A Comparative Analysis among Different Control Strategies for Shunt Active Filters Paper Code: 074

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1 A Comarate Analyss among Dfferent Control Strateges for Shunt Acte Flters Luís F.C.Montero and Mauríco Aredes Federal Unersty of Ro de Janero Electrcal Engneerng Program (PEE COPPE/UFRJ Vst our home-age: e-mal: ABSTRACT: In ths work, a comarate analyss wll e done among three dfferent control strateges to determne the comensaton currents n a shunt acte flter. The frst control strategy s ased on the PQ Theory roosed y Akag et al., n 98. The second one, s ased on the set of ower defntons roosed y Fryze n the 0 s of the last century, whch has een extended to ower electroncs alcatons n the 90 s and s known as the Generalzed Fryze Currents. Then, a noel control strategy s roosed and named as the Snusodal Fryze Currents. Ths control strategy s a comnaton of the LaGrange s mnmum multler method and the rncles of the PQ Theory. These rncles are useful to roerly adat a Phase-Locked-Loo (PLL for the control strategy that forces the comensated currents drawn from the network to ecome alanced, free of harmoncs and n hase wth the fundamental oste-sequence oltage, een under non-snusodal oltage condtons. Smulaton results wll e used to comare the erformance of the control strateges. eywords: M Shunt Acte Flter, PQ Theory, Generalzed Fryze Currents, Snusodal Fryze Currents. INTRODUCTION ANY efforts hae een exended to deelo acte ower qualty condtoners that can soften the rolems of ower qualty n electrc systems. The ncreasng numer of non-lnear loads connected y the consumers s one of the most serous rolems related to ower qualty that has to e soled n the modern concets of Custom Power. Among those ower qualty condtoners, there are acte flters, whch hae the caalty to comensate suly oltages or load currents to force them to reman snusodal and alanced. Ths aer focuses on the shunt acte flter for current comensaton, as llustrated n Fg.. One of the cornerstones of the acte flter s ts control strategy that s mlemented n the acte flter controller. Many knds of control strateges n a shunt acte flter hae een tred so far. Here, a noel control strategy, called as Snusodal Fryze Currents, s roosed and comared wth other two control strateges founded n the lterature. One of these strateges s the Snusodal Source Current Control Strategy [][] ased on the q Theory roosed y Akag et al., n 98 []. It can guarantee alanced, snusodal comensated currents, een when the system oltage at the ont of common coulng (PCC s tself already dstorted and/or unalanced. Although t requres some calculaton effort, ths control strategy s ersatle and roust. The q Theory s totally defned n the tme doman and many controllers of ower electroncs deces hae used successfully. In the 0 s of the last century, Fryze roosed a set of acte and reacte ower defntons n the tme doman. From these concets, a control strategy, that s known as the Generalzed Fryze Currents were created and extended to ower electroncs alcatons n the 90 s [4][5][6]. Ths algorthm s ased on the Lagrange Multlers Method, whch soles a rolem of fndng the mnmum (acte current comonent that transorts the same energy of a generc three-hase load current. The dfference etween the generc load current and that mnmzed current comrses all harmonc current comonents that does not contrute to the transort of energy etween the ower suly and the generc load. As a consequence of the aled method, the results cannot guarantee snusodal and alanced comensated currents f the system oltage at the PCC s dstorted and/or unalanced. Instead, t can guarantee comensated currents that are roortonal (they hae the same waeforms to the system oltage. If comared wth the reous one, the Generalzed Fryze Currents control strategy requres less comutaton effort. The thrd control strategy s a comnaton of that two strateges mentoned efore. It tres to kee the comensaton flexlty of the frst one whle reduces comutaton efforts as n the second one. It s called Snusodal Fryze Currents Control Strategy and has the same kernel of the Generalzed Fryze Currents, ut an addtonal fundamental oste-sequence oltage de- C S PWM control S C L C C acte flter controller Fg. : Shunt acte flterng of non-lnear loads.

2 A Comarate Analyss among Dfferent Control Strateges for Shunt Acte Flters tector s needed. Ths noel control strategy dffers from that roosed n [7], n the way of fndng the fundamental, oste-sequence, oltage comonent. CONTROL STRATEGY BASED ON THE PQ THEORY The followng Snusodal Source Current Control Strategy [] s ased on the q Theory. The snusodal source current control strategy s a rncle of comensaton that makes the acte flter to comensate the current of a non-lnear load to make the comensated source current snusodal and alanced. In the resence of oltage unalances or oltage dstortons, t s mossle to satsfy oth condtons smultaneously: to hae snusodal and alanced comensated currents and to draw (only constant real ower from the source. Fg. ges a general oerew n the control strategy. The rncal dfference etween ths control algorthm and the orgnal one roosed y Akag et al. [] s the addton of the oste-sequence oltage detector. In order to roerly comensate the orton of the fundamental oste-sequence current of the load that s orthogonal to the fundamental oste-sequence oltage, the hase angle and frequency of the fundamental oste-sequence oltage ( V& must e accurately determned. Otherwse, the acte flter controller cannot exactly determne the fundamental reacte ower of the load ( q, that n turns cannot roduce ac current ( I& orthogonal to the ac oltages ( V& to roduce only q. The comensatng owers ~ and q n the acte flter controller nclude all fundamental negatesequence ower, the fundamental reacte ower, as well as the harmonc ower. In other words, the acte flter controller handles the load as "connected to a snusodal alanced oltage source". Thus, f ~, q, q ~ are comensated y the acte flter, the source currents must e now snusodal and contan only the acte orton of fundamental oste-sequence comonent that s n hase wth V&. Fg. ncludes also a dc oltage regulator that roduces the control sgnal loss. Ths sgnal s handled n the acte flter controller as real (acte ower comonent and forces the PWM conerter to synthesze an addtonal fundamental oste-sequence current comonent to draw or nject energy from(to the network, n order to kee the dc caactor charged at V REF. It should e noted that the control sgnal loss s also useful to rode long term, energy alance, nsde the acte flter. That means the acte flter controller can cause transent comensaton errors that generate undesrale energy flow nto or from the dc caactor, whch causes oltage aratons that are corrected y. loss a c V dc ' ' V REF Postesequence Detector ( V PI- Controller a c c c ' a ' ' c nstantaneous owers calculaton loss ~ loss 0 0 ~ q currents calculaton q q loss Clarke Transformaton ' ' The oste-sequence oltage detector has almost the same comlexty of the man algorthm shown n Fg.. The fundamental oste-sequence oltage detector s ased on the Dual q Theory and the concets of oltage comensaton. Fg. shows the comlete functonal control lock dagram of the fundamental oste-sequence oltage detector. It extracts contnuously and accurately the amltude, hase angle and frequency of the fundamental oste-sequence oltage ( V& and ges n the form of nstantaneous alues (' a, ', ' c for the man algorthm of Fg.. An mortant art of the oste-sequence oltage detector s the Phase-Locked-Loo (PLL crcut. Detals of the PLL wll e gen later, snce the same crcut s used n the thrd control strategy. a c ca c cc a c q Flter 0 c c Inerse Clarke Transformaton Fg. : The control lock dagram for the Snusodal Source Current Control Strategy. a c ' PLL Crcut Clarke Transformaton a 0 c ' ' ' q oltage calculaton q ' ' Flter Flter a c ' nstantaneous ower calculaton q 0 Inerse Clarke Transformaton Fg. : Fundamental oste-sequence oltage detector. q' a c ' a ' ' c

3 A Comarate Analyss among Dfferent Control Strateges for Shunt Acte Flters GENERALIZED FRYZE CURRENTS CONTROL STRATEGY Deste of the usefulness and flexlty of the q Theory as a ase for desgnng acte flter controllers, other aroaches may e found also sutale, deendng on the ojectes to e accomlshed. For nstance, the decomoston of the load current nto acte and non-acte currents, as results from current mnmzaton method, can e used as a ase for desgnng controllers for shunt acte flters. Controllers for shunt acte flters that guarantees comensated currents roortonal to the suly oltages can e mlemented y usng the concets of current mnmzaton and the concet of Generalzed Fryze Currents. If the suly oltage s snusodal and alanced, the comensated source current wll e also snusodal and alanced. An adantage of the generalzed Fryze current control s the reduced calculaton effort, snce t handles drectly wth the ac hase oltages and lne currents. The elmnaton of the Clarke Transformaton makes ths control strategy ery smle. Fg. 4 shows the comlete control crcut for a real mlementaton of the Generalzed Fryze Current Control Strategy. The nstantaneous equalent conductance G e s calculated from the nstantaneous acte three-hase ower and the squared nstantaneous aggregate oltage: aa cc Ge. ( a c Then, the nstantaneous acte currents (mnmzed currents can e calculated drectly from the nstantaneous conductance as: wa Ge a w Ge. ( wc Ge c The acte currents aoe (mnmzed currents resent the mnmum rms alue to draw the same aerage acte three-hase ower as the orgnal load currents ( a,, c. Hence, the comensaton leads to reducton of losses n the transmsson system. In terms of q Theory, t s the same as to say that the shunt acte flter s comensatng the whole magnary ower (q q q ~ of the load and remanng the real ower ( ~ unchanged. Howeer, ths analogy etween q Theory and Mnmzaton Method s ald only f the oltage and the current do not contan any zero-sequence comonent. The results from the mnmzaton method and the q Theory dffers a lot n the resence of zerosequence comonents. The nstantaneous conductance G e ares f the oltage and/or current contan harmoncs. Thus, the aerage conductance G e s otaned assng G e through a low-ass flter, whch guarantees acte currents ( wa, w, wc roortonal (same waeforms to the oltages. In a real mlementaton, some flterng n the measured system oltages ( a,, c s needed. Noses related to the swtchng frequency of the PWM conerter of the shunt acte flter should e attenuated efore usng the system oltage n the control algorthm, n order to aod unstale feedack loo. Moreoer, n a real mlementaton, a control sgnal loss wth the same functons of that n the reous control strategy s also needed here. Here, the sgnal loss s treated as conductance, nstead of real ower. A crtcal drawack of the Generalzed Fryze Currents s when the system oltages hae unalances and/or dstortons. In the next control algorthm, a new fundamental oste-sequence oltage detector s roosed to assocate to the control algorthm shown n Fg SINUSOIDAL FRYZE CURRENTS CONTROL STRATEGY Ths control strategy has the same kernel as the Generalzed Fryze Currents of Fg. 4. The dfference s a fundamental oste-sequence oltage detector ( V& s nserted, nstead of usng drectly measured system oltages. Thus, f the nstantaneous alue of V& s gen to the Generalzed Fryze Currents control crcut, a new control strategy, the Snusodal Fryze Currents Control Strategy, s mlemented. Now, lke n the frst control strategy ased on the q Theory, t s ossle to guarantee snusodal and alanced comensated currents. A new oste-sequence detector n terms of "mnmzed oltages" s deeloed. That s, the dual mnmzaton method for "oltage comensaton" s emloyed. a c a c a c. G V REF V dc PI- Controller loss Acte Fryze Conductance Calculaton Ge Ge Flter a a. c. c e a c G e loss Acte Current Calculaton wa w wc ( Ge loss ( Ge loss ( Ge loss a c wa w wc Comensatng Currents ca c cc w a a w w c c a c Fg. 4: Generalzed Fryze Currents Control Strategy. ca c cc

4 A Comarate Analyss among Dfferent Control Strateges for Shunt Acte Flters Fg. 5 shows the roosed oste-sequence oltage detector. An mortant art of ths crcut conssts n a PLL crcut that determnes accurately the frequency and hase angle of the fundamental ostesequence comonent of the measured system oltage. Fg. 6 shows a PLL crcut, wdely used y the authors. A detaled descrton of ts functonalty can e found n [8] and s not ncluded here due to lack of sace. The most mortant characterstc of ths crcut s hghlghted: t tracks accurately the fundamental oste-sequence comonent ( V&, een under hgh dstorton/unalance condtons, and has a unque stale ont of oeraton that s the feedack sgnal a (ω t leadng y π/ the fundamental oste-sequence oltage. Thus, Na sn(ω t π/ certanly stays n hase wth V& a (t V sn(ω tφ. In other words, the sgnals Na, N and Nc are snusodal tme functons wth unty amltude, hae the same frequency, and are n hase wth the fundamental oste-sequence comonent of the measured hase oltages. To fully determne the oste-sequence comonent of the system oltage, ts amltude should also e calculated, whch s erform y the rest of the control crcut of Fg. 5. In fact, to fully determne V &, only a "dynamc factor " s mssng to multly the sgnals Na, N and Nc. If the factor s known, then, t s ossle to form the followng tme functons, corresondng to the nstantaneous alues of the fundamental ostesequence oltages. ( ωt π ( ωt π π ( ωt π π a Na sn N sn c Nc sn. ( As exlaned efore, the outut sgnals Na, N and Nc of the PLL (Fg. 6 are n hase wth the comonent V & of the system oltage. Hence, the roduct of V & wth I & N roduces, n terms of q Theory, only a constant real ower,, and does not generate any magnary ower, q. Ths means that the calculated to- sn a a Σ X φ ω Σ PI-Controller c Σ X! c sn ( ω t π gether wth I & N s suffcent to desgn a control algorthm for determnng the amltude of V &. Agan, to aod the use of Clarke Transformaton, the ower s relaced y the nstantaneous acte ower calculaton from the ac "lne currents" ( Na, N Nc and hase oltages, as shown n Fg. 5. As mentoned efore, the dual method from that aled n Fg. 4 s used. Instead of equalent conductance G e calculaton, as n (, an nstantaneous equalent resstance R e s calculated from the nstantaneous acte three-hase ower and the squared nstantaneous aggregate current: R e φ a Na N c Nc. N Na N Σ Nc a (ω t c (ω t ( ω t Na sn N sn sn Nc ω t (4 The calculaton of R e n (4 can e smlfed, snce the auxlary currents Na, N and Nc are comosed only from a fundamental oste-sequence comonent and the nstantaneous aggregate alue s constant and equal to /. By flterng R e, the aerage alue s acheed, whch corresonds to the "dynamc factor " that s needed n (. The nstantaneous, fundamental, oste-sequence oltage (sgnals a, and c s calculated, whch relace the measured system oltages (sgnals a, and c n Fg. 4, to comlete the new control strategy. s ( ω t π ( ω t π π ( ω t π π Fg. 6: The synchronzng crcut PLL crcut. Na N Nc Next, smulaton results are shown to comare the erformances of the control strateges. The system s mlemented n the Saer Desgner smulator. The er unt system cannot e used drectly n ths smulator. Thus, V (hase to ground and A (lne current were used as the ass of the system. A alanced, V, three-hase, oltage source s used. A ery hard stuaton of unalance and dstorton s created through the addton of 5% of negate-sequence oltage at the fundamental frequency, lus 5% of negate-sequence oltage at the 5 th harmonc, and 5% of ostesequence oltage at the 7 th harmonc. The system m a c PLL Crcut R e ( ana N cnc low-ass flter Na N Nc a c Na N Nc a c! " Fg. 5: Poste-sequence oltage detector. 5 SIMULATION RESULTS

5 A Comarate Analyss among Dfferent Control Strateges for Shunt Acte Flters edance s R Ω (% and L 8. µh (0%. A three-hase thyrstor conerter s used as non-lnear load. It has 0º frng angle, A dc current, and 59.5 µh commutaton nductances. The commutaton nductance of the shunt acte flter (L n Fg. s 59.5µH, and a RC ranch, not shown n Fg., wth C 47 µf and R.5 Ω s used as hgh-ass flter. The dc oltage reference alue (V REF n Fg. and Fg. 4 s set.8 V and a.4 mf caactor s used as energy storage element. Ths caactance roduces a short Unt Caactor Constant (UCC, CV (04 (.8 UCC 5. 8ms, S.. (5 n accordance to usual alues aled n shunt acte flters, aalale n the market. The total smulaton tme s 0.8 s. The thyrstor conerter s connected at t 0. s and the shunt acte flter s started at t 0.5 s. Three smulaton cases are shown elow. The aoe-descred system s the same for all cases. Only the control strategy s changed. The system oltage at the PCC s strongly unalanced and dstorted, as can e seen n Fg. 7. The frst control strategy (Fg. and Fg. extracts the V& comonent from that measured system oltage, whereas the second strategy (Fg. 4 uses a low-ass flter wth khz cut-off frequency to flter noses an swtchng harmoncs. The thrd strategy utlzes the noel oste-sequence detector of Fg. 5 and Fg. 6. Fg. 8 shows the erformance of the q Theoryased strategy, Fg. 9 for the Generalzed Fryze Currents strategy, and Fg. 0 for the Snusodal Fryze Currents strategy. As exected, qute smlar results are otaned from the frst and thrd control strateges. The comensated currents ecome almost snusodal and alanced, as well as mnmzed, snce the fundamental reacte ower of the load s also eng comensated y the shunt acte flter. Fg. 9 confrms that the Generalzed Fryze Currents control strategy forces the source currents to hae the same waeform of the system oltages. A frst order load A comarate analyss among three dfferent control strateges s erformed. A noel control strategy, the Snusodal Fryze Currents Control Strategy, s roosed. The fundaments of the q Theory was exloted and ntroduced nto a mnmzaton method, whch to load a load c Fg. 7: Dstorted and unalanced system oltage measured at the PCC ref sa s sc com load Fg. 8: Performance of the q Theory control strategy under dstorted system oltage ref sa s sc com load Fg. 9: Performance of the Generalzed Fryze Currents control strategy under dstorted system oltage. ref sa s sc com load Fg. 0: Performance of the Snusodal Fryze Currents control strategy under dstorted system oltage. low ass flters s used to flter hgh-order harmoncs (hgher than.0 khz n the measured oltages. 6 CONCLUSIONS

6 A Comarate Analyss among Dfferent Control Strateges for Shunt Acte Flters gether wth a roust synchronzng crcut allowed the deeloment of the new control strategy. It has comensaton characterstcs smlar to the well-known strategy ased on the q Theory, wth the adantage of usng reduced comutatonal efforts. The controller calculates comensatng currents that comrse all comonents that dffer from the acte orton of the fundamental oste-sequence current. Thus, t ncludes zero-sequence comonents and s ale to e used n three-hase four-wre systems. The Generalzed Fryze Currents control strategy resented oor erformance under dstorted/unalanced system oltages. That erformance would worsen sgnfcantly f zero-sequence comonents would e added. The algorthm used to achee the fundamental oste-sequence oltage detector can e emloyed n acte ower lne condtoners for oltage comensaton, lke seres acte flters or Unfed Power Qualty Condtoners (UPQC. Moreoer, wth the estalshed dual method of the Generalzed Fryze Currents, that could e named as Generalzed Fryze Voltages, an Unersal Acte Power Lne Condtoner could e comletely desgned wthout hel of Clarke Transformaton, as well as real and magnary ower calculatons. 7 REFERENCES [] M. Aredes, J. Häfner,. Heumann, "Three-Phase Four-Wre Shunt Acte Flter Control Strateges, IEEE Trans. on Power Electroncs, ol., no.,. -8, March 997. [] M. Aredes, "Acte Power Lne Condtoners," Ph.D. Thess (honors, Technsche Unerstät Berln, Berln, March 996. [] H. Akag, Y. anazawa and A. Naae, "Generalzed Theory of the Instantaneous Reacte Power n Three-Phase Crcuts," n Proc. IPEC-Tokyo'9 Int. Conf. Power Electroncs, , Tokyo, 98. [4] T. Furuhash, S. Okuma, Y. Uchkawa, "A Study on the Theory of Instantaneous Reacte Power," IEEE Trans. on Industral Electroncs, ol. 7, no., , Fe [5] L. Rossetto, P. Tent, "Ealuaton of Instantaneous Power Terms n Mult-Phase Systems: Technques and Alcaton to Power-Condtonng Equments," ETEP Eur. Trans. Elect. Power Eng., ol. 4, no. 6, , No./Dec [6] M. Deenrock, D. A. Marshall, J. D. an Wyk, "Formulatng Requrements for a Unersally Alcale Power Theory as Control Algorthm n Power Comensators," ETEP Eur. Trans. Elect. Power Eng., ol. 4, no. 6, , No./Dec [7] F.P.Marafão, S.M.Deckmann, J.A.Pomlo, R.Q.Machado, "Control Strateges to Imroe Power Qualty," COBEP 00 - The 6 th Brazlan Power Electroncs Conf., Floranóols,. 78-8, No. 00. [8] M. Aredes, A.F.C. Aquno, G. Santos Jr., "Multulse Conerters and Controls for HVDC and FACTS Systems," Electrcal Engneerng Research Journal Arch für Elektrotechnk, ol. 8, no.,. 7-45, March BIOGRAPHIES Luís F.C.Montero was orn n Ro de Janero State on March 975. He s fnshng hs graduaton on Electrcal Engneerng at Federal Unersty of Ro de Janero. He s enrolled n M.Sc. at COPPE/UFRJ n Power Electroncs and, wth Dr. Aredes, s deelong new control strateges for acte flters snce 000. He s a student memer of the Brazlan Power Electroncs Socety. Mauríco Aredes (S 94, M 97 was orn n São Paulo State, Brazl, on August 4, 96. He receed the B.Sc. degree from Flumnense Federal Unersty, Ro de Janero State n 984, the M.Sc. degree n Electrcal Engneerng from Federal Unersty of Ro de Janero n 99, and the Dr.-Ing. degree (honors from Technsche Unerstät Berln n 996. From 985 to 988 he worked at the Itau HVDC Transmsson System and from 988 to 99 n the SCADA Project of Itau Power Plant. From 996 to 997 he worked wthn CEPEL Centro de Pesqusas de Energa Elétrca, Ro de Janero, as R&D Engneer. In 997, he ecame an Assocate Professor at the Federal Unersty of Ro de Janero, where he teaches Power Electroncs. Hs man research area ncludes HVDC systems, FACTS systems, acte flters, Custom Power and Power Qualty. Dr. Aredes s a memer of the Brazlan Socety for Automatc Control and the Brazlan Power Electroncs Socety.