IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING, VOL. 7, NO. 1, WINTER-SPRING M. Rahimi, H. Mokhtari, and Gh.

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1 IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING VOL. 7 NO. WINTER-SPRING A New Atie Method in Damping Poible Reonane in Atie Filter M. Rahimi H. Mokhtari and Gh. Zaarabadi Abtrat Thi paper inetigate reonane phenomenon in atie ilter. The paper tudie the eet o ytem/ilter parameter on reonane ondition. It alo propoe an atie tehnique or ing uh reonane. The tudy i baed on modal analyi in whih untable mode or mode with low ing are irt etrated. Then uing a new tehnique uh mode are oniderably ed. PSCAD/EMTDC otware i alo employed to eriy the perormane o the propoed tehnique. Inde Term Reonane phenomenon atie ilter ing reonane modal analyi. R I. INTRODUCTION ESONANCE i tated a harmoni urrent magniiation phenomenon. Thi phenomenon our where a load inlude reonane omponent uh a apaitor bank or power ator orretion or paie ilter []. Reonane ondition may alo happen during operation o atie ilter due to the interation between ilter d link apaitor and ytem/load indutane. Suh undeired ondition deteriorate the ilter perormane and may alo damage it omponent. To ue atie ilter with line urrent detetion a ontrol method to uppre the harmoni urrent magniiation phenomenon i needed. To tudy thi a ytem ompoed o a load oure and an atie ilter i eleted. Then time domain equation goerning the ytem behaior are tranormed to dq rame and modal analyi i perormed. Three main part o the ytem are: Atie ilter power iruit Atie ilter ontrol iruit Load and oure power iruit The truture o thi paper i a ollow. In the net etion blok diagram o the three aorementioned part are deried and the mode with low/no ing are etrated uing modal analyi. Then a new method or ing uh mode i introdued. Sine the ing ation i ahieed by uing the atie ilter; the method i alled atie ing []-[]. The main ontribution o thi work with repet to preiou one i that in thi paper the ytem mode with low ing are ound irt. Then the ontribution o tate ariable on thee mode i determined. Thereore the ontrol ation i taken baed on Arhie o SID Manuript reeied Noember 006; reied May Thi work wa upported by the Eletrial Department o Shari Unierity o Tehnology Tehran Iran. M. Rahimi and H. Mokhtari are with the Eletrial Department o Shari Unierity o Tehnology Tehran Iran. ( m_rahimi@hari.edu mokhtari@hari.edu). Gh. Zaarabadi i with the Iranian Aademi Center or Eduation Culture and Reearh (ACECR) Shari Branh Tehran Iran. ( zaarabadigh@alum.hari.edu). Publiher Item Identiier S (08) /08$0 008 ACECR Fig. Voltage oure inerter. Fig.. Balaned oltage oure inerter (VSI) model. the tate ariable with maimum ontribution. II. SYSTEM BLOCK DIAGRAM In thi etion the modeling o the ytem under tudy i eplained. A. Voltage Soure Inerter Model Fig. depit a oltage oure inerter (VSI) whih i onneted to an a oure through R and L. A threephae mathematial model or the oltage oure onerter (VSC) o Fig. i deried in [5]-[6]. In [7] by uing thi mathematial model it i hown that a VSC in balaned three phae operation without neutral wire an be modeled a hown in Fig.. In thi igure d and q are the tranormed oltage o the inerter output i.e. a b and uing Park Tranormation and a b and are deined a: k = k / k = a b and. d and q alo repreent a b and in the tranorm dq ae. I the ytem i a our-wire ytem and the ilter an pa neutral urrent through the d link enter point then power balane equation or zero equene oltage/urrent an be written a V 3 0. i0 =. i0 () where 0 and i 0 are the zero equene o the inerter output oltage and urrent and i 0 i the d link urrent due to the zero equene urrent at the a ide and V i the d link oltage. 0 0 I = rom () V

2 6 IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING VOL. 7 NO. WINTER-SPRING 008 Fig. 3. 3phae wire VSI model. Fig.. Load and oltage oure. (a) (b) Fig. 5. Load and oltage oure model (a) three phae three wire ytem and (b) neutral wire model i = i () and 0 = L di 0 + R. i (3) From () and (3) and onidering the eet o zero and non-zero equene omponent the blok diagram o Fig. i hanged to the one depited in Fig. 3. Arhie o SID B. Load/Soure Model Fig. how a load onneted to the oure through a erie impedane o R and L. In [7] the blok diagram o uh ytem i etrated or a three-phae three-wire ytem (Fig. 5(a)). To inorporate the eet o the neutral wire blok diagram o Fig. 5(b) an alo be added. C. Control Sytem A VSI ytem normally employ two ontrol ytem. One i a urrent ontroller whih produe oltage o i at the inerter terminal. A oltage ontroller i alo reponible or keeping the d bu oltage at a ontant alue. Fig. 6 depit the VSI ontrol ytem. In Fig. 6 I and I q _ reg are the ynhronou rame d _ reg Fig. 6. Control ytem blok diagram. TABLE I SYSTEM DATA FOR SIMULATION L =.5mH R = 0.3Ω V = 30 V C = C = 7000µF urrent regulator and u _ reg i the d bu oltage regulator. For the ontroller imple PI ontroller are onidered. III. RESONANCE CONDITION ANALYSIS To tudy the reonane behaior o the ytem modal analyi i employed. Dierent operating ae are onidered. Firt a ontant nonlinear load onneting to a ti oure i tudied. Then the eet o oure impedane i alo taken into onideration. The inal tudy i arried out on a ombination o a nonlinear load and a apaitor bank. A. Cae : Contant Nonlinear Load Fig. 7 depit the blok diagram o a omplete ytem i.e. ilter load and oure. The eet o oure impedane i negleted. Sytem data i alo gien in Table I. The ytem ha 0 tate ariable a lo : : id 3 : d : 5: id : i : i : : i : 6 dh 7 q 8 q The dierential equation (tate equation) o the ytem are etrated rom Fig. 7. They are lited a below d i = = d id d id qiq 6 0i (a) 0 d i R L L L d = i d + d d (b) k i re Vd ( ) = ( k p + )( id id d d re d re d = k p ( id id ) + ki ( id id ) k i V( ) = ( )( ) + Td d = + T T d d () (d)

3 RAHIMI et al.: A NEW ACTIVE METHOD IN DAMPING POSSIBLE RESONANCES IN ACTIVE FILTERS 63 Fig. 7. Load ilter and oltage oure model in dq rame. lo k id * Id ( ) = ( k pd + )( V V) d lo d * d * id = k p( ) + ki ( ) Tde Idh ( ) = ( )( Idl + T del d d i = i + i T dh dh dl del q q i q (e) () d R i q = + (g) L L L k i re Vq ( ) = ( k p + )( iq iq d d re d re q = k p ( iq iq ) + ki ( iq iq ) 0 i (h) d R i = + (i) L L L k i re V0 ( ) = ( k p + )( i0 i0 d d re d re 0 = k p( i0 i0 ) + ki ( i0 i0 ) d = d q q =. Arhie o SID (j) A it an be een (a) i the produt o tate ariable o the dierential equation o the ytem are nonlinear and they are linearized about nominal operating point. For alulating the ytem mode the ollowing tep are perormed:. The tate equation o ytem are etrated.. The nonlinear tate equation are linearized about the nominal operating point. 3. The mode o ytem are the eigenalue o the linear ytem etrated in tep. By writing the goerning dierential equation and linearizing the equation about nominal operating point the Fig. 8. D-link apaitor oltage ariation ( = = 500 ) (a) aro (b) aro + and () aro. TABLE II STATE VARIABLES WITH MAXIMUM CONTRIBUTION TO THE SYSTEM MODES Mode State with the larget partiipation ator ollowing mode are obtained = ( /67± j 0.30).0 = = ± j8 89 = (.67 ± j 0.9).0 0 = 5. 3 = =.9 0 Sine the oure i ti and the load i onidered a an input blok in Fig. 7 the reulted mode illutrate the interation between the a and d ide o the ilter. It an be een that all the mode hae deirable ing. Uing partiipation ator (partiipation ator indiate the eet o dierent tate ariable on dierent mode o the ytem) deribed in [8] the degree o ontribution o eah tate ariable in ytem mode an be deteted. In Table II the tate ariable with maimum ontribution to the ytem mode are gien.

4 6 IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING VOL. 7 NO. WINTER-SPRING 008 Fig. 9. Capaitor and nonlinear load ilter and oltage oure model in dq rame. TABLE III SYSTEM DATA FOR SIMULATION L =.5mH R = 0.3Ω V = 30V R = Ω ' L = 0. mh = 33 µf C = C = 7000 µf Inreaing the ilter indutane ha little eet on the ing and no mode will get loe to the untable region. Howeer dereaing the apaitor alue will reult in oillation o apaitor mode. Thereore the apaitor alue mut be greater than a ritial alue. For C = C = 600 µf the mode orreponding to apaitor are 56 = + j 00. I oure impedane i onidered in the blok diagram o Fig. 7 L and R will hange to L L and R R repetiely. Howeer the eet o oure impedane i negligible and een with R = R = 0 no mode will beome untable. For R = R = 0 L = 0.5 mh and L =.5 mh ytem mode are: =.9 0 = = ± j8 5 = 9 6 =. 0 7 = = =. 0 0 = 5 Fig. 8 how d-link oltage ariation in ae = = 500 µf (a) oltage ariation aro d-link apaitor ( % ) (b) oltage ariation aro total d-link apaitor + ( % + ) () oltage ariation aro dlink apaitor ( % ). A it an be een ine all mode hae uiient ing the d link oltage ariation i mall and normal. Arhie o SID B. Cae : Nonlinear Load in Parallel with a Capaitor Load Thi ae preent the tudy reult when the load i a ombination o a nonlinear load in parallel with a apaitie load. The oure i alo onneted to the ilter through an impedane o R and L. Fig. 9 depit the ytem blok diagram. Sytem data i alo gien in Table III. lo d 3 d 5 d 6 dh : : i : : : i : i 7: iq 8: q 9: i0 0: 0 : d : id : : i : : i 3 q q Sytem mode are = (.67 ± j 0.3).0 3 = (.67 ± j 0.33).0 56 = 5 ± j77 7 = 9 89 = ( 0.5± j 0.7).0 0 = ( 0.5± j 0.).0 3 = (.67 ± j 0.3).0 5 = ( 0.5± j 0.5).0 6 = 5. Uing the partiipation ator the degree dependene o ytem mode and tate ariable an be ound. In thi ae all the mode hae aeptable ing. Mode 5 6 orrepond to the d link apaitor. Now R i et to zero and the new mode are etrated. The reult are = (.67 ± j 0.33).0 3 = (.67 ± j 0.060).0 56 = ± j8 7 = 9 89 = ( ± j 595) 0 = ( ± j 53) 3 = (.67 ± j 0.).0 5 = ( ± j 5637 ) 6 = 5. It an be een that i mode o the ytem i.e hae low ing. In Table IV the tate ariable with maimum ontribution to the ytem mode are gien. It an be een that the oure urrent apaitor urrent and oure oltage hae maimum ontribution in mode with low ing. Thee mode reult in an inreae in apaitor and oure urrent. Thi urrent will alo reult in a oniderable hange in apaitor/oure oltage and urrent a hown in Fig. 0 and. Fig. 0 how imulation without atie ing and R = 0 (a) oure oltage ( ) (b) ilter urrent ( i ) () oure urrent ( i ). Fig. how d-link oltage ariation in ae = = 7000 µf (a) oltage aro total d-link apaitor + ( + ) (b) oltage ariation aro d-link apaitor ( % ) () oltage ariation aro total d-link apaitor + ( % ). +

5 RAHIMI et al.: A NEW ACTIVE METHOD IN DAMPING POSSIBLE RESONANCES IN ACTIVE FILTERS 65 Fig. 3. Atie er and urrent ontrol loop. Fig. 0. Simulation without atie ing and R = 0 (a) oure oltage (b) ilter urrent and ()oure urrent. Fig.. D-link apaitor oltage ariation ( = = 7000 µf ) (a) oltage aro apaitor + (b) oltage ariation aro apaitor and () oltage ariation aro apaitor +. Fig.. Current ontrol loop. Sytem ing an be inreaed by adding etra reitane in the ytem e.g. inreaing. But thi would reult in higher loe and lower eiieny. To inreae ytem ing atie ing i employed. In thi method the mode with little ing are ound irt. Then the tate ariable orreponding to uh mode are determined. At the end by adding uitable ontroller ytem ing i improed. Arhie o SID IV. RESONANCE ACTIVE DAMPING Conider the ilter urrent ontroller o Fig.. The tak o atie ing i to dereae oltage/urrent oillation by a modulating ignal i.e. m or ilter output oltage by the ue o a uitable ignal. Thi ignal i the one with the mot ontribution to the orreponding mode() i.e. oure urrent apaitor urrent and oure oltage. Fig. 3 how atie er and urrent ontrol loop. Fig. eplain priniple o operation o the atie er. Fig.. Filter load and oure equialent iruit. TABLE IV STATE VARIABLES WITH MAXIMUM CONTRIBUTION TO THE SYSTEM MODES Mode State with the larget partiipation ator From Fig. one an write l i + i = i + i (5) di () t () t = L + () t (6) di () t e = L + () t (7) From ()-(6) and knowing that i = ( d ( t) ) then d () t + ( + ). ( t) = L L di l () t + e() t L L L Charateriti equation or (8) i + ( + ) = 0 L L It an be een that or R = 0 L = 0. and L =.5 mh the ytem ing i zero and the natural requeny i ω n = ( + ) = 5838 rad/ L L I ha a term in oppoite phae with d / ( urrent) then a poitie ing i ahieed. (8) (9)

6 66 IRANIAN JOURNAL OF ELECTRICAL AND COMPUTER ENGINEERING VOL. 7 NO. WINTER-SPRING 008 Fig. 5. imulation ater atie ing (a) oure oltage (b) ilter urrent and () oure urrent. Thereore i a term o K i i added to the harateriti equation will hange to k dmp + + ( + ) = 0. (0) L L L Conidering a ing ator o ξ = 0.5 k an be ound a k = One again ytem mode are etrated but thi time a term o k. i i added to the output urrent regulator. The mode are: = (.35 ± j 0.90).0 3 = (-.3 ± j 0.97).0 56 = ± j8 7 = 9 89 = ( 85 ± j 6099) 0 = ( 86 ± j 5) 3 = (-.3 ± j 0.93).0 5 = ( 83± j 5770) 6 = 5. A it an be een adding the term o k. i ha inreaed the ing o the oure and apaitor urrent by 0.3 but ha dereaed the ing o ilter mode. Simulation reult alo indiate that inreaing k will deteriorate the ituation. We epeted to ee an inreae o 0.5 in the ing but thi did not happen. Thi i due to the at that in hooing k all ytem dynami were not onidered but the dominant mode o ilter apaitor and oure nd order ytem were onidered. Thi time we try to deign another er by getting a eedbak rom the oure urrent. Subtituting (7) into (8) yield 3 () () + ( + ) = 3 L L de () t e L d i t di t di L L LL L Arhie o SID L () I () t ha a omponent in phae with the oure urrent the ing will inreae. Thereore by adding a i term o k i in the ontrol loop the eet are tudied. i The alue o k i hoen uh that it ha little eet on the oure urrent and apaitor oltage. A alue o i eleted. The new ytem mode in the ae o adding i / k i and k i are: = (.9 ± j 0.99).0 3 = (.9 ± j 0.93).0 56 = ± j8 7 = 9 89 = ( 59 ± j 606) 0 = ( 8 ± j 5388) 3 = (.9 ± j 0.96).0 5 = ( 505 ± j 57).0 6 = -5. Correponding imulation reult are hown in Fig. 5 and 6. Fig. 5 how imulation ater atie ing (a)oure oltage ( ) (b) ilter urrent ( i ) () oure urrent ( i ). Fig. 6 how d-link apaitor oltage ater atie ing (a) oltage ariation aro + Fig. 6. DC-link apaitor oltage ater atie ing (a) oltage ariation aro + (b) oltage aro + () oltage ariation aro and (d) oltage aro. ( % + ) (b) oltage aro + ( + ) () oltage ariation aro ( % ) and (d) oltage aro ( ). A it an be een by applying atie ing ariation o oure oltage ilter urrent oure urrent and d link oltage i oniderably dereaed and the ytem perormane i improed. V. CONCLUSIONS In thi paper the reonane phenomenon in an atie ilter operation i tudied. It i hown that in ome ae the ytem may beome untable due to the interation o ilter omponent and load/oure indutane. The equialent blok diagram o a omplete ytem i etrated and dierent operating ae are preented. It i hown that the mode o the ytem may hae little ing in ome ae. To alleiate the problem a reonane atie ing method i propoed. It i hown analytially and uing PSCAD/EMTDC otware that the new method an oniderably inreae ytem ing and preent the ytem rom beoming untable. REFERENCES [] H. Tokuda I. Amano and N. E. Fuji "A reonane ing ontrol or a line-urrent detetion type atie ilter" IEEE Tran. on Power Sytem ol. 3 no. pp May 00. [] T. Le M. Pereira K. Renz and G. Vaupel "Atie ing o reonane in power ytem" IEEE Tran. on Power Deliery ol. 9 no. pp Apr. 99. [3] M. Ratogi N. Mohan and A. Edri "Filtering o harmoni urrent and ing o reonane in power ytem with a hybrid-atie ilter" in Pro. Applied Power Eletroni Conerene and Epoition ol. pp Mar [] Y. Sato and T. Kataoka "A urrent-type PWM retiier with atie ing untion" IEEE Tran. on Indu. App. ol. 3 no. 3 pp May 996. [5] R. Wu S. B. Dewan and G. R. Slemon "A PWM AC to DC onerter with ied withing requeny" IEEE Tran. Ind. Appl. ol. 6 no. 5 pp [6] R. Wu S. B. Dewan and G. R. Slemon "Analyi o an a-to-d oltage oure onerter uing PWM with phae and amplitude ontrol" IEEE Tran. on Indu. App. ol. 7 no. pp Mar. 99. [7] V. Blako and V. Kaura "A Noel ontrol to atiely reonane in input LC ilter o a three phae oltage oure onerter" IEEE Tran. on Indu. App. ol. 33 no. pp Mar./Apr [8] P. Kondur Power Sytem Dynami and Control Seond Edition Plenum Pre New York and London.

7 RAHIMI et al.: A NEW ACTIVE METHOD IN DAMPING POSSIBLE RESONANCES IN ACTIVE FILTERS 67 M. Rahimi Obtained hi B.S. degree in Eletrial Engineering rom Eahan Unierity o Tehnology Ehan Iran in 00 and the M.S. degree rom Shari Unierity o Tehnology Tehran Iran in 003. He i preently a Ph.D. tudent in the Department o Eletrial Engineering Shari Unierity o Tehnology Tehran Iran. H. Mokhtari wa born in Tehran Iran on Aug He obtained hi B.S. degree in Eletrial Engineering in 989 rom Tehran Unierity in Tehran Iran. He joined Eletri Power Reearh Center Intitute in 989 and worked or three year in the onulting diiion o power dipathing projet. In 99 he wa granted a holarhip rom Iran Minitry o Culture and Higher Eduation or hi M.S. degree. He inihed hi mater program in the ield o power eletroni in Unierity o Newbrunwik Canada in 99. In 99 he entered Toronto Unierity in Toronto Canada. In 999 he inihed hi Ph.D. degree. Sine 000 he ha been with the Shool o Eletrial Engineering at Shari Unierity in Tehran Iran. He i urrently an aoiate proeor in thi department. Hi reearh interet inlude power quality power eletroni and appliation o power eletroni in power ditribution ytem. He i alo a enior onultant to eeral utilitie and indutrie. G. Zaarabadi wa born in Shiraz Iran in 978. He reeied hi B.S. degree in Eletrial Power engineering rom Mazandaran Unierity in 00. In 00 he reeied hi M.S. in Power Engineering rom Shari Unierity o Tehnology Tehran Iran. From 00 to 007 he wa employed a a reearher at Iranian Aademi Center or Eduation ulture and Reearh (ACECR) - Shari Branh. He i now reearher at the Eletri Power Sytem Reearh Center o Niroo Reearh Intitute (NRI). Hi reearh interet inlude dynami o powerplant (identiiation tuning o powerplant ontroller uh a AVR PSS and Goernor and ) and ditributed generation. Arhie o SID