Steady Sate Analysis of Self-Excited Induction Generator using Phasor-Diagram Based Iterative Model

Transcription

1 WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi Stedy Ste nlysis of Self-xcited Induction Genertor using Phsor-Digr Bsed Itertive Model KNWJIT SINGH SNDHU & DHJ JOSHI Deprtent of lectricl ngineering Ntionl Institute of Technology Kurukshetr,Hryn INDI bstrct: Induction genertors in self excited ode re found to be suitble for reote nd windy loctions. Prior to instlltion there is need to predict the behviour of chine under ll possible operting conditions. This is possible through stedy stte odeling of such genertors. Stedy stte nlysis of self excited induction genertor (SIG) needs n estition of generted frequency nd gnetizing rectnce under ll possible operting conditions. So fr ost of the reserchers hve used loop ipednce, nodl dittnce or itertive techniques to deterine the stedy stte perfornce of such chines. In this pper new odel bsed upon phsor digr of induction genertor hs been proposed to nlyze the behviour of self excited induction genertor. Modeling results in third order eqution in generted frequency nd siple expression for gnetizing rectnce. oplete theticl nlysis to derive the different expressions is presented here. oputed results hve been copred with experientl results on test chines. loseness between the two proves the vlidity of proposed odeling. Keywords: - Non-conventionl sources, enewble energy, Stedy stte nlysis, Self-excited induction genertor (SIG), Wind energy. Noenclture b rr rr rr3 I I per unit frequency per unit speed excittion cpcitnce per phse ir gp voltge per phse t rted frequency error in successive vlues of generted frequency error in successive vlues of gnetizing rectnce per phse error in successive vlues of sttor voltge per phse sttor current per phse rotor current per phse, referred to sttor I cpcitor current per phse I L lod current per phse I rc core loss current per phse I gnetizing current per phse c V t lod resistnce per phse sttor resistnce per phse core loss resistnce per phse rotor resistnce per phse, referred to sttor sttor voltge per phse lod rectnce per phse sttor rectnce per phse ISSN: Issue, Volue 3, Deceber 8

2 WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi rotor rectnce per phse, referred to sttor cpcitive rectnce due to t rted frequency gnetizing rectnce per phse t rted frequency. Introduction rpid increse in power dend nd continuous depletion of fossil fuels hs diverted the ttention of scientists fro conventionl energy sources to nonconventionl energy sources. Wind energy is eerging s n potentil source ong vrious non conventionl energy sources. Most of the countries cross the world re prooting such wind energy generting units. siple expression for gnetizing rectnce. oprison of coputed nd experientl results on test chines confirs the vlidity of proposed odeling.. Stedy-Stte nlysis The stedy-stte opertion of the selfexcited genertor y be nlyzed by using the equivlent circuit representtion s shown in Fig.. In this circuit ll preters re ssued to be constnt except gnetizing rectnce. Induction genertors with cge rotor re found to be ost suitble for wind energy conversion due to their dvntges such s siple nd rugged construction, low cost nd no need of synchroniztion with existing grid. These chines cn be operted in grid connected s well s in self-excited ode. Induction genertor in self-excited ode is found to be cpble to generte the power even in the bsence of power grid. This kes it to be ost useful chine for the reote windy loctions. Fig. quivlent circuit representtion. nlysis of Fig. in the bsence of ny power source & with V t & s potentil of node & gives. j V t c Z j b () Vrious ethodologies dopted for the nlysis of SIG by reserchers [-9] re; Where, Z ( /) j Loop ipednce technique Nodl dittnce technique Itertive technique bove ethods require either lengthy derivtions or solution of nonliner equtions. In this pper n ttept hs been de to estite the generted frequency nd gnetizing rectnce for self-excited induction genertor using new strtegy bsed upon phsor digr of the chine. Proposed odeling results in the third order eqution in generted frequency nd Z j qution () nd () gives; j c j b () j (3) ISSN: Issue, Volue 3, Deceber 8

3 WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi Seprtion of rel nd iginry prts of (3), results in the following; b b nd b c (4) (5) ω b nlysis of phsor digr of induction genertor s shown in Fig. gives; V t y I (7) cosθ I sinθ (8) Siplifiction of (4) gives siple expression in s; 3 3 (6) Fig.. Phsor digr of induction genertor Where 3 b c b c V t cb c c b cb Solution of (6) gives the generted frequency for known vlues of operting speed nd lod resistnce. Further exclusion of core loss brnch leds to qudrtic eqution in unknown frequency, in contrst to higher order polynoil eqution in s obtined by other reserch persons. qution (5) gives the unknown gnetizing rectnce s; Where I sinθ y I cosθ, I I L I y is resolved coponent of long n xis perpendiculr to terinl voltge. 3. Itertion Technique Generted voltge nd frequency for SIG cn be estited using the following proposed itertion technique. Step. oputtion of initil vlues of generted frequency nd gnetizing rectnce using following expression; ISSN: Issue, Volue 3, Deceber 8

4 WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi Initil vlues s; ( b) ( b) pu,. 9999b Step. oputtion of ir gp voltge, fro gnetiztion chrcteristics (see ppendix- nd ppendix-). Step3. oputtion of odified vlues of sttor voltge fro (8). Step4. stition of generted frequency nd gnetizing rectnce fro (6) nd (7) fter using the odified vlues of nd V t. Step5.oprison of the new vlue of generted frequency with previous vlue i.e. s used in step. If rr ε, Where ε., is treted s generted frequency nd odified vlue of V t y be treted s terinl voltge for SIG. If it is not so, process y be repeted by replcing with until difference in the successive vlues for generted frequency coes out to be ε. It is lso possible to copute the generted voltge nd frequency by copring the successive vlues of nd V t obtined fter ech itertion. For such coprison itertive procedure terintes only if following expressions re stisfied. rr rr3 ε V t V t ε 4. esults nd Discussions Modeling proposed in the pper is found to be useful for estition of generted frequency nd gnetizing rectnce of SIG. Further, inclusion of core loss brnch kes the nlysis ore relistic. TBL. OMPISON OF PIMNTL ND SIMULTD SULTS (MHIN-). ISSN: Issue, Volue 3, Deceber 8

5 WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi Tble shows the coprison of experientl nd siulted results on Mchine- [ppendix-] using itertive process s explined in section-3. It is observed tht irrespective of error function (in ters of / / V t ) the finl vlues for generted voltge nd frequency turns out to be se up to 3 rd digit fter decil. However iniu nubers of itertions re required for finl results in cse error function is in ters of frequency. Tble shows the siulted results for Mchine-. The closeness between the experientl nd siulted results s shown proves the vlidity of odeling dopted. Siulted results y be obtined for ny type of lod connected cross the chine provided equtions (6) nd (7) re odified s given in ppendix-. Fig 3 nd Fig 4 shows the vrition of generted frequency nd terinl voltge with lod for different lod power fctors. Unity power fctor lod sees to be justified for better frequency nd voltge regultion. Fig. 3. Vrition of generted frequency with lod. Fig. 4 Vrition of sttor voltge with lod. ISSN: Issue, Volue 3, Deceber 8

6 WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi TBL :- OMPISON OF PIMNTL ND SIMULTD SULTS (MHIN-) 5. onclusions In this pper ttept hs been de to estite the stedy-stte perfornce of self-excited induction genertor using new itertive technique pproch bsed upon phsor digr of the chine. The proposed technique hs not been used by ny other reserch person so fr. Itertive technique is found to be very siple nd effective. Siulted results re verified using experientl results on two test chines with different rtings. lose greeent between siulted nd experientl results proves the vlidity of proposed odeling. In future this reserch work y be extended to estite the excittion cpcitnce nd operting speed to obtin constnt voltge constnt frequency ISSN: Issue, Volue 3, Deceber 8

7 WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi opertion. This y be helpful to proote the pplictions of self excited induction genertors in reote nd windy res. In turn it y be helpful to preserve the conventionl fuels which re likely to be finished with tie. ppendix The detils of the induction Mchine- used to obtin the experientl results re; Specifictions 3-phse, 4-pole, 5 Hz, str connected, squirrel cge induction chine 75W/HP, 38 V,.9 Preters The equivlent circuit preters for the chine in pu re.83,.696,.766 Bse vlues Bse voltge 9.3 V Bse current.9 Bse ipednce5.4 Ω Bse frequency5 Hz Bse speed5rp ir gp voltge The vrition of gnetizing rectnce with ir gp voltge t rted frequency for the induction chine is s given below ppendix The detils of the induction Mchine- used to obtin the experientl results re; Specifictions 3-phse, 4-pole, 5 Hz, delt connected, squirrel cge induction chine.kw/3hp, 3 V, 8.6 Preters The equivlent circuit preters for the chine in pu re.73,.379,.47. Bse vlues Bse voltge 3 V Bse current 4.96 Bse ipednce46.3 Ω Bse frequency5 Hz Bse speed5rp ir gp voltge The vrition of gnetizing rectnce with ir gp voltge t rted frequency for the induction chine is s given below ppendix-iii se I: For lod (excluding c ) xpression in cn be written s; Where b b V b t The expression of gnetizing rectnce cn be written s; ω b ISSN: Issue, Volue 3, Deceber 8

8 WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi Here sttor current, I expression is se s written in the IV section. se II: For L lod (including c ) xpression in cn be written s; Where; c 5 4 b 3 c b b c c b V t cb c b c cb pf The expression of gnetizing rectnce cn be written s; 3 b b V b V b t t pf The expression of gnetizing rectnce cn be written s; ω b Here sttor current, I expression for cse III nd cse IV, is odified nd written s; ( I I sinϕ) ( I ϕ) I L L cos ω b se IV: For lod (including c ) xpression in cn be written s; Where; se III: For L lod (excluding c ) xpression in cn be written s; 3 3 Where; 5 4 c b 3 b c b se c c b c b se c b ISSN: Issue, Volue 3, Deceber 8

9 WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi b se se c se se c se b pf The expression of gnetizing rectnce cn be written s; V t b se V: For lod (excluding c ) xpression in cn be written s; Where; V 4 t t 3 V b b se b se eferences V t se ( ) [] K.S.Sndhu, Stedy stte nlysis of isolted induction genertors, WSS Trnsctions on nvironent nd se Developent, issue, volue 4, pp 66-77, Jn 8 [] K.S.Sndhu & Dheerj Joshi, Siple pproch to stite the Stedy-Stte Perfornce of Self-xcited Induction Genertor, WSS Trnsctions on Systes nd ontrol, issue 3, volue,3, pp 8-8, Mrch 8 [3] K.S.Sndh & Shelly Vdher, ective Power equireents of Grid onnected Induction Genertor in Wek Grid, WSS Trnsctions on ircuits nd Systes, issue3, volue7, pp 5-59, Mrch 8. [4] K.S. Sndhu & S.P.Jin, Stedy Stte Opertion of Self-xcited Induction Genertor with Vrying Wind Speeds, Interntionl Journl Of ircuits, Systes nd Signl Processing,Issue, Volue, 8. [5] S.S.Murthy,O.P.Mlik, nd.k.tndon, nlysis of self-excited induction genertors, Proc. I,vol. 9,pt., no. 6,98, pp [6] L.Quzene nd G. McPherson, nlysis of the isolted induction genertor, I Trns. Power pprtus nd Systes, vol. PS-, no. 8, 983, pp [7] G. in nd O. P. Mlik, Wind energy conversion using self-excited induction genertor, I Trns. Power pprtus nd Systes, vol. PS-, no.,983,pp [8]. K. Tndon, S. S. Murthy nd. S. Jh, New ethod of coputing stedystte response of cpcitor self-excited induction genertor, I(I) Journl-L, vol. 65,985, pp [9] N. H. Mlik nd S.. Hque, Stedystte nlysis nd perfornce of n isolted self-excited induction genertor, I Trns. nergy onversion, vol. -, no.3, 986,pp [] T. F. hn, Stedy-stte nlysis of self-excited induction genertors, I Trns. nergy onversion, vol. 9, no., 994, pp ISSN: Issue, Volue 3, Deceber 8

10 WSS TNSTIONS on POW SYSTMS Knwrjit Singh Sndhu, Dheerj Joshi [] T. F. hn, nlysis of self-excited induction genertors using n itertive ethod, I Trns. nergy onversion, vol. no. 3, 995,pp [] K. S. Sndhu, Itertive odel for the nlysis of self-excited induction genertors, lectric Power oponents nd Systes, vol. 3, no., 3, pp [3] Dheerj Joshi, K.S. Sndhu nd M.K. Soni, Perfornce nlysis of three-phse self excited induction genertor using genetic lgorith, lectric Power oponents nd Systes, vol. 34, no. 4, 6, pp ISSN: Issue, Volue 3, Deceber 8