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Evaluation of Harmonic Detection Methods

for Active Power Filter Applications

Lucian Asiminoaei, Frede Blaabjer, !teffan Hansen,

"nstitute of Ener# $echnolo#, Danfoss Drives A%!,

Aalbor &niversit#, D'()*++, raasten, Denmar-,

D'(.//+, Aalbor !E, Denmar-, s0hansen1d anfoss0com0

las1iet0aau0d-, fbl1iet0aau0d-0

Abstract In the attempt to minimize the harmonic disturbances $HD reduction, the inverter efficienc# or the cost of the entire

created by the non-linear load s the choice of the active power active filter 234(2540 &suall# the comparisons are madefilters comes out to improve the filtering efficie ncy and to solve b etween different active filters, each considered as a wholemany issues existing with classical passive filters. One of the key unit, 6sometimes treated as a blac-(bo78, in which onl# thepoints for a proper implementation of an active filter is to use a

harmonic detection method used is stressed out and the rest isgood method for current/voltage reference generation. There

left behind 234, 2*4, 2940 $here is no doubt that the active filterexist many imple mentations supported by diffe re nt theories

includes beside the harmonic detection method 6alias theeither in time- or fre!uency-domain"# which continuously debatecurrent%voltae reference enerators8 also other parts such astheir performances prop osing ever better solutions. This paper

the A%D devices, the current and the dc(voltae controllers, thegives a survey of the common used t he orie s. Then# the work here

proposes a simulation setup that decouples the harmonic P:M inverter and the protection elements0 Fi0 3 shows a

reference generator from t he active filter model and its t#pical diaram of a shunt active power filters for adjustab lecontroller. In t his way the selected methods can be e !ually speed drive application0analyzed and compared with respect to their performance# which

A! D

helps anticipating possible imple mentation issues. The Po we r en eratedconclusions are collected and a comparison is given at the end# !2 " 4su pp l# h armon ic cur rent s Lo ad

h

which is useful in deciding the fut ure hardware setup

implementation. The comparison shows that the choice of Prot ect i on ;u rren t(!2 " 4

numerical filtering is a key factor for obtaining good accuracies circui t senso rsh

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$he onl# differences between the old and the new window components and the harmonics as ac(sinals0

are the first and the last samples, but all the other samples are

/ / i( @cos cos6 8 cos6 8i 68/the same0 !ince the result of the DF$ was calculated before a* * id/ /for the old window, a recursive e7pression as in 6/8 is found to i * b

( sin ( sin6 ( 8 ( sin6 @ 8 iqavoid the same calculation for the new wind ow0 "t is also * * c

demonst ra ted tha t 6/8 can be rearraned as a t ransfer funct ion where i * i and i , i , i are the currents in the d(frame respective ind q a b c

abc(frameG and is the reference anle06*8 in the form of a finite impulse response F"> filter 23+4,

23340 "t can be proved that the transfer function 6Bode plot in$hus, the detection of the harmonics becomes a matter of

Fi0 8 has the attenuation eual to Cero 6dB8 at the detectedremovin the dc(sinal with a Hih(Pass Filter 6HPF in Fi0 9

f reuenc#, for this selec ted case of h9 6 the 9 harmonic8 0thwith a cuttin freuenc# between /9 HC ( 3/+ HC8 2354, 23I4,

!uch F"> representation, or ma#be more advanced forms 23+42/34, 2//40

is ver# convenient to isolate a specific harmonic from the( Ni i i @i i

iabc dinput sinal0 a d d d d aHPF Ni

i( d abc

b i i @i i bFilterin Ni

i3/!( 3 c c"#i+ +

$ 6 8 G e7p( h i(h

! ! 6/8i +3 68 u" 6 (

,8 # 6,8 ( #6,( !8 @ + " 6, 38h au PLL!h h ubc

" 68 (3 3 ( !

6*8 68 Fi0 90 Princip le alorithm of the s#nch ronous fundamental d(frame0h# 68 ! 3( + h h ( 3

h/.&. 0ynchronous harmonic dq-frame is similar in

principle as the fundamental d(frame method0 $he e7ceptionBo de D ia ram3 ++

is that the harmonic d( frame rotates now with a fre uenc#

eual to the selected harmonic0 $hus, in the harmonic d(+ frame, onl# the respective harmonic will be a dc(sinal and all

o ther freuencies includin the fundamental will be ac(

components0 $he detection of the respective harmonic(3 ++

resumes in removin the ac(sinals with low(pass filters 6LPF

in Fi0 )8 2/+4, 2/*4, 2/40!#st em >D F $(/ ++

F r e uen c# 6 HC8 /9+i i( @ i

i(

abc dd9 d9 d9 d9LPF9i i( @ i i(

d abc(* ++ Filterin9 9 9 9+ 3 / * 9

3+ 3 + 3+ 3 +F r e uen c# 6 H C8 (

9 9

i i @ i i( (

abc d iN

i d5 d5 d5 d5Fi0 0 Bode plot of >ecursive Discrete Fourier transform

aLPFa i

N

5i i i @ i(

i(db abc

b

as in 6*8 with h9 and !)0 5 5 5

Filterin 5 iNi 5 cc(

$he common drawbac-s of the Fourier theories and its 5 5i i @ i i( (

dvariants ma# be listed as a proper usae of the !hannon abc d- d- d- d- LPF -i i @ i(

i(d abctheorem, a proper desin of the anti(aliasin filter, a careful Filterin - - - -

-

s#nchroniCation between the samplin and fundamental (u

freuencies, a careful application of the windowin function, a ua PLLub

proper usae of the Cero(paddin if the inter(harmonics arec

Fi0 )0 Diaram of the multiple s#nchronous harmonic d( transformations0

reuired, lare memor# reuirements to store the samples of ?ne drawbac- is the necessit# of the anular positionthe last fundamental period, lare co mputation power reuired

possibl# from an PLL, that reuires a careful implementationfor the D!P, the impossibilit# of havin precise results in

if the voltaes are not balanced and sinusoidal0 Another issuetransient conditions 2*40

is the numerical implementation of the filters 6HPF respective/. Time-domain Methods

LPF8 that have influence in the APF d#namic and accurac#0

$he time(domain methods are mainl# used to ain more Due to the non(ideal filterin rejection and the phase shiftin

speed or fewer calculations compared to the freuenc#(domain introduced b# the numerical filters, the reference sinal will

methods . not be e7actl# in the opposite phase nor with the same shape

as the acuired disturbance0 $his limitation adds to the/.1. 0ynchronous fundamenta dq-frame is derived from

e7istin dela#s from the A%D and P:M bloc-s reuirinthe space vector transformation of the input sinals, which

separate compensation alorithms0 $his can turn to be difficultinitiall# are achieved in the abc(coordinates 6stationar#

in practice especiall# for the harmonic d(frame where thesereference frame8 from the sensors and then transformed into

compensations and the respective controllers must be tunedthe d(coordinates 6rotatin reference frame with fundamental

individuall# 2/*40 Another issue is encountered for unbalancedfreuenc#8 b# means of the Par- transformation 680 $he d(

load currents, therefore, the s#stem must include all positive,frame rotates with the fundamental anular freuenc# that

Cero and neative components, which aain amplifies thema-es in this frame the fundamental currents to appear as dc(

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number of calculations and ma-es a more difficult tunin of @!

"nput sin al ? utpu tK s(

1

each controller0 @ 2s / /1However, the d(theor# is e7tensivel# used in active filters @

! ? utp utK s &because o f well(covered literatures and individual co ntrol of ( 2 @s / /&hamronics0 @

! ? utp ut( K s '2@s

/.'. 2nstantaneous ower theory (and ariants) !/ /

'

determines the harmonic distortion from the instantaneous

Fi0 I0 Diaram of the eneraliCed interators app roach0power calculation in a three(phase s#stem, which is the

multiplication of the instantaneous values of the currents and $he transfer function of the s#stem in Fi0 I is iven in

Fi0 . fo r different values of the interation constant K 6herevoltaes 2/.40 $he calculations ma# be done in aO (coordinatesi

chosen the same for all interators80 As it can be seen oneas in 6980

issue is the determination of optimum interation constant K i 698 a 3 a i * since a smaller value ives a ood selectivit# but determines a(q i3 a 3

slow d#namic response0 Furthermore, the controller must be$he values of the instantaneous power and q* which are

tuned dependin on the e7istin plant 6not present in Fi0 Ithe real respective imainar# powers, contain dc( and ac(

and Fi0 .8, which ma-es the method dependent on thecomponents 2/94, 2/I4 dependin on the e7istin active,

transfer function of the e7istin process0reactive and distorted powers in the s#stem0 $he dc(

+components of and q represent the active and reactive

powers and must b e remo ved with hih(pass filters 6HPF in(3 ++

Fi0 5 with a cuttin freuenc# between 9 HC ( *9 HC8 to

retain onl# the ac(sinals0 $he ac(components calculated bac-(/ ++

to the abc(frame represent the harmonic d istortion, which is

iven as the reference for the current controller0 Aain the 'i 3 +(* ++

presence of the numerical filters have influence in the d #namic 'i 3 ++

' i9 + +and the accurac# for the entire APF0( ++

3++ 3+ 33 +/ 3+ *3+

Freu enc# 6HC8P has e < ol t a es

Fi0 .0 Bode ch aracteristic of the s#stem in Fi0 I for d ifferent values of the K ia; alcu l at io n constant0 $he interators are tuned for th e 9 , 5 and 33 harmonics of a 9+ th th t h N

ibHP F a4al c ul a t i on HC fundamental freuenc#0 a 3 4a lc u l a ti onc Fi l t er in ; al cul at i on N Ni ia b i N ?ther attempts for harmonic detection methods areLo ad ; ur rent s aq

q i Nq HP F b

i Ni i N3 enumerated in the literature li-e sinusoidal subtraction, notchi N c a ;al cu l ati o n Fi l t er in i c b

i ifilterin, Fr#Ce(BucholC(Depenbroc-, 'alman filters 2+4,a 3i

c

234, 2/4, but because of different issues with non(idealFi0 50 Principle diaram of the instantaneous power theor#0

conditions met in a real implementation, these methods are not$he calculatio n in 698 is affected if the s#stem has Cero(

larel# used in active power filters0seuence component due to an e7istin unbalance0 $herefore,

also a p 6also referred sometime as + power8 component+

must be added to provide a complete anal#sis 2/I40 ?ther"""0 ; H D M? MPA>"!?= ? F A>M ? ="; E$E;$"? = E$H ?D !techniues based on the same principle improve different

other feature, as li-e the cancellation of the neutral currents A comparison is done ne7t b# simulations to reveal the

2*+4, the minimiCation of the ener# storae element 2*/4, the performance for some of the presented methods in respect to

pre(processin of the input voltaes to -eep onl# the positive the settlin time and the accurac# of the results0 An inputseuence 2/I40 sinal 6the load current for a shunt APF8 is artificiall#

/.5. 6eneraied inte7rator (and ariants) comes out from constructed from the 9+ HC fundamental component and the

the limitation that a P" controller in d(frame which does not t hsum of several harmonics0 $he 9 harmonic has an amplitudehave a ood trac-in capabilit# for non(continuous sinals of about *+ Q from the fundamental and is injected alone for a

6i0e0 harmonics8 and therefore creates stead#(states errors0 specific time interval0 Fi0 3+ shows how the test inp ut sinal$hus for non(continuous sinals a better approach is b# usin is created for a sinle phase0 $he parameters used to obtain the

eneraliCed interators0 A eneraliCed interator derives the resultant sinal in Fi0 3+ are iven in more details in $able ""0interation in time(domain as a second order transfer function "t can be noticed that the resultant sinal has a similar shape as

in 8aace- domain 6Fi0 I8, which will ive an infinite ain at the line currents obtained from a three(phase diode rectifier0the selected resonant freuenc#0 $hus both the filterin and

$able ""0 $he characteristics of the input sinal0the controllers can be implemented in the statio nar#(frame

Indices 'mpl itude (hase )tarting time *s+instead of the rotatin(frame0 !uch approach leads to a numberFundamental *+ +, 3/+, /+ +

of different implementations since one can decide either for9 harmonic 3+ 976+, 3/+, /+8 +0+9th

individual harmonic compensation 6notch filter8 2*)4 or for a Hi h er h arm on ics 3 09broadband approach 6band(pass, hih(pass or low(pass filters8 65 , 33 , 3* , 35 8 e ac h h 7 6+, 3/+, /+8 + 039 a ll at the s am e t im et h t h th th

2**4, 2*94, 2*.40

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thAs the 9 harmonic is separated from the other hiher $he methods considered for this comparison are listed in

harmonics between the time(interval of +0+9 s R +039 s, the $able """ where also some of their characteristics are provided

o ut put obta ined fro m eac h de te cti on meth od sho ul d be fr om dif fe re nt re fe renc es in S""0

predictable now and eas# to be studied durin this interval0 Fi0 3/ illustrates the results of the simulation as time

$herefore, the oal is to record the output of the harmonic waveforms obtained from each method0 $he settlin time, the

detection method in respect to the settlin time and the accurac# overshoot and the phase error are measured for each detectiont hi n d ete ct in t he 9 ha rmo nic 6 as ill ust rat ed in Fi 0 33 80 me th od a s i ve n in t he $ab le " DF$ method

the abc(frame0 the response is better but still limited to the duration of the

"n the case of a real active filter implementation the output window as an# F"> filter response0

of each method represents the reference imposed to the inner $he fundamental d(frame has a faster response and a ood

loop controller 6i0e0 current for a shunt APF80 $his controller, overshoot but suffers from a lare phase error due to the phase

which has a certain response time, will introduce even more shift created b# the HPF0 $herefore, the compensation currents

dela#s in the loop due to the limited trac-in capabilit#, but this are not in phase with the disturbance, which is an impediment

limitation does not appear here0 $he alebraic reconstruction for an e7act harmonic cancellation0

into the abc(frame emulates an ideal inner loop controller0 ! t ar t o f t h e 9 h a r mo n i cth!inle P has e! ina l

/ +Fu ndament al ;urren t 2A4

+/+ 2A4

(/+ 2A4

++0+ +0+)+0+I +03 +03/+ 03 +03)+03I +0/

( / + D F $ 9 t h2A43 +2A4

6 a 8+++0+ /+0 + +0+)+0+I +03 +03 /+03 +03)+ 03I +0/

9th Harmonic

(3+3+ 2A4 2A4

+0+ +0+)+0+I +03 +03/+ 03 +03)+03I +0/

>ecursiv eDF $+ 3 +2A4

+

( 3 +2A4 6 b8(3+ 2A4

++0+ /+0 + +0+)+0+I +03 +03 /+03 +03)+ 03I +0/

Hihe r Harmonics+0+ +0+)+0+I +03 +03/+ 03 +03)+03I +0/

92A4 Fundamen tald(Fram e3 +2A4

++

(3+ 2A4

(9 2A4 6c8 +0+ +0+)+0+I +03 +03/+ 03 +03)+03I +0/

++0+ /+0 + +0+)+0+I +03 +03 /+03 +03)+ 03I +0/ 9th Harm onic d(Fram e3 +2A4

>es ultan t!in al6phase A8

+/+ 2A4

(3+ 2A4+

+0+ +0+)+0+I +03 +03/+ 03 +03)+03I +0/

( / +2A4p( $ heor#

3 +2A46 d8

++0+ /+0 + +0+)+0+I +03 +03 /+03 +03)+ 03I +0/+

$ime 2s4

Fi0 3+0 ?btainin the input test sinal for testin the harmonic detection (3+ 2A4

techniues0 a8 fundamental current, b8 9 harmonic cu rrent, c8 hiherth +0+ +0+)+0+I +03 +03/+ 03 +03)+03I +0/

harmonics currents, d8 resultant test sinal0 9 eneraliC ed "nt eratorth3 +2A4

9 +HC+

* (p h a s e

! (3+si nal $armonic 2A4>e c o rd th e%etectio n&eth o d r e s p o n s e fo r 9 th +0+ +0+)+0+I +03 +03/+ 03 +03)+03I +0/th

t h e 9tun ed fo r, th

$ime 2s4Hihe r ;o m p a re

Fi0 3/0 $he d#namic responses obtained for the an al#Ced methodsharmonics t o th eori inal

accordin to Fi0 330Fi0 330 !imulation setup realiCed to stud# the performance of different

$able "esults obtained from the harmonic detection methods 6Fi0 3/80harmonic detection meth ods isolated from the model of the active filter0(hase error Overshoot

$armonic detection method )ettling time$able """0 !ettins used for confiurin the harmonic detection method0

*ms+ *deg+ or ripple *+$armonic detection method haracteristi cs DF$ 9 *+ ms +T +Qth

DF$ for the 9 harmonic /9) samples % fundamentalth >ecursive DF$ /+ ms +T +Q>DF$ /9) samples % fundamental Fundamental d(Frame 3+ ms **0T 3Q overshootF und amen tal d (fr am e HP F 3 /+ HC, / o rd er Bu tt er wo rt hnd

9 Harmonic d(Frame /+ ms +T 3+Q rippleth9 harmo nic d (frame LPF /+HC, / o rder Butterwo rthth n d

p( $heor# 3+ ms *0/T *+Q overshoot"n st ant an eo us p th eo r# H PF 3+ HC, * o rd er Bu tter wo rt hst

9 eneraliCed "nterator *+ ms +T +Qth9 eneraliCed interator T*++th

2

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As a compromise the HPF ma# be implemented with a low HPF techniues, the second method ives a better result,

pass filter 6LPF8 as in 3(LPF, where in this case the dc(sinals e7plicable b# the smaller phase(shift, as measured in $able "eardin which o f these techniues is be tter for a iven

selectivit# or a low cuttin freuenc# must be selected in order case, some assumptions ma# be made as li-e the e7istence of a

to reduce it0 However, increasin the filter order or decreasin fast D!P that will alleviate the numerical issues0 Also the

the cuttin freuenc# will derade the response time0 acuisition of both voltaes and currents miht be beneficial for

For the p(theor# the output has a characteristic iven b # the the APF circuit protections or other enhanced features provided

HPF used0 "n this case the o vershoot suffers, while the response b # the APF0 $herefore, the desin should mainl# consider the

time is relativel# fast0 $he phase error of the HPF ma# be characteristics of the distorted currents for instance, the

improved also b# selectin a 63(LPF8 implementation instead0 dominant harmonic currents, their levels, the variation in time,

"n the case o f the eneraliCed interator the main limitation and the e7istence of certain unbalance in the s#stem0

is iven b# the settlin time, which depends of the inter ation ;u rre n t p h as e(A$H D *3 0+ Qconstant Tused0 !uch lare response time 6comparable the / ii 2A4

i * +QDF$ case8 is not suitable for applications where the harmonics 9

+

freuentl# var# within a few fundamental c#cles0(/ 2A4

>eardin the presence of the hiher harmonics it was

observed that the# are well rejected b# harmonic d(frame, + +0+3 +0+/ +0+* +0+ +0+9 +0+) +0 +5F un d am e nt a l d (F ra m e

while the DF$ and >DF$ are disturbed at least 3 fundamental $ HD 3 0 )Q/2A4 i

c#cle0 $he eneraliCed interator method is however, affected i 3 Q9

+b# these hiher harmonics since there was no other controller

(/tuned to remove these harmonic components0

2A4

$he influence of the filter s ma# be seen in Fi0 3*, wher e thr ee+ +0+3 +0+/ +0+* +0+ +0+9 +0+) +0 +5

of the presented methods are practicall# tested with a d!pace 9 t h H a rmo ni c d (F r am e$ H D . 0 /Q

s#stem 6$M!*/+F/+8 for an active filter implementation0 $he /2A4 ii ) 0/ Q9

load currents from a three(phase diode rectifier ar e processed b# the +

respective harmonic detection methods and the sinal obtained 6i0e0 (/ 2A4

current reference8 is summed with the distorted current0 $he+ +0+3 +0+/ +0+* +0+ +0+9 +0+) +0 +5

summation done here e7cludes the contribution of the currentp $ h eo r#

$ H D ) 0 )Qcontroller and the P:M inverter that will actuall# decrease the /2A4 ii ) 0 Q

trac-in speed even more b# introducin more dela#s0 $he results 9+

t hare presented in Fi0 3* where both the $HD and the level of the 9i (/ 2A4

harmonic are calculated for each result0

Based on the conclusions obtained from the above + +0+3 +0+/ +0+* +0+ +0+9 +0+) +0 +5

simulations the practical results in Fi0 3* have no w an easier $ime 2s4

Fi0 3*0 P ractical validation of the fundamental d(frame, harmonic d(frameinterpretation0 For instance even if both methods, fundamentaland instantaneous p(theor#0 $he choice of the filter implementation is

d(frame and instantaneous p(theor# are implemented withresponsible for a ood current reference framewor-0

$able

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2/+4 M0 Aredes, L0F0;0 Monteiro, J A contro strate7y for shunt a ctie fiter K,"ech-a, $0 =andui, 0 Wianhon, P0 !icard,J A comaratie study of matrices in three-hase four-wire systems K, Proc0 of Power ;onversionharmonic detection a7orithms fo r actie fiters and hybrid actie fiters K, ;onference 3..5, adar and !inal Processin, 24;0#/oo7na* 3.., pp0 *)+(*)0Proc0 of PE!;Y.5,

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