter with repetitive control for three-level 2 4

      t-type converters.

      TABLE I

      HARMONIC SPECTRUM WITHOUT AND WITH PROPOSED ACTIVE

      H.

      Order

      Without filter

      With APF

      IEEE Standard

      Source current THD

      %age

      Source current THD %age

      % age Indv THD

      % age Indv THD

      THD

      16.66

      4.84

      8

      3

      4.04

      4.42

      7

      5

      5

      14.48

      4.83

      7

      5

      7

      6.38

      1.72

      7

      5

      9

      0.924

      1.37

      7

      5

      11

      1.82

      1.98

      7

      5

      13

      1.27

      0.31

      3.5

      5

      15

      0.42

      0.89

      3.5

      5

      17

      0.79

      0.66

      3.5

      5

      H.

      Order

      Without filter

      With APF

      IEEE Standard

      Source current THD

      %age

      Source current THD %age

      % age Indv THD

      % age Indv THD

      THD

      16.66

      4.84

      8

      3

      4.04

      4.42

      7

      5

      5

      14.48

      4.83

      7

      5

      7

      6.38

      1.72

      7

      5

      9

      0.924

      1.37

      7

      5

      11

      1.82

      1.98

      7

      5

      13

      1.27

      0.31

      3.5

      5

      15

      0.42

      0.89

      3.5

      5

      17

      0.79

      0.66

      3.5

      5

      FILTER

      15

      10

      is(A)

      is(A)

      5

      0

      -5

      -10

      2 sin (r 3 ) and phase C, vs,c = 242 2si n (r 3 ) and balanced nonlinear load.

      isa

      isb isc isn

      0.12 0.14 0.16 0.18 0.2 0.22 0.24

      a)

      2

      2

      4

      4

      Fig. 15. Uncompensated source current for unbalanced source voltage of phase A, vsa = 198 2 sin (r 0) phase B, vs,b = 220

      2 sin ( ) and phase C, v = 242 2si n ( ) and

      r 3 s,c r 3

      balanced nonlinear load.

      TABLE II

      Parameters

      Units

      Source voltage,

      380 V

      Source inductance,

      0.1 mH

      Filter inductance,

      3 mH

      DC-link capacitance,

      2*3940

      Dc voltage ,

      580V

      Load inductance ,

      10 mH

      Load resistance ,

      100, 80,110 ,

      Load Capacitance ,

      1100

      Parameters

      Units

      Source voltage,

      380 V

      Source inductance,

      0.1 mH

      Filter inductance,

      3 mH

      DC-link capacitance,

      2*3940

      Dc voltage ,

      580V

      Load inductance ,

      10 mH

      Load resistance ,

      100, 80,110 ,

      Load Capacitance ,

      1100

      SPECIFICATION FOR PROPOSED ACTIVE FILTER

      d) Unbalanced source voltage and nonlinear loads

      The system with an unbalanced source voltage of phase

      A , vsa

      = 210 2 sin (r

      2

      • 0) phase B, v

      s,b

      = 220

      3

      3

      2 sin (r ) and phase C, vs,c = 230 2 sin (r

      4

      ) and unbalanced nonlinear loads are used to investigate its

      3

      performance for unbalanced source voltage and unbalanced nonlinear loads.

    3. Unbalanced source voltage and balanced nonlinear 5

    isa

    loads

    The system with an unbalanced source voltage of phase A, vsa = 210 2 sin (r 0) phase B, vs,b = 220

    2

    4 isb

    isc

    3 isn

    2

    is(A)

    is(A)

    1

    0

    2 sin (r

    4

    ) and phase C, vs,c = 230 2 sin (r -1

    3

    3

    -2

    3

    3

    ) are used to investigate its performance for unbalanced -3

    source voltage.

    -4

    -5

    0.515 0.52 0.525 0.53 0.535 0.54 0.545 0.5

    a)

    Fig. 16. Uncompensated unbalanced source and unbalanced nonlinear

    load source current.

    isa

    isb

    isc isn

    isa

    isb

    isc isn

    4

    3

    2

    1

    is(A)

    is(A)

    0

    -1

    -2

    -3

    -4

    0.35 0.36 0.37 0.38 0.39 0.4 0.41

    a)

    Fig. 17. Compensated unbalanced source and unbalanced nonlinear load

    source current

  5. CONCLUSION

    A three-phase four-wire active power filter based on three- level T-type converter topology was investigated to perform harmonics elimination, reactive power compensation, neutral line current reduction, and split dc capacitor voltages balance. The dc-link voltage and capacitor voltage differences are regulated with the PI controller. A repetitive controller is applied for the inner current loop controller. The loss current is applied for unit power factor regulation. The PWM strategy is applied for the converter. The adopted controller achieves for harmonic compensation, reactive power regulation and minimizes neutral current and unbalance in unbalanced nonlinear or linear loads. The three-phase three-level T-type converter has a potential advantage for low power applications.

  6. ACKNOWLEDGMENTS

The project is supported by the National Natural Science Foundation of China (No.51777025); and the Fundamental Research Funds for the Central Universities (No.DUT19ZD219).

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