Mathematical Model and Control Strategy on DQ Frame for Shunt Active Power Filters

Transcription

1 ' ' ' Worl Aaemy of Sene, Engneerng an Tehnology nternatonal Jornal of Eletral, ompter, Energet, Eletron an ommnaton Engneerng ol:5, No:, Mathematal Moel an ontrol Strategy on DQ Frame for Shnt Ate Poer Flters P. Santprapan, -. Areerak an -N. Areerak nternatonal Sene nex, Eletral an ompter Engneerng ol:5, No:, aset.org/pblaton/68 Abstrat Ths paper presents the mathematal moel an ontrol strategy on DQ frame of shnt ate poer flter. The strtre of the shnt ate poer flter s the oltage sore nerter (S). The plse th molaton (PWM) th P ontroller s se n the paper. The onept of DQ frame to apply th the shnt ate poer flter s esrbe. Moreoer, the etal of the P ontroller esgn for to rrent loops an one oltage loop are flly explane. The DQ axs th Forer (DQF) metho s apple to allate the referene rrents on DQ frame. The smlaton reslts sho that the ontrol strategy an the esgn metho presente n the paper an proe the goo performane of the shnt ate poer flter. Moreoer, the %THD of the sore rrents after ompensaton an follo the EEE St eyors shnt ate poer flter, mathematal moel, DQ ontrol strategy, DQ axs th Forer, plse th molaton ontrol. S S S S S S5 S S S4 S SS6 P. Santprapan, master stent n eletral engneerng, PQRU Researh nt, PeM Researh grop, Shool of Eletral Engneerng, Sranaree Unersty of Tehnology Nakhon Rathasma,, THAAND. -. Areerak, Assstant Professor, PQRU Researh nt, PeM researh grop, Shool of Eletral Engneerng, Sranaree Unersty of Tehnology Nakhon Rathasma,, THAAND (orresponng athor: kongpol@st.a.th). -N. Areerak, letrer, PeM researh grop, Shool of Eletral Engneerng, Sranaree Unersty of Tehnology Nakhon Rathasma,, THAAND. t Fg. onsere poer system an ontrol strategy. NTRODUTON oaays, nonlnear loas are ely se n nstres. NThese loas generate harmons nto the poer system asng a lot of saantages [] [4]. Therefore, t s onserable to ree or elmnate the harmons n the system. The shnt ate poer flter (SAPF) s the tool to sole the harmon problem bease ths flter proes hgher effeny an more flexble ompare th a passe poer flter [5]. There are three man parts to be onsere for sng the shnt ate poer flter as shon n Fg.. The frst s the harmon eteton metho to allate the referene rrents of the shnt ate poer flter. θ β θ tan α There are many methos to allate the referene rrents sh as the nstantaneos poer theory (PQ) [6], the synhronos referene frame (SRF) [7], the a-b- referene frame [8], the synhronos eteton (SD) [9] an the DQ axs th Forer (DQF) []. n ths paper, the DQF s selete for the harmon eteton bease ths metho proe the fast allaton tme n hh t s stable for the real tme applaton. The seon part s the strtre of shnt ate α β nternatonal Sholarly an Sentf Researh & nnoaton 5() 664 sholar.aset.org/999.5/68

2 Worl Aaemy of Sene, Engneerng an Tehnology nternatonal Jornal of Eletral, ompter, Energet, Eletron an ommnaton Engneerng ol:5, No:, nternatonal Sene nex, Eletral an ompter Engneerng ol:5, No:, aset.org/pblaton/68 poer flter. The oltage sore nerter (S) th sx GBTs s se for the shnt ate poer flter. The last one s the ontrol tehne an ontrol strategy to ontrol the ompensatng rrents (, an ). There are many tehnes to ontrol the ompensatng rrents sh as the hysteress rrent ontrol [], the elta molaton ontrol [], the fzzy log ontrol [] an the plse th molaton ontrol [4]. The plse th molaton (PWM) th P ontrollers on DQ frame s se n ths paper as shon n Fg.. Therefore, the etals of P ontrollers esgn th the PWM tehne for the rrent an oltage loops on DQ frame are presente. The paper s strtre as follos. The ree of the DQF metho s aresse n Seton. The mathematal moel of shnt ate poer flter s flly presente n Seton. The esgns of to rrent loop ontrollers an one oltage loop ontroller on DQ frame an ontrol strategy are explane n Seton an Seton, respetely. n Seton, the smlaton reslts an sssons are presente. Fnally, Seton onles the ork n the paper.. REEW OF THE DQ AXS WTH FOURER (DQF) METHOD A A ( ne ( ne) ) A A h α β os( θ ) sn( θ ) ( ol ( ol) ) [( N ) T] [( N N) T] N [( N ) T] N [( N N) T] ( kt) A /, ( kt) A / h, sn( θ ) os( θ ) Fg. Flohart of the DQF metho The DQF algorthm s the exellent metho to entfy the harmon n the poer system. Ths metho s a ombnaton beteen the aantages of the synhronos referene frame metho (SRF) [7] an the slng no Forer analyss (SWFA) [5]. The DQF metho s frstly presente n 7 by Sarat Sjtjorn, ongpol Areerak an Thanatha α β loraanhpong []. n 7, the DQF metho s operate th only the shnt ate poer flter to elmnate all harmon omponents n the system. n 8 [6], ongpol Areerak extens the ork n [] to apply the DQF metho operate th the hybr poer flter to elmnate some harmon omponents epenng on the engneerng esgn. n ths seton, the etal of the DQF metho to entfy the harmon rrent on the - axs n the system s presente. The flohart of oerall proere to allate the harmon rrents on - axs (, ) sng the DQF metho s h h llstrate as shon n Fg.. The more etals of the DQF metho an be fon n [] an [6].. THE MATHEMATA MODE OF SHUNT ATE POWER FTER SS S S SS5 ' SS S ' ' S4 S6 Fg. The ealent rt of shnt ate poer flter The rt n Fg. s the onsere system se to ere the ynam moel of the shnt ate poer flter. On the A se, the rhhoff s oltage la () s se to etermne the three-phase oltage ( n, n, n ) at the P pont as shon n ()-(). M Mn t () n R M Mn t () n R M Mn t () n R M The three-phase system n ths ork s the balane threephase three-re system. Ths s the assmpton to ere the mathematal moel n the paper. Therefore, the smmaton of the three-phase oltages at the P pont an the three-phase ompensatng rrents are eal to zero as gen n (4) an (5), respetely. (4) n n n (5) M M Mn R n n n P nternatonal Sholarly an Sentf Researh & nnoaton 5() 665 sholar.aset.org/999.5/68

3 Worl Aaemy of Sene, Engneerng an Tehnology nternatonal Jornal of Eletral, ompter, Energet, Eletron an ommnaton Engneerng ol:5, No:, nternatonal Sene nex, Eletral an ompter Engneerng ol:5, No:, aset.org/pblaton/68 n the steay state onton, sbstttng the three-phase oltage from ()-() nto (4) ges the relaton n (6) as follos: Mn km k,, The relaton of the npt D oltage ( ) an otpt threephase oltages of the nerter ( M, M, M ) s explane by (7). n ths eaton, k s eal to, an for phase, phase an phase, respetely. The k n (7) s the sthng fnton of the GBTs. (7) km k Rearrangng ()-() sng (6) an (7) obtans the fferental eaton of the three-phase ompensatng rrents as shon by (8). R t (6) k kn k nk (8) here the sthng state fnton ( nk ) s explane by: nk ( k k ) (9) k,, On the D se of the rt n Fg., the fferental eaton of the D bs oltage aross the apator ( ) s shon n (). t k k,, k nk k k,, () The ynam moel of the shnt ate poer flter on three-phase system n term of the state arable moel an be rtten by (). R n R n n n () t R n n n n n n ths paper, the DQ approah s se to esrbe the ontrol strategy of the system. Therefore, the mathematal moel on three-phase system n () an be transforme nto the DQ frame sng the transformaton matrx by (). The f, f, an f are the rrent or oltage on three-phase system hle the f an f are the rrent or oltage on DQ frame. The transformaton matrx () n () s shon n (). On the other han, the DQ frame ales an transform to the threephase ales sng (4). The θ n matrx s the phase angle of the sore oltage etor as shon n the etor agram of Fg. 4. n the paper, e set the -axs on the sore oltage etor th the same phase angle. f f f f f () π π os( θ ) os( θ ) os( θ ) () π π sn( θ) sn( θ ) sn( θ ) f f f f f Fg. 4 The etor agram of the DQ frame (4) From (), the fferental eaton of the ompensatng rrent on three-phase frame an be transforme to the DQ frame sng () an (4) as gen n (5). Rearrangng (5) obtans (6). nternatonal Sholarly an Sentf Researh & nnoaton 5() 666 sholar.aset.org/999.5/68

4 Worl Aaemy of Sene, Engneerng an Tehnology nternatonal Jornal of Eletral, ompter, Energet, Eletron an ommnaton Engneerng ol:5, No:, [ ] t [ ] n n R [ ] [ n ] n (5) t n n R ω ω R n n (6) nternatonal Sene nex, Eletral an ompter Engneerng ol:5, No:, aset.org/pblaton/68 From (), the fferental eaton of the D bs oltage an be transforme to the DQ frame as shon n (7). t T n [ ] ([ ][ ] ) (7) n Rearrangng (7) obtans (8). t n [ ] (8) n From (6) an (8), the ynam moel of the shnt ate poer flter on DQ frame n term of the state arable moel an be rtten by (9). t R ω n ω R n n n n n. THE DESGN OF URRENT OOP ONTROERS AND ONTRO STRATEGY (9) n the paper, the P ontrollers are se to ontrol the ompensatng rrents of the shnt ate poer flter for harmon elmnaton n the system. The P ontrollers esgn an the ontrol strategy of rrent loop base on the ynam moel on DQ frame s presente n ths seton. From (9), the fferental eatons of the ompensatng rrent on DQ frame are explane by () an (). t R n ω () R n t ω () n n The otpt oltages of the oltage sore nerter represente as the shnt ate poer flter on DQ frame ( l an l ) are shon by () an (). () l l n n () Sbstttng l an l to () an () ges the oltage at P pont on DQ frame as shon by (4) an (5). n R ω l t (4) n R ω l t (5) On the DQ frame, the oltage on -axs an -axs at P pont are eal to an, respetely. ω l (6) t R ω t R (7) From (6) an (7), the referene oltages of the shnt ate poer flter on DQ frame (, ) are shon n (8) an (9). l ω l ω l l l (8) (9) The otpt sgnals of plant on -axs an -axs (, ) are shon n () an (), respetely. R () t nternatonal Sholarly an Sentf Researh & nnoaton 5() 667 sholar.aset.org/999.5/68

5 Worl Aaemy of Sene, Engneerng an Tehnology nternatonal Jornal of Eletral, ompter, Energet, Eletron an ommnaton Engneerng ol:5, No:, R () t From (8) an (9), the ontrol strategy of the ompensatng rrents of the shnt ate poer flter s epte n Fg.. The plants to esgn the P ontrollers for to rrent loops an ere from () an () by sng aplae transform as shon n (). h h P s s R ( P P ) s (6) Eaton (6) s se to ompare th the stanar seon orer haraterst eaton as shon n (7). U U s R () n G( s) ω s ξω s ω (7) n n nternatonal Sene nex, Eletral an ompter Engneerng ol:5, No:, aset.org/pblaton/68 From Fg., the transfer fntons of the P ontrollers on -axs an -axs an ere from () an (4), respetely. P P t t () (4) From () an (4), the transfer fntons of the P ontrollers on DQ frame are shon n (5). ( s ) U U P (5) s From () an (5), the blok agrams for the P ontrollers esgn on DQ frame are epte n Fg. 5. h h ( s ) P s U (a) rrent loop of -axs ( s ) P s U (b) rrent loop of -axs s R s R Fg. 5 The blok agram to esgn the P ontrollers on DQ frame for to rrent loops From the blok agram n Fg. 5, the lose-loop transfer fntons on DQ frame are shon n (6). omparng (6) th (7), the P an of the P ontrollers an be allate from (8) an (9), respetely. P ξω R (8) n n ω (9) The ampng rato (ξ ) n (8) s efne to.77. The natral freeny ( ω ) eal to 5π ra/s bease of the n harmon orer onsere n the system s set to 5. The resstane (R ) of the shnt ate poer flter s neglet hle the ntane ( ) s set to 9 mh from Table. Sbstttng all ales n (8) an (9) ges P 866 an THE DESGN OF OTAGE OOP ONTROER The fferental eaton of the D bs oltage an rrent n Fg. on DQ frame are shon n (4) an (4), respetely. t n n (4) (4) t Sbstttng from (4) to (4) ges the relaton n (4). (4) n n The plant for esgn the P ontroller of oltage loop an ere from (4) by sng aplae transform as shon n (4). (4) s From Fg.., the otpt of the P ontroller an be esrbe by (44). Therefore, the transfer fnton of the P ontroller for oltage loop s shon n (45). nternatonal Sholarly an Sentf Researh & nnoaton 5() 668 sholar.aset.org/999.5/68

6 Worl Aaemy of Sene, Engneerng an Tehnology nternatonal Jornal of Eletral, ompter, Energet, Eletron an ommnaton Engneerng ol:5, No:, nternatonal Sene nex, Eletral an ompter Engneerng ol:5, No:, aset.org/pblaton/68 t (44) P ( s ) P (45) s From Fg., the A se poer s eal to the D se poer as shon n (46). The losses n apator, resstor an ntor are neglet as the onton of ths eaton. (46) n n n the paper, the PWM tehne s se to generate the sthng sgnals. The poer onserng onenton of the DQ transformaton s also se. Therefore, (46) an be rertten as shon n (47). The m n ths eaton s the molaton nex of the esre operatng pont. m (47) Takng aplae transform n (47) ges (48). m (48) From (4), (45) an (48), the blok agram sng for the P ontroller esgn of the D bs oltage ontrol s epte n Fg. 6. ( s ) P s m s Fg. 6 The blok agram to esgn the P ontroller for oltage loop From the blok agram n Fg. 6, the lose-loop transfer fnton s shon n (49). m s P m ( s P m ) s (49) Eaton (49) s se to ompare th the stanar seon orer haraterst eaton as shon n (7). From ths omparson, the P an of the P ontroller an be allate from (5) an (5), respetely. P 4 ξωn (5) m ω n (5) m The apator ale of the shnt ate poer flter s set to µf from Table. The ampng rato stll be set to.77. The natral freeny of the oltage loop ( ) s set to π ra/s n ths paper. The D bs oltage omman ( ) s set to 75. Therefore, the molaton nex (m) s eal to.8. Sbstttng all ales n (5) an (5) obtans P.75 an.884. ω. SMUATON RESUTS AND DSUSSONS The smlaton reslts of the system n Fg. th the system parameters from Table are epte n Fg. 7. n the paper, the aerage total harmon storton (%THD a ) s se as the performane nex for the harmon mtgaton. The %THD a an be allate by (5). n Fg. 7, the sore rrents before ompensaton (,, ) are hghly storte aeform. From Table, the %THD a of the sore rrents before ompensaton s eal to 4.4%. Ths ale s extremely greater than the EEE St When the shnt ate poer flter njets the ompensatng rrents (,, ), the sore rrents ( s, s, s ) are nearly snsoal aeform. The %THD a of these rrents after ompensaton s eal to.69% that s satsfe ner EEE St k,, % THD k % THD a (5) ne oltage an freeny ne mpeane Three phase oe retfers parameters Shnt ate poer flter parameters Sthng freeny TABE SYSTEM PARAMETERS n s (peak), f s5 Hz s. mh,max4 H, R,max Ω,mn H, R,mn 65 Ω 9 mh, µf f s5 Hz rrent loop ontrollers parameters P 866, oltage loop ontroller parameters P.75,.884 nternatonal Sholarly an Sentf Researh & nnoaton 5() 669 sholar.aset.org/999.5/68

7 Worl Aaemy of Sene, Engneerng an Tehnology nternatonal Jornal of Eletral, ompter, Energet, Eletron an ommnaton Engneerng ol:5, No:, 5 s s s nternatonal Sene nex, Eletral an ompter Engneerng ol:5, No:, aset.org/pblaton/68 s s s tme (se) Fg. 7 The smlaton reslts nternatonal Sholarly an Sentf Researh & nnoaton 5() 67 sholar.aset.org/999.5/68

8 Worl Aaemy of Sene, Engneerng an Tehnology nternatonal Jornal of Eletral, ompter, Energet, Eletron an ommnaton Engneerng ol:5, No:, nternatonal Sene nex, Eletral an ompter Engneerng ol:5, No:, aset.org/pblaton/68 From Fg., the loa mpeane of the three-phase brge retfer s hange at t.4.8 s. Therefore, the amplte of sore rrents at ths pero nreases. The shnt ate poer flter an stll ompensate the harmon rrent een thogh the loa s are. From Fg. 8, t onfrms that the P ontrollers of to rrent loops an ontrol the ompensatng rrents to trak the referene rrents (,, ). n ths paper, the referene rrents an be allate from the DQF metho. Moreoer, the D bs oltage s stll onstant at 75 as shon n Fg. 7. For ths reason, the P ontroller of the oltage loop an reglate the D bs oltage. & & & phase TABE %THD OF THE SOURE URRENTS BEFORE AND AFTER OMPENSATON %THD of the sore rrents %THD before ompensaton tme (se) Fg. 8 The ompensatng an referene rrents of the system. ONUSON Ths paper presents ho to ere the mathematal moel of the shnt ate poer flter on DQ frame. The plse th molaton (PWM) tehne s apple to generate the sthng sgnals of the shnt ate poer flter. The oltage sore nerter (S) s se as the shnt ate poer flter. The P ontrollers are apple to ontrol the njeton of the ompensatng rrents an the D bs oltage follong on the omman ale. The esgn metho of these ontrollers s ompletely presente n the paper. Moreoer, the oerall ontrol strategy of the system on DQ frame s also presente. n the paper, the DQF metho s se to allate the referene rrents of the shnt ate poer flter. The smlaton reslts %THD after ompensaton %THD a sho that the ontrol strategy an the esgn metho presente n the paper an proe the goo performane of the shnt ate poer flter. Frthermore, the %THD of the sore rrents after ompensaton an follo the EEE St an these aeforms are nearly snsoal. ANOWEDGMENT Ths ork as spporte by Sranaree Unersty of Tehnology (SUT) an by the offe of the Hgher Eaton ommsson ner NRU projet of Thalan. REFERENES [] nrajt P. an Pal J.S., Effet of Harmon on Poer Measrement, EEE Petrolem an hemal nstry onferene, 989, pp. 9. [] Elham B.M., larene.w., an Aly A.G., A Harmon Analyss of the nton Watthor Meter s Regstraton Error, EEE Transaton on Poer Delery, ol. 7, no., 99, pp [] Ho J.M.,.., The Effets of Harmons on Dfferental Relay for a Transformer, EEE nternatonal onferene an Exhbton on Eletrty Dstrbton (RED), ol.,. [4] EEE St , EEE Reommene prates an rerement for harmon ontrol n eletral poer system. [5] Peng, F. Z., Akag, H., an Nabae, A., A Ne Approah to ompensaton n Poer Systems, nstry Applatons Soety Annal Meetng., onferene Reor of the 988 EEE, ol., Ot 988, pp [6] Peng F. Z. an a J-S, 996, Generalze nstantaneos reate poer theory for threephase poer system EEE Trans. nstrm. Meas.,ol.45, no., Febrary, pp [7] B. Zhang, "The Metho base on a Generalze k oornate Transform for rrent Deteton of an Ate Poer Flter an Poer System", EEE Poer Eletrons Spealsts onforene, 7, pp [8] hang, G.W. an hen, S.., An a-b- Referene Frame-Base ontrol Strategy for the Three-Phase For-Wre Shnt Ate Poer Flter, EEE nternatonal onferene on Harmons an Qalty of Poer, ol., pp [9] hen,.., n,.e. an Hang,.., An Ate Flter for Unbalane Three-Phase System Usng Synhronos Deteton Metho, EEE onferene on Poer Eletrons Spealsts 994 (PES '94), ol., pp [] Sjtjorn, S., Areerak,.-. an loraanhpong, T., The DQ Axs Wth Forer (DQF) Metho for Harmon entfaton, EEE Transatons on Poer Delery, ol., no., pp , Jan. 7. [] Zeng J., Y.,Q Q., Yan Z., N Y., Zhang B..,hen S., an W F. F., A Noel Hysteress rrent ontrol for Ate Poer Flter th onstant Freeny, Eletr Poer Systems Researh 68, pp.75-/8, Jan. 4. [] azmerkosk M.P. an Dzenakosk, M.A. (99). Ree of rrent reglaton methos for S-PWM nerters, EEE nternatonal Symposm on nstral Eletrons 99 (SE '9), pp [] P. Prasomsak, ongpol Areerak, ongpan Areerak, an A. Srkae, ontrol of Shnt Ate Poer Flters sng Fzzy og ontroller, The ASTED nternatonal onferene Moelng, entfaton, an ontrol (AsaM ), Thalan, pp. 7-, No.. [4] N. Menalek,. A-Haa, F. Fnaeh an.a. Dessant, Nonlnear ontrol tehne to enhane ynam performane of a shnt ate poer flter, n EE Pro. Eletr Poer Applatons, ol.5, no.4, pp. 7 79, Jly. [5] M. E-Habrok an M.. Darsh, Desgn an mplementaton of a mofe Forer analyss harmon rrent omptaton tehne for poer ate flter sng DSPs, Pro. nst. Elet. Eng., Elet. Poer Appl., ol. 48, no., pp. 8, Jan.. [6] Areerak,.-., Harmon Deteton Algorthm base on DQ Axs th Forer Analyss for Hybr Poer Flters, WSEAS TRANSATONS on POWER SYSTEMS, ol., no., pp , No. 8. nternatonal Sholarly an Sentf Researh & nnoaton 5() 67 sholar.aset.org/999.5/68

9 Worl Aaemy of Sene, Engneerng an Tehnology nternatonal Jornal of Eletral, ompter, Energet, Eletron an ommnaton Engneerng ol:5, No:, P. Santprapan as born n Ranong, Thalan, n 988. He reee the B.S. egree n eletral engneerng from Sranaree Unersty of Tehnology (SUT), Nakhon Rathasma, Thalan, n 9, here he s rrently styng toar the M.Eng. egree n eletral engneerng. Hs man researh nterests nle the shnt ate poer flter, harmon elmnaton, artfal ntellgene applatons, smlaton an moelng. -. Areerak reee the B.Eng, M.Eng, an Ph.D. egrees n eletral engneerng from Sranaree Unersty of Tehnology (SUT), Thalan, n,, an 7, respetely. Sne 7, he has been a letrer an Hea of Poer Qalty Researh Unt (PQRU) n the Shool of Eletral Engneerng, SUT. He reee the Assstant Professor n Eletral Engneerng n 9. Hs man researh nterests nle ate poer flter, harmon elmnaton, artfal ntellgene applatons, motor re, an ntellgene ontrol systems. nternatonal Sene nex, Eletral an ompter Engneerng ol:5, No:, aset.org/pblaton/68 -N. Areerak reee the B.Eng. an M.Eng egrees from Sranaree Unersty of Tehnology (SUT), Nakhon Rathasma, Thalan, n an, respetely an the Ph.D. egree from the Unersty of Nottngham, Nottngham, U., n 9, all n eletral engneerng. n, he as a letrer n the Eletral an Eletron Department, Rangst Unersty, Thalan. Sne, he has been a etrer n the Shool of Eletral Engneerng, SUT. Hs man researh nterests nle system entfatons, artfal ntellgene applatons, stablty analyss of poer systems th onstant poer loas, moelng an ontrol of poer eletron base systems, an ontrol theory. nternatonal Sholarly an Sentf Researh & nnoaton 5() 67 sholar.aset.org/999.5/68