Control techniques for active power filters

Control techniques for active power filters

T.C. Green and J.H. Marks

Abstract: There have been many variants of the active power filter proposed and these variationscover both the circuit topology and the control system employed. Some of the control variantsreflect different control objectives but there are still many variants within similar objectives. Theavailable control techniques are described and contrasted in a structured way to identify theirperformance strengths. Objectives are classified by the supply current components to be correctedand by the response required to distorted grid voltage. The various signal transformations aredescribed in terms of their impact on the distortion identification problem. Time-domain,frequency-domain, instantaneous power and impedance synthesis methods are examined.Additional control functions such as DC-bus voltage and current reference following are alsodiscussed. It is found that a key difference between control methods is the way in which currentdistortion is treated in the presence of distorted grid voltage.

1 Introduction

The idea of active filtering of distortion found in powerdistribution lines appears in the literature from the 1970s [1–4]. The terms active filter and active power filter (APF) areboth in common use. Here active power filter is preferred todistinguish a filter that must process instantaneous powerfrom active filters for signal processing. Since the earlyschemes, many APF variants have been proposed and theliterature has been reviewed from several standpoints. Anearly review was [5]. It categorises active power lineconditioners according to whether time or frequency-domainsignal processing is used and whether current or voltage typeconverters are used. Akagi reviewed the emerging APFtechnologies [6] in terms of their objectives, configurationand controllers and discussed the unified power qualityconditioner (a combination of a shunt and a series APF).

In [7], Peng reviewed the literature regarding shuntagainst series forms of APF and articulated clearly the needto match the form of filter to the form of distortion. Thus,shunt APFs are effective against current-stiff (inductive)non-linear loads that inject distortion current, whereas seriesAPFs are effective against voltage-stiff (capacitive) non-linear loads that inject distortion voltage. While it is possibleto use the other combinations, the ratings required of ashunt APF when used to compensate for a current-stiffnon-linear load can become large if the line impedance issmall [7, 8]. In [9] Peng develops the theme and expands thediscussion to the several forms of hybrid active/passivepower filters (hybrid APFs) appearing in the literature. Thepaper uses the idea of duality to populate fully the matrix ofpossible combinations of shunt and series impedances andcontrolled sources. The features and operating character-istics of each combination are examined. Another categor-isation of topologies for hybrid filters was presented in [10].

Singh et al. [11] categorise a large number of reportedactive filters under headings of converter, topology, supplylines, signal conditioning and compensation derivation. El-Habrouk et al. [12] categorise published work underheadings of power rating, circuit configuration, compensa-tion quantity, control method and reference identification.The assessment under each heading is necessarily brief butthe reviews are comprehensive.

There are several papers that compare certain controlschemes for the quality of the results they produce, such as[13, 14]. Execution speed and time response of threeharmonic identifiers were reviewed in [15].

This paper draws together the various control schemesreported and identifies their characteristics. The literatureon APFs contains reports of many different circuittopologies, but these are not a focus of this review. Tosimplify the discussion here, attention is focused on the caseof a shunt active filter injecting compensating current into aline. A control method for a shunt filter can normally beapplied to a series compensation case using the ideas ofduality discussed in [9]. Only where a control method istailored to a different circuit topology is that topologyexample used. APF control includes subtasks such asreference generation, current control and DC-bus voltagecontrol. Each of these topics is covered. The focus is onthree-phase methods as the more general situation. Where amethod can be applied with modification to a single-phaseAPF this is discussed.

2 APF structure

Figure 1 shows the shunt-connected APF used as theprincipal example and illustrates the five basic elements ofan APF:

1 Distortion identifierFa signal-processing function thattakes the distorted waveform (the line current or voltage),d(t), and forms a reference waveform, r(t), which will reducethe distortion.

2 InverterFa power converter (and coupling inductance/transformer) able to reproduce the reference waveform atsuitable amplitude, IAPF (or VAPF).

The authors are with the Department of Electrical and Electronic Engineering,Imperial College London, South Kensington, London, SW7 2AZ, UK

r IEE, 2004

IEE Proceedings online no. 20040759

doi:10.1049/ip-epa:20040759

Paper first received 12th November 2003 and in revised form 20th May 2004.Originally published online: 25th October 2004

IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005 369

3 Inverter controllerFa pulse-width modulator and, in thecase of a voltage-source inverter used to inject current, alocal current control loop that ensures that IAPF tracks r(t).

4 SynchroniserFa signal-processing block based on phase-locked loop techniques that ensures that the cancellationwaveforms are correctly synchronised to the mains voltage.Certain methods do not require explicit synchronisation.

5 DC-busFan energy store that supplies the fluctuatinginstantaneous power demand of the inverter. Errors andlosses that cause the energy store to engage in long-term realpower flows must be compensated for by additional actionof the inverter controller.

An example series APF is shown in Fig. 2. It uses thesame basic elements but the inverter is configured to injectseries voltage. According to the classification in [6], Fig. 1would be described as current injecting and load-currentsensing. Figure 2 would be described as voltage injectingand load-current sensing. Voltage detecting configurations

are also possible and can be used with voltage or currentinjection.

The system shown in Fig. 1 has been described as openloop in the discussion in [16]. It is open loop in that id (not is)is measured. The distortion generated by the load is thenidentified and a correction term fed forward to correct thedistortion in the supply. There may be errors in thecalculation process or inaccuracy in the current injectionthat result in imperfect correction. There may also be somecoupling such that the injected current perturbs the sourceor the load such that the distortion changes and thecorrection is unstable. The calculation of the feed forwardcorrection is subject to processing delay and so the transientresponse is a concern. (Although Fig. 1 contains a controlloop, it is a local loop to operate the voltage-source inverteras a current source.)

In contrast, the closed-loop approach measures is,identifies any remaining distortion and updates the injectionreference. In some cases this update will be a low samplerate process with perhaps one update per mains period. Thisrequires that the update coefficient (gain) is low so that astable approach is made to the zero-distortion target [16].Slow convergence of this loop provides a degree of

smoothing in the compensation current of a fluctuatingdistortion load. Continuous versions of closed-loop controlhave also been reported but with a relatively slowadjustment of the target [17].

3 Choice of cancellation objective

In principle, an APF is capable of correcting a wide varietyof power quality problems such as:

� harmonic distortion (of any phase sequence)

� fundamental-frequency reactive power (non-unity displa-cement factor)

� negative-sequence fundamental components (unbalancecomponents)

� zero-sequence fundamental components (neutral linecurrent)

� flicker (low-frequency modulation of power flow).

Correction of harmonic distortion is taken as a corefunction present in all APFs. Displacement factor correc-tion with fundamental frequency reactive power is oftenalso included [18]. Correction of the fundamental frequencynegative-sequence component can be provided and willbalance unbalanced load currents in a three-wire system[19]. With a four-wire system, zero-sequence harmonics andzero-sequence fundamental can flow as a result of single-phase distorting loads and a four-wire APF can be used tocorrect these terms. Flicker correction is normally afunction of a dynamic voltage restorer (DVR) but can fallwithin the remit of an APF [20]. Functions such ascombating voltage sag and swell are considered to be DVRfunctions. The use of an APF in response to various powerquality problems is discussed in [21].

It is tempting to consider that all the various powerquality issues can be dealt with by simply adding controlfunctions to the basic APF power converter circuit.However, each corrective action contributes to the volt-ampere rating of the power converter and hence to the costof the equipment. Compensation of unbalance and flickeralso has implications for the DC-side energy store since theenergy flows represented by peaks in the instantaneouspower can be large. With this acknowledged, it is importantto note that a control scheme designed to correct harmonicdistortion might provide unintentional action to correctflicker and thereby cause the APF to exceed its rating whenfaced with large flicker components. Control schemes needto be assessed for their effectiveness in correcting theproblems they were explicitly designed for and assessed forany unintended additional action. The largest energyexchanges with the DC-side are likely to arise fromfundamental-frequency unbalance and low-frequencypower variation (flicker).

Any discussion of APF control rests on the definition ofthe distortion that is to be corrected. Viewed from thestandpoint of an ideal power system with balancedsinusoidal voltages, the ideal load current is also a balancedsinusoid set. A non-sinusoidal current or an unbalancedcurrent can be decomposed and the distortion termsidentified. This identification of distortion can also beapproached from an analysis of the instantaneous power.For the case of a sinusoidal voltage and distorted current,identification of the active power is equivalent to identifica-tion of the in-phase fundamental component of current. Forthe general case of an unbalanced, non-sinusoidal voltageand an unbalanced non-sinusoidal current there is still

d (t)r(t)

dIsI

DCbus

APFV

source

APF

distorting load

syncinverter inverter

controldistortionidentifier

Fig. 2 Schematic of an example series APF

d (t)

r(t)

dIsI

APFI

DC-bus

source

APF

distorting load

syncinverter

invertercontrol

distortionidentifier

Fig. 1 Schematic diagram of an example shunt APF

370 IEE Proc.-Electr. Power Appl., Vol. 152, No. 2, March 2005

debate over the most appropriate form of decomposition.There are two long-standing approaches. Fryze [22] definedactive current, iA(t), as being responsible for the real powerflow and having the same form as the voltage, (1). Theactive current is the minimum RMS current required totransmit the active power. The remaining current wasdefined as non-active current, iN(t) (2), and is found to beorthogonal to the active current (3):

iA tð Þ ¼ P

vk k2v tð Þ ð1Þ

where 77�77 is the RMS value and P is the real (average)power.

iN tð Þ ¼ i tð Þ � iA tð Þ ð2Þ

ik k2¼ iAk k2þ iNk k2 ð3ÞThe Fryze non-active power, QF, and the apparent power,S, are defined by multiplying the current equation by theRMS voltage:

S2 ¼ P 2 þ Q2F ð4Þ

Budeanu used a frequency-domain decomposition ofvoltage and current to define the active (5) and reactivepowers (6):

P ¼XN

n¼1VnIn cos fnð Þ ð5Þ

QB ¼XN

n¼1VnIn sin fnð Þ ð6Þ

A third power term, D, needs to be introduced to completethe apparent power equation:

S2 ¼ P 2 þ Q2B þ D2 ð7Þ

Enslin and Van Wyk surveyed possible approaches todecomposing power into terms that can be separated outfor compensation (or not) [23, 24]. There are several otherviews of this topic [25] and much debate [26]. Peng [27]has shown the relationship between the definition of activepower and the definitions of instantaneous active andreactive power that have become popular in APF applica-tions (to be reviewed in Section 5).

The shunt current-correcting APF will often be placed inthe low-voltage distribution network where there is asignificant degree of existing voltage distortion caused bydistant non-linear loads and their common-impedancecoupling to the APF site. A significant question to addressis what is the most desirable response of the combinedAPF+load to the distortion components of the supplyvoltage. As will be shown in Section 4, many of the reportedmethods set an objective of achieving sinusoidal currentflow. This can be interpreted as presenting a very highimpedance to harmonic voltages (and a moderate impe-dance to the fundamental term). In contrast, the instanta-neous power method (to be described in Section 5) drawssignificant harmonic current in response to harmonicvoltages. The response is complex and, as will be shownin Section 5, the process is non-linear and results in currentharmonics at different frequencies from the voltageexcitation. The non-sinusoidal current has been noted andseveral attempts have been made to force sinusoidal current.However, the authors of [28] and [29] argue (from differingstarting points) that the APF should respond to voltagedistortion but should do so with a resistive characteristic.Harmonic currents will be drawn in phase with theharmonic voltage excitation and the power extracted by

the APF+load will provide damping of the excitation. Ifthe same resistance is presented at all frequencies then thecurrent waveform will have the same shape as the voltagewaveform. This matches the definition of active currentdiscussed by Fryze and used in [23]. Three categories ofcompensation can be defined:

1. Waveform compensation: Commonly the objective is toachieve a supply current with fundamental active currentonly. In impedance terms, the APF+load is resistive atfundamental frequency and open circuit at harmonicfrequencies.

2. Instantaneous power compensation: Commonly theobjective is to achieve a constant instantaneous powerdrawn from the supply. The APF+load present a complex,non-linear response to distorted excitation and cannot bedescribed in terms of an impedance.

3. Impedance synthesis: Commonly the objective is topresent a resistive characteristic. Power is absorbed at allfrequencies present in the excitation and APF+load can bemade to closely approximate a passive system.

4 Waveform compensation

Waveform correction can be approached in many ways.There are many signal-processing techniques that candecompose the current waveform into various componentsand separate those that should remain from those thatshould be cancelled (the cancellation reference). This isessentially a filtering task and the non-ideal properties ofreal filters must be recognised. In addition to the analyticalapproaches, there are pattern-learning techniques such asneural networks.

4.1 Filter-based methodsDistortion identification is a signal-filtering task and can beconducted with time-domain filters or by Fourier basedfrequency decomposition. As with all filtering tasks, thefilters need to be considered in terms of the following:

� Attenuation: it is important that the identified compo-nents have their magnitude preserved, that the othercomponents are heavily attenuated and that the transitionband between the pass- and stopbands is narrow

� Phase distortion: because the cancellation relies oninjecting cancellation signals in phase opposition, it isimportant to preserve the phase of the identifiedcomponents

� Time response: the (distorted) load current will be subjectto change and the filter should respond rapidly withoutlarge overshoot.

These three performance considerations are inextricablylinked for time-domain filters: flatness of magnituderesponse has to be traded off against phase response (atleast for causal filters) and a well-damped transient responseis in conflict with a narrow transition region.

Applying a filter to determine directly the distortionmeans that the cancellation process is subject to thetransient response of the filter. The alternative is indirectidentification, i.e. use the filter to determine the fundamentalsignal f(t) that should remain and subtract that from theinstantaneous distorted signal d(t) to form the reference r(t)(illustrated in Fig. 3). There are two stages of inversion inachieving the desired component: first it is subtracted fromthe measured current to form the reference and then thereference is subtracted from the actual line current. The


difference between the direct and indirect methods isapparent during a transient. Real-time filters are causaland, during a transient, there is a time lag between theoutput of the filter and the component to be identified.Thus, the direct method will have an out-of-date distortionterm and the distortion cancellation will be in error. Theindirect method will have an out-of-date fundamental termand, while the distortion terms will be cancelled, real powerwill also be exchanged through the inverter. Real powerexchange disturbs the DC-bus voltage and requires that theinverter be rated to cope with a real power component,which might be large.

When considering unintended action of a distortionidentifier it must be borne in mind that, for a directidentifier, only those components specifically separated bythe signal filter will be compensated by the APF, whereasfor an indirect identifier, any component not specificallyidentified by the signal filter for retention will becompensated by the APF.

Most APF implementations opt for indirect distortionidentification since it yields the best distortion cancellationduring transients. The inadvertent exchange of real power(caused by incomplete separation of the real powercomponent in an indirect identifier) can be corrected, asexplained in Section 7. Direct identification is used wheredifferent groups of harmonics are to be treated differentlyor where only a specific range of harmonics are to becompensated for [19]. This might be desirable where itallows the rating of the filter to be kept within a limit orwhere interaction with a system resonance is a danger ifcancellation is attempted in a certain frequency band.

The well known transformations of three-phase systemsare widely used in APF controllers to facilitate separation ofa current or voltage term for cancellation. The transform toorthogonal components in a stationary reference frame (theab0 reference frame) and the transform to a rotatingreference frame (the dq0 reference frame) are both useful.The choice of reference frame in which to operate has animportant impact on the filter design; in particular:

� The width of the transition band between passband andstopband is different in different domains.

� The decomposition of the fundamental into variouscomponents depends on the domain used and gives choiceover what type of distortion is cancelled.

Both the transforms separate out the zero-sequencecomponent into a separate term (or axis). The ab0–transform does not separate sequence sets (although thesequence can be determined from whether the a or bcomponent leads). The rotation transformation shiftsfundamental frequencies to DC and separates out theactive and reactive components. Components of the sameharmonic order but of opposite rotation (phase sequence),i.e., +n and �n, are separated from each other because

positive sets are shifted to order n�1 and negative sets toorder �(n�1).

An early example of using the synchronous frame is [30,31]. In [32] it is argued that, especially for high sample ratesystems, the overhead in performing ab0 and rotationtransformations is too much of a burden. A method isdemonstrated of transforming a filter designed in a rotatingframe to an exact equivalence in the stationary frame.Importantly, the method preserves the ability of asynchronous frame filter to distinguish between negativeand positive sequence sets through the retention of couplingbetween the axes.

Figure 4 shows the form of the spectrum expected from adistorting load as it would be in each of the domains beingdiscussed. The load is assumed to be three-wire, non-linearand unbalanced. Figure 4a is the spectrum of a phasecurrent and shows the expected harmonic distortion of anon-linear three-wire, three-phase load, i.e., harmonics oforder 6k71 (where k is any positive integer).

Figure 4b shows the spectrum of the currents trans-formed by the ab-transform. This has no effect on thefrequencies present but, with all three phases represented,the phase sequence can be observed in the phase relation-ship between the a and b components. In this Figure,negative sequence terms are shown as having a negativefrequency (i.e., to be backward rotating). Thus, theunbalance of the fundamental is shown by the presence ofa harmonic of order�1. Balanced non-linear loads producecharacteristic harmonics of order �5, +7, �11, +13, y6k+1 (where k is any integer). Unbalanced non-linear loadsproduce further non-characteristic harmonic distortion oforder +5, �7, +11, �13, y 6k�1.

Figure 4c shows the spectrum of the signal after therotation transform has been applied. All components havebeen shifted down one harmonic order. The positive-sequence fundamental becomes a DC term whereas thenegative-sequence fundamental becomes a double frequencyterm (order �2). The characteristic distortion is of order 6kand the non-characteristic distortion of order 6k�2.

There is no difference between filtering in the phase orab0-domains but the dq0-domain does offer an alternative.In the phase domain the fundamental can be separated(for indirect identification of the harmonics) with a lowpassfilter that cuts off between orders 1 and 5 (1 and 3 if there is

d (t )

d (t )

f (t )

r (t )

r (t )LPF

HPF

L(s)

H(s)

Fig. 3 Direct and indirect distortion identifiers in the time domainSignal f(t) is the identified fundamental frequency signal that is allowedto remain un-cancelled

1 5 7 11 13

1 5 7 11 13−1−5−7−11−13

0 4 6 10 12−2−6−8−12−14am

plitu

de

harmonic order

characteristiccomponents

non-characteristiccomponents

negative

negativesequence sequence

sequencepositivesequence

positive

a

b

c

Fig. 4 Spectrum of a distorted and unbalanced 3-wire, 3-phasesignal ina Phase domainb ab0 domainc dq0 domain


zero-sequence/four–wire harmonic distortion). In the dq-domain the filter cutoff should be between 0 and 6 forbalanced conditions. For unbalanced conditions a cutoffbetween 0 and 2 will allow negative-sequence fundamental(unbalanced fundamental) to be corrected and a cutoffbetween 2 and 4 will not cancel unbalanced fundamentalbut will still cancel harmonic distortion. Zero-sequencedistortion conveniently appears in a separate term and canbe cancelled or not as required. Thus, the dq-domain offersfrequency separation of unbalance components and theplacement of key components at DC, where they arerelatively easy to filter.

Filters that are required to pass the DC term alone (in thedq0-domain) can be designed as lowpass filters with verylow cutoff frequencies and more than a decade of transitionregion. It is important to realise that using a very low cutofffrequency will mean that flicker components in the currentwill not be retained in the desired waveform and will becancelled by the APF. The cancellation of flicker compo-nents might be desirable but there will be substantial powerexchange between the load and the DC-bus of the APFwith implications for the ratings of both the inverter and theDC energy store.

Filters that are required to pass fundamental and rejecthigher terms (an indirect identifier in the phase or ab0-domain) can in principle be lowpass filters since no DC termis expected. However, it is not possible to obtain satisfactorypass- and stopband performance from a practical lowpassfilter with a transition band as narrow as a few harmonicorders. However, a notch filter with a very narrow notchcan be realised. There can be difficulties, too, with notchfilters [33]. If the system frequency is subject to widevariation the width of the notch must be compromised.Selectable filters will be needed to cover both 50 and 60Hzoperation.

Because the passband and stopband are separated byonly a few harmonic orders it is inevitable that there will beincomplete separation between distortion and the allowedcomponents. In a direct identifier, passband errors inmagnitude or phase will lead to incomplete cancellation ofdistortion whereas incomplete rejection in the stopband willlead to the APF exchanging some fundamental real andreactive power with the AC system. In an indirect identifierthe situation is reversed: errors of phase or magnitude in thepassband of the filter lead to the exchange of fundamental-frequency real and reactive power, and incomplete rejectionin the stopband leads to incomplete cancellation ofharmonics. The use of high-order filters to provide anarrower transition band has the disadvantage of greaterphase error and a more complex transient response.

4.2 Frequency-domain filteringFiltering in the frequency domain is somewhat differentfrom filtering in the time domain and involves a discrete orfast fourier transform (DFT or FFT) on a block of datathat contains at least one cycle of the lowest frequency ofinterest and that has been sampled at over twice the highestfrequency present. The advantage of filtering in thefrequency domain is that completely abrupt cutoffs (withno transition band) can be obtained. Passband ripple andphase distortion can be avoided provide care is taken overthe transformation into and out of the frequency domain interms of synchronisation, buffer length and windowfunction. The accompanying disadvantage is that fre-quency-domain filters are not real-time filters. Time mustelapse for sufficient samples to be gathered and, when thatis complete, processing time is required to perform thetransform.

As discussed in [16], the signals to be processed must besteady and periodic before frequency-domain processing isappropriate. The FFT implicitly assumes periodicity of thesampled waveform. If the FFT window is properlysynchronised to the fundamental signal then the phaseand magnitudes of the components can be accuratelydetermined. If the window does not cover an integernumber of fundamental cycles then spectral leakage willoccur and accuracy is degraded and windowing functionswill be required to partially overcome this problem. Theselectivity of Fourier methods with respect to time-domainfilters is one of the aspects of the discussion in [19].

Figure 5 shows direct and indirect distortion identifica-tion using frequency-domain filtering. In the direct methodthe fundamental component is set to zero to form acancellation reference for harmonic distortion. If only thereal (in-phase) component is set to zero, then the APF willalso cancel the reactive component. In the indirect case theharmonic terms are set to zero so that the fundamental issubtracted from the instantaneous signal to yield thereference. If the imaginary (quadrature) fundamentalcomponent is set to zero, it will not be subtracted fromthe instantaneous signal and will be cancelled by the APF.In [19], the harmonic identifier used a direct method inwhich individual components were separately identified.For certain harmonics, the compensation current and theload current were compared and integrator action appliedto any error. Where it was judged that this closed-loopcontrol might interact with a resonance in the electricalsystem, it was omitted and open-loop control was used.

During a transient the periodicity of the distortion is lostand the cancellation is not accurate. In addition, there is atime delay in the filtering that affects the distortionidentification. In the simple case, one complete cycle ofdata is required, which is stored in a buffer and thenprocessed during the following cycle and de-buffered for useas a cancellation reference in the cycle after that. Thus, thecancellation reference is two cycles out of date. Shorterupdate rates are possible, such as performing an FFT everyhalf-cycle using one half-cycle of fresh data plus data fromthe previous half-cycle. The delay is then one completecycle. Faster updates are possible, limited by the computa-tional power available to process data in real time. De-buffering can present problems with the continuity of theresulting waveform. Full- or half-cycle buffers aligned to thezero crossings of the fundamental can be de-buffered toyield a continuous signal. Buffer edges at other points(smaller buffers or buffers of three-phase data aligned toone particular phase) can cause a step change in thecancellation reference during transient conditions. Asmoothing function can be applied to the buffer edges,but response times are affected.

FFT−1FFT

0LF

HF

FFT−1FFT

LF

HF0

d (t )d (f )

R (f )

r (t )

f (t )

r (t )F (f )

d (f )d (t ) buffer

buffer de-buffer

de-buffer

Fig. 5 Direct and indirect filtering in the frequency domainD( f), R( f) and F( f) are the frequency domain form of the signals d(t),r(t) and f(t) in Figs. 1 and 3


4.3 Heterodyne methodsThe heterodyne method of waveform compensationinvolves multiplying a distorted signal by a sinusoid. Ifthe sinusoid is at fundamental frequency then the funda-mental frequency component that is in phase withheterodyning signal transforms to a DC term and adouble-frequency term. The DC term can be separatedwith a lowpass filter. If the heterodyning sinusoid is in phasewith the voltage, this method will identify the fundamentalactive current. The fundamental reactive current could beidentified by using a quadrature sinusoid. This is a methodof signal processing that has become popular in single-phasesystems where ab0 and dq0 transforms are not applicable. Adiscussion of the method is presented in [34].

Heterodyning can be applied to three-phase systems byusing a phase-locked loop to form a sinusoid locked to thefundamental of the supply voltage [35]. The choice of filteris a compromise: the DC term must be passed and thedouble-frequency term rejected. A sharp, high-order filterwill give a long step response whereas a low-order filter willgive poor separation of the terms and imperfect currentcancellation. In [35] the identification was done inclosedloop with integral action. This overcame parametererrors in the system. The resulting system had a responsetime of 2-3 mains cycles.

The dq0 transformation, as already discussed, is a form ofheterodyning with the fundamental frequency that exploitsthe properties of a balanced three-phase set. The advantageof the dq0 transform over applying heterodyning to eachphase is that the double fundamental-frequency term iseliminated if the variables are balanced and the filter neednot be designed to reject this term. The filter can bedesigned to remove only the higher-order terms. The dq0transform has been applied to individual phases as a formof heterodyning [36] by using time-delay/phase-shifting toform pseudo three-phase sets.

A DFT can be considered as a succession of heterodyneoperations for each harmonic followed by averaging to filterout all unwanted components. In the classification here, theheterodyne category is reserved for methods that select outa small number of distortion components using heterodynetechniques. In [15] a method described as a recursive DFTwas studied. It is equivalent to a heterodyne followed bymoving average filtering. It was shown to be computation-ally efficient compared to other methods provided that thenumber of terms required was small. The method in [37] isdescribed in terms of an adaptive filter that eliminates thefundamental from the load current signal to yield thecancellation reference. In fact, the adaptive element isheterodyning function followed by integration to detect thefundamental term.

Direct identification methods using multiple synchronousreference frames, each synchronous with a particularharmonic of interest, have been reported [38, 39].

4.4 Pattern learning and identificationBecause of the time delay in frequency-domain identifica-tion and the compromises in filter design in time-domainbased methods, several attempts have been made to usepattern learning to perform the separation of a current intoa portion to cancel and a portion that should remain. Thedirect and indirect principles can both be used.

An early attempt to use a neural network as an harmonicidentifier is reported in [40]. A 2-layer neural network wasused to estimate the Fourier coefficients of a distortedwaveform. A digital implementation is described but it isdoubtful that it is more computationally efficient than anFFT.

An early application of a neural network to an APF wasarranged to learn the characteristics of the local grid systemsuch that a suitable correction current could be set toachieve a target level of voltage distortion in the grid [41]. Itwas anticipated that several distorting loads exist and thatmeasurement of load current was not feasible. Theharmonic components of the supply voltage are found byconventional means and the network conductance used toassess the appropriate current. This current is the trainingreference for the neural network. As the neural networkadapts, the injected current is adjusted until the voltageerror is driven to zero. A separate network is required foreach harmonic frequency. This technique was assessed in[42]. Successful operation was confirmed but it was notedthat the response to a change in load took more than tenmains cycles to converge. From this, it was proposed in [42]to combine a traditional harmonic identifier acting on themeasured load current and to supplement this with theneural network acting on the voltage error.

Also examined in [42] is a neural network that acceptstime-domain samples of load current (as a vector of time-delayed samples covering a cycle) and is trained to producethe cancellation reference as time-domain samples. Simula-tion results show that this can achieve acceptable resultswith some useful generalisation around the training data.However, it is noted that the network requires a relativelylarge number of hidden-layer neurons and has correspond-ingly large training time and recall time. A differentarrangement of the time-domain method is presented in[43, 44]. Here the network again uses a vector of time-delayed load current samples as its input but it has beentrained to identify the active component of current thatshould remain in the supply after cancellation.

The ambition of using a neural network to provide fastfrequency decomposition for an APF is explored in [45]. Anetwork was trained to identify the 3rd and 5th harmoniccosine coefficients for a range of load current amplitudes.This is a direct algorithm. The algorithm can be applied toeach half-cycle of load current data and simulation testingshows an accuracy of better than 1% using 100 samples andten middle layer neurons. The computational effort in recallis not identified but the network is relatively small becauseonly two terms are identified. The estimation ofFourier series terms is also undertaken by an ANN in[46]. The fundamental active power is then calculatedand a fundamental current reference formed. A furtherANN is used to implement the selection of inverterstates to force current reference following. Results aregiven for an example four-wire system that show thesystem makes response to a change in load duringthe following cycle and achieves its full response after 2-3cycles.

A neural network has been used in an indirect algorithmto identify the fundamental component for indirectgeneration of a reference [47]. In fact the neural networktracks all the terms of the harmonic series but only thefundamental is then used. At each sample point, thepredicted load current (generated from Fourier terms) iscompared with the measured load current. The error is usedto adapt the network weights. Simulation results in [47]show convergence of the estimated fundamental in 2-3fundamental cycles. Following a step change in load, goodperformance is noted in the following cycle. The sample rateused was high (12.5kHz) and there remains the questionover whether the neural network adaptation and recall canbe completed at that rate in real time and whether thecomputational effort compares favourably with analytictechniques in Sections 4.1–4.3.


The predict-ahead ability of neural networks is attractivefor an APF correcting a load in transient. In [48] a neuralnetwork was trained to predict the fundamental componentof load current for the next period given input data from theload. The example given was the DC current and firingangle of the thyristor bridge load. This may be feasible foran APF dedicated to a specific load but is not generallyapplicable. Another approach in [49] uses current data froma rectifier load to predict the fundamental active andreactive currents on a sample-by-sample basis. It was shownthat the neural network is sufficiently small for real-timecomputation.

5 Instantaneous power compensation

One view of an active power filter is that it should cancel thefluctuating component of instantaneous power and perhapsalso fundamental-frequency reactive power. A commonapproach is to use the definitions of instantaneous activepower as traditionally defined and the definition ofinstantaneous reactive power introduced by Akagi [50].The definitions apply in either the ab0- or dq0-domains, andfor balanced sinusoidal three-phase systems would yieldconstant values.

There are various representations of the equations suchas complex power or a two-dimensional cross product. Inthe ab-domain (i.e. without the zero-sequence term):

s ¼p þ jq ¼ vab�i�ab ¼ va þ jvb� �

ia � jib� �

¼ vaia þ vbib� �

þ j vbia � vaib� � ð8Þ

where * is used to denote a complex conjugate.

p

q

� �¼

vaia þ vbib� �vbia � vaib� �" #

¼va vbvb �va

� �iaib

� � ð9Þ

or in the dq-domain:

s ¼p þ jq ¼ vdq�i�dq ¼ vd þ jvq� �

id � jiq� �

¼ vd id þ vqiq� �

þ j vqid � vdiq� � ð10Þ

In a four-wire system there is an additional term for thezero-sequence instantaneous power. In [51] this wasallocated to active power but more recent work recognisesthe non-active element of the zero-sequence term [52].

It is common to show the instantaneous powers ascomposed of a steady average term and a variation (oroscillation) around this:

p tð Þ ¼ �pp þ ~pp tð Þ ð11Þ

q tð Þ ¼ �qqþ ~qq tð Þ ð12ÞTaking the case of an undistorted supply voltage but aharmonically distorted and unbalanced current (as used inFig. 4), the spectrum of the instantaneous power has theform shown in Fig. 6. It is, therefore, relatively easy to use afilter to extract the fundamental frequency real and reactivepowers. For a current composed of an in-phase funda-mental and a single harmonic term the instantaneous poweris:

p ¼ V1I1 þ V1In cos 1� nð Þotð Þ ð13Þ

�pp ¼ V1I1 ~pp ¼ V1In cos 1� nð Þotð Þ ð14Þ

q ¼ �V1In sin 1� nð Þotð Þ ð15Þ

�qq ¼ 0 ~qq ¼ �V1In sin 1� nð Þotð Þ ð16Þ

Characteristic harmonic distortion (of order n¼ 6k+1, i.e,.�11th, �5th, 7th, 13th etc., where negative orders representnegative-sequence sets) yields power terms of order 67k7.Non-characteristic harmonic distortion (of harmonic ordern¼ 6k�1, i.e., �13th, �7th, 5th, 11th etc.) gives additionalpower terms at 67k772.

The inverse transform for conversion from the powerdomain to the phase domain is defined as:

i�ab ¼ia � jib ¼s

vab

¼pva þ qvb� �

þ j qva � pvb� �

v2a þ v2b

ð17Þ

or

iaib

� �¼ 1

v2a þ v2b

va vbvb �va

� �pq

� �ð18Þ

Direct and indirect identifiers can be constructed asshown in Fig. 7 following the principles established for thefiltering techniques in Section 4.1. Although not shown inthe Figure, the p and q terms are available separately and soone can choose whether the APF should or should not

1 5 7 11 13harmonic

0 2 6 8 124 10

curr

ent

p

0 2 6 8 124 10

q

characteristiccomponent

non-characteristiccomponent

negative

negative

sequence sequence

sequencepositivesequence

positive

order

Fig. 6 Phase-current and instantaneous power in the frequencydomain

HPFH (s)

L (s)

LPF

v��(t )

s(t ) =

s(t )

p(t ) + jq(t )s(t )

sd(t )

v��(t )

id*��(t )

id*��(t )

id��(t )

id��(t ) ir��(t )

ir��(t )

ifdq(t )

conj conj

conjconj Π

Π

÷

÷

Fig. 7 Direct and indirect distortion identifiers in the instantaneouspower domain


compensate the fundamental reactive power. In the directcase, the q-term is left unfiltered if reactive powercompensation is required: in the indirect case the q-term isset to zero. Fundamental-frequency negative sequencecurrent appears as a second harmonic in the instantaneouspower domain and is cancelled or not by the APFdepending on the cutoff chosen for the identifier’s filter.

The instantaneous power method applied in the ab0-domain is attractive because it has a low processing burden(no rotational transformation) and does not rely on explicitsynchronisation.

The description so far has concentrated on a shunt filtercorrecting the current drawn from a voltage source.Instantaneous power decomposition can be used for thedual of this situation in which a series APF injects voltage toensure constant instantaneous power when current flowsinto a voltage-distorting load [53]. The instantaneous powermethod has been applied to a series APF such that it passesonly active power and seeks to block other terms [54]. Thisproposal also included additional injected voltage to correctvoltage unbalance in the grid.

An alternative formulation of instantaneous active andreactive powers using space vectors was reported in [55].This and several other methods were compared in [56].

It should be emphasised that the preceding discussionassumed that the voltage was free of distortion. Severalstudies have noted that the instantaneous power methodcauses harmonic currents to flow when the voltage isdistorted or unbalanced [57–59]. It is particularly importantto note that unbalanced voltage can cause an APFcontrolled on instantaneous power to inject harmoniccurrent. The relationship between the amplitude of thevoltage distortion and the consequent current distortion wasshown to be approximately proportional [60]. This studydid not reveal the detailed relationship between theexcitation and the response.

With a distorted grid voltage, a system drawingsinusoidal current would not have constant instantaneouspower [53] and, as a corollary, an APF controlled oninstantaneous power and subjected to distorted voltagecannot achieve sinusoidal current. To maintain a constantinstantaneous power by drawing a current from aharmonically distorted voltage requires a non-sinusoidalcurrent. Similarly, a non-sinusoidal current is required todraw constant instantaneous power from a voltage contain-ing a fundamental-frequency negative sequence term.

It is worth noting that a balanced resistive load does notdraw constant instantaneous power when supplied by adistorted three-phase voltage set. Where supply voltagecontaining a balanced nth harmonic and a balancedfundamental voltage (19) is applied to a resistive load, anoscillatory power at the difference frequency is found toflow (24):

va ¼ V1 cos otð Þ þ Vn cos notð Þ ð19Þ

vb ¼ V1 sin otð Þ þ Vn sin notð Þ ð20Þ

ia ¼V1

Rcos otð Þ þ Vn

Rcos notð Þ ð21Þ

ib ¼VR1

sin otð Þ þ Vn

Rsin notð Þ ð22Þ

�pp ¼ V 21

Rþ V 2

n

Rð23Þ

~pp ¼ 2V1Vn

Rcos 1� nð Þotð Þ ð24Þ

If an APF using a constant instantaneous power approachwas applied to this situation, the APF would ‘correct’ thecurrent drawn by the resistor. The supply currentcorresponding to constant power and distorted voltagewould be:

ia ¼Pva

v2a þ v2b

¼ P V1 cos otð Þ þ Vn cos notð Þð ÞV 21 þ 2V1Vn cos 1� nð Þotð Þ þ V 2

n

ð25Þ

ib ¼�Pvb

v2a þ v2b

¼ P V1 sin otð Þ þ Vn sin notð Þð ÞV 21 þ 2V1Vn cos 1� nð Þotð Þ þ V 2

n

ð26Þ

Both the numerators and denominators in these equationscontain harmonic terms. Interestingly, the current harmo-nics created by these functions are not of the same order asthe voltage excitation and a single voltage harmonic givesrise to an infinite series of current harmonics. In the case ofnegative-sequence voltage unbalance (the presence of ann¼�1 term), the inverse transform introduces unbalance inthe currents and harmonic distortion, as was observedin [57].

In [58] it was suggested that the inverse transform shouldbe changed so that the correction power is divided by asinusoidal voltage set of the same amplitude as thefundamental voltage component. This prevents voltagedistortion causing current distortion and means that theAPF+load presents a high impedance to voltage distortion.It is also noted as part of the discussion in [27] that the(positive-sequence) fundamental component of the gridvoltage should be used in the calculation of active power ifthe requirement is to obtain sinusoidal current aftercompensation. A different approach is taken in [61, 62] inwhich alternative definitions of p and q are used. Theadvantage is that the denominator term in the inversetransform is more nearly constant when the voltages aredistorted or unbalanced. The implementation requireselements able to time-shift the instantaneous voltages byone-quarter of the fundamental period.

If the inverse transform (17) were modified to use themean square current, e.g. (27), the denominator would notbe time varying and would not introduce modulation of thecurrent. This will have so modified the method that it is nowequivalent to the definition of active power in (1) and is thebasis of the impedance synthesis methods to be discussed inSection 6.2.

ia ¼�ppva

vak k þ vb�� ð27Þ

A method that bears some similarity to the instantaneouspower method and to the dq0 transformation is reported in[63, 64]. No phase-locked loop is used; instead currentsignals are rotated by an angle derived from theinstantaneous voltages (y ¼ tan�1 va=vb

� �). This can also

be expressed as:

id 0

iq0

� �¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

v2a þ v2bq va vb

�vb va

� �iaib

� �ð28Þ

These currents were described as instantaneous active andreactive current but not in the sense of [22]. In a similarmanner to instantaneous active and reactive power, thesecurrents can be decomposed into steady and oscillatoryterms. Results in [63] show that under unbalanced and non-


sinusoidal voltage conditions the proposed method offers alower total harmonic distortion than the instantaneouspower method but does not eliminate harmonics or providea resistive characteristic. Under unbalanced voltage, har-monic distortion is created but to as lesser extent than ininstantaneous power methods.

6 Impedance methods

There have been two themes of development in which anAPF is controlled so that alone, or in combination withanother element, voltage and current are related by achosen value of impedance.

6.1 Impedance-based blockingA traditional filter arranges shunt and series elements withhigh and low impedance values to block or enable a signalpath. An inverter can be made to act as an impedance (by,for instance, relating its voltage to its current by a simpletransfer function) and can form one element of a filter. Foran active power filter, this normally takes the form of ahybrid of active and passive elements, although combina-tions of active units are also possible. There are many formsof hybrid filter and a discussion of their relative merits isoutside the scope of this paper. Here they will be discussedsimply to illustrate the use of impedance-based blocking.

In [65] and in [31] a series APF is used together with ashunt passive filter as part of a hybrid filter. The role of theseries APF is to block harmonic current by presenting ahigh impedance. The method used in [65] is based oninstantaneous power theory to separate the distortion termsin the current. The APF then injects voltage proportional tothis current to synthesise moderately high impedance. It isnoted that the filter used to separate the oscillatory terms inthe instantaneous power will not be perfect and willinfluence the impedance presented by the overall APF.The method in [31] is to operate the series element as acontrolled current source. A filter (in a synchronous frame)is used to identify the fundamental frequency current, whichis allowed to flow unimpeded. Any other current flowing istreated as an error, which when multiplied by the controllergain, will produce an opposing voltage. The approach takenin [66] is to use the series APF to follow a sinusoidaltemplate. Analysis of the response of the current controlloop shows that it presents an impedance to higherharmonic terms and that proper design of this controllerelement means that it forms an effective filter in combina-tion with passive filter elements. Methods in which theinjected series voltage is made proportional to the currentare described as supply current detection in [6].

6.2 Impedance-based compensationA difficulty faced in designing an APF for generalapplication is that the dynamics of the system into whichthe APF is introduced are unknown. This is a particularproblem with an APF correcting a group of loads suppliedvia a section of distribution network. The network willcontain both inductive and capacitive elements and there-fore is resonant at one or more frequencies. The correctioncurrent, which is injected by an APF into the network inresponse to the detected current distortion, perturbs thevoltage and can cause instability [67]. An alternativeapproach is to arrange a shunt element to draw a currentproportional to the voltage. This is described as voltagedetection in [6] and [67]. An interesting view of this problemfollows from ideas of passivity [28]. The APF is configuredso that it is dissipative (i.e., energy absorbing) at harmonicfrequencies such that voltage harmonics detected in the

network are damped and reduced in amplitude. Thecontroller is passive in that it presents a resistivecharacteristic. The operation of the APF is stable regardlessof line structure and parameters. The controller of [28]detects the load voltage and then sets a current reference inproportion. It works in the frequency domain using a filterbank to detect each harmonic term of interest. With asufficiently low value of synthesised resistance at aparticular frequency, the harmonics can be reduced toacceptably small values. An additional technique isintroduced so that the harmonics can be eliminated if theline structure and parameters are known. Results are shownto demonstrate the instability due to load dynamics in astandard APF, and further results show zero steady-stateerror in an adaptive version of the passivity design.

From a different standpoint, an alternative techniquebased on a resistive characteristic is obtained [29]. Thestarting point is a recognition that correcting a load so thatit draws sinusoidal current means that the load+APFpresents infinite impedance to harmonic voltages andtherefore provides no damping. A distribution systemcontaining an inductive-capacitive resonance relies on loaddamping to attenuate the resonance. The approachproposed is to control the load+APF current to synthesisea resistance. This is achieved by defining the ratio betweenthe instantaneous voltage and current. The value of thatresistance is set such that the power requirement of the loadis met. This objective is achieved by adjusting the resistancein response to error in the DC-bus voltage of the APF.Similarly, a single-phase APF compensating several loadshas been described [68], in which the supply current isforced to follow a reference current of the same shape as thegrid voltage. Again, the reference shape is scaled in responseto error in the DC-bus voltage.

A single-phase impedance scheme has been reported inwhich the voltage of the shunt APF is made to have aresistive relationship to the overall supply current [69]. TheAPF is connected via a coupling inductor and forms onebranch of the filter. Results in [69] show that the supplycurrent is corrected to approximately the same harmonicdistortion as the grid voltage.

7 DC-bus energy balance

The DC-bus of the inverter in an APF is not a DC-link butan energy store. It is normal to use a voltage-source inverterand so the link contains a capacitor. The link voltage willremain constant provided that there is no real powerexchange between the APF and the AC-grid and providedthat the power converter operates without losses. Neithercondition is realised in practice. Power loss in the powerconverter (through conduction and switching losses) mustbe compensated for by drawing a balancing power into theDC-bus from the AC-grid. Loss balancing is normallyachieved through a simple DC-bus voltage regulator, suchas shown in Fig. 8. Voltage error is acted on by a controller,the output of which is taken as a demand for fundamental-frequency active current. This term is added to thecompensation reference. The control can take place in anyconvenient domain.

The second reason that the DC-bus may deviate from itsreference is that the compensation reference falsely includesa real power component. Typically this will be an in-phasefundamental frequency component that arises from phaseor magnitude error in the distortion identifier or from timedelay in responding to a transient condition. There will alsobe some error between the identified correction current andthe current the inverter actually achieves and this may lead


to power exchange. Another possibility is that the gridvoltage is distorted and real power is being exchangedthrough harmonic terms. The DC-bus regulator must bedesigned to make up for these deficiencies in the distortionidentification.

It is important to choose the bandwidth of this controllercarefully. If the bandwidth is set too high (comparable withthe fundamental frequency), the balancing current injectedby this controller will contain components at harmonicfrequencies and will add distortion to the system. If thebandwidth is set too low, the DC-link voltage may deviatetoo far from its nominal value. An upswing of voltage mayexceed the ratings of the inverter switches and a downswingmight leave insufficient voltage for the APF to inject thecorrect compensation. A PI compensator operating on thevoltage error is often used and can be easily arranged tohave a low cross-over frequency so as to avoid interactionwith the compensation system. A predictive (dead-beat)method of DC-bus voltage control was given in [70].

In a single-phase APF there is an additional considera-tion in regulation of the DC-bus: the fundamentalfrequency reactive power of the load, if compensated, isexchanged with the DC-bus as a double-frequency term.The regulator should not respond to voltage ripple at thisdouble-frequency term. Similarly, if a three-phase APF isarranged to correct negative-sequence fundamental current,there will be a double-frequency voltage ripple on the DC-bus, which should not be responded to by the DC-busregulator.

The DC-bus regulator can make up for deficiencies ineffective separation of active and non-active current in thedistortion identifier. Taken to its extreme, the distortionidentifier can be omitted altogether. In this case, the mainAPF controller is set to eliminate all components of the loadcurrent. The APF will then seek to supply the real power ofthe load and the DC-bus regulator will respond by drawinga balancing real power from the AC grid. The advantage ofthis method is that the processing burden of the distortionidentifier is avoided. It is still necessary to control theinjected current with a feedback loop. The disadvantage isthat the APF cancels everything except the long-termaverage real power. Thus the APFmust be rated sufficientlyfor the total burden of harmonics, unbalance, reactivepower, flicker and transient real power. A variation of thisscheme has been described [58, 59] in which the DC-energy-balance term is used to set the amplitude of a reference setof supply waveforms. The inverter is then placed in closed-loop control to force these currents to flow in the supply. Asimilar approach is used in [71] but with a fuzzy elementproviding the control of the DC-bus voltage level. The useof DC-bus voltage control in impedance compensation wasnoted in Section 6.2 [29, 68].

DC energy balance methods of harmonic identificationare popular in single-phase systems where some of the

control schemes that exploit the properties of three-phasesystems are not available. In [72] a PI compensator actingon the DC bus voltage error is used to identify theamplitude of the fundamental active current componentrequired by the load. When multiplied by a unit sinusoid,this gives the reference value for the supply current. Thesupply current is then controlled in closed loop to followthis reference by applying the current error to a PWMcontrolled bridge. The relationship between the DC-buscapacitor size, the allowed voltage deviation and thecontroller design is also described in [72].

There is a special consideration for four-wire systems. Ifthere is zero-sequence voltage and zero-sequence current ofthe same frequency (commonly fundamental frequency, butthis can also apply to harmonics), there is real power carriedin the zero-sequence set. This will show as zero-sequencepower under the instantaneous power transform. If theAPF is set to cancel this term in the supply, the APF willneed to source this real power for delivery to the load [53].This requires an additional positive sequence power term tobe drawn from the supply to maintain the DC-bus balance.

8 Reference following

In the discussion so far it has been assumed that, onceidentified, the current to be injected can be accuratelyachieved. Control of current injected by the APF such thatit follows the identified reference is challenging because ofthe high rates of change and the wide bandwidth of thatreference [73]. The errors in reference following introducedby the di/dt limit of a voltage source inverter wereinvestigated in [74]. The limits arise from the interfaceinductance between the inverter and the line and the voltagethat can be imposed by the inverter. The imposed voltage isthe difference between the available DC-bus voltage and theinstantaneous voltage of the AC system. Increasing the DC-bus voltage to improve the reference following has a directimpact on the ratings of the inverter. There are alsoconstraints on the choice of interface inductor. It plays adual role. First, it defines the current given the imposedvoltage from the inverter and second it is a filter (or part ofa filter) that attenuates the switching frequency voltagecomponents created by the inverter such that acceptablysmall switching-frequency current is injected into the ACsystem. Better reference following would compromise theattenuation of the switching-frequency components. Alsodiscussed in [74] is the effect of processing delay on theformation of the reference waveform. The delay iscomposed of signal acquisition, computation and signaloutput delays. Even small delays in this signal path cancreate significant errors because the delay represents asignificant phase displacement of high-order harmonicterms. It was shown that delays of 28 ms (in a 50Hz, 128sample-per-cycle system) cause significant mis-cancellationof distortion terms. A different view of delays affecting APFaccuracy is given in [16]. Here it is argued that delay in thereference-following controller can be compensated for byapplying compensating time shifts to the individualharmonic terms in a frequency-domain identification ofthe reference. Similarly, it was argued in [75] that eachharmonic term could be adjusted for identification delay inorder to provide better tracking of the correct compensationcurrent.

Three approaches are available to force the outputcurrent of an inverter to follow a reference: current-regulated PWM, hysteresis regulation and dead-beat/predictive control [76]. The discussion here will focus on

APFI

PI

refDC

V

r(t)r´(t)

dIsI

DC-link

d (t)

sync

inverter invertercontrol

distortionidentifier

Fig. 8 An example DC-bus voltage regulator


the control of voltage source inverters, although there hasbeen discussion of the use of current-source inverters [77].

8.1 Current regulated PWMCurrent-regulated PWM is well established in manyapplication areas. The current error is acted on by, typically,a PI element and the result used in a standard pulse-widthmodulator or space-voltage vector modulation to set thevoltage synthesised by the inverter. The controller can act inany convenient domain. The design of a current-regulatedPWM system is described in [78] for closed-loop control ofgrid currents in a single-phase APF. Control in the dq0domain, including feedforward of the AC voltage, iscombined with SVM in [47].

8.2 HysteresisIn general, hysteresis regulation has the advantages that it isunconditionally stable, does not require detailed plant dataand can achieve high rates of change in the controlledvariable. These advantages are attractive in APF applica-tion where the reference can have sharp transitions and thenetwork into which the APF injects is not perfectly known.A comparison was undertaken in [79] that concluded thatthe fast response and absence of following error ofhysteresis control is advantageous in APF applications.The acknowledged disadvantage of hysteresis control is thebroadband switching noise injected by the non-constantswitching frequency. Several approaches have been exploredto maintain the switching frequency constant (or nearly so)and to synchronise the switching of all phases. Theapplication of these methods to an APF and comparisonwith other control methods is given in [73]. This paper alsoproposes a combination of feedforward and feedback(PLL) methods for setting the hysteresis bands to achievea constant switching frequency.

8.3 Dead-beat and predictive controlDead-beat or predictive control applied to current regula-tion aims to choose a voltage command for an inverter thatwill cause the current to reach a target value by the end ofthe next sample period and is therefore attractive infollowing rapidly changing references in an APF [19]. Itrequires knowledge of the system so that the rate of changeof current can be accurately modelled and the voltagechosen. The interface inductance of the inverter is a keyparameter and the opposing voltage (the AC system voltagein this case) must be measured or estimated. A developmentof a predictive current controller is described in [76]. This isa general method, not specific to an APF, and is developedin two variants for either measured or estimated EMF.Dead-beat control was considered in [80] for the case inwhich there is parameter uncertainty with particularreference to the value of the coupling inductor. Theunderlying control is a method that forms a resistive totalload. Stability limits of a current controller under parametermismatch were described and the influence of the APFcontrol properties examined. In [81] an adaptive FIR filter isused to predict ahead the current reference so that the dead-beat controller uses the predicted current at the end of thesample period as the target current.

9 Discussion

Mitigating harmonics is a key function of an active powerfilter, but there are three competing definitions of the basisfor form of current that should remain in the distributionnetwork after mitigation and hence three approaches takento mitigation. The options are: (i) the current should

contain only fundamental frequency components, (ii) thecurrent should be such that the instantaneous active poweris constant and instantaneous reactive power is zero, and(iii) the current should be entirely active current (as definedby Fryze). If it is assumed that the distribution networkvoltage is free of harmonic distortion and unbalance, thesethree objects are equivalent and in much of the publishedwork the distinction between the objectives is not madeexplicit. In choosing one objective over another as the basisfor APF control, ease of implementation and the instru-mentation requirement can be allowed to dominate if thesupply is distortion free. The waveform-compensation(fundamental-only) method is the obvious approach giventhe use of harmonic distortion limits in the relevantstandards. The major issue is the implementation of thefiltering to identify the fundamental from the harmonics.Time-domain filters have advantages over frequency-domain filters for continuity during transients, butfrequency-domain filters can achieve better selectivity inthe steady state. In three-phase systems, the synchronousreference frame (dq transform) can ease the filter imple-mentation at the expense of some processing overhead. Theinstantaneous power method is advantageous in three-phasesystems because of the ease of filter design without the needof a dq transform. The active current approach requiresidentification of the real (average) power and so is arelatively simple filtering task. This approach is implicit inmethods that use energy balance of the DC-bus voltage asthe basis of identifying the desired current.

Product standards and testing methods for harmonicdistortion often assume a ‘clean’ supply and all threeapproaches are successful. However, important issues arisewhen APFs are operated on weak sections of distributionnetwork where the voltage is distorted. From a networkoperator’s point of view, the performance of the APF canaffect the propagation of harmonic voltages through thenetwork. From the consumer’s point of view, the distortedvoltage may increase the apparent power requirement of theAPF. It would be desirable to encourage consumers toadopt a ‘model citizen’ approach and configure APFs tocontribute to a better electrical environment across thenetwork. An APF operated to draw fundamental currentonly presents an open circuit to harmonic-voltage excita-tion. This does not contribute extra distortion but neitherdoes it provide damping of the existing distortion in the waythat traditional resistive loads would. Instantaneous activepower methods respond to harmonic voltages by introdu-cing additional harmonic currents at other frequencies andcould produce unfortunate interactions with resonances inthe network. Most notably, negative sequence fundamentalvoltage causes the APF to inject harmonic current. Theactive current APF presents a resistive characteristic at allfrequencies and therefore converts non-linear loads intolinear loads. Thus, the network is provided with damping toreduce the propagation of harmonic voltages. If thisapproach is to be exploited there will need to be some co-ordination of the design of APFs with the existingapproaches to the damping of network resonances em-ployed by network operators. As yet this form of loadcurrent response is not addressed by standards.

Harmonic mitigation is not the only objective or responseof interest in an APF. Unbalanced load currents can berebalanced provided that the exchange of instantaneouspower between the phases is within the rating of the APF.All approaches to compensation can rebalance currentwhen implemented in three-phase form. Waveform com-pensation and active current methods can be implementedon a phase-by-phase basis specifically to avoid rebalancing.


Unbalance from the network voltage must also beexamined, and it has already been noted that instantaneouspower methods have an unacceptable response. Modifica-tions have been proposed to lessen or remove the harmonicgeneration through redefining the inverse transform. Takento their conclusion, these modifications result in a methodclose to one of the other known approaches. Fundamental-only methods result in balanced current despite unbalancedvoltage, whereas active current methods present a balancedimpedance to the unbalanced voltage and hence draw leastcurrent from the lowest phase voltage. The constantinstantaneous power method would draw greatest currentfrom the lowest phase voltage.

10 Conclusions

The many competing control techniques for active powerfilters have been compared and discussed under three broadapproaches to distortion compensation. There are imple-mentation advantages of some methods over others butthey can produce broadly similar performance if the supplyvoltage is undistorted. When applied in practice, distortionand unbalance of the network voltage will make theperformance of the instantaneous power method (inunmodified form) unacceptable. The fundamental-onlycompensation method will meet the necessary standardsbut does not take the next step of contributing to improvingthe network voltage. Methods based on achieving active-only current, which are equivalent to presenting a resistivecharacteristic at all frequencies, could contribute to voltagequality in the network if network planning could incorpo-rate this feature. The choice of control objective and thefiltering approach taken to separate desired from undesiredcomponents of current needs careful examination in allcases to ensure that the terms explicitly or implicitlycompensated for, which might include harmonics, funda-mental reactive power, fundamental negative sequence, zerosequence and flicker originating from either the non-linearload or the distorted network voltage, can be accommo-dated within the apparent power rating of the active filter.The choice of domain and reference frame in which toimplement the filter affects the ease with which certaincomponents can be accurately identified and separated incases where pass- and stop-bands are in close proximity,however, the processing overhead and dependence on three-phase configuration limits the choice in some cases.

11 References

1 Sasaki, H., and Machida, T.: ‘A new method to eliminate ACharmonic current by magnetic flux compensationFconsiderationson basic design’, IEEE Trans. Power Appar. Syst., 1971, 90, (5), pp.2009–2019

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Control techniques for active power filters

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