GHBladed282/BR/0091320054EABossanyiDVWitcherDCQuartonGarradHassanandPartners:::GHP:GH::©2005GarradHassanandPartnersLimitedGarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL-i-1.11.111.221.321.421.532.42.142.1.142.1.252.1.352.1.472.282.2.182.2.282.2.382.392.493.113.1113.1.1113.1.2133.2133.2.1133.2.2143.2.3153.3154.164.1164.1.1164.1.2164.1.3164.2174.2.1174.2.2174.2.3194.2.4204.3204.4214.522GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL-ii-5.235.1235.2235.2.1245.2.2245.3245.3.1255.3.2265.4275.4.1275.4.2275.5295.6295.7PI325.7.1335.8345.9345.10356.366.1Start-up366.2366.3376.4376.5376.6386.6.1386.6.2386.7Teeterrestraint397.407.1417.1.1417.1.2417.2417.2.1417.2.2427.2.3427.3427.3.1437.3.2447.4467.4.1467.4.23D467.4.3IEC467.5477.5.1vonKarman48GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL-iii-497.5.3Kaimal537.5.43548.558.1558.2568.2.1JONSWAP/Pierson-Moskowitz568.2.2568.3578.4578.5588.6588.7598.8608.8.1618.8.2618.8.3618.9628.10628.10.1Morison628.10.2629.649.1649.2649.36410.6610.16610.26610.36610.47010.57010.67110.6.17110.6.27210.77210.87310.97411.75GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL1of841.1.1GHBladed•••••◊◊◊◊◊•◊◊◊◊◊◊•◊◊◊◊◊◊◊◊◊()◊WORDGarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL2of841.2GarradHassanGHBladed•WEGMS-1,,1991•HowdenHWP300HWP330,,1993•ECN25mHAT,,1993•Newinco500kW,,1993•Nordex26m,,1993•NibeA,,1993•HolecWPS-30,,1993•Nordtank300kW,,1993•RivaCalzoniM30,,1993•Tjaereborg2MW,,1994•ZondZ-40,,1994•NordicWindPowerPrototype,,1995•Nordtank500kW,,1995•VestasV27,,1995•Danwin200kW,,1995•Carter300kW,,1995•NedWind1MW,,1995•WindMasterWM750-P750kW,,1995.GHBladed1.3GHBladed+44(0)1179729900+44(0)1179729901E-mailbladed@bristol.garradhassan.co.uk1.4GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL3of84GHBladed1.5GHBladedJOULEII,JOU2-CT92-0198.GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL4of842.Bladed[2.1]Bladed2.1Bladed2.1.1UdUoUaUdo=−()1aaPPAUaao=−2133ρ()ρATTAUaao=−212ρ()CPCTCPAUaaPo==−/()()123241ρCTAUaaTo==−/()()12241ρGarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL5of84a1/3CP16/27a1/2CT12.1.2QΩa’0rΩra’2Ωra’QRaaUo=−π41(),Ω2.1.3rdrdTdTWCCcdrLD=+122ρφφ(cossin)WφcCLCDCLVSL=/()122ρCDVSD=/()122ρLDSVrdrdQdQWrCCcdrLD=−122ρφφ(sincos)GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL6of842.1.12.1.2agg=+111/()agg,/()=−221gBcrCCFHLD1224=+πφφφ(cossin)singBcrCCFLD224=−πφφφφ(sincos)sincosBF2.1.4HaH≤=0353910.,.aHaaaa=−++0353941060610792.,()(...)a0.52.1.1CaaT=−41()CaaT=++060610792...Bladeda0.35390.5aa’aa’g1g2aa’aa’aa’Bladedaatolkk−≤−1GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL7of84aatolkk''−≤−1tol2.1.4aaFtFt1FtFtPrandtl[2.2],FtFsdt=−2ππarccos[exp()]sd0FhFFFth=2.1.3GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL8of842.22.2.12.2.2aUoa’rΩaa’2.2.340BladedPittPeters[2.3]Gaonkar[2.4]PittPetersBladedR1R2UodTdTUamUmaooA=+2&mmAaGarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL9of84mUadAo=−ρ()1dARTuckerman,[2.5]:mRA=833ρCaaURRRRaTo=−+−−4116323132212()()()&π2.3[2.6,2.7]Bladed2.4GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL10of84Beddoes[2.8]BeddoesHarris[2.9]Galbraith[2.10]BladedBeddoes[2.8]••KirchoffBladedGarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL11of843.70Bladed3.1FloquetBladed3.1.1.•ωi•ξiGarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL12of84•,φir()ii(kg/m)BladedBladedGarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL13of843.1.2(kg/m)3.2Bladed3.2.1Bladed•••GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL14of84••43.2.2&&&/qqqFMiiiiiii++=22ξωωqiMmrrdriirotor=∫()()φ2Ffrrdriirotor=∫()()φf(r)Bladed[]&&[]&[]MqCqKqF++=[M][C][K]qF•••GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL15of84•3.2.3-3.3GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL16of844.4.14.1.14.1.21-4.34.1.34.1.2GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL17of84-4.34.2•(),•()•()4.2.1hτQ&[()]QhQ=−−10τωωωω0hPrrr=−εωωω()0ωrPrωr=ω0(1+S/100)Sε4.2.2Bladed()4.1Rs=xs=Rr=xr=xm=C=Ra=Xa=GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL18of84xrxmRr/sRsxsCRaXa4.1:-4.44.1••••4.1[4.1]τ(s)(Rr/s)τω=−XXxXRsrmsrs2Xs=xs+xm,Xr=xr+xm,ωsrad/sX’=Xs-xm2/Xrεis(rs+jX’)=vs-εisvsψr11ωψψsrrrrsrijs()&+=−+s()irεψεrmrjxX=−TrjXrjXjsTjXXrjXvsssssss00&εωε=−++′−⎛⎝⎜⎞⎠⎟+−′+′GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL19of84TXrrsr0=ω.d-q()Park’s[4.2]3[4.3]xxxddtiixrjxsxrjxxrsxrjxxsxrjxxsiixxvsrmssrrsmmrmmsmssrsrsrrms−⎡⎣⎢⎤⎦⎥=−++−++−−+−+⎡⎣⎢⎤⎦⎥⎡⎣⎢⎤⎦⎥+−⎡⎣⎢⎤⎦⎥221111ω()()()()4.2.3QQsgde=+()1τQdQgτeBladed5sQgGarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL20of84QQsNumsDensgdeg=++()()()1τωNum(s)Den(s)4.2.4[4.3,4.4]4.2.1.(4.2.3)4.2.2PIPI4.24.2:–4.3PI1|I||I|GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL21of844.4()/LNεPePsPe=ε(Ps-LN)L(Ps)PsPePe=Ps-L(Ps)GarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL22of844.5(4.3PCC)4.3:R1+jX1R2+jX2()PCCGarradHassanandPartnersLtdDocument:282/BR/009ISSUE:013FINAL23of845.5.11.2.3.4.5.2GarradHassanandPartne