Evaluation of Harmonic Detection Methods for Active Power Filter Applications

Transcription

1 Evaluaton of Harmonc Detecton Metods for Actve Power Flter Applcatons Lucan Asmnoae, Frede Blaabjerg, Insttute of Energy Tecnology, Aalborg Unversty, DK-922, Aalborg SE, Denmark, Abstract In te attempt to mnmze te armonc dsturbances created by te non-lnear loads te coce of te actve power flters comes out to mprove te flterng effcency and to solve many ssues exstng wt classcal passve flters. One of te key ponts for a proper mplementaton of an actve flter s to use a good metod for current/voltage reference generaton. Tere exst many mplementatons supported by dfferent teores (eter n tme- or frequency-doman), wc contnuously debate ter performances proposng ever better solutons. Ts paper gves a survey of te common used teores. Ten, te work ere proposes a smulaton setup tat decouples te armonc reference generator from te actve flter model and ts controller. In ts way te selected metods can be equally analyzed and compared wt respect to ter performance, wc elps antcpatng possble mplementaton ssues. Te conclusons are collected and a comparson s gven at te end, wc s useful n decdng te future ardware setup mplementaton. Te comparson sows tat te coce of numercal flterng s a key factor for obtanng good accuraces and dynamcs for an actve flter. Keywords power system armonc; armonc dstorton; actve flters; armoncs analyss; Dscrete Fourer Transform; dgtal sgnal processng, sgnal detecton. I. INTRODUCTION It s a fact tat te contnuous prolferaton of te electronc equpments eter for ome applances or for ndustral use as te drawback of ncreasng te nonsnusodal currents nto te power network. Dfferent mtgaton solutons are currently proposed and used nvolvng eter passve tecnques, actve tecnques or peraps more elaborated combnatons suc as wave-sapng or ybrd flters. In te last decades te use of actve tecnques as become more nterestng due to te tecnologcal progress n swtcng devces, DSP s, numercal metods and control algortms. As a result, f ntally te actve flters were tested manly n laboratory condtons now tend to be mplemented more and more n real-lfe applcatons. Terefore, tere s an ncreased nterest to develop and use te best detecton metod of te dstorted currents/voltages tat ave to be compensated. Tere are numerous publsed metods tat descrbe dfferent topologes and dfferent algortms used for actve flterng. In many of tem t usually prevals te descrpton of a sngle metod but tere are publcatons wc explan and compare couples of suc metods descrbng ter advantages and dsadvantages by gvng as fnal ndces te dynamcs, te Steffan Hansen, Danfoss Drves A/S, DK-63, Graasten, Denmark, s.ansen@danfoss.com. THD reducton, te nverter effcency or te cost of te entre actve flter [1] [7]. Usually te comparsons are made between dfferent actve flters, eac consdered as a wole unt, (sometmes treated as a black-box), n wc only te armonc detecton metod used s stressed out and te rest s left bend [1], [3], [5]. Tere s no doubt tat te actve flter ncludes besde te armonc detecton metod (alas te current/voltage reference generators) also oter parts suc as te A/D devces, te current and te dc-voltage controllers, te PWM nverter and te protecton elements. Fg. 1 sows a typcal dagram of a sunt actve power flters for adjustable speed drve applcaton. Power supply Voltage sensors Energy storage element Protecton crcut Current sensors PWM Inverter Controller Controller [ I ] [ I ] Generated armonc currents A/D Current sensors Pre-Processng Harmonc Detecton Metod Current reference generator ASD Load Fg. 1. One-lne dagram of a sunt actve flter n a feed-forward confguraton wt an adjustable speed drve as load. Te dagram sows te place of te armonc detecton block nsde te actve flter. If some of te elements enumerated above are te same for dfferent actve flter topologes, owever, ts wll not be te case for te controller block of wc performance and tunng precson mgt gve dfferent responses for te entre actve flter. Consequently, te comparson done between dfferent actve flters tat use respectvely dfferent armonc detecton metods s not a drect effect of only te performance of te detecton block, but also of te qualty of te controller. Terefore, ts work analyzes te armonc detecton metods decoupled from te entre actve flter n order to see ts contrbuton. At frst, te work nvestgates te teoretcal background of te common used armonc detecton metods. Terefore te paper gves a concse descrpton of eac. Te actual study contrbutes to te exstng comparsons [1]-[7] by addng a

2 new trend for te armonc detecton wt resonant controllers [34]-[39]. Ten, as an nvestgaton ts paper extends te exstng comparsons found n [2] wt a proposed smulaton study. Te study solates te armonc detecton metod from te actve flter and replaces te nput sgnal from te sensors wt a known sgnal, artfcally constructed. Tus, te output sgnal tat sould be predctable now s recorded and compared between eac analyzed armonc detecton metod. Te paper presents te most relevant results of te smulatons. Dfferent ssues observed n te study are lsted and also te lmtatons of ts approac are descrbed. Te results ndcate tat te coce of numercal flters s a key factor for obtanng good accuraces and dynamcs. Fnally te released conclusons are compared n respect to dfferent crtera, wc gves an overvew and elps decdng on te fnal expermental setup for an actve flter. II. HARMONIC DETECTION METHODS One of te most dscussed software part (n te case of an DSP mplementaton) of an actve flter s te armonc detecton metod. In bref, t represents te part tat as te capablty of determnng specfc sgnal attrbutes (for nstance te frequency, te ampltude, te pase, te tme of occurrence, te duraton, energy, etc.) from an nput sgnal (tat can be voltage, current or bot) by usng a specal matematcal algortm. Ten, wt te aceved nformaton, te controller (current controller n Fg. 1) s mposed to compensate for te exstng dstorton. It can be easly seen tat f tere are some errors wen estmatng one of te above attrbutes, te overall performance of te actve flter could be serously degraded n suc a way tat even sopstcated control algortms cannot recover te orgnal nformaton. Terefore, dfferent algortms emerged for te armonc detecton, wc led to a large scentfc debate on wc part te focus sould be put on, te detecton accuracy, te speed, te flter stablty, easy and nexpensve mplementaton, etc. Te classfcaton of tese metods can be done relatve to te doman were te matematcal model s developed [7]. Tus, two major drectons are descrbed ere, te tmedoman and te frequency-doman metods. Suc classfcaton s gven Table I. Te descrpton of te metods wll be provded n te followng. TABLE I: Classfcaton of te most used armonc detectons n APF. Doman Harmonc Detecton Metod Frequency-doman Dscrete Fourer Transform (DFT) Fast Fourer Transform (FFT) Recursve Dscrete Fourer Transform (RDFT) Tme-doman Syncronous fundamental -frame Syncronous ndvdual armonc -frame Instantaneous power pq-teory and varants Generalzed ntegrators and varants A. Frequency-doman Metods Te frequency-doman metods are manly dentfed wt Fourer analyss, rearranged n suc a manner tat ts provdes te result as fast as possble wt a reduced number of calculatons, to allow a real-tme mplementaton n DSP s. A.1. Dscrete Fourer Transform (DFT) s a matematcal transformaton for dscrete sgnals wc gves bot te ampltude and pase nformaton of te desred armonc by calculatng (1). N 1 N 1 n n X = x( n) cos j x( n) sn n= N n= N X = X r j X (1) 2 2 X = X r X ; X ϕ = arctan X r were: N s te number of samples per fundamental perod; x(n) s te nput sgnal (voltage or current) at pont n; X s te complex Fourer vector of te t armonc of te nput sgnal; X r s te real part of X ; X s te magnary part of X. X s te ampltude of te vector; ϕ s te pase of te vector. Once te armoncs are detected and solated wt (1) t s just a matter of reconstructon back n tme-doman to create te compensaton sgnal for te controller [8], [9]. A.2. Fast Fourer Transform (FFT) follows te same matematcal representaton as n (1) but n a dfferent form [14] to reduce te number of calculatons and ence te requred DSP tme. Te algortms use an operaton called decmaton (wc can be n tme- or frequency-doman) tat reles on te recursve decomposton of an N pont transform nto 2 pont transforms of N/2 (Fg. 2). Ts process can be appled to any N-sampled sgnal f N s a regular power of 2, so te decomposton can be appled repeatedly untl te trval 1-pont transform s reaced and calculated. Tus, te total number of calculatons are reduced from N 2 to N log 2 (N). x() x(2) x(1) x(3) x(n-1) N/2 Pont DFT x(n-2) N Pont Recombne X(N/2-1) f(n k ) F(ω Algebra X(N/2) k ) N/2 Pont DFT X() X(1) X(N-1) Fg. 2. Exemplfcaton of te decmaton n tme algortm for te Fast Fourer Transform (FFT). A.3. Recursve Dscrete Fourer Transform (RDFT) uses te same prncple of te DFT (1) but calculated on a sldng wndow [13], [16]. Suc sldng wndow s movng at every samplng tme wt a number of samples (usually just one for smplcty). Tus, te DFT analyss can actually be performed on te new set of samples (te new wndow). RDFT Fundamental perod Movng wndow Sampled nput sgnal Fg. 3. Te prncple of te movng wndow DFT.

3 Te only dfferences between te old and te new wndow are te frst and te last samples, but all te oter samples are te same. Snce te result of te DFT was calculated before for te old wndow, a recursve expresson as n (2) s found to avod te same calculaton for te new wndow. It s also demonstrated tat (2) can be rearranged as a transfer functon (3) n te form of a fnte mpulse response FIR flter [1], [11]. It can be proved tat te transfer functon (Bode plot n Fg. 4) as te attenuaton equal to zero (db) at te detected frequency, for ts selected case of =5 (te 5 t armonc). Suc FIR representaton, or maybe more advanced forms [1] s very convenent to solate a specfc armonc from te nput sgnal. Magntude (db) N 1 1 X = x( ) W ; W = exp j N = N (2) 1 X ( k) = ( x( k) x( k N) ) W X ( k 1) N N X ( z) 1 1 z H ( z) = = 1 (3) x ( z) N 1 W z Bode Dagram System: RDFT Frequency (Hz): Frequency (Hz) Fg. 4. Bode plot of Recursve Dscrete Fourer transform as n (3) wt =5 and N=64. Te common drawbacks of te Fourer teores and ts varants may be lsted as: a proper usage of te Sannon teorem, a proper desgn of te ant-alasng flter, a careful syncronzaton between te samplng and fundamental frequences, a careful applcaton of te wndowng functon, a proper usage of te zero-paddng f te nter-armoncs are requred, large memory requrements to store te samples of te last fundamental perod, large computaton power requred for te DSP, te mpossblty of avng precse results n transent condtons [3]. B. Tme-doman Metods Te tme-doman metods are manly used to gan more speed or fewer calculatons compared to te frequency-doman metods. B.1. Syncronous fundamental -frame s derved from te space vector transformaton of te nput sgnals, wc ntally are aceved n te -coordnates (statonary reference frame) from te sensors and ten transformed nto te -coordnates (rotatng reference frame wt fundamental frequency) by means of te Park transformaton (4). Te frame rotates wt te fundamental angular frequency tat makes n ts frame te fundamental currents to appear as dccomponents and te armoncs as ac-sgnals. a d 2 cosθ cos( θ ) cos( θ ) = 3 3 b q 3 (4) snθ sn( θ ) sn( θ ) 3 3 c were: d, q and a, b, c are te currents n te -frame respectve n -frame; and θ s te reference angle. Tus, te detecton of te armoncs becomes a matter of removng te dc-sgnal wt a Hg-Pass Flter (HPF n Fg. 5 wt a cuttng frequency between 25 Hz - 12 Hz) [17], [18], [21], [22]. a b c θ d = d d q = q - q ~ u a u b u c - ~ HPF Flterng θ PLL d ~ q ~ θ Fg. 5. Prncple algortm of te syncronous fundamental -frame. B.2. Syncronous armonc -frame s smlar n prncple as te fundamental -frame metod. Te excepton s tat te armonc d-q frame rotates now wt a frequency equal to te selected armonc. Tus, n te armonc frame, only te respectve armonc wll be a dc-sgnal and all oter frequences ncludng te fundamental wll be accomponents. Te detecton of te respectve armonc resumes n removng te ac-sgnals wt low-pass flters (LPF n Fg. 6) [2], [23], [24]. d5 = - d5 ~ - d5 d5 LPF q5 = - q5 ~ q5-5 q5 5 Flterng θ 5 θ 5 d7 = - d7 ~ - d7 d7 a LPF a q7 = - q7 ~ q7-7 b b q7 c 7 Flterng c θ 7 θ 7 dk = - dk ~ dk - dk LPF qk = - qk ~ qk - k qk k Flterng θ κ θ κ a u b PLL θ c Fg. 6. Dagram of te multple syncronous armonc d-q transformatons. One drawback s te necessty of te angular poston possbly from an PLL, tat requres a careful mplementaton f te voltages are not balanced and snusodal. Anoter ssue s te numercal mplementaton of te flters (HPF respectve LPF) tat ave nfluence n te APF dynamc and accuracy. Due to te non-deal flterng rejecton and te pase sftng ntroduced by te numercal flters, te reference sgnal wll not be exactly n te opposte pase nor wt te same sape as te acqured dsturbance. Ts lmtaton adds to te exstng delays from te A/D and PWM blocks requrng separate compensaton algortms. Ts can turn to be dffcult n practce especally for te armonc -frame were tese compensatons and te respectve controllers must be tuned ndvdually [23]. Anoter ssue s encountered for unbalanced load currents, terefore, te system must nclude all postve, zero and negatve components, wc agan amplfes te a b c

4 number of calculatons and makes a more dffcult tunng of eac controller. However, te -teory s extensvely used n actve flters because of well-covered lteratures and ndvdual control of amroncs. B.3. Instantaneous power teory (and varants) determnes te armonc dstorton from te nstantaneous power calculaton n a tree-pase system, wc s te multplcaton of te nstantaneous values of te currents and voltages [29]. Te calculatons may be done n αβ-coordnates as n (5). p vα vβ α = (5) q vβ vα β Te values of te nstantaneous power p and q, wc are te real respectve magnary powers, contan dc- and accomponents [25], [28] dependng on te exstng actve, reactve and dstorted powers n te system. Te dccomponents of p and q represent te actve and reactve powers and must be removed wt g-pass flters (HPF n Fg. 7 wt a cuttng frequency between 5 Hz - 35 Hz) to retan only te ac-sgnals. Te ac-components calculated back to te -frame represent te armonc dstorton, wc s gven as te reference for te current controller. Agan te presence of te numercal flters ave nfluence n te dynamc and te accuracy for te entre APF. Pase Voltages va v Calculaton b vc v α v β Load Currents la Calculaton lb α lβ lc l p Calculaton p q q HPF Flterng HPF Flterng p ~ q ~ Calculaton α β Calculaton a b c Fg. 7. Prncple dagram of te nstantaneous power teory. Te calculaton n (5) s affected f te system as zerosequence component due to an exstng unbalance. Terefore, also a p (also referred sometme as "" power) component must be added to provde a complete analyss [28]. Oter tecnques based on te same prncple mprove dfferent oter feature, as lke te cancellaton of te neutral currents [3], te mnmzaton of te energy storage element [32], te pre-processng of te nput voltages to keep only te postve sequence [28]. B.4. Generalzed ntegrator (and varants) comes out from te lmtaton tat a PI controller n -frame wc does not ave a good trackng capablty for non-contnuous sgnals (.e. armoncs) and terefore creates steady-states errors. Tus for non-contnuous sgnals a better approac s by usng generalzed ntegrators. A generalzed ntegrator derves te ntegraton n tme-doman as a second order transfer functon n Laplace-doman (Fg. 8), wc wll gve an nfnte gan at te selected resonant frequency. Tus bot te flterng and te controllers can be mplemented n te statonary-frame nstead of te rotatng-frame. Suc approac leads to a number of dfferent mplementatons snce one can decde eter for ndvdual armonc compensaton (notc flter) [36] or for a broadband approac (band-pass, g-pass or low-pass flters) [33], [35], [39]. a b c Input sgnal s s s s KI 2 ω 2 1 s KI 2 ω 2 2 s KI 2 ω 2 3 Outputω 1 Outputω 2 Outputω 3 Fg. 8. Dagram of te generalzed ntegrators approac. Te transfer functon of te system n Fg. 8 s gven n Fg. 9 for dfferent values of te ntegraton constant K (ere cosen te same for all ntegrators). As t can be seen one ssue s te determnaton of optmum ntegraton constant K, snce a smaller value gves a good selectvty but determnes a slow dynamc response. Furtermore, te controller must be tuned dependng on te exstng plant (not present n Fg. 8 and Fg. 9), wc makes te metod dependent on te transfer functon of te exstng process. Magntude (db) K=1 K=1 K= Frequency (Hz) Fg. 9. Bode caracterstc of te system n Fg. 8 for dfferent values of te K constant. Te ntegrators are tuned for te 5 t, 7 t and 11 t armoncs of a 5 Hz fundamental frequency. Oter attempts for armonc detecton metods are enumerated n te lterature lke snusodal subtracton, notc flterng, Fryze-Bucolz-Depenbrock, Kalman flters [4], [41], [42], but because of dfferent ssues wt non-deal condtons met n a real mplementaton, tese metods are not largely used n actve power flters. III. COMPARISON OF HARMONIC DETECTION METHODS A comparson s done next by smulatons to reveal te performance for some of te presented metods n respect to te settlng tme and te accuracy of te results. An nput sgnal (te load current for a sunt APF) s artfcally constructed from te 5 Hz fundamental component and te sum of several armoncs. Te 5 t armonc as an ampltude of about 3 % from te fundamental and s njected alone for a specfc tme nterval. Fg. 1 sows ow te test nput sgnal s created for a sngle pase. Te parameters used to obtan te resultant sgnal n Fg. 1 are gven n more detals n Table II. It can be notced tat te resultant sgnal as a smlar sape as te lne currents obtaned from a tree-pase dode rectfer. Table II. Te caracterstcs of te nput sgnal. Indces Ampltude Pase Startng tme [s] Fundamental 3, 12, 24 5 t armonc 1 5x(, 12, 24).5 Hger armoncs (7 t, 11 t, 13 t, 17 t x (, 12, 24) ) eac all at te same tme

5 As te 5 t armonc s separated from te oter ger armoncs between te tme-nterval of.5 s.15 s, te output obtaned from eac detecton metod sould be predctable now and easy to be studed durng ts nterval. Terefore, te goal s to record te output of te armonc detecton metod n respect to te settlng tme and te accuracy n detectng te 5 t armonc (as llustrated n Fg. 11). In order to ave te same base of comparson for all metods, te output results wll be dsplayed n te same frame as te orgnal nput sgnal. Tus, for example for te -frame te d and q components are transformed back nto te -frame. In te case of a real actve flter mplementaton te output of eac metod represents te reference mposed to te nner loop controller (.e. current for a sunt APF). Ts controller, wc as a certan response tme, wll ntroduce even more delays n te loop due to te lmted trackng capablty, but ts lmtaton does not appear ere. Te algebrac reconstructon nto te -frame emulates an deal nner loop controller. 2 [A] Fundamental Current -2 [A] (a) t Harmonc 1 [A] -1 [A] (b) Hger Harmoncs 5[A] -5 [A] (c) Resultant Sgnal (pase A) 2 [A] -2 [A] (d) Tme [s] Fg. 1. Obtanng te nput test sgnal for testng te armonc detecton tecnques. a) fundamental current, b) 5 t armonc current, c) ger armoncs currents, d) resultant test sgnal. 5 Hz 5 t Hger armoncs 3-pase sgnal Harmonc Detecton Metod tuned for 5 t Record te response for te 5 t Compare to te orgnal Fg. 11. Smulaton setup realzed to study te performance of dfferent armonc detecton metods solated from te model of te actve flter. Table III. Settngs used for confgurng te armonc detecton metod. Harmonc detecton metod Caracterstcs DFT for te 5 t armonc 256 samples / fundamental RDFT 256 samples / fundamental Fundamental -frame HPF 12Hz, 2 nd order Butterwort 5 t armonc -frame LPF 2Hz, 2 nd order Butterwort Instantaneous pq teory HPF 1Hz, 3 st order Butterwort 5 t generalzed ntegrator T I=3 Te metods consdered for ts comparson are lsted n Table III were also some of ter caracterstcs are provded from dfferent references n II. Fg. 12 llustrates te results of te smulaton as tme waveforms obtaned from eac metod. Te settlng tme, te oversoot and te pase error are measured for eac detecton metod as gven n te Table IV. In te case of te DFT metods, te settlng tme s lmted to at least te wndowng tme (1 fundamental perod n ts case), and te requrement s tat te armonc sould be constant durng te wndowng nterval. For te RDFT metod te response s better but stll lmted to te duraton of te wndow as any FIR flter response. Te fundamental -frame as a faster response and a good oversoot but suffers from a large pase error due to te pase sft created by te HPF. Terefore, te compensaton currents are not n pase wt te dsturbance, wc s an mpedment for an exact armonc cancellaton. 2 [A] -2 [A] 1 [A] -1 [A] 1 [A] -1 [A] 1 [A] -1 [A] 1 [A] -1 [A] 1 [A] -1 [A] 1 [A] Start of te 5 t armonc Sngle Pase Sgnal DFT 5t Recursve DFT Fundamental -Frame t Harmonc -Frame p-q Teory t Generalzed Integrator -1 [A] Tme [s] Fg. 12. Te dynamc responses obtaned for te analyzed metods accordng to Fg. 11. Table IV. Results obtaned from te armonc detecton metods (Fg. 12). Harmonc detecton metod Settlng tme Pase error Oversoot [ms] [deg] or rpple [%] DFT 5 t 3 ms % Recursve DFT 2 ms % Fundamental -Frame 1 ms % oversoot 5 t Harmonc -Frame 2 ms 1% rpple p-q Teory 1 ms 3.2 3% oversoot 5 t Generalzed Integrator 3 ms %

6 As a compromse te HPF may be mplemented wt a low pass flter (LPF) as n 1-LPF, were n ts case te dc-sgnals comng from te LPF ave no pase sft, terefore, te armonc dstorton keeps te same pase after te dc-sgnal subtracton. Te armonc -frame does not ave te ssue wt te pase sft because te 5 t armonc becomes dc-component fltered by a LPF, but ere due to a low cuttng frequency, te response tme beng degraded. Anoter ssue s wt te large exstng rpple because te fundamental frequency (bgger n ampltude) appears n te armonc -frame as an ac-sgnal, wc must be removed by te LPF, and terefore, a good selectvty or a low cuttng frequency must be selected n order to reduce t. However, ncreasng te flter order or decreasng te cuttng frequency wll degrade te response tme. For te pq-teory te output as a caracterstc gven by te HPF used. In ts case te oversoot suffers, wle te response tme s relatvely fast. Te pase error of te HPF may be mproved also by selectng a (1-LPF) mplementaton nstead. In te case of te generalzed ntegrator te man lmtaton s gven by te settlng tme, wc depends of te ntegraton constant T used. Suc large response tme (comparable te DFT case) s not sutable for applcatons were te armoncs frequently vary wtn a few fundamental cycles. Regardng te presence of te ger armoncs t was observed tat tey are well rejected by armonc -frame, wle te DFT and RDFT are dsturbed at least 1 fundamental cycle. Te generalzed ntegrator metod s owever, affected by tese ger armoncs snce tere was no oter controller tuned to remove tese armonc components. Te nfluence of te flters may be seen n Fg. 13, were tree of te presented metods are practcally tested wt a dspace system (TMS32F24) for an actve flter mplementaton. Te load currents from a tree-pase dode rectfer are processed by te respectve armonc detecton metods and te sgnal obtaned (.e. current reference) s summed wt te dstorted current. Te summaton done ere excludes te contrbuton of te current controller and te PWM nverter tat wll actually decrease te trackng speed even more by ntroducng more delays. Te results are presented n Fg. 13 were bot te THD and te level of te 5 t armonc are calculated for eac result. Based on te conclusons obtaned from te above smulatons te practcal results n Fg. 13 ave now an easer nterpretaton. For nstance even f bot metods, fundamental -frame and nstantaneous pq-teory are mplemented wt HPF tecnques, te second metod gves a better result, explcable by te smaller pase-sft, as measured n Table IV. Table V presents oter conclusons, wc are mportant for a practcal mplementaton of te actve flter (were a sgn ndcates an advantage or an ncrease n performance). For example, te pq-teory as good dynamcs but needs snusodal nput voltages, wle te -tecnques depend on te angular speed. Te generalzed ntegrator metod requres ndvdual tunng for eac frequency but does not need te voltage nformaton and also does not ave te flterng ssues. Regardng wc of tese tecnques s better for a gven case, some assumptons may be made as lke te exstence of a fast DSP tat wll allevate te numercal ssues. Also te acquston of bot voltages and currents mgt be benefcal for te APF crcut protectons or oter enanced features provded by te APF. Terefore, te desgn sould manly consder te caracterstcs of te dstorted currents for nstance, te domnant armonc currents, ter levels, te varaton n tme, and te exstence of certan unbalance n te system. 2 [A] -2 [A] THD = 31.% 5 = 3% Current pase-a Fundamental -Frame THD = 14.6% 2[A] 5 = 14% -2[A] t Harmonc -Frame THD = 9.2% 2[A] 5 = 6.2% -2[A] pq Teory THD = 6.6% 2[A] 5 = 6.4% -2 [A] Tme [s] Fg. 13. Practcal valdaton of te fundamental -frame, armonc -frame and nstantaneous pq-teory. Te coce of te flter mplementaton s responsble for a good current reference framework. Table V. Evaluaton of te studed armonc detecton metod. FFT DFT RDFT Fund. -frame Harm. -frame pq Teory Generalz. ntegr. No of sensors (3-pase applcaton) 3 x I 3 x I 3 x I 3 x I, 2 x V 3 x I, 2 x V 3 x I, 3 x V 3 x I No of numercal flters / / / 2 x HPF 2 x LPF 2 x HPF N x controllers Requres addtonal tasks Wndowng Wndowng / PLL PLL Voltage Preproc. / No of calc. (excludng flters) Numercal mplementaton ssues Number of Number of Instablty for low Flterng, Flterng calculatons calculatons precson Tunng control Flterng Tunng control Related mplementatons Decmatons 4 k, 16 k / Rotatng frame Dfferent flterng Dfferent flterng Flters type; oter Dfferent flterng approaces approaces teores pqr, pq approaces Sngle-pase/Tree-pase applcatons 1-p / 3-p 1-p / 3-p 1-p / 3-p Inerently 3-p Inerently 3-p Inerently 3-p 1-p / 3-p Requres voltage usage No No No Yes Yes Yes No Performance wen unbalanced voltages Performance wen unbalanced currents Selectve armonc compensaton No Yes Yes No Yes No Yes Transent response tme Steady state accuracy

7 IV. CONCLUSION Te paper gves an evaluaton of te common used metods for armonc detecton n actve power flter applcatons. Te descrpton of te related teores s provded ere togeter wt a number of references and some of te ssues are ponted out. Ten te paper proposes a smulaton setup to study te performance of te detecton metods ndependent from te actve flter. Te smulatons sow tat te coce of numercal flterng s a key factor for obtanng good accuracy and dynamcs. REFERENCES [1] H.L. Jou, Performance comparson of te tree-pase actve-powerflter algortms, IEE Proc. of Gener. Transm. Dstb. Vol. 142, 1995, pp [2] S.D. Round and D.M.E. Ingram, An evaluaton of tecnques for determnng actve flter compensatng currents n unbalanced systems, Proc. of European Conf. on Power Electroncs and Applcatons, Vol. 4, 1997, pp [3] J. Jacobs, D. O. Detjen, R. W. De Doncker, An overvew of metods to determne te armoncs n tree-pase systems, IEEE Young Researcers Symposum n Electrcal Power Engneerng Dstrbuted Generaton, 22. [4] S. Recka, T. Ngandu, X. Janong, P. Scard, A comparatve study of armonc detecton algortms for actve flters and ybrd actve flters, Proc. of PESC 2, Vol. 1, 22, pp [5] M.Macmoum, N. Bruyant, Control metods for tree-pase actve power flters under non-deal mans voltages, Proc. of PowerCon 2, Vol. 3, 2, pp [6] G.W. Cang, S. Ta-Cang, A comparatve study of actve power flter reference compensaton approaces, Proc. of Power Engneerng Socety 22, Vol. 2, 22, pp [7] W.M. Grady, M.J. Samotyj, A.H. Noyola, Survey of actve power lne condtonng metodologes, IEEE Trans. on Power Delvery, Vol. 5, Issue 3, 199, pp [8] O.M. Solomon, Te use of DFT wndows n sgnal-to-nose rato and armonc dstorton computatons, IEEE Trans. on Instrum. and Measur., Vol. 43, Issue 2, 1994, pp [9] M. El-Habrouk, M.K. Darws, Desgn and mplementaton of a modfed Fourer analyss armonc current computaton tecnque for power actve flters usng DSPs, Proc. of Electrc Power Applcatons, Vol. 148, 21, pp [1] S. Srantumrong, S. Sangwongwanc, An actve power flter wt armonc detecton metod based on recursve DFT, Proc. of Harmoncs And Qualty of Power 1998, Vol. 1, 1998, pp [11] R. Hartley, K. Welles, Recursve computaton of te Fourer transform, Proc. of Crcuts and Systems, Vol.3, 199, pp [12] A.A. Grgs, W.B. Cang, E.B. Makram, A dgtal recursve measurement sceme for onlne trackng of power system armoncs, IEEE Trans. on Power Delvery, Vol. 6, Issue 3, 1991, pp [13] J.A. Rosendo Macas, A. Gomez Exposto, Effcent movng-wndow DFT algortms, IEEE Trans. on Crcuts and Systems, Vol. 45, Issue 2, 1998, pp [14] J. W. Cooley and J. W. Tukey, An algortm for te macne calculaton of complex Fourer seres, Mat. Comput., vol. 19, 1965, pp [15] M. Dolen, R.D. Lorenz, An ndustrally useful means for decomposton and dfferentaton of armonc components of perodc waveforms, Proc. of Industry Applcatons 2, Vol. 2, 2, pp [16] B.G. Serlock, D.M. Monro, Movng dscrete Fourer transform, Proc. of Radar and Sgnal Processng, Vol. 139, Issue 4, 1992, pp [17] V. Soares, P. Verdelo, G. Marques, Actve power flter control crcut based on te nstantaneous actve and reactve current d-q metod, Proc. of PESC'97, Vol. 2, 1997 pp [18] P. Verdelo and G. Marques, An actve power flter and unbalanced current compensator control crcut, Proc. of EPE 95, Vol. 1, 1995, pp [19] S. Kostkasame, S. Sangwongwanc, Desgn of armonc current detector and stablty analyss of a ybrd parallel actve flter, Proc. of Power Converson Conference 1997, Vol. 1, 1997, pp [2] M. Aredes, L.F.C. Montero, A control strategy for sunt actve flter, Proc. of HQPC 22, Vol. 2, 22, pp [21] S. Battacarya, A. Veltman, D.M. Dvan, R.D. Lorenz, Flux-based actve flter controller, IEEE Trans. on Industry Applcatons, Vol. 32, Issue 3, 1996, pp [22] N. Mendalek, K. Al-Haddad, F. Fnaec, L.A. Dessant, Sldng mode control of 3-pase 3-wre sunt actve flter n te frame, Proc. of Electrcal and Computer Engneerng 21, Vol. 2, 21, pp [23] S. Battacarya, T.M. Frank, D.M. Dvan, B. Banerjee, Actve flter system mplementaton, IEEE Trans. on Industry Applcatons, Vol. 4, Issue 5, 1998, pp [24] C. Po-Ta, S. Battacarya, D. Dvan, Operatons of te domnant armonc actve flter (DHAF) under realstc utlty condtons, Proc. of Industry Applcatons 2, Vol. 4, 2, pp [25] E.H. Watanabe, M. Aredes, Compensaton of non-perodc currents usng te nstantaneous power teory, Proc. of Power Engneerng Socety 2, Vol. 2, 2, pp [26] E.H. Watanabe, E.H. Stepan, R.M. Aredes, New concepts of nstantaneous actve and reactve powers n electrcal systems wt generc loads, IEEE Trans. on Power Delvery, Vol. 8, Issue 2, 1993, pp [27] A. Nakata, A. Ueda, A. Tor, A new metod for separatng AC component of nstantaneous real power and magnary power sutable for actve flters, Proc. of Power Converson Conference 1997, Vol. 2, 1997, pp [28] H. Km, H. Akag, Te nstantaneous power teory based on mappng matrces n tree-pase four-wre systems, Proc. of Power Converson Conference 1997, Vol. 1, 1997, pp [29] H. Akag, S. Ogasawara, H. Km, Te teory of nstantaneous power n tree-pase four-wre systems: a compreensve approac, Proc. of Industry Applcatons Conference 1999, Vol. 1, 1999, pp [3] F.Z. Peng, H. Akag, A. Nabae, A new approac to armonc compensaton n power systems, Proc. of Industry Applcatons Socety 1988, Vol. 1, 1988, pp [31] H. Km, F. Blaabjerg, B. Bak-Jensen, C. Jaeo, Instantaneous power compensaton n tree-pase systems by usng p-q-r teory, IEEE Trans. on Power Electroncs, Vol. 17, Issue 5, 22, pp [32] K. Hyosung H. Akag, Te nstantaneous power teory on te rotatng p-q-r reference frames, Proc. of Power Electroncs and Drve Systems 1999, Vol. 1, 1999, pp [33] W.le Roux, J.D. van Wyk Modelng of dstorton compensaton neffectvely n flters for non actve power, IEEE Trans. on Industral Electroncs, Vol. 48, 21, pp [34] X. Yuan, W. Merk, H. Stemmler, J. Allmelng, Statonary-frame generalzed ntegrators for current control of actve power flters wt zero steady-state error for current armoncs of concern under unbalanced and dstorted operatng condtons, IEEE Trans. on Industry Applcatons, Vol. 38, Issue 2, 22, pp [35] J. Allmelng, A control structure for fast armoncs compensaton n actve flters, IEEE Trans. on Power Electroncs, Vol. 19, Issue 2, 24, pp [36] M.J. Newman, D.N. Zmood, D.G. Holmes, Statonary frame armonc reference generaton for actve flter systems, IEEE Trans. on Industry Applcatons, Vol. 38, Issue 6, 22, pp [37] P. Mattavell, A closed-loop selectve armonc compensaton for actve flters, IEEE Trans. on Ind. App., Vol. 37, Issue 1, 21, pp [38] D.N. Zmood, D.G. Holmes, G.H. Bode, Frequency-doman analyss of tree-pase lnear current regulators, IEEE Trans. on Industry Applcatons, Vol. 37, Issue 2, 21, pp [39] U. Grossmann, T. Ellnger, G. Berger, J. Petzoldt, H.G. Mall, G. Frako, Actve Flter Control n te Statonary Reference Frame Usng Lowpass to Bandpass Transformaton, Proc. of PCIM 3, 23, pp [4] L. S.Czameck, "On some defcences of Fryze's approac to descrbng power propertes of systems under nonsnusodal condton," Proc. of IEEE ICHPS, Bologna, 1994, pp [41] M. Aredes, L.F.C. Montero, J.M. Mguel, Control strateges for seres and sunt actve flters Proc. of Power Tec 23, Vol. 2, 23, pp [42] S. Lu, An adaptve Kalman flter for dynamc estmaton of armonc sgnals, Proc. of. of Harmoncs and Qualty of Power 1998, Vol. 2, 1998, pp