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Metaheuristics-based Optimal Management of Reactive Power Sources in Offshore Wind Farms Aimilia-Myrsini Theologi

Challenge(the(future(

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METAHEURISTICS,BASED!OPTIMAL!!MANAGEMENT!OF!REACTIVE!SOURCES!IN!

OFFSHORE!WIND!FARMS!!!

Master'thesis'

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Aimilia,Myrsini!Theologi!

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to#be#defended#publicly#on#Wednesday,#October#5,#2016#at#15:00#PM.#

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###########Supervisors:## Dr.#ir.#Jose#L.#Rueda#Torres,#TU#Delft## # # Mario#Ndreko,#PhD#Candidate,#TU#Delft#

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########Thesis#committee:## ########Dr.#ir.#Jose#L.#Rueda#Torres,#TU#Delft############################Prof.#ir.#Mart#A.M.M.#van#der#Meijden,#TU#Delft#

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The#MSc#thesis#project#conducted#in#the#framework#of#exchange#between#Delft#University#of#Technology#and# Aristotle# University# of# Thessaloniki# in# partial# fulfilment# of# the# requirements# for# the# Diploma# of#Electrical# and# Computer# Engineering.# The# diploma# certificate# is# given# by# Aristotle# University# of#Thessaloniki.##

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Faculty#of#Electrical#Engineering,#Mathematics#and#Computer#Science#(EEMCS)#·#Delft#University#of#Technology#

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Copyright#©#2016#Intelligent#Electrical#Power#grids#(IEPG)#

All#rights#reserved.#

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Acknowledgements !

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The! accomplishment! of! my! thesis! would! not! have! been! possible! without! the! contribution! of!numerous!people!around!me.!

First,! I! am! grateful! to! my! supervisor! in! Greece,! Georgios! Andreou,! because! without! his!support!I!would!not!have!been!able!to!conduct!my!thesis!abroad.!Second!and!foremost,! I!would!to!express!my!profound!gratitude! to!my!supervisor! in!TU!Delft,! Jose!Luis!Rueda!Torres,!who!gave!me!the! opportunity! to! work! on! this! really! challenging! topic! and! provided! me! with! everything! that! I!needed! to! complete! this! work.! His! continuous! optimism! concerning! this! project! was! challenging!myself!to!push!boundaries!and!his!useful!comments,!remarks!and!engagement!through!the!learning!process!of!this!master!thesis!was!invaluable.!

! My!sincere!appreciation!goes!also!to!the!PhD!student,!Mario!Ndreko,!for!his!contribution!and!support!in!the!second!part!of!my!thesis.!The!insightful!conversations!with!him!was!providing!me!new!ideas!and!useful!comments.!!

! My!friends!and!colleagues!from!the!office,!Adedotun,!Behzad,!Meng,!Chetan!and!Nishant,!for!their!support!and!the!moments!that!we!shared!together.!And!especially!my!friend!Digvijay!for!being!always!next!to!me!every!time!that!new!problems!were!coming!up!in!my!project.!Without!his!support!with!Python!and!PowerFactory,!this!thesis!would!have!never!been!completed.!

! !Laura,!Anastasia,!Marietta!and!Eva!for!being!always!next!to!me!since!the!beginning!of!time.!Maki!and!Gianni!for!supporting!me!these!months!even!when!it!was!not!easy.!

! My! entire! family,! for! their! irreplaceable! support! during! all! these!months! and!my! cousins,!Katerina! and! Chrysostomo,! for! believing! in! me! so! much.! Most! thanks! for! my! parents,! Lena! and!Dimitri,!firstly,!for!sponsoring!my!stay!and!education!in!Netherlands!and!mostly!for!their!emotional!support.!You!both!have!always!supported!my!vision!right!from!a!very!young!age!and!encouraging!me!in!all!of!my!pursuits.!Your!advice,!principles!and!motivations!inspiring!me!never!to!give!up!and!follow!my!dreams.!I!would!have!never!been!the!person!I!am!right!now!without!you.!!

! Finally,!this!work!is!dedicated!to!my!beloved!little!brother,!Sotiris,!whom!I!admire,!and!I!hope!my!concern!for!new!experiences!to!be!a!motivation!for!him!in!the!next!years.!

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Aimilia&Myrsini,Theologi,

Delft,,June,2016.,

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Μερικές φορές πρέπει να σηκώσεις το ανάστηµά σου σε κάτι µεγαλύτερο

από σένα – you must be a fighter –,για να σωθείς και για να καταφέρεις.

Στον αδερφό µου...

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Contents !

Abstract!...................................................................................................................................................!ii!

List!of!abbreviations!...............................................................................................................................!iv!

List!of!symbols!........................................................................................................................................!vi!

List!of!figures!........................................................................................................................................!viii!

List!of!tables!...........................................................................................................................................!ix!

1! Introduction!....................................................................................................................................!1!

1.1! Background!............................................................................................................................!1!

1.2! Problem!definition!and!analysis!.............................................................................................!2!

1.3! Objective!and!research!questions!..........................................................................................!2!

1.3.1! Research!aim!.....................................................................................................................!2!

1.3.2! Research!tasks!...................................................................................................................!2!

1.3.3! Research!questions!............................................................................................................!3!

1.4! Research!approach!................................................................................................................!3!

1.5! Outline!of!the!Thesis!..............................................................................................................!3!

2! Literature!review!.............................................................................................................................!6!

2.1! Overview!................................................................................................................................!6!

2.2! Wind!industry!.........................................................................................................................!6!

2.2.1! Wind!power!.......................................................................................................................!6!

2.2.2! Offshore!wind!power!.........................................................................................................!7!

2.3! Controllable!devices!...............................................................................................................!9!

2.3.1! Wind!Turbines!...................................................................................................................!9!

2.3.1.1! DFIG!Generator!Model!..............................................................................................!9!

2.3.1.2! Fully\Rated!Converter!Generator!Model!................................................................!10!

2.3.2! On\Load!Tap!Changer!......................................................................................................!10!

2.4! Interconnection!link!.............................................................................................................!11!

2.4.1! HVAC!Technology!............................................................................................................!11!

2.4.1! HVDC!Technology!............................................................................................................!12!

2.5! Wind!speed!prediction!.........................................................................................................!13!

2.5.1! Value!of!forecasting!.........................................................................................................!13!

2.5.2! Classification!of!forecasting!methods!..............................................................................!13!

2.6! Grid!code!requirements!.......................................................................................................!15!

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2.7! Optimal!Reactive!Power!Management!................................................................................!18!

3! NN\based!forecast!.........................................................................................................................!21!

3.1! Introduction!.........................................................................................................................!21!

3.2! Neural!Networks!..................................................................................................................!22!

3.2.1! Definition!.........................................................................................................................!22!

3.2.2! Usage!...............................................................................................................................!22!

3.3! Day\ahead!wind!speed!prediction!.......................................................................................!22!

3.3.1! NN!Structure!....................................................................................................................!22!

3.3.2! Implementation!in!MATLAB!............................................................................................!23!

3.3.3! Data!Partition!..................................................................................................................!25!

3.3.4! Evaluation!Criteria!...........................................................................................................!26!

4! Optimization!algorithm!.................................................................................................................!29!

4.1! Introduction!.........................................................................................................................!29!

4.2! Methodology!........................................................................................................................!29!

4.2.1! Definition!of!Objective!Function!......................................................................................!29!

4.2.1! Constraints!.......................................................................................................................!32!

4.3! MVMO!Procedure!................................................................................................................!32!

4.3.1! Flowchart!.........................................................................................................................!32!

4.3.2! Initialization!.....................................................................................................................!34!

4.3.3! Fitness!evaluation!and!local!search!.................................................................................!34!

4.3.4! Solution!archive!...............................................................................................................!34!

4.3.5! Offspring!generation!........................................................................................................!35!

4.4! Implementation!...................................................................................................................!37!

5! Results!...........................................................................................................................................!40!

5.1! Introduction!.........................................................................................................................!40!

5.2! Wind!Speed!Forecasting!......................................................................................................!40!

5.3! Optimal!Management!of!Reactive!Sources!..........................................................................!43!

5.3.1! Study!cases!......................................................................................................................!43!

5.3.2! MVMO!for!far!offshore!wind!farm!..................................................................................!43!

5.3.2.1! Case!1!......................................................................................................................!45!

5.3.2.2! Case!2!......................................................................................................................!46!

5.3.3! MVMO!for!Borssele!wind!farm!........................................................................................!48!

5.3.3.1! Case!3!......................................................................................................................!49!

5.3.3.2! Case!4!......................................................................................................................!51!

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5.3.3.3! Case!5!......................................................................................................................!52!

5.3.3.4! Case!6!......................................................................................................................!54!

5.3.3.5! Case!7!......................................................................................................................!56!

5.3.3.6! Case!8!......................................................................................................................!58!

5.3.1! Convergence!Behavior!of!MVMO!....................................................................................!59!

5.3.2! MVMO!Robustness!..........................................................................................................!61!

6! Conclusions!&!Future!Research!.....................................................................................................!63!

6.1! Introduction!.........................................................................................................................!63!

6.2! Conclusions!..........................................................................................................................!63!

6.3! Recommendations!on!future!research!................................................................................!64!

References!.............................................................................................................................................!66!

Appendices!............................................................................................................................................!71!

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Abstract !

Nowadays,! the! Transmission! System! Operators! (TSO)! of! each! country! have! defined! Grid! Code!Requirements! in! order! to! ensure! the! safe,! secure! and! reliable! operation! of! power! systems.!Traditionally,! the! optimal! reactive! power! management! sources! in! the! synchronous! transmission!systems!are!designed!for!operation!in!an!uncoordinated!manner,!i.e.!meeting!local!targets!as!seen!at!the!terminal!bus!of!each!device.!Although!the!reactive!power!requirement!at!the!point!of!common!coupling!(PCC)!can!be!achieved!without!major!drawbacks,!the!traditional!approach!mentioned!above!is! quite! conservative.! The! emerging! approach! involving! coordinated! management! of! reactive!sources,!however,!allows!the!achievement!of!several!operational!objectives,!such!as!minimum!power!losses! and! reduction! of! stress! or! disturbances! for! the! controllable! devices,! i.e.! transformers,!simultaneously.! The! existing! technologies! for! data! communication! and! acquisition! render! the!coordinated!planning! feasible.! Since,! reactive!power!management! appertains! to! the!mixed\integer!optimization! problem! with! restricted! computing! budget,! a! new! heuristic! algorithm! called! Mean\Variance!Mapping!Optimization!is!used.!

In!this!project,!two!different!approaches!for!the!optimal!dispatch!of!reactive!sources!are!suggested.!According!to!the!first!approach,!the!optimization!is!performed!for!every!current!operating!point!and!results!in!minimum!transmission!losses.!However,!the!cost!of!the!on\load!tap!changer!(OLTC)!is!not!considered.!In!order!to!solve!this!problem,!a!second!approach!is!proposed,!which!include!the!number!of! tap! changes! in! the! objective! function.! Besides,! the! optimization! is! performed! over! a! predicted!time! period! by! incorporating! with! a! wind! speed! forecasting! method,! which! is! based! on! neural!networks!(NN)!and!accounts!for!the!active!power!per!each!wind!turbine.!

Simulations!have!been! conducted! for! a! far\offshore!wind! farm! interconnected!with!HVDC! link!and!the!AC\connected!Dutch!near\shore!wind!farm!Borssele,!located!in!North!Sea.!Several!test!cases!have!been!investigated,!in!order!to!demonstrate!the!effectiveness!of!MVMO.!

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–,Index,Terms,–,

,optimal!reactive!power!management,!offshore!wind!farms,!mean5variance!mapping!optimization,!metaheuristic! optimization,! artificial! neural! network,! reactive! power! dispatch,! wind! speed!forecasting,!on5load!tap!changer!

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List of abbreviations !

!ABC! Artificial!Bee!Colony!Algorithm!AC! Alternating!Current!ACO! Ant!Colony!Optimization!AI! Artificial!Intelligence!AIS! Artificial!Immune!System!!ANFIS! Adaptive!Neuro\Fuzzy!Inference!System!ANN! Artificial!Neural!Network!AR! Autoregressive!ARIMA! Autoregressive!Integrated!Moving!Average!ARMA! Autoregressive!Moving!Average!BA! Bee!Algorithms!BFO! Bacterial!Foraging!Optimization!CAT! Centre!for!Alternative!Technology!COA! Chaotic!Optimization!Algorithm!CRO! Coral!Reef!Optimization!Algorithm!CS! Cuckoo!Search!Algorithm!DC! Direct!Current!DE! Differential!Evolution!ENTSO5E! European!Network!of!Transmission!System!Operators!for!Electricity!EOA! Evolutionary!Optimization!Algorithm!EP! Evolutionary!Programming!ES! Evolutionary!Strategy!EU! European!Union!FA! Firefly!Algorithm!FACTS! Flexible!Alternating!Current!Transmission!System!FL! Fuzzy!Logic!FWA! Firework!Algorithm!GA! Genetic!Algorithms!GSA! Gravitational!Search!Algorithm!HS! Harmony!Search!Algorithm!HV! High!Voltage!HVAC! High!Voltage!Alternating!Current!HVDC! High!Voltage!Direct!Current!!ICA! Imperialistic!Competition!Algorithm!IGBT! Insulated\Gate!Bipolar!Transistor!IWD! Intelligent!Water!Drops!Algorithm!LBBO! Linearized!Biogeography\based!Optimization!LCC! Line!Commutated!Converters!

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LCC5HVDC! High!Voltage!Direct!Current!based!on!Line!Commutated!Converters!LSSVM5GSA! Least!Squares!Support!Vector!Machine!and!Gravitational!Search!Algorithm!LV! Low!Voltage!MLP! Multilayer!Perceptron!!MOA! Magnetic!Optimization!Algorithm!MSP! Maritime!Spatial!Planning!MV! Medium!Voltage!MVMO! Mean\variance!Mapping!Optimization!!NFN! Neuro\Fuzzy!Network!NN! Neural!Network!NWP! Numerical!Weather!Prediction!OF! Objective!Function!OF! Objective!Function!OLTC! On\Load!Tap!Changes!OPF! Optimal!Power!Flow!ORPD! Optimal!Reactive!Power!Dispatch!ORPM! Optimal!Reactive!Power!Management!OTEP! Optimal!Transmission!Expansion!Planning!PCC! Point!of!Common!Coupling!PIO! Pigeon!Inspired!Optimization!PSO! Particle!Swarm!Optimization!PWM! Pulse!Width!Modulation!SA! Simulated!Annealing!SFLA! Shuffled!Frog!Leaping!Algorithm!SHWIP! Statistical!Hybrid!Wind!Power!SOA! Stochastic!Optimization!Algorithm!!STATCOM! Static!Synchronous!Compensator!SVC! Static!VAR!Compensator!SVM! Support!Vector!Machines!TLBO! Teaching\Learning!Based!Optimization!Algorithm!TS! Tabu!Search!Algorithm!TSO! Transmission!System!Operator!VSC! Voltage!Source!Converters!VSC5HVDC! High!Voltage!Direct!Current!based!on!Voltage!Source!Converters!WPP! Wind!Power!Plant!WTG! Wind!Turbine!Generator!ZCB2030! Zero!Carbon!Britain!2030!Project!AMAPE! Average!Mean!Absolute!Percentage!Error!MAPE! Mean!Absolute!Percentage!Error!RMSE! Root!Mean!Square!Error!MAE! Mean!Absolute!Error!

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List of symbols !

!",$! Total!real!power!losses!of!hour!t!

$! Hour!

%&,%', %(!Weight!coefficients!

)"*+,-.$,$! Total!operation!cost!of!the!OLTC!for!hour,t!

$/0*1! Tap!position!of!transformer!Tr!

2! Wind!turbine!radius!

34! Measured!wind!speed!of!the!studied!location!

+0! Power!coefficient!

5! Air!density!of!the!studied!location!

!! Active!Power!

6! Reactive!Power!

4.7! Mean!Square!Error!

8! Number!of!iterations!(epochs)!for!the!training!of!!NN!

$/197$:! The!target!value!for!iteration,i!for!the!training!of!!NN!

:;0<$:! The!input!value!for!iteration!i!for!the!training!of!!NN!

$/0$! Tap!position!of!hour!t,

$/0$=&! Tap!position!of!hour!t&1!

$/0*1,4:;! Minimum!Tap!position!of!transformer!Tr!

$/0*1,4/>! Maximum!Tap!position!of!transformer!Tr!

34:;! Minimum!voltage!magnitude!of!the!buses!

34/>! Maximum!voltage!magnitude!of!the!buses!

3! Voltage!magnitude!of!the!buses!

.4/>! Maximum!flow!limit!through!the!transmission!line!

.! Flow!through!the!transmission!line!

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????@A*B4:; ! Minimum!reactive!power!limit!of!WTG!

@A*B4/> ! Maximum!reactive!power!limit!of!WTG!

@A*B! Reactive!power!reference!of!WTG!

:! Current!flow!through!the!cables,!lines!and!transformers!

:4/>! Maximum!current!flow!through!the!cables,!lines!and!transformers!

>::;:$! Initial!candidate!solution!for!iteration!i!

>:4:;! Minimum!bound!of!the!decision!variable!x!

>:4/>! Maximum!bound!of!the!decision!variable,x!

C! Number!of!decision!variables!

D>! Output!of!mapping!function!for!x=xi*!

D&! Output!of!mapping!function!for!x=1!

DE! Output!of!mapping!function!for!x=0!

>:∗! Random!number!

>G! Mean!value!

>! Decision!variable!

.:,?.&,??.'! Shape!variables!

3:! Variance!

H.! Scaling!factor!

!4! Wind!turbine!mechanical!power!

I! Mathematical!constant!

2! Wind!turbine!radius!

5! Air!density!

+0! Power!coefficient!

34! Wind!speed!

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List of figures Figure,1:,Global,Wind,Power,Cumulative,Capacity,1996&2014,[6],.........................................................................,7!Figure,2:,Electricity,generation,by,technology,in,the,ZCB2030,scenario,.................................................................,8!Figure,3:,Typical,layout,of,a,DFIG,generator,model,................................................................................................,9!Figure,4:,Typical,layout,of,a,FRC&based,generator,model,.....................................................................................,10!Figure,5:,On&Load,tap,changer,..............................................................................................................................,11!Figure,6:,Economic,comparison,of,HVAC,and,HVDC,.............................................................................................,12!Figure,7:,Classification,of,wind,speed,forecasting,methods,..................................................................................,14!Figure,8:,Requirements,for,reactive,power,supply,in,several,voltage,levels,,without,active,power,limitation,.....,16!Figure,9:,Minimum,requirements,for,the,P/Q&operation,range,of,a,generation,unit,...........................................,16!Figure,10:,Grid,Code,Requirements,at,the,PCC,for,AC,connected,wind,farm,........................................................,17!Figure,11:,Reactive,power,capability,of,HVDC,station,..........................................................................................,18!Figure,12:,Classification,of,optimization,algorithms,according,to,the,under,laying,principle,..............................,19!Figure,13:,Multilayer,perceptron,...........................................................................................................................,23!Figure,14:,Work,flow,of,the,neural,network,design,process,.................................................................................,23!Figure,15:,Division,of,historical,data,.....................................................................................................................,26!Figure,16:,Predictive,control,optimization,by,MVMO,for,the,far,offshore,wind,farm...........................................,30!Figure,17:,Predictive,control,optimization,by,MVMO,for,the,Borssele,wind,farm,................................................,31!Figure,18:,MVMO&based,procedure,for,optimal,reactive,power,management,....................................................,33!Figure,19:,Solution,archive,....................................................................................................................................,35!Figure,20:,Variable,mapping,.................................................................................................................................,36!Figure,21:,Interaction,between,,MATLAB,,Python,and,DIgSILENT,PowerFactory,.................................................,37!Figure,22:,Wind,turbine,power,output,..................................................................................................................,38!Figure,23:,Wind,speed,for,July,..............................................................................................................................,41!Figure,24:,Wind,speed,for,October,........................................................................................................................,41!Figure,25:,Wind,speed,for,January,........................................................................................................................,42!Figure,26:,Wind,speed,for,April,.............................................................................................................................,42!Figure,27:,Far&offshore,wind,farm,layout,with,HVDC,interconnection,link,...........................................................,44!Figure,28:,Wind,speed,variation,–,Far,offshore,wind,farm,...................................................................................,44!Figure,29:,Aggregated,results,of,Case,1,................................................................................................................,46!Figure,30:,Aggregated,results,of,Case,2,................................................................................................................,47!Figure,31:,Borssele,wind,farm,layout,with,AC,cable,.............................................................................................,48!Figure,32:,Wind,speed,variation,–,Borssele,wind,farm,.........................................................................................,49!Figure,33:,Aggregated,results,of,Case,3,................................................................................................................,50!Figure,34:,Aggregated,results,of,Case,4,................................................................................................................,52!Figure,35:,Aggregated,results,of,Case,5,................................................................................................................,54!Figure,36:,Aggregated,results,of,Case,6,................................................................................................................,55!Figure,37:,Aggregated,results,of,Case,7,................................................................................................................,57!Figure,38:,Aggregated,results,of,Case,8,................................................................................................................,59!Figure,39:,Convergence,graphs,of,MVMO,............................................................................................................,60!Figure,40:,Time,series,and,bounds,of,the,the,fitness,function,value,.....................................................................,61!Figure,42:,Neural,network,training,window,in,MATLAB,toolbox,..........................................................................,77!Figure,43:,Performance,of,the,trained,neural,network,.........................................................................................,78!Figure,44:,Regression,plot,of,the,trained,neural,network,.....................................................................................,78!!

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List of tables Table,1:,Termination,criteria,for,the,training,of,the,neural,network,....................................................................,25!Table,2:,MVMO,parameters,..................................................................................................................................,34!Table,3:,Optimization,study,cases,.........................................................................................................................,43!Table,4:,Siemens,SWT&6.0&154,[58],.......................................................................................................................,73!Table,5:,Doubly,Fed,Induction,Generator,..............................................................................................................,74!Table,6:,Fully,Rated,Converter,wind,turbine,of,6,MW,–,Model,in,PowerFactory,.................................................,74!Table,7:,2&winding,Transformer,for,6,MW,DFIG,wind,turbine,(0.69/33,kV),.........................................................,74!Table,8:,2&winding,Transformer,for,6,MW,Fully,Rated,Converter,wind,turbine(0.69/66,kV),...............................,74!Table,9:,Available,training,algorithms,..................................................................................................................,76!!

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1!Introduction !

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1.1! Background!!Over!the!last!decades,!renewable!energy!sources!have!attracted!significant!interest.!!Wind!power!is!considered!as!the!leader!in!the!field!of!renewable!energy!industry,!since!the!use!of!wind!for!electrical!power! generation! is! rapidly! increasing.!However,! the!high!penetration!of! the!wind!power! into! the!energy! systems! holds! many! technical/operational! challenges,! which! require! further! analysis.! The!variability! and! uncertainty! issues! that! the! Transmission! System!Operators! (TSO)! are! facing! can! be!deal!with!accurate!wind!speed!forecasting!methods.!

By!examining!different!cases,!over!long!distances!the!AC!transmission!is!no!longer!possible!due!to!the!capacity!of!the!cable.!Thus,!for!the!interconnection!of!a!far!offshore!wind!farm!to!the!grid,!a!DC!link!is!essential.! DC! link! offers! various! advantages,! such! as! the! high! control! capability,! low! voltage! drops!and!losses.!Specifically,!the!grid!integration!via!high!voltage!direct!current!(HVDC)!based!on!voltage!source!converters!(VSC\HVDC)! !supposed!to!be!the!most!appropriate!solution!for!far!offshore!wind!power!plants![1].!!

In!power!system!operation,!apart!from!HVDC!link,!another!important!issue!that!should!be!taken!into!consideration! is! the! transmission! losses,! which! impacts! both! technical! (e.g.! voltage! profiles)! and!economic!(e.g.!costs)!aspects.! In!many!literatures!has!been!reported,!that!the!minimization!of!total!system! losses! is! a! necessity! and! can! be! achieved! with! appropriate!management! (i.e.! coordinated!operation)!of!controllable!devices.!!!!!

2!!

1.2! Problem!definition!and!analysis!!!Study!cases!regarding!two!different!offshore!wind!farms!are!the!subject!under!investigation!in!this!project.!Reactive!power!support!is!being!considered!as!part!of!the!grid!code!requirements!for!wind!farms! in!many!countries!worldwide![2].!However!the!high!penetration!of!the!wind!power! intro!the!energy!systems!holds!many!technical/operation!challenges,!which!require!further!analysis.!Offshore!wind!power!plants!are! required!to!provide!reactive!power!support!during!both!the!steady\state!as!well!as!during!AC!fault!conditions![3].!After!the!occurrence!of!system!contingencies,!such!as!the!loss!of! a! generator! or! a! transmission! line,! the! increased! current! flows! can! produce! greatly! increased!reactive! power! absorption! in! transmission! lines.! Although! the! production! cost! of! reactive! power!generation! is! non\existent,! the! insertion! of! transmission! losses! into! the! generation! influences! the!overall! cost.! Practically,! the! additional! current! flow,! which! is! associated! with! the! reactive! power,!causes! increased! losses! and! excessive! voltage! sags.! Thus,! the! reactive! power! dispatch! problem,!which! is! a! particular! form! of! optimal! power! flow,! affects! significantly! the! economical! and! secure!operation! of! power! systems! [4].! Consequently,! an! optimization! is! necessary,! in! order! to! solve! the!mixed\integer!non\linear!ORPDP.!!!

!!

1.3! Objective!and!research!questions!!

1.3.1! Research!aim!!The,aim,of,the,thesis,is,to,optimally,coordinate,the,reactive,power,sources,in,offshore,wind,farms,in,a,predictive, manner, based, to, the, principle, of, minimizing, the, wind, farm, power, losses,, as, well, the,variations, of, the, transformers, tap, positions., Optimal, Reactive, Power, Management, falls, into, the,category, of, complex, mixed&integer, optimization, problems,, since, the, parameters, to, be, optimized,,namely, the, reactive, power, reference, of, the, wind, turbines, and, the, transformers, tap, positions, are,continuous,and,discrete,variables,respectively.,Due,to,the,stochastic,nature,of,the,wind,,the,quality,of,the,optimal,solution, is, influenced,by,the,forecasting,error., In,addition,,this,research,project,aims,to,prove, the, ability, of, an, emerging, meta&heuristic, algorithm, namely,, the, mean&variance, mapping,optimization,algorithm, (MVMO), to, solve, this,problem, in, the,most, computationally, efficient,way, in,far&,and,,near&,shore,wind,farms.,

!

1.3.2! Research!tasks!!The!first!task,!which!has!to!be!accomplished,!is!the!formulation!of!the!ORPD!problem.!The!research!focuses!on!the!short\term!operational!planning!(e.g.!day\ahead!or!intra\day).!Then,!an!accurate!wind!speed!forecasting!method!for!the!considered!time!is!developed!in!order!to!sample!the!future!values!of!wind!speed!within!acceptable! tolerance!errors! (e.g.! indicate!a! reference!value!of! tolerance!with!citation! of! the! corresponding! reference)! and! finally,! the! optimal! management! of! the! available!reactive! sources! is! tackled! by! MVMO.! By! addressing! the! aforementioned! tasks,! the! research!questions,!defined!in!the!next!subsection,!will!be!answered.!

3!!

1.3.3! Research!questions!!The!main!research!questions!can!be!formulated!as:!!

Q1)!How!the!wind!speed!forecasting!can!be!incorporated!in!the!formulated!Optimal!Reactive!Power!Management?!Q2)!How!the!available!reactive!power!sources!can!be!optimally!coordinated!in!offshore!wind!!!!power!plants?!!Q3)! How! the! computational! efficiency! can! be! ensured! in! solving! the! problem! of! Optimal!Reactive!Power!Management?!

The!aforementioned!research!questions!will!be!answered!throughout!the!following!chapters!of!the!thesis,!whose!structure!is!presented!in!Section!1.5.!

!

1.4! Research!approach!!In!the!current!project,!a!short\term!wind!speed!forecasting!method! is!developed!to!be!used! in!the!ORDP!problem.!A!stochastic!technique!is!essential!for!deriving!the!time!series!and!modeling!the!wind!speed,! since! typically! the! length! of! wind! data! sets! is! short.! The! method,! mentioned! above,! is!implemented!in!MATLAB.!!

However,! the! essence! of! this! research! is! the! Optimal! Reactive! Power! Management,! in! order! to!support! reliability! and! expedite! the! transactions! across! networks.! Reactive! power! control! is!indispensable! for! voltage! control! and! flow!of! active!power! through! the! transmission! systems.! This!problem!will!be!addressed!with!a!recently!introduced!evolutionary!algorithm,!which!is!performed!for!the!optimal!control!of!the!reactive!power!in!offshore!WPPs.!The!influence!of!the!number!of!on\load!tap! changes! of! the! transformers! is! also! investigated.! For! the! optimal! distribution! of! the! reactive!sources,!the!Grid!Code!Requirements!at!the!PCC!are!also!considered.!!In!order!to!include!also!a!set!of!future!operating!points!for!a!given!time!horizon,!the!optimization!must!be!performed!in!a!predictive!manner,!while!definitely!the!short\term!prediction!of!active!power!outputs!is!required!in!parallel![5].!!

A!software!based!platform!for!automated!calculations,!e.g.!forecasting,!power!flow!calculations!and!iterations!via!optimization!algorithm!is!built!by!creating!special!routines/scripts!in!MATLAB!R2015b,!Python!3.5!and!DIgSILENT!PowerFactory!2016.!!

!

1.5! Outline!of!the!Thesis!!Chapter!2! includes! the! literature! review! related! to!wind!power,!offshore! installations,! controllable!devices,!HVDC!transmission!systems!and!Grid!Code!Requirements.!Wind!speed!forecasting!methods!and!the!ORPDP!are!briefly!described!as!well.!!

Chapter! 3! provides! the! theoretical! background! and! the! methodology! that! is! used! for! the!development!of!the!preferred!wind!power!forecasting!method.!The!implementation!of!the!method!in!MATLAB!is!also!described.!

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!Chapter!4!describes!the!problem!formulation!and!the!function!of!MVMO.!!Additionally,! it!presents!the! tuning! of! MVMO! in! Python! and! illustrates! the! implementation! of! the! overall! optimization!method!in!DIgSILENT!PowerFactory.!!

Chapter!5!presents!the!results!of!the!wind!speed!prediction!tool,!as!well!the!performance!of!MVMO!in!the!two!different!offshore!wind!farms!under!investigation.!In!this!chapter,!the!results!derived!from!the!comparison!between!the!different!cases!for!each!type!of!wind!power!plant!are!also!analyzed.!!

Finally,!in!Chapter!6!the!conclusions!drawn!from!the!results!are!discussed!and!recommendations!for!follow\up!research!are!proposed.!

!

! !

5!!

! !

6!!

!

!

!

!

2! Literature review !

!

2.1! Overview!!A! selection!of! topics! related! to!wind!energy,!optimization!and!wind!prediction! is!presented! in! this!literature! review.! Section! 2.2! begins! with! the! current! situation! of! wind! industry! in! offshore!installations.!Hereafter,!Section!2.3!presents!the!controllable!devices!used!in!the!project.!Section!2.4!introduces! the!different! technologies!used! for! the! interconnection!of!offshore!wind! farms.!Section!2.5!describes!the!value!of!the!wind!power!forecasting!and!the!currently!available!models!and!Section!2.6! refers! to! the! Grid! Code! Requirements! regarding! the! steady! state! operation! in! offshore! wind!farms.! Finally,! Section! 2.7! presents! the! ORPD! problem! and! a! review! on! the! different! types! of!optimization!algorithms.!!

!

2.2! Wind!industry!

2.2.1! Wind!power!!Wind!energy!is!widely!accepted!as!the!most!promising!energy!source!of!the!21st!century,!since!it!is!an! inexhaustible,! cost\effective,! environmentally! friendly! and! domestic! source.! While! the! whole!world!is!facing!problems,!such!as!global!warming!and!greenhouse!effect,!the!necessity!for!clean!and!renewable!energy!sources!is!growing.!The!limited!natural!resources!and!increasing!power!demand!of!industrial! society! have! created! an! energy! crisis,! thus! energy! sources! for! better! present! and! future!have! become! imperative.! According! to! statistics,! wind! is! the! fastest\growing! renewable! energy!source!and!recently!had!yet!another!record\breaking!year.!In!2015,!which!is!characterized!as!“stellar”!year! for! the! energy! revolution,! the! wind! industry! has! widened! significantly,! bringing! the! global!installed!capacity!close!to!433!GW,!since!more!than!63!GW!of!new!wind!power!was!brought!on!line!in!a!single!year.!!Fig.1!confirms!the!rapidly!increasing!global!wind!power!capacity.!!

7!!

!Figure,1:,Global,Wind,Power,Cumulative,Capacity,1996&2014,(Figure,created,by,author,from,data,in,

source,[6]),

!

2.2.2! Offshore!wind!power!!During!the!last!years!the!wind!industry!has!further!developed!with!offshore!installations,!which!refer!to! the! construction! of!wind! farms! in! large! bodies! of!water.!Offshore!wind,! often! described! as! the!“energy!of!the!future”,!is!a!competitive!power!source!and!an!increasingly!attractive!investment!with!stable! income! returns,! that! provides! various! benefits! in! electric! power! generation.! The! rapid!evolution! of! the! offshore! installations! is! not! accidental,! because! over! the! sea! surface! higher! and!more! persistent! wind! speeds!with! lower! disturbance! can! be! found,! which! leads! to!more! efficient!operation!of!wind!turbines.!Furthermore,!offshore!WPPs!reduce!the!visual!impact!for!the!shore!and!generally,!they!are!ideal!for!countries!where!the!mainland!is!limited!compared!with!the!sea.!

Europe!is!considered!as!the!front\runner!in!this!field,!since!has!had!wind!steel!in!water!for!over!two!decades!and!after!2012!has!been!growing!at!gigawatt!levels.!With!the!first!offshore!wind!farm!being!installed!in!Denmark!in!1991,!nowadays!more!than!91%!of!all!offshore!installations!can!be!found!in!European!waters! in!11!different! countries,!mainly! in! the!North!Sea,!Baltic! Sea!and!Atlantic!Ocean.!The!remaining!9%!of! the! installed!capacity! is! located! in!China,! followed!by!Japan!and!South!Korea.!According!to!European!statistics,!UK!has!the!largest!amount!of!installed!offshore!wind!representing!45.9%!of!all!installations;!Germany!follows!with!29.9%,!Denmark!with!11.5%,!Belgium!with!6.5%!and!Netherlands!with!3.9%![9].!!

The! wind! energy! penetration! levels! can! be! calculated! using! average! capacity! factors! onshore! or!offshore! and!electricity! consumption! figures.! The!outstanding!3,018.5!MW!of! new!offshore!power!capacity! connected! to! the! grid! during! 2015! in! Europe,! corresponds! to! an! increase! of! 108.3%!over!2014!and!the!biggest!yearly!addition!to!capacity!to!date![7].!At!the!end!of!2015,!the! installed!wind!power!capacity!could!produce!315!TWh,!enough!to!cover!11.4!%!of!the!EU’s!electricity!consumption,!of!which!1.5!%!comes! from!offshore!wind.!The!currently! installed!offshore!wind!power!capacity! in!

8!!

Europe! is! approximately! 11! GW,!while! six! other! offshore!wind! projects! are! under! construction! or!only!partially!connected!to!the!grid.!Once!completed,!the!Europe’s!cumulative!capacity!derived!from!offshore!installations!would!be!12.9!GW![8].!In!Fig.2!the!project!“ZeroCarbonBritain2030”!(ZCB2030)!of!Centre!for!Alternative!Technology!(CAT)!is!presented,!which!aims!to!the!change!of!Britain’s!energy!technology!for!the!elimination!of!carbon!dioxide!emissions![9].!

!

!

!!

Figure,2:,Electricity,generation,by,technology,in,the,ZCB2030,scenario,(Figure,created,by,author,from,data,in,source,[10]),

!!The!prevalent!situation!in!the!energy!market!requires!the!consolidation!of!a!European!transnational!offshore! grid,! in! order! to! integrate! the! envisaged! 150! GW! of! offshore! wind! power! by! 2030! and!ensure!Europe’s!energy!security.!The!perspective!of!such!an!offshore!grid!will!increase!the!security!of!supply!and!contribute!the!further!market! integration!and!enhancement!of!competition![11].!A!step!above!would!be!Maritime!Spatial!Planning!(MSP)!in!order!to!optimize!the!integration!of!wind!farms!into!the!marine!environment!and!to!provide!stability!for!the!investors![12].!!

Apart!from!the!advantages,!offshore!wind!power!poses!some!challenges,!such!as!the!interconnection!link! from! offshore! WPPs! to! the! grid! and! the! cost\minimization! of! the! turbine! installations.! The!paramount! issue! that! should! be! taken! into! consideration! in! this! case,! is! the! determination! of! the!electricity!production! for! the!adequate! integration!of!wind!energy! into! the!grid.! !The!dynamic!way!that!wind!interacts!with!the!waves!and!the!laminated!marine!boundary!layer,!combined!with!the!sea!surface!roughness,!create!special!requirements!as!far!as!the!wind!speed!forecasting!concerned.!For!this!reason,!the!short\term!prediction!methods!applied!until!now!to!onshore!wind!farms!should!be!adapted!to!the!specific!circumstances!of!offshore!installations.!Subsequently,!a!brief!analysis!of!the!available!wind!speed!forecasting!methods!for!any!kind!of!installation!is!presented.!

!

9!!

2.3! Controllable!devices!!

2.3.1! Wind!Turbines!!A!review!regarding!the!wind!turbines!types!is!presented!as!a!precursor!to!the!comprehension!of!wind!farm’s!connection!to!the!transmission!system.!In!comparison!with!onshore!turbines,!several!factors!affect! the! design! of! the! offshore! wind! turbines,! such! as! the! wave\induced! loads,! which! have!significant!impact!on!offshore!platforms.!The!most!important!requirement!of!offshore!technology!is!the! construction!of! larger! turbines!with! the! concurrent!decrease!of! costs.! The!wind! turbine! types,!used!in!this!project,!belong!to!the!variable!speed!wind!turbines!(VSIG)!and!are!extensively!described!in!the!following!sections.!!

!

2.3.1.1! DFIG!Generator!Model!!!The!most!widespread! type!of! this! technology! is! the!Double!Fed! Induction!Generator! (DFIG),!which!offers!higher! reactive!power!regulation!ability!and!better!voltage!control.!For! the!operation!of! this!type!of! turbines!power!electronic!converters!essential! [13].!Due! to! the!utilization!of! the!machine’s!turn!ratio,!the!converter!is!required!to!be!rated!for!the!machine’s!partial!rated!power.!While!the!line!side! converter! (LSC)! keep! the!DC\link! constant,! the! rotor! side! converter! (RSC)! equips! the!machine!with!active!and!reactive!power!control.!The!additional!freedom!of!reactive!power!generation!by!RSC!is!usually!used!more!preferable.!However,! it! is!possible! to!control!LSC,!within! the!available!current!capacity,!to!be!involved!in!reactive!power!generation!during!steady!state.!It!is!worth!mentioning,!that!current! DFIG! wind! turbines! are! capable! of! providing! the! necessary! Grid! Code! Requirements! for!support!to!the!grid.!!

!

!Figure,3:,Typical,layout,of,a,DFIG,generator,model,[14],

10!!

2.3.1.2! Fully5Rated!Converter!Generator!Model!!!As!presented!in!the!following!figure,!the!turbine!is!mechanically!coupled!to!the!rotor!of!a!high\pole!permanent! magnet! synchronous! machine! (PMSM).! Voltage! source! converters! and! a! step\up!transformer!is!used!for!the!connection!of!PMSM!stator!winding!with!the!grid.!The!controller!on!the!machine!side!(MSC)!provides!machine!speed!control!according!to!the!maximum!power!point!tracking!(MPPT)!algorithm.!On!the!other!hand,!for!both!voltage!regulation!of!the!DC\link!at!its!set\point!and!control! of! reactive! power! exchange! between! the! grid! and! the! wind! generator,! the! network\side!converter!(NSC)!is!used.!

!

!Figure,4:,Typical,layout,of,a,FRC&based,generator,model,[14],

!In! the! most! popular! control! method! for! FRC\based! generators,! a! two\level! cascade! controller! is!implemented,! where! the! DC\link! voltage! and! reactive! power! set\points! are! compared! to! the!measured!values.!For!processing!the!resulting!error!two!PI!compensators!are!used.!

!

2.3.2! On5Load!Tap!Changer!!The!OLTC!of!power! transformers!has!been!proven! to!have!a! fundamental! importance!as!a!voltage!regulating!mechanism.!The!switching!principle!is!that!the!turn!ratio!of!a!transformer!can!be!changed!by!adding! to!or! subtracting! turns!either! the!primary,!or! the! secondary!winding.!As! indicated!by! its!name,!changing!the!tap!position!is!possible!only!when!the!power!transformer!is!carrying!load.!In!the!case! of! transformers! equipped! with! OLTC! the! wind! farm! voltage! can! be! controlled! within! the!available!range.!

The!OLTC!can!be! located!at! the!primary!or! the! secondary! side!of! the! transformer,!although! in! the!most!case!the!variable!tap!is!on!the!HV!side![15].!One!reason!for!this!choice!is!that!the!current!on!the!HV! side! is! lower,! and! consequently! the! commutation! easier.! In! addition,! the!more! turns! that! are!available! in! this! side! enable! a! more! accurate! voltage! regulation.! The! following! figure! shows!graphically!one!type!of!on\load!tap!changing!transformer.!!

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!

Figure,5:,On&Load,tap,changer,(Figure,created,by,author,from,data,in,source,[15]),

!One! important! constraint! is! the! finite! number! of! tap! positions! existing! in! the! device.! Thus,! the!voltage!regulation!is!restricted!to!a!range!defined!by!the!lower!and!the!upper!voltage!limit.!Typical!values!of!the!lower!limit!are!from!0.85!\!0.90!p.u.!and!for!the!upper!limit!1.10!\!1.15!p.u.!

The!strong!fluctuations,!characterizing!the!wind!speed,!require!more!frequent!change!of!the!reactive!sources! optimal! settings.! As! a! result,! the! OLTC! have! to! be!more! frequently! regulated! in! order! to!maintain!the!voltage!profiles!between!the!acceptable!range.!This!leads!to!an!increased!operation!and!maintenance! cost! of! the! transformers.! Consequently,! the! limitation! of!OLTC! operations! number! is!including!in!the!presented!approach.!!

!

2.4! Interconnection!link!!

2.4.1! HVAC!Technology!!The! transmission! system! of! the! generated! energy! from! the! offshore! wind! farm! to! the! mainland!constitutes!an!important!challenge.!The!fluctuation!of!the!transmitted!energy!requires!a!flexible!and!reliable! system,! which! will! overcome! the! difficulties! of! the! installation,! regarding! the! cables!impregnation!and!the!submarine!connections.!!An!HVAC!system!represents!a!possible!solution,!which!nevertheless! leads! to! deadlock! [16].! The! conventional! HVAC! technology! introduces! a! simple! and!economically! feasible! connection! type! for! an!offshore!wind! farm!and!has!been!adopted! in! several!projects.! However,! HVAC! are! faced!with! difficulties! and!may! be! limitative! in! case! of! large! and! far!offshore! installations,!due!to! installations!costs!and!high!losses.!The!aforementioned!constrains!are!based!on!the!concurrent!decrease!of!the!transmission!capability!with!the!produced!reactive!power!and! the! distance! [17].! In! this! case,! reactive! power! compensators,! such! as! SVCs! or! STATCOMs,! are!placed!near! the! shore! for!high!quality! supplied!power!and! the!obstruction!of!high\order!harmonic!penetration!into!the!grid.!Consequently,!as!far!as!the!transmission!link!to!the!shore!concerned,!the!attention!turns!to!HVDC!technology,!which!offers!various!connection!options.!

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2.4.1! HVDC!Technology!!With!respect!to!the!AC!link,!the!DC!link!provides!fast!active!and!reactive!power!control,!low!voltage!drops! and! losses! for! long! distances! and! zero! production! of! charging! currents.! Additionally,! the!connection! of! asynchronous! AC! networks! becomes! feasible! and! the! resonance! between! the! ac!equipment!and!the!cables!is!insignificant.!Thus,!for!the!optimal!management!of!electrical!grids,!HVDC!transmission!systems!are!requisite![18].!In![17]!the!comparison!of!HVAC!and!HVDC!in!terms!of!total!costs!is!stated!and!the!results!are!presented!in!the!figure!below.!

!

Figure,6:,Economic,comparison,of,HVAC,and,HVDC,changer,(Figure,created,by,author,from,data,in,source,[19]),

!Concerning!the!HVDC!transmission,!there!are!two!different!connection!types!for!offshore!wind!parks:!LCC\HVDC! and! VSC\HVDC.! LCC! refers! to! the! “classic”! HVDC! system,! which! is! using! thyristors! as!primary! components! and! requires! an! existing! AC! network! for! commutation.! Although,! this!technology! allows! asynchronous! connection! and! power! magnitude! control,! an! ancillary! start\up!system! is! imperative! from! an! offshore! perspective.! Other! restrictions,! such! as! AC! grids! with!determinate!reactive!power!compensation!and!short!circuit!capacity,!disqualify!LCC\HVDC!for!large\scale!wind!farms![20].!

The! most! bleeding\edge! technology! to! overcome! the! grid! integration! problems! in! offshore! wind!farms!is!the!VSC\HVDC,!which!is!named!by!ABB!manufacturers!as!“HVDC!Light”![21].!In!this!case,!the!thyristors!have!been!replaced!with!fully\controlled!IGBTs!with!high\frequency!PWM!operation,!which!leads!to!lower!harmonic!content!and,!consequently,!to!reduced!size!of!filters.!This!technology!lacks!an!extra!compensating!equipment!and!is!able!to!operate!in!weak!networks,!since!active!and!reactive!power! are! independently! controlled.! An! additional! advantage! is! that! the! compact! and! lightweight!VSC\HVSC! converter! stations! enable! smaller! and! cheaper! offshore! platform! size.! Ultimately,! VCS\HVDC! converters! are! appropriate! for! isolated! operation! and! for! creating! a!multi\terminal! DC! grid![20].! For! long\distance! installations,! the! HVDC! Light! Cable! System! is! presented! in! [22],! which! has!thinner! insulation,! offers! higher! power!density! and! is! suitable! for! both! land! and! submarine! cables!

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[23].! ! The! major! disadvantage! of! the! aforementioned! technology! is! the! higher! switching! losses!caused!by!the!high\frequency!PWM![20].!!!

It!is!worth!mentioned,!that!when!a!cable!reaches!a!certain!length,!the!value!of!the!capacitance!is!so!large! that! the! cable’s! impedance! can! be! considered! purely! capacitive,! since! the! cable! has! a! large!capacitance!per! length!unit.! In!such!case,!the!cable!provides!only!reactive!power,!due!to!the!phase!shift!between!the!voltage!and!the!current.!The!possible!length!of!the!cable!can!be!made!longer!with!phase!compensation! in!both!ends!of!the! line.!By!using!HVDC!for!this!purpose,!no!reactive!power! is!produced!or!consumed!in!the!cables.!This!means,!that!all!of!the!cable’s!transfer!capacity!can!be!used!to!transfer!active!power.!!

!

2.5! Wind!speed!prediction!!

2.5.1! Value!of!forecasting!!Wind! power! is! a! fluctuating! source! of! electric! energy,!with! variations! related! to! the! temperature,!pressure,!and!season,!characteristics!of!the!surface!and!the!rotation!of!earth.!From!the!comparison!of!wind!power!with!other!energy!sources!turns!out!that!the!main!difference!is!the!stochastic!nature!of!wind,!hence!wind!speed!forecasting!is!beneficial!for!the!optimal!operation!of!a!power!system.!In!many!applications,!when!disturbances!in!power!quality!or!supply!occur,!wind!power!forecast!reduces!the!risk!of!uncertainty.!Thus,!when!we!have!to!choose!the!best!option!between!the!maximization!of!reliability! and! minimization! of! operating! costs,! an! accurate! wind! forecast! helps! to! overcome! this!doubt! and! contributes! to! better! grid! planning.! Furthermore,! it! reduces! the! need! of! additional!balancing! energy! and! reserves! power! to! integrate! wind! power.! The! accuracy! of! wind! forecast!contributes!to!the!increase!of!wind!power!penetration!and!the!reduction!of!the!reserve!capacity.!!If!the! total! output! of! WPPs! can! be! predicted! with! high! accuracy,! more! useful! information! can! be!provided!and!help!in!scheduling!power!generation![5].!!!

!

2.5.2! Classification!of!forecasting!methods!!Extensive! research! has! been! conducted! up! to! the! present! for! predicting! the! wind.! Based! on! the!existing!mathematical!models,!the!wind!forecast!can!be!broadly!classified!in!persistence,!statistical,!physical,! spatial! correlation,! artificial! intelligence! and! hybrid! methods! [24].! The! wind! speed!forecasting!methods! can! be! also! described! in! terms! of! different! time\scales;! very, short&term! (few!minutes!to!1!hour),!!short&term!(1!hour!to!several!hours),!medium&term!(several!hours!to!1!week)!and!long&term! (1!week!to!1!year!or!more!ahead)! [25].!The!high! integration!of!the!wind!energy! into!the!power!system!and!the!necessity!for!reactive!power!planning!sighted!the!research!towards!the!short\term!prediction.!

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Figure,7:,Classification,of,wind,speed,forecasting,methods,changer,(Figure,created,by,author,from,data,in,source,[24]),

!The!persistence,method! constitutes! the! simplest! and!most! economical! solution,!which! is! based!on!the! assumption! that! at! a! specified! future! time! the! wind! speed! will! be! identical! as! during! the!formation!of!the!prediction!model![24].!Statistical,methods!refer!to!time!series!analysis!approaches,!such!as!AR![26],!ARMA!and!ARIMA![24],!which!take!advantage!of!the!interrelationship!between!the!predicted!and!the!actual!wind!data.!In![27]!it!is!observed!that!autoregressive!models!are!inexpensive!and!can!be!easily!formed,!although!prediction!accuracy!and!time!horizon!are!inversely!proportional.!In!physical,methods,!it!usually!involved!numerical!weather!prediction!(NWP),!particularly!appropriate!for! long\term! forecasts! and! as! source! data! in! other! prediction! methods! [28].! By! virtue! of! high!computation!time!and!information!acquisition!difficulties,!the!short\term!wind!prediction!is!beyond!reach! [27].! Additional,! the! dependency! of! NWP! models! on! several! factors,! such! as! orography,!roughness! and! obstacles! [29],! reduces! the! accuracy! in! case! of! complex! terrain! or! locations! with!instability!under!extreme!weather!conditions![27].!!

On! the! other! hand,! artificial, intelligence, methods! show! remarkable! effectiveness,! since! they! can!provide!average!or!peak!wind! speeds!over! short!periods.!ANNs!constitute!a!data\driven!approach,!which!could!deal!with!non\linear!and!complex!problems!in!terms!of!forecasting.!Although!they!don’t!require!absolute!detection!of!weather!dynamics!and!are!accurate!enough! for! short! forecast! times,!over!a!year!of!training!data!is!indispensable!for!learning!seasonal!patterns!![25],![30].!

To! overcome! this! problem,! Support! Vector! Machines! with! highly! competitive! performance! in!numerous! real\world! applications! have! been! developed.! A! SVM\based!method! uses! regression! in!order! to! increase! the! confidence! interval! of! learning! [8]! and! conduces! to! the! remarkable!minimization! of! the! structural! risk! [31].! However,! the! fact! of! solving! a! quadratic! programming!problem! leads! to! complex! computations!and! constitutes! the!main!obstacle!of! the!described!mode![32].! In! [33]! the! SVM\enhanced! Markov! model! is! presented,! which! refers! to! a! “non\parametric”!distributional! forecast,! which! deals! with! wind! ramps! and! takes! into! account! the! diurnal! non\stationarity! of! wind! generation.! In! addition,! the! offline! training! of! the! aforementioned! model!reduces!the!computational!complexity!and!achieves!higher!accuracy.!Eventually,!in!order!to!achieve!higher!prediction!precision!for!short!times!the!LSSVM\GSA!model!has!been!developed.!In!comparison!with!ANN!and!the!other!SVM!models,!LSSVM\GSA!reduces!the!computation!time!of!model! learning!by! solving! a! linear! system! and! increases! the! correlation! coefficient! value,! despite! its! highly!

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dependence!on!the!selection!of!the!kernel!function!and!its!parameters![32].!Regarding!to!short\term!prediction,!the!FL!methods,!NFNs!and!EOAs,!are!also!thoroughly!analyzed!in![25]!and![34].!ANFIS! is!also!another!AI!method,!which! is! introduced!in![25]!for!the! interpolation!of!the! invalid!and!missing!wind!data.!

Finally,!the!object!of!the!hybrid,methods!is!the!combination!of!different!approaches,!although!in!this!case!the!complexity! is! increasing.!Recently,!a!new!method!called!SHWIP!proposed!the!combination!of!dynamic!clustering!with!linear!regression.!The!major!advantage!of!this!model!is!the!need!for!less!amount!of!historical!data!in!comparison!with!ANN!and!SVM![35].!

Conclusively,!some!of!the!selection!criteria!for!the!most!accurate!wind!forecast!method!are:!

!! stability!on!extreme!weather!conditions!!! minimization!of!structural!risk!!! less!computation!time!and!low!computational!complexity!!! considering!the!diurnal!non\stationarity!and!the!seasonality!of!wind!generation!!! less!amount!of!historical!data!!! dealing!with!wind!ramp!dynamics!!

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2.6! Grid!code!requirements!!!The! term! grid! code! is! largely! interwoven! with! the! electricity! transmission! systems.! Grid! codes!determine!the!responsibilities!and!obligations!of!the!transmission!system!(or!distribution!network),!to! which! power! producers! and! electricity! consumers! are! connected.! The!main! objective! is! to! set!requirements,! which! the! network! shall! fulfil! to! ensure! the! overall! system! performance! from! both!technical!and!economical!point!of!view.!In!Europe,!a!catholic!network!code!is!adopted,!which!refers!to!the!entire!European!grid!and!gives!guidelines,!according!to!which!the!grid!codes!of!all!European!countries!should!be!harmonized.!These!requirements!have!been!defined!by!the!European!Network!of!Transmission!System!Operators!for!Electricity!(ENTSO\E)![36].!Depending!on!the!specific!features!of!each! network,! the! characteristics! of! the! code! applied! in! every! region! can! possibly! differ! for! each!country.!

The! increasing! penetration! of! wind! energy! in! power! systems! contributed! to! the! development! of!codes!provide!that!WPPs!should!no!longer!be!involved!in!the!regulation!of!the!networks!in!a!manner!similar!to!that!of!conventional!plants.! !These!codes!refer!to!both!the!contribution!of!wind!farms! in!the!control! system!and!the!desired!response! in!case!of!disturbance!on!the!network! that! farms!are!connected.!Some!of!the!technical!requirements,!for!wind!farms!interconnected!in!the!system,!are!the!ability!to!remain!connected!to!the!grid!for!specific!boundaries!of!voltage!and!frequency!for!as!long!as!it! is! necessary,! the! control! of! voltage! and! reactive! power! and! their! involvement! in! regulating!frequency!through!variation!of!the!generated!active!power.!The!operators!demand!the!adjustment!of!reactive!power! at! the!point! of! common! coupling! (PCC)!not!only! in! fault!mode,! but! also! in! steady\state!operation.!Fig.8!shows!that!the!wind!farm!produces!and!consumes!reactive!power,!in!over\!and!under\! excited!mode! respectively.! Consequently,! by! controlling! reactive! power! the! grid! voltage! is!also!controlled.!

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!Figure,8:,Requirements,for,reactive,power,supply,in,several,voltage,levels,,without,active,power,

limitation!changer,(Figure,created,by,author,from,data,in,source,[37]),

!Nowadays,! the! TSOs! have! included! in! the! grid! codes,! specifications! related! to! the! widespread!development! of! the! offshore! wind! installations,! which! are! similar! to! onshore.! According! to! the!requirements,!which! TenneT! TSO! has! determined! for! offshore! grid! connections,! a! generation! unit!consists! of! a! single!wind! energy! turbine!with! the! corresponding! generator,! generator! transformer!and!busbars!in!the!turbine!tower.!The!following!P/Q\operation!range!as!represented!by!Fig.9,!applies!for! the! static! operation! of! the! respective! generating! units.! This! specification! is! valid! within! the!voltage!variation!range!of!+/\!5%!of!the!nominal!voltage.!The!values!of!the!active,!reactive!power!and!voltage!refer!to!the!low!voltage!side!of!the!machine!transformer.!Shortening!is!allowed!beyond!the!defined!voltage!variation!range!in!case!of!founded!technical!restrictions!at!the!generating!unit.!!

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Figure,9:,Minimum,requirements,for,the,P/Q&operation,range,of,a,generation,unit,changer,(Figure,created,by,author,from,data,in,source,[38]),

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In!order!to!influence!the!reactive!power!throughout!the!grid,!the!offshore!wind!farm!grid!connection!system! mandated! some! reactive! power! capabilities.! In! the! case! of! a! near\shore! wind! farm,!connected!with!AC!cable,!these!requirements!are!presented!in!Fig.10.!The!reactive!power!capabilities!are! valid! for! both!offshore! and!onshore!PCC,!which! refers! to! the!busbar! on! the!offshore!platform!!and!the!onshore!grid!connection,!respectively.!Under!normal!conditions!the!vertical! line!at!0!MVar!according! to! Fig.10!must!be! followed.!On!demand!of! the!onshore!grid!owner,!we!must!be!able! to!absorb!or!inject!the!reactive!power,!determined!by!the!graph!below.!The!offshore!wind!turbines!are!expected!to!contribute!to!the!fine!regulation!of!reactive!power!at!both!PCC!with!+/\!0.1!p.u.!

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Figure,10:,Grid,Code,Requirements,at,the,PCC,for,AC,connected,wind,farm(Figure,created,by,author,from,data,in,source,[39]),

!In!the!case!of!DC!interconnection,!which! is!also!elaborated!in!the!present!project,!the!most!special!feature!is!the!necessity,!that!the!HVDC!station!shall!be!capable!to!provide!reactive!power!even!in!the!case!of!the!maximum!active!power!exchanging!with!the!network!at!each!connection!point.!In!order!to! respond! to! these! particularities,! ENTSO\E! published! a! draft! network! code! [39],! which! refers!exclusively!in!HVDC!interconnections!and!in!generation!units!that!are!connected!via!HVDC!systems!to!the! grid.! The! requirements! referring! to! voltage! stability,!which! the!HVDC! station! shall! fulfil! at! the!PCC,!are!presented!in!the!Fig.11.!For!voltage!range!of!0.85!to!1.15!p.u.!the!ratio!of!the!reactive!power!and!the!maximum!capacity!shall!not!exceed!the!following!envelope.!

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Figure,11:,Reactive,power,capability,of,HVDC,station,changer,(Figure,created,by,author,from,data,in,source,[39]),

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2.7! Optimal!Reactive!Power!Management!!A!particular! form!of!optimal!power! flow!(OPF)!and!a!subject!of! remarkable!research! is! the!optimal!reactive!power!dispatch!(ORPD)![40],!which!has!immense!significance!on!the!security!and!economical!operation!of!the!power!systems![41].!The!ORPD!refers!to!a!non\linear,!mixed\integer!programming!problem![42],![43]!and!consists!of!the!control!of!generators!output,!shunt!reactors,!FACTS!devices!,!transformer!tap!settings!and!other!reactive!sources![4],![40],![41],![43],![42],![44].!!

The!ORPDP!is!decisive!for!the!operation,!power!system!control!and!optimization!of!wind!farms![2].!In!order!to!solve!this!problem!mathematically!various!optimization!algorithms!have!been!developed.!In![45]–[47]! the! application! of! classical! gradient\based! algorithms! in! different! ORPD! problems! is!described.! Although! the! previous!mentioned! techniques! have! a! reduced! computational! time,! they!struggle! with! nonlinear! and! non\convex! problems! characterized! by! discontinue! and! multimodal!landscape! [48].! Conclusively,! the! classical! optimization! tools! are! not! flexible! to! be! applied! in! high!dimensional! search! space! and!are! sensitive! to! the! initial! points! as!well! [49].! In!order! to!overcome!these! disadvantages! in! solving! the!ORPDP,! the! research! interests! focus! on!metaheuristic! solutions!due!to!their!conceptual!simplicity,!easy!adaptability!and!reduced!human!intervention.!

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Figure!12:!Classification,of,optimization,algorithms,according,to,the,under,laying,principle,(Figure,created,by,author,from,data,in,source,[50]),

Eventually,! algorithms! such!as! genetic! algorithm! (GA)! [51],! differential! evolution! (DE)! [52],! particle!swarm!!optimization!(PSO)![53],!evolutionary!programming!(EP)![54],!bacterial!foraging!optimization!(BFO)![55],!ant!colony!optimization!(ACO)![56]!and!bee!algorithm!(BA)![57],!have!been!developed!and!implemented!for!reactive!power!optimization.!!

The!capability!of!these!algorithms!in!overcoming!the!aforementioned!disadvantages!is!contradicted!by! the!high!dependence!of! their! searching!performance!on!proper!parameter! settings.! In!order! to!avoid! unwanted! occurrences,! such! as! local! stagnation! or! premature! convergence,! this! reliance!should!be! taken! into!consideration! [48],! [49].!As!a! result,!nowadays,!new!metaheuristic!algorithms!are! emerging,! for! instance! mean\variance! mapping! optimization! (MVMO)! [58],! linearized!biogeography\based! optimization! (LBBO)! [59],! firework! algorithm! (FWA),! firefly! algorithm! (FA),!cuckoo! search! (CS)! [60],! bat! algorithm! [61]! and! teaching\learning\based! optimization! (TLBO)! [62].!Despite! the! advantages,! the! performance! of! these! techniques! by! evolving! a! set! of! candidate!solutions! within! a! relative! large! number! of! fitness! evaluations,! entails! a! tremendous! computing!effort.! This! owed! to! ! the! computationally! intensive! computer! simulations,!which! the!evaluation!of!the! fitness! associated! to! each! candidate! solution! usually! requires.! Thus,! an! optimization! tool! that!performs!successfully!within!a!limited!number!of!function!evaluations!is!essential.!

The! comparisons! between! MVMO! and! the! other! evolutionary! algorithms,! in! power! systems!optimization!problems,!prove!the!enhanced!performance!of!MVMO,!in!terms!of!convergence!speed.!This! is!mainly!attributed!to!the!so\called!mapping!function!evolutionary!operator,!which!adaptively!switches! the!search!priority!between!exploration!to!exploitation!according!to!recorded!statistics!of!the!evolved!best!solutions!so!far!in!a!continuously!updated!“solution!archive”!(i.e.!adaptive!memory).!In!Chapter!4,!the!theoretical!background!behind!MVMO!and!the!implementation!of!the!optimization,!is!further!analyzed.!

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3! NN-based forecast !

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3.1! Introduction!!!The!estimation!of!the!wind!energy!output!requires!configuration!procedures,!the!implementation!of!which! is! facilitated! by! the! use! of! statistical! methods.! Consequently,! the! highly! volatility! and! non\linearity!of!a!signal,!such!as!wind,!leads!to!a!non\linear!power!curve!for!every!wind!farm.!Thus,!the!identification!problem!of!wind!power!is!comprised!of!the!appraisal!of!the!remarkable!wind!behavior,!and!the!correlation!of!this!behavior!to!the!corresponding!output.!In!comparison!with!other!methods,!the!ANNs! can!work! in! a! non\linear!way!with!better! performance,! by! virtue!of! their! propensity! for!storing!the!aforementioned!knowledge!and!rendering!it!available!for!use.!

ANNs!are!strictly!based!on!the!historical!time\series!of!the!problem!and!are!capable!to!describe!the!relation!between! input!and!output,! including!unidentified!cases.!Nevertheless,! for! their! training,! in!order! to! achieve!optimum!efficiency,! there! is! requisition! for! large! amount!of!data.!During! the! last!years,!ANNs!have!been!proven!as!an!excellent!prediction\simulation!tool!and!they!have!been!used!successfully! in! many! comparable! problems.! Before! analyzing! the! methodology! adopted! for! the!development!of!the!current!model,!it!is!appropriate!to!refer!concisely!to!the!theoretical!background!of!the!ANNs!and!the!particular!networks!implemented.!

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3.2! Neural!Networks!!

3.2.1! Definition!!!ANNs!refers!to!an!information!processing!paradigm!inspired!by!the!way!that!the!biological!nervous!systems! work.! The! novel! structure! of! their! information! system! constitutes! the! keystone! of! this!mechanism.! They! consist! of! a! large! number! of! highly! interconnected! processing! elements,! called!neurons,! which! are! performing! in! concert! to! solve! specific! problems.! Due! to! their! attribute,! for!learning!by!example,!they!are!configured!through!a!learning!process!!for!a!specific!application,!such!as! pattern! recognition! or! data! classification.! Similar! to! the! biological! systems,! ANNs! involve!adjustments!to!the!existing!synaptic!connections!between!the!neurons.!

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3.2.2! Usage!!Some! of! the! main! advantages! of! neurons! are! the! large! degree! of! interconnection,! the! massive!parallelism,!the!non\linear!proportional!feedback,!as!well!their!learning!ability.!The!variability!of!the!adaptive! weights,! i.e.! the! connection! strengths! between! the! neurons,! constitutes! a! memory!representation! and! enables! the! storage.! Self\organization,! generalization! and! the! ability! to! derive!meaning! from! complicated! or! imprecise! data,! belong! to!major! properties! of! NN.! Additionally,! the!large!amount!of!processing!units,! locally! interconnected,! confers! robustness!and! fault! tolerance! to!the!network.!In!the!case!of!NN,!some!capabilities!may!be!retained!even!with!major!network!damage,!despite! the! fact! that! partial! destruction! of! a! network! leads! to! the! corresponding! degradation! of!performance.!!

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3.3! Day5ahead!wind!speed!prediction!!

3.3.1! NN!Structure!!Existing! types! of! layered! NN! consists! of! neurons! arranged! in! different! layers.! A! multilayer! feed!forward! neural! network! is! used! for! the! wind! speed! prediction! model! developed! in! the! current!project.!The!network!architecture!is!defined!as!follows:!the!input!and!output!layer,!and!one!hidden!layer!in!between.!The!benefit!of!the!hidden!layer!presence!is!the!improved!accuracy!of!the!network,!by! increasing! computations! and! enabling! more! complex! operations.! It! is! indicated,! that! a! feed!forward! type!of!network!permits!only!unidirectional!data! flow! from! the! input! to! the!output! layer,!without!feedback!connections.!Each!neuron!can!be!identified!with!a!simple!logistic!regression,!whose!input!values!are!weighted!with!the!appropriate!weights,!subsequent!to!their!import.!Ultimately,!the!output!is!resulting!from!a!sigmoid!transfer!function,!in!which!the!summation!of!the!weights!and!bias!is!used!as!input.!!

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Figure,13:,Multilayer,perceptron,

In!order!to!find!the!structure!of!the!network,!which!leads!to!the!most!accurate!results,!the!following!tests!were!made:!

!! re\initialization!and!re\training!!! increase!the!number!of!hidden!neurons!!! different!training!functions!!! additional!training!data!

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3.3.2! Implementation!in!MATLAB!!

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Figure,14:,Work,flow,of,the,neural,network,design,process,

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Step!1:!Data!Collection!

The! wind! speed! time\series! of! one! year! is! considered! as! input! data! for! the! development! of! the!method!and!is!collected!from!the!experimental!wind!farm,!Sotavento,!located!in!the!north\west!part!of!Europe,!in!Galicia,!Spain.!Specifically,!the!historical!data!cover!the!period!from!31!December!2012!–!31!December!2013!(366!days).!

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Step!2:!Network!Creation!

!In!order!to!build!the!neural!network,!the!available!function!of!the!toolbox!for!network!formation!was!used.!The!selection!of!NN!structure!in!Section!3.3.1! led!to!the!creation!of!a!two\layer!feed\forward!network.!

!Step!3:!Network!Configuration!

!After!the!creation!of!the!NN,!it!must!be!configured.!The!configuration!was!done!manually!by!using!a!function,!which!examines! input!and!target!data.!Therefore,! the!network! input!and!output!sizes!are!set!to!match!the!data.!Finally,!the!optimal!settings!for!input!and!output!processing!have!been!chosen!in!order!to!achieve!better!performance!for!the!network.!

!Step!4:!Weights!&!Biases!Initialization!

!Before! training! the! network,! weights! and! biases! must! be! initialized,! whose! values! are! updated!according!to!the!network!initialization!function,!which!is!used.!Since,!a!back\propagation!network!has!been!created,!the!weights!and!bias!for!every!layer!are!initialized!using!the!Nquyen\Widrow!method[].!

!Step!5:!Network!training!

!For! the! training! process! a! set! of! data! is! required,! representative! of! proper! network! behavior!required,!i.e.!inputs!and!target!outputs.!For!multilayer!networks!the!general!practice!is!to!first!divide!the!data!into!three!subsets.!!

The!first!subset!is!the!training!set,!which!is!used!for!the!computation!of!the!gradient!with!!the!back\propagation! algorithm! and! the! updating! of! the! optimal! weights! and! biases.! Then,! validation! set!constitutes!the!second!subset,!which!leads!to!the!selection!of!the!optimal!network!architecture.!The!network! parameters,! such! as! the! number! of! hidden! units,! ! are! tuned! ! and! finally,! the!weight! and!biases!are!saved!at!the!minimum!of!the!validation!set!error.!The!error!on!the!validation!is!monitored!through! the! training! process.! The! third! is! the! test! set,! which! is! not! used! during! the! training,! but!contributes! to! the! comparison! of! different! trained!models.! An! approach! regarding! the! division! of!data!suggested!for!the!optimal!network!training!is!further!analyzed!in!Section!3.3.3.!

In! this! case,! the! training! is! implemented! in! batch! mode,! which! means! that! all! the! inputs! of! the!training! set! are! applied! to! the! network! before! the! weights! are! updated.! In! contrast! with! the!incremental!mode,!batch!training!is!significantly!faster!and!produces!smaller!errors.!Additionally,!the!training! process! involves! the! tuning! of! weights! and! biases! for! the! optimization! of! network!performance,! as! defined! by! the! mean! square! error! (MSE)! performance! function.! The! following!equation!represents!the!average!squared!error!between!network!inputs!and!target!outputs.!

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4.7 = ? &8 $/197$: − :;0<$: '8

:L&???????????????????(NO. 1)#

In!Neural!Network!Toolbox!software!various!training!algorithms!are!available,!which!use!gradient\!or!Jacobian\based!method.!In!terms!of!speed,!the!Leven\Marquardt!and!the!Quasi\Newton!method!are!the!most!efficient!for!small!networks.!Both!training!functions!have!been!used!in!the!forecasting!tool.!

The!criteria!to!be!satisfied!for!the!termination!of!the!training!are!the!number!of!validation!checks!and!the! magnitude! of! the! gradient.! The! validation! checks! represent! the! successive! iteration! that! the!validation! performance! failed! to! decrease.! Concerning! the! gradient,! as! the! training! reaches! the!minimum!of!the!performance,!it!becomes!very!small.!In!the!following!table,!the!criteria!used!to!stop!the!network!training!are!listed:!

!Table,1:,Termination,criteria,for,the,training,of,the,neural,network,

Description! Value!Minimum!Performance!Value! 0.001!

Maximum!Number!of!Training!Epochs! 1500!Maximum!Number!of!validation!Increases! 6!

Minimum!gradient!magnitude! 1e\5!!

!Step!6:!Network!validation!

Once! the! training! is! complete,! the! network! performance! is! checked!with! validation! process! (post\training! analysis).! At! this! step,! any! possible! changes! regarding! the! training! process,! the! network!architecture!or!the!data!sets!are!made.!

!Step!5:!Network!testing!

After!the!network!is!trained!and!validated,!the!network!object!can!be!used!to!calculate!the!network!response!to!any!input.!In!our!case,!a!vector!with!the!wind!speed!measurements!from!the!previous!24!hours!are!given!as! input! to! the! trained!network,! in!order! to!predict! the!hourly!wind!speed! for! the!next!day.!!

!

3.3.3! Data!Partition!!In! order! to! obtain! the!most! possible! cases,! included! in! the! input! sample,! the!widespread!method!applied!so!far,! is!based!on!the!increase!of!the!amount!of! input!data.!However,!due!to!the!different!characteristics,! which! wind! speed! displays! between! one! year! or! another,! this! method! is!controversial.!For!more!apprehension!of!the!wind!speed!data!characteristics!for!the!input!year,!less!amount!of!input!data!will!be!used!for!the!prediction!tool.!Therefore,!just!one!year!of!historical!data!is!used!as!input!and!the!dataset!is!divided!into!days.!

!

26!!

!

The!input!year! is!divided!into!two!different!parts!for!the!training!and!validation!of!the!NN!method,!respectively.! Due! to!wind! variations! between! the! four! seasons! of! the! year,! it! is! essential! that! the!prediction!tool!will!capture!all!these!particularities.!Finally,!a!new!approach!is!adopted!in!the!current!project,! in!order!to!fully!exploit!the!historical!data!and!consider!all!the!days!of!the!year.!Finally,!we!choose!to!create!two!new!datasets!from!the!input!year!for!training!and!validation,!with!data!size!of!one!year!each.!This!is!achieved!by!using!the!division!presented!in!Fig.15,!where!the!1st!day!is!chosen!for!training!and!the!2nd!day!for!testing,!afterwards!the!2nd!day!and!the!3rd!day!for!training!and!testing,!respectively!and!so!on.!It!should!be!mentioned!that!each!day!corresponds!to!a!vector!of!24!values,!since!the!historical!data!consists!of!hourly!wind!speed!measurements.!The!best!results!were!achieved!with!five!hidden!artificial!neurons!in!the!hidden!layer.!

!

!

Figure,15:,Division,of,historical,data!

!

3.3.4! Evaluation!Criteria!!!!In! order! to! evaluate! the! accuracy! of! the! trained! neural! network,! it! is! necessary! to! calculate! the!forecasting!error!and!compare!the!results!between!different!proposed!prediction!tools.!In!this!case,!we!use!three!different!error!measurements.!!!The!root!mean!square!error!(RMSE)!is!used!as!error!metric!in!wind!speed!forecasting!and!is!defined!as!follows:!

STUV = 124 YZ,[\] ^ − YZ,_`ab ^

ccd

]Le

e/c

????????????(Eq. 2)!

!The!second!criteria,!which!is!used,!is!the!mean!absolute!error!(MAE)!given!by!the!following!equation:!

TiV = 124 YZ,[\] ^ − YZ,_`ab ^

cd

]Le????????????????????????????????(Eq. 3)!

!

27!!

The!most!frequently!used!evaluation!criteria!is!the!mean!absolute!percentage!error!(MAPE):!

!

TikV = 124

YZ,[\] ^ − YZ,_`ab ^YZ,[\] ^

cd

]Le?????????????????????????????????(Eq. 4)!

!However,!because!in!the!case!of!wind!speed!forecasting!at!some!periods!close!to!zero!values!occur,!which! result! to! infinite!MAPE.!For! this! reason,!a!modified!version!of!MAPE! is!used.!This!method! is!called!average!mean!absolute!percentage!error! (AMAPE)!and!takes! into!consideration!the!mean!of!wind!speed!values.!The!definition!of!AMAPE!is!given!by!the!following!equation:!

!

iTikV? % = 124

YZ,[\] ^ − YZ,_`ab ^YZ,[\]mnopmqo

cd

]Le????????????????????????(Eq. 5)!

!

sℎuvu,???????????????????YZ,[\]mnopmqo =124 YZ,[\] ^

cd

wLe??????????????(Eq. 6)!

!

!

!

!

!

! !

28!!

! !

29!!

!

!

!

!

!

!

4! Optimization

algorithm !

4.1! Introduction!!Chapter!4!laid!the!groundwork!for!the!first!objective!of!the!approach!proposed!in!this!project,!since!the!methodology!and! the! implementation!of! the!wind!speed!prediction! tool!was!described.! In! this!chapter,!the!optimization!method!is!explained,!which!is!the!second!objective!of!the!thesis!after!the!development!of!an!accurate!wind!forecaster.!The!process!of!optimization!problems!consists!of!two!different! steps:! the! mathematical! formulation! of! the! problem! and! the! determination! of! the!optimization!algorithm.!Subsequently,!in!the!following!sections,!first!the!problem!is!stated!and!then,!the!optimization!algorithm!MVMO!further!analyzed,!as!well!its!implementation.!

!!

4.2! Methodology!!

4.2.1! Definition!of!Objective!Function!!ORPDP! refers! to! the! minimization! or! maximization! of! an! objective! function! with! one! or! several!variables,! which! are! defined! as! design! variables! and! take! actual! or! integer! values.! In! the! current!project,!for!solving!the!problem!the!following!formulations!have!been!adopted:!!

!

30!!

!!(a)!Optimization!for!the!current!operating!point!

The!optimization!task!aims!to!the!minimization!of!the!total!transmission!losses!in!the!system!and!the!formulation!of!the!objective!function!is!presented!below.!!

yz{zyz|u?????????}~ = k�,], ???^ = 1,2, … ,24???????????????(Eq. 7)##########!

!(b)!Optimization!for!a!predicted!time!horizon!

!In!this!approach,! the!optimization! is!performed!for!a!given!scenario,!which! includes!a!set!of! future!operating!points!on!a!24\hour! time!horizon! [53].!The!predictive! control! for! the! two!different!wind!farms!is!performed!as!detailed!below.!First,!the!wind!speed!scenario!for!the!considered!time!period!results!directly!from!the!NN\based!wind!speed!forecasting!method,!described!in!Chapter!3.!MVMO,!as!the!optimization!algorithm,!receives!the!wind!speed!prediction!for!24!time!steps!ahead!as!input.!Then,! the! optimal! power! flow! program! suggests! the! optimal! OLTC! tap! settings! together! with! the!optimal!reactive!power!reference!for!each!wind!turbine!of!the!wind!farm!for!the!next!24!time!steps.!In!Fig.16! the! approach! is! presented! for! the! far! offshore!wind! farm!case!with!maximum!generated!capacity!288!MW.!MVMO!in!this!case!optimizes!the!reactive!power!set\points!of!the!wind!turbines!and!the!tap!positions!of!the!two!offshore!transformers.!

!Figure,16:,Predictive,control,optimization,by,MVMO,for,the,far,offshore,wind,farm,(Figure,created,by,

author,from,data,in,source,[63]),

!

31!!

Additionally,!Fig.17!describes!the!aforementioned!approach! in!the!case!of!Borssele!wind!farm!with!maximum!generated!capacity!700!MW.!MVMO!in!this!case!optimizes!the!reactive!power!set\points!of!the!wind!turbines!and!the!tap!positions!of!both!offshore!and!onshore!transformers.!

!!Figure,17:,Predictive,control,optimization,by,MVMO,for,the,Borssele,wind,farm(Figure,created,by,

author,from,data,in,source,[63]),

!The!stochastic!nature!of!the!wind!poses!a!serious!problem!to!the!reactive!power!management!of!the!wind!farms.!In!contrast!to!the!traditional!reactive!power!dispatch!in!transmission!grids!the!update!of!optimal!settings!of!reactive!sources!is!required!more!frequently.!As!a!result,!in!order!to!maintain!the!voltage!profiles!within!acceptable!or!optimal!range,!OLTC!have!to!be!more!frequently!regulated.!This!increases! the! operation! and!maintenance! cost! of! the! transformers.! For! this! reason,! in! the! second!case!the!problem!is!formulated!as!a!multi\objective!function!as!shown!in!(2),!although!the!problem!is!treated!as!single!objective!due!to!the!use!of!the!weight!coefficients.!

yz{zyz|u???????????}~ = ? se ∙ k�,] + sc ∙ }ÑÖÜ\áà],]cd

]Le??????????????????? Eq. 8 !

sℎuvu,????????????}ÑÖÜ\áà],] = sä ∙ ^ãå?] − ^ãå?]=e ???????????????????????????????(Eq. 9)!

!!While! the! internal! voltage! profiles! shall! be! kept! within! acceptable! ranges,! the! significance! of! the!minimum!gained!!value!of!the!objective!function!is!twofold:!!

!! Operation!of!the!wind!farm!with!minimum!losses!and!number!of!tap!changes.!!! Meeting!the!Grid!Code!Requirements.!

!

32!!

!!

4.2.1! Constraints!!

Eventually,!the!generic!formulation!of!the!problem!in!both!approaches!is!stated!as!follows:!

Min.,,,,,,Objective,Function,(OF),

!!!!Subject!to,,,,,,Technical,Constraints,

!!!! !!!!and!search!space!given!by,,,,,,Bound,Constraints,

,

The!bounds!on!the!decision!variables!include!the!wind!turbines!Var!settings!and!the!transformers!discrete!tap!change!limits.!!They!have!the!form!described!in!the!following!equations:!

????éèêqZëí ≤ éèêq ≤ éèêq

Z[î??????????????????????(Vé. 10)??#

^ãåê`,Zëí ≤ ^ãåê` ≤ ^ãåê`,Z[î??????(Eq. 11)!

The!system!operating!constraints!constitute!the!inequality!constraints!on!the!dependent!variables!such!as!the!voltage!magnitude!of!the!buses,!current!through!the!cables,!line!and!transformer!flow!limits.!They!have!the!form!described!in!the!following!equations:!!

YZëí ≤ Y ≤ YZ[î??????????????????????(Eq. 12)#

z ≤ zñëZ?????????????????????????????????????????(Eq. 13)##

ó ≤ óñëZ???????????????????????????????????????(Eq. 14)#

!!

4.3! MVMO!Procedure!!

4.3.1! Flowchart!!So! far,!MVMO!has! been! applied! on! several! optimization! problems,! such! as!ORPDP,!OTEP! and! the!identification! of! dynamic! equivalents.! In! the! Fig.18,! the!methodology! of!MVMO! for! the! proposed!approach!is!described![5],![7],![52],![65].!!!

The!procedure! starts!with! the! initialization!of! the!parameter! settings,! such!as! the!archive! size,! the!selection!method!and!the!maximum!number!of!iterations.!The!searching!space!range!of!all!variables!is! confined! in! [0,!1]!and! therefore! the! real!min/max!have! to!be!normalized! to! this! interval.!During!every! iteration!step,!the!solution!vector!cannot!violate!the!demanded!boundaries!and!only!a!single!offspring!is!generated.!Thus,!the!characterization!of!MVMO!as!single\agent!search!algorithm!is!owed!to! the! latter! property.!With! respect! to! other! heuristic! techniques,!MVMO!uses! a! special!mapping!function! described! by! mean! and! shape! variables,! which! transforms! a! variable! òë∗! with! unity!

33!!

distribution! to! another! variableòë.! Subsequently,! during! fitness! evaluation,! the! archive! is! updated!only! if! the! new! solution! is! better! compared! with! the! previously! stored.! ! The!major! advantage! of!MVMO!is!the!minimization!of!the!risk!associated!with!premature!convergence,!which!contributes!to!the!confrontation!of!zero\variance.!

!!

Figure,18:,MVMO&based,procedure,for,optimal,reactive,power,management,(Figure,created,by,author,from,data,in,source,[64]),

34!!

4.3.2! Initialization!!The! parameters! required! for! MVMO! are! set! to! predefined! values,! which! are! summarized! in! the!following!table.!!!

Table,2:,MVMO,parameters,

Description! Value!Size!of!archive! 4!

Number!of!variables!changed!randomly! 15!Maximum!number!of!iterations! 1000!

Scaling!Factor! 2!!!In!the!first!approach,!where!the!optimization!is!performed!for!the!current!operating!point,!the!initial!candidate!solution!is!randomly!generated!between!the!specified!boundaries!as!follows:!

òëëíë] = òëZëí + vã{ô? òëZ[î − òëZëí ,???????z = 1,2, … , ö????????????????????????????(Eq. 15),

!The! index! z = 1,2, … , ö! stands! for!problem!dimension!and?ö! for! the!number!of!decision!variables.!However,!when!the!optimization!is!performed!in!a!predictive!manner,!after!the!first!hour!of!the!day,!the!initial!candidate!solution!for!the!subsequent!hours!are!generated!by!the!best!solutions!obtained!from!the!previous!hour.!!

!

4.3.3! Fitness!evaluation!and!local!search!!The! decision! variables! are! de\normalized! from! the! interval! [0,! 1]! to! their! original! [min,! max]!boundaries! before! the! fitness! evaluation! is! performed.! Since! MVMO! performs! within! normalized!range,! no! violation! of! bound! constraints! can! occur.! Finally,! the! search! process! stops! after! the!termination! criteria! are! satisfied,! which! is! usually! specified! as! a! predefined! number! of! fitness!evaluations.! Otherwise,! if! there! is! no! improvement! of! fitness! over! successive! fitness! evaluations,!then!the!process!can!be!also!terminated.!Local!search!strategy,!e.g.!by!subordinating!other!classical!or!heuristic!algorithms,!can!be!added!into!the!fitness!evaluation!stage!in!order!to!intensify!the!search!one!MVMO!has!found!an!attractive!region.!Nevertheless,!this!option!is!not!used!in!this!work!due!to!the!very! restricted!computing!budget!and! in!order! to!exclusively!ascertain! the!effectiveness!of! the!evolutionary!mechanism!of!MVMO!in!this!pure!form.!!

!

4.3.4! Solution!archive!!

The! solution!archive! serves! as! the! knowledge!base! for! guiding! the!algorithm’s! searching!direction,!the!size!of!which!is!set!in!the!initialization!stage!and!remains!constant!for!the!entire!process![65].!The!n! best! individuals! obtained! so! far! by!MVMO! are! stored! in! the! solution! archive.! The! filling! of! the!archive!obeys!a!descending!order!of!fitness!over!the!iterations,!as!presented!in!Fig.!19.!Consequently,!the!overall!best!found!so!far!is!always!the!first!ranked!individual.!Once!the!archive!is!full,!an!update!is!

35!!

conducted!only!if!the!solution!fitness!evaluation!revealed!that!the!new!solution!is!better!than!these!already! stored! in! the! archive.! Finally,! because! the! fitness! improves! over! iterations,! the! stored!solutions!in!the!archive!keep!changing.!

!!

!

Figure,19:,Solution,archive,(Figure,created,by,author,from,data,in,source,[66]),

!After!every!update!of!the!archive!for!each!optimization!variable!òë,!the!mean!òõ!and!variance!Yë !are!calculated! by! the! following! equations,! respectively.! The! variance! is! calculated! only! for! different!variables!in!the!archive:!

?òõ =1{ òë ?ú ?????????????????????????

í

ùLe(Eq. 16)#

Yë =1{ òë ?ú − òõ c???????????

í

ùLe???(Eq. 17)#

!Then,!the!shape!variable!óë !is!computed!as!follows:!

óë = − û{ Yë ∙ üà ????????????????????????????(Eq. 18),

!At! the! beginning,! Yë ! is! set! to! 1,! since! òõ! corresponds! with! the! initialized! value! of! òë.! The! shape!variable!óë !is!one!of!the!mapping!function!inputs!with!strong!influence!on!its!geometric!characteristic!shape.! For! this! reason,! the! scaling! factor! üà,! which! allows! controlling! the! form! of! the! mapping!function!and!the!search!process,!is!involved!in!the!calculation!of!óë !

!

4.3.5! Offspring!generation!!!The!major! distinction! of!MVMO! from!other! SOAs! is! the! random! sampling! function! for! creating! an!offspring.!In!order!to!generate!a!new!solution,!at!every!iteration!the!solution!with!the!best!fitness!so!far!is!used.!The!distribution!of!the!new!variable!òë !does!not!correspond!with!any!of!the!well\known!

36!!

distribution! functions.! Given! a! random! number!òë∗! from! the! interval! [0,1],! the! new! value! of! each!selected!dimension!!òë !is!described!mathematically!by:!

òë = ℎî + 1 − ℎe + ℎ† ∙ òë∗ − ℎ†???????????????????????????????(Eq. 19)'

!where!ℎî, ℎeand!ℎ†are!the!inputs!of!the!mapping!function!based!on!different!inputs!given!by:!

ℎî = ℎ ò = òë∗ ?????????????????????(Eq. 20)'

ℎe = ℎ ò = 1 ???????????????????????(Eq. 21)'

ℎ† = ℎ ò = 0 ????????????????????????(Eq. 22)'

Both!input!and!output!of!the!mapping!function!are!always!between!the!range![0,1].!The!definition!of!the!transformation!mapping!h\function!is!the!following:!

!ℎ òõ, óe, óc, ò = òõ ∙ 1 − u=î∙à°¢ + 1 − òõ ∙ u= e=î ∙à°£???????????(Eq. 23)'

!As!illustratively!shown!in!Fig.20,!the!h\function!transforms!the!variable!òë∗!varied!randomly!with!unity!distribution!to!another!variable!òë,!which!is!concentrated!around!the!mean!value!calculated!from!the!archive.! The! variation! of! òõ! implies! shifting! of! the! curve! between! the! original! lower! and! upper!boundaries!of!the!search!range,!while!the!variation!of!óëe!and!óëc!affects!the!bent!shape!of!the!curve,!i.e.!emphasizes!either!exploration!or!exploitation.!

!

!

Figure,20:,Variable,mapping,(Figure,created,by,author,from,data,in,source,[66]),

!When!the!accuracy!needs!to!be!improved!or!more!global!search!is!required,!!the!factor!üà!should!be!increased! (üà > 1)! and! decreased! (üà < 1),! respectively.! Therefore,! üà! can! be! used! to! change! the!shape!of!the!function.!

!!

37!!

4.4! Implementation!!The! general! implementation! procedure! of! the! optimal! reactive! power! management! approach,!proposed!in!this!project,!is!presented!in!the!following!figure.!

!

Figure,21:,Interaction,between,,MATLAB,,Python,and,DIgSILENT,PowerFactory,

!Initially,! the!NN\based!wind!speed! forecasting!method! is!performed! in!MATLAB,! from!where!a!24\hour!time!series!is!emerging!for!the!wind.!As!mentioned!in!Section!4.2,!the!Var!reference!of!the!wind!farm!and!tap!settings!of!the!transformers!are!the!parameters!to!be!optimized.!Finally,!a,Python,script!is!used!to!link!the!models!in!DIgSILENT,PowerFactory,with!MVMO!optimization!algorithm!and!obtain!these!parameters.!

Considering! the! output! wind! speed! data! of! the! prediction! model,! the! calculation! of! the! power!produced! by! a! wind! turbine! is! carried! out! also! in! the! Python, script! by! using! Eq.24.! Then,! the!calculated! power! is! fed! into! the! simulation! software,! in! order! to! perform! the! optimization.! The!aforementioned!procedure!is!conducted!continuously!for!24\hour!time!horizon.!

!

kZ = 12 ∙ ¶ ∙ S

c ∙ ß ∙ Ü_ ∙ YZä???????????????????(Eq. 24),

!The!result!of!multiplying!the!wind!turbine!radius!squared!Sc!by!the!mathematical!constant!¶!refers!to!the!swept!area!i?(yc)!of!the!wind!turbine.!

In! the! following! figure,! the!generated!power!by!a!wind! turbine! is!presented!as! a! function!of!wind!speed!between! the! cut\in! and! cut\out! speed.! The! cut\in! speed! corresponds! to! the!minimum!wind!speed!at!which!the!turbine!blades!overcome!friction!and!begin!to!rotate!and!the!cut\out!speed!is!the!wind! speed! at!which! the! turbine! blades! are! brought! to! rest,! in! order! to! avoid! damage! from! high!winds.!!

38!!

!

Figure,22:,Wind,turbine,power,output,

!!

! !

39!!

! !

40!!

!

!

!

!

5! Results !

5.1! Introduction!!In!this!chapter,! the!different!results!obtained!from!this!study!will!be!shown!and!discussed,!starting!with!the!results!of!building!the!NN\based!wind!speed!forecasting!tool,!as!well!the!results!of!testing!that!tool.!For!the!optimization!part,!the!Mean!Variance!Optimization!Algorithm!was!implemented!for!two!different!grids:!A!far!offshore!wind!farm!interconnected!with!HVDC!link!and!the!real!study!case!of! the! Dutch! offshore! wind! farm! zone! BORSSELE,! which! are! presented! in! Fig.27! and! Fig.31!respectively.! As! described! in! the! preceding! chapter! (Chapter! 4)! the! grid! was! optimized! for! both!transmission! losses!and!number!of! tap!changes!of!OLTC.!Multiple!cases!have!been! investigated!for!each!grid!and!the!results!demonstrate!the!advantages!and!the!flexibility!of!MVMO!over!the!different!cases.!

!

5.2! Wind!Speed!Forecasting!!The!proposed!prediction!tool!has!been!applied!for!wind!speed!forecasting! in!an!experimental!wind!farm! in! Spain.!Historical!wind! speed!data! are! the!main! inputs! to! train! the!NN.! In!order! to!make!a!clear! comparison,! no! exogenous! variables,! such! as! temperature! or! pressure! are! considered.! The!implemented!NN\based!method!predicts!the!value!of!the!wind!speed!time!series!for!24!hours!ahead,!taking! into!account! the!wind!speed!data!of! the!previous!24!hours!with!a! time\step!of!one!hour.! It!should!be!noted,! that!both! the! input!and!output! layer! is! comprised!of!one!artificial!neuron,!which!corresponds!to!a!single!column!vector!with!24!elements.!!!

Corresponding!to!the!four!seasons!of!the!year,!single!days!from!January,!April,!July!and!October!were!randomly! selected.! In! order! to! have!more! illustrative! representation!of! the! results,! the! day\ahead!wind!speed!forecasting!method!was!applied!for!all!the!days!of!these!months.!Conclusively,!although!the!forecasting!period!was!24\hours,!the!aggregated!results!of!each!month!are!presented.!!

The!numerical!results!of!the!proposed!approach!are!shown!in!Fig.!23!to!26!for!summer,!fall,!winter!and!spring,!respectively.!Each!figure!shows!the!actual!wind!speed!together!with!the!predicted!wind!speed.!!

41!!

®©®!™? % = &´, (¨!

!

Figure,23:,Wind,speed,for,July,

!

!

®©®!™?(%) = &≠, '´!

!

Figure,24:,Wind,speed,for,October,

!

42!!

®©®!™?(%) = '&, EÆ!

!

Figure,25:,Wind,speed,for,January,

!

®©®!™?(%) = &Ø, ≠'!

!

Figure,26:,Wind,speed,for,April,

The!values!obtained!for! the!AMAPE!(%)!are!acceptable!and!proves!the!accuracy!of! the!wind!speed!forecasting!method.!

43!!

5.3! Optimal!Management!of!Reactive!Sources!!

5.3.1! Study!cases!!As!described!in!the!previous!chapter!the!grid!was!optimized!for!only!transmission!losses,!and!then!for!losses! and! number! of! tap! changes! together.! The! characteristics! of! the! different! cases! under!examination!are!summarized!in!the!following!table.!

!Table,3:,Optimization,study,cases,,

! Wind!Farm! Optimization!for! Optimize!tap!positions!for! Optimization!Variables!

Case!1! Far5offshore!DC!connected!

Current!Operating!Point! Offshore!Transformers!(x2)! 50!

Case!2! A!Predicted!Time!Horizon!

Case!3!

Borssele!AC!connected!

Current!Operating!Point! Onshore!Transformers!(x2)! 102!

Case!4! A!Predicted!Time!Horizon!

Case!5! Current!Operating!Point! Offshore!Transformers!(x2)! 102!

Case!6! A!Predicted!Time!Horizon!

Case!7! Current!Operating!Point! On\!&!Off\shore!Transformers!(x2)! 104!

Case!8! A!Predicted!Time!Horizon!!!Concerning!the!optimization!for!a!predicted!time!horizon,!the!energy!costs!are!evaluated!by!80!Euro!per!MWh!and!one!OLTC!movement!by!1!Euro.!

!

5.3.2! MVMO!for!far!offshore!wind!farm!!In! this! case,! the! wind! farm! is! located! far! away! from! the! shore.! The! wind! farm! network! under!consideration! for! this! study! case! of! the! project! is! shown! in! Fig.27! and! is! connected! to! the! HVDC!platform!via! two!AC! cables.! The!electric! power! is! converted! from!AC! to!DC! in! a! converter! station,!then!converted!back!to!AC!in!a!second!converter!station!and!injected!into!the!receiving!AC!system.!In!order! to! perform! the! optimization,! only! the! part! of! the! layout! up! to! the! PCC! is! investigated.! The!nominal!total!capacity!of!the!connected!wind!farm!is!288!MW!and!consists!of!48!DFIG!wind!turbines!each! rated!at!6!MW.!The! internal!power! transmission! is! realized!by! the!wind! turbine! transformers!each! rated! at! 0.69/33! kV,! multiple! cables! with! different! lengths! and! two! step! up! on\load! tap\changing!transformers!of!6.7!MVA!rated!at!155/33/33!kV!each.!

!

44!!

!

Figure,27:,Far&offshore,wind,farm,layout,with,HVDC,interconnection,link,

!The!wind!scenario!for!the!considered!time!period!of!next!24\hour!is!the!result!of!the!NN\based!wind!speed!forecasting!method.!The!wind!profile,!shown!in!following!figure,!is!used!for!the!simulations!in!the!case!of!the!far\offshore!wind!farm.!

2 4 6 8 10 12 14 16 18 20 22 244

5

6

7

8

9

10

11

12

Predicted(Wind(Speed(((m(/(s()

Time(((h()!

Figure,28:,Wind,speed,variation,–,Far,offshore,wind,farm,

45!!

The! problem! in! this! study! case! has! 50! optimization! variables,! comprising! 48! continuous! variables!associated! to! wind! generator! reactive! power! set\points! and! 2! discrete! variables! associated! to!stepwise!adjustable!on\load!transformers!tap!positions.!The!computing!budget!is!restricted!to!1000!problem!evaluations!(i.e.!1000!AC!power!flow!calculations).!

5.3.2.1! Case!1!!!A!real\time!reactive!power!management! is!performed.!The!active!power!generation!at!one!specific!operating!point,! is!supplied!to!the!optimization!algorithm!at!each!time!step.!Similar!optimization! is!performed!for!a!new!operating!point!at!the!next!time!step!for!24\hour!time!horizon.!In!this!case,!the!vector! with! the! parameters! to! be! optimized! and! the! formulation! of! the! objective! function! is! the!following!respectively:!!

ò = [±èêq,e, … , ±èêq,d≤, ^ãåá≥≥,êe, ^ãåá≥≥,êc]! !!!!!!!!!!!!!!(Eq. 25)!

yz{.????????????????????}~ = k�,], ???^ = 1,2, … ,24????????????????????????(Eq. 26)!

The!reactive!power!reference!for!each!wind!turbine!derived!from!the!optimization!are!according!to!the!Grid!Code!Requirements! [38],! since!all! the!values!are! inside! the!curve!presented! in!Fig.!29! (a).!!Each!color!refers!to!different!value!of!the!wind!speed.!

!

!2,0 !1,5 !1,0 !0,5 0,0 0,5 1,0 1,5 2,0 2,5

P"("%"PN")

Q"("MVar")

80

20

100

! !

2 4 6 8 10 12 14 16 18 20 22 24

6

8

10

12

14

16

18

20

22

Reduction*of*losses*(*%*)

Time*(*h*)!

(c)!(b)!

(a)!

2 4 6 8 10 12 14 16 18 20 22 24

'5

'4

'3

'2

'1

0

Time%(%h%)

Tap%Positions

%Offshore%Transformer%T1*Offshore%Transformer%T2

5,02!m/s

11,51!m/s

8,33!m/s

.

.

.

.

.

.

46!!

!!

0 2 4 6 8 10 12 14 16 18 20 22 240,80

0,85

0,90

0,95

1,00

1,05

1,10

1,15

1,20

!BUS!A*BUS!B*BUS!C!*BUS!D

Voltages!of!33!kV!Buses

Time!(!h!)!!

,

!Figure,29:,Aggregated,results,of,Case,1,(a),Q,set&point,of,every,wind,turbine,for,each,hour,(b),Hourly,reduction,pf,wind,farm,active,power,losses,(c),OLTC,tap,positions,–,T1,&,T2,,(d),Bus,voltages,in,p.u.,of,

the,33,kV,buses,,at,the,MV,and,LV,,side,of,the,3&winding,transformers,,respectively,(e),Reactive,power,at,the,PCC,

!As!presented! in!Fig.29! (b),! the!maximum!hourly! reduction!of! the!real!power! losses! is!around!20!%!and!occurs!for!higher!wind!speed!values!between!the!range!of!10\11,5!m/s.!On!the!other!hand,!when!the!wind! speed! is! lower! between! the! range! of! 7\8,5!m/s,! the! hourly! reduction! percentage! of! the!losses!is!around!14!%.!and!reaches!a!maximum!value!of!12!%.!The!minimum!hourly!reduction!of!the!real!power!losses!in!this!case!is!6!%.!

The!voltage!levels!of!the!MV\!and!LV\side!of!the!offshore!transformers!(33!kV!buses)!are!within!the!acceptable! range,! as! shown! in!Fig.29! (d).! According! to!Fig.29! (e),! the! reactive!power!of! the!HVDC!station!is!also!maintained!within!the!predefined!capability!curve!at!the!PCC.!The!reason!that!all!the!results!are!located!at!the!value!of!1!p.u.!voltage!is!owed!to!the!consideration!of!the!PCC!as!a!PV!bus.!with! constant! the! voltage! magnitude.! The! transformers! tap! positions,! as! derived! from! the!optimization!algorithm!are! shown! in!Fig.29! (b).! The! total!number!of! the! tap!movements!within!24!hours! is!0!and!9! for!T1!and!T2!onshore!transformers,! respectively.!Consequently,! the! fulfillment!of!the!requirement!regarding!the!HVDC!station!(PCC)!proves!that!the!optimum!wind!farm!Var!reference!and!transformers!tap!positions!result!in!efficient!operation!of!the!system!with!minimum!losses.!!

5.3.2.2! Case!2!!A!predictive!reactive!power!management! is!performed.!The!active!power!generation,!calculated!by!the!day\ahead!wind!speed!prediction!according! to!Eq.24,! is! supplied! to! the!optimization!algorithm!for!the!next!24!hours.!The!vector!with!the!parameters!to!be!optimized! is!defined!as! in!Case!1.!The!formulation!of!the!objective!function!is!the!following:!

yz{.???????????????}~ = ? se ∙ k�,] + sc ∙ }ÑÖÜ\áà],] ??????????(Eq. 27)cd

]Le!

(d)! (e)!

!0,45 !0,30 !0,15 0,00 0,15 0,30 0,45 0,60

0,8

0,9

1,0

1,1

1,2U"("p.u.")

Q/Pmax"at"PCC

Q/Pmax

47!!

!2,0 !1,5 !1,0 !0,5 0,0 0,5 1,0 1,5 2,0 2,5

0

20

40

60

80

100

Q"("MVar")

P"("%"PN")

!

2 4 6 8 10 12 14 16 18 20 22 240

1500

3000

4500

600010,97&%&reduction

Time&(&h&)

Cost&(&Euro&)

&Cumulative&Initial&Cost&&Cumulative&Optimum&Cost

!

!

0 2 4 6 8 10 12 14 16 18 20 22 240,80

0,85

0,90

0,95

1,00

1,05

1,10

1,15

Voltages)of)33)kV)Buses

Time)()h))

)BUS)A*BUS)B*BUS)C)*BUS)D

!!!!!Figure,30:!Aggregated,results,of,Case,2,,(a),Hourly,Q,set&points,of,every,wind,turbine,(b),Reduction,of,cumulative,cost,in,the,wind,farm,(c),OLTC,tap,positions,–,A,&,B,,(d),Bus,voltages,in,p.u.,of,the,33,kV,buses,,at,the,MV,and,LV,,side,of,the,3&winding,transformers,,respectively,(e),Reactive,power,at,the,

PCC,

(b)!! (c)!

!0,45 !0,30 !0,15 0,00 0,15 0,30 0,45 0,60

0,8

0,9

1,0

1,1

1,2U"("p.u.")

Q/Pmax

,Q/Pmax"at"PCC

(a)!

5,02!m/s

11,51!m/s

8,33!m/s

.

.

.

.

.

.

(d)! (e)!

48!!

The!reactive!power!reference!for!each!wind!turbine!derived!from!the!optimization!are!according!to!the!Grid!Code!Requirements! [38],! since!all! the!values!are! inside! the!curve!presented! in!Fig.!30! (a).!!Each! color! refers! to! different! value! of! the! wind! speed.! As! presented! in! Fig.30! (b),! the! difference!between!the!cumulative!initial!and!optimum!cost!is!estimated!around!10,97!%!for!the!24\hour!time!horizon!under!investigation.!The!voltage!levels!of!the!MV\!and!LV\side!of!the!offshore!transformers!(33!kV!buses)!are!maintained!within!the!acceptable!range,!as!shown!in!Fig.30!(c).!According!to!Fig.!30!(e),!the!reactive!power!of!the!HVDC!station!is!also!maintained!within!the!predefined!capability!curve!for!the!PCC.!The!total!number!of!the!tap!movements!within!24!hours,!as!shown!in!Fig.30!(b),!is!zero!for!both!of!the!transformers.!Consequently,!the!tap!changes!are!eliminated!by!performing!predictive!optimization.!

5.3.3! MVMO!for!Borssele!wind!farm!!The!near\shore!wind!farm!under!consideration,!radially!connected!through!an!AC!link!to!the!PCC,!is!presented!in!Fig.31.!The!test!system!layout!used!is!taken!from!a!future!wind!power!plant!project!to!be!connected! in! the!Dutch!transmission!system!with!nominal! total!capacity!of!700!MW,!termed!as!the!Borssele!plant.!The!plant!consists!of!two!zones,!I!and!II,!connected!via!a!22km!HVAC!cable.!Due!to!limitations!of!PowerFactory!library,!since!the!provided!wind!turbine!templates!are!rated!maximum!at!6!MW,!a!wind!farm!of!nominal!total!capacity!600!MW!is!implemented!in!this!case.!The!selection!of!the!wind!turbine!type!was!arbitrary!and!consequently,!for!comparison!reasons!with!the!far\offshore!wind! farm! case! (Section! 5.3.2),! 100! Fully\Rated\Converter!wind! turbines! each! rated! at! 6,MW!are!used!for!the!simulations.!The!internal!power!transmission!of!each!300!MW!zone!of!the!wind!farm!is!realized!by! the!wind! turbine! transformers!each! rated!at!0.69/66!kV,!multiple! cables!with!different!lengths!and!four!step!up!on\load!tap\changing!transformers!of!6.7!MVA,!at!the!offshore!and!onshore!side,!rated!at!230/66/66!kV!and!380/225/33!kV!respectively.!

!

Figure,31:,Borssele,wind,farm,layout,with,AC,cable,

49!!

The!wind! scenario! for! the! considered! time! period! of! 24\hours! is! the! result! of! the!NN\based!wind!speed!forecasting!method.!The!wind!profile,!shown!in!following!figure,!is!used!for!the!simulations!in!the!case!of!the!near\offshore!wind!farm.!

2 4 6 8 10 12 14 16 18 20 22 246

7

8

9

10

11

12Predicted(Wind(Speed(((m(/(s()

Time(((h()!

Figure!32:!Wind,speed,variation,–,Borssele,wind,farm,

!The!problem! in! this! study!case!has!102! (or!104)!optimization!variables,! comprising!100!continuous!variables! associated! to! wind! generator! reactive! power! set\points! and! 2! (or! 4)! discrete! variables!associated! to! stepwise! adjustable! on\load! transformers! tap! positions.! The! computing! budget! is!restricted!to!1000!problem!evaluations!(i.e.!1000!AC!power!flow!calculations).!

5.3.3.1! Case!3!!A!real\time!reactive!power!management! is!performed.!The!active!power!generation!at!one!specific!operating!point,! is!supplied!to!the!optimization!algorithm!at!each!time!step.!Similar!optimization! is!performed!for!a!new!operating!point!at!the!next!time!step!for!24\hour!time!horizon.!In!this!case,!the!vector! with! the! parameters! to! be! optimized! and! the! formulation! of! the! objective! function! is! the!following!respectively:!!

ò = [±èêq,e, … , ±èêq,e††, ^ãåáí,m, ^ãåáí,¥]!!????????(Eq. 28)!

yz{.????????????????????}~ = k�,], ???^ = 1,2, … ,24???????????(Eq. 29)!

The!reactive!power!reference!for!each!wind!turbine!is!derived!from!the!optimization!are!according!to!the!Grid!Code!Requirements![38],!as!presented!in!Fig.!33!(a),!due!to!the!normalized!search!space!of!MVMO,!which!ensures!that!bound!constraints!are!never!violated.!This!is!an!advantage!with!regard!to!other!algorithms,!since!the!algorithm!does!not!require!extra!computing!effort!to!repair!solutions!to!lie!within!the![min,!max]!boundaries.!Each!set!of!points!arranges!in!the!same!horizontal!line!refers!to!different!value!of!wind!speed.!

50!!

!2,0 !1,5 !1,0 !0,5 0,0 0,5 1,0 1,5 2,0 2,5

0

20

40

60

80

100

Q"("MVar")

P"("%"PN")

!

2 4 6 8 10 12 14 16 18 20 22 2410

15

20

25

30

35

40

45

50

55

60

Reduction*of*losses*(*%*)

Time*(*h*)!!

!

!60 !45 !30 !15 0 15 30 45 60

0

20

40

60

80

100

Q"at"Offshore"PCC"("MVar")

P"("p.u.")*LV_A"66"kV"Bus*MV_A"66"kV"Bus*LV_B"66"kV"Bus*MV_B"66"kV"Bus

!!

!

Figure!33:,Aggregated,results,of,Case,3,(a),Q,set&point,of,every,wind,turbine,for,each,hour,(b),Hourly,reduction,pf,wind,farm,active,power,losses,(c),OLTC,tap,positions,–,Onshore,transformers,,(d),

Reactive,power,at,the,offshore,PCC!!(e),Reactive,power,at,the,onshore,PCC,

(b)! (c)!

(d)! (e)!

!150 !120 !90 !60 !30 0 30 60 90 120

0

20

40

60

80

100

+Onshore(PCC(A+Onshore(PCC(B

P(((p.u.()

Q(at(Onshore(PCC(((MVar()

initial(curveacceptable(deviation

(a)!

7,4!m/s

11,51!m/s

9,15!m/s

.

.

.

.

.

.

2 4 6 8 10 12 14 16 18 20 22 24

'10

'8

'6

'4

'2

0

2

4

6

Time%(%h%)

Tap%positions

(Onshore%Transformer%A(Onshore%Transformer%B

51!!

!As!presented!in!Fig.33!(b),!the!smallest!hourly!reduction!of!the!real!power!losses!with!regard!to!the!initial!losses!calculated!for!zero!reactive!power!reference!at!every!wind!turbine,!is!around!15!%!and!occurs!for!higher!wind!speed!values!between!the!range!of!8,5\11,5!m/s!(cf.!Fig.32).!By!contrast,!for!lower!wind!speed!values,!e.g.!between!the!range!of!7\8,5!m/s,! the!hourly! reduction!percentage!of!the!losses!is!much!higher!and!reaches!a!maximum!value!of!48!%.!!

While!the!reactive!power! levels!of! the!MV\!and!LV\side!of! the!offshore!transformers! (66!kV!buses)!are! maintained! within! the! predefined! envelope,! as! shown! in! Fig.33! (d),! it! is! observed! that! the!requirements! for! specific! reactive!power! absorption/injection!at! the!onshore!PCC!are!not! satisfied!according!to!Fig.33!(e).!This! is!due!to!the!transformers!tap!positions,!shown!in!Fig.33!(c)!as!derived!from!the!optimization!algorithm.!The!total!number!of!the!tap!movements!within!24!hours!is!38!and!85!for!T1!and!T2!onshore!transformers,!respectively.!Consequently,!the!change!of!the!tap!positions!exclusively!at! the!onshore!transformers! is!not! feasible,!since!the!deviation!of! the!reactive!power! is!more!than!the!acceptable!+/\!0,1!p.u!(=+/\!30!MVAr)!at!the!onshore!PCC.!

!

5.3.3.2! Case!4!!A!predictive!reactive!power!management!scheme!is!applied.!The!active!power!generation,!calculated!by!the!day\ahead!wind!speed!prediction!according!to!Eq.24,!is!supplied!to!the!optimization!algorithm!for!the!next!24!hours.!Here,!the!vector!of!the!parameters!to!be!optimized!is!defined!as!in!Case!3.!The!formulation!of!the!objective!function!is!the!following:!

!

yz{.???????????????}~ = ? (se ∙ k�,] + sc ∙ }ÑÖÜ\áà],])cd

]Le???????????(Eq. 30)!

!The!reactive!power!reference!for!each!wind!turbine!is!derived!from!the!optimization!are!according!to!the!Grid!Code!Requirements! [38],! since!all! the!values!are! inside! the!curve!presented! in!Fig.!34! (a).!Each!set!of!points!arranges!in!the!same!horizontal!line!refers!to!different!value!of!wind!speed.!

!2,0 !1,5 !1,0 !0,5 0,0 0,5 1,0 1,5 2,0 2,5

0

20

40

60

80

100

Q"("MVar")

P"("%"PN")

!(a)!

7,4!m/s

11,51!m/s

9,15!m/s

.

.

.

.

.

.

52!!

2 4 6 8 10 12 14 16 18 20 22 240

5000

10000

15000

20000

25000

30000

Cost%(%Euro%)

%Cumulative%Initial%Cost%%Cumulative%Optimum%Cost

Time%(%h%)

38,16%%%reduction

!!!

!60 !45 !30 !15 0 15 30 45 60

0

20

40

60

80

100

*LV_A%66%kV%Bus*MV_A%66%kV%Bus*LV_B%66%kV%Bus*MV_B%66%kV%Bus

Q%at%Offshore%PCC%(%MVar%)

P%(%p.u.%)

!! !!Figure,34:!Aggregated,results,of,Case,4,,(a),Hourly,Q,set&points,of,every,wind,turbine,(b),Reduction,of,cumulative,cost,in,the,wind,farm,(c),OLTC,tap,positions,–,Onshore,transformers,,(d),Reactive,power,at,

the,offshore,PCC!!(e),Reactive,power,at,the,onshore,PCC,

!As! presented! in! Fig.34! (b),! the! difference! between! the! cumulative! initial! and! optimum! cost! is!estimated! around! 38,16! %! for! the! 24\hour! time! horizon! under! investigation.! The! reactive! power!levels!of!the!MV\!and!LV\side!of!the!offshore!transformers!(66!kV!buses)!are!maintained!within!the!predefined! envelope,! as! shown! in! Fig.34! (d).! In! addition,! it! is! observed! that! the! reactive! power!absorption/injection!at!the!onshore!PCC!is!within!the!required!boundaries!according!to!Fig.34!(e),!in!comparison!with!Case!3.!Eventually,! the!main! target!of! this!approach,! for!minimizing! the!OLTC!tap!changes!during!daily! operation! is! achieved.!As!displayed! in!Fig.34! (c),! the!number!of! the! total! tap!movements!within!24!hours!was!reduced!to!28!for!each!of!the!A!and!B!onshore!transformers.!

!

5.3.3.3! Case!5!!A!real\time!reactive!power!management! is!performed.!The!active!power!generation!at!one!specific!operating!point,! is!supplied!to!the!optimization!algorithm!at!each!time!step.!Similar!optimization! is!

2 4 6 8 10 12 14 16 18 20 22 24

'10

'8

'6

'4

'2

0

(Onshore(Transformer(A(Onshore(Transformer(B

Tap(positions

Time(((h()

(Onshore(Transformer(A(Onshore(Transformer(B

!150 !120 !90 !60 !30 0 30 60 90 120

0

20

40

60

80

100

Q"at"Onshore"PCC"("MVar")

+Onshore"PCC"A+Onshore"PCC"B

P"("p.u.")

(b)! (c)!

(d)! (e)!

53!!

performed!for!a!new!operating!point!at!the!next!time!step!for!24\hour!time!horizon.!In!this!case,!the!vector! with! the! parameters! to! be! optimized! and! the! formulation! of! the! objective! function! is! the!following!respectively:!!

ò = [±èêq,e, … , ±èêq,e††, ^ãåá≥≥,m, ^ãåá≥≥,¥]!! ! (Eq. 31)!

yz{.????????????????????}~ = k�,], ???^ = 1,2, … ,24??????????????????????(Eq. 32)!

The!reactive!power!reference!for!each!wind!turbine!derived!from!the!optimization!are!according!to!the!Grid!Code!Requirements! [38],! since!all! the!values!are! inside! the!curve!presented! in!Fig.!35! (a).!!Each!set!of!points!arranges!in!the!same!horizontal!line!refers!to!different!value!of!wind!speed.!

!2,0 !1,5 !1,0 !0,5 0,0 0,5 1,0 1,5 2,0 2,5

0

20

40

60

80

100

P"("%"PN")

Q"("MVar")!

!

As!presented!in!Fig.35!(b),!the!minimum!hourly!reduction!of!the!real!power!losses!is!around!18,5!%!and! occurs! for! higher!wind! speed! values! between! the! range! of! 8,5\11,5!m/s.! The!minimum!point!corresponds!to!an!hourly!reduction!of!17,5!%.!For!lower!wind!speed!values!between!the!range!of!7\8,5!m/s,!the!hourly!reduction!percentage!of!the!losses!is!much!higher!and!reaches!a!maximum!value!of!32!%.!!

2 4 6 8 10 12 14 16 18 20 22 24

17,5

20,0

22,5

25,0

27,5

30,0

32,5

Reduction*of*OF*(*%*)

Time*(*h*)!!

!

2 4 6 8 10 12 14 16 18 20 22 24

'6

'4

'2

0

2

4

6

(Offshore(Transformer(A(Offshore(Transformer(B

Tap(positions

Time(((h()

(b)! (c)!

(a)!

7,4!m/s

11,51!m/s

9,15!m/s

.

.

.

.

.

.

54!!

!60 !45 !30 !15 0 15 30 45 60

0

20

40

60

80

100

*LV_A%66%kV%Bus*MV_A%66%kV%Bus*LV_B%66%kV%Bus*MV_B%66%kV%Bus

P%(%p.u.%)

Q%at%Offshore%PCC%(%MVar%)!!

!

Figure!35:!Aggregated,results,of,Case,5,(a),Q,set&point,of,every,wind,turbine,for,each,hour,(b),Hourly,reduction,pf,wind,farm,active,power,losses,(c),OLTC,tap,positions,–,Offshore,transformers,,(d),

Reactive,power,at,the,offshore,PCC!(e),Reactive,power,at,the,onshore,PCC,

!While!the!reactive!power! levels!of! the!MV\!and!LV\side!of! the!offshore!transformers! (66!kV!buses)!are! maintained! within! the! predefined! envelope,! as! shown! in! Fig.35! (d),! it! is! observed! that! the!reactive!power!absorption/injection!at!the!onshore!PCC!is!completely!out!of!the!required!boundaries!according!to!Fig.35!(e).!This!owed!to!the!transformers!tap!positions,!shown!in!Fig.35!(c)!as!derived!from!the!optimization!algorithm.!The!total!number!of!the!tap!movements!within!24!hours!is!43!and!25! for! A! and! B! offshore! transformers,! respectively.! Consequently,! the! change! of! the! tap! positions!exclusively!at! the!onshore!transformers! is!not! feasible,!since!the!deviation!of! the!reactive!power! is!more!than!the!acceptable!+/\!0,1!p.u!(=!+/\!30!MVAr)!at!the!onshore!PCC.!

!

5.3.3.4! Case!6!!A!predictive!reactive!power!management! is!performed.!The!active!power!generation,!calculated!by!the!day\ahead!wind!speed!prediction!according! to!Eq.24,! is! supplied! to! the!optimization!algorithm!for!the!next!24!hours.!The!vector!with!the!parameters!to!be!optimized!is!defined!as! in!Case!5.!The!formulation!of!the!objective!function!is!the!following:!

!

yz{.???????????????}~ = ? (se ∙ k�,] + sc ∙ }ÑÖÜ\áà],])cd

]Le??????????????(Eq. 33)!

!The!reactive!power!reference!for!each!wind!turbine!derived!from!the!optimization!are!according!to!the!Grid!Code!Requirements! [38],! since!all! the!values!are! inside! the!curve!presented! in!Fig.!36! (a).!!Each!set!of!points!arranges!in!the!same!horizontal!line!refers!to!different!value!of!wind!speed.!

(d)! (e)!

!250 !200 !150 !100 !50 0 50 100 150

0

20

40

60

80

100

)Onshore(PCC(A)Onshore(PCC(B

P(((p.u.()

Q(at(Onshore(PCC(((MVar()

initial(curveacceptable(deviation

55!!

!2,0 !1,5 !1,0 !0,5 0,0 0,5 1,0 1,5 2,0 2,5

0

20

40

60

80

100

Q"("MVar")

P"("%"PN")

!

2 4 6 8 10 12 14 16 18 20 22 240

5000

10000

15000

20000

25000

30000

!Cumulative!Initial!Cost!!Cumulative!Optimum!Cost

Time!(!h!)

Cost!(!Euro!)

31,31!%!reduction

!! !

! !

!60 !45 !30 !15 0 15 30 45 60

0

20

40

60

80

100

Q"at"Offshore"PCC"("MVar")

P"("p.u.")*LV_A"66"kV"Bus*MV_A"66"kV"Bus*LV_B"66"kV"Bus*MV_B"66"kV"Bus

!!,,

Figure,36:,Aggregated,results,of,Case,6,,(a),Hourly,Q,set&points,of,every,wind,turbine,(b),Reduction,of,cumulative,cost,in,the,wind,farm,(c),OLTC,tap,positions,–,Offshore,transformers,,(d),Reactive,power,

at,the,offshore,PCC!(e),Reactive,power,at,the,onshore,PCC,

2 4 6 8 10 12 14 16 18 20 22 24

'6

'4

'2

0

2

4

6

(Offshore(Transformer(A(Offshore(Transformer(B

Tap(positions

Time(((h()

(b)!(c)!

(d)! (e)!

!250 !200 !150 !100 !50 0 50 100 150

0

20

40

60

80

100

)Onshore(PCC(A)Onshore(PCC(B

Q(at(Onshore(PCC(((MVar()

P(((p.u.()initial(curveacceptable(deviation

(a)!

7,4!m/s

11,51!m/s

9,15!m/s

.

.

.

.

.

.

56!!

!As! presented! in! Fig.36! (b),! the! difference! between! the! cumulative! initial! and! optimum! cost! is!estimated! around! 31,31! %! for! the! 24\hour! time! horizon! under! investigation.! The! reactive! power!levels!of!the!MV\!and!LV\side!of!the!offshore!transformers!(66!kV!buses)!are!maintained!within!the!predefined! envelope,! as! shown! in! Fig.36! (d).! In! addition,! it! is! observed! that! the! reactive! power!absorption/injection! at! the! onshore! PCC! is! again! completely! outside! the! required! boundaries!according! to! Fig.36! (e),! since! the! deviation! is! more! than! the! accepted! tolerance! (+/\! 0,1! p.u.).!Although,! the! main! target! of! this! approach,! for! minimizing! the! OLTC! tap! changes! during! daily!operation!is!achieved,!as!displayed!in!Fig.36!(c),!the!big!deviation!of!the!reactive!power!proves!that!the!presented!predictive!optimization!by!changing!only!offshore!transformers!tap!positions!does!not!satisfy!the!Grid!Code!Requirements.!

!

5.3.3.5! Case!7!!A!real\time!reactive!power!management! is!performed.!The!active!power!generation!at!one!specific!operating!point,! is!supplied!to!the!optimization!algorithm!at!each!time!step.!Similar!optimization! is!performed!for!a!new!operating!point!at!the!next!time!step!for!24\hour!time!horizon.!In!this!case,!the!vector! with! the! parameters! to! be! optimized! and! the! formulation! of! the! objective! function! is! the!following!respectively:!!

!ò = [±èêq,e, … , ±èêq,e††, ^ãåáí,m, ^ãåáí,¥, ^ãåá≥≥,êe, ^ãåá≥≥,êc]!!!!!!!!!(Eq. 34)!

yz{.????????????????????}~ = k�,], ???^ = 1,2, … ,24????????????????????????????????????????????????????(Eq. 35)!

!The!reactive!power!reference!for!each!wind!turbine!derived!from!the!optimization!are!according!to!the!Grid!Code!Requirements! [38],! since!all! the!values!are! inside! the!curve!presented! in!Fig.!37! (a).!!Each!set!of!points!arranged!in!the!same!horizontal!line!refers!to!different!value!of!wind!speed.!

!

!2,0 !1,5 !1,0 !0,5 0,0 0,5 1,0 1,5 2,0 2,5

0

20

40

60

80

100

P"("%"PN")

Q"("MVar")!

!(a)!

2 4 6 8 10 12 14 16 18 20 22 2410

15

20

25

30

35

40

45

50

55

60

Reduction*of*the*OF*(*%*)

Time*(*h*)

(b)!

7,4!m/s

11,51!m/s

9,15!m/s

.

.

.

.

.

.

57!!

2 4 6 8 10 12 14 16 18 20 22 24

'10

'9

'8

'7

'6

'5

'4

'3

'2

'1

0Tap$positions

Time$($h$)

,Onshore$Transformer$A,Onshore$Transformer$B

! !!

!

!60 !45 !30 !15 0 15 30 45 60

0

20

40

60

80

100

P"("p.u.")P"("p.u.")*LV_A"66"kV"Bus*MV_A"66"kV"Bus*LV_B"66"kV"Bus*MV_B"66"kV"Bus

Q"at"Offshore"PCC"("MVar")!!

!

Figure!37:!Aggregated,results,of,Case,7!!(a),Hourly,Q,set&points,of,every,wind,turbine,(b),Hourly,reduction,of,wind,farm,active,power,losses,(c),OLTC,tap,positions,–,Onshore,transformers,(d),OLTC,

tap,positions,–,Offshore,transformers,(e),Reactive,power,at,the,offshore,PCC!(f),Reactive,power,at,the,onshore,PCC!

!As!presented!in!Fig.37!(b),!the!hourly!reduction!of!the!real!power!losses!is!around!17,5!%!and!occurs!for!higher!wind!speed!values!between!the!range!of!8,5\11,5!m/s.!The!minimum!point!corresponds!to!an!hourly!reduction!of!15!%.!On!the!other!hand,!when!the!wind!speed!is!lower,!between!the!range!of!7\8,5!m/s,!the!hourly!reduction!percentage!of!the!losses!is!much!higher!and!reaches!the!remarkable!maximum!value!of!55!%.!!

The! reactive! power! levels! of! the!MV\! and! LV\side! of! the! offshore! transformers! (66! kV! buses)! are!maintained!within!the!predefined!envelope,!as!shown!in!Fig.37!(e).!In!addition,!it!is!observed!that!the!reactive! power! absorption/injection! at! the! onshore! PCC! is! completely! between! the! required!boundaries! according! to! Fig.37! (f),! while! the! onshore! and! offshore! transformers! tap! settings,! as!derived! from! the! optimization! algorithm,! are! shown! in! Fig.37! (c)! and! (d),! respectively.! The! total!number!of!the!tap!movements!within!24!hours!is!42!for!each!of!the!A!and!B!onshore!transformers.!

2 4 6 8 10 12 14 16 18 20 22 24

'6

'4

'2

0

2

4

6

8

Tap$positions

Time$($h$)

(Offshore$Transformer$A(Offshore$Transformer$B

(c)! (d)!

(e)! (f)!

!150 !120 !90 !60 !30 0 30 60 90 120

0

20

40

60

80

100

P"("p.u.") +Onshore"PCC"A+Onshore"PCC"B

Q"at"Onshore"PCC"("MVar")

initial"curveacceptable"deviation

58!!

Concerning!also!the!offshore!transformers!A!and!B,!the!total!number!of!the!tap!movements!is!43!and!26,!respectively.!The!small!deviation!displayed!in!Fig.37!(f)!is!acceptable,!because!the!offshore!wind!turbines!are!expected!to!contribute!to!the!fine!regulation!of!reactive!power!at!PCC!with!+/\!0,1!p.u.!(=!+/\30!MVAr)!according!to!the!Grid!Code!Requirements!defined!by!TenneT!TSO![38].!!

!

5.3.3.6! Case!8!!A!predictive!reactive!power!management! is!performed.!The!active!power!generation,!calculated!by!the!day\ahead!wind!speed!prediction!according! to!Eq.24,! is! supplied! to! the!optimization!algorithm!for!the!next!24!hours.!The!vector!with!the!parameters!to!be!optimized!is!defined!as! in!Case!7.!The!formulation!of!the!objective!function!is!the!following:!

yz{.???????????????}~ = ? se ∙ k�,] + sc ∙ }ÑÖÜ\áà],] ????????????cd

]Le(Eq. 36)!

!The!reactive!power!reference!for!each!wind!turbine!derived!from!the!optimization!are!according!to!the!Grid!Code!Requirements! [38],! since!all! the!values!are! inside! the!curve!presented! in!Fig.!38! (a).!!Each!set!of!points!arranged!in!the!same!horizontal!line!refers!to!different!value!of!wind!speed.!

As!presented!in!Fig.38!(b),!the!difference!between!the!cumulative!initial!and!optimum!cost!reaches!a!percentage!of!41,12!%!for!the!24\hour!time!horizon!under!investigation.!The!reactive!power!levels!of!the!MV\!and!LV\side!of!the!offshore!transformers!(66!kV!buses)!are!maintained!within!the!predefined!envelope,! as! shown! in! Fig.38! (e).! In! addition,! it! is! observed! that! the! reactive! power!absorption/injection!at!the!onshore!PCC!is!also!between!the!required!boundaries!according!to!Fig.38!(f),! since! the! deviation! is! lower! than! the! accepted! +/\! 0,1! p.u.! Eventually,! the!main! target! of! this!approach,! for!minimizing! the! OLTC! tap! changes! during! daily! operation! is! achieved.! In! comparison!with!Case!7,!as!displayed!in!Fig.38!(c)!and!(d),!the!tap!positions!of!the!A!and!B!onshore!transformers!within!24!hours!are!constant,!while!the!number!of!total!tap!movements!was!reduced!to!2!and!0!for!the!onshore!transformers!A!and!B,!respectively.!

!

!2,0 !1,5 !1,0 !0,5 0,0 0,5 1,0 1,5 2,0 2,5

0

20

40

60

80

100

Q"("MVar")

P"("%"PN")

! (b)!(a)!

2 4 6 8 10 12 14 16 18 20 22 240

5000

10000

15000

20000

25000

30000

35000

41,12%%%reduction

%Cumulative%Initial%Cost%%Cumulative%Optimum%Cost

Cost%(%Euro%)

Time%(%h%)

7,4!m/s

11,51!m/s

9,15!m/s

.

.

.

.

.

.

59!!

!

!

2 4 6 8 10 12 14 16 18 20 22 24

'9

'8

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'6

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'4

'3

'2

'1

0

,Onshore(Transformer(A,Onshore(Transformer(B

Tap(positions

Time(((h()

!!!!!

!60 !45 !30 !15 0 15 30 45 60

0

20

40

60

80

100

*LV_A%66%kV%Bus*MV_A%66%kV%Bus*LV_B%66%kV%Bus*MV_B%66%kV%Bus

Q%at%Offshore%PCC%(%MVar%)

P%(%p.u.%)

!!!!

Figure,38:,Aggregated,results,of,Case,8,(a),Hourly,Q,set&points,of,every,wind,turbine,(b),Reduction,of,cumulative,cost,in,the,wind,farm,(c),OLTC,tap,positions,–,Onshore,transformers,(d),OLTC,tap,positions,–,Offshore,transformers,(e),Reactive,power,at,the,offshore,PCC!(f),Reactive,power,at,the,onshore,PCC,

!!

5.3.1! Convergence!Behavior!of!MVMO!!

The! effectiveness! of! MVMO! at! solving! different! complex! problems,! within! a! reduced! number! of!allowed! function!evaluations,! is! presented! in! following! figures.! The! fast! convergence!behavior! and!the! quick! discovery! of! the! optimum! solution! with! minimum! risk! of! premature! convergence! is!revealed! thanks! to! the!well\designed!balance!between! search!diversification! and! intensification!of!MVMO.! In!Fig.39! (a),!which!refers! to! the!results!of! the!minimization!of! total! transmission! losses! in!

2 4 6 8 10 12 14 16 18 20 22 24

'2

'1

0

1

2

Tap$positions

Time$($h$)

(Offshore$Transformer$A(Offshore$Transformer$B

(c)!

(e)! (f)!

!150 !120 !90 !60 !30 0 30 60 90 1200

20

40

60

80

100

+Onshore(PCC(A+Onshore(PCC(B

Q(at(Onshore(PCC(((MVar()

P(((p.u.()initial(curveacceptable(deviation

(d)!

60!!

the! far\offshore! wind! farm! for! every! operating! point! (Section! 5.3.2.1),! it! is! shown! that! MVMO!converges!almost!before!300!iterations.!

On! the!contrary,! in!Fig.39! (b),!which! refers! to! the! results!of! the!minimization!of! total! transmission!losses! in! the! near\shore! wind! farm! for! every! operating! point! (Section! 5.3.3.1),! it! is! shown! that!MVMO!converges!around!900!iterations.!This!owed!to!the!different!topology!of!the!wind!turbines!in!the!AC!connected!wind!farm.!In!Fig.39!(c),!the!performance!of!MVMO!in!terms!of!convergence!speed!is!presented,!regarding!the!tap!positions!of!the!transformers.!!

!

!

,

,

,

,

Figure,39:,Convergence,graph,of,(a),wind,farm,active,losses,in,far&offshore,wind,farm,(b),wind,farm,active,losses,in,Borssele,wind,farm,(c)!transformers,tap,positions,

!

(b)!(a)!

(c)!

61!!

!

!

5.3.2! MVMO!Robustness!!

The!obtained!values!of!the!fitness!function!given!by!Eq.36!in!the!last!evaluation!done!in!the!MVMO!procedure!are!presented!in!Fig.40.!The!fitness!corresponds!with!the!value!of!the!24\hour!cumulative!optimum! cost! of!Case! 8,! since! all! the! constraints! are! satisfied! at! this! stage! (i.e.! no! penalty! value!affecting! the! fitness).! The! worst,! mean! and! best! fitness! values! obtained,! with! regard! to! the!cumulative! initial! cost,! are! included! in! the! figure.! These! values! were! computing! by! repeating! the!optimization!30!times.!The!small!difference!between!best!and!worst!values!shows!that!the!proposed!MVMO\based! solution! approach! is! robust! to! randomness! in! initialization! and! evolutionary!operations.!!

2 4 6 8 10 12 14 16 18 20 22 240

5000

10000

15000

20000

25000

30000

35000

Cost%(Euro)

Time%(h)

)best))worst))mean))Cumulative)Initial)Cost

%reduction

!

Figure,40:,Time,series,and,bounds,of,the,the,fitness,function,value,

!

!

!

! !

62!!

!

!

!

!

! !

63!!

!

6! Conclusions &

Future Research !

!

6.1! Introduction!!This!chapter!summarizes!and!brings!to!an!end!all! the!work!and!contribution!to!research.!The!main!goal!as!described!at!the!beginning!was!to!minimize!the!wind!farm!power!losses,!as!well!the!variations!of! the! transformers! tap!positions,!while! the!reactive!power!sources!are!operating! in!a!coordinated!manner.!The!first!step!was!the!implementation!of!a!NN\based!wind!speed!forecasting!method,!which!provides! the! inputs! to! the!optimization!algorithm.!Then,! two!different! reactive!power!optimization!approaches!were!presented.!Optimization! for!any!given!operating!point! results! in!minimum!losses,!but!it!doesn’t!allow!the!consideration!of!the!OLTC!costs.!Optimization!over!a!predicted!24\hour!time!horizon!solves!this!problem!by!including!in!the!objective!function!the!number!of!the!tap!changes.!The!Var!reference!of!the!entire!wind!farm,!as!well!the!tap!positions!of!the!transformers!are!provided!by!the!optimization!algorithm.!The!method!is!applied!in!both!far\offshore!and!near\shore!wind!farm.!A!metaheuristic!optimization!algorithm!called!MVMO!is!used!for!all!the!introduced!optimization!tasks.!!

!

6.2! Conclusions!!!

!! The!proposed!approach! for!performing!optimization!over! a!predicted! time!horizon!leads! to! significant! reduction!of! total! transmission! losses! and!minimum!number!of!transformer!tap!changes.!As!a!matter!of!fact,!the!life\time!of!the!switchable!devices!(e.g.! transformers)! is! reduced! and! consequently,! the! total! operational! cost! of! the!wind!farm!is!reducing.!!

64!!

!! The!numerical!results,!including!the!comparative!study!of!two!different!wind!farms,!demonstrate!that!the!application!of!MVMO!for!the!optimal!coordination!of!reactive!power!sources!in!both!near\!and!far\!offshore!wind!power!plants,!entails!robustness!and!enhanced!performance!in!terms!of!convergence!speed.!!

!!! The! convergence! speed!of!MVMO! is! strongly!affected!by! the! topology!of! the!wind!

turbines.!When!the!topology!of!the!wind!farm!is!balanced,!e.g.!equal!number!of!wind!turbines! in! each! bus,!MVMO! converges! faster! in! contrast!with! unequally! allocated!wind!turbines.!!!

!

6.3! Recommendations!on!future!research!!!

•! The! structure! of! the! NN! used! for!wind! speed! prediction!was! selected! by! trial! and!error!method,!where!various!attempts!were!made!in!order!to!reach!the!satisfactory!result.!However,! an!optimization! technique! can!be!used! in! order! to!determine! the!best!NN!architecture,!prior!to!the!training!and!learning!process!of!the!network.!The!optimization!problem!can!be!stated!as!the!most!appropriate!selection!of!number!of!input! and! hidden! layer! neurons,! as! well! the! learning! and! training! function! of! the!network.!In!addition,!a!metaheuristic!procedure!can!be!also!used!for!training!neural!networks.! Training! procedures! involves! selecting! the! optimal! values! of! the!parameters! such! as! weight! between! the! hidden! and! the! output! layer! and! bias!parameters!of!the!output!layer!neurons.!!!

•! A!stochastic!scenario!method!can!be!formulated,!by!including!the!forecasting!error!in!the! optimization! problem.! The! planning! of! the! reactive! power! can! be! done! for!several!scenarios!by!taking!into!consideration!the!stochastic!nature!of!wind,!as!well!the!uncertainties!in!wind!speed!forecasting.!!!

•! Extra! constraints,! e.g.! the! current! of! overloaded! lines,! can! be! added! in! the!formulation! of! the! objective! function,! in! order! to! achieve! better! results! for! the!optimal!coordination!of!the!reactive!power!sources.!!

!

65!!

!

66!!

References ![1]! P.!Bresesti,!W.!L.!Kling,!and!R.!Vailati,!“Transmission!expansion!issues!for!offshore!wind!farms!

integration!in!Europe,”!in!2008,IEEE/PES,Transmission,and,Distribution,Conference,and,Exposition,!2008,!pp.!1–7.!

[2]! A.!R.!Bhowmik!and!A.!K.!Chakraborty,!“Application!of!Non!Dominated!Sorting!Gravitational!Search!Algorithm!for!Solving!Optimal!Reactive!Power!Dispatch,”!in!third,IEEE,international,conference,on,computation,of,power,,energy,,information,and,communication,&,ICCPEIC,2014,!2014.!

[3]! I.!Erlich,!W.!Nakawiro,!and!M.!Martinez,!“Optimal!dispatch!of!reactive!sources!in!wind!farms,”!in!2011,IEEE,Power,and,Energy,Society,General,Meeting,!2011,!pp.!1–7.!

[4]! Q.!H.!Wu,!Y.!J.!Cao,!and!J.!Y.!Wen,!“Optimal!reactive!power!dispatch!using!an!adaptive!genetic!algorithm,”!Int.,J.,Electr.,Power,Energy,Syst.,!vol.!20,!no.!8,!pp.!563–569,!Nov.!1998.!

[5]! G.!K.!Venayagamoorthy,!K.!Rohrig,!and!I.!Erlich,!“One!Step!Ahead:!Short\Term!Wind!Power!Forecasting!and!Intelligent!Predictive!Control!Based!on!Data!Analytics,”!IEEE,Power,Energy,Mag.,!vol.!10,!no.!5,!pp.!70–78,!Sep.!2012.!

[6]! GWEC,!“Global!Wind!Report,”!Wind,energy,Technol.,!p.!72,!2014.!

[7]! “The!European!offshore!wind!industry!\!key!trends!and!statistics!2015,”!no.!February,!2016.!

[8]! S.!Saroha!and!S.!K.!Aggarwal,!“A!Review!and!Evaluation!of!Current!Wind!Power!Prediction!Technologies!2!Input!Variables!&!Their!Selection,”!vol.!10,!pp.!11–14,!2015.!

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[67]! B.!Length,!“Wind!Turbine!SWT\6!.!0\154,”!Siemens,AG.!

,,

!

!

!

!

!

!

!

!

!

!

!

!

!

!

!

71!!

!

!

!

!

!

!

!

Appendices

!

72!!

!

73!!

A Appendix

!

!

Technical!Specifications!of!Wind!Turbines!

!Description! Value!

Number!of!blades! 3!Speed!Range! 5\11!rpm!

Rotor!Diameter! 154!m!Swept!Area! 18600!m2!

Power!Regulation! Pitch!regulation!with!variable!speed!Cut\in!Wind!Speed! 4!m/s!Nominal!Power!at!! 10!m/s!Cut\out!Wind!Speed! 25!m/s!

Power! 6000!kW!Generator!Output!Voltage! 690!V!

Frequency! 50!Hz!Hug!Height! Site\specific!

!Table,4:,Siemens,SWT&6.0&154,[67],

!!Wind!Turbine!Configuration!in!PowerFactory!

!The! wind! turbine! models,! which! are! available! in! the! global! template! library! of! DIgSILENT!PowerFactory! is! used! for! the! load! flow! studies.! The! characteristics! of! the! wind! turbine! models!DFIG_WTG_0.69kV_6.0! MW! and! ! FullyRatedConverterWTG_0.4kV_6.0! MW! are! presented! in! the!following!tables,!respectively:!

!!

74!!

Description! Value!Apparent!power! 6667!kVA!Rated!Voltage! 0.69!kV!

Nominal!Frequency! 50!Hz!No.!of!Pole!Pairs! 2!Stator!Resistance! 0.01!p.u.!Stator!Reactance! 0.1!p.u.!

!Table,5:,Doubly,Fed,Induction,Generator,

!

Description! Value!Rated!Apparent!power! 6.669!MVA!Rated!Power!Factor! 0.9!

!Table,6:,Fully,Rated,Converter,wind,turbine,of,6,MW,–,Model,in,PowerFactory,

Wind!Turbine!Transformers!Configuration!in!PowerFactory!

!

The!transformer!types!included!in!the!wind!turbine!models!are!also!presented!below.!!

Description! Value!Rated!Apparent!Power! 6.7!MVA!Nominal!Frequency! 50!Hz!Rated!Voltage!(HV)! 33!kV!Rated!Voltage!(LV)! 0.69!kV!

Short\Circuit!Voltage!(uk)! 6!%!Copper!Losses!! 6.699069!kW!Vector!Group! Dyn5!

!Table,7:,2&winding,Transformer,for,6,MW,DFIG,wind,turbine,(0.69/33,kV),

,

Description! Value!Rated!Apparent!Power! 6.7!MVA!Nominal!Frequency! 50!Hz!Rated!Voltage!(HV)! 66!kV!Rated!Voltage!(LV)! 0.4!kV!

Short\Circuit!Voltage!(uk)! 6!%!Copper!Losses!! 5.599069!KW!Vector!Group! Dyn5!

Voltage!per!Tap!(HV!side)! 2.5!%!Range! [\2,!+2]!

!Table,8:,2&winding,Transformer,for,6,MW,Fully,Rated,Converter,wind,turbine(0.69/66,kV),

!

75!!

!Load!Flow!Analysis!in!PowerFactory!

The! load! flow!calculation!determines! the!active!and! reactive!power! flows! for! all! branches!and! the!voltage!magnitude!and!phase!for!all!nodes.!!

In!order!to!calculate!the!electrical!losses!of!the!system,!the!DPL!script!TimeSweep,is!used.!

76!!

B Appendix

Neural!Network!ToolboxNMATLAB!R2015b!

!A!list!of!the!training!algorithms!that!are!available!in!the!Neural!Network!Toolbox!software!and!use!gradient\!or!Jacobian\based!methods,!is!shown!in!the!following!table.!

!Function! Algorithm!

trainlm! Levenberg\Marquardt!trainbr! Bayesian!regularization!

trainbfg! BFGS!Quasi\Newton!

trainrp! Resilient!Backpropagation!

trainscg! Scaled!Conjugate!Gradient!

traincgb! Conjugate!gradient!with!Powell/Beale!restarts!

traincgf! Fletcher\Powell!Conjugate!Gradient!

traincgp! Polak\Ribiere!Conjugate!Gradient!!

trainoss! One!step!secant!traingdx! Variable!descent!rate!gradient!descent!!

traingdm! Gradient!descent!with!momentum!!

traingd! Gradient!descent!!

Table,9:,Available,training,algorithms,

!MATLAB!Software!provides!the!Neural!Network!Toolbox,!which!includes!functions!and!algorithms!in!order! to! create,! train!and! simulate!neural!networks.!The!Back\Propagation!Neural!Network!can!be!determined!by!using!the!following!functions:!

!

!

77!!

"! The! command, newff! generates! a! feed\forward! network! called! net,! with! the! default! tan\sigmoid!transfer!function!in!the!hidden!layer!and!transfer!function!in!the!output!layer.!

net,=,newfit(trainX,,trainY,,neurons)!

where,!!

! trainX:!the!measured!input!vector!of!dimension!n!(inputs)!! trainY:!the!measured!output!vector!of!dimension!m!(targets)!

neurons:!number!of!neurons!used!in!the!hidden!layer!!In!order!to!modify!some!settings!parameters,!such!as!the!performance!function,!the!training!function!and!the!number!of!epochs,!the!following!commands!are!used,!respectively:!!!,, , , , ,,,,,,,net.performFcn,=,'mse';,

,,,,,,,net.trainFcn='trainlm';,net.trainParam.epochs=1500;,

,"! The!command,train!actualizes!the!training!process!of!the!initial!network!generated!by!newff.!

netx,=,train(net,,trainX,,trainY),

During!the!training!the!following!training!window!opens.!The!window!displays!the!training!progress!and!allows!you!to!interrupt!training!at!any!point!by!clicking!Stop,Training!button.!

!

!

Figure,41:,Neural,network,training,window,in,MATLAB,toolbox,

78!!

After!the!training!is!stopped,!by!clicking!the!Performance!button!in!the!training!window,!a!plot!of!the!training!errors,!validation!errors,!and!test!errors!appears,!as!presented!in!the!following!figure.!

!

Figure,42:,Performance,of,the,trained,neural,network,

!Then,! by! clicking! the! Regression! button,! a! regression! plot! appears,! which! shows! the! relationship!between! the! outputs! of! the! network! and! the! targets.! The! three! plots! represent! the! training,!validation!and!testing!data.!The!dashed!line! in!each!plot!represent!the!perfect!relationship!and!the!solid!line!the!best!fit!linear!regression!line!between!outputs!and!targets.!!

!

!

Figure,43:,Regression,plot,of,the,trained,neural,network,

79!!

"! The! command, sim! simulates! the! network! and! is! used! for! testing! how! well! the! resulting!network!approximates!the!data.!

testY,=,sim(netx,,testX),

where,!!

! netx:!the!network!trained!by!train,!! testX:!the!input!vector!of!dimension!n!!!In!order!to!compare!the!measured!output!trainY!with!the!output!testY!of!the!trained!neural!network,!the!error!difference!is!computing!at!every!operating!point,!as!stated!below:!!!

Error,=,trainY&testY,!

!The!final!validation!must!be!done!with!independent!data.!!

!

!

! !

80!!

C Appendix

In!the!following!pages!the!layouts!used!in!DIgSILENT!PowerFactory!are!presented!for!the!far\offshore!and! near\shore! wind! farm! respectively.! The!main! part! of! every! wind! farm! is! shown,! because! the!layout!of!the!wind!turbines!is!considered!as!confidential!and!it!cannot!be!presented.!!In!each!of!the!buses,!at!the!LV\!and!MV\side!of!the!3\winding!transformers,!a!set!of!wind!turbines!is!connected.!!!

!

WF33D

EW

F33BB

WF33B

CW

F33CH

WF33C

FW

F33AD

SLA

CK

HE

LWIN

1

HN

2H

N1

HN

22H

N11

PC

C2

PC

C1

WF33A

A

TPC

C2

TPC

C1

TWF33D

TWF33B

TWF33C

TWF33A

WF33D

WF33B

WF33C

WF33A

WF33D

G

lne_HN22_HN2_1submarine_400mm..

lne_HN11_HN1_1submarine_400mm..

brk_WF33D_TWF33D_1

brk_WF33B_TWF33B_1

brk_WF33C_TWF33C_1

brk_WF33A_TWF33A_1

brk_HELWIN1_SLACK_1

brk_WF33DG_WF33D_1

brk_WF33DE_WF33D_1

brk_WF33BB_WF33B_1

brk_WF33BC_WF33B_1

brk_WF33CH_WF33C_1

brk_WF33CF_WF33C_1

brk_WF33AD_WF33A_1

brk_WF33AA_WF33A_1

brk_TPCC2_PCC2_1 brk_PCC2_HN22_1 brk_HN22_HELWIN1_1

brk_HN11_HELWIN1_1

brk_PCC1_HN11_1brk_TPCC1_PCC11

GR

ID

lne_D28H

V_W

F33DG

_1800m

m2_A

Llne_D

30HV

_WF33D

E_1

800mm

2_AL

lne_D21H

V_W

F33BB

_1800m

m2_A

Llne_D

22HV

_WF33B

C_1

800mm

2_AL

lne_D26H

V_W

F33CH

_1800m

m2_A

Llne_D

29HV

_WF33C

F_1800m

m2_A

Llne_D

23HV

_WF33A

D_1

800mm

2_AL

lne_D20H

V_W

F33AA

_1800m

m2_A

L

T2O

ff..

-4

T1O

ff..

-4

DIgSILENT

OW

P_B

_LVO

WP

_A_LV

OW

P_B

_MV

OW

P_A

_MV

Onshore_M

V_B

Onshore_M

V_A

Rail_B

Rail_A

3w_O

ffshore_Transf_B

3w_O

ffshore_Transf_A

Dum

my_Load

Breaker/S

..

Breaker/S

..

Breaker/S

..

Breaker/S

..

Onshore_Transf_B

Onshore_Transf_A

GR

ID

Breaker/S..

Breaker/S..Subcable_B

Subcable_A

Breaker/S..

Breaker/S..

Breaker/S..

Breaker/S..

Breaker/S..

Breaker/S..

12_9

11_9

10_8

5_8

2_8

6_9

9_7

8_9

7_9

4_7

3_7

1_9

Off_react_HV_A

Off_react_HV_B

On_react_HV_A

On_react_HV_B

On_capac_bank_MV_A

On_capac_bank_MV_B

On_react_MV_B2

On_react_MV_B1

On_react_MV_A2

On_react_MV_A1

DIgSILENT

Challenge the future