mühendislikdergisi
Dicle Üniversitesi Mühendislik Fakültesi
'LFOHhQLYHUVLWHVL0KHQGLVOLN)DNOWHVL
Cilt: 5,
3-9
1, PKHQGLVOLNGHUJLVL
Mart 2014
Yatay eksenli r]JDUWUELQOHULnin GLQDPLNGDYUDQÕúÕ-teorik
bir model
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GDYUDQÕúODUÕLoLQHQHUMLG|QúPOHULHVDVDOÕQDUDNWHRULN\HQLELUPRGHOROXúWXUXOPXúWXU%XPRGHO
LOH WDVDUÕP SDUDPHWUHOHUL NDQDW IL]LNVHO YH JHRPHWULN E\NONOHUL GH÷HUOHQGLULOLS PRPHQW
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Anahtar Kelimeler: 5]JDUWUELQLGLQDPLNDQDOL]teorik model.
<D]ÕúPDODUÕQ\DSÕODFD÷Õ\D]DU0DKPXW&DQù(1(/PDKPXWFDQVHQHO#RPXHGXWU7HO
69
M. C. ùenel, E. Koç
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. Onedimensional 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,
theoretical model.
70
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GLULú
Enerji, ekonomik, sosyal ve kültürel
NDONÕQPDQÕQ
WHPHO
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enerjiye olan ba÷ÕPOÕOÕ÷ÕPÕ]ÕQ DUWPDVÕQD VHEHS
ROPDNWDGÕU %X GXUXPGD VUGUOHELOLU ELU
GHQJHQLQ ROXúWXUXODELOPHVL LoLQ HQHUML ND\QDN
oHúLWOLOL÷LQLQ VD÷ODQPDVÕ YH IRVLO \DNÕWOÕ HQHUML
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|QHP DU] HWPHNWHGLU <HQLOHQHELOLU HQHUML
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enerjisinin \DNODúÕN 1-¶VL U]JkU HQHUMLVLQH
oHYULOPHNWHGLU g]WUN YH dHOLN ùHQHO
2012).
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\HUHO LNOLP |]HOOLNOHULQH J|UH GH÷LúPHNOH
beraber ortalama 20- \ÕOGÕU Yatay eksenli
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NXOH GLúOL NXWXVX MHQHUDW|U \DWDN NDYUDPD
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SLWFK PHNDQL]PDVÕ YH NRQWURO QLWHVLQGHQ
ROXúPDNWDGÕUùHQHO.
Kanat
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Anemometre
Jeneratör
(÷LP (yaw)
PHNDQL]PDVÕ
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Kule
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kDSÕVÕ
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LOJLOL OLWHUDWUGH ELUoRN oDOÕúPD PHYFXWWXU $WD
YH dHWLQ (2008) \UWWNOHUL oDOÕúPDGD &HODO
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<UWOHQELUGL÷HUoDOÕúPDGD*UHJJYG. (2010),
kanat eleman tHRULVL Xo-KÕ] RUDQÕ Ȝ Jo YH
YHULP JLEL WHPHO HúLWOLNOHUGHQ ID\GDODQDUDN
U]JDUWUELQLLoLQWHRULNELUPRGHOROXúWXUXSEX
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Huiying vd. (2010) \UWWNOHUL oDOÕúPDGD
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SUHQVLSOHUL YH PKHQGLVOLN X\JXODPDODUÕQGDNL
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71
M. C. ùenel, E. Koç
%XoDOÕúPDGDLVH WDVDUÕP SDUDPHWUHOHULQHL Ȝ
ș&P, CQoDOÕúPDSDUDPHWUHOHULQH9ȦȦGĮ
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WDKPLQHWPHNDPDFÕ\ODWUELQHWNLQOLNNDWVD\ÕVÕ
diye yeni boyutsuz bir parametre WDQÕPODQDUDN
DQDOL]OHUJHUoHNOHúWLULOPLúWLU
Rüzgar türbini tDVDUÕPeVDVODUÕ
5]JkUWUELQOHULQGHJoHQHUMLROXúXPXU]JkU
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bir U]JDU WUELQ modeli ùHNLO¶GHVXQXOPXúWXU.
Vuç Ȧ5
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z1 kutusu
R
V
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i1
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ȦG, TG
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ȦYH U]JkUKÕ]Õna 9ED÷OÕGÕUùHNLO.
(1)
l = Vuç / V = wR / V
7HN NDQDWOÕ U]JkU WUELQOHULQGH NDQDWODU oRN
KÕ]OÕ G|QG÷QGHQ Xo-KÕ] RUDQÕ Ȝ -20
DUDVÕQGD\NHQoNDQDWOÕU]JkUWUELQOHULQGHXoKÕ]RUDQÕȜ-FLYDUÕQGDGÕr (Emniyetli, 2007).
Aerofoil
Ȧ Vuç Ȧ5
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r
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y
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72
ș
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olarak verilmektedir. 0DNVLPXP Jo NDWVD\ÕVÕ
aerodinamik olarak lineer momentum teorisine
J|UHEHW]Oimitini(Cpmaks DúDPDPDNWDGÕU
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Rüzgar türbini dinamik analiz-teorik
model
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NDQDWODUGD EDúODPDNWDGÕU .DQDWODUGD ROXúDQ
PRPHQW IDUNOÕ \DNODúÕPODUOD EHOLUOHQHELOmektedir. Kanat eleman teorisine dayanarak
U]JDUÕQ HWNLVL\OH NDQDWODUGD ROXúDQ PRPHQW
(TR1);
ܶோଵ ൌ ͲǤͷߩߨܴ ଷ ܸ ଶ ‫ܥ‬ொ
73
(3)
M. C. ùenel, E. Koç
úHNOLQGHGLU%XUDGD9U]JDUKÕ]ÕPV5NDQDW
\DUÕoDSÕPȡKDYD\R÷XQOX÷XNJP3), CQ tork
NDWVD\ÕVÕGÕU 5]JkUÕQ HWNLVL\OH NDQDWODUGD
ROXúDQPRPHQW ER\XWVX]ODúWÕUÕOÕUVD
ܶതோଵ ൌ ͲǤͷߨ‫ܥ‬௉ Ȁߣ
(4)
úHNOLQGHHOGHHGLOLU%XUDGD
ܶതோଵ ൌ ܶோଵ Ȁሺߩܸ ଶ ܴ ଷ ሻ
(5)
úHNOLQGH EXOXQXU6LVWHPLoLQNXOODQÕODQWHPHO
SDUDPHWUHOHU VÕUDVÕ\OD 7J GLúOL NXWXVX oÕNÕú
momenti (Nm), TG MHQHUDW|UPRPHQWL1P ,G
MHQHUDW|UQ NWOHVHO DWDOHW PRPHQWL NJP2), IHú
NWOHVHO HúGH÷HU DWDOHW PRPHQWL NJP2 ȦG
\NVHNKÕ]OÕúDIWÕQDoÕVDOKÕ]ÕUDGVĮG \NVHN
KÕ]OÕ úDIWÕQ DoÕVDO LYPHVL UDGV2 úHNOLQGHGLU
6LVWHPLoLQPRPHQWHúLWOL÷L
ܶ௃ െ ܶீ ൌ ‫ீߙ ீܫ‬
úHNOLQGH WDQÕPODQDQ ER\XWVX] U]JDU HWNLVL\OH
NDQDWODUGD ROXúDQ PRPHQW ROXS ER\XWOX
SDUDPHWUHOHU ȡ 9 YH 5¶\H ED÷OÕGÕU %R\XWVX]
moment ifadesi, CP YHȜ¶\DED÷OÕRODUDNELUGHID
WHVSLW HGLOGLNWHQ VRQUD (úLWOLN NXOODQÕODUDN
GH÷LúLN KDYD \R÷XQOX÷X U]JDU KÕ]Õ YH NDQDW
\DUÕoDSÕQGD JHQLú ELU DUDOÕNWD ER\XWOX PRPHQW
(TR1) belirlenebilmektedir.
úHNOLQGH EHOLUOHQPLúWLU 'LúOL YHULPL Șd) ve
oHYULPRUDQÕQDLED÷OÕRODUDNGLúOLNXWXVXJLULú
momenti (TS YH GLúOL NXWXVX oÕNÕú YH\D
MHQHUDW|UJLULúPRPHQWL7JDUDVÕQGDNLLOLúNL
ܶ௃ ൌ ܶௌ ߟௗ Ȁ݅
ܶோଶ ൌ ƒ
ସ
െ ƒሻߩܸܴ߱ ߨ
(6)
(11)
6LVWHP YH VLVWHP ELUOLNWH GH÷HUOHQGLULOLS
moment tek mile indirgenirse MHQHUDW|UPRPHQWL
(TG);
'|QHQGLVNLoLQPomentum teorisine dayanarak
Ȝ Ȧ59 WDQÕPÕ NXOODQÕOÕS U]JDUÕQ HWNLVL\OH
NDQDWODUGDROXúDQPRPHQW7R2);
ܶீ ൌ ܶோ ߟௗ Ȁ݅ െ ‫ܫ‬௘ç ߙீ
ᇱ ሺͳ
(10)
(12)
úHNOLQGHHOGHHGLOLU(úLWOLNWH\HUDODQ,Hú;
úHNOLQGHGLU %XUDGD D HNVHQHO LQGNVL\RQ ‫ ܫ‬ൌ ‫ ߟ ܫ‬Ȁ݅ ଶ ൅ ‫ܫ‬
(13)
௘ç
ோ ௗ
ீ
IDNW|U D
DoÕVDO LQGNVL\RQ IDNW|U ROXS
boyutsuz moment;
VLVWHPLQ NWOHVHO HúGH÷HUDWDOHW PRPHQWLRODUDN
WDQÕPODQPDNWDGÕU%XUDGD,R NDQDWODUÕQNWOHVHO
ᇱ ሺͳ
ത
ܶோଶ ൌ ƒ െ ƒሻߣߨ
(7) atalet momenti (kgm2), I MHQHUDW|UQ NWOHVHO
G
atalet momenti (kgm2LoHYULPRUDQÕ Șd GLúOL
RODUDNWDQÕPODQPÕúWÕU%XUDGD
YHULPLúHNOLQGHLIDGHHGLOPHNWHGLU
ܶതோଶ ൌ ܶோଶ Ȁሺߩܸ ଶ ܴ ଷ ሻ
(8)
'LúOL YHULPL Șd GLúOL NXWXVX oÕNÕúÕQGDNL
HQHUMLQLQ GLúOL NXWXVX JLULúLQGHNL HQHUML\H RUDQÕ
úHNOLQGHLIDGHHGLOHQERyutsuz momenttir.
RODUDN WDQÕPODQDELOPHNWHGLU %X GXUXPGD GLúOL
verimi;
- 5]JDUtUELQLjHQHUDW|Umomenti:
5]JDU WUELQ WHRULN PRGHOLQGH VLVWHP LoLQ
NXOODQÕODQ WHPHO SDUDPHWUHOHU VÕUDVÕ\OD 7R
U]JkUÕQ HWNLVL\OH NDQDWODUGD ROXúDQ PRPHQW
(Nm), TS GLúOL NXWXVX JLULú PRPHQWL 1P ,R
NDQDWODUÕQ NWOHVHO DWDOHW PRPHQWL NJP2 Ȧ
NDQDWODUÕQDoÕVDOKÕ]ÕUDGVĮR NDQDWODUÕQDoÕVDO
ivmesi (rad/s2 Șd GLúOL YHULPL úHNOLQGHGLU
6LVWHPLoLQPRPHQWHúLWOL÷L
ܶோ െ ܶௌ ൌ ‫ܫ‬ோ ߙோ
(9)
ߟௗ ൌ ሺͲǤͷ‫ீ߱ ீܫ‬ଶ ሻȀሺͲǤͷ‫ܫ‬ோ ߱ଶ ሻ ൌ ‫ ݅ ீܫ‬ଶ Ȁ‫ܫ‬ோ
(14)
úHNOLQGHEHOLUOHQPHNWHGLU .DQDWODUNWOHVLnden
ଶ
GROD\Õ ‫ܫ‬ோ ൌ ݉ோ ܴ௘ç
E\NO÷QGH ELU NWOHVHO
atalet momentine (IR VDKLSWLU 7HN ELU NDQDGÕQ
NWOHVLmR' RODUDNDOÕQGÕ÷ÕQGDNDQDWODUÕQWRSODP
NWOHVL ݉ோ ൌ ͵݉ோ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
74
Yatay eksenli U]JDUWUELQOHULQLQGLQDPLNGDYUDQÕúÕ-teorik bir model
biri (R/3) olarak kabul edilmektedir (Morren Ieú , ĮG ve m R LIDGHOHUL GH÷HUOHQGLULOGL÷LQGH
vd., 2006) %X GXUXPGD NDQDWODUÕQ NWOHVHO
ER\XWVX]MHQHUDW|UPRPHQWL ( TG1 );
atalet momenti (IR);
ଶ
‫ܫ‬ோ ൌ ݉ோ ܴ௘ç
ൌ ሺ݉ோ ܴ ଶ ሻȀͻ
(15)
ҧ ߙതீ
ܶതீଵ ൌ ܶതோଵ ߟௗ Ȁሺ݅݉
ഥ ோ ሻ െ ‫ܫ‬௘ç
(23)
RODUDN EXOXQPDNWDGÕU %XUDGD PR NDQDWODUÕQ úHNOLQGHEXOXQXS T NDUúÕOÕ÷Õ\HUOHúWLULOLUVH
R1
WRSODPNWOHVLGLUNJ,R NDUúÕOÕ÷Õ(úLWOLN
NXOODQÕODUDN VLVWHPLQ NWOHVHO HúGH÷HU DWDOHW
ҧ ߙതீ
ܶതீଵ ൌ ‫ܥ‬௉ ߨߟௗ Ȁሺʹߣ݅݉
ഥ ோ ሻ െ ‫ܫ‬௘ç
(24)
momenti (IHú) ifadesi;
‫ܫ‬௘ç ൌ ሺʹ݉ோ ܴ ଶ ߟௗ ሻȀሺͻ݅ ଶ ሻ
(16)
úHNOLQGH EHOLUOHQPLúWLU%XUDGD
úHNOLQGH\HQLGHQG]HQOHQHELOPHNWHGLU%XHOGH ܶതீଵ ൌ ܶீଵ Ȁ݉ோ ܸ ଶ
(25)
HGLOHQ E\NONOHU ,R, IG, IHú Șd) ve moment
HúLWOLNOHUL 7R1, TR2ୖభ ǡ ୖమ NXOODQÕODUDN IDUNOÕ úHNOLQGH WDQÕPODQDQ ER\XWVX] MHQHUDW|U
\DNODúÕPODUOD MHQHUDW|U PRPHQWL 7G) momentidir.
bulunabilmektedir.
-HQHUDW|U PRPHQWL JHQHO LIDGHVLQGH (úLWOLN
-HQHUDW|U PRPHQWL JHQHO LIDGHVLQGH (úLWOLN (12)), TR2 ve IHú NDUúÕOÕNODUÕ NXOODQÕOÕS JHUHNOL
(12)), TR1 ve IHú LIDGHVL NXOODQÕOÕUVD MHQHUDW|U G]HQOHPHOHU\DSÕOÕUVDMHQHUDW|UPRPHQWL (TG2);
momenti (TG1);
ܶீଵ
ܶீଶ ൌ
ܴ ଶ ߟௗ
Ͷ݉ோ ߙீ
ൌ
൬ͻߩߨܴܸ ଶ ‫ܥ‬ொ െ
൰ሺͳ͹ሻ
ͳͺ݅
݅
ܴ ଶ ߟௗ ᇱ
ʹ݉ோ ߙீ
൬ƒ ሺͳ െ ƒሻߩܸܴ߱ ଶ ߨ െ
൰ሺʹ͸ሻ
݅
ͻ݅
úHNOLQGHHOGHHGLOLU%XLIDGH\DUGÕPÕ\ODȘd GLúOL
YHULPL L oHYULP RUDQÕ 5 NDQDW \DUÕoDSÕ ĮG
úHNOLQGHEXOXQPDNWDGÕU%XLIDGH\DUGÕPÕ\OD&Q \NVHNKÕ]OÕúDIWÕQDoÕVDOLYPHVL 9U]JDU KÕ]Õ
WRUN NDWVD\ÕVÕ L GLúOL oHYULP RUDQÕ ĮG \NVHN Ȧ NDQDW G|Qú KÕ]Õ ȡ KDYD \R÷XQOX÷X PR
KÕ]OÕúDIWÕQDoÕVDOLYPHVLȘd GLúOLYHULPL5NDQDW NDQDWODUÕQ WRSODP NWOHVL D HNVHQHO LQGNVL\RQ
\DUÕoDSÕ YH 9 U]JDU KÕ]Õ FLQVLQGHQ ER\XWOX IDNW|U D
DoÕVDO LQGNVL\RQ IDNW|U FLQVLQGHQ
RODUDNMHQHUDW|UPRPHQWLKHVDSODQDELOPHNWHGLU MHQHUDW|U
PRPHQWL
ER\XWOX
RODUDN
hesaplanabilmektedir.
-HQHUDW|U PRPHQWLQL 7G) ER\XWVX]ODúWÕUPDN
DPDFÕ\OD NXOODQÕODQ \NVHN KÕ]OÕ úDIW DoÕVDO -HQHUDW|U PRPHQWL JHQHO LIDGHVL (úLWOLN LYPHVLQLQ ĮG NDQDWODUÕQ WRSODP NWOHVLQLQ HVDV DOÕnarak TR2 , Ieú , ĮG ve m R ifadeleri
(mR NDQDW \DUÕoDSÕQÕQ 5 \NVHN KÕ]OÕ úDIW
GH÷HUOHQGLULOGL÷LQGH
ER\XWVX]
MHQHUDW|U
DoÕVDOKÕ]ÕQÕQȦGYHHúGH÷HUDWDOHWPRPHQWLQLQ
);
momenti
(
T
G2
(I ) boyutsuz ifadeleri;
Hú
ߙതீ ൌ ߙீ ܴ ଶ Ȁܸ ଶ (18)
݉
ഥ ோ ൌ ݉ோ Ȁߩܴ ଷ
(19)
ܴത ൌ ߩܸ ଶ ܴȀሺ݉ோ ߙீ ሻ
(20)
߱
ഥீ ൌ ߱ீ ܴȀܸ
(21)
ҧ ൌ ‫ܫ‬௘ç Ȁሺ݉ோ ܴ ଶ ሻ
‫ܫ‬௘ç
(22)
ҧ ߙതீ
ܶതீଶ ൌ ܶതோଶ ߟௗ Ȁሺ݅݉
ഥ ோ ሻ െ ‫ܫ‬௘ç
(27)
úHNOLQGHEXOXQXS TR2 NDUúÕOÕ÷Õ\HUOHúWLULOLUVH
ƒᇱ ሺͳ െ ƒሻߣߨߟௗ
ҧ ߙതீ ሺʹͺሻ
െ ‫ܫ‬௘ç
݅݉
ഥோ
úHNOLQH G|QúU%XUDGD
ܶതீଶ ൌ
(29)
ܶതீଶ ൌ ܶீଶ Ȁሺ݉ோ ܸ ଶ ሻ
úHNOLQGH WDQÕPODQPDNWDGÕU -HQHUDW|U PRPHQWL
JHQHO LIDGHVL (úLWOLN HVDV DOÕQDUDN TR1 , úHNOLQGH LIDGH HGLOHQ ER\XWVX] MHQHUDW|U
momentidir.
75
M. C. ùenel, E. Koç
-5]JkU WUELQOHULQGH NDQDWODU WDUDIÕndan
U]JDUGDQHOGHHGLOHQJo
5]JDUWUELQOHULQGHNDQDWODUGDROXúDQPRPHQW
(TR1 YH DoÕVDO KÕ] Ȧ GH÷HUOHQGLULOHUHN
NDQDWODUD LOHWLOHQ Jo NROD\OÕNOD EHOLUOHQHbilmektedir. Bu durumda NDQDWODU WDUDIÕQGDQ
rüzgardan elde edilen güç (NR1);
úHNOLQGH LIDGH HGLOHQ NDQDWODU WDUDIÕQGDQ
U]JkUGDQHOGHHGLOHQER\XWVX]JoWU
ܰோଵ ൌ ܶோଵ ൈ ߱ ൌ ͲǤͷߩߨܴ ଶ ܸ ଷ ‫ܥ‬௉
ܰீ ൌ ሺܶோ ߟௗ ߱ீ ሻȀ݅ െ ‫ܫ‬௘ç ߙீ ߱ீ
(30)
olarak bulunabilmektedir. Bu ifadeden, R kanat
\DUÕoDSÕ 9 U]JDU KÕ]Õ YH &P Jo NDWVD\ÕVÕQÕQ
NDQDWODU WDUDIÕQGDQ U]JDUGDQ HOGH edilen gücü
EHOLUOH\HQ
WHPHO
SDUDPHWUHOHU
ROGX÷X
J|UOPHNWHGLU 1R1 LIDGHVL HVDV DOÕQDUDN
NDQDWODU WDUDIÕQGDQ U]JkUGDQ HOGH HGLOHQ
ഥ ‫;) ܀‬
ER\XWVX]Jo (‫ۼ‬
૚
ഥோଵ ൌ ͲǤͷ‫ܥ‬௉ ߨ
ܰ
(31)
úHNOLQGHEXOXQPXúWXU%XUDGD
ഥோଵ ൌ ܰோଵ Ȁሺߩܸ ଷ ܴ ଶ ሻ
ܰ
-5]JDUWUELQOHULQGHMHQHUDW|UJF
Jeneratör gücü (NGMHQHUDW|UPRPHQWLQLQ7G)
\NVHNKÕ]OÕúDIWÕQDoÕVDOKÕ]Õ\ODȦGoDUSÕPÕQD
HúLWWLU %XGXUXPGDMHQHUDW|UJF
(36)
úHNOLQLDOÕU%XUDGDȦG \NVHNKÕ]OÕúDIWÕQDoÕVDO
KÕ]ÕUDGVĮG \NVHNKÕ]OÕúDIWÕQDoÕVDOLYPHVL
(rad/s2 úHNOLQGH LIDGH edilmektedir. TR1 ve IHú
NDUúÕOÕNODUÕ\D]ÕOGÕ÷ÕQGDMHQHUDW|UJF (NG1);
ܴ ଶ ߟௗ ߱ீ
Ͷ݉ோ ߙீ
ଶ
൬ͻߩߨܴܸ ‫ܥ‬ொ െ
൰ሺ͵͹ሻ
ܰீଵ ൌ
ͳͺ݅
݅
ҧ , Ȧ ve R
(úLWOLN HVDV DOÕQÕS ഥୖభ , ୣç
G
LIDGHOHULGH÷HUOHQGLULOGL÷LQGHER\XWVX]MHQHUDW|U
ഥ ۵ ሻǢ);
JF‫ۼ‬
૚
(32)
ഥீଵ ൌ ൫ܶതோଵ ܴത ߟௗ Ȁ݅ െ ‫ܫ‬௘ç
ҧ ൯߱
ܰ
ഥீ
(38)
úHNOLQGH WDQÕPODQDQ NDQDWODU WDUDIÕQGDQ
úHNOLQGHEXOXQPXúROXSഥୖభ NDUúÕOÕ÷Õ\D]ÕOÕUVD
U]JkUGDQHOGHHGLOHQER\XWVX]JoWU
.DQDWODU WDUDIÕQGDQ U]JDUGDQ HOGH HGLOHQ ܰ
ഥீଵ ൌ ቀሺ‫ܥ‬௉ ߨߟௗ ܴത ሻȀሺʹߣ݅ሻ െ ‫ܫ‬௘ç
ҧ ቁ߱
ഥீ
moment (TR2 YH NDQDWODUÕQ G|Qú KÕ]Õ Ȧ
GH÷HUOHQGLULOLS JHUHNOL G]HQOHPHOHU \DSÕOGÕ÷ÕQGD úHNOLQGHHOGHHGLOLU%XUDGD
NDQDWODU WDUDIÕQGDQ U]JDUGDQ HOGH HGLOHQ Jo
(NR2);
ഥீଵ ൌ ܰீଵ Ȁሺ݉ோ ܴܸߙீ ሻ
ܰ
ܰோଶ ൌ ܶோଶ ൈ ߱ ൌ ƒᇱ ሺͳ െ ƒሻߩܸ߱ଶ ܴ ସ ߨ
(33)
(39)
(40)
úHNOLQGH LIDGH HGLOHQ ER\XWVX] MHQHUDW|U
JFGU
úHNOLQGHEXOXQDELOPHNWHGLU%XLIDGH\DUGÕPÕ\OD
GD D HNVHQHO LQGNVL\RQ IDNW|U D
DoÕVDO Jeneratör gücü (N ), benzer úHNLOGH |QFHGHQ
G2
LQGNVL\RQ IDNW|U 9 U]JDU KÕ]Õ Ȧ NDQDW HOGH HGLOHQ MHQHUDW|U PRPHQWL 7 YH \NVHN
G2
G|Qú KÕ]Õ 5 NDQDW \DUÕoDSÕ JLEL WHPHO KÕ]OÕúDIWÕQDoÕVDOKÕ]ÕȦ ) oDUSÕODUDN;
G
SDUDPHWUHOHU ELOLQGL÷LQGH NDQDWODUGDQ UHWLOHQ
Jo ER\XWOX RODUDN EXOXQDELOPHNWHGLU 1R2 esas
ܴ ଶ ߟௗ ߱ீ ᇱ
ʹ݉ோ ߙீ
൬ƒ ሺͳ െ ƒሻߩܸܴ߱ ଶ ߨ െ
൰ ሺͶͳሻ
DOÕQDUDN NDQDWODU WDUDIÕQGDQ U]JkUGDQ HOGH ܰீଶ ൌ
݅
ͻ݅
ഥ ‫;) ܀‬
HGLOHQER\XWVX]Jo‫ۼ‬
૛
úHNOLQGH EXOXQXU (úLWOLN HVDV DOÕQÕS TR1 ,
ᇱ
ഥோଶ ൌ ƒ ሺͳ െ ƒሻߨ
ܰ
(34)
I , Ȧ ve R LIDGHOHUL GH÷HUOHQGLULOGL÷LQGH
eú
ഥோଶ ൌ ܰோଶ Ȁሺߩܸ߱ଶ ܴ ସ ሻ
ܰ
G
ഥ ۵ ሻǢ);
ER\XWVX]MHQHUDW|UJF (‫ۼ‬
૛
RODUDNEHOLUOHQPLúWLU%XUDGD
(35)
ഥீଶ ൌ ൫ܶതோଶ ܴത ߟௗ Ȁ݅ െ ‫ܫ‬௘ç
ҧ ൯߱
ܰ
ഥீ
(42)
Yatay eksenli U]JDUWUELQOHULQLQGLQDPLNGDYUDQÕúÕ-teorik bir model
úHNOLQGHROXSഥୖమ NDUúÕOÕ÷Õ\D]ÕOÕUVD
ഥீଶ ൌ ൫ƒᇱ ሺͳ െ ƒሻߣߨߟௗ ܴത Ȁ݅ െ ‫ܫ‬௘ç
ҧ ൯߱
ܰ
ഥீ
‫ܭ‬௧ଶ ൌ ൬ʹܽᇱ ሺͳ െ ܽሻߣܴ െ
(43)
úHNOLQGHHOGHHGLOLU%XUDGD
ഥீଶ ൌ ܰீଶ Ȁሺ݉ோ ܴܸߙீ ሻ
ܰ
(44)
úHNOLQGHWDQÕPODQDQER\XWVX]MHQHUDW|UJFGU
ߟௗ ߱ீ
Ͷ݉ோ ߙீ
൰ൈቀ
ቁሺͶͺሻ
ͻߩߨܸ ଶ ݅
ܸ݅
úHNOLQGH HOGH HGLOLU %X LIDGHGHQ D D
ȡ Ȝ 5
V, mR ĮG L Șd YH ȦG¶QLQ WUELQ HWNLQOLN
NDWVD\ÕVÕQÕ EHOLUOH\HQ SDUDPHWUHOHU ROGX÷X
J|UOPHNWHGLU
$UDúWÕUPDEXOJXODUÕ
-5]JDUWUELQOHULQGHWUELQHWNLQOLNNDWVD\ÕVÕ
%R\XWVX]SDUDPHWUHOHUOHWDVDUÕPoHúLWOLER\XWOX
E\NONOHU NXOODQÕODUDN JHQLú ELU DUDOÕNWD oRN
HVQHNELUWDVDUÕPLPNDQÕVD÷ODGÕ÷ÕQGDQER\XWOX
E\NONOHU ER\XWVX]ODúWÕUÕOPÕúWÕU %X úHNLOGH
EHOLUOLELUJHRPHWULNE\NONWHYH\DEHOLUOLELU
birimde olan parametreler yerine boyutsuz
SDUDPHWUHOHU HOGH HGLOHUHN DQDOL] NROD\OÕ÷Õ
2 3
5]JDU JF 1 ȡʌ5 V ile NG1 WUELQ VD÷ODQPÕúWÕU
MHQHUDW|U úDIWÕQGDNL Jo (úLWOLN GH÷HUOHQGLULOHUHNWUELQHWNLQOLNNDWVD\ÕVÕ (Kt1);
)DUNOÕ &P GH÷HUOHULQGH Ȝ¶GDNL GH÷LúLPLQ
ER\XWVX] MHQHUDW|U JF ]HULQH RODQ HWNLVL
ܰீଵ
‫ܭ‬௧ଵ ൌ
ሺͶͷሻ DQDOL] HGLOPLúWLU ùHNLO *o NDWVD\ÕVÕQGDNL
ܰ
DUWÕúÕQ ER\XWVX] MHQHUDW|U JFQ oRN D]
DUWWÕUGÕ÷Õ D\QÕ Jo NDWVD\ÕVÕQGD Xo-KÕ]
JoOHU RUDQÕQGDQ JHUHNOL G]HQOHPHOHU
RUDQÕQGDNLDUWÕúÕQLVHER\XWVX]MHQHUDW|UJFQ
\DSÕODUDN
GúUG÷ EHOLUOHQPLúWLU CP Ȝ ROGX÷X
ഥ ୋ ROPDNWDGÕU PR=19500 kg,
durumda ܴ‫ܥ‬௉ Ͷ݉ோ ߙீ
ߟௗ ߱ீ
భ
‫ܭ‬௧ଵ ൌ ൬
െ
൰
ൈ
ቀ
ቁሺͶ͸ሻ
5
P
9 PV ĮG=1 rad/s2 DOÕQGÕ÷ÕQGD
ߣ
ͻߩߨܸ ଶ ݅
ܸ݅
(úLWOLN NXOODQÕODUDN 1G1=2.01 MW olarak
úHNOLQGH EHOLUOHQPLúWLU %XUDGD WUELQ HWNLQOLN EXOXQPXúWXUmR59YHĮG GH÷LúWLULOHUHND\QÕ
NDWVD\ÕVÕ .t1) CP Ȝ ȡ 5 9 PR ĮG L Șd ve ER\XWVX] PRPHQWWH oRN GH÷LúLN ER\XWOX
ȦG¶\H ED÷OÕ RODUDN GH÷LúPHNWHGLU %HQ]HU moment (NG1) tahmin edilebilmektedir. NG1¶LQ
úHNLOGHU]JDUJF1 ȡʌ52V3 ile NG2 WUELQ referans DOÕQDQ 0: Jo NDSDVLWHOL U]JDU
MHQHUDW|U úDIWÕQGDNL Jo (úLWOLN WUELQL 5 P PR=19500 kg) nominal
JFQHoRN\DNÕQROGX÷XEHOLUOHQPLúWLU$UDGDNL
GH÷HUOHQGLULOHUHNWUELQHWNLQOLNNDWVD\ÕVÕ (Kt2);
Jo IDUNÕQÕQ LVH MHQHUDW|UGHNL ND\ÕSWDQ
ND\QDNODQGÕ÷Õ GúQOPHNWHGLU %X VHEHSOH
ܰீଶ
‫ܭ‬௧ଶ ൌ
ሺͶ͹ሻ QRPLQDO JoWH HOHNWULN HQHUMLVL UHWLPL LoLQ
ܰ
CP=0.42, Ȝ ROPDVÕ WUELQ WDVDUÕPÕ DoÕVÕQGDQ
JoOHU RUDQÕQGDQ JHUHNOL G]HQOHPHOHU X\JXQRODFD÷ÕGúQOPHNWHGLU
\DSÕODUDN
5]JDU JF 1¶GHQ KDQJL HWNLQOLNWH MHQHUDW|U
JF 1G HOGH HGLOHELOHFH÷LQL EHOLUOHPHN
DPDFÕ\ODER\XWVX]WUELQ HWNLQOLNNDWVD\ÕVÕ (Kt)
WDQÕPODQDELOPHNWHGLU %X E|OPGH LNL IDUNOÕ
WUELQHWNLQOLNNDWVD\ÕsÕJHOLúWLULOPLúWLU
77
M. C. ùenel, E. Koç
1,8
ഥୋ
భ
ve N G2 IDUNOÕ \DNODúÕPODUOD EHOLUOHQHQ
MHQHUDW|U PLOLQGH ROXúDQ JoOHU ROXS ER\XWOX
NDUúÕOÕNODUÕ 1G1=NG2=2.01 MW olarak tahmin
HGLOPLúWLU-HQHUDW|UYHULPLȘgDOÕQGÕ÷ÕQGD
HOHNWULNVHO Jo oÕNÕúODUÕ 1E1,2) NE1,2 Șg x NG1,2
HúLWOL÷LQGHQ ID\GDODQÕODUDN 1E1,2=1.97 MW
RODUDN KHVDSODQPÕúWÕU 5HIHUDQV DOÕQDQ U]JDU
WUELQLQLQ PDNVLPXP HOHNWULNVHO Jo oÕNÕúÕ
NE 0: ROGX÷XQGDQ 1E1,2 \DNODúÕN RODUDN
GR÷UXWDKPLQHGLOPLúWLU
CP=0.42
1,6
CP=0.44
1,4
CP=0.46
O
=0.97
d
1,2
i=100
N G1
1,0
0,8
0,6
0,4
0,2
0,0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
z
ùHNLO)DUNOÕ&P GH÷HUOHULQGHȜ¶GDNLGH÷LúLPLQ
ഥ ୋ ]HULQHRODQHWNLVL
భ
)DUNOÕD
GH÷HUOHULQGHD¶GDNLGH÷LúLPLQboyutsuz
MHQHUDW|U JF ]HULQH RODQ HWNLVL ùHNLO ¶GH
YHULOPLúWLU D¶GDNL DUWÕúÕQ ER\XWVX] MHQHUDW|U
JFQ GúUG÷ D
¶GHNL DUWÕúÕQ LVH ER\XWVX]
MHQHUDW|U JFQ DUWWÕUGÕ÷Õ EHOLUOHQPLúWLU
ഥ ୋ =
ഥ ୋ =0.174
D D
ROGX÷XGH÷HUGH భ
మ
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
JF
GH÷LúLPL
WDKPLQ
edilebilmektedir. NG2¶QLQ GH EHQ]HU úHNLOGH
UHIHUDQV DOÕQDQ WUELQ QRPLQDO JFQH 0:
oRN \DNÕQ ROGX÷X EHOLUOHQPLúWLU $UDGDNL Jo
IDUNÕQÕQ
LVH
MHQHUDW|UGHNL
ND\ÕSWDQ
kaynaklDQGÕ÷ÕGúQOPHNWHGLU
7UELQ HWNLQOLN NDWVD\ÕVÕ U]JDU JFQQ QH
RUDQGD MHQHUDW|UH LOHWLOGL÷LQL J|VWHUHQ ER\XWVX]
ELUSDUDPHWUHGLU5]JDU WUELQWHRULNPRGHOLQH
J|UH.t IDUNOÕSDUDPHWUHOHUHED÷OÕRODUDNGH÷LúLN
\DNODúÕPODUOD .t1 ve Kt2 |QFHGHQ EHOLUOHQPLú
ROXS EX E|OPGH DQDOL] HGLOPLúWLU gQFHOLNOH
Kt1 (úLWOLN HVDV DOÕQDUDN WUELQ HWNLQOLN
NDWVD\ÕVÕDQDOL]HGLOPLúWLU*oNDWVD\ÕVÕCP) ve
U]JDUKÕ]ÕQGDNL9GH÷LúLPLQWUELQLQHWNLQOLN
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|Qú
KÕ]Õ QG GHYGDN ȦG UDGV DOÕQDUDN
DQDOL]OHU JHUoHNOHúWLULOPLúWLU 9 PV
CP ROGX÷X GXUXPGD .t1 ROPDNWDGÕU
V=10 m/s, CP LoLQ .t1=0.36 olarak
EHOLUOHQLSU]JDUJFQQ¶VÕQÕQMHQHUDW|UH
LOHWLOGL÷LQLLIDGHHWPHNWHGLU
0,42
0,40
1 *
CP=0,35
0,38
CP=0,40
0,36
CP=0,45
0,34
CP=0,50
0,30
z=7
R=40 m
i=100
2
HG=1 rad/s
0,28
O
=0.98
d
0,32
K t1
D
D
D
D
D
L z
Š G=157 rad/s
0,26
0,24
0,22
0,20
mR=19500 kg
3
ˆ=1,2 kg/m
0,18
10
11
12
13
14
15
V (m/s)
D
ùHNLO)DUNOÕD
GH÷HUOHULQGHD¶GDNLGH÷LúLPLQ
ഥ ୋ ]HULQHRODQHWNLVL
మ
ùHNLO)DUNOÕCP GH÷HUOHULQGH9¶GHNLGH÷LúLPLQ
Kt1 ]HULQHRODQHWNLVL
78
Yatay eksenli U]JDUWUELQOHULQLQGLQDPLNGDYUDQÕúÕ-teorik bir model
.DQDW \DUÕoDSÕ 5 YH NDQDWODUÕQ NWOHVLQGHNL
(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] GúUG÷ J|UOPúWU PR=10500 kg,
5 PROGX÷XQGD ୲భ =0.37 iken; mR=19500 kg,
5 PROGX÷XQGD ୲భ ¶HGúPúWU ୲భ ¶LQ
PDNVLPXP ROPDVÕ LoLQ mR¶QLQ GúN YH 5¶QLQ
\NVHNROPDVÕLVWHQPHNWHGLU
'H÷LúLN NDQDW \DUÕoDSODUÕQGD 5 NDQDWODUÕQ
NWOHVLQGHNL PR GH÷LúLPLQ ୲మ ¶\H HWNLVL ùHNLO
¶GH J|VWHULOPLúWLU 5¶QLQ DUWPDVÕ\OD ୲మ ¶QLQ
DUWWÕ÷ÕPR¶QLQDUWPDVÕ\OD୲మ ¶QLQoRND]D]DOGÕ÷Õ
EHOLUOHQPLúWLU 5 P PR=19500 kg
DOÕQGÕ÷ÕQGD ୲మ =0.25 iken; R=40 m, mR=19500
NJDOÕQGÕ÷ÕQGD ୲మ 2 ROPDNWDGÕU0DNVLPXP
୲మ 2 LoLQ5!PROPDOÕYHPR LVHRODELOGL÷LQFH
GúNROPDOÕGÕU
5
5
5
5
5
5
5
5
. W
&3 Š * UDGV
ˆ NJP
ˆ NJP
Š * UDGV
P5NJ
ùHNLOR ve mR¶GHNLGH÷LúLPLQ୲మ
üzerine olan etkisi
P5NJ
ùHNLO)DUNOÕ5GH÷HUOHULQGHPR’deki
GH÷LúLPLQ୲భ üzerine olan etkisi
%HQ]HU úHNLOGH ୲మ 2 (úLWOLN HVDV DOÕQDUDN
WUELQHWNLQOLNNDWVD\ÕVÕDQDOL]HGLOHELOPHNWHGLU
(NVHQHO LQGNVL\RQ IDNW|U D YH DoÕVDO
LQGNVL\RQ IDNW|UQGHNL D
GH÷LúLPLQ ୲మ ¶\H
HWNLVL DQDOL] HGLOPLúWLU ùHNLO D¶GDNL DUWÕúÕQ
୲మ ¶\LGúUG÷D
¶GHNLDUWÕúÕQ ୲మ ¶\LDUWWÕUGÕ÷Õ
J|UOPúWU D D
ROGX÷XQGD
୲మ LNHQ D D
ROGX÷XQGD
୲మ 2 ¶HGúPúWU
0,45
0,40
0,35
.DQDWODUÕQ NWOHVLQLQ mR) 15000-19500 kg
DUDVÕQGDNL GH÷LúLPLQLQ ୲మ 1 ve ୲మ ]HULQH RODQ
HWNLVL LQFHOHQGL÷LQGH mR¶QLQ DUWPDVÕ\OD Kt¶QLQ
D]DOGÕ÷Õ J|UOPúWU PR NJ LoLQ
୲భ 1=0.358, ୲మ =0.352 iken; mR NJ LoLQ
୲భ 1=0.352, ୲మ =0.344 ROPDNWDGÕU. Referans
DOÕQDQ U]JDU WUELQL WHPHO E\NONOHUL
(mR=19500 kg, R PL LoLQ ୲మ 1=0.38,
୲మ RODUDNEXOXQPXúWXU%XGXUXPU]JDU
JFQQ 37-¶LQLQ MHQHUDW|UH LOHWLOHELOGL÷LQL
J|VWHUPHNWHGLU
Sonuçlar
0,50
a=0.2
a=0.3
a=0.4
a=0.5
<DSÕODQ DQDOL]OHU QHWLFHVLQGH
VRQXoODUDXODúÕOPÕúWÕU
z
V=10 m/s
R=40 m
i=100
2
H
=1 rad/s
G
0,30
K t2
D D
z
9 PV
L H
UDGV
*
O
G
O
G
z
9 PV
L H
UDGV
*
. W
P
P
P
P
P
P
P
P
0,25
x
O
=0.98
d
0,20
Š G=157 rad/s
0,15
mR=19500 kg
3
ˆ=1.2 kg/m
0,10
0,05
0,002
0,004
0,006
0,008
0,010
a'
ùHNLO)DUNOÕDGH÷HUOHULQGHD
¶GHNL
GH÷LúLPLQ୲మ üzerine olan etkisi
79
DúD÷ÕGDNL
Teorik modelH J|UH; go NDWVD\ÕVÕQGDNL
DUWÕúÕQ MHQHUDW|U JFQ oRN D] DUWWÕUGÕ÷Õ
D\QÕ Jo NDWVD\ÕVÕQGD Xo-KÕ] RUDQÕQGDNL
DUWÕúÕQ LVH MHQHUDW|U JFQ GúUG÷
EHOLUOHQPLúWLU $\UÕFD HNVHQHO LQGNVL\RQ
IDNW|UQGHNL DUWÕúÕQ ER\XWVX] MHQHUDW|U
JFQ GúUG÷ DoÕVDO LQGNVL\RQ
IDNW|UQGHNL DUWÕúÕQ LVH boyutsuz jeneUDW|U
JFQDUWWÕUGÕ÷ÕEHOLUOHQPLúWLU
M. C. ùenel, E. Koç
x 5HIHUDQV DOÕQDQ U]JDU WUELQi temel
E\NONOHUL PR=19500 kg, R=39.5 m,
L LoLQ ୲మ 1=0.38, ୲మ =0.37 olarak
EHOLUOHQPLúWLU .t GH÷HUOHUL OLWHUDWUGHNL &P
GH÷HUOHUL\OH NDUúÕODúWÕUÕOGÕ÷ÕQGD (CP=0.400.45); Kt¶QLQ &P¶GHQ NoN ROGX÷X
EHOLUOHQPLúWLU %X \]GHQ .t GH÷HUOHULQLQ
PDQWÕNOÕ ROGX÷X NDQÕVÕQD YDUÕOPÕúWÕU
*HOLúWLULOHQPRGHOLQ WUELQ WDVDUÕPÕLoLQHVDV
DOÕQDELOHFH÷L oRN LGGLDOÕ ROPDNOD ELUOLNWH
U]JDU WUELQ WHPHO E\NONOHULQLQ WDKPLQ
HGLOPHVL DoÕVÕQGDQ JHUoH÷H \DNÕQ ELU
\DNODúÕP J|VWHUPHNWHGLU %X QHGHQOH WHRULN
PRGHO WDVDUÕP LoLQ NXOODQÕODELOHFHN ELU
model olarak tavsiye edilmektedir.
Semboller
i
Șd
CP
ȡ
NJ
TJ
NG
TG
Șg
IG
R
TR
TS
Ȧ
ĮR
V2
IR
mR
VXo
NR
IHú
N
V
NE
Kt
Ȝ
ȦG
ĮG
dHYULPRUDQÕ
'LúOLYHULPL
: *oNDWVD\ÕVÕ
: Hava \R÷XQOX÷X (kg m-3)
: -HQHUDW|UJLULúJF:DWW
: JeneraW|UJLULúPRPHQWL1P
: -HQHUDW|UJF:DWW
: Jeneratör momenti (Nm)
: Jeneratör verimi
-HQHUDW|UQNWOHVHODWDOHWPRPHQWLNJP2)
: .DQDW\DUÕoDSÕP
: .DQDWODUGDROXúDQPRPHQW1P
: Kanatlardan DQDúDIWDDNWDUÕODQPRPHQW1P
: .DQDWODUÕQDoÕVDOKÕ]ÕUDGs-1)
: .DQDWODUÕQDoÕVal ivmesi (rad s-2)
.DQDWODUÕQKHPHQ|QQGHNLU]JDUKÕ]ÕPV-1)
.DQDWODUÕQNWOHVHODWDOHWPRPHQWLNJP2)
: .DQDWODUÕQNWOHVLNJ
.DQDWODUÕQXoKÕ]ÕPV-1)
: .DQDWODUWDUDIÕQGDQHOGHHGLOHQJo:DWW
: .WOHVHOHúGH÷HUDWDOHWPRPHQWLNJP2)
: 5]JDUJF:DWW
: 5]JkUKÕ]ÕPs-1)
5]JDUWUELQLHOHNWULNVHOJooÕNÕúÕ:DWW)
: 7UELQHWNLQOLNNDWVD\ÕVÕ
: Uç-KÕ]RUDQÕ
: YükseNKÕ]OÕúDIWÕQDoÕVDOKÕ]ÕUDGs-1)
: Yüksek KÕ]OÕúDIWÕQDoÕVDOLYPHVLrad s-2)
7HúHNNU
%X oDOÕúPD 2QGRNX] 0D\ÕV hQLYHUVLWHVL
3<208+¶ nolu proje ile destekOHQPLúWLU.
Kaynaklar
$WD 5 YH dHWLQ 16 N: RWRQRP ELU
U]JDU WUELQL NXUXOXPX YH HQHUML HOGHVL Gazi
hQLYHUVLWHVL 0KHQGLVOLN-0LPDUOÕN )DNOWH
Dergisi, 23, 1, 41-47.
(PQL\HWOL * (YVHO HOHNWULN LKWL\DFÕQÕQ
NDUúÕODQPDVÕ LoLQ U]JDU WUELQL WDVDUÕPÕ Yüksek
Lisans Tezi 7UDN\D hQLYHUVLWHVL )HQ %LOLPOHUL
(QVWLWV(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
WUELQOHULPHNDQLNWDVDUÕPHVDVODUÕYHSHUIRUPDQV
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]WUN ø YH dHOLN $ (2006). 'Q\D¶GD YH
7UNL\H¶GH U]JDU Hnerjisi NXOODQÕP Gurumu ve
gHOHFH÷H\|QHOLNEeklentiler, Atatürk Üniversitesi
Ziraat FakOWHVL'HUJLVL, 37, 2, 267-274.
ùHQHO 0 & (2012). 5]JDU WUELQOHULQGH Jo
iletim PHNDQL]PDODUÕQÕQWDVDUÕPHVDVODUÕ-dinamik
dDYUDQÕú <NVHN /LVDQV 7H]L 2QGRNX] 0D\ÕV
hQLYHUVLWHVL Fen BilimOHUL(QVWLWV6DPVun.
ùHQHO 0 & ve .Ro ( (2013). 5]JDU tUELQOHUL
dinamik dDYUDQÕú analizi-teorik boyutsuz bir
model, 2. Anadolu Enerji Sempozyumu, 301-313,
'L\DUEDNÕU
80
m
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Yatay eksenli rüzgar türbinlerinin dinamik