3. !
!
METAHEURISTICS,BASED!OPTIMAL!
!MANAGEMENT!OF!REACTIVE!SOURCES!IN!
OFFSHORE!WIND!FARMS!
!
!
Master'thesis'
by#
Aimilia,Myrsini!Theologi!
#
to#be#defended#publicly#on#Wednesday,#October#5,#2016#at#15:00#PM.#
!
!
###########Supervisors:## Dr.#ir.#Jose#L.#Rueda#Torres,#TU#Delft#
# # # Mario#Ndreko,#PhD#Candidate,#TU#Delft#
##
#
#
########Thesis#committee:## ########Dr.#ir.#Jose#L.#Rueda#Torres,#TU#Delft#
###########################Prof.#ir.#Mart#A.M.M.#van#der#Meijden,#TU#Delft#
!
!
#
#
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.##
#
#
#
#
Faculty#of#Electrical#Engineering,#Mathematics#and#Computer#Science#(EEMCS)#·#Delft#University#of#Technology#
5. !
!
Acknowledgements
!
!
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.!
!
!
Aimilia&Myrsini,Theologi,
Delft,,June,2016.,
7. !
!
!
!
!
!
!
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...
10. !
!
2.7! Optimal!Reactive!Power!Management!................................................................................!18!
3! NNbased!forecast!.........................................................................................................................!21!
3.1! Introduction!.........................................................................................................................!21!
3.2! Neural!Networks!..................................................................................................................!22!
3.2.1! Definition!.........................................................................................................................!22!
3.2.2! Usage!...............................................................................................................................!22!
3.3! Dayahead!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!
11. !
!
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!
!
!
13. ii!
!
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!mixedinteger!
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!onload!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!faroffshore!wind!farm!interconnected!with!HVDC!link!and!
the!ACconnected!Dutch!nearshore!wind!farm!Borssele,!located!in!North!Sea.!Several!test!cases!have!
been!investigated,!in!order!to!demonstrate!the!effectiveness!of!MVMO.!
!
!
!
!
!
–,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!
15. iv!
!
List of abbreviations
!
!
ABC! Artificial!Bee!Colony!Algorithm!
AC! Alternating!Current!
ACO! Ant!Colony!Optimization!
AI! Artificial!Intelligence!
AIS! Artificial!Immune!System!!
ANFIS! Adaptive!NeuroFuzzy!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! InsulatedGate!Bipolar!Transistor!
IWD! Intelligent!Water!Drops!Algorithm!
LBBO! Linearized!Biogeographybased!Optimization!
LCC! Line!Commutated!Converters!
16. v!
!!
!
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! Meanvariance!Mapping!Optimization!!
NFN! NeuroFuzzy!Network!
NN! Neural!Network!
NWP! Numerical!Weather!Prediction!
OF! Objective!Function!
OF! Objective!Function!
OLTC! OnLoad!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! TeachingLearning!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!
17. vi!
!
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!
$/0*1,4/>! Maximum!Tap!position!of!transformer!Tr!
34:;! Minimum!voltage!magnitude!of!the!buses!
34/>! Maximum!voltage!magnitude!of!the!buses!
3! Voltage!magnitude!of!the!buses!
.4/>
! Maximum!flow!limit!through!the!transmission!line!
.! Flow!through!the!transmission!line!
18. vii!
!
????@A*B
4:;
! Minimum!reactive!power!limit!of!WTG!
@A*B
4/>
! Maximum!reactive!power!limit!of!WTG!
@A*B! Reactive!power!reference!of!WTG!
:! Current!flow!through!the!cables,!lines!and!transformers!
:4/>
! Maximum!current!flow!through!the!cables,!lines!and!transformers!
>:
:;:$
! 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!
!
!
!
! !
19. viii!
!
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!
!
20. ix!
!
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!
!
22. 1!
!
?
1!Introduction
!
!
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!(VSCHVDC)!!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.!!
!
!
!
23. 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!steadystate!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! nonexistent,! 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!
mixedinteger!nonlinear!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!shortterm!operational!planning!(e.g.!dayahead!or!intraday).!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.!
24. 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!shortterm!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!onload!
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!shortterm!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.!
25. 4!
!
!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!
followup!research!are!proposed.!
!
! !
27. 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,! costeffective,! 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! fastestgrowing! renewable! energy!
source!and!recently!had!yet!another!recordbreaking!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.!!
28. 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!frontrunner!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!
29. 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! costminimization! 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!shortterm!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.!
!
30. 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! waveinduced! 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!DClink!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],
31. 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!highpole!
permanent! magnet! synchronous! machine! (PMSM).! Voltage! source! converters! and! a! stepup!
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!DClink!at!its!setpoint!and!
control! of! reactive! power! exchange! between! the! grid! and! the! wind! generator,! the! networkside!
converter!(NSC)!is!used.!
!
!
Figure,4:,Typical,layout,of,a,FRC&based,generator,model,[14],
!
In! the! most! popular! control! method! for! FRCbased! generators,! a! twolevel! cascade! controller! is!
implemented,! where! the! DClink! voltage! and! reactive! power! setpoints! 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!onload!tap!changing!transformer.!!
32. 11!
!
!
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!highorder!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.!
33. 12!
!
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:!
LCCHVDC! and! VSCHVDC.! 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! startup!
system! is! imperative! from! an! offshore! perspective.! Other! restrictions,! such! as! AC! grids! with!
determinate!reactive!power!compensation!and!short!circuit!capacity,!disqualify!LCCHVDC!for!large
scale!wind!farms![20].!
The! most! bleedingedge! technology! to! overcome! the! grid! integration! problems! in! offshore! wind!
farms!is!the!VSCHVDC,!which!is!named!by!ABB!manufacturers!as!“HVDC!Light”![21].!In!this!case,!the!
thyristors!have!been!replaced!with!fullycontrolled!IGBTs!with!highfrequency!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!
VSCHVSC! converter! stations! enable! smaller! and! cheaper! offshore! platform! size.! Ultimately,! VCS
HVDC! converters! are! appropriate! for! isolated! operation! and! for! creating! a! multiterminal! DC! grid!
[20].! For! longdistance! 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!
34. 13!
!
[23].! ! The! major! disadvantage! of! the! aforementioned! technology! is! the! higher! switching! losses!
caused!by!the!highfrequency!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! timescales;! 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.!
35. 14!
!
!
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! longterm! forecasts! and! as! source! data! in! other! prediction! methods! [28].! By! virtue! of! high!
computation!time!and!information!acquisition!difficulties,!the!shortterm!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!datadriven!approach,!
which!could!deal!with!nonlinear!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! realworld! applications! have! been! developed.! A! SVMbased! 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! SVMenhanced! Markov! model! is! presented,! which! refers! to! a! “nonparametric”!
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!LSSVMGSA!model!has!been!developed.!In!comparison!
with!ANN!and!the!other!SVM!models,!LSSVMGSA!reduces!the!computation!time!of!model!learning!
by! solving! a! linear! system! and! increases! the! correlation! coefficient! value,! despite! its! highly!
36. 15!
!
dependence!on!the!selection!of!the!kernel!function!and!its!parameters![32].!Regarding!to!shortterm!
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!nonstationarity!and!the!seasonality!of!wind!generation!
!! less!amount!of!historical!data!
!! dealing!with!wind!ramp!dynamics!!
!
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!(ENTSOE)![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.!
37. 16!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !
!
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/Qoperation!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.!!
!
Figure,9:,Minimum,requirements,for,the,P/Q&operation,range,of,a,generation,unit,changer,(Figure,
created,by,author,from,data,in,source,[38]),
!
38. 17!
!
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! nearshore! 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.!
!
!
!
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,! ENTSOE! 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.!
39. 18!
!
!
!
Figure,11:,Reactive,power,capability,of,HVDC,station,changer,(Figure,created,by,author,from,data,in,
source,[39]),
!
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!nonlinear,!mixedinteger!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! gradientbased! algorithms! in! different! ORPD! problems! is!
described.!Although!the!previous!mentioned!techniques!have!a!reduced!computational!time,!they!
struggle! with! nonlinear! and! nonconvex! 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.!
40. 19!
!
!
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! meanvariance! mapping! optimization! (MVMO)! [58],! linearized!
biogeographybased! optimization! (LBBO)! [59],! firework! algorithm! (FWA),! firefly! algorithm! (FA),!
cuckoo! search! (CS)! [60],! bat! algorithm! [61]! and! teachinglearningbased! 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!socalled!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.!
42. 21!
!
3! NN-based forecast
!
!
!
!
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!nonlinear!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!nonlinear!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!timeseries!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!predictionsimulation!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.!
!
!
43. 22!
!
!
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.!
!
3.2.2! Usage!
!
Some! of! the! main! advantages! of! neurons! are! the! large! degree! of! interconnection,! the! massive!
parallelism,!the!nonlinear!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.! Selforganization,! 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.!!
!
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.!!
44. 23!
!
!
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:!
!! reinitialization!and!retraining!
!! increase!the!number!of!hidden!neurons!
!! different!training!functions!
!! additional!training!data!
!
3.3.2! Implementation!in!MATLAB!
!
!
Figure,14:,Work,flow,of,the,neural,network,design,process,
!
Step!1:!Data!Collection!
The! wind! speed! timeseries! 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!northwest!part!
of!Europe,!in!Galicia,!Spain.!Specifically,!the!historical!data!cover!the!period!from!31!December!2012!
–!31!December!2013!(366!days).!
45. 24!
!
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!twolayer!feedforward!
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!backpropagation!network!has!
been!created,!the!weights!and!bias!for!every!layer!are!initialized!using!the!NquyenWidrow!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.!
46. 25!
!
4.7 = ?
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???????????????????(NO. 1)#
In!Neural!Network!Toolbox!software!various!training!algorithms!are!available,!which!use!gradient!or!
Jacobianbased!method.!In!terms!of!speed,!the!LevenMarquardt!and!the!QuasiNewton!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! 1e5!
!
!
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.!
!
47. 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 =
1
24
YZ,[] ^ − YZ,_`ab ^
c
cd
]Le
e/c
????????????(Eq. 2)!
!
The!second!criteria,!which!is!used,!is!the!mean!absolute!error!(MAE)!given!by!the!following!equation:!
TiV =
1
24
YZ,[] ^ − YZ,_`ab ^
cd
]Le
????????????????????????????????(Eq. 3)!
!
48. 27!
!
The!most!frequently!used!evaluation!criteria!is!the!mean!absolute!percentage!error!(MAPE):!
!
TikV =
1
24
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? % =
1
24
YZ,[] ^ − YZ,_`ab ^
YZ,[]
mnopmqo
cd
]Le
????????????????????????(Eq. 5)!
!
sℎuvu,???????????????????YZ,[]
mnopmqo
=
1
24
YZ,[] ^
cd
wLe
??????????????(Eq. 6)!
!
!
!
!
!
! !
51. 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!24hour!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!NNbased!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!setpoints!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]),
!
52. 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!setpoints!
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!multiobjective!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 ∙ }ÑÖÜáà],]
cd
]Le
??????????????????? Eq. 8 !
sℎuvu,????????????}ÑÖÜáà],] = 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.!
!
53. 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:!
????éèêq
Zëí
≤ 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!singleagent!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!
54. 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!zerovariance.!
!
!
Figure,18:,MVMO&based,procedure,for,optimal,reactive,power,management,(Figure,created,by,
author,from,data,in,source,[64]),
55. 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:!
òë
ëíë]
= òë
Zëí
+ vã{ô? òë
Z[î
− òë
Zëí
,???????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! denormalized! 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!
56. 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!wellknown!
57. 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!hfunction!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!hfunction!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.!
!
!
58. 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!NNbased!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!24hour!time!horizon.!
!
kZ =
1
2
∙ ¶ ∙ Sc
∙ ß ∙ Ü_ ∙ YZ
ä
???????????????????(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!cutin!and!cutout!speed.!The!cutin!speed!corresponds!to!the!minimum!wind!
speed!at!which!the!turbine!blades!overcome!friction!and!begin!to!rotate!and!the!cutout!speed!is!the!
wind!speed!at!which!the!turbine!blades!are!brought!to!rest,!in!order!to!avoid!damage!from!high!
winds.!!
61. 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!NNbased!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!NNbased!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!timestep!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!dayahead!
wind!speed!forecasting!method!was!applied!for!all!the!days!of!these!months.!Conclusively,!although!
the!forecasting!period!was!24hours,!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.!!
62. 41!
!
®©®!™? % = &´, (¨!
!
Figure,23:,Wind,speed,for,July,
!
!
®©®!™?(%) = &≠, '´!
!
Figure,24:,Wind,speed,for,October,
!
63. 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.!
64. 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!&!Offshore!
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! onload! tap
changing!transformers!of!6.7!MVA!rated!at!155/33/33!kV!each.!
!
