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Ofshore wind arm layout

optimization using mathematicalprogramming techniques

Renewable Energy Journal

EnvironmentalHydraulics Institute“IH!antabria”"#antander" #pain$

%eatriz &'rez" Roberto()nguez*" Ra*l+uanche

,ame- .ndre /elipe 0orres #enra

&roessor- Richard (ar1 /rench

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,ature o 0he &roblem

• Ofshore wind power is a renewable energy ogrowing relevance in current electric energysystems2

• &resenting avorable wind conditions incomparison with the sites on land2

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,ature o 0he &roblem

• However" the higher energy yield has tocompensate the increment in installation andmaintenance costs" thus the importance o

optimizing resources$

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3esign 4ariables

 0he e5act location coordinates o each turbine65i"yi72 ∨i 8 92$$$2, 0$ 0hese variables are

integrated into the variable decision vector 5:R,t5; 

as ollows-

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!onstraints

•  0he set o constraints determine which decisionsare admissible" i$e$ de

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!onstraints

• >ind arm area limits- 0urbines must be allocated to a prede

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ObAective /unction

• .nnual Energy &roduction 6.E&72• Equation which ta1es into consideration the

wa1e efects and allows quantiying the

bene

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#teps to #olve &roblem

• #tep 9- !ross sectionalarea intersection

• #tep ;- 3e

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#teps to #olve &roblem

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#teps to #olve &roblem

i7 0he starting points used toloo1 or conve5 subregions" ii7the local ma5ima and iii7 theglobal ma5imum$ ,ote that

although there is noguarantee that xB is the trueglobal solution" the chances o

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!onclusion

• In order to veriy the efectiveness a test wasperormed using the +erman ofshore wind arm.lpha 4entus" yielding an increment o the

e5pected annual power production o @$CDFcompared to the actual con