Modeling and Dynamic Analysis of Gearless Variable-Speed Permanent Magnet Synchronous Generator Based Wind Energy Conversion System

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1 Europan ssociation for th Dvlopmnt of Rnabl Enrgis, Environmnt and or Quality (E4EQ) Intrnational onfrnc on Rnabl Enrgis and or Quality (IREQ 12) Santiago d ompostla (Spain), 28th to 30th March, 2012 Modling and Dynamic nalysis of Garlss Variabl-Spd rmannt Magnt Synchronous Gnrator asd Wind Enrgy onvrsion Systm M. I. Mari and H. S. K. El-Gohary Elctrical or and Machins Dpartmnt aculty of Enginring, in Shams Univrsity 1 El-Sarayat St., bdo asha sq., bbassya, airo (Egypt) -mail: mostafamari@yahoo.ca, hamdyk@hotmail.com bstract. This papr invstigats th dynamic bhavior of a garlss variabl-spd Wind Enrgy onvrsion Systm (WES) basd on rmannt Magnt Synchronous Gnrator (MSG). Modls and quation that dscrib diffrnt componnts of th WES ar addrssd and thir implmntations into SD/EMTD ar dscribd. Th control systm of th back to back convrtrs is dvlopd for capturing th maximum nrgy from varying ind spd, rgulating th D-link voltag at a constant valu, and maintaining ractiv por gnration at a pr-dtrmind lvl hich is zro in this study. Morovr, th pitch-angl controllr is dsignd to rgulat th machin spd at its ratd valu for high ind vlocitis. Simulation is prformd in SD/EMTD softar to valuat th prformanc of diffrnt controllrs and to study th dynamic bhavior of th garlss WES undr varying ind spds. This modling study can b usd for valuating th control schm, dynamic prformanc and impacts of a variabl-spd WES on th lctrical grids. Ky ords ack to back convrtrs, MSG, WES. 1. Introduction During th last dcads, Wind Enrgy onvrsion Systm (WES) has gron dramatically. Variabl-spd ind turbins (VSWTs) attract considrabl intrst around th orld, hich is on of th solutions ith th highst potntial to rduc ind nrgy cost [1]. Th VSWT systms ar usually basd on doubly fd induction gnrators (DIGs) or prmannt magnt synchronous gnrators (MSGs). Dirct-driv MSG raiss grat intrst bcaus of its high fficincy and limination of th garbox [2]. Many por lctronic convrtrs ar usd to intrfac th MSG ith th grid. Hovr, th most commrcial WESs ar basd on back to back voltag sourc convrtrs [3]. This papr prsnts a dtaild study of th dynamic prformanc of th garlss WES basd on MSG. Th intrfac systm ith th grid is basd on back to back convrtrs. Th machin-sid convrtr rgulats th machin spd to absorb maximum por from th turbin. simpl Maximum or oint Tracking (MT) tchniqu is utilizd. In addition, th pitch-angl controllr is usd to limit th machin spd at its ratd spd during high ind incidnts. inally, th grid-sid convrtr rgulats th D-link voltag by fding th xtractd por from th turbin to th grid. Morovr, it controls th ractiv por fd to th grid. SD/EMTD softar packag is usd to simulat th modl of th WES basd on MSG. Th dynamic bhavior of th turbin and th MSG is analyzd to invstigat th opration of th diffrnt control subsystms. Th papr is organizd as follos. irst, th systm configuration and modling of th variabl-spd MSG ind turbin is prsntd in sction to. Th control systms for th machin-sid convrtr, grid-sid convrtr, and th pitch angl ar xplaind in sction thr. Th rsults ar analyzd and discussd in sction four. inally, sction fiv concluds th papr. 2. Modling of th garlss ind turbin Th main componnts of th garlss variabl-spd WES ar th ind-turbin, th prmannt magnt synchronous gnrator, th back to back convrtrs ith thir control, and th pitch controllr. 1.3 MW dirctdriv WT unit is considrd for this analysis [4].. Wind turbin Th turbin modl is basd on th stady-stat por charactristics of th turbin. Th friction factor and th inrtia of th turbin ar combind ith thos of th gnrator coupld to th turbin. Th output por of th turbin is givn by: 3 m = 0.5ρ pv (1) hr, m is th mchanical output por of th turbin, ρ is th air dnsity (Kg/m 3 ), is th turbin spt ara RE&QJ, Vol.1, No.10, pril 2012

2 dcvltg m Tshaft m Tm ha 3 has M Synchronous hb M/ hc ia ib ic ia ib ic g1 01 [ohm] 01 [ohm] 01 [ohm] or g4 g3 g g6 g [u] g1n g4n g3n g5n g6n g2n Ian Ibn Icn 01 [H] 01 [H] 01 [H] or Q Vs a 1 Vs b Vs c Q g ig. 1. ack to back convrtrs for intrfacing th MSG ith th grid. 2 πr, R is th blad radius (lngth), p is th prformanc cofficint of th turbin, and v is th ind spd (m/s). Th prformanc cofficint, p, dtrmins th por convrsion fficincy from ind to mchanical. It is rlatd to blad arodynamic charactristics and turbin dsign. Th prformanc cofficint is calculatd from: p i = 0.22(116λ 0.4β 5) (2) 1 35 λi = 3 λ + 8β 1+ β i 12.5λ (3) hr: β is th pitch angl (dgr) and λ is th tip spd ratio (TSR), dfind by λ = ωmr / V. inally, th output mchanical torqu is calculatd from: Tm = m / ωm (4) hr ω m is th rotor angular spd (rad/sc).. Th rmannt Magnt Synchronous gnrator third ordr modl is usd to rprsnt th MSG on SD/EMTD softar packag. Th mathmatical quations of th MSG modl in th rotor fram ar: Rs d i ds = Ld dt iqs Ld ωm Lq hr, ds iqs Lq ωm L i d R s i L q ds qs v qs v ds Ld ω ψ L q m pm (5) i, Stator dirct and quadratur currnt componnts, ds vqs v, Stator dirct and quadratur voltag componnts, R s is th stator rsistanc, L d and L q ar th dirct and quadratur inductancs, is th numbr of pol pairs, and Ψ pm is th magnt flux (Wbr). Th lctromagntic torqu is givn by: T = 3/2 (i qs Ψ pm + (L d -L q ) i qs i ds ) (6) inally, th lctromchanical quation is rittn as: T m - T = J dω m /dt + ω m (7) hr J is th quivalnt inrtia of th machin and turbin, is th friction cofficint.. Th back to back convrtrs Th back to back convrtrs, shon in ig. 1, ar usd to connct th MSG to th grid. Th capacitor voltag must b rgulatd to avoid dangrous voltag ris hich may damag th por lctronics sitchs. Th main function of th grid-sid convrtr is to rgulat th dc link voltag at a constant valu. On th othr hand, th machin sid convrtr is usd to xtract th maximum por from th ind turbin and to rgulat th rotational spd. hystrsis currnt control tchniqu is usd for both convrtrs [5], [6], as shon in ig. 2. iarf D + - Ia ibrf D + - Ib icrf D + - Ic trl trl = 0 nabl trl = 0 trl trl nabl g4 g1 trl = 0 g6 nabl trl = 0 trl trl nabl g3 trl = 0 g2 nabl trl = 0 trl nabl ig. 2. Modling of th hystrsis currnt control for th machin-sid convrtr. g RE&QJ, Vol.1, No.10, pril 2012

3 3. Th proposd control systm Th control systm of th garlss ind turbin is dividd into thr parts, hich ar dscribd as in th folloing subsctions.. ontrol of th machin-sid convrtr Th machin-sid convrtr is controlld to rgulat th spd of th MSG at a rfrnc valu that rsults in Maximum or oint Tracking (MT). t zro pitch angl, th maximum por cofficint p of th ind turbin, hich varis ith th TSR, λ, is as calculatd from (2) and (3). It occurs at an optimum TSR of 6.3. Th MT tchniqu is basd on oprating th turbin at its optimum TSR to gt its maximum por at any incidnt ind vlocity. Sinc λ = ωmr / V, th MT can b achivd by rgulating th gnrator spd using th folloing quation: ω = λ V / R = 6.3V / 25 = V (8) rf optimum Th indirct rotor fild orintd control is usd for th machin-sid convrtr [7]. ig. 3 prsnts th block diagram of th control systm of th machin-sid convrtr. Th spd rfrnc, calculatd from (8), is limitd by th maximum angular spd of th gnrator/turbin, hich is 3.5 rad/sc. I controllr is usd to rgulat th spd of th gnrator/turbin. Th output of th I controllr is th quadratur currnt rfrnc, iqrf, for th MSG. Zro currnt rfrnc is assignd to th dirct componnt of th stator currnt, idrf, to achiv maximum torqu/ampr capability. Th d- and q- componnts ar applid to th ark and lark transforms to gnrat th thr-phas rfrnc currnts for th machin-sid convrtr. V * m D - + rf I N 100 K N/D D TIME Iqrf m m t dt IaRf idrf Indirct iarf IbRf iqrf Rotor ibrf Iqrf O IcRf icrf ig. 3: lock diagram of th machin-sid convrtr controllr.. ontrol of th grid-sid convrtr Th objctiv of th grid-sid convrtr is to kp th D link voltag constant rgardlss of th magnitud of th MSG por. vctor-control approach is usd ith a rfrnc fram orintd along th grid voltag vctor position, nabling indpndnt control of th activ and ractiv pors floing btn th grid and th grid-sid convrtr. ig. 4 shos a block diagram of th control structur of th grid-sid convrtr. Th q-axis currnt componnt of th grid-sid convrtr is usd to rgulat th D link voltag, Dlta-T dcvltg, at 1.3 Kv using a I controllr. Th d-axis componnt is usd to control th flo of ractiv por and is st to zro. Dcoupld control of activ and ractiv pors floing btn th MSG and grid is don by using grid voltag vctor orintd control. phas lockd loop (LL) circuit is usd to calculat th spac vctor angl of th grid-voltag, thta. This angl is usd for th invrs ark transformation of th d and q componnts of th grid-sid convrtr to thr-phas rfrnc currnts. Ths thr-phas rfrnc currnts and th actual currnts of th grid-sid invrtr ar usd by th currnt control of ig. 2 to gnrat th corrsponding firing signals for th sitchs to mt th currnt rquirmnts. 1.3 Rfrnc apacitor Voltag Igrf D + - dcvltg Va Vsa Vb Vsb Vc Vsc D Q 0 LL I thta thta ianrf ibnrf icnrf ig. 4. lock diagram of th grid-sid convrtr controllr. Th itch-angl ontrollr * -1 Igrf Whn th maximum spd is rachd, at th ratd ind vlocity, th pitch-angl controllr is activatd to rduc th availabl por from th turbin and hnc th spd is rgulatd at its maximum limit. This action maks th gnratd por constant at ind vlocitis highr than th ratd ind spd. ig. 5 shos th block diagram of th pitch-angl controllr. It is basd on a I controllr to procss th rror btn th angular spd of th turbin/gnrator and th ratd valu. Th output from th I controllr is th pitch angl, tarf. lo ratd angular vlocity, th input to th I controllr is zro to dactivat th controllr, β =0. rat limitr of 10 dgr/sc. is usd to prvnt suddn motion of th blads [8]. 3.5 D - ratd spd + Max 3.5 ratd spd D E m I d/dt tarf ig. 5. lock diagram of th pitch-angl controllr 4. Simulation Rsults ig. 6 xplors th dynamic bhavior of th proposd dirct-driv ind turbin systm. Th ind vlocity is RE&QJ, Vol.1, No.10, pril 2012

4 hypothtically changd ith tim according to th squnc dran in ig. 6(). Th MT controllr calculats th optimum rfrnc for th gnrator spd as shon in ig. 6(b). Th machin-sid convrtr succds in rgulating th gnrator spd at its optimum variabl stting from th MT. This action rsults in xtracting th maximum por from th ind turbin as shon in ig. 6(c). ig. 7 portrays th trajctory of th turbin por and spd, hich clarifis and xplains th maximum por tracking procss. During any intrval of constant ind vlocity, th rfrnc rotor spd for maximum por tracking is dtrmind. Th oprating point ( and ω) is movd along a corrsponding turbin por-spd charactristic (por curv) and is trackd by th controllr of th machin-sid convrtr until th point of maximum por is achivd. Ths tracs ar parts of th turbin charactristics shon in ig. 8. If th ind vlocity changs, th gnrator sid convrtr fixs th rfrnc rotor spd to a n valu hich corrsponds to maximum por tracking, and anothr por curv ill b follod until maximum por is rachd. This procss is continud until th MSG rachs its ratd spd at a ind vlocity highr than th ratd valu (13.5 m/s). t this ind vlocity, th pitch controllr is activatd to rduc th turbin spd and hnc th por. This can b obsrvd from ig. 9 hich is a zoom of ig. 7 that focuss on th trajctory of th mchanical por hn th ind vlocity is changd from 13.4 m/s to 15 m/s. Th stady stat oprating point at ind vlocity of 13.4 m/s is 1, hil 2 is th oprating point at ind spd of 15m/s. ig. 7: Trajctory of turbin por and spd for th first 24 sconds of th simulation. (a) (b) ig. 8: haractristics of th ind turbin. (c) (d) () (f) (g) 1 2 ig. 6: Dynamic prformanc of th garlss ind turbin. (h) ig. 9: Trajctory of turbin por and spd hn th ind vlocity is changd from 13.4 m/s to 15m/s (t= 18s. to t = 24s). s xpctd, th pitch controllr is continuously adjusting th pitch angl, as shon in ig. 6(f), to RE&QJ, Vol.1, No.10, pril 2012

5 rgulat th angular spd at 3.5 rad/sc. s a rsult of this opration, th mchanical por xtractd from th ind turbin is vry clos to th ratd valu of th gnrator. ig. 6(d) shos th action of th currnt controllr as it displays both th d- and q-axis currnt componnts (iq and id rspctivly) of th machin-sid convrtr. It rvals that iq coincids ith its rfrnc valu, iqrf, and id is rgulatd at zro valu. ig. 6(a) portrays both th turbin and lctromagntic torqus of th MSG. Th figur shos th proportionality btn th lctromagntic torqu and th q-axis currnt componnt. or any incras in ind vlocity, th turbin por is incrasd and hnc th mchanical torqu. Th machinsid convrtr rducs th lctromagntic torqu to zro to maximiz th acclrating torqu to rach th optimum rotational spd. Onc th gnrator spd is rgulatd at th optimum valu, th acclrating torqu is diminishd and th lctromagntic torqu bcoms qual to th mchanical torqu of th turbin. Th grid-sid convrtr rgulats th dc-link voltag at its dsird rfrnc valu of 1.3 kv, ig. 6(g). Th voltag rgulation is achivd by transfrring th variabl por of th gnrator to th grid. This has bn don by controlling th rfrnc currnt of th machin-sid convrtr, Igrf. ig. 6(c) shos that th diffrnc btn th gnrator and grid pors is vry small, hich rprsnts th losss in th back-to-back convrtrs. ig. 6(c) and (h) indicat that th grid por and th rfrnc currnt of th gridsid convrtr xhibit similar shaps. lso, ig. 6(d) and (h) sho that th torqu producing currnt componnt of th MSM (q-axis currnt componnt iq) and th rfrnc currnt of th grid-sid convrtr (Igrf) hav similar shaps, xcpt hn th ind spd xcds its ratd valu (t > 18 sc) hn iq is limitd to th ratd valu of th MSG currnt. ig. 10 shos a snapshot for th dynamic bhavior of th dirct-driv ind turbin systm folloing th occurrnc of to ind spd changs; a small chang from 15 to 15.2 m/s at t= 25 s, and a larg chang from 15.2 to 16 m/s at t= 29 s. Th purpos of th study is to focus on th coordination btn th controllrs of th machin-sid convrtr and th pitch-angl. or th cas of small ind spd chang, th machin-sid convrtr rgulats th gnrator spd to its limit (3.5 rad/s), ithout th nd for pitching mor th turbin blads, ig. 10(f), only if th quadratur currnt componnt (por producing componnt) dosn t xcd its limit valu. This situation is shon in ig. 10(d) hr th spd rgulation is don by controlling iq as long as it dosn t rach its currnt limit valu. On th othr hand, for larg ind spd chang abov th ratd ind spd, hr iq is saturatd at its limit valu as shon in ig. 10(d), th pitch controllr acts to kp th gnrator spd fixd at its ratd valu as shon from ig. 10(b) and (f). t stady-stat and for both typs of disturbancs, th grid por is lss than th gnrator por, and th lattr is lss than th turbin por, ig. 10(d). Th diffrnc btn th turbin and gnrator pors is th mchanical losss, hil th diffrnc btn th gnrator and grid pors is th lctrical losss. In summary, th machin-sid convrtr taks ovr control for small ind spd changs as long as th q-axis rfrnc currnt, iqrf, is lss than its limit. or larg ind spd changs, th pitch-angl controllr taks th action of rgulating th turbin/gnrator spd by incrasing th pitch angl, as Iqrf of th machin-sid convrtr rachs its limit valu. ig. 10: Dynamic prformanc of th garlss ind turbin systm at high ind vlocitis. ig. 11 and 12 sho th turbin por/spd trajctory for both small and larg ind spd disturbancs. Ths figurs support th intrprtation givn abov for th action of th controllrs. In ig. 11, folloing th occurrnc of small ind spd disturbanc, th systm oprating point movs dirctly upard from 2 to 3, hich mans that th gnrator provids highr por at constant gnrator spd ( = rf = 3.5 m/s). This dmonstrats th action of th controllr of th machinsid convrtr. ig. 12 rvals that, folloing th occurrnc of a larg ind spd chang, th oprating point 3 movs cyclically to 4, hich is vrtically blo 3. This dmonstrats th intrfrnc of th pitch control systm hich maintains th turbin por constant and rgulats th gnrator spd such that = rf. inally, th grid-sid convrtr continuously rgulats th dc-link voltag, ig. 10(g), and transfrs th xtractd maximum por to th grid. Th magnitud of th gridsid convrtr currnt, ig. 10(h) follos th shap of th MSG por, ig. 10(c). igur 13(a) shos a snapshot of th MSG (machinsid convrtr) currnt. ig. 13(b) illustrats that th grid-sid convrtr currnt is in phas ith th grid voltag; hnc no ractiv por is supplid to th grid. (a) (b) (c) (d) () (f) (g) (h) RE&QJ, Vol.1, No.10, pril 2012

6 prov th ffctivnss of th convrtr controllr prformanc. 5. onclusion 3 ig. 11: Trajctory of turbin por and spd hn th ind vlocity is changd from 15 m/s (2) to 15.2 m/s (3). 2 Th papr prsnts a dtaild modl for garlss variablspd WES basd on MSG. This modl is simulatd on SD/EMTD softar packag. Th dynamic prformanc of th machin-sid convrtr, th grid-sid convrtr, and th pitch-angl controllrs ar invstigatd. Th trajctoris of th turbin por and spd illustrat th action of th MT controllr of th machin-sid convrtr. Th oprating point is movd along th turbin por-spd charactristics and is trackd by th machin-sid convrtr until th point of maximum por is achivd. Th rsults dmonstrat th coordination btn th controllrs of th machin-sid convrtr and th pitch-angl. Th machin-sid convrtr taks ovr controlling th gnrator spd as long as th q-axis rfrnc currnt is lss than its limit. Th pitch-angl controllr taks th action of rgulating th turbin/gnrator spd as th currnt of th machinsid convrtr rachs its limit valu. Th prsntd modl can b usd for invstigating th dynamic intractions btn variabl-spd WES and th grid. cknoldgmnt This projct as supportd financially by th Scinc and Tchnology Dvlopmnt und (STD), Egypt, Grant No ig. 12: Trajctory of turbin por and spd hn th ind vlocity is changd from 15.2 m/s (3) to 16 m/s (4). ig. 13: Th currnts of th MSG and th grid-sid convrtr. This agrs ith th stting for zro ractiv por on th grid-sid convrtr. Th currnt of both convrtrs ar sinusoidal and tracks thir rfrncs. Th prvious rsults 3 Rfrncs [1] Z. hn, J. Gurrro, and. laabjrg, rvi of th stat of th art of por lctronics for ind turbins, IEEE Transactions on or Elctronics, vol. 24, no. 8, pp , ug [2] H. olindr,. van dr ijl, G.-J. d Vildr, and. Tavnr, omparison of dirct-driv and gard gnrator concpts for ind turbins, IEEE Transactions on Enrgy onvrsion, vol. 21, no. 3, pp , Spt [3] X. Tan, J. Dai, and. Wu, Novl onvrtr onfiguration for Wind pplications Using WM SI ith Diod Rctifir and uck onvrtr IEEE Intrnational Elctric Machins & Drivs onfrnc (IEMD), pp , [4] ZU Hui, ZHNG Guo-ao, EI Shu-Min, WEI Zi-ong, Zhu Hai-Rong, and EI Shu-min, H Robust ontrol of Dirct-Driv rmannt Magntic Synchronous Gnrator onsidring th Uncrtainty of Stator aramtrs, rocdings of th 30th hins ontrol onfrnc, July 22-24, 2011, Yantai, hina. [5] D. M. ord and D. W. Novotony, urrnt control of VSI- WM invrtrs, IEEE Trans. On Ind. ppl., Vol. 21, pp , May/Jun [6] L. Malsani and. Tnti, Novl hystrsis control mthod for currnt-controlld voltag-sourc WM invrtrs ith constant modulation frquncy, IEEE Trans. on Ind. ppl, Vol. 26, pp 88-92, Jan./b [7]. Vas, Snsorlss vctor control and dirct torqu control, Oxford rss, N York (1998). [8]. Uhara,. ratap, T. Goya, T. Snjyu,. Yona, N. Urasaki, and T. unabashi, oordinatd ontrol Mthod to Smooth Wind or luctuations of a MSG-asd WES IEEE Transactions on nrgy convrsion, vol. 26, no. 2, Jun RE&QJ, Vol.1, No.10, pril 2012