Performance Investigation of Shunt Active Power Filter Using Hysteresis Current Control Method

DOI : 10.17577/IJERTV1IS4151

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Performance Investigation of Shunt Active Power Filter Using Hysteresis Current Control Method


M.Tech. (Power Electronics & Drives) Electrical Engineering Department

Madan Mohan Malviya Engineering College Gorakhpur-273010(U.P), India


Associate Professor

Electrical Engineering Department

Madan Mohan Malviya Engineering College Gorakhpur-273010 (U.P),India


The simulation study of PI Controlled, three phase shunt active power filter to improve power quality by compensating harmonics and reactive power required by a non-linear load is presented. The shunt active filter employs a simple method for the reference compensation current based on Fast Fourier Transform. Classic filters may not have satisfactory performance in fast varying conditions. But auto tuned active power filters give better results for harmonics minimization, reactive power compensation and power factor improvement. This paper has proposed an auto tuned shunt active filter, which maintains the THD well within the IEEE-519 standards. The results are found to be quite satisfactory to mitigate harmonic distortion, reactive power compensation and power factor improvement.


Power System, Shunt Active Filter, PI Controller, Hysteresis Current Pulse Width Modulation.


    Harmonics contamination is a serious and a harmful problem in Electric Power System. Active Power filtering constitutes one of the most effective proposed solutions. A shunt active power filter that achieves low current total harmonic distortion (THD), reactive power compensation and power factor correction is presented. Hence, it is necessary to reduce the dominant harmonics below 5% as specified in IEEE-519-1992 harmonic standard [1].

    Harmonic Amplification is one the most serious problem. It is caused by harmonic resonance between line inductance and power factor correction (PFC) capacitors installed by consumers. Active filters for damping out harmonic resonance in industrial and

    utility power distribution systems have been researched [1]-[5].

    Traditionally based, passive L-C filters were used to eliminate line harmonics in [2]-[4]. However, the passive filters have the demerits of fixed compensation, bulkiness and occurrence of resonance with other elements. The recent advances in power semiconductor devices have resulted in the development of Active Power Filters (APF) for harmonic suppression. Various topologies of active filters have been proposed for harmonic mitigation. The shunt APF based on Voltage Source Inverter (VSI) structure is an attractive solution to harmonic current problems. The SAF is a pulse width modulated (PWM) VSI that is connected in parallel with the load. It has the capability to inject harmonic current into the AC system with the same amplitude but opposite phase than that of the load [1]-[2]. The principal components of the APF are the VSI, a DC energy storage device that in this case is capacitor, a coupling transformer and the associated control circuits. The performance of an active filter depends mainly on the technique used to compute the reference current and the control method used to inject the desired compensation current into the line.

    There are two major approaches that have emerged for the harmonic detection [2], namely, time domain and the frequency domain methods. The frequency domain methods include, Discrete Fourier Transform (DFT), Fast Fourier Transform (FFT), and Recursive Discrete Fourier Transform (RDFT) based methods. The frequency domain methods require large memory, computation power and the results provided during the transient condition may be imprecise [4]. On the other hand, the time domain methods require less calculation and are widely followed for computing the reference current.

    There are several current control strategies proposed in the literature [5]-[7], [8]-[9], namely, PI control, Average Current Mode Control (ACMC), Sliding Mode Control (SMC) and hysteresis control. Among the various current control techniques, hysteresis control is the most popular one for active power filter applications. Hysteresis current control [6] is a method of controlling a voltage source inverter so that the output current is generated which follows a reference current waveform in this paper. Generally, PI controller

    [7] is used to control the DC bus voltage of SAF. The PI controller based approach requires precise linear mathematical model.

    This chapter basically deals with the modeling and design of shunt active power filter for compensation of harmonics and reactive power. Designs of different parameters like power circuit, control circuit, control strategies, EMI/ Ripple factor are discussed.

  2. Basic Compensation Principle

    Fig.1 shows the basic compensation principle of shunt active power filter. A voltage source inverter (VSI) is used as the shunt active power filter. This is controlled so as to draw or supply a compensating current Ic from or to the utility, such that it cancels current harmonics on the AC side i.e. this active power filter (APF) generates the nonlinearities opposite to the load nonlinearities [3].

    Fig.1 Basic compensation principle

    Fig.2 Waveform for actual load current (A), desired source current (B) and the compensating filter current (C).

    Fig.3 Single line diagram of the shunt active power filter showing power flow

    Total instantaneous power drawn by the nonlinear load can be represented as:-

    pL(t) = pf (t) + pr (t) + ph (t)


    pf(t) – instantaneous fundamental (real) power absorbed by the load,

    pr(t) instantaneous reactive power drawn by the load, and

    ph(t) instantaneous harmonic power drawn by the load.

    In order to achieve unity power factor operation and drawing sinusoidal currents from the utility, active power filter must supply all the reactive and harmonics power demand of the load. At the same time, active filter will draw real component of power (PLoss) from the utility, to supply switching losses and to maintain the DC link voltage unchanged.

    Power components (reactive and the harmonic) should be supplied by the active power filters i.e. pc (t) = pr (t) + ph (t)

    1. Estimation of Reference Source Current

      From the single line diagram shown in fig.3

      is(t) = iL(t) – ic(t) (1)


      is(t), iL(t), ic(t) are the instantaneous value of source current, load current and the filter current.

      And the utility voltage is given by

      vs(t) = Vmsint (2)


      vs(t) is the instantaneous value of the source voltage, Vm – is the peak value of the source voltage.

      If non-linear load is connected then the load current will have a fundamental component and the harmonic components which can be represented as

      iL(t) = In sin(nt + n) n =1

      Is(t) = Imax sint (8)

      Where, Imax (= I1 cos1 + IsL) is the amplitude of the desired source currents. The phase angles can be obtained from the source voltages. Hence, the

      waveform and phases of the source currents are known

      I1sin(t +1) + In sin(nt + n)

      n =2


      and only the magnitude of the source currents needs to be determined.

      Where, I1 and 1 are the amplitude of the fundamental current and its angle with respect to the fundamental voltage, and

      In and n are the amplitude of the nth harmonic current

      and its angle.

      Instantaneous load power pL(t) can be expressed as

      pL(t) = vs(t) iL(t)

      = Vmsint I1sin(t +1) +

      <>The peak value or the reference current Imax is estimated by regulating the DC link voltage of the inverter. This DC link voltage is compared by a reference value and the error is processed in a PI controller. The output of the PI controller is considered as the amplitude of the desired source currents and the reference currents are estimated by multiplying this peak value with the unit sine vectors in phase with the source voltages.


      In sin(nt + n) n =2

    2. Design of Shunt Active Power Filter

      The shunt active power filter mainly consists of DC

      = pf (t) + pr (t) + ph (t)

      = pf (t) + pc (t)

      In the equation (4) and (5)

      pf (t) is the real power (fundamental),

      pr (t) represents the reactive power and



      link capacitor, filter inductor, PI controller and the

      hysteresis controller.

      1. DC Link Capacitor

        The DC link capacitor mainly serves two purposes-

        1. It maintains almost a constant DC voltage.

        2. It serves as an energy storage element to supply

        ph (t) represents the harmonic power drawn by the load.

        For ideal compensation only the real power (fundamental) should by supplied by the source while all other power components (reactive and the harmonic) should be supplied by the active power filters i.e.

        pc (t) = pr (t) + ph (t)


        The total peak current supplied by the source

        real power difference between load and source during transients.

        In this scheme the role of the DC link capacitor is to absorb/supply real power demand of the load during transient. Hence the design of the DC link capacitor is based on the principle of instantaneous power flow.

        Equalizing the instantaneous power flow on the DC and AC side of the inverter considering only


        = Ism

        + IsL


        fundamental component [3].

        Where, Ism = I1 cos1

        and IsL is the loss component of current drawn from the source.

        If active power filter provide the total reactive and harmonic power, then is(t) will be in phase with the utility and pure sinusoidal. At this time, the active filter must provide the following compensation current:

        Ic(t) = IL(t) is(t) (7)

        Hence, for the accurate and instantaneous compensation

        Vdc Idc = vca(t) ica(t)+ vcb(t) icb(t)+vcc(t) icc(t) (9)

        Assuming that three phase quantities are displaced by 1200 with respect to each other, is the phase angle

        by which the phase current lags the inverter phase

        voltage, and 2 Vc and 2 Ic are the amplitudes of the phase voltage and current, respectively of the input side of the inverter.

        Vdc Idc = 2Vca Ica sin 1t sin (1t- a) + 2Vcb Icb sin ( t-1200) sin ( t -1200 – ) + 2V I sin ( t

        of reactive and harmonic power it is very necessary to 1

        1 b cc cc 1

        calculate the accurate value of the instantaneous current supplied by the source.

        +1200) sin (1t +1200 – c) (10)

        Case I: If the three phase system is balanced- Then, Vca = Vcb = Vcc = Vc

        Ica = Icb = Icc = Ic, and

        a = b = c =


        Vdc Idc = 3 Vc Ic cos (11)

        i.e. the DC side capacitor voltage is a DC quantity and ripple free.

        Case II: If the three phase system is unbalanced- Vdc Idc =(Vca Ica cos a + Vcb Icb cos b + Vcc Icc cos c) – [Vca Ica cos (21t- a) + Vcb Icb cos (21t – 2400 – b) +

        Vcc Icc cos (21t + 2400 – c)] (12)

        1. The AC source voltage is sinusoidal.

        2. For Lc, the AC side line current distortion is assumed to be 5%.

        3. Reactive power compensation capability of the active filter.

        4. The PWM converter is assumed to operate in the linear modulation mode (i.e 0 ma 1).

        For satisfactory operation the magnitude of Vdc,ref should be higher than the magnitude of the source voltage Vs. By suitable operation of switches a voltage Vc having fundamental component Vc1 is generated at the ac side of the inverter. This results in flow of

        fundamental frequency component Is1, as shown in fig.4.The phasor diagram for V >V representing the

        c1 s

        The above equation shows that the first term is a dc component, which is responsible for the power transfer from dc side to the AC side. Here it is responsible for the loss component of the inverter and to maintain the DC side capacitor voltage constant.

        The peak to peak ripple voltage is given by

        Vpp = * Ipp * Xc = ( * Ipp) / ( * Cf) (13)

        Where, Ipp is the peak to peak second harmonic ripple of the DC side current. Assuming that Vpp is much less than Vdc then using equations (14) and (15) the maximum value of the Vpp can be obtained as-

        Vpp = ( * Ic1, rated) / ( 3 * Cf) (14)

        Case III: Since the total load power is sum of the source power and compensator power (i.e. PL = Pc + Ps), so that when load change takes place, the changed load power must be absorbed by the active power filter and the utility i.e.

        PL = Pc + Ps (15)

        Hence, selection of capacitor value Cf can be governed by reducing the voltage ripple. As per the specification of Vpp, max and Ic1, rated the value of the capacitor can be

        reactive power flow is also shown in this figure. In this Is1 represent fundamental component [3]-[11].

        Fig.4 Single line and vector diagrams for shunt APF

        As per the compensation principle active power filter adjusts the current Ic1 to compensate the reactive power of the load. In order to maintain Is1 in phase with Vs, active filter should compensate all the fundamental reactive power of the load. The vector diagram represents the reactive power flow in which Is1 is in phase with Vs and Ic1 is orthogonal to it.

        Form the vector diagram,

        Vc1 = Vs + j Lf Ic1 (17)

        i.e. to know Vc1 it is necessary to know Ic1

        found from the following equation

        Cf = ( * Ic1, rated) / ( 3 * Vpp, max) (16)

        Vc1 – Vs

        Ic1 =

        = Vc1 1- Vs



        Lf f Vc1

        It is observed that the value of Cf depends on the maximum possible variation in load and not on the steady state value of the load current. Hence, proper forecasting in the load variation reduces the value of Cf.

        Now the three phase reactive power delivered from the active power filter can be calculated from the vector diagram as

      2. Selection of Lc and Reference Capacitor Voltage (V )

        Qc1 = QL1

        = 3 Vs Ic1

        = 3 Vs

        Vc1 1- Vs

        Lf Vc1



        The design of these components is based on the following assumptions:

        From these equations

        If Vc1 > Vs, Qc1 is positive.

        If Vc1 < Vs, Qc1 is negative.

        i.e. active power filter can compensate the lagging reactive power from utility only whenVc1>Vs. From[11], If the inverter is assumed to operate in the linear modulation mode i.e. modulation index varies between 0 and 1, then the amplitude modulation index is given by-

        ma =

        2 2Vc1


        (where, Vm= 2 Vc ) (20)

        And the value of Vdc is taken as

        Vdc = 2 2


        (for ma =1) (21)

        The filter inductor Lf is also used to filter the ripples of the inverter current,and hence the design of Lf is based on the principle of harmonic current reduction.The ripple current of the inverter can be given in terms of the maximum harmonic voltage, which occurs at the frequency mf.

        Ich(mf) = (22)

        Where,mf is the frequency modulation ratio of PWM converter.

        On solving (19) and (22) simultaneously, the value of Lf and Vc1(i.e Vdc) can be calculated. Vc1 and Vdc ref,

        Fig.5 Basic principle of hysteresis band control

        The rate of change of inductor current is then given by


        Making assumption that the ac supply does not change during a cycle of switch operations, the time taken t


        must be set according to the capacity requirement of the system (i.e Vs< Vc1 2Vs ).As the switchingfrequency is not fixed with the hysteresis controller, a practically feasible value of 10kHz has been assumed.

    3. PI Controller

      taken to cross a dead band is

      The switching frequency f



      is, therefore variable.

      The controller used is the discrete PI controller that takes in the reference voltage and the actual voltage and gives the maximum value of the reference current depending on the error in the reference and the actual values. The mathematical equations for the discrete PI controller are:

      The voltage error V (n) is given as: V (n) =V*(n) – V (n)

      The output of the PI controller at the nth instant is given as:

      I(n)=I(n-1) + Kp[V(n)-V(n-1)] + Ki V(n)

    4. Hysteresis Current Controller

      With the hysteresis control, limit bands are set on either side of a signal representing the desired output waveform. The inverter switches are operated as the generated signals within limits. Hysteresis-band PWM is basically an instantaneous feedback control method of PWM where the actual signal continually tracks the command signal within a hysteresis band [10].

      Combining above two equations (23) and (24) to obtain the switching period, and inverting, gives

  3. Simulation And Performance Investigation Of Shunt APF

    In this section the simulation analysis of shunt APF is described, first for R-L load and then for DC machine load and the FFT analysis has been carried out simultaneously.

    1. Operation of Simulation Model

      The operation of the simulation model shown below is described as first the capacitor voltage is sensed which is compared with the reference voltage and the error signal is given to the PI controller for processing to obtain the maximum value (Im) of the reference current which is multiplied with the unit vector template i.e. sint to get the reference current Im sint for phase a. This signal is now delayed by 1200 for getting the reference current for phase b, which is further delayed by 1200 to get the reference current for the phase c. these reference currents are now

      compared with the actual source currents and the error is processed in the hysteresis controller to generate the firing pulses for the switches of the inverter. And the switches are turned on and off in such a way that if the reference current is more than the actual source current then the lower switch is turned on and the upper switch is turned off and if the reference current is less than the actual source current then the upper switch of the same leg is turned on and the lower switch is turned off. The output of the shunt active power filter is such that the source current is purely sinusoidal and the harmonic current is drawn or supplied by the filter.

      Fig.6 MATLAB model for Shunt active power filter

    2. Simulation Result And Discussion

      Fig.7 Three phase supply voltages

      The waveform shown in fig.7 demonstrates that supply voltage is almost sinusoidal of Vpeak=100 volt in phase 0,- 120 and +120 degree of a, b and c phase respectively.

      Fig.8 Load current

      The waveform shown in fig.8 demonstrates that load current is in sinusoidal nature with containing small amount harmonic .

      Fig.9 Source current before and after compensation

      The waveform shown in fig.9 demonstrates that source current before compensation (i.e from 0 to 0.1 sec.) and after compensation (i.e from 0.1 sec.), it is almost sinusoidal with reduced harmonic content.

      Fig.10 Source voltage, source current and filter current for phase A

      The waveform shown in fig.10 demonstrates that source voltage, source current before and after compensation and filter current for phase A.

      Fig.11 Capacitor voltage and capacitor current

      The waveform shown in fig.11 demonstrates that capacitor voltage settles at nearly constant value of Vdc ref. and capacitor current settles at almost equal to the value of filter current.

      Fig.12 FFT Analysis for load current

      Fig.13 FFT Analysis for source current

      The waveform shown in fig.12 and fig.13 demonstrates that source current is reduced THD from 21.83% to 0.89%.

      THD analysis of shunt active power filter for RL-Load is shown in table 1.

      Load type


      Load Current


      Source Current

      R-L Load

      21.83 %

      0.89 %

      Table 1

  4. Conclusion

The performance of the system improves and the THD is reduced up to very large extent. Also, it is seen from the simulation results that the source current and the source voltages are in same phase i.e. the input power factor is unity and there is no reactive power from the source.


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    The values of the different parameters used for shunt active power filter.

    • Source voltage:3-phase, 100V, 50Hz

    • Proportional gain Kp: 0.5

    • Integral gain Ki : 10

    • Capacitor reference voltage: 300V

    • RL load parameters: 10 , 100mH

    • line parameters : 0.2 , 1.5mH

    • Filter inductor : 5mH

    • Hysteresis band gap : -0.01 to 0.01

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