Approach Method to Evaluate the Total Harmonic Distortion for a System Has Multiple Nonlinear Loads

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1 eriol Jourl of Egieerig Reserc SSN:39-689(olie,347-53(pri Volume No.4, ssue No., pp : Nov. 5 Approc eod o Evlue e ol rmoic Disorio for Sysem s uliple Nolier Lods. A. omed Elecricl Power d cies Deprme, Divisio of edi Egieerig, eriol Acdemy For Egieerig & edi Sciece, Six Of Ocober Ciy, Giz, Egyp. m4@gmil.com Absrc power quliy, rmoics problems re worse rsie eves, suc s ligig or volge sgs. e rmoics problems could ge worse if more oe olier lod were coeced o sysem. erefore, suc disorio sould be voided o proec e power sysem source d e elecricl devises. is ricle ew ecique ws developed o esime e ol rmoic disorio for sysem s muliple olier lods wiou performig deiled iercoeced sysem lysis. is ecique ws successfully uilized o lb. e ecique gives ccepble resuls. Keyword rmoics, ol rmoic disorio, olier lods, mlb/simulik.. roducio Power sysems re desiged o opere frequecies of 5 or 6 z, wic is clled e fudmel frequecy. Nevereless, some ypes of lods produce curres d volges wi frequecies re ieger muliples of e sysems fudmel frequecy. ese iger frequecies re kow s power sysem rmoics [, [. rmoics were kow log ime go, s erly s e 89s [3. did o cuse lo of problems ime becuse e equipme used ws o sopisiced. ody s elecroic devices re widely used d ey re very sesiive o power quliy deeriorios. Also, e umber of rmoics producig devices icresed [4. Power elecroic lods provide sigific dvges i efficiecy d corollbiliy [5. owever, ey drw osiusoidl curre from e AC power sysem, d is curre iercs wi e sysem impedce creig volge rmoics. rmoics sudies were doe i e ps, cocered mosly o e iercio bewee e olier lod d e power source [6, [7. owever, is esis will iroduce ew sudy focuses o e iercio mog olier lods wile coeced o e power grid, d e esime e rmoics effec o e sysem before coecig e lods. e coveiol D formul co be used o deermie e rmoics effec of lods iercio, uless e lods re lredy coeced i e sysem d eir equivle curre d volge re lyzed [8, [9. erefore, i co be used o esime e rmoics effec before ruig e sysem or performig deiled compuer simulios. e clssicl D formul is modified i is ricle resulig i D formul fcilies deermiig e overll D for ierced olier lods. is formul uilizes idepede lod d before iercio o deermie e cul iercio effec. A pproc meod is iroduced o fcilie e proposed process.. Fourier series lysis Volge d curre i elecricl drive pplicio re ypiclly periodic i sedy se. Periodic wveforms c be described by Fourier series expsio [3, [ : f ( cos( b si( ( Were ω is e fudmel gulr frequecy of e wveform. is reled o e period s follows: e mgiude d pse of e seleced rmoic ( compoe re clculed by e followig equios. DC compoe f ( d b giude b ( Pse Were, f w d ( cos( b f w d ( si( (5 Afer fidig e mgiude of ec rmoic, e ol rmoics disorio c be esily foud usig e followig equio. D % (6 Fourier lysis is useful wy of brekig dow y periodic sigl. Uforuely, some periodic sigls re very compliced i i becomes rd o solve e Fourier ( (4 (3 JER@5 Pge 68

eriol Jourl of Egieerig Reserc SSN:39-689(olie,347-53(pri Volume No.4, ssue No., pp : 68-64 Nov. 5 lysis by d.

2 eriol Jourl of Egieerig Reserc SSN:39-689(olie,347-53(pri Volume No.4, ssue No., pp : Nov. 5 lysis by d. is ricle preses Fourier lysis of periodic sigl s well s clculig e ol rmoics disorio (D usig mlb/simulik. is meod will elp us fid e mgiude d pse of e differe rmoics. oer words, oe mus fid e mgiude d pse of e fudmel compoe, DC compoe d rmoics compoe seprely. A power elecroics recifier circui [, [ is used i is secio exmple o demosre pplyig Fourier series lysis; firs usig d clculios d secod uilizig compuer compuiol ools (lb/simulik.. d Clculios lb is used o cree e periodic wveform of e ipu curre o semi-corolled recifier. e figures d sow e mlb block digrm d e ipu curre of semicorolled recifier were e fudmel frequecy is 5 z d e firig gle α =.3 secod. e, d clculios for e Fourier series lysis is used o fid e fudmel compoe of e wveform d is rmoics compoes. Figure (: Semi-Corolled Recifier. Fourier series lysis Figure (: pu curre. i( cos( b si( (7 Dc compoe: JER@5 Pge 69 i( d (8 were e fudmel frequecy is 5 z e =.s = π rd d e firig gle α =.3 sec =.945 rd. erefore, [ si si d d.945 [( cos.945 ( cos [ Fudmel compoe: f w d ( cos( [ si( cos( d si( cos( d (9 ( si ( si ( [( (.834 b f w d ( si( ( b [ si ( si ( d d si( si( [( ( 4 4 [(.3373 ( (.83 ( (.853 ( (3 rmoics compoes: rmoics mgiude d pse c be foud by subsiuig e rmoics umber i e ex equios. f w d ( cos( (4 [ si( cos( d si( cos( d (5

3 eriol Jourl of Egieerig Reserc SSN:39-689(olie,347-53(pri Volume No.4, ssue No., pp : Nov. 5 cos( cos( [( ( ( cos( cos( ( ( ( b b f w d ( si( [ si( si( d si( si( d si( si( [( ( ( si( si( ( ( ( giude b ( Pse ble ( sows d soluios. b (6 (8 (7 V. lb/simulik soluio e Fourier block o lb/simulik is progrmmed o clcule e mgiude d pse of e DC compoe, e fudmel, d y rmoic compoe of e ipu sigl. Also, e D block clcules e ol rmoics disorio for e sme semi-corolled recifier. Figure 3 sows e semi-corolled recifier wi D block d Fourier block. Fourier series lysis d D of e ipu curre is deermied gi wi lb/simulik for vlidio; ble (. Figure (3: Semi-corolled recifier wi D block d Fourier block ble (: d soluios for rmoics mgiude d pse rmoics giude Pse umber From e give ble, e ol rmoic disorio c be clculed s: e Fourier block, e fudmel frequecy is 5 z wile e rmoics compoes c be djused o perform e desired mgiude d pse. Before uilizig e Fourier series lysis i lb, oe d o do some correcios o e Fourier series oolbox. e process of coverig e Fourier oolbox block digrm io memicl equio, e followig equios were foud: b ( b ( By comprig e bove equios wi equios ( d (3 [. c be see e pse equio is icorrec. erefore, i sould be correced before usig e Fourier oolbox. Figure 4 sows e block digrm of e Fourier oolbox of lb. D rms rms % 3.87% (9 Figure (4: block digrm of e Fourier oolbox. JER@5 Pge 6

eriol Jourl of Egieerig Reserc SSN:39-689(olie,347-53(pri Volume No.4, ssue No., pp : 68-64 Nov. 5 ble ( : lb soluios for rmoics mgiude d pse rmoics o. giude Pse.8753 3.9 3.83-7.45 5.345 7.49 7.7 5.

4 eriol Jourl of Egieerig Reserc SSN:39-689(olie,347-53(pri Volume No.4, ssue No., pp : Nov. 5 ble ( : lb soluios for rmoics mgiude d pse rmoics o. giude Pse From ble ( e ol rmoic disorio c be clculed s: D = 3.79% ( Equio ( sow good greeme wi is couerpr (9; s sow i ble (3. ble (3: Compriso of e wo lysis meods rmoi Number giude d.87 soluio giude lb.8753 soluio Figure (5: Fourier series grp Figure 5 sows grp of e curre sigl usig e 5 rmoics compoes. is grp is o ideicl o of Figure due o e egleced rmoics beyod e 5. V. e D for wo olier lods by usig mlb/simulik. is sudy is limied o e cse were e firig gles of e olier lods re fixed. erefore, e feeder lie is e mi medium of iercio wii e sysem. order o sudy e rmoics iercio bewee e wo lods, oe mus deermie e sysem curre rmoics uder wo operig codiios [7, [8. Firs, by deermiig e curre rmoics durig e iercio d secod, by fidig e curre rmoics for ec isoled lod loe d e dd em ogeer mully. bles 4 d 5 sow compriso of e curre rmoics wi d wiou e rmoics iercio for differe vlues of feeder impedce. ble (4: Compriso of e curre rmoics rmoics L=. Order Wi iercio Wiou iercio ble (5: Compriso of e curre rmoics rmoic Order L=.7 Wi iercio Wiou iercio JER@5 Pge 6

5 eriol Jourl of Egieerig Reserc SSN:39-689(olie,347-53(pri Volume No.4, ssue No., pp : Nov. 5 From e previous bles, D c be foud usig e followig equio: D % ( (Noe: Dw is e D durig e iercio d Dwo is e D before e iercio. ble 6 sows compriso bewee e clculed D for differe feeder impedce vlues. ble (6: e D uder differe feeder impedce. L ( Dw (% Dwo (% Diff is cler from e bove ble e D decreses s e feeder impedce icrese. is peomeo is expeced becuse s e feeder impedce icrese, e lod coeced ode volge decreses, resulig i lower lod curre. Nevereless, oe sould o ge side rcked sice e mi cocer i is ricle is o fid e reliosip bewee e Dw d Dwo. V. ol rmoic disorio esimio is ricle, pproc meod focuses o e iercio mog olier lods wile coeced o e power grid, d e esime e rmoics effec o e sysem before coecig e lods, for deermiig e modified D (D, is proposed. Usig D, oe c esime Dw from decoupled lod d d wiou compuer simulio of e iercoeced lod ework cofigurio. By replcig ec lod wi is effecive fudmel d rmoics impedces, oe c solve for e grid s curre rmoics by usig e ijeced curre divider meod. is cse, e grid s curre rmoics re clculed wice; oce wiou e iercio (Fig. 6 (A d oce wi e iercio (Fig. 6 (B [. (A (B Figure (6: (A wo olier lods coeced seprely, (B wo olier lods iercig roug e lie feeder. Source rmoics curre before e iercio. From Fig. 6 (A, e fudmel curre compoe my be deermied s follows. V L L (3 V L L (4 erefore, e ol source curre, S L L L L S V ( L ( L (5 Equio (3 c be rewrie i e followig form, o represe ec rmoic compoe (. Vs( L L S [( L ( L (6 Were Vs is virul rmoics source.. Source rmoics curre wi e iercio lods. From Fig. 6 (B, e fudmel curre compoe my be deermied s follows. L L S V L L ( L L (7 e bove equio c be rewrie i e followig form o represe ec rmoic compoe (, were Vs is ssumed o be e sme like e idepede lods cse. L L S VS L L ( L L (8 JER@5 Pge 6

6 eriol Jourl of Egieerig Reserc SSN:39-689(olie,347-53(pri Volume No.4, ssue No., pp : Nov. 5 From equio (4 d (6, equio (7 resuls. ( L L S S / ( ( L L L L ( L L [( L ( L (9 erefore, S my be obied from S usig e modifier ; equio (8. ( L L / ( ( erefore, [( L ( L L L S S L L ( L L (3. (3 e modified D (D c e be foud by subsiuig e bove expressio io e regulr D formul. ble (8: Comprisos of D & D ble (9: Ccomprisos of D & D D ( s f s. f (3 V. compriso, e sysem wic clculed by mlb d wic obied from e pproc meod e sme seps were repeed o fid e D for differe lie impedce vlues, ex ble for compriso, e sysem Dw wic clculed by mlb d D wic obied from e pproc meod is icluded i e sme ble(7. ble(7: Compriso of Dm d Dw Feeder Dm (% Dw (% Percege lie ( Esimed Acul error Above ble demosres e Dm gives ccepble esime of e cul D for muliple lod sysem. V. Exmples d simuled resuls d clculio exmples for compriso of ol rmoic disorio (D of wo olier lods before e iercio d modified ol rmoic disorio (D fer e iercio by usig icrosof excel. A compriso of D for s lod, d lod d source (before e iercio d e modified D s e flowig bles (8&9. e Resul of e Compriso is cler from e bove ble e modified D is more decrese e D for s lod, d lod d source (before e iercio s e feeder impedce is iducive lod. Also cpciive lod we e sysem o er from e resoce cse were e modified D is more icrese s e sysem is er from e resoce cse. X. Coclusios power quliy, rmoics problems re worse rsie eves, suc s ligig or volge sgs, wic ls for sor periods of ime. rmoics re sedy-se periodic peome produce coiuous disorio of volge d curre wveform. e rmoics problems could ge worse if more oe olier lod were coeced o sysem. erefore, suc disorio sould be voided o proec e power sysem source d e elecricl devises. is ricle, proposed ecique ws developed o esime e D for sysem s muliple olier lods wiou performig deiled iercoeced sysem lysis. is ecique ws successfully uilized o lb. e ecique gives ccepble swer for wo lod sysems. JER@5 Pge 63

7 eriol Jourl of Egieerig Reserc SSN:39-689(olie,347-53(pri Volume No.4, ssue No., pp : Nov. 5 Refereces i. omed,. A., "Esimig ol rmoic Disorio for Nolier Lods," esis of ser Degree, Fculy of Egieerig Ciro Uiversiy, Jury 9. ii. Kumr, S. V. D., d Reddy, K. R., "rmoic Polluio Esimio i Disribuio Sysem vig uliple Lods wi Lod posiio Sifig," eriol Jourl of Compuiol Sciece, emics d Egieerig Volume, ssue3, rc 5. iii. Priydrsii, A., Devrj, N., sry, A.U., d Ai, R., "Survey of rmoics i No Lier Lods," eriol Jourl of Rece ecology d Egieerig (JRE SSN: , Volume-, ssue-, April. iv. Ko, A., Swe, W., d ey, A., "Alysis of rmoic Disorio i No-lier Lods," eriol Jourl of e Compuer, e ere d geme, Vol. 9 No. SP, Jue,. v. p:// De: vi. Wkile, G. J., "Power Sysems rmoics: Fudmels, Alysis d Filer Desig," pp Spriger-Verlg, Germy,. vii. Grdy, W.., "Udersdig Power Sysem rmoics, EEE, Vol., ssue, Nov., pp. 8. viii. Jlli, S. G., d Lsseer, R.., "rmoics ercio of power sysem wi sic Swicig Circuis," d EEE Power Elecroics Speciliss Coferece, Jue 4-7, 99, pp ix. Ksski, J. G., " Priciples of Power Elecroics," pp Addiso-Wesley, Redig, Jue 99. x. Spiegel,. R., "emicl dbooks of Formuls d bles," Secod Ediio, pp cgrow ill, 998. xi. Erickso, R. W., "Fudmel of Power Elecroics," Secod Ediio, pp Kluwer Acdemic Publisers, Boso,. JER@5 Pge 64

Time-domain Aeroelastic Analysis of Bridge using a Truncated Fourier Series of the Aerodynamic Transfer Function

Time-domain Aeroelastic Analysis of Bridge using a Truncated Fourier Series of the Aerodynamic Transfer Function Te 8 Ci-Jp-ore eriol Worksop o Wid Egieerig My, 3 Time-domi Aeroelsic Alysis of ridge usig Truced Fourier Series of e Aerodymic Trsfer Fucio Jiwook Prk, Seoul iol iversiy, ore ilje Jug, iversiy of ore