Simulation of series active filter for unbalanced loads

Transcription

1 Proceedigs of the 3th WSEAS tertiol Coferece o CRCUTS Simultio of series ctive filter for ublced lods P.ALAAN M.E (P.S.E) Power system egieerig A Uiversity Guidy, Chei Tmil Ndu NDA gretkli_ssi@yhoo.co.i d ssikumrkli@gmil.com Abstrct: - The use of power electroics circuits i wide rge of pplictios hs resulted i distorted curret wveforms i the power system. This result i o-siusoidl voltge drops cross the trsformers d trsmissio lie impedces, resultig i o-siusoidl voltge supply t the poit of commo couplig. Asymmetricl distributio of lrge sigle phse lods further complictes the issue by cusig ublce i the lie currets of the three phse system. Ublce i lod curret leds to excessive eutrl currets, power fctor, icresed losses d reduced i overll efficiecy. The use of series ctive filter i the lod side to mitigte the ublce i the system. Her we use proposed optimiztio techique for blcig the currets d obtiig the best compromise betwee the power fctor d curret distortio uder o-siusoidl voltge coditios. t does ot use p-q theory. ey-words: - Hrmoics, No-siusoidl voltge, Optimiztio, Power fctor, Series ctive Filter, Ublce. troductio A series ctive filter (SAF), show i Fig., c be used to compeste for both hrmoic distortio d imblce i the supply voltge. The voltges, either o the supply side or the lod side, c be compested s desired. However, this pper dels with pplictios where the lods re sesitive to voltge wveform qulity. Hece, the compestio is cosidered oly o the lod side. The compestio voltges, required to elimite voltge hrmoics d mke the system blced, re ijected cross the compestig trsformers secodry widigs which re i series with the lie. t c be observed tht if ttempt is mde to reduce the voltge, the power fctor my decrese, while y ttempt t chievig higher power fctor my result i higher voltge. This trdeoff betwee the power fctor d voltge distortio () must be optimized to chieve the best compromise. Thus, there is trdeoff betwee the power fctor d voltge d suitble optimiztio [0], [] of the two is ecessry. The proposed scheme lso hs the followig desirble fetures. i) A optimized power fctor. ii) A optimized voltge totl hrmoic distortio () which is withi the limit stipulted by power qulity orms. iii) A blced source curret SSN: SBN:

2 Proceedigs of the 3th WSEAS tertiol Coferece o CRCUTS. Proposed compestio techique Cosider power system with olier lod beig supplied with osiusoidl supply voltge. Let the supply voltge coti hrmoic compoets v s tht produce lod curret of ideticl frequecies d other compoets tht do ot result i the correspodig lod curret compoets. The correspodig expressio for voltge my be writte s v s si s ( ω t + α ) () Where α is the rbitrry gle of the supply voltge d s is the root-me-squre vlue of the th order hrmoic compoet of voltge. Let the lod curret coti compoets of curret, hvig o correspodig frequecy compoets i the supply voltge, due to their o lierity. Also, for simplicity, ssume tht there is o phse gle betwee the voltge d the curret hrmoic. The correspodig expressio for curret my be writte s i s si s ( ωt + α ψ Where is the rms vlue of the th order hrmoic compoet of source curret d ψ is the phse gle betwee voltge d s ) () curret of the correspodig hrmoic compoets. For chievig optimum power fctor, expressio for the desired lod voltge v is obtied by usig (), by settig l the order of hrmoics preset i the supply voltge the sme s tht of curret. This mes tht the hrmoic compoets represeted by i the supply voltge should be replced by the order of hrmoics preset i the curret. The expressio for the desired lod voltge fter compestio is v l l ( ω t + α ) si (3) where l s d re the cotrol vrible which is rel qutity d is defied s the rtio of the th order lod voltge d curret hrmoic compoets d idetified s impedce of the th order fter compestio. By cotrollig, both the power fctor d voltge c be cotrolled d optimized. The most pproprite vlue of is computed by usig optimiztio techique. The referece compestig voltge is give by v c v s v l where v s is the supply or lod voltge before compestio, v l v is the desired voltge cross the lod, d is the referece compestio voltge c which must be ijected cross the compestio trsformer widigs to compeste the supply voltge. 3. Optimiztio techique The Lgrgi multiplier optimiztio techique is used to optimize the olier equtio for volt-mpere (ppret power) subject to equlity d iequlity costrits. Rel power demded by the lod is tke s equlity costrit d voltge limit s the iequlity costrit. A ugmeted Lgrge fuctio c be writte s L f + λ g + μ u (4) Where f is the objective fuctio, g is the equlity costrit, u is the iequlity costrit, d λ d μ re to be determied. The ecessry coditio for costried locl miim of L is tht the SSN: SBN:

3 Proceedigs of the 3th WSEAS tertiol Coferece o CRCUTS derivtive of (4) with respect to its vribles should be zero. Sice the iequlity costrit is lso preset, uh Tucker coditios must be stisfied. For miimum ppret power, ll of the eigevlues of the Hessi mtrix, evluted t optimum vlue of, should be positive. 3.. Objective Fuctio Let be the rms vlue of the curret represeted by () d v l be the rms vlue of the voltge represeted by (3). For give ctive power, the power fctor c be improved by miimizig S the totl Where ppret iput power. Thus, the objective fuctio f is costructed s f S s (5) Similrly for other phses S b d S c., b d c re cotrol vrible 3... Equlity Costrits The mgitude of v l is clculted i such wy tht it supplies the me vlue of the istteous rel power demded by the lod. Therefore, the equlity costrits c be writte s P dc g 0 (6) s 3 Similrly for other phses. P dc ( ψ ) s s cos + b sb cos( ψ b + c sc 3.3. equlity Costrits Let the voltge be limited to. The iequlity costrit (u ) is clculted s u cos s s ( ψ ) c 0 (7) (8) ) 3.4. Lgrge Fuctio The objective is to miimize S, give by (5), subject to the equlity costrit (6) d the iequlity costrit (8). Thu s, the ugmeted fuctio ( L )is give by + Pdc L s s λ s 3 + μ s s (9) Where λ d μ re the vribles correspodig to the equlity d iequlity costrits. The ecessry coditios for costried locl miim of L re L b [ ( μ ) λ ] 0 (0) L b L g λ L u μ Where [ ( + μ ) ] s λ () d b s Solve the bove four equtio we fid the cotrol vrible equtios re s λ ( + ) s s s s + λ s ( ) ( + ) s s + ( ) s ( + ) () (3) (4) (5) Pdc s λ (6) 3( s + s ) The flow chrt of proposed lgorithm is show i below SSN: SBN:

4 Proceedigs of the 3th WSEAS tertiol Coferece o CRCUTS 4.. Simultio prmeter S ource Lie voltge s45 Fudmetl frequecy, f 50 Hz Source iductce, Ls40mH Source X/R rtio, 8 Lod Ublced RL lod R l 50Ω, R lb 75Ω, L l 00mH L lb 5mH R lc 5Ω, L lc 75mH Nolier lod Three phse diode rectifier R d 5Ω L d 30mH SAF specifictios L 30 mh f R f dc dc _ref C dc R dc fs ohm 000 volts 000 volts 4000 μf 6000 ohms 00f Hz Ts /fs Hz 4.. Simultio wve forms.ublced curret t source side 4. Simultio results The proposed lgorithm is verified usig MATLAB simultios o blced, three phse, 50-Hz, 45- siusoidl voltge power supply. The simultio wveforms d redigs re show below SSN: SBN:

5 Proceedigs of the 3th WSEAS tertiol Coferece o CRCUTS.No-lier Lod voltge 3. Referece curret Tble:- oltge thd Before compestio After compestio Phse Phse-b Phse-c Coclusio 4. After compestio the lod voltge A importt feture of this lgorithm is tht it is lso pplicble i the cse of combitio of series d shut ctive filter (series-shut ctiv e filter) to geerte referece compestio voltge d curret. t is possible to completely elimite the hrmoics preset i the voltge d curret usig series-shut ctive filter d, s such, there is o eed for y optimiztio. However, optimiztio will be eeded, if it is sufficiet to limit the voltge d curret hrmoics to withi o zero limit imposed by stdrds, isted of their complete elimitio. 5. oltge thd before compestio 6. Refereces.E.Wger, Effect of hrmoics o equipmet, EEE Trs. Power Delivery, vol8,o, pp67-80apr oltge thd fter compestio S.George d.agrwl, A ovel techique for optimizig the hrmoics d rective power uder o-siusoidl voltge coditios, i poc. Au. cof. EEE d.electro, Soc.(eco 0), 00,vol,pp S. George d. Agrwl, A ovel techique for optimizig the hrmoics d rective power uder o-siusoidl supply d ublced lod coditios, i Proc. Power Electroics Specilist SSN: SBN:

6 Proceedigs of the 3th WSEAS tertiol Coferece o CRCUTS Cof. 003, Ju. 003, vol. 4, pp S.D.Roud d R.M.Duke, Active filter optimiztio for efficiet vrible frequecy remotegeertio, i Proc. d. Appl, Soc. Au. Meetig, 993,vol, pp Hdi sdt, power system lysis, McGrw-Hill compy, pp S.George d.agrwl, A DSP bsed optiml lgorithm for shut ctive filter uder o-siusoidl supply d ublced lod coditios, EEE Trs. Power electro, vol,.no., mrch 007. S. M.-R. Rfiei, A. H. Toliyt, R. Ghi, d T. Goplrthm, A optiml d flexible cotrol strtegy for ctive filterig d power fctor correctio uder o-siusoidl lie voltges, EEE Trs. Power Del., vol. 6, o., pp , Apr. 00. Z. Wg, Q. Wg, W. Yo, d J. Liu, A series ctive power filter doptig hybrid cotrol pproch, EEE Trs. Power Electro., vol. 6, o. 3, pp , My 00. SSN: SBN: