International Journal of Electrical Engineering Education 43/3Understanding the modelling and analysis ofa shunt active power filter usingMATLAB/SimulinkK. ag atay Bayndr1and Muammer Ermis 21Department of Electrical and Electronics Engineering, University of ukurova, Balcali-Adana, Turkey2Department of EEE, METU, Ankara, TurkeyE-mail: mtumaycu.edu.trAbstractThis paper deals with the modelling and analysis of a shunt active power filter by the use ofa MATLAB/Simulink program. The modelling approach adopted in the paper is graphical in nature, asopposed to mathematical models embedded in code using a high-level computer language. The modelis presented clearly and in a detailed manner, targetted especially at postgraduate students. Theperformance of the active power filter is illustrated by considering a 400kV A, six-pulse, fully controlledbridge rectifier supplied from a typical distribution system via a rectifier transformer.Keywordsactive power filter; MATLAB/SimulinkIn typical distribution systems the proliferation of diode and thyristor rectifiers hasresulted in serious utility interface issues as well as power quality degradation suchas supply current and voltage harmonics, reactive power, flicker and resonance prob-lems in industrial applications. Voltage distortion due to current harmonics is becom-ing a major problem for the utilities at distribution levels. Utilities more frequentlyencounter harmonic related problems, such as higher transformer and line losses,reactive power and resonance problems, required derating of distribution equipment,harmonic interactions between customers or between the utility and load, reducedsystem stability and reduced safe operating margins.1This has led to the proposalof more stringent requirements regarding power quality; standards such as IEEE-519 reflect these preoccupations.2Passive filters are being used widely for harmonic elimination. However, they maycreate system resonances, need to be significantly overrated to account for possibleharmonic absorption from the power system, must be coordinated with reactivepower requirements of the loads and need a separate filter for each harmonic fre-quency to be cancelled.The concept of using active power filters to mitigate harmonic problems and tocompensate reactive power was proposed more than two decades ago.3Since thenthe theories and applications of active power filters have become more popular andhave attracted great attention. Without the drawbacks of passive harmonic filters, theactive power filter appears to be a viable solution for reactive power compensationas well as for eliminating harmonic currents.In this paper modelling and analysis of a shunt active power filter by the use ofa MATLAB/Simulink program is presented. The modelling approach adopted in thepaper is graphical in nature, as opposed to mathematical models embedded in codeusing a high-level computer language as in Ref. 4. Modelling of shunt active powerfilters with simulation programs is presented in many studies.57However, themodels are not presented in detail and only results are emphasised. In this paper themodel is presented clearly and in a detailed manner so that the reader can easilyunderstand and use the model for her further studies. Performance of the modelledshunt active power filter is illustrated by considering a 400kV A, six-pulse, fullycontrolled bridge rectifier supplied from a typical distribution system via a rectifiertransformer. Characteristic values for rectifier load and power system parameters aretaken which are typical for industry.For modelling, SIMULINK provides a graphical user interface for buildingmodels as block diagrams. Models are hierarchical, so models can be built usingtop-down and bottom-up approaches. The system can be viewed at a high level andit is possible to go down through the levels to see the increasing levels of modeldetail. This approach provides an insight into how a model is organised and how itsparts interact.MATLAB/Simulink model for active power filter system simulationActive power filter configurationThe active power filter uses power electronic switching to generate harmonic cur-rents that cancel the harmonic currents from a load. The active power filter config-uration investigated in this study is based on a voltage source inverter that interfacesto the system through an interface reactor. In this configuration, the filter is con-nected in parallel with the load being compensated. Therefore the configuration isoften referred to as a shunt (parallel) active power filter. The approach is based onthe principle of injecting harmonic current into the a.c. system, of the same ampli-tude and reverse phase to that of the load current harmonics.Figure 1 illustrates the concept of the harmonic current cancellation so that thecurrent being supplied from the source is sinusoidal.Figure 2 shows the MATLAB/Simulink model of the active power filter system.As seen from the figure, the model consists of the following main parts:Main customer bus;Voltage source inverter;Interface reactor;Reference current generator;Firing pulse generator;400kV A nonlinear load;Measurement and feedback components.Voltage source inverterThe voltage source inverter used in the active power filter makes the harmoniccontrol possible. This inverter uses a d.c. capacitor as the supply and can switch at186K. . Bayndr and M. Ermi sInternational Journal of Electrical Engineering Education 43/3a high frequency to generate a signal which will cancel the harmonics from the non-linear load.The current waveform for cancelling harmonics is achieved with the voltagesource inverter and an interface reactor. The interface reactor converts the voltagesignal created by the inverter to a current signal. The desired waveform is obtainedby accurately controlling the switches in the inverter. Control of the current wave-shape is limited by the switching frequency of the inverter and by the availabledriving voltage across the interface reactor. The driving voltage across the interfacereactor determines the maximum di/dt that can be achieved by the filter. This isimportant because relatively high values of di/dt may be needed to cancel higher-order harmonic components.The voltage source inverter is the heart of the active power filter. TheMATLAB/Simulink model of the voltage source inverter is shown in Fig. 3.This three-phase, full-wave inversion bridge is built using three identical inverterlegs each consisting of two ideal switches and two antiparallel diodes. The idealswitch is modelled as a resistor (Ron) and inductor (Lon) in series with a switch con-trolled by a logical signal in the MATLAB/Simulink model. It switches between theon and off state instantaneously when triggered.Interface reactorThe interface reactor provides the isolation and filtering between the output of the voltage source inverter and the power system where the active power filter is connected. The MATLAB/Simulink model of the interface reactor is shown inFig. 4.The inductance allows the output of the active power filter to look like a currentsource to the power system. The inductance makes it possible to charge the d.c.Shunt active power filter modelling187International Journal of Electrical Engineering Education 43/3Voltage Source InverterReference CurrentGeneratorInterface ReactorSiMain Customer BusNonlinear LoadLiAPFiCurrent ControllerFig. 1Diagram illustrating components of the shunt connected active power filter withwaveforms showing cancellation of harmonics from a nonlinear load.188K. . Bayndr and M. Ermi sInternational Journal of Electrical Engineering Education 43/3Fig. 2MATLAB/Simulink model of the active power filter system.Shunt active power filter modelling189International Journal of Electrical Engineering Education 43/3Fig. 3MATLAB/Simulink model of voltage source inverter.Fig. 4MATLAB/Simulink model of interface reactor.capacitor to a voltage greater than the a.c. line-to-line peak voltage. The inductancealso functions like a commutation impedance. It limits the magnitude of a currentspike during commutation and prevents the switching device from seeing an exces-sive rate of current change. Besides these, it is not possible to connect a sinusoidalvoltage supply to the nonsinusoidal output of the voltage source inverter without a reactor. Sizing of the reactor value must take into account control of the inverter switching frequencies and the characteristics of the nonlinear load to becompensated.Reference current generatorIn this shunt active power filter, control is accomplished by monitoring the three-phase line currents to the nonlinear load and the three-phase line-to-neutral voltagesat the load bus, and then generating the three-phase reference currents that shouldbe supplied by the voltage source inverter. In this simulation study the compensat-ing current reference signal is derived from the measured quantities by the use ofthe instantaneous reactive power theory based method. The general definitions ofactive and reactive power have been presented in Refs 8 and 9. In this formulation,active and reactive power are expressed as the dot-and-cross product of voltage andcurrent vectors.Once the compensating currents are detected, they are used as a reference signalin the inverter current control loop and thus compared with the real voltage sourceinverter current to generate the switch control signals.To deal with instantaneous voltages and currents in three-phase circuits mathe-matically, it is adequate to express their quantities as instantaneous space vectors.For simplicity the three-phase voltages and currents excluding zero-phase sequencecomponents will be considered.In a,b,c coordinates, the a,b and c axes are fixed on the same plane, apart fromeach other by 2p/3. The instantaneous space vectors eaand iaare set on the a axisand their amplitude and direction vary with the passage of time. These space vectorsare easily transformed into a, b coordinates as follows:(1)(2)where the a and b axes are the orthogonal coordinates. Necessarily, eaand iaare onthe a axis and eband ibare on the b axis. Their amplitude and direction vary withthe passage of time.The conventional instantaneous power on the three-phase circuit can be definedas follows:(3)pe ie ie ie ie ia ab bc c=+=+a ab biiiiiabcab=2311 21 203 23 2eeeeeabcab=2311 21 203 23 2190K. . Bayndr and M. Ermi sInternational Journal of Electrical Engineering Education 43/3In order to define instantaneous reactive power, the instantaneous imaginary powerspace vector is defined as follows:(4)This space vector is the imaginary axis vector and is perpendicular to the real planeon the a, b coordinates, to be in compliance with the right-hand rule. Taking intoconsideration that eais parallel to iaand ebto ib, the conventional instantaneouspower p and the instantaneous imaginary power q, are expressed by(5)By using the theory explained above, the transformation of the three-phase bus voltages va,vband vcand the three-phase nonlinear load currents iLa,iLband iLcintothe a b orthogonal coordinates gives the following expressions:(6)(7)The instantaneous real power pLand the instantaneous imaginary power qLon theload side can be defined as(8)Equation (8) is changed into(9)The determinant with respect to eaand ebin (9) is not zero.Land Lare the d.c. and a.c. components of pL. Likewise, Land Lare the d.c.and a.c. components of qL, respectively. Then the following relation exists:(10)From eqn (9), the a-phase load current iLais divided into the following components:(11)The first term of the right-hand side of (11) is the instantaneous value of the con-ventional fundamental active current. The second term is the instantaneous value ofthe conventional fundamental reactive current. The third term is the instantaneousieeepeeeqeeepeeeqLLLLLaaabbabaabbab=+22222222pppqqqLLLLLL=+=+ qq ppiieeeepqLLLLababba=1pqeeeeiiLLLL=abbaabiiiiiLLLaLbLcab=2311 21 203 23 2eeabcabnnn=2311 21 203 23 2pqeeeeii=abbaabqeiei=+abbaShunt active power filter modelling191International Journal of Electrical Engineering Education 43/3value of the harmonic currents which represents the a.c. component of the instanta-neous real power. The fourth term is the instantaneous value of the harmonic cur-rents which represents the a.c. component of the instantaneous imaginary power.From (11) it is seen that the active power filter should compensate second, third andfourth terms to compensate for the harmonics and the reactive power. Figure 5 showsa basic compensation scheme of the instantaneous reactive power and harmonic cur-rents. From the scheme it is seen that the active power filter supplies the reactivepower and harmonic real power so that only real power at fundamental frequencyis drawn from the mains.In the calculation circuit of the compensating reference currents, the followingexpression results:(12)where pavis the instantaneous real power corresponding to the loss of the activepower filter, and p* and q* are given by(13)Figure 6 shows the calculation circuit of p* and q*. This basically consists of ahigh-pass filter configuration using a Butterworth low-pass filter. So, this circuitoutputs Lfrom pL. The design of the low-pass filter is the most important in thecontrol circuit, because various compensation characteristics are obtained in accor-dance with the cutoff frequency and order of the low-pass filter. pppqqLL*= = iiieeeeppqrefarefbrefca=+23101 23 21 23 21abban*192K. . Bayndr and M. Ermi sInternational Journal of Electrical Engineering Education 43/3NONLINEAR LOAD ACTIVE POWER FILTER LSpp =0=SqLLqp ,SSii ,ii ,ffii ,Lfpp=ee ,Lfqq=ii ,SOURCEFig. 5Compensation scheme.The d.c. bus voltage VDCof the voltage source inverter can not be kept constant,owing to the power loss of the inverter circuit as no suitable d.c. voltage controlcircuit is used. This problem can be solved by controlling the magnitude of the mainscurrent.A PI controller is used to control the d.c. capacitor voltage. Its transfer functioncan be represented as(14)where Kpis the proportion constant that determines the dynamic response of the d.c.bus voltage and KIis the integration constant that determines its settling time.The d.c. bus voltage is controlled by trimming the instantaneous real power pav,which corresponds to the loss of the active power filter, while the instantaneousimaginary power does not have any effect on the d.c. capacitor voltage. The controlcircuit has the negative feedback loop to trim pavautomatically. The actual d.c. busvoltage value is fed back and compared with the desired d.c. bus voltage value. Thedifference is fed to a PID controller whose output is pav. pavis added to p* and pavadds a positive or negative d.c. value to p* which corresponds to an active currentat fundamental frequency. So the active line current at fundamental frequency flowsinto or out of the d.c. capacitor to regulate the d.c. voltage. Figure 7 shows a blockdiagram of the reference current generator including the d.c. capacitor voltagecontrol.Figure 8 shows the MATLAB/Simulink model of the reference current generator.The model includes three-phase to alpha-beta converter, multiplication, addition,summation and function blocks, a PID controller whose D parameter is 0 and a high-pass filter block.Firing pulse generatorThe MATLAB/Simulink model of the firing pulse generator is shown in Fig. 9.H sKKspI( )=+Shunt active power filter modelling193International Journal of Electrical Engineering Education 43/3Lp + LP - - Lp Low-Pass Filter (Butterworth) Fig. 6Calculation circuit of p* and q*.Hysteresis current control is used for the generation of switching pulses. Amongthe various current control techniques, hysteresis current control is the most exten-sively used technique. As indicated in Refs 10 and 11 a review of used current controltechniques for PWM converters reveals that hysteresis control shows a certain supe-riority for active power filter applications. Hysteresis control provides a better low-order harmonic suppression than PWM control, which is the main target of the activepower filter.12It is easier to realise with high accuracy and fast response. However,as a disadvantage its switching frequency might fluctuate. In the hysteresis controltechnique the error function is centered in a preset hysteresis band. When the errorexceeds the upper or lower hysteresis limit the hysteretic controller makes an appro-priate switching decision to control the error within the preset band.In Fig. 9 Iref is a vector of the desired compensation current reference signals.Ifb is a vector of the fed back actual voltage source inverter output currents. Memoryblock is a requirement of the simulation program. Iref and Ifb signals are each demul-tiplexed to 3 signals, phase A, B and C reference current signals and phase A, B,and C actual fed back current signals. Reference and actual signals are comparedand fed into a hysteresis block and the output of the hysteresis block is the firingpulse. For explaining the technique it is best to consider only phase A.When Irefa is greater than Ifba, the resultant difference I is positive. If the mag-nitude of I is bigger than the upper boundary of the specified hysteresis band, thehysteresis block output goes high, firing the upper bridge device of the leg andmaking the leg current increase. When Ifba becomes greater than Irefa, I becomesnegative. If the magnitude of I is smaller than the lower boundary of the hystere-sis band, the hysteresis block goes low, firing the lower bridge device of the leg and194K. . Bayndr and M. Ermi sInternational Journal of Electrical Engineering Education 43/3cbaiii, cbavvv, refairefbirefciqlosspp +Lq DCVpavpLp + + +DCSETV Calculation of Lpand LqCalculation of pand q PID control Calculation of refcrefbrefaiii,Fig. 7Block diagram of reference current generator.Shunt active power filter modelling195International Journal of Electrical Engineering Education 43/3Fig. 8MATLAB/Simulink model of the reference current signal generator.making the leg current decrease. If I is within the limits of upper and lower bound-aries of hysteresis band hysteresis block keeps its current state. The outputs of thehysteresis blocks are directly fed as the firing pulse of upper bridge device of eachleg of the inverter and NOT of that signal is fed as the firing pulse of lower bridgedevice of each leg. This is necessary for operation and avoiding the conduction ofsame leg switches simultaneously.Nonlinear loadThe nonlinear load block is a three-phase fully controlled bridge rectifier feeding ad.c. motor. The d.c. motor is modelled with a resistance, inductance and a back e.m.f.It is possible to control the firing angle of the controlled three-phase rectifier. Accord-ing to German VDE standards minimum of 5% series reactor should be connectedto the supply side of the rectifier. The MATLAB/Simulink model of the nonlinearload block is shown in Fig. 10.196K. . Bayndr and M. Ermi sInternational Journal of Electrical Engineering Education 43/3Fig. 9MATLAB/SIMULINK model of firing pulse generator.Fig. 10MATLAB/Simulink model of the nonlinear load.Shunt active power filter modelling197International Journal of Electrical Engineering Education 43/3Short circuit MVA at 34.5kV bus is 250 MVA154 kV bus 154/34.5kV 34.5/0.4 kV Other feedersand loads 400 kVA FULLY CONTROLLED RECTIFIER ACTIVE POWER FILTER Fig. 11Single line diagram of the modelled system.3154kV 34.5 kV bus 0.4 kV bus to rectifierSX LXto APF 0.06+j0.64 m j19 mFig. 12Equivalent circuit on per phase wye basis referred to the low voltage side.Performance of the designed active power filter: a case studyExample system in the case studyThe single line diagram of the modelled system is shown in Fig. 11. The equivalentcircuit on per phase wye basis of the above system at the 0.4kV level is shown inFig. 12. In the simulation study a resistance of 0.06m and an inductance of 2His put in place of XS(source impedance), an inductance value of 60H is put in placeof XL(line impedance). The nonlinear load is a 400kVA fully controlled rectifierwith a 10 firing angle at nominal current. According to German VDE standards aminimum of 5% rectifier input choke needs to be placed on the a.c. side of the rec-tifier. For a 400kV A load that corresponds to a 20m reactance, so by calculationan inductance of 63H is placed on the a.c. input side of the rectifier.Power circuit of the active power filterThe power circuit consists of the voltage source inverter and the interface reactor.Figures 3 and 4 (see previous) show the MATLAB/Simulink model of the voltagesource inverter and interface reactor respectively.The value of the interface reactor, d.c. bus voltage setting, and capacitance of thed.c. bus capacitor are the important parameters to be determined. Power circuit para-meters are dependent on the load, so before designing the power circuit components,the characteristics of the load should be known.The design of the interface reactor and choice of d.c. bus voltage are based uponthe following criteria:The high frequency components of the injected currents should be limited.The instantaneous di/dt generated by the active power filter should be greaterthan the di/dt of the harmonic component of the load, so that proper harmoniccancellation can take place.An analysis of the power circuit and the above criteria yield the following equation:(15)whereVS, line-to-line voltage of mains supplyLf, interface reactor, di/dt of the harmonic component of the load currentVDC, d.c. bus voltage.The above equation has two unknowns, Lfand VDC. VSand should be known by the designer. It is known that VDCshould be greater than the peak valueof the line-to-line mains supply voltage. Therefore one can specify a minimum d.c.voltage by taking into account standard voltage ratings for commercially availableelectrolytic capacitors and by using this VDCvalue in (15) a minimum Lfvalue canbe found. However, the selection of VDCand Lfrequire a compromise. To cancel theharmonics perfectly, the converter must generate a high di/dt, which requires a smallinductance. However, decreasing the inductance increases the current ripple and asa result the supply side exhibits a current with a higher THD. The same effect isobserved for the d.c. bus voltage. High di/dt can be obtained by increasing the d.c.voltage which in turn increases the current ripple generated by the active power filter.The results of the simulation study are therefore very important for the designer inorder to find the answers to such problems. Starting from initially estimated valuesfor system parameters, by repeating the simulation study for different design para-meters one can reach an optimum design in which a smaller current ripple and ade-quate harmonic cancellation take place.On the d.c. bus of active power filters electrolytic capacitors with proper ripplecurrent capability are to be used. Therefore the constraints in the design are that thed.c. bus voltage should be greater than peak value of line-to-line supply voltage andthe designed capacitor bank can be formed by series, parallel connection of com-mercially available voltage and F ratings of capacitors. These will give us a fewmaximum allowable values for the d.c. bus voltage.didtloaddidtloadVLdidtVsfloadDC22+198K. . Bayndr and M. Ermi sInternational Journal of Electrical Engineering Education 43/3To eliminate the harmonics fully, it is necessary to compensate for Land qL. Elim-ination of Lhowever gives rise to a 300Hz ripple component superimposed on thed.c. capacitor voltage, because Lis absorbed by the d.c. capacitor. The capacitanceof the d.c. capacitor should be chosen to keep the peak-to-peak ripple within anallowable range. Therefore, in the calculation of CDCLis to be known. In the sim-ulation the variations in Lwith time can be obtained by connecting a probe to Lin the reference function generator block and connecting a d.c. voltage source insteadof a capacitor to the d.c. bus. After obtaining the Lwaveforms and assuming thatit is sinusoidal i.e.(16)The d.c. bus capacitance CDCcan be calculated from equation (17).(17)In eqn (17) peak-to-peak ripple cannot be chosen arbitrarily. This is because themanufacturers of electrolytic capacitors specify in their catalogues the maximumallowable value of ripple content for different classes of capacitors. A higher ripplecontent withstanding capability means a more costly d.c. bus capacitor. The optimumdesign is reached by running the simulation for several values of CDCaround theinitial estimate calculated from (17).Performance of the modelled shunt active power filterThe performance of the designed active power filter is evaluated by using the systemgiven in the case study. The active power filter is designed by assuming that thefiring angle of the three-phase bridge rectifier is 10 during normal operation. Theinterface reactor is selected as 90H, d.c. bus capacitance is selected as 10mF andthe set d.c. bus voltage is selected as 650V according to the above-mentioned cri-teria. Related current waveforms are obtained also for different firing angles of the rectifier for the purpose of comparison. Figure 13 shows the nonlinear loadcurrent, source current, compensating reference current and active power filteroutput current for a 10 firing angle of the rectifier. The compensating referencecurrent signal is derived from the measured quantities by the use of the instanta-neous reactive power theory based method for the active power filter to inject har-monic currents of the same amplitude and reverse phase to that of the load currentharmonics and also to inject reactive power consumed by the load into the a.c.system. As seen from the figure, the active power filter output current tracks thecompensating reference current and the shunt active power filter effectively com-pensates for the harmonic currents and reactive power. The THD of the load currentis 24% while the THD of the source current is 3.5%. This THD value of the sourcecurrent easily conforms to the required standard of THD values mentioned in IEEEStd. 5191992.13The percentage of fundamental current component is taken to be100%. The load current contains harmonics at the frequencies of h times the fun-damental frequency, whereCPwVVDCmDCDC=sinppwtLm=() p p p p p p pShunt active power filter modelling199International Journal of Electrical Engineering Education 43/3The percentage of the 5thharmonic current (250Hz) is 20% and 7th(350Hz) is 15%.Harmonics at 550Hz and 650Hz are also considerable. In the source current the har-monics are observed to be decreased effectively.Figures 14 to 16 show the nonlinear load current, source current, compensatingreference current and active power filter output current for a 30, 45 and 60 firingangle of the rectifier respectively. In each case the active power filter output currenttracks the compensating reference current and the shunt active power filter effec-tively compensates for the harmonic currents and reactive power. The reason of theincreased distortion as the firing angle increases is explained in the discussionsection below.Figure 17 shows the nonlinear load current, source current, compensating refer-ence current and active power filter output current for a changing firing angle of theload. At time t = 40ms the firing angle of the load is changed from 45 to 10. Thecontroller acts and compensating reference currents are changed instantly with the changing load current and the active power filter output follows the change in the compensating reference current. From Fig. 17 it is seen that the dynamic responsehnn=611 2 3, , ,.200K. . Bayndr and M. Ermi sInternational Journal of Electrical Engineering Education 43/3Fig. 13Nonlinear load current, source current, compensating reference current andactual active power filter output current for 10 firing angle of rectifier.of the active power filter is adequate. There is no response delay introduced by thecompensating current calculation circuits and current tracking. The d.c. capacitorcontrol loop determines the response of the active power filter. When the load currentchanges abruptly, the d.c. capacitor voltage deviates from the set value so the con-troller acts and the voltage settles to the set value again. This time is determined bythe proportional and integral constants of the PI controller. These parameters shouldbe chosen carefully.DiscussionTable 1 lists the harmonic current limits recommended by IEEE13based on the sizeof the load with respect to the size of the power system to which the load is con-nected. The recommended current distortion limits are concerned with the indiceTDD, which is the harmonic current distortion in % of maximum demand loadcurrent. The ratio ISC/ILis the ratio of the short-circuit current available at the pointof common coupling (PCC), to the maximum fundamental load current. It is rec-ommended that the load current IL, be calculated as the average current of themaximum demand for the preceding 12 months. Thus, as the size of the user loadShunt active power filter modelling201International Journal of Electrical Engineering Education 43/3Fig. 14As Fig. 13, for 30 firing angle of rectifier.decreases with respect to the size of the system, the percentage of harmonic currentthat the user is allowed to inject into the utility system increases.The modelled system in the case study is a moderate bus and it is not a weaksupply problem. ISC/ILis 500, so the modelled system belongs to the 4thgroup where100 ISC/IL 1000. In Table 1 ILis the average load demand current. For our casewe dont know the regime of operation so ILis accepted as the nominal current when202K. . Bayndr and M. Ermi sInternational Journal of Electrical Engineering Education 43/3Fig. 15As Fig. 13, for 45 firing angle of rectifier.TABLE 1Current distortion limits for general distribution systems13(120V through 69kV)Maximum harmonic current distortion in percentage of ILIndividual harmonic order (odd harmonics)ISC/IL1111 h 1717 h 2323 h 3535 hTDD204.02.01.50.60.35.020 507.03.52.51.00.58.050 10010.04.54.01.50.712.0100 100015.07.06.02.51.420.0the firing angle is 10. Looking at Table 1 it is seen that in the class of the modelledsystem TDD is required to be less than or equal to 15. This is more than satisfiedwith the designed active power filter. Even the requirements for a weak bus whereISC/ILis less than 20, is satisfied by the designed active power filter.Even harmonics are limited to 25% of the odd harmonic limits above.From Fig. 13 to Fig. 16 it can be observed that the source current becomes moredistorted as the firing angle increases. This is an expected result and the phenome-non can be explained as follows. First, as the firing angle increases the nonlinearload current decreases. Since the hysteresis bandwidth of the voltage source inverteris constant in amps for all cases, the ratio of the nonlinear load current to hystere-sis bandwidth decreases, resulting in more distortion. Secondly, as the firing angleincreases the magnitude of higher order harmonics increases and the active powerfilter can not achieve the necessary di/dt at some points to compensate these harmonics.However, despite the increasing distortion, with an increase in firing angle, themagnitude of harmonic components in the load current waveform becomes lowerand lower in comparison with the nominal or base value of the fundamental currentcomponent at full load. Consequently, at increased firing angles of the rectifier totaldistortion is not expected to be out of the required standard values.Shunt active power filter modelling203International Journal of Electrical Engineering Education 43/3Fig. 16As Fig. 13, for 60 firing angle of rectifier.For the designed active power filter the hysteresis bandwidth is constant in amps.If an increased performance is required from the active power filter with increasingfiring angles of the rectifier an adaptive hysteresis band scheme should be imple-mented, which decreases the bandwidth as the load current decreases within thedevice switching frequency limitations.The reactive power compensation performance of the active power filter isobserved to be unaffected by an increase in firing angle. The filter can provide reac-tive power compensation adequately.ConclusionsThis paper has successfully presented a detailed MATLAB/Simulink model of ashunt active power filter. The highly developed graphic facilities available inMATLAB/Simulink were used to conduct all aspects of model implementation andto carry out extensive simulation studies. The performance of the active power filteris evaluated with a 400kV A six-pulse fully controlled rectifier operating with dif-ferent firing angles as a load. The simulation results show that full reactive power204K. . Bayndr and M. Ermi sInternational Journal of Electrical Engineering Education 43/3Fig. 17Nonlinear load current, source current, compensating reference current andactual active power filter output current for change of firing angle of rectifier from 45 to10 at time t = 40ms.compensation and proper elimination of harmonics is achieved. Obtained THDvalues for the source current are much less than the required standard values.In the model, control loops of the system are modelled in detail, but simplifiedswitch models are employed. Consequently this model is very useful for conceptualanalysis and for obtaining steady state waveforms. The model is presented in a hier-archical and step-by-step manner, so that these user-defined models can be easilyimplemented by other MATLAB/Simulink users.During simulation, the sampling resolution of the simulated system should not bevery different from the real system sampling resolution. Otherwise, significant errorscan be introduced.References1T. Thomas, K. Haddad, G. Joos and A. Jaafari, Design and performance of active power filters,IEEE Industry Applications Magazine, September/October (1998), 3846.2S. Bhattacharya, T. M. Frank, D. M. Divan and B. Banerjee, Active filter system implementation,IEEE Industry Applications Magazine, September/October (1998), 4763.3L. Gyugyi and E. C. Strycula, Active a.c. power filters, in Conference Record of IEEE-IAS AnnualMeeting, 1976, pp. 529535.4O. Anaya-Lara and E. 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