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bir model

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Anahtar Kelimeler: 5]JDUWUELQLGLQDPLNDQDOL]teorik model.

mühendislikdergisi

Cilt: 3-9

Dicle Üniversitesi Mühendislik Fakültesi Mart 20145, 1,

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70 Dynamic behaviour of horizontal axis

wind turbines-a theoretical model

Extended abstract

Within renewable energy sources, wind energy is a natural, clean energy sources being observed that there is increasing use in recent years. Wind turbines are used to generate electricity energy from wind energy. Kinetic energy in wind turbine blades is converted into mechanical energy via power transmission systems, then, electrical energy is obtained from generator. They are classified as horizontal axis and vertical axis wind turbines according to the axis of rotation.

In horizontal axis wind turbines, various power transmission mechanisms have been developed in order to obtain torque and power. These are direct drive, integrated, and conventional power transmission mechanisms. In a direct drive power transmission mechanism, torque and power are transmitted to the generator through a rotor. In an integrated power transmission mechanism, a gearbox and rotor are both used. In this study, conventional power transmission mechanism was used.

Moreover, aerodynamic theories are used to determine the effect that wind has on the forces, torque, and power of blades of horizontal axis wind turbines. There are three main aerodynamic theories (one-dimensional lineer momentum theory, actuator disc momentum theory and blade element theory) related to wind turbine aerodynamics. One-dimensional momentum theory examines the force on the disc in the air flow tube. It is assumed that the disc consists of an infinite number of blades. The maximum power coefficient is limited to 0.593 based on Betz' Law. Actuator disc momentum theory assumes that the disc consists of an infinite number of blades. Additionally, friction caused by the blade is neglected but the vortex effect of the flow is considered. Blade element theory is used to determine the forces and torque that affect on aerofoil. In present study, two different aerodynamic theories (actuator disc momentum theory, blade element theory) investigated in order to define the amount of torque affecting on the blades

In this study, a new theoretical model was designed based on energy conversion for basic dynamic behaviour of the three blades-horizontal axis wind turbines. By this model, dynamic behaviour of wind turbine was assessed by evaluating design parameters, geometrical and physical sizes of the blade in accordance with torque equations. In addition, dimensional parameters were converted to dimensionless parameters. Thus, effect of many parameters such as wind speed, blade radius, mass of the blades, power coefficient, tip-speed ratio, axial induction factor and angular induction factor were analyzed.

By this model, various dimensional torques could be estimated by changing mR59DQGĮG in the same

nondimensional torque. Consequently, it was found that NG1 is very close to the nominal power of the

referenced wind turbine (2 MW).

Different dimensionless parameters so called as the coefficient of effectiveness (Kt1, Kt2) were defined in

order to estimate the wind power transmitted to the generator and they were used for analyzing the wind turbines. It was determined that the dimensional parameters (wind speed (V), blade radius (R), the mass of the blades (mR)) and the non-dimensional

parameters (tip-VSHHG UDWLR Ȝ EODGH DQJOH ș power coefficient (CP)) directly affected the

coefficient of effectiveness (Kt).

In conclusion, Kt1 and Kt2 could be 0.38 and 0.37

respectively if the wind turbine parameters being as mR=19500 kg, R= 39.5 m, i=100. In addition, it was

approximately determined that 38% of wind power was transmitted to the generator. When Kt values

were compared to CP values (when CP=0.40-0.45),

the Kt values were less than the CP values.

Finally, this theoretical model presents a more realistic approach in terms of estimating the main parameters of wind turbine. Consequently, it is suggested that this theoretical study is used as a model for designing horizontal axis wind turbines.

Keywords: Wind turbine, dynamic analysis,

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72

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/ /

uç V

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l = =w

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(5)

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d GLúOL YHULPL úHNOLQGHGLU 6LVWHPLoLQPRPHQWHúLWOL÷L

ܶோെ ܶௌൌ ܫோߙோ (9)

úHNOLQGH EXOXQXU6LVWHPLoLQNXOODQÕODQWHPHO SDUDPHWUHOHU VÕUDVÕ\OD 7J GLúOL NXWXVX oÕNÕú momenti (Nm), TG MHQHUDW|UPRPHQWL1P,G MHQHUDW|UQ NWOHVHO DWDOHW PRPHQWL NJP2_{), I}

Hú NWOHVHO HúGH÷HU DWDOHW PRPHQWL NJP2_Ȧ

G \NVHNKÕ]OÕúDIWÕQDoÕVDOKÕ]ÕUDGVĮG \NVHN KÕ]OÕ úDIWÕQ DoÕVDO LYPHVL UDGV2 úHNOLQGHGLU 6LVWHPLoLQPRPHQWHúLWOL÷L

ܶ௃െ ܶீൌ ܫீߙீ (10)

úHNOLQGH EHOLUOHQPLúWLU 'LúOL YHULPL Șd) ve oHYULPRUDQÕQDLED÷OÕRODUDNGLúOLNXWXVXJLULú momenti (TS YH GLúOL NXWXVX oÕNÕú YH\D MHQHUDW|UJLULúPRPHQWL7JDUDVÕQGDNLLOLúNL ܶ௃ൌ ܶௌߟௗȀ݅ (11)

6LVWHP YH VLVWHP ELUOLNWH GH÷HUOHQGLULOLS moment tek mile indirgenirse MHQHUDW|UPRPHQWL (TG); ܶீൌ ܶோߟௗȀ݅ െ ܫ௘çߙீ (12) úHNOLQGHHOGHHGLOLU(úLWOLNWH\HUDODQ,Hú; ܫ௘çൌ ܫோߟௗȀ݅ଶ൅ ܫீ (13) VLVWHPLQNWOHVHOHúGH÷HUDWDOHWPRPHQWLRODUDN WDQÕPODQPDNWDGÕU%XUDGD,R NDQDWODUÕQNWOHVHO atalet momenti (kgm2), IG MHQHUDW|UQ NWOHVHO atalet momenti (kgm2_{LoHYULPRUDQÕȘ}

d GLúOL YHULPLúHNOLQGHLIDGHHGLOPHNWHGLU

'LúOL YHULPL Șd GLúOL NXWXVX oÕNÕúÕQGDNL HQHUMLQLQ GLúOL NXWXVX JLULúLQGHNL HQHUML\H RUDQÕ RODUDN WDQÕPODQDELOPHNWHGLU %X GXUXPGD GLúOL verimi;

ߟௗൌ ሺͲǤͷܫீ߱ீଶሻȀሺͲǤͷܫோ߱ଶሻ ൌ ܫீ݅ଶȀܫோ

(14) úHNOLQGHEHOLUOHQPHNWHGLU .DQDWODUNWOHVLnden GROD\Õ ܫோൌ ݉ோܴ௘çଶ E\NO÷QGH ELU NWOHVHO

atalet momentine (IR VDKLSWLU 7HN ELU NDQDGÕQ NWOHVLmR' RODUDNDOÕQGÕ÷ÕQGDNDQDWODUÕQWRSODP

NWOHVL ݉ோൌ ͵݉ோᇱ ROPDNWDGÕU .DQDWODUÕQ

JHRPHWULN \DSÕVÕQGDQ GROD\Õ NDQDWODU J|EH÷H \DNÕQ E|OJHOHUGH GDKD NDOÕQ NHVLWOLGLU %X QHGHQOH NDQDW D÷ÕUOÕN PHUNH]LQLQ J|EH÷H RODQ X]DNOÕ÷Õ RHú NDQDW \DUÕoDSÕQÕQ \DNODúÕN oWH

(7)

Yatay eksenli U]JDUWUELQOHULQLQGLQDPLNGDYUDQÕúÕ-teorik bir model

biri (R/3) olarak kabul edilmektedir (Morren vd., 2006) %X GXUXPGD NDQDWODUÕQ NWOHVHO atalet momenti (IR);

ܫோൌ ݉ோܴ௘çଶ ൌ ሺ݉ோܴଶሻȀͻ (15)

RODUDN EXOXQPDNWDGÕU %XUDGD PR NDQDWODUÕQ WRSODPNWOHVLGLUNJ,R NDUúÕOÕ÷Õ(úLWOLN NXOODQÕODUDN VLVWHPLQ NWOHVHO HúGH÷HU DWDOHW momenti (IHú) ifadesi;

ܫ௘çൌ ሺʹ݉ோܴଶߟௗሻȀሺͻ݅ଶሻ (16)

úHNOLQGH\HQLGHQG]HQOHQHELOPHNWHGLU%XHOGH HGLOHQ E\NONOHU ,R, IG, IHú Șd) ve moment HúLWOLNOHUL 7R1, TR2ୖభǡ ୖమ NXOODQÕODUDN IDUNOÕ

\DNODúÕPODUOD MHQHUDW|U PRPHQWL 7G) bulunabilmektedir.

-HQHUDW|U PRPHQWL JHQHO LIDGHVLQGH (úLWOLN (12)), TR1 ve IHú LIDGHVL NXOODQÕOÕUVD MHQHUDW|U momenti (TG1); ܶீଵൌܴ ଶ_ߟ ௗ ͳͺ݅ ൬ͻߩߨܴܸଶܥொെ Ͷ݉ோߙீ ݅ ൰ሺͳ͹ሻ úHNOLQGHEXOXQPDNWDGÕU%XLIDGH\DUGÕPÕ\OD&Q WRUN NDWVD\ÕVÕ L GLúOL oHYULP RUDQÕ ĮG \NVHN KÕ]OÕúDIWÕQDoÕVDOLYPHVLȘd GLúOLYHULPL5NDQDW \DUÕoDSÕ YH 9 U]JDU KÕ]Õ FLQVLQGHQ ER\XWOX RODUDNMHQHUDW|UPRPHQWLKHVDSODQDELOPHNWHGLU -HQHUDW|U PRPHQWLQL 7G) ER\XWVX]ODúWÕUPDN DPDFÕ\OD NXOODQÕODQ \NVHN KÕ]OÕ úDIW DoÕVDO LYPHVLQLQ ĮG NDQDWODUÕQ WRSODP NWOHVLQLQ (mR NDQDW \DUÕoDSÕQÕQ 5 \NVHN KÕ]OÕ úDIW DoÕVDOKÕ]ÕQÕQȦGYHHúGH÷HUDWDOHWPRPHQWLQLQ (IHú) boyutsuz ifadeleri; ߙതீൌ ߙீܴଶȀܸଶ (18) ݉ഥோൌ ݉ோȀߩܴଷ (19) ܴത ൌ ߩܸଶ_ܴȀሺ݉ ோߙீሻ (20) ߱ഥீൌ ߱ீܴȀܸ (21) ܫҧ௘çൌ ܫ௘çȀሺ݉ோܴଶሻ (22)

úHNOLQGH WDQÕPODQPDNWDGÕU -HQHUDW|U PRPHQWL JHQHO LIDGHVL (úLWOLN HVDV DOÕQDUDN T , _R1

eú I , Į ve G m LIDGHOHUL GH÷HUOHQGLULOGL÷LQGHR ER\XWVX]MHQHUDW|UPRPHQWL (T ); _G1 ܶതீଵൌ ܶതோଵߟௗȀሺ݅݉ഥோሻ െ ܫҧ௘çߙതீ (23) úHNOLQGHEXOXQXST NDUúÕOÕ÷Õ\HUOHúWLULOLUVH R1 ܶതீଵൌ ܥ௉ߨߟௗȀሺʹߣ݅݉ഥோሻ െ ܫҧ௘çߙതீ (24) úHNOLQGH EHOLUOHQPLúWLU%XUDGD ܶതீଵൌ ܶீଵȀ݉ோܸଶ (25)

úHNOLQGH WDQÕPODQDQ ER\XWVX] MHQHUDW|U momentidir.

-HQHUDW|U PRPHQWL JHQHO LIDGHVLQGH (úLWOLN (12)), TR2 ve IHú NDUúÕOÕNODUÕ NXOODQÕOÕS JHUHNOL G]HQOHPHOHU\DSÕOÕUVDMHQHUDW|UPRPHQWL (TG2); ܶீଶൌ ܴଶ_ߟ ௗ ݅ ൬ᇱሺͳ െሻߩܸܴ߱ଶߨ െ ʹ݉ோߙீ ͻ݅ ൰ሺʹ͸ሻ úHNOLQGHHOGHHGLOLU%XLIDGH\DUGÕPÕ\ODȘd GLúOL YHULPL L oHYULP RUDQÕ 5 NDQDW \DUÕoDSÕ ĮG \NVHNKÕ]OÕúDIWÕQDoÕVDOLYPHVL9U]JDU KÕ]Õ Ȧ NDQDW G|Qú KÕ]Õ ȡ KDYD \R÷XQOX÷X PR NDQDWODUÕQ WRSODP NWOHVL D HNVHQHO LQGNVL\RQ IDNW|U D DoÕVDO LQGNVL\RQ IDNW|U FLQVLQGHQ MHQHUDW|U PRPHQWL ER\XWOX RODUDN hesaplanabilmektedir.

-HQHUDW|U PRPHQWL JHQHO LIDGHVL (úLWOLN HVDV DOÕnarak T , R2 I , eú Į ve G m ifadeleri R

GH÷HUOHQGLULOGL÷LQGH ER\XWVX] MHQHUDW|U momenti (T ); _G2 ܶതீଶൌ ܶതோଶߟௗȀሺ݅݉ഥோሻ െ ܫҧ௘çߙതீ (27) úHNOLQGHEXOXQXST NDUúÕOÕ÷Õ\HUOHúWLULOLUVHR2 ܶതீଶൌ ᇱ_{ሺͳ െ ሻߣߨߟ} ௗ ݅݉ഥோ െ ܫҧ௘çߙതீሺʹͺሻ úHNOLQH G|QúU%XUDGD ܶതீଶൌ ܶீଶȀሺ݉ோܸଶሻ (29)

úHNOLQGH LIDGH HGLOHQ ER\XWVX] MHQHUDW|U momentidir.

(8)

-5]JkU WUELQOHULQGH NDQDWODU WDUDIÕndan U]JDUGDQHOGHHGLOHQJo

5]JDUWUELQOHULQGHNDQDWODUGDROXúDQPRPHQW (TR1 YH DoÕVDO KÕ] Ȧ GH÷HUOHQGLULOHUHN NDQDWODUD LOHWLOHQ Jo NROD\OÕNOD EHOLUOHQH-bilmektedir. Bu durumda NDQDWODU WDUDIÕQGDQ rüzgardan elde edilen güç (NR1);

ܰோଵൌ ܶோଵൈ ߱ ൌ ͲǤͷߩߨܴଶܸଷܥ௉ (30)

olarak bulunabilmektedir. Bu ifadeden, R kanat \DUÕoDSÕ 9 U]JDU KÕ]Õ YH &P Jo NDWVD\ÕVÕQÕQ NDQDWODU WDUDIÕQGDQ U]JDUGDQ HOGH edilen gücü EHOLUOH\HQ WHPHO SDUDPHWUHOHU ROGX÷X J|UOPHNWHGLU 1R1 LIDGHVL HVDV DOÕQDUDN NDQDWODU WDUDIÕQGDQ U]JkUGDQ HOGH HGLOHQ ER\XWVX]Jo (ۼഥ_܀ ૚); ܰഥோଵൌ ͲǤͷܥ௉ߨ (31) úHNOLQGHEXOXQPXúWXU%XUDGD ܰഥோଵൌ ܰோଵȀሺߩܸଷܴଶሻ (32)

úHNOLQGH WDQÕPODQDQ NDQDWODU WDUDIÕQGDQ U]JkUGDQHOGHHGLOHQER\XWVX]JoWU .DQDWODU WDUDIÕQGDQ U]JDUGDQ HOGH HGLOHQ moment (TR2 YH NDQDWODUÕQ G|Qú KÕ]Õ Ȧ GH÷HUOHQGLULOLS JHUHNOL G]HQOHPHOHU \DSÕOGÕ÷ÕQGD NDQDWODU WDUDIÕQGDQ U]JDUGDQ HOGH HGLOHQ Jo (NR2);

ܰோଶൌ ܶோଶൈ ߱ ൌ ᇱሺͳ െ ሻߩܸ߱ଶܴସߨ (33)

úHNOLQGHEXOXQDELOPHNWHGLU%XLIDGH\DUGÕPÕ\OD GD D HNVHQHO LQGNVL\RQ IDNW|U D DoÕVDO LQGNVL\RQ IDNW|U 9 U]JDU KÕ]Õ Ȧ NDQDW G|Qú KÕ]Õ 5 NDQDW \DUÕoDSÕ JLEL WHPHO SDUDPHWUHOHU ELOLQGL÷LQGH NDQDWODUGDQ UHWLOHQ Jo ER\XWOX RODUDN EXOXQDELOPHNWHGLU 1R2 esas DOÕQDUDN NDQDWODU WDUDIÕQGDQ U]JkUGDQ HOGH HGLOHQER\XWVX]Joۼഥ_܀ ૛); ܰഥோଶൌ ᇱሺͳ െ ሻߨ (34) RODUDNEHOLUOHQPLúWLU%XUDGD ܰഥோଶൌ ܰோଶȀሺߩܸ߱ଶܴସሻ (35)

úHNOLQGH LIDGH HGLOHQ NDQDWODU WDUDIÕQGDQ U]JkUGDQHOGHHGLOHQER\XWVX]JoWU -5]JDUWUELQOHULQGHMHQHUDW|UJF Jeneratör gücü (NGMHQHUDW|UPRPHQWLQLQ7G) \NVHNKÕ]OÕúDIWÕQDoÕVDOKÕ]Õ\ODȦGoDUSÕPÕQD HúLWWLU %XGXUXPGDMHQHUDW|UJF ܰீൌ ሺܶோߟௗ߱ீሻȀ݅ െ ܫ௘çߙீ߱ீ (36) úHNOLQLDOÕU%XUDGDȦG \NVHNKÕ]OÕúDIWÕQDoÕVDO KÕ]ÕUDGVĮG \NVHNKÕ]OÕúDIWÕQDoÕVDOLYPHVL (rad/s2_{úHNOLQGH LIDGH edilmektedir. T}

R1 ve IHú NDUúÕOÕNODUÕ\D]ÕOGÕ÷ÕQGDMHQHUDW|UJF (NG1); ܰீଵൌܴ ଶ_ߟ ௗ߱ீ ͳͺ݅ ൬ͻߩߨܴܸଶܥொെ Ͷ݉ோߙீ ݅ ൰ሺ͵͹ሻ (úLWOLN HVDV DOÕQÕSഥୖభ, ҧୣç, Ȧ ve R G LIDGHOHULGH÷HUOHQGLULOGL÷LQGHER\XWVX]MHQHUDW|U JFۼഥ_۵ ૚ሻǢ); ܰഥீଵൌ ൫ܶതோଵܴതߟௗȀ݅ െ ܫҧ௘ç൯߱ഥீ (38) úHNOLQGHEXOXQPXúROXSഥୖభ NDUúÕOÕ÷Õ\D]ÕOÕUVD ܰഥீଵൌ ቀሺܥ௉ߨߟௗܴതሻȀሺʹߣ݅ሻ െ ܫҧ௘çቁ ߱ഥீ (39) úHNOLQGHHOGHHGLOLU%XUDGD ܰഥீଵൌ ܰீଵȀሺ݉ோܴܸߙீሻ (40)

úHNOLQGH LIDGH HGLOHQ ER\XWVX] MHQHUDW|U JFGU

Jeneratör gücü (NG2), benzer úHNLOGH |QFHGHQ HOGH HGLOHQ MHQHUDW|U PRPHQWL 7G2 YH \NVHN KÕ]OÕúDIWÕQDoÕVDOKÕ]ÕȦG) oDUSÕODUDN; ܰீଶൌ ܴଶ_ߟ ௗ߱ீ ݅ ൬ᇱሺͳ െሻߩܸܴ߱ଶߨ െ ʹ݉ோߙீ ͻ݅ ൰ ሺͶͳሻ

úHNOLQGH EXOXQXU (úLWOLN HVDV DOÕQÕST , R1 eú

I , Ȧ ve G R LIDGHOHUL GH÷HUOHQGLULOGL÷LQGH

ER\XWVX]MHQHUDW|UJF (ۼഥ_۵

૛ሻǢ);

(9)

Yatay eksenli U]JDUWUELQOHULQLQGLQDPLNGDYUDQÕúÕ-teorik bir model úHNOLQGHROXSഥୖమ NDUúÕOÕ÷Õ\D]ÕOÕUVD ܰഥீଶൌ ൫

ᇱሺͳ െ

ሻߣߨߟௗܴതȀ݅ െ ܫҧ௘ç൯߱ഥீ (43) úHNOLQGHHOGHHGLOLU%XUDGD ܰഥீଶൌ ܰீଶȀሺ݉ோܴܸߙீሻ (44) úHNOLQGHWDQÕPODQDQER\XWVX]MHQHUDW|UJFGU -5]JDUWUELQOHULQGHWUELQHWNLQOLNNDWVD\ÕVÕ 5]JDU JF 1¶GHQ KDQJL HWNLQOLNWH MHQHUDW|U JF 1G HOGH HGLOHELOHFH÷LQL EHOLUOHPHN DPDFÕ\ODER\XWVX]WUELQHWNLQOLNNDWVD\ÕVÕ (Kt) WDQÕPODQDELOPHNWHGLU %X E|OPGH LNL IDUNOÕ WUELQHWNLQOLNNDWVD\ÕsÕJHOLúWLULOPLúWLU 5]JDU JF 1 ȡʌ52_V3_{ile N}

G1 WUELQ MHQHUDW|U úDIWÕQGDNL Jo (úLWOLN GH÷HUOHQGLULOHUHNWUELQHWNLQOLNNDWVD\ÕVÕ (Kt1); ܭ௧ଵൌܰ_ܰீଵሺͶͷሻ

JoOHU RUDQÕQGDQ JHUHNOL G]HQOHPHOHU \DSÕODUDN

ܭ௧ଵൌ ൬ܴܥ_ߣ௉െ_ͻߩߨܸͶ݉ோߙଶீ_݅൰ ൈ ቀ

ߟௗ߱ீ

ܸ݅ ቁሺͶ͸ሻ úHNOLQGH EHOLUOHQPLúWLU %XUDGD WUELQ HWNLQOLN NDWVD\ÕVÕ .t1) CP Ȝ ȡ 5 9 PR ĮG L Șd ve ȦG¶\H ED÷OÕ RODUDN GH÷LúPHNWHGLU %HQ]HU úHNLOGHU]JDUJF1 ȡʌ52_V3_{ile N}

G2 WUELQ MHQHUDW|U úDIWÕQGDNL Jo (úLWOLN GH÷HUOHQGLULOHUHNWUELQHWNLQOLNNDWVD\ÕVÕ (Kt2); ܭ௧ଶൌܰ_ܰீଶሺͶ͹ሻ

JoOHU RUDQÕQGDQ JHUHNOL G]HQOHPHOHU \DSÕODUDN ܭ௧ଶൌ ൬ʹܽᇱሺͳ െ ܽሻߣܴ െ Ͷ݉ோߙீ ͻߩߨܸଶ_݅൰ ൈ ቀ ߟௗ߱ீ ܸ݅ ቁሺͶͺሻ úHNOLQGHHOGHHGLOLU %X LIDGHGHQ D Dȡ Ȝ5 V, mR ĮG L Șd YH ȦG¶QLQ WUELQ HWNLQOLN NDWVD\ÕVÕQÕ EHOLUOH\HQ SDUDPHWUHOHU ROGX÷X J|UOPHNWHGLU

$UDúWÕUPDEXOJXODUÕ

%R\XWVX]SDUDPHWUHOHUOHWDVDUÕPoHúLWOLER\XWOX E\NONOHU NXOODQÕODUDN JHQLú ELU DUDOÕNWD oRN HVQHNELUWDVDUÕPLPNDQÕVD÷ODGÕ÷ÕQGDQER\XWOX E\NONOHU ER\XWVX]ODúWÕUÕOPÕúWÕU %X úHNLOGH EHOLUOLELUJHRPHWULNE\NONWHYH\DEHOLUOLELU birimde olan parametreler yerine boyutsuz SDUDPHWUHOHU HOGH HGLOHUHN DQDOL] NROD\OÕ÷Õ VD÷ODQPÕúWÕU

)DUNOÕ &P GH÷HUOHULQGH Ȝ¶GDNL GH÷LúLPLQ ER\XWVX] MHQHUDW|U JF ]HULQH RODQ HWNLVL DQDOL] HGLOPLúWLU ùHNLO *o NDWVD\ÕVÕQGDNL DUWÕúÕQ ER\XWVX] MHQHUDW|U JFQ oRN D] DUWWÕUGÕ÷Õ D\QÕ Jo NDWVD\ÕVÕQGD Xo-KÕ] RUDQÕQGDNLDUWÕúÕQLVHER\XWVX]MHQHUDW|UJFQ GúUG÷ EHOLUOHQPLúWLU CP Ȝ ROGX÷X durumda ഥ_ୋ

భ ROPDNWDGÕU PR=19500 kg,

5 P 9 PV ĮG=1 rad/s2 DOÕQGÕ÷ÕQGD (úLWOLN NXOODQÕODUDN 1G1=2.01 MW olarak EXOXQPXúWXUmR59YHĮG GH÷LúWLULOHUHND\QÕ ER\XWVX] PRPHQWWH oRN GH÷LúLN ER\XWOX moment (NG1) tahmin edilebilmektedir. NG1¶LQ referans DOÕQDQ 0: Jo NDSDVLWHOL U]JDU WUELQL 5 P PR=19500 kg) nominal JFQHoRN\DNÕQROGX÷XEHOLUOHQPLúWLU$UDGDNL Jo IDUNÕQÕQ LVH MHQHUDW|UGHNL ND\ÕSWDQ ND\QDNODQGÕ÷Õ GúQOPHNWHGLU %X VHEHSOH QRPLQDO JoWH HOHNWULN HQHUMLVL UHWLPL LoLQ CP=0.42, Ȝ ROPDVÕ WUELQ WDVDUÕPÕ DoÕVÕQGDQ X\JXQRODFD÷ÕGúQOPHNWHGLU

(10)

78

0 1 2 3 4 5 6 7 8 9 10 11 12 13 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 NG 1 z C_P=0.42 C_P=0.44 C_P=0.46 Od=0.97 i=100 1* D D D D D D L z ùHNLO)DUNOÕ&P GH÷HUOHULQGHȜ¶GDNLGH÷LúLPLQ ഥ_ୋ భ ]HULQHRODQHWNLVL )DUNOÕDGH÷HUOHULQGHD¶GDNLGH÷LúLPLQboyutsuz MHQHUDW|U JF ]HULQH RODQ HWNLVL ùHNLO ¶GH YHULOPLúWLU D¶GDNL DUWÕúÕQ ER\XWVX] MHQHUDW|U JFQGúUG÷D¶GHNL DUWÕúÕQLVHER\XWVX] MHQHUDW|U JFQ DUWWÕUGÕ÷Õ EHOLUOHQPLúWLU D D ROGX÷XGH÷HUGHഥ_ୋ

భ=ഥୋమ=0.174

ROPDNWDGÕU PR=19500 kg, R=39.5 m, V=15 PV ĮG=1 rad/s2 ROGX÷X GXUXPGD (úLWOLN NXOODQÕODUDN 1G2 0: EXOXQPXúWXU $\QÕ boyutsuz momentte mR 5 9 YH ĮG GH÷LúWLULOHUHN oRN JHQLú ELU DUDOÕNWD ER\XWOX MHQHUDW|U JF GH÷LúLPL WDKPLQ edilebilmektedir. NG2¶QLQ GH EHQ]HU úHNLOGH UHIHUDQV DOÕQDQ WUELQ QRPLQDO JFQH 0: oRN \DNÕQ ROGX÷X EHOLUOHQPLúWLU $UDGDNL Jo IDUNÕQÕQ LVH MHQHUDW|UGHNL ND\ÕSWDQ kaynaklDQGÕ÷ÕGúQOPHNWHGLU ùHNLO)DUNOÕDGH÷HUOHULQGHD¶GDNLGH÷LúLPLQ ഥ_ୋ మ ]HULQHRODQHWNLVL ഥ_ୋ

భ ve N IDUNOÕ \DNODúÕPODUOD EHOLUOHQHQG2

MHQHUDW|U PLOLQGH ROXúDQ JoOHU ROXS ER\XWOX NDUúÕOÕNODUÕ 1G1=NG2=2.01 MW olarak tahmin HGLOPLúWLU-HQHUDW|UYHULPLȘgDOÕQGÕ÷ÕQGD HOHNWULNVHO Jo oÕNÕúODUÕ 1E1,2) NE1,2 Șg x NG1,2

HúLWOL÷LQGHQ ID\GDODQÕODUDN 1E1,2=1.97 MW

RODUDN KHVDSODQPÕúWÕU 5HIHUDQV DOÕQDQ U]JDU WUELQLQLQ PDNVLPXP HOHNWULNVHO Jo oÕNÕúÕ NE 0: ROGX÷XQGDQ 1E1,2 \DNODúÕN RODUDN

GR÷UXWDKPLQHGLOPLúWLU

7UELQ HWNLQOLN NDWVD\ÕVÕ U]JDU JFQQ QH RUDQGD MHQHUDW|UH LOHWLOGL÷LQL J|VWHUHQ ER\XWVX] ELUSDUDPHWUHGLU5]JDU WUELQWHRULNPRGHOLQH J|UH.t IDUNOÕSDUDPHWUHOHUHED÷OÕRODUDNGH÷LúLN \DNODúÕPODUOD.t1 ve Kt2|QFHGHQEHOLUOHQPLú ROXS EX E|OPGH DQDOL] HGLOPLúWLU gQFHOLNOH Kt1 (úLWOLN HVDV DOÕQDUDN WUELQ HWNLQOLN NDWVD\ÕVÕDQDOL]HGLOPLúWLU*oNDWVD\ÕVÕCP) ve U]JDUKÕ]ÕQGDNL9GH÷LúLPLQWUELQLQHWNLQOLN NDWVD\ÕVÕ .t1 ]HULQH RODQ HWNLVL ùHNLO ¶GH YHULOPLúWLU &P¶QLQ DUWPDVÕ\OD .t1¶LQ DUWWÕ÷Õ 9¶QLQ DUWPDVÕ\OD .t1¶LQ D]DOGÕ÷Õ WHVSLW HGLOPLúWLU %XUDGD \NVHN KÕ]OÕ úDIWÕQ DoÕVDO LYPHVLĮG) 1 rad/s2 YH\NVHNKÕ]OÕúDIWÕQG|Qú KÕ]Õ QGGHYGDNȦG UDGVDOÕQDUDN DQDOL]OHU JHUoHNOHúWLULOPLúWLU 9 PV CP ROGX÷X GXUXPGD .t1 ROPDNWDGÕU V=10 m/s, CP LoLQ .t1=0.36 olarak EHOLUOHQLSU]JDUJFQQ¶VÕQÕQMHQHUDW|UH LOHWLOGL÷LQLLIDGHHWPHNWHGLU ùHNLO)DUNOÕCP GH÷HUOHULQGH9¶GHNLGH÷LúLPLQ Kt1 ]HULQHRODQHWNLVL 10 11 12 13 14 15 0,18 0,20 0,22 0,24 0,26 0,28 0,30 0,32 0,34 0,36 0,38 0,40 0,42 z=7 R=40 m i=100 H_G=1 rad/s2 O_d=0.98 _G=157 rad/s mR=19500 kg =1,2 kg/m3 Kt1 V (m/s) C_P=0,35 CP=0,40 C_P=0,45 CP=0,50

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Yatay eksenli U]JDUWUELQOHULQLQGLQDPLNGDYUDQÕúÕ-teorik bir model &3 z 9 PV L H* UDGV O G * UDGV NJP .W P5NJ 5 P 5 P 5 P 5 P 0,002 0,004 0,006 0,008 0,010 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 z V=10 m/s R=40 m i=100 HG=1 rad/s 2 O d=0.98 G=157 rad/s mR=19500 kg =1.2 kg/m3 Kt2 a' a=0.2 a=0.3 a=0.4 a=0.5

.DQDW \DUÕoDSÕ 5 YH NDQDWODUÕQ NWOHVLQGHNL (mR GH÷LúLPLQ .t1¶H HWNLVL ùHNLO ¶GD YHULOPLúWLU 5¶QLQ P P P YH P ROGX÷X GH÷HUOHUGH PR¶QLQ -19500 kg DUDVÕQGDNLGH÷LúLPLGH÷HUOHQGLULOGL÷LQGH5¶GHNL DUWÕúÕQ .t1¶L DUWWÕUGÕ÷Õ PR¶GHNL DUWÕúÕQ LVH .t1¶L oRN D] GúUG÷ J|UOPúWU PR=10500 kg, 5 PROGX÷XQGD୲భ=0.37 iken; mR=19500 kg,

5 PROGX÷XQGD୲భ ¶HGúPúWU୲భ¶LQ

PDNVLPXP ROPDVÕ LoLQ mR¶QLQGúNYH5¶QLQ \NVHNROPDVÕLVWHQPHNWHGLU

ùHNLO)DUNOÕ5GH÷HUOHULQGHPR’deki GH÷LúLPLQ୲భ üzerine olan etkisi %HQ]HU úHNLOGH୲మ2 (úLWOLN HVDV DOÕQDUDN

WUELQHWNLQOLNNDWVD\ÕVÕDQDOL]HGLOHELOPHNWHGLU (NVHQHO LQGNVL\RQ IDNW|U D YH DoÕVDO LQGNVL\RQ IDNW|UQGHNL D GH÷LúLPLQ୲మ¶\H HWNLVL DQDOL]HGLOPLúWLUùHNLOD¶GDNL DUWÕúÕQ ୲మ¶\LGúUG÷D¶GHNLDUWÕúÕQ୲మ¶\LDUWWÕUGÕ÷Õ J|UOPúWU D D ROGX÷XQGD ୲మ LNHQ D D ROGX÷XQGD ୲మ2 ¶HGúPúWU ùHNLO)DUNOÕDGH÷HUOHULQGHD¶GHNL GH÷LúLPLQ୲మ üzerine olan etkisi

'H÷LúLN NDQDW \DUÕoDSODUÕQGD 5 NDQDWODUÕQ NWOHVLQGHNL PR GH÷LúLPLQ୲మ¶\H HWNLVL ùHNLO

¶GH J|VWHULOPLúWLU 5¶QLQ DUWPDVÕ\OD୲మ¶QLQ

DUWWÕ÷ÕPR¶QLQDUWPDVÕ\OD୲మ¶QLQoRND]D]DOGÕ÷Õ

EHOLUOHQPLúWLU 5 P PR=19500 kg DOÕQGÕ÷ÕQGD୲మ=0.25 iken; R=40 m, mR=19500 NJDOÕQGÕ÷ÕQGD୲మ2 ROPDNWDGÕU0DNVLPXP ୲మ2 LoLQ5!PROPDOÕYHPR LVHRODELOGL÷LQFH GúNROPDOÕGÕU ùHNLOR ve mR¶GHNLGH÷LúLPLQ୲మ

üzerine olan etkisi

.DQDWODUÕQ NWOHVLQLQ mR) 15000-19500 kg

DUDVÕQGDNL GH÷LúLPLQLQ୲మ1 ve ୲మ ]HULQH RODQ

HWNLVL LQFHOHQGL÷LQGH mR¶QLQ DUWPDVÕ\OD Kt¶QLQ D]DOGÕ÷Õ J|UOPúWU PR NJ LoLQ

୲భ1=0.358, ୲మ=0.352 iken; mR NJ LoLQ

୲భ1=0.352, ୲మ=0.344 ROPDNWDGÕU. Referans

DOÕQDQ U]JDU WUELQL WHPHO E\NONOHUL (mR=19500 kg, R PL LoLQ୲మ1=0.38, ୲మ RODUDNEXOXQPXúWXU%XGXUXPU]JDU JFQQ 37-¶LQLQ MHQHUDW|UH LOHWLOHELOGL÷LQL J|VWHUPHNWHGLU

Sonuçlar

<DSÕODQ DQDOL]OHU QHWLFHVLQGH DúD÷ÕGDNL VRQXoODUDXODúÕOPÕúWÕU

x Teorik modelH J|UH; go NDWVD\ÕVÕQGDNL DUWÕúÕQ MHQHUDW|U JFQ oRN D] DUWWÕUGÕ÷Õ D\QÕ Jo NDWVD\ÕVÕQGD Xo-KÕ] RUDQÕQGDNL DUWÕúÕQ LVH MHQHUDW|U JFQ GúUG÷ EHOLUOHQPLúWLU $\UÕFD HNVHQHO LQGNVL\RQ IDNW|UQGHNL DUWÕúÕQ ER\XWVX] MHQHUDW|U JFQ GúUG÷ DoÕVDO LQGNVL\RQ IDNW|UQGHNL DUWÕúÕQ LVH boyutsuz jeneUDW|U JFQDUWWÕUGÕ÷ÕEHOLUOHQPLúWLU D D z 9 PV L H* UDGV OG * UDGV NJP 5 P 5 P 5 P 5 P .W P5NJ

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80

m

M. C. ùenel, E. Koç x 5HIHUDQV DOÕQDQ U]JDU WUELQi temel

E\NONOHUL PR=19500 kg, R=39.5 m,

L LoLQ ୲మ1=0.38, ୲మ=0.37 olarak

EHOLUOHQPLúWLU .t GH÷HUOHUL OLWHUDWUGHNL &P

GH÷HUOHUL\OH NDUúÕODúWÕUÕOGÕ÷ÕQGD (CP

=0.40-0.45); Kt¶QLQ &P¶GHQ NoN ROGX÷X

EHOLUOHQPLúWLU %X \]GHQ .t GH÷HUOHULQLQ

PDQWÕNOÕ ROGX÷X NDQÕVÕQD YDUÕOPÕúWÕU

*HOLúWLULOHQPRGHOLQWUELQWDVDUÕPÕLoLQHVDV DOÕQDELOHFH÷L oRN LGGLDOÕ ROPDNOD ELUOLNWH U]JDU WUELQ WHPHO E\NONOHULQLQ WDKPLQ HGLOPHVL DoÕVÕQGDQ JHUoH÷H \DNÕQ ELU \DNODúÕP J|VWHUPHNWHGLU %X QHGHQOH WHRULN PRGHO WDVDUÕP LoLQ NXOODQÕODELOHFHN ELU model olarak tavsiye edilmektedir.

Semboller

i dHYULPRUDQÕ Șd 'LúOLYHULPL CP : *oNDWVD\ÕVÕ ȡ : Hava \R÷XQOX÷X (kg m-3₎ NJ : -HQHUDW|UJLULúJF:DWW TJ : JeneraW|UJLULúPRPHQWL1P NG : -HQHUDW|UJF:DWW TG : Jeneratör momenti (Nm) Șg : Jeneratör verimi IG -HQHUDW|UQNWOHVHODWDOHWPRPHQWLNJP2) R : .DQDW\DUÕoDSÕP TR : .DQDWODUGDROXúDQPRPHQW1P TS : Kanatlardan DQDúDIWDDNWDUÕODQPRPHQW1P Ȧ : .DQDWODUÕQDoÕVDOKÕ]ÕUDGs-1₎

ĮR : .DQDWODUÕQDoÕVal ivmesi (rad s-2)

V2 .DQDWODUÕQKHPHQ|QQGHNLU]JDUKÕ]ÕPV-1) IR .DQDWODUÕQNWOHVHODWDOHWPRPHQWLNJP2) mR : .DQDWODUÕQNWOHVLNJ VXo .DQDWODUÕQXoKÕ]ÕPV-1) NR : .DQDWODUWDUDIÕQGDQHOGHHGLOHQJo:DWW IHú : .WOHVHOHúGH÷HUDWDOHWPRPHQWLNJP2) N : 5]JDUJF:DWW V : 5]JkUKÕ]ÕPs-1₎ NE 5]JDUWUELQLHOHNWULNVHOJooÕNÕúÕ:DWW) Kt : 7UELQHWNLQOLNNDWVD\ÕVÕ Ȝ : Uç-KÕ]RUDQÕ ȦG : YükseNKÕ]OÕúDIWÕQDoÕVDOKÕ]ÕUDGs-1) ĮG : Yüksek KÕ]OÕúDIWÕQDoÕVDOLYPHVLrad s-2)

7HúHNNU

%X oDOÕúPD 2QGRNX] 0D\ÕV hQLYHUVLWHVL 3<208+¶ nolu proje ile destek-OHQPLúWLU.

Kaynaklar

$WD 5 YH dHWLQ 16 N: RWRQRP ELU U]JDU WUELQL NXUXOXPX YH HQHUML HOGHVL Gazi

hQLYHUVLWHVL 0KHQGLVOLN-0LPDUOÕN )DNOWH Dergisi, 23, 1, 41-47.

(PQL\HWOL * (YVHO HOHNWULN LKWL\DFÕQÕQ NDUúÕODQPDVÕ LoLQ U]JDU WUELQL WDVDUÕPÕ Yüksek

Lisans Tezi 7UDN\D hQLYHUVLWHVL )HQ %LOLPOHUL

(QVWLWV(GLUQH

Gregg, J. R., Trendrup ve J. J., Treuren, K.W.V., (2010). Developing a wind turbine design procedure with experimental vertification, 2010

ECTC Proceedings ASME Early Career Technical Conference, Tulsa.

Huiying, C., Datong, Q. M. Z., Haitao, D., Yonggang, D. ve Wei, L., (2009). Research on

evaluating of wind turbine drive train systems, Association of the Electricity Supply Industry of East Asia and Western Pacific CEO.

.Ro(YHùHQHO0&<DWD\HNVHQOLU]JDU WUELQOHULPHNDQLNWDVDUÕPHVDVODUÕYHSHUIRUPDQV DUDúWÕUPDVÕ Anadolu Enerji Sempozyumu, 610-(OD]Õ÷

Morren, J., Pierik, J. ve Haan, S. W. H., (2006) .

Inertial response of variable speed wind turbines, Electric Power Systems Research, 76, 980-987.

g]WUN ø YH dHOLN $ (2006). 'Q\D¶GD YH 7UNL\H¶GH U]JDU Hnerjisi NXOODQÕP Gurumu ve gHOHFH÷H\|QHOLNEeklentiler, Atatürk Üniversitesi

Ziraat FakOWHVL'HUJLVL, 37, 2, 267-274.

ùHQHO 0 & (2012). 5]JDU WUELQOHULQGH Jo iletim PHNDQL]PDODUÕQÕQWDVDUÕPHVDVODUÕ-dinamik dDYUDQÕú <NVHN /LVDQV 7H]L 2QGRNX] 0D\ÕV hQLYHUVLWHVL Fen BilimOHUL(QVWLWV6DPVun. ùHQHO 0 & ve .Ro ( (2013). 5]JDU tUELQOHUL

dinamik dDYUDQÕú analizi-teorik boyutsuz bir model, 2. Anadolu Enerji Sempozyumu, 301-313, 'L\DUEDNÕU