electrical cable optimization in offshore wind farms -a review · danish waters of lolland in the...

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Electrical Cable Optimization in Offshore Wind Farms -A review

Peacuterez-Ruacutea Juan-Andreacutes Cutululis Nicolaos Antonio

Published inIEEE Access

Link to article DOI101109ACCESS20192925873

Publication date2019

Document VersionPeer reviewed version

Link back to DTU Orbit

Citation (APA)Peacuterez-Ruacutea J-A amp Cutululis N A (2019) Electrical Cable Optimization in Offshore Wind Farms -A reviewIEEE Access 7 85796-85811 httpsdoiorg101109ACCESS20192925873

This work is licensed under a Creative Commons Attribution 30 License For more information see httpcreativecommonsorglicensesby30

This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI101109ACCESS20192925873 IEEE Access

Date of publication xxxx 00 0000 date of current version xxxx 00 0000

Digital Object Identifier 101109ACCESS2017DOI

Electrical Cable Optimization in OffshoreWind Farms - A reviewJUAN-ANDREacuteS PEacuteREZ-RUacuteA1 and NICOLAOS A CUTULULIS (SENIOR MEMBER IEEE) 212Department of Wind Energy Technical University of Denmark Frederiksborgvej 399 4000 Roskilde Denmark

Corresponding author Juan-Andreacutes Peacuterez-Ruacutea (e-mail jurudtudk)

This research has received funding from the Baltic InteGrid Project httpwwwbaltic-integrideu

ABSTRACT A state-of-the-art review of the optimization of electrical cables in Offshore Wind Farms(OWFs) is presented in this paper One of the main contributions of this work is to propose a generalclassification of this problem framed in the general context of the Offshore Wind Farms Design andOptimization (OWiFDO) The classification encompasses two complementary aspects First the optimumsizing of electrical cables with the three main approaches used nowadays static rated sizing dynamic loadcycle profile and dynamic full time series being conceptually analyzed and compared The latest techniquesand advances are described along with the presentation of potential research areas not thoroughly addressedtoday such as Dynamic Cable Rating and cablersquos lifetime estimation under time-varying conditionsSecond the network optimization of large OWFs is thoroughly presented dividing the problem witha bottom-top approach cable layout of collection system Wind Turbines (WTs) allocation to OffshoreSubstations (OSSs) number and location of OSSs and interconnection between OSSs and OnshoreConnection Points (OCPs) A comparison among different methods is performed taking into considerationthe main engineering constraints Global optimization specifically Binary Programming (BIP) or MixedInteger Linear Programming (MILP) is envisaged as the best way to tackle this topic The full combinatorialproblem is found to be better addressed following a Top-Bottom approach combining exact formulationswith high level heuristics or holistically with evolutionary algorithms

INDEX TERMS Balance of plant Cable sizing Combinatorial optimization Dynamic rating Electricalcables Heuristics Global optimization Mathematical programming Metaheuristics Offshore Wind FarmStatic rating

I INTRODUCTION

OFFSHORE Wind Farms (OWFs) represent one of thefastest and most steadily growing types of renewable

energy technologies for electricity generation The penetra-tion level has increased almost five times in the last sevenyears reaching a globally total installed power of nearly 19GW [1] This growth is mainly explained by reductions incosts of the technology [2] the Levelized Cost of Energy(LCOE) has dropped recently from 240 USDMWh to 170USDMWh accounting for the last five yearsOne of the main drivers for cost reduction is the economiesof scale which has been evident in the OWF industry bythe accelerated increase of Wind Turbines (WTs) individualpower and consequently the scaled up of the total installedcapacity of state-of-the-start OWFs The latter brings as sideeffect the increase of complexity for designing efficient andcost-effective infrastructure such as the electrical systems

given that i) the WTs are larger in power and numberbeing less uniformly scattered around the project area ii)the Offshore Substations (OSSs) are built farther away fromthe Onshore Connection Point (OCP) increasing the exportsystems transmission length and iii) more stiff completeand complex requirements from the Transmission SystemsOperators (TSOs) to the OWFs for providing auxiliaryservices are demanded All added up means the electricalinfrastructure costs can go up to 15 compared to the totalcapital expenses (CAPEX) [3] The last point together withthe remarkable impact in terms of efficiency and reliabilityover the operational performance of OWFs (OPEX) [4]turn the electrical infrastructure into a cornerstone matter indesigning the full systemBetween 2018 and 2028 more than 19000 km of cablesfor collection systems are prognosed to be installed worthpound536bn [5] while longer and bigger cables for export are

VOLUME XXX 2019 1



Peacuterez-Ruacutea J-A et al Electrical Cable Optimization in Offshore Wind Farms - A review

the trend Hence power cables represent an important aspectof the electrical infrastructure to be studied in the design ofOWFs not only because its obvious weight on economicmetrics but also due to its impact in the overall availabilityof these type of projectsThe OWFs electrical infrastructure design and optimizationis a multidisciplinary problem This fact that has been provedby a comprehensive literature survey performed in the mostimportant academic sources detecting a wide variety ofdefinitions strategies models and frameworks to optimizeperformance metrics related to electrical infrastructure Ad-ditionally this is a relatively new research area with no morethan 15 years of studies by scientists from different fieldstherefore plethora of methodologies and mathematical for-mulations have been proposed this is reflected by a relativelylarge pallet of objectives and requirements identified in thescholar literatureThere is a lack of a comprehensive review articles summariz-ing classifying and critically assess the current state of thistopic with only [6] published six years ago being identifiedHowever this manuscript focuses on micrositing collectionsystems optimization techniques transmission systems andbriefly addresses other topics consequently improvable bydeepening the scope of the cable sizing subject incorporatingnew developments and proposing a general classification ofitBy virtue of the above a literature review of the latesttechniques for optimizing electrical cables in OWFs is per-formed in this paper intending to provide a classificationof the problem while underlying its most important aspectshighlighting the advancements and finally identifying theopen challenges according to the authorsrsquo research

The current state of offshore wind farmsThe earliest OWF venture known as Vindeby located at theDanish waters of Lolland in the Baltic sea was decommis-sioned last September 2017 after 25 years of operation and243 GWh of energy produced [7] Vindeby was located ata distance from shore of 2 km and concrete foundationswere installed above seabed with maximum depth of 4 mThe project consisted of 11 WTs of 450 kW (495 MW totalinstalled power) By comparing the previous numbers withthe largest OWFs under operation nowadays (see Table 1)the accelerated growth of the industry in a rather short time isbecoming obvious with total installed powers in the order ofhundreds of MW export route lengths close to 100 km andmaximum water depths across the projectsrsquo area of almost40 m The escalation of those parameters means that somefactors become more relevant and complex to handle such asthe electrical infrastructure due to the increased investmentcomplexity in the designs and the requirement for newtechnologies able to withstand such new environmental andoperating conditions For instance on the one hand theincrease of WTs number causes the collection system designto scale up exponentially in terms of brute force designevaluation on the other hand the increase of WTs individual

power challenge the traditional voltage level used currently(33 kV) opening the door for new technologies of cableswith higher insulation capacities (66 kV) and in contrastlower power in WTs would require larger amounts of themdepending upon more sophisticated clustering techniques toallocate them in OSSs groups See in the Table 1 LondonArray doubles in WTs number to Walney Extension butthe last one has bigger WTs to compensate such differenceLikewise export route length is linked to decision-makingproblems such as choosing between AC and DC technologyvoltage level cables type converters type system structureand so on These trends are foreseen to remain as presentedin the Table 2 with OWFs projects already reaching the orderof GW (both because of bigger WTs and larger amountsof them) distances between OSSs and OCPs of more thana hundred of kilometers and water depths higher than 40m In fact among the list of OWFs under proposal stageprojects in the order of several thousands of MW are waitingfor consents to start construction stage The previous trendsmean that the share of the electrical infrastructure overeconomic metrics will be higher putting these concepts ina major role to be taken into account when planning OWFs

Design and optimization of offshore wind farmsThe Offshore Wind Farms Design and Optimization problem(OWiFDO) can be defined as the body of decisions tobe made in order to design reliable secure and efficientOWFs while maximizing their performance through theevaluation of a quantifiable target The definition of the set ofmodelling options constraints objective function variablesand parameters is up to the OWF developers accordingto established and particular practices The OWiFDO is anon-linear non-convex problem with integer and continuousvariables laying in the category of NP class [8] Due tothe mathematical complexity of the problem the full pic-ture of it can be split following a sequential divide-and-conquer approach such as the one illustrated in the theFig 1 where four subsequent sub-problems are defined i)macrositing ii) micrositing iii) infrastructures (includingstructural electrical and civil design) iv) and definition ofcontrol protection and operation schemes The main inputsare minimum and maximum number of WTs minimum andmaximum OWFrsquos total installed power and definition of theobjective constraints and other parameters The macrositingproblem encompasses i) analysis of the available infras-tructure (power system capacity at OCP logistic resourcesaccessibility etc) ii) evaluation of the environmental suit-ability (specially relevant in marine spatial planning) iii)wind resource potential assessment and iv) geographicaladequacy (most importantly maximum water depths) Themain output of this block is the selection of the OWF siteand the upper bound of projectrsquos area important economicfactors such as energy regulatory framework financing andfunding must be taken into consideration in this stage aswell in order to assess the financial sustainability of theproject Micrositing involves the OWF layout design where

2 VOLUME XXX 2019




TABLE 1 Largest OWFs under operation

OWF Capacity [MW] Turbines Export Route Length [km] Maximum Depth [m] Commissioning Year

Walney Extension 659 40x825MW47x7MW

75 23 2018

London Array 630 175x36MW 55 25 2013

Gemini 600 150x4MW 110 36 2017

TABLE 2 Largest OWFs under construction


Hornsea One 1218 174x7MW sim 120 37 2020

East Anglia One 714 102x7MW sim 73 40 2020

Kriegers Flak 6048 72x84MW sim 45 25 2021

Macrositing

Micrositing

InfrastructuresStrucElectCivil

ControlProtOper

OWiFDO(Inputs)

OWiFDO(Outputs)

1

FIGURE 1 Offshore Wind Farms Design and Optimization Problem (OWiFDO)An Overview

the arrangement of the individual WTs is decided in this sub-problem the number and geographical locations of the WTsalong with their sizing are defined After this the electricalinfrastructure is designed each of the civil structural andelectrical designs has its own mathematical entity hence inthis paper the electrical infrastructure is studied individuallyIt is important to note at this point that in order to guaranteean optimum design (or near) of the OWF the best possiblesolution in each block should be found while balancing theireffect on following blocks For instance when deciding theupper bound of the projectrsquos area care should be taken toharmonize the micrositing and the electrical infrastructuredesign because the minimization of the wake losses leadsto increased separation between WTs but at the expenseof longer cables required for the collection systems As analternative the loop in the Fig 1 can be closed to come upwith an iterative design processWith the electrical cables as main target in the followinga classification of the set of possible actions to optimize itsdesign according to common practices innovative solutionsand future actions to be considered in the short panorama isproposed

Optimization of electrical cables in offshore wind farmsA classificationThe problem classification can be seen in the Fig 2 In theleft branch the topics corresponding to optimum sizing ofelectrical cables are presented The definition of a cablersquosnominal current must take into account the high variabilityof offshore wind power and its relatively low capacity factor[9] This implies that a smaller nominal value can be chosengiven certain conditions The three main techniques used inOWFs cable sizing from the perspective of thermo-electricalconditions are presented in the followingStatic rated sizing represents the classic technique recom-mended in [10] [11] and [12] (industrial technical stan-dards) It a is straight-forward approach consisting only ina multi-parameter static equation for calculating the contin-uous current It to be transmitted during infinite time inorder to obtain a continuous conductor temperature equalto 90C The smaller cable t with It equal or greater than

Optimum Sizing NetworkOptimization

OWFs ElectricalCables Optimization

Static rated sizing

Dynamic loadcycle profile

Dynamic fulltime series

WTs CollectionSystem

WTs allocationto OSSs

Number andLocation of OSSs

InterconnectionOSSs to OCPs

1

FIGURE 2 OWFs electrical infrastructure problem classification

the total current (including capacitive currents) at hot spotis selected The aforementioned IEC and CIGREacute standardsconsider static conditions at rated operation however OWFsare characterized by low capacity factors and high powerproduction variability

VOLUME XXX 2019 3




In the last lustrum an emerging topic in OWFs cable sizingis being studied Dynamic Rating The two main approachesusing this technique are described in the followingDynamic load cycle profile consists in finding the worst casedynamic load profiles as presented in [13] (CIGREacute WorkingGroup B140) This approach is taking into account theinherent variability of power production representing a moresophisticated method that is emerging as industrial practiceas detailed in [13] It consists of a four-step signal calculatedusing the highest RMS values computed through differentperiods sweeping through the yearly data set by means of arolling RMS filter starting at each singular data point A pre-processing analysis is needed to be carried out to find the setof periods of interest In the study presented in [14] it hasbeen concluded that the periods of 7 days 10 days 40 daysand 365 days capture reasonably the most representativewindy days in a windy year Thus in a temporal sequentialordering the pre-conditioning current is derived calculatingthe RMS value for the whole data set lasting 308 days(remaining days after the periods 7 10 and 40) then thegreatest yearly RMS value using a period length of 7 daysis obtained keeping the same procedure for the periods of10 days and 40 days while not overlapping the periodsbetween them With the calculated four-step signal (includingcapacitive currents) the maximum conductor temperature iscalculated and similarly to the previous method the smallercable t with maximum calculated temperate lower than 90Cis chosen Note that this sequential arrangement represents aconservative criterion itself because of the assumed steadilyincrease of current with time Equivalent step-wise cyclicload profiles as in [15] and [16] represent other approach tooptimally size cables by obtaining cyclic currents followedby the application of the standard [11]Finally Dynamic full time series encompasses the use offull and high resolution time series for performing electro-thermal analysis The previous two methods exclude reliabil-ity analysis therefore new advances and strategies requiringtime series information such as generated power seabedsurface temperature thermal parameters among others arerequired Related to cables so far work has been focusedon i) conductor temperature estimation and ii) cables sizingconsidering a maximum instantaneous temperature neverexceeding 90C (which also is assumed in the previous twoapproaches) For conductor temperature estimation severalmethods have been developed Step Response (SR) FiniteMethod Analysis (FEM) and Thermo-Electrical Equivalent(TEE) model [17] A TEE (1-D) represents the model withthe best computation time-quality performance and is appli-cable for single-core and three-core type cables albeit new 2-D models are under study and proposed as per [18] Limitingthe conductor temperature to 90C is a well-establishedpractice as presented in [19] however a re-evaluation of therisk of exceeding this constraint in different time horizonsbecomes relevant and might be a way to avoid underuse ofthese componentsImportant progress has been done in this topic however there

is still room for new advancements such as the application oflifetime methods and probabilistic techniques for sizing thesecomponentsThe dynamics of the system must be consideredholistically being able to estimate fatigue factors to which areal operating cable is exposed to This can be achieved bydeveloping new lifetime models validating their parametersby real experiments in the frame of accelerated tests based onhistorical information and forecast values of produced powerseabed temperature soil thermal parameters and so onReal time control of OWFs while abiding thermal constraintscan be also merged with these concepts In general theprevious statements can be extrapolated to other power com-ponents like transformers [20] filters and compensationsunits In fact not much work has been found related to thelatter therefore representing a potentially important researchtopic in the short to medium termThe right branch of the Fig 2 represents the combinatorialoptimization problem related to the electrical infrastructurein OWFs The main objective is to achieve an optimized interms of length andor investment costs cable layout Giventhe mathematical complexity computational optimizationis required however project-specific particularities must betaken into account For instance the number of OSSs canbe defined in function of the number of constructing stagesof the project or the WTs clustering can obey to practicalreasons such as power balancing or standardization Specialattention is given to this topic as it has been addressed moreintensively in the scientific papers Section II deals with theseaspects

II NETWORK OPTIMIZATIONThe set of activities shaping the problem of the topologicalnetwork optimization can be seen in the right branch of theFigure 2 i) WTs collection system design ii) WTs allocationto OSSs iii) Number and location of OSSs and finally iv) theinterconnection between OSSs to OCPs It should be noticedthat the selected classification assumes classic OWFs designlarge AC OWFs (MV at collection system level and HV attransmission system operating at fn = 50 Hz) and HVDCconnected OWFs (with AC collection system and the ACDCstation next to the OSS) because those are the types plannedbuilt and under operation nowadays

A WTS COLLECTION SYSTEM DESIGNThis problem resembles to historical mathematical problemssuch as Minimum Spanning Tree (MST) and its constrainedversion the Capacitated Minimum Spanning Tree (C-MST)which classifies under the category of NP-hard class [21] andthe Travelling Salesman Problem (TSP) with all its variants[22] also NP-hard Problems from other fields map to thisone like telecommunication networks design back in the 60rsquosand 70rsquos [23] or network planning [21] however in the caseof OWFs Ad hoc methods are necessitated in function ofparticular spatial (nature reserve or occupied areas seabedbathymetry among others) planarity (non-crossing of cablestrenching requirements and so on) and technical (stochas-

4 VOLUME XXX 2019




Variables Parameters Objectives Constraints

Collection SystemDesign and Optimization

Which topology

Radial Radial+Star Radial+Star+Splices Single looped Others

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

OSS

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

Which objective

Length(L)

Invt(I)

Invt+Reliab(IR)

Invt+Losses(IL)

Invt+Reliab+Losses (IRL)

Choose solution method

1

FIGURE 3 OWFs collection systems design and optimization Decisionflowchart

ticity on power generation cables capacities topologicalstructure ancillary services support etc) constraintsBased on the literature review the set of actions used for thecollection system design and optimization are represented inthe flow chart of the Fig 3 starting from the data relatedto variables (binary integer continuous etc) parameters(unitary costs bounds etc) objectives and constraints defi-nition and continuing with selecting the topological networktype The range of options span networks ensuing differentpatterns i) radial ii) radial plus star iii) radial plus starplus splices iv) single looped and v) others as illustratedwith sample schemes in the same figure Each topologicalstructure must be defined along with the desired optimizationtarget i) Length (L) ii) Investment (I) iii) Investment plusReliability (IR) iv) Investment plus Losses (IL) and iv)Investment plus Reliability plus Losses (IRL) Finally thesolution method must be chosen for which the modellingchoices have to be in accordance with it The classifica-tion of the solution methods is shown in Fig 4 Clustering

Clustering Heuristics Metaheuristics Global optimization

Solution Methods for the CollectionSystem Design and Optimization

Enhanced heuristics Enhanced global optimization

1

FIGURE 4 OWFs collection systems design and optimization Solution meth-ods

techniques split the group of WTs into smaller subgroups

by maximizing the resemblance characteristics among indi-viduals in the same cluster and minimizing them for twoelements belonging to different subgroups the most usedalgorithms are [24] Quality Threshold (QT) (deterministic)K-means and Fuzzy C-Means (FCM) (both unsupervisedmachine learning processes) Heuristics are algorithms whichsequentially solve a problem by taking decisions in chainedsteps such as Prim [25] Dijkstra [26] Kruskal [27] Esau-Williams (EW) [28] Vogels Approximation Method (VAM)[29] among others in general following a deterministic man-ner Heuristics can be combined with clustering techniquesin order to cope with limitations in the former like cablescapacities Metaheuristics are designed to enhance tradi-tional heuristics for avoiding issues like falling into a localminimals [30] by use of probabilistic criteria for smartlysearching the entire design space Well-acknowledged meth-ods are Genetic Algorithm (GA) [31] Particle Swarm Op-timization (PSO) [32] Simulated Annealing (SA) [33] andAnt Colony Optimization (ACO) Ant Colony System (ACS)[34] Metaheuristics present a flexible approach and therecan be as many formulations as different authors Lastlyglobal optimization approaches are more transparent [35]and different formulations have been proposed Binary Inte-ger Programming (BIP) Mixed Integer Linear Programming(MILP) Mixed Integer Quadratic Programming (MIQP) andMixed Integer Non-Linear Programming (MINLP) the mostefficient formulations are commonly used since they map todifferent fields Global optimization requires external solvers(usually used as black box) which use algorithms such asBranch-and-Cut or Benders Decomposition [36]Combining different paradigms lead to new hybrid methodswhich mix their strengths in order to palliate the weaknessesAn example of that is merging global optimization withheuristics for accelerating the convergence into global min-imum resulting in new formulations called MatheuristicsA qualitative comparison between the fundamental versionsof the methods is presented in the Table 3 The main func-tional advantage of heuristics over the other methods is theirpolynomial running time this allows for obtaining solutionpoints very quickly However typically those solutions areconsiderably far away from the global minimum and ro-bust algorithms proposed so far optimize mostly for cablestotal length (L) The stochastic nature of the operators inmetaheuristic methods improve heuristic by offering betterquality solutions Similarly to heuristics metaheuristics areself-implementable exluding the need to use external black-box solvers However metaheuristics do not quantify thequality of the calculated solutions In order to cope withthe last drawback global optimization by means of math-ematical programming provide with a dual value during thecomputation which is translated into an assessment of thesolution quality Nonetheless external solvers are necessi-tated and the capacity to model the physics behind is ratherlimited (inherent to the mathematical program) In functionof the priorities established by the developer any solutionmethod could be categorized as best hence a clear distinction

VOLUME XXX 2019 5




between brightsides and drawbacks must be delimited priorto the selection of the method

TABLE 3 OWFs collection systems design and optimization Qualitative com-parison among the methods

Method Brightsides Drawbacks

Heuristics

bull Available bound forworst-case behavior

bull Polynomial runningtime

bull No need of externalsolvers

bull Primal bound ismostly weak

bull Purpose-builtalgorithms

bull Optimizes mostlyfor total length

Metaheuristics

bull Frameworks allowhigh modellingflexibility

bull Provides good pri-mal bound


bull No theory on qualityand running time

bull No worst-case anal-ysis

bull Computationally ex-pensive

GlobalOptimization

bull Dual bound avail-able during compu-tation

bull Transparent formu-lation

bull Similar to graph the-ory problems

bull Uncertainty on com-putational time andmemory

bull External solver is re-quired

bull Lacks modellingflexibility

The distribution on the application of these methods in ad-dressing the the OWFs collection systems optimization prob-lem in the scholarly literature (using the web search engineGoogle Scholar) is presented in Fig 5 It can be noted thatthe largest portion of the works apply GA (34) followed byBIP and MILP global optimization formulations (25) andheuristics - solely or combined with clustering techniques(19) Minorities are defined by other metaheuristics andglobal mathematical modelling types Different conclusionscan be drawn from this illustration Firstly GA shapes as themost preferred metaheuristic algorithm given its flexibilityand wide application in different fields [37] Secondly dueto their fast computation time heuristics represent a goodway of finding initial feasible points They are also subject

34

GA

25

BIP+MILP

19

Heuristics

8

PSO

4

MIQP

4

MINLP

4

ACO

2 SA

1

FIGURE 5 OWFs collection systems design and optimization Distribution ofapplied methods in the scientific literature

to the creativity of the designer to come up with differentimplementations Lastly global optimization represents onlythe third part of the options spectrum (BIP MILP MIQP and

MINLP) therefore a significant potential in this area is iden-tified especially on the proposition of efficient formulationsand how to integrate high fidelity models with them Hybridmethods combining global optimization with heuristics andmetaheuristics are scarce (apart of embedded heuristics in-cluded in commercial solvers such as [36]) albeit potentiallybeing able to solve large (between 80 and 100 WTs) andvery large instances (more than 100 WTs) Consequentlyparticular focus is directed towards global optimization inthis paperAccording to the literature review the distribution of theobjective functions as per the used solution methods is dis-played in the Fig 6 Total length (L) Investment (I) andInvestment plus total electrical losses (IL) have been han-dled using heuristics metaheuristics and global optimizationmethods on the other hand when reliability is involved asa target for the system mathematical formulations emergeas the best approach due to the flexibility easiness andexactness offered by analytical expressions integrated intothe framework Reliability assessment weighted out in theobjective function was addressed in [38] through a GAnevertheless the collection system was based on a grid-based pattern while limiting the possible connections to pre-established alternatives (radial looped etc) After selectingthe solution method the modelling choices must be carriedout taking into account the inherent biased caused by thechosen methodology Mainly five aspects needs to be exam-ined i) wake effects ii) wind stochasticity iii) power flow iv)electrical losses and v) reliability as schematized in Fig 7Wake effects are mostly important for micrositing optimiza-tion one of the most used models being the Katic-Jensengiven its linear behaviour and simplicity as implemented inthe pioneer work of more more advanced and accurate mod-els based on Computational Fluid Dynamics (CFD) are com-ing up nonetheless they are expensive computationally andhard to couple with computational optimization techniques[39] The impact of wake effect on the collection system op-

Heuristics Metaheuristics

Math Form

LI

IL

IRIRL

1

FIGURE 6 OWFs collection systems design and optimization Applicability ofsolution methods

timization has not yet been addressed on the literature henceassumed to be negligible Wind stochasticity deals with mod-elling the wind power production basically done by applying

6 VOLUME XXX 2019




either discretization of typical probability density functionsdepending on particular sites [40] or by simulating timeseries using computational models and historical information[41] the main two variables in this matter are wind speed anddirection The effect of change on the wind direction on thecollection system optimization has not yet been addressed inthe literature Power flow models going from low complexityto high complexity are transportation (Kirchhoffrsquos 2nd law)DCPF (assuming nominal voltages ignoring losses and reac-tive power) ACPF (full system of non-linear equations) andPoint-to-Point (in-detail transmission line modelling using aninfinitesimal lumped model with non-trivial differential equa-tions) [42] The power flow model drives to different optionsfor modelling the electrical losses as seen in Fig 7 In thisfigure is expressed the interrelation between several blocksFor instance a DCPF assumes no losses however they canbe computed by doing iterative methods [43] Likewise atransportation model can ignore losses or allows integratingit by means of linear or quadratic approximations AC powerflow inherently includes quadratic losses but can be ignoredin the objective function formulation Point-to-Point flowsyield to exact losses calculations [44] Reliability can bemodelled using deterministic and probabilistic approaches[45]The solution method selection and modelling choice arehighly interrelated Generalizing mathematical formulationshave the enormous advantage of being able to provide certi-fied optimum solutions when the problem is convex how-ever their application is subject to the use of commercialsolvers and certain mathematical knowledge of the problemis required for formulating it efficiently and taking advan-tage of its structure Therefore heuristics and metaheuristicscan be important because of their easiness in implemen-tation without the need of external solvers using highlyefficient programming languages Additionally formulationslike MILP do not allow explicit (pre-processing techniquescan be used as approximation) quadratic modelling of losses(therefore limiting power flow to either DCPF or transporta-tion models) and probabilistic reliability approaches arehandled by scenario numeration in a tree fashion or maybe simply ignored MIQP formulations can include quadraticlosses in the objective function however they are less ef-ficient computationally compared to BIP or MILP MINLPcan capture to a high degree the complexity of the problembut having the risk of formulating a non-convex problemOn the other hand heuristics and metaheuristics are moreflexible in that sense due to in theory the possibility toconsider all the complexity on physical modelling at expenseof not having an optimality guarantee The proper balancebetween solution method complexity and model fidelityrepresents one of the main challenges for the designer andcompromises have to be adopted within certain assumptionsEach of the different topological network options accordingto the literature are discussed in the following describingthe most sound solution methods modelling choices andspatialplanarity constraints handling

Wake EffectsOther

VertexPacking

Katic-JensenMachineLearning

CFD

No

Wind Stochasticity

Deter

SampWind pdf

Sim Wind

SampWindDir

pdf

SimWindDir

Other

Power Flow

No

Transportation

DCPF

ACPF

Point-to-Point

Electrical Losses

Exact

Quadratic

No

Other

Linear

Reliability

NoDeter

Probabilistic

1

FIGURE 7 OWFs collection systems design and optimization Modellingchoices The black edges express the relation between different blocks

1) Radial topology

As presented in Fig 3 a radial network is that for whichbranching is not allowed in the nodes corresponding toWTs mathematically it represents a tree graph with degreeequal to 1 or 2 for all vertices belonging to the WTs setTwo publications dealing with this issue are analyzed in theTable 4 and Table 5 Two approaches are developed in [46]one by means of modifications to the probably best-knownVehicle Routing Planning (VRP) heuristic (O(|Vc|2 log|E|+|E||Vc| + |Vc|C)) the Clarke and Wright savings and theother through the formulation of an BIP model using astraight-forward hop-indexed formulation with planarity con-straints (this is very practical for instances where the largestcable capacity C is between 5 and 10 nodes as in OWFs[47]) These two methods were compared in 18 differentinstances for three OWFs (Barrow with 30 WTs and 1 OSSSheringham Shoal with 88 WTs and 2 OSSs and Walney 1with 51 WTs and 1 OSS) The BIP model takes up to 20minutes for solving to optimality all the evaluated instanceswhile the best heuristic requires less than 0060 secondsalbeit generating solutions on average 2 more expensiveThose are positive results however the level of complexityfor the models is rather limited as presented in the Table4 ignoring wake effects windreliability stochasticity andpower losses Additionally the available set of cables isrestricted to only 1 and computational experiments pointout the escalation on computation time when the capacity Cand number of allowed cables are augmented An importantaspect about the heuristics is their inability to optimize thetotal investment when choosing the cable type therefore onlyapplying to minimizing total length (L) this limitation isovercome by the BIP formulation Similar choices are madein [48] but applying a GA algorithm Comprehensive costmodels have been used in this work encompassing the costof cables WTs transformers and OSSs however advantagesover exact formulations can not be embodied Nevertheless

VOLUME XXX 2019 7




enhancements over heuristics are achieved by including thecable type selection and improving solutions quality Re-garding the spatial and planarity constraints handling a wayto model non-crossing cables for mathematical formulationsis by implementing a lazy constraint callback consisting instating the corresponding constraints during the constructionof the branch-and-cut tree when incumbents are found at anynode By means of this procedure finding of the maximalcliques in the graph is circumvent Both works neglect spatialmodellings such as seabed bathymetry and restricted zones

2) Radial plus star topologyA collection system network considering simultaneously ra-dial and star structures is presented in Fig 3 This prob-lem is equivalent to a C-MST considering the capacitatedconstraint to be equal to the power capacity of the largestavailable cable (U) and it is a superset of the radial versionAs demonstrated in [31] and [49] branched trees performbetter in terms of total trenching length compared to non-branched trees however the decision of whether permittingbranching at WTs or not from an optimization point ofview depends strongly on the cost models assumed forcables WTs switchgears and other electrical components[50] A comprehensive summary of publications related tothis problem is given in Table 6 and Table 7 and based on thissurvey it has been identified a lack of consideration aboutthe previous point meaning papers has not implementedany strategy for accounting these expenses perhaps due tothe scarce information about cost functions of all electricalcomponents involved in the design Likewise the impact ofwake effects on the electrical collection systems has not yetbeen addressed applying exact mathematical formulationsthis includes the effects of wind directionOne of the main contributions in [51] is the proposition ofheuristics (with proof of admissibility) for optimizing invest-ment of WTs interconnections with multiple cables selectionhowever being feasible to implement for up to 14 WTs inthis work the exponential time complexity of BIP models isalso remarked Large instances of OWFs collection systemdesign applying heuristic is proposed in [52] taking intoconsideration cable choices and power losses neverthelessformalities such as Big O notation and proofs are dispensedMetaheuristics have been widely used in the literature suchas the work in [53] where results compared to deterministicheuristics are considerably improved by means of a PSOframework Exact mathematical formulations encompass ba-sically 4 different types i) BIP ii) MILP iii) MIQP and iv)MINLPBIP and MILP modelling represent the most basic ap-proaches and cover problems instances where is required tooptimize length or investment Many scientists agree on thefact that BIP and MILP present the best balance betweensolution quality and computation time The challenge con-sists on finding efficient strategies for adapting high fidelitymodels into those programs for incorporating for instanceelectrical power losses or reliability pre-processing decom-

position or heuristics shape up as the way to go to cope withthis issueThe base formulations of BIP and MILP models are pre-sented These are able to cope with an arbitrary numberof WTs wn and considering only one OSS although withfurther modifications can be extended for multiple OSSs Letthe OSS define the set No such as No = 1 likewise forthe WTs Nw = 2 middot middot middot 1 + wn The I2 norm betweenpoints i and j is defined as dij These sets and parameters are condensed as a weighteddirected graph G(N AD) where N represents the vertexset (N = No cupNw) A the set of available arcs arrangedas a pair-set and D the set of associated weights for eachelement aij isin A where i isin N and j isin N For instance foraij = (i j) d = dij where d isinD In general G(N AD)is a complete directed graphAdditionally a predefined list of available cables types isdefined Let the set of cables be T In this sense let thecapacity of a cable t isin T be ut (in terms of number ofsupportable WTs connected downstream) Hence let U bethe set of capacities sorted as in T Furthermore each cabletype t has a cost per unit of length ct in such a way thatut and ct describe a perfect positive correlation The set ofmetric costs is defined as C In this sense the parameterctij defines the cost of installing a cable t between i andj The set χ stores pairs of arcs (i j) (u v) which arecrossing between each other this constraint also includes theinverse arcs of those elements This constraint is a practicalrestriction in order to avoid hot-spots and potential single-points of failure caused by overlapped cablesBIP

minsumiisinN

sumjisinNw

|T |sumt=1

utsumk=1

ctij middot yktij (1)

subject to

sumiisinN

|T |sumt=1

utsumk=1

yktij = 1 forallj isinNw (2)

sumiisinN

|T |sumt=1

utsumk=1

k middot yktij minussum

iisinNw

|T |sumt=1

utsumk=1

k middot yktji = 1 (3)

forallj isinNw

xij + xji + xuv + xvu le 1 forall (i j) (u v) isin χ (4)

|T |sumt=1

utsumk=1

yktij minus xij le 0 forall(i j) isin A (5)

xij isin 0 1 yktij isin 0 1 (6)

forall(i j) isin A and t isin 1 middot middot middot |T | and k isin 1 middot middot middot ut

MILP

minsumiisinN

sumjisinNw

|T |sumt=1

ctij middot ytij (7)

8 VOLUME XXX 2019




TABLE 4 Radial Collection Systems Papers Objective Solution Method and Modelling Choices

Objective Solution Method Wake Effects Wind Stochasticity Power Flow Elect Losses Reliability Paper

L Heuristics Modified Clarke andWright

No Deterministic Transportation No No

[46]I Global optimization BIP

hop-indexedNo Deterministic Transportation No No

I Metaheuristic GA No Deterministic Transportation No No [48]

TABLE 5 Radial Collection Systems Papers Spatial and Planarity constraints handling

Seabed bathymetry Non-crossing cables Restricted zones Paper

No Lazy Constraint Callback No [46]

No No No [48]

subject to sumiisinN

fij minussum

iisinNw

fji = 1 forallj isinNw (8)

sumiisinN

|T |sumt=1

ytij = 1 forallj isinNw (9)

|T |sumt=1

ut middot ytij ge fij forall(i j) isin A (10)


|T |sumt=1

ytij minus xij le 0 forall(i j) isin A (12)

fij ge 0 xij isin 0 1 ytij isin 0 1 (13)

forall(i j) isin A and t isin 1 middot middot middot |T |

The main features of the basic BIP formulation are

bull Variables Two set of binary variables are required Onthe one hand xij is equal to one if an arc with head in jis selected on the other hand yktij is one if the arc (i j)is selected using the cable type t and connecting k WTsdownstream (including the one in j) Thus the worst-case maximum number of variables is |N |2 + U middot |T | middot|N |2

bull Constraints Constraint (2) permits keeping the topologyof the solution and selecting only one cable type perarc Constraint (3) is the flow conservation equation thisalong with the variables definition allows for respect-ing the cables capacity constraints Constraint (4) andConstraint (5) avoid the use of crossing cables FinallyConstraint (6) defines the variables type Excluding thecrossing constraints which are not fundamental restric-tions the number of constraints is given by 2 middot |Nw|

bull Flexibility In this context flexibility is defined as thecapability to reformulate the objective function withoutaltering the nature of the whole formulation if totalelectrical active losses are required to be optimizedsimultaneously with investment (IL) In this case thefollowing term can be added into the objective (1)

sumiisinN

sumjisinNw

|T |sumt=1

utsumk=1

3 middot dij middotRt middot k2 middot I2n middot yktij middot wf

where Rt is the resistance per unit of length of cablet In is the nominal current of a single WT and wf isthe weighting factor to quantify the losses in the samedomain as the investment

Correspondingly the features of the basic MILP formulationarebull Variables Three set of variables are required fij is

linear and models the flow in the arcs xij is one if thearc (i j) is considered in the solution and ytij if a cablet is used in that arc Thus the worst-case maximumnumber of variables is 2 middot |N |2 + |T | middot |N |2

bull Constraints The Constraint (8) is the flow conservationequation and avoids also cycles (loops) Constraint (9)allows keeping the topology of the solution Constraint(10) ensures not exceeding the cables capacity Con-straint (11) and Constraint (12) avoid the use of crossingcables Constraint (13) defines the variables type Thenumber of fundamental constraints is |N |2 + 2 middot |Nw|

bull Flexibility There is no possibility to include total elec-trical active losses without reformulating the model Byincluding a quadratic term utilizing the flow variablesa MIQP formulation can be obtained additionally alinear loss function can be considered and through themultiplication of ytij and fij a MINLP model is formu-lated (may be linerizable)

Comparing the basic BIP and MILP formulations one canconclude that the number of variables are in the same orderwhilst the number of constraints are considerable less inBIP than in MILP Other important advantage of the binaryformulation over the mixed one is its flexibility to be adaptedfor IL problems The advantage of modelling explicitly theflow in the arcs in MILP formulations may be useful whentrying to optimize taking into account the wake losses inthe WTs when different WTs models are considered andwhen including the active power losses in the computation ofupstream WTsIt must be stated that further simplification to both modelscan be proposed either by strategies to reduce the number

VOLUME XXX 2019 9




of variables [54] by means of pre-processing techniquesor by adding valid inequalities or cuts [55] Particularly ithas been shown in [56] how to include total active lossesusing a MILP formulation through pre-processing and howto smartly limit the search space to speed up the terminationunder certain optimality conditions These hybrid methodscombining classical global optimization with heuristics rulesare called MatheuristicsIt is still an open research question to prove analyticallyin this context which formulation is better than the otherGiven a set X sube Rn and two formulations P1 and P2

for X P1 is a better formulation than P2 if P1 sub P2

[57] This means that if P1 is a strict subset of P2 thenP1 is a better formulation than P2 because the feasible setis smaller Suppose P1 P2 are two formulations for theprogram mincx x isin Zn with P1 a better formulationthan P2 If zLP

i = mincx x isin Pi for i = 1 2 arethe values of the associated linear programming relaxationsthen zLP

1 ge zLP2 Nevertheless the required solution time

and memory capacities for both programs may not have anylink with this fact given the unpredictability of combinatorialproblems Further experiments need to be implemented tocome up with a representative statistical sample to infer aboutwhich formulation solves more efficientlyAnother action to include losses in a linear model is by aniterative method as in [43] where the structure of the problemis exploited by Bendersrsquo Decomposition reducing drasticallycomputation time Wind power stochasticity and reliabilitycan be included in linear formulations with scenario numer-ation as in [43] and [45] where a Markov model is used tocalculate the states probabilities of cables and finally a tree isformed numbering all possible operating scenarios The latteropened the door for stochastic optimization in the collectionsystem problem concepts that is also applied in transmissionexpansion planning or unit commitment for example Themodel is formulated as a two-stage stochastic problem wherethe first-stage variables represent the set of connections tobuild and the second ones power and energy curtailmentThe resulting system considers parallel cables installed in thesame trench which is not common in practiceMIQP formulation permits including quadratic approxima-tion of electrical losses embedded in the optimization modelincorporating probabilistic modelling of the stochasticity ofwind and reliability in the same framework but its computa-tional efficiency is low compared to linear formulations [58]and is dependant on the positive semidefinite nature of theobjective function to be a convex problemFinally a MINLP formulation [59] captures the full complex-ity of wind stochasticity power flow and electrical lossesand with Benders decomposition solving iteratively a masterand subproblems the feasibility of the final solution may beobtained by adding constraints The main drawback is thenon-convex nature of these problems and the possibility tofall into local minimalsModelling the complexity of terrains initially by a WRP inonshore cases (see Table 7) is proposed in [51] where the

terrain is modelled as a grid and each cell is attributed witha coefficient to modify the cablesrsquo length This may be theway to go in OWFs For exact mathematical formulations themost used way to add up cables crossing constraints is byfollowing the explained lazy constraint callback approachalthough additional experiments are required to infer aboutthe possibility to exploit these constraints as valid inequal-ities in small problem instances concerning metaheuristicspenalization strategies when dectecting the crossings usingspecialized algorithms such as Bentley-Ottmann [64] aregenerally appliedModelling restricted zones is transparently achieved byadding up fixed edges in order to approximate the areas withpolygons as in [56] and [61] The main disadvantage of thelatter is that for complex shapes useful areas can be discon-sidered forcing the final solution to be non-optimal thereforein [62] (linearized MINLP) a more detailed approach withDelaunay triangulation and shortest path algorithms is pro-posed [65]

3) Radial plus star plus splices topologyCollection systems with optional intermediate nodes (splicesfor connecting cables outside of WTs switchgears) is illus-trated in Fig 3 An exhaustive handbook of Steiner tree prob-lems is available in [66] for NP-Complete variants Currentlythere are no OWFs implementing this approach not evenunder planning stage however it is presented in this paper asa way to show its applicability from an academic perspectiveSteiner tree formulation has been used in [67] [68] and[69] In all these articles the objective function is the totaltrenching length of cables this being the biggest advantage ofSteiner tree formulations However this does not necessarilymeans that the total investment cost is optimized Likewiseall these articles use greedy heuristics for solving the prob-lem which provide good solutions but without proofs ofcorrectness and optimality Regarding modelling choices thesimplest approaches were chosen no wakes deterministicwind speed transportation power flow and no reliabilityconsidered since the adopted solution methods were nottailored for OWFs application

4) Single looped topologyLondon Array OWF described in Table 1 follows a singlelooped collection system pattern as the one presented inFig 3 Tailored methods for single looped design have beenproposed in [70] and [71] A set of different algorithmscombined and nested are used in [70] in a hierarchicalfashion having as most internal block a Multiple TravelingSalesman Problem (MTSP) solver which is an extension ofthe classical Travelling Salesman Problem (TSP) but withM salesmen s1 middot middot middot sM who have to visit each ci citiesc1 middot middot middot cM There are plenty of heuristics to obtain goodquality solutions for the TSP as Farthest Insertion algorithmand the Chained Lin Kernigan algorithm [72] the latterpresents a gap with the Held-Karp lower bound of 02The objective function of this particular sub-problem is the

10 VOLUME XXX 2019




TABLE 6 Radial plus Star Collection Systems Papers Objective Solution Method and Modelling Choices

Objective Sol Method Wake Effects Wind Stoch Power Flow Elect Losses Reliability Paper

IRL Global optimization MILPBendersrsquo Decomposition

No Sampling Wind pdf DCPF Other Iterative Probabilistic [43]

IL Global optimization MILPMatheuristics

No Sampling Wind pdf Transportation OtherPreprocessing

No [56]

I Heuristics BacktrackingDivide-and-Conquer




IL Heuristics Modified Prim Katic-Jensen Simulation Wind Transportation Quadratic No [52]

I Metaheuristics PSO No Deterministic Transportation No No [53]

I Global optimization MILPhop-indexed

No Deterministic Transportation No No [60]

I Global optimization BIPhop-indexed




IL Global optimization MINLP No Deterministic Transportation Linear No [62]

IL Global optimization MINLPBendersrsquo Decomposition

No Simulation Wind ACPF Quadratic No [59]

L Heuristics Enhanced MST No Deterministic Transportation No No [63]

IL Global optimization BIP basichop-indexedBIP reformulated

hop-indexed

No Deterministic Transportation OtherPreprocessing

No [54]

IRL Global optimization MIQP No Sampling Wind pdf Transportation Quad Probabilistic [45]

TABLE 7 Radial plus Star Collection Systems Papers Spatial and Planarity constraints handling


No No No [43]

Weighted Region Problem (WRP) No No [51]

No Lazy Constraint Callback Steiner nodes [56]

No No No [52]

No No No [53]

No No No [60]



No Lazy Constraint Callback Delaunay triangulationShortest Path [62]

No No No [59]

No No No [63]

No No No [54]

No No No [45]

cablersquos total trenching length and the simplest modellingoptions are considered Special attention must be paid to theforbidding of cables crossing which must be also handled bythe strategy for clustering the feeders

5) Others topologiesThe proposition of different types of topologies not map-ping to mathematical formulations but carried out followingparticular criteria of the OWF developers has also beenadressed in the literature in articles such as [73] [74] and[75] Those designs are the result of a case-by-case analysis

where limited networks are studied by means of economicspower flow reliability and dynamic analyses applying spe-cialized software The main output of these studies is thebest topology for a particular OWF from a set of finite self-designed networks Examples of these special designs arestar design single-sided ring design combined double-sidedhalf design single-sided ring design modified double-sidedhalf ring design and others

VOLUME XXX 2019 11




B WT ALLOCATION TO OSSIn Section II-A the assumption is that there is only 1 OSSwith a specified geographical location In this Section weconsider one step up in the complexity layer (bottom-upapproach) Given a large OWF with pre-defined number ofOSSs (greater than 1) and WTs (typically greater than 100WTs) with given geographical locations design the collec-tion systems in such a way that a WT is allocated unequivo-cally only to one OSS (ie no direct electrical coupling fromone WT to more than one OSS) while guaranteeing the OSSscapacities (in terms of nominal power) are not exceededTo solve this there are three alternatives i) a single approachwhere this is solved simultaneously with the collection sys-tem problem ii) a multi-step approach where as a first stepthe WTs are clustered and then each WTs-OSS problem issolved individually by means of one of the methods explainedin the previous Section or iii) a nested approach whichbasically consists on an iterative calculation process wherein the outer loop the WTs allocation problem is addressedand in the inner loop in turn the collection system is tackledIn the single approach mathematical formulations can beused transparently to leave the optimization set up to dealwith the full problem as in [46] or [56] however for largeOWFs this may be computationally expensive as presented in[51] Nevertheless this is the exact way to solve the problemto optimality Given the flexibility of metaheuristics methodsthey can be easily designed to handle this issue but due tothe combinatorial complexity it may be challenging to beadapted as explained in [31] Using a multi-step approachhelps handling the problem complexity with two ways tosplit up the WTs in OSSs groups a) mathematically byformulating the problem using network theory for instanceas a Minimum Cost Flow Problem (MCFP) [76] or b)by applying clustering algorithms like QT K-means FCMamong others MCFP allows shaping the problem with anBIP mathematical formulation and the network simplex al-gorithm can be applied to solve it to optimality by exploitingthe problem structure and the duality conditions Finally aniterative approach similar to the one used in [63] where usingpattern search the WTs clustering can be updated based oniterative calculations of collection systems searching for acheaper solutions

C NUMBER AND LOCATION OF OSSIn the Section II-B it was considered the number and locationof OSSs are defined as inputs however when these pointsare part of the decision-making problem there are differentalternatives to go through it As a generalization authors haveregarded this problem including the WTs allocation to OSSstherefore one could consider it as a variant with the addedcomplexity of deciding the OSSs number and geographicallocation Three different alternatives of this problem havebeen found i) variable OSSs number and variable OSSslocation ii) fixed OSSs number and variable OSSs locationand iii) variable OSSs number and fixed OSSs positionVariable number and location of OSSs has been coped by

means of a multi-step approach in [77] (MILP formulation)[78] (GA) [79] (FCM plus Prim algorithm) and [80] (im-mune GA) The work of [77] may be the first work dealingwith this issue (onshore case) using mathematical modelsdividing the full problem into wind farm production opti-mization model and wind farm infrastructure optimizationmodel the potentials of MILP formulations for solving thisproblem were pointed out although basic physical modellingchoices were selected The impact of different number andlocation of OSSs is studied in [78] but the set of potentialalternatives were rather limited and the collection system isassumed to be symmetrically distributed in terms of WTsA FCM algorithm for clustering WTs into OSSs and findingtheir location considering the shapes centroid (the maximumnumber of OSSs must be pre-defined) followed by a FCMalgorithm to group the WTs into feeders is used in [79]Listing heuristically the possible set of OSSs number iscarried out in [80] this is accompanied by the subsequentdesign of the WTs collection system A nested approach hasbeen applied in [32] and in [70] An external layer using aPSO algorithm deciding the number of OSSs and locationis designed with an internal layer clustering the WTs intoOSS groups by means of a FCM algorithm in [32] In everyiteration the OSSs number and location are updated and thisis followed by an internal recalculation of the WTs divisionand collection system Likewise a nested hierarchical designis proposed in [70]Fixed OSSs number with variable position is more typicallyintegrated in single approaches using mathematical formula-tions like in [43] and [81] although of course using meta-heuristics is also possible A multi-step approach is proposedin [62] where a Capacitated Centred Clustering Problem(CCCP) and a heuristic is used to find the OSS locationLastly a nested approach can be found in [63]Variable OSSs number with fixed position is not so commonthe work in [82] is considered to follow this procedurebecause it is clear the number of OSSs is encoded in theGA but not their positioning therefore it is assumed they arefixed

D INTERCONNECTION OF OSS TO OCPLet divide this problem into two variants i) point-to-pointinterconnection between a single (or few) OSS to a single(or few) OCP and ii) interconnection between multiple OSSsand multiple OCPs (large OWFs spread out in a large area)Regarding the first problem it basically consists on findingthe proper balance between the collection system design(including the OSS positioning) and the transmission systemdesign (export system to connect the OSS to the OCP)given that the shorter distance between OSS to OCP themore expensive the collection system but the cheaper thetransmission system Most of the authors assume negligiblethe influence of OSSs location to the transmission systemcosts inside of a given range Nevertheless in works like [83](onshore case) [84] multi-fidelity and heuristics approachesrespectively are considered to analyze the trade-off between

12 VOLUME XXX 2019




these two costs Other works taking into consideration simul-taneously the collection system design (with OSSs location)and the transmission system design are [43] [32] [85] [70][82] [86] [87] and othersWhen the problem is seen from a broader perspective theinterconnection between multiple OSSs and multiple OCPsgets more interesting In this case the OWFs are seen in anaggregated way disconsidering the collection system designand calculating the total installed power of the OWF A GAalgorithm to support decision-makers about OWF transmis-sion system developing and long-term offshore grid planningis proposed in [88] in this work the objective is to providea ranking sorted by their total lifetime costs of differentelectrical options to interconnect OWFs between each otherand to OCPs using either HVAC or HVDC technology andsupporting radial ring and meshed designs At the enddecisions of whether new connections or reinforcements inthe onshore grid are required are also provided One of themain disadvantages of this work is that the implementationhas to be improved to apply the developed methodology tolarger power systems and also other types of technologiesfor electricity generation are not considered which can bevery important for a holistic offshore grid planning Thelatter aspects has been handled in the series of publications[89] [90] and [91] A MILP model to solve the transmissionexpansion problem accounting for fluctuations in wind powergeneration and load is proposed in [89] where not onlyoffshore energy is considered but also other types such ashydro gas among others The tool helps to decide about thefeasibility to install DC breakers compared to AC breakers inmeshed systems This work was extended in [90] includingclustering of OWFs into larger groups in order to reducecomputation time followed by an offshore grid optimizationThe tool seeks to find a balance between new OWFs projectand the integration with new or reinforced interconnectorsbetween countries while having present other types of elec-tricity generation connected to OCPs Lastly the designedtool was applied to the case study of Baltic Sea in thetime horizon 2030 in [91] Main results indicate that radialconnections are preferred when OWFs are highly scatteredbetween each other in contrast to meshed grids which aremore benefitial for agglomerated OWFs in a given area Thelatest works can be improved considering optimal power flow(AC or DC) and integrating more sophisticated platforms toforecast the energy produced in different time horizons

III CONCLUSIONSA detailed review regarding the optimization of electricalcables in Offshore Wind Farms (OWFs) is carried out in thisarticle As a result the full picture of the problem is dividedin two main branches optimum sizing of electrical cablesand network optimizationRegarding the former the three main techniques availabletoday in the industry practices and scientific literature are pre-sented They span from a lower to higher level of complexity

as follows static rated sizing dynamic load cycle profile anddynamic analysis with full time series The most commonlyused one today is the dynamic load cycle profile givenits simplicity and representability of more realistic powergeneration scenarios It intends to exploit the high variabilityand low capacity factor of the power production (no superiorto 50) Likewise the third technique embodies an importanttopic that is shaping up as crucial Dynamic rating of electri-cal components further studies through this technique yieldsto lifetime estimation which can be done offline with modelscalibrated in laboratories or online by sensing in real timevariables such as power external temperature or mechanicalstresses In order to do so novel models encompassing ther-mal analysis of cables (extendable to other electrical com-ponents) including detailed physical components modellingwhile not compromising the computation requirements arenecessitated Development of lifetime models of electricalcables represents an important research area investigatingthe impact of real static and dynamic operation conditionssuch as total length and systemrsquos dynamicsIn general onecan say that the trend is towards combining dynamic sizingwith lifetime estimation ensuring that the chosen solutiondoes not adversely impacts eitherRelated to topological network optimization the cable lay-out in collection system sub-problem is envisaged to beaddressed by applying BIP andor MILP formulations giventhat this approach brings a proper balance between solutionquality and computation time with a physical modellingchoices inside of a permitted level of complexity In thereviewed works applying this methodology it was not foundthe inclusion of wake effects and the power losses are com-puted either by pre-processing strategies linearization or it-erative processes Models with dynamic location of OffshoreSubstations are required Details experiments for assessingthe efficiency between different mathematical programs arehighly encouraged Given the trend in OWFs towards largerand larger projects focus must be directed into this aspectby proposing methodologies able to provide solutions inreasonable computation timeThere is also space for new global optimization formula-tions including a probabilistic approach for reliability as-sessment to obtain looped networks instead of installingparallel cables in the same trench The effects of the WindTurbines (WT) fatigue over the cable layout design is becom-ing increasinglyh important More elaborated cost modelsare required as well including more components cablestransformers switchgears and installation costs None of thereviewed works deal with modelling the seabed bathymetrywhich can have a great impact over final collection systems asthis can significantly impact the cablesrsquo length Case studiescomparing the new proposed collection system voltage (66kV) with the classic one (33 kV) can be interesting as wellIn the impossibility to use external solvers (hence exactmathematical formulations) metaheuristics seem to be thebest choice to solve this problem stage despite the fact thedoor is open for designing heuristics with cable choice and

VOLUME XXX 2019 13




accounting for electrical losses with time and quality boundproofs The full picture of the topological network optimiza-tion has been addressed until today by means of multi-step and nested approaches however evolutionary algorithmsmixed with mathematical formulations might be an appealingoptionFinally the two branches can be combined for instance aresultant collection system network can use dynamic ratingwith probabilistic lifetime models of cables for sizing suchelements in order to provide a more tuned stage after theconvergence of combinatorial algorithms

ACKNOWLEDGMENTThis research has received funding from the Baltic InteGridProject httpwwwbaltic-integrideu Authors thank ProfPoul Soslashrensen Dr Kaushik Das and Prof Mathias Stolpe fortheir contributions to the development of the manuscript

REFERENCES[1] GWEC ldquoGlobal Wind Report Annual Market Update 2017rdquo

Tech Rep 2017 [Online] Available httpgwecnetpublicationsglobal-wind-report-2[AccessedOct292018]

[2] International Renewable Energy Agency ldquoInnovation Outlook OffshoreWind Summary for Policy Makersrdquo p 16 2016

[3] X Sun D Huang and G Wu ldquoThe current state of offshore wind energytechnology developmentrdquo Energy vol 41 no 1 pp 298ndash312 2012

[4] ReNEWS ldquoRampion suffers cable faultrdquo 2017 [Online] Available httprenewsbiz105889rampion-suffers-cable-fault[AccessedOct292018]

[5] RenewableUK ldquoRenewableUK - Project Intelligencerdquo 2018 [Online]Available httpswwwrenewableukcompageProjectIntelligenceHome[AccessedMarch32019]

[6] S Lumbreras and A Ramos ldquoOffshore wind farm electrical design areviewrdquo Wind Energy vol 16 pp 459ndash473 2013

[7] W Offshore ldquoDecommissioning of worldrsquos firstoffshore site now completerdquo 2017 [Online]Available httpswwwwindpowermonthlycomarticle1443779video-decommissioning-worlds-first-offshore-site-complete[AccessedNov072018]

[8] J Herbert-Acero O Probst P-E Reacutethoreacute G Larsen and K Castillo-Villar ldquoA Review of Methodological Approaches for the Design andOptimization of Wind Farmsrdquo Energies vol 7 no 11 pp 6930ndash70162014

[9] M Koivisto K Das F Guo P Soslashrensen E Nuntildeo Martinez N ACutululis and P Maule ldquoUsing time series simulation tool for assessingthe effects of variable renewable energy generation on power and energysystemsrdquo WIREs Energy and Environment no June pp 1ndash15 2018

[10] IEC ldquoIEC-60287-1 Electric cables - Calculation of the current ratingrdquoTech Rep 2014 [Online] Available httpswwwevseeproductsiec-60287-1-1-2006[AccessedApril152019]

[11] mdashmdash ldquoIEC-60853-2 - Calculation of the cyclic and emergency currentrating of cablesrdquo Tech Rep 2008

[12] CIGREacute ldquoCurrent Ratings of Cables for Cyclic and Emergency Loads Part1 Cyclic Ratings (Load Factor Less Than 100) and Response to a StepFunctionrdquo Tech Rep 24 1976

[13] CIGREacute Working Group B140 ldquoOffshore Generation Cable Connec-tionsrdquo Tech Rep 1 2015

[14] T Kvarts ldquoSystematic Description of Dynamic Load for Cables forOffshore Wind Farms Method and Experiencerdquo CIGREacute pp 1ndash13 2016

[15] S Catmull R D Chippendale J A Pilgrim G Hutton and P CangyldquoCyclic Load Profiles for Offshore Wind Farm Cable Ratingrdquo IEEETransactions on Power Delivery vol 31 no 3 pp 1242ndash1250 2016

[16] R Chippendale J Pilgrim A Kazerooni and D Ruthven ldquoCyclic ratingof wind farm cable connectionsrdquo CIRED - Open Access ProceedingsJournal vol 2017 no 1 pp 91ndash95 2017

[17] R Olsen ldquoDynamic Loadability of Cable Based Transmission GridsrdquoPhD dissertation Technical University of Denmark 2013

[18] D Chatzipetros and J A Pilgrim ldquoReview of the Accuracy of SingleCore Equivalent Thermal Model for Offshore Wind Farm Cablesrdquo IEEETransactions on Power Delivery vol 33 no 4 pp 1ndash1 2017

[19] M A H Colin and J A Pilgrim ldquoOffshore Cable Optimization byProbabilistic Thermal Risk Estimationrdquo in IEEE International Conferenceon Probabilistic Methods Applied to Power Systems (PMAPS) IEEE2018 pp 1ndash6

[20] T Zarei K Morozovska T Laneryd P Hilber M Wihleacuten and O Hans-son ldquoReliability considerations and economic benefits of dynamic trans-former rating for wind energy integrationrdquo International Journal of Electri-cal Power and Energy Systems vol 106 no December 2017 pp 598ndash6062019

[21] R Jothi and B Raghavachari ldquoApproximation algorithms for the capaci-tated minimum spanning tree problem and its variants in network designrdquoACM Transactions on Algorithms (TALG) vol 1 no 5 pp 265ndash2822005

[22] E L Lawler ldquoThe traveling salesman problem a guided tour of combina-torial optimizationrdquo Wiley-Interscience Series in Discrete Mathematics1985

[23] A Kershenbaum ldquoComputing capacitated minimal spanning trees effi-cientlyrdquo Networks vol 4 no 4 pp 299ndash310 1974

[24] A Saxena M Prasad A Gupta N Bharill O P Patel A TiwariM J Er W Ding and C-T Lin ldquoA review of clustering techniques anddevelopmentsrdquo Neurocomputing vol 267 pp 664ndash681 2017

[25] R C Prim ldquoShortest Connection Networks And Some GeneralizationsrdquoBell System Technical Journal vol 36 no 6 pp 1389ndash1401 1957

[26] E W Dijkstra ldquoA note on two problems in connexion with graphsrdquoNumerische mathematik vol 1 no 1 pp 269ndash271 1959

[27] J B Kruskal ldquoOn the Shortest Spanning Subtree of a Graph and theTraveling Salesman Problemrdquo Proceedings of the American MathematicalSociety vol 7 no 1 pp 48ndash50 1956

[28] L R Esau and K C Williams ldquoOn teleprocessing system design Part IIA method for approximating the optimal networkrdquo IBM Systems Journalvol 5 no 3 pp 142ndash147 1966

[29] K M Chandy and R A Russell ldquoThe Design or Multipoint Linkages ina Teleprocessing Tree Networkrdquo IEEE Transactions on Computers vol100 no 10 pp 1062ndash1066 1972

[30] P R M Duailibe T T Borges A F Schiochet and C A P SoaresldquoImpact of the Objective Function on the Construction of Internal Gridsof Wind Farms Using Genetic Algorithmrdquo Open Journal of Civil Engi-neering vol 06 no 05 pp 705ndash721 2016

[31] A M Jenkins M Scutariu and K S Smith ldquoOffshore wind farm inter-array cable layoutrdquo in IEEE PowerTech at Grenoble 2013 pp 1ndash6

[32] P Hou W Hu Z Chen and C Chen ldquoOverall Optimization for OffshoreWind Farm Electrical Systemrdquo Wind Energy vol 20 no 2016 pp 1017ndash1032 2017

[33] S Lehmann I Rutter D Wagner and F Wegner ldquoA Simulated-Annealing-Based Approach for Wind Farm Cablingrdquo in Proceedings ofthe Eighth International Conference on Future Energy Systems 2017 pp203ndash215

[34] J Nedlin ldquoAnt-based Algorithms for the Wind Farm Cable Layout Prob-lem Bachelor Thesis ofrdquo no January 2017

[35] A Wedzik T Siewierski and M Szypowski ldquoA new method for simulta-neous optimizing of wind farmrsquos network layout and cable cross-sectionsby MILP optimizationrdquo Applied Energy vol 182 pp 525ndash538 2016

[36] IBM ldquoIBM ILOG CPLEX Optimization Studio CPLEX User ManualrdquoTech Rep 2015 [Online] Available httpswwwibmcomsupportknowledgecenter[AccessedApril112019]

[37] K Deb Optimization for engineering design Algorithms and examplesPHI Learning Pvt Ltd 2012

[38] M Zhao Z Chen and F Blaabjerg ldquoApplication of genetic algorithm inelectrical system optimization for offshore wind farmsrdquo in Proceedingsof Third International Conference on Electric Utility Deregulation andRestructuring and Power Technologies (DRPT) 2008 pp 1ndash6

[39] G Mosetti C Poloni and D Diviacco ldquoOptimization of wind turbinepositioning in large wind farms by means of a Genetic algorithm JWind Eng Ind Aerody 51105acircAS116rdquo Wind Engineering and IndustrialAerodynamics vol 51 no 51 p 105acircAS116 1994

[40] J Serrano Gonzaacutelez M Burgos Payaacuten and J Riquelme Santos ldquoOptimumdesign of transmissions systems for offshore wind farms including deci-sion making under riskrdquo Renewable Energy vol 59 pp 115ndash127 2013

[41] L Amaral and R Castro ldquoOffshore wind farm layout optimization re-garding wake effects and electrical lossesrdquo Engineering Applications ofArtificial Intelligence vol 60 no November 2016 pp 26ndash34 2017

14 VOLUME XXX 2019




[42] J J Grainger and W D J Stevenson Power System Analysis 2nd edMcGraw-Hill Education 1994

[43] S Lumbreras and A Ramos ldquoOptimal design of the electrical layout of anoffshore wind farm applying decomposition strategiesrdquo IEEE Transactionson Power Systems vol 28 no 2 pp 1434ndash1441 2013

[44] H Brakelmann ldquoLoss Determination for Long Three-Phase High-VoltageSubmarine Cablesrdquo European Transactions on Electrical Power vol 13no 3 pp 193ndash197 2003

[45] M Banzo and A Ramos ldquoStochastic Optimization Model for ElectricPower System Planning of Offshore Wind Farmsrdquo IEEE Transactions onPower Systems vol 26 no 3 pp 1338ndash1348 2011

[46] J Bauer and J Lysgaard ldquoThe offshore wind farm array cable layout prob-lem A planar open vehicle routing problemrdquo Journal of the OperationalResearch Society vol 66 no 3 pp 360ndash368 2015

[47] M T Godinho L Gouveia and T L Magnanti ldquoCombined route capacityand route length models for unit demand vehicle routing problemsrdquoDiscrete Optimization vol 5 no 2 pp 350ndash372 2008

[48] F M Gonzaacutelez-Longatt P Wall P Regulski and V Terzija ldquoOptimalelectric network design for a large offshore wind farm based on a modifiedgenetic algorithm approachrdquo IEEE Systems Journal vol 6 no 1 pp 164ndash172 2012

[49] A Klein D Haugland J Bauer and M Mommer ldquoAn integer pro-gramming model for branching cable layouts in offshore wind farmsrdquoin Modelling Computation and Optimization in Information Systems andManagement Sciences vol 1 2015 pp 27ndash36

[50] M Fischetti and D Pisinger ldquoMixed Integer Linear Programming fornew trends in wind farm cable routingrdquo Electronic Notes in DiscreteMathematics vol 64 pp 115ndash124 2018

[51] C Berzan K Veeramachaneni J McDermott and U-M OrsquoReillyldquoAlgorithms for cable network design on large-scale wind farmsrdquo TechRep 2011 [Online] Available httpsthirldcomfilesmsrp_techreportpdf[AccessedApril152019]

[52] P Hou W Hu C Chen and Z Chen ldquoOptimisation of offshore windfarm cable connection layout considering levelised production cost usingdynamic minimum spanning tree algorithmrdquo IET Renewable Power Gen-eration vol 10 no 2 pp 175ndash183 2016

[53] P Hou W Hu and Z Chen ldquoOptimisation for offshore wind farm cableconnection layout using adaptive particle swarm optimisation minimumspanning tree methodrdquo IET Renewable Power Generation vol 10 no 5pp 694ndash702 2016

[54] A Cerveira A F de Sousa E J Pires and J Baptista ldquoOptimal CableDesign of Wind Farms The Infrastructure and Losses Cost MinimizationCaserdquo IEEE Transactions on Power Systems vol 31 no 6 pp 4319ndash4329 2016

[55] L Gouveia and P Martins ldquoThe capacitated minimum spanning treeproblem revisiting hop-indexed formulationsrdquo Computers amp operationsresearch vol 32 no 9 2005

[56] M Fischetti and D Pisinger ldquoOptimizing wind farm cable routing consid-ering power lossesrdquo European Journal of Operational Research vol 270no 3 pp 917ndash930 2018

[57] L Wolsey and G L Nemhauser Integer and combinatorial optimizationJohn Wiley amp Sons 2014

[58] A Hertz O Marcotte A Mdimagh M Carreau and F Welt ldquoDesign ofa wind farm collection network when several cable types are availablerdquoJournal of the Operational Research Society vol 68 no 1 pp 62ndash732017

[59] Y Chen Z Y Dong K Meng F Luo Z Xu and K P Wong ldquoCollectorSystem Layout Optimization Framework for Large-Scale Offshore WindFarmsrdquo IEEE Transactions on Sustainable Energy vol 7 no 4 pp 1398ndash1407 2016

[60] A Cerveira and J Baptista ldquoOptimization design in wind farm distributionnetworkrdquo in International Joint Conference SOCOacircAZ13-CISISacircAZ13-ICEUTEacircAZ13 2014 pp 109ndash119

[61] A Klein and D Haugland ldquoObstacle-aware optimization of offshore windfarm cable layoutsrdquo Annals of Operations Research vol 272 no 1-2 pp373ndash388 2017

[62] A C Pillai J Chick L Johanning M Khorasanchi and V De LaleuldquoOffshore wind farm electrical cable layout optimizationrdquo EngineeringOptimization vol 47 no 12 pp 1689ndash1708 2015

[63] J S Shin and J O Kim ldquoOptimal Design for Offshore Wind Farmconsidering Inner Grid Layout and Offshore Substation Locationrdquo IEEETransactions on Power Systems vol 32 no 3 pp 2041ndash2048 2017

[64] J L Bentley and T A Ottmann ldquoAlgorithms for reporting and countinggeometric intersectionsrdquo IEEE Transactions on computers no 9 pp 643ndash647 1979

[65] B Delaunay ldquoSur la sphere viderdquo Izv Akad Nauk SSSR OtdelenieMatematicheskii i Estestvennyka Nauk vol 7 no 1 pp 793ndash800 1934

[66] M Hauptmann and M Karpinski ldquoA Compendium onSteiner Tree Problemsrdquo Tech Rep 2015 [Online] Avail-able httptheoryinformatikuni-bonndeinfo5steinerkompendiumnetcompendiumpdf[AccessedNov232018]

[67] S Dutta and T J Overbye ldquoOptimal Wind Farm Collector System Topol-ogy Design Considering Total Trenching Lengthrdquo IEEE Transactions onSustainable Energy vol 3 no 3 pp 339ndash348 2012

[68] S Dutta and T Overbye ldquoA Graph-theoretic Approach for AddressingTrenching Constraints in Wind Farm Collector System Designrdquo in IEEEPower and Energy Conference at Illinois (PECI) 2013 pp 1ndash5

[69] B Neagu and G Georgescu ldquoWind Farm Cable Route Optimization Usinga Simple Approachrdquo in Proceedings of the International Conference andExposition on Electrical and Power Engineering (EPE) 2014 pp 1004ndash1009

[70] S Wei L Zhang Y Xu Y Fu and F Li ldquoHierarchical Optimizationfor the Double-Sided Ring Structure of the Collector System Planning ofLarge Offshore Wind Farmsrdquo IEEE Transactions on Sustainable Energyvol 8 no 3 pp 1029ndash1040 2017

[71] R Srikakulapu and U Vinatha ldquoOptimal Design of Collector Topologyfor Offshore Wind Farm Based on Ant Colony Optimization Approachrdquo inIEEE International Conference on Power Electronics Drives and EnergySystems (PEDES) 2016 pp 1ndash6

[72] D Applegate W Cook and A Rohe ldquoChained Lin-Kernighan for largetraveling salesman problemsrdquo INFORMS Journal on Computing vol 15no 1 pp 82ndash92 2003

[73] G Quinonez-Varela G Ault O Anaya-Lara and J McDonald ldquoElectri-cal collector system options for large offshore wind farmsrdquo IET Renew-able power generation vol 1 no 2 pp 107ndash114 2007

[74] H J Bahirat B A Mork and H K Hoidalen ldquoComparison of wind farmtopologies for offshore applicationsrdquo in IEEE Power and Energy SocietyGeneral Meeting (PES) 2012 pp 1ndash8

[75] S Lundberg ldquoConfiguration study of large wind parksrdquo PhD dissertationChalmers University of Technology 2003

[76] R Ahuja T L Magnanti and J B Orlin Encyclopedia of OptimizationSpringer 2008

[77] P Fagerfjaumlll Optimizing wind farm layout acircAS more bang for the buckusing mixed integer linear programming (MSc Thesis) 2010

[78] M Sedighi M Moradzadeh O Kukrer M Fahrioglu and L VandeveldeldquoOptimal Electrical Interconnection Configuration of Off-Shore WindFarmsrdquo Journal of Clean Energy Technologies vol 4 no 1 pp 66ndash712016

[79] H Ling-ling C Ning Z Hongyue and F Yang ldquoOptimization of large-scale offshore wind farm electrical collection systems based on improvedFCMrdquo in International Conference on Sustainable Power Generation andSupply (SUPERGEN) 2012 pp 67ndash67

[80] D Li C He and Y Fu ldquoOptimization of internal electric connectionsystem of large offshore wind farm with hybrid genetic and immune algo-rithmrdquo in 3rd International Conference on Deregulation and Restructuringand Power Technologies (DRPT) no April 2008 pp 2476ndash2481

[81] S Lumbreras A Ramos and S Cerisola ldquoA Progressive ContingencyIncorporation Approach for Stochastic Optimization Problemsrdquo IEEETransactions on Power Systems vol 28 no 2 pp 1452ndash1460 2013

[82] H Lingling F Yang and G Xiaoming ldquoOptimization of Electric Con-nection System of Large Offshore Wind Farm with Genetic Algorithmrdquoin International Conference on Sustainable Power Generation and Supply(SUPERGEN) IEEE 2009 pp 1ndash4

[83] J Castro Mora ldquoOptimizacioacuten Global de Parques Eoacutelicos Mediante Algo-ritmos Evolutivosrdquo PhD dissertation Unversidad de Sevilla 2008

[84] P Hopewell F Castro and D Bailey ldquoOptimising the design of offshorewind farm collection networksrdquo in Proceedings of the 41st InternationalUniversities Power Engineering Conference (UPEC) no 1 2006 pp 84ndash88

[85] M Zhao Z Chen and F Blaabjerg ldquoOptimization of Electrical Systemfor a Large DC Offshore Wind Farm by Genetic Algorithmrdquo in NordicWorkshop on Power and Industrial Electronics 2004 p 8

[86] O Dahmani S Bourguet M MacHmoum P Guerin P Rhein andL Josse ldquoOptimization of the Connection Topology of an Offshore WindFarm Networkrdquo IEEE Systems Journal vol 9 no 4 pp 1519ndash1528 2015

VOLUME XXX 2019 15




[87] W S Moon J C Kim A Jo and J N Won ldquoGrid optimizationfor offshore wind farm layout and substation locationrdquo in ConferenceProceedings of IEEE Transportation Electrification Conference and Expo(ITEC) 2014 pp 1ndash6

[88] H Ergun D Van Hertem and R Belmans ldquoTransmission system topol-ogy optimization for large-scale offshore wind integrationrdquo IEEE Trans-actions on Sustainable Energy vol 3 no 4 pp 908ndash917 2012

[89] T Troumltscher and M Korparings ldquoA framework to determine optimal offshoregrid structures for wind power integration and power exchangerdquo WindEnergy vol 14 p 977acircAS992 2011

[90] H G Svendsen ldquoPlanning Tool for Clustering and Optimised GridConnection of Offshore Wind Farmsrdquo Energy Procedia vol 35 pp297ndash306 2013 [Online] Available httpdxdoiorg101016jegypro201307182

[91] V C Tai and K Uhlen ldquoDesign and Optimisation of Offshore Grids inBaltic Sea for Scenario Year 2030rdquo Energy Procedia vol 53 pp 124ndash134 2014

JUAN-ANDREacuteS PEacuteREZ-RUacuteA received theBSc degree in Electrical Engineering withSumma Cum Laude distinction from the Techno-logical University of Bolivar Colombia in 2012and the MSc degree in Sustainable Transporta-tion and Electrical Power Systems from the Supe-rior Institute of Engineering from Coimbra Portu-gal the University of Nottinghan England and theUniversity of Oviedo Spain in 2016 Currentlyhe is pursuing the PhD degree in the Department

of Wind Energy in the Technical University of Denmark From 2012 to2014 he worked with HMV Engineers in Colombia as a protection systemsdesign engineer His present-day areas of interest include integration ofrenewable energies in power systems optimization techniques for electricalinfrastructure in offshore wind farms dynamic cableslines rating andcontrol

NICOLAOS A CUTULULIS received the MScand PhD degrees both in Automatic Controlin 1998 and 2005 respectively Currently he isProfessor in the Department of Wind Energy atthe Technical University of Denmark His mainresearch interests are integration of wind powerwith a special focus on offshore wind power andgrids involving a variety of technical disciplinesincluding modeling optimization control of windturbines and farms wind power variability and

ancillary services from wind power

16 VOLUME XXX 2019



Date of publication xxxx 00 0000 date of current version xxxx 00 0000

Digital Object Identifier 101109ACCESS2017DOI

Electrical Cable Optimization in OffshoreWind Farms - A reviewJUAN-ANDREacuteS PEacuteREZ-RUacuteA1 and NICOLAOS A CUTULULIS (SENIOR MEMBER IEEE) 212Department of Wind Energy Technical University of Denmark Frederiksborgvej 399 4000 Roskilde Denmark

Corresponding author Juan-Andreacutes Peacuterez-Ruacutea (e-mail jurudtudk)

This research has received funding from the Baltic InteGrid Project httpwwwbaltic-integrideu

ABSTRACT A state-of-the-art review of the optimization of electrical cables in Offshore Wind Farms(OWFs) is presented in this paper One of the main contributions of this work is to propose a generalclassification of this problem framed in the general context of the Offshore Wind Farms Design andOptimization (OWiFDO) The classification encompasses two complementary aspects First the optimumsizing of electrical cables with the three main approaches used nowadays static rated sizing dynamic loadcycle profile and dynamic full time series being conceptually analyzed and compared The latest techniquesand advances are described along with the presentation of potential research areas not thoroughly addressedtoday such as Dynamic Cable Rating and cablersquos lifetime estimation under time-varying conditionsSecond the network optimization of large OWFs is thoroughly presented dividing the problem witha bottom-top approach cable layout of collection system Wind Turbines (WTs) allocation to OffshoreSubstations (OSSs) number and location of OSSs and interconnection between OSSs and OnshoreConnection Points (OCPs) A comparison among different methods is performed taking into considerationthe main engineering constraints Global optimization specifically Binary Programming (BIP) or MixedInteger Linear Programming (MILP) is envisaged as the best way to tackle this topic The full combinatorialproblem is found to be better addressed following a Top-Bottom approach combining exact formulationswith high level heuristics or holistically with evolutionary algorithms

INDEX TERMS Balance of plant Cable sizing Combinatorial optimization Dynamic rating Electricalcables Heuristics Global optimization Mathematical programming Metaheuristics Offshore Wind FarmStatic rating

I INTRODUCTION

OFFSHORE Wind Farms (OWFs) represent one of thefastest and most steadily growing types of renewable

energy technologies for electricity generation The penetra-tion level has increased almost five times in the last sevenyears reaching a globally total installed power of nearly 19GW [1] This growth is mainly explained by reductions incosts of the technology [2] the Levelized Cost of Energy(LCOE) has dropped recently from 240 USDMWh to 170USDMWh accounting for the last five yearsOne of the main drivers for cost reduction is the economiesof scale which has been evident in the OWF industry bythe accelerated increase of Wind Turbines (WTs) individualpower and consequently the scaled up of the total installedcapacity of state-of-the-start OWFs The latter brings as sideeffect the increase of complexity for designing efficient andcost-effective infrastructure such as the electrical systems

given that i) the WTs are larger in power and numberbeing less uniformly scattered around the project area ii)the Offshore Substations (OSSs) are built farther away fromthe Onshore Connection Point (OCP) increasing the exportsystems transmission length and iii) more stiff completeand complex requirements from the Transmission SystemsOperators (TSOs) to the OWFs for providing auxiliaryservices are demanded All added up means the electricalinfrastructure costs can go up to 15 compared to the totalcapital expenses (CAPEX) [3] The last point together withthe remarkable impact in terms of efficiency and reliabilityover the operational performance of OWFs (OPEX) [4]turn the electrical infrastructure into a cornerstone matter indesigning the full systemBetween 2018 and 2028 more than 19000 km of cablesfor collection systems are prognosed to be installed worthpound536bn [5] while longer and bigger cables for export are

VOLUME XXX 2019 1








2 VOLUME XXX 2019







75 23 2018

London Array 630 175x36MW 55 25 2013

Gemini 600 150x4MW 110 36 2017






Macrositing

Micrositing


ControlProtOper

OWiFDO(Inputs)

OWiFDO(Outputs)

1






Static rated sizing







1



VOLUME XXX 2019 3








4 VOLUME XXX 2019






Which topology


WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

OSS

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

Which objective

Length(L)

Invt(I)

Invt+Reliab(IR)

Invt+Losses(IL)



1






1




VOLUME XXX 2019 5







Heuristics







Metaheuristics







GlobalOptimization








34

GA

25

BIP+MILP

19

Heuristics

8

PSO

4

MIQP

4

MINLP

4

ACO

2 SA

1





Math Form

LI

IL

IRIRL

1



6 VOLUME XXX 2019





Wake EffectsOther

VertexPacking


CFD

No

Wind Stochasticity

Deter

SampWind pdf

Sim Wind

SampWindDir

pdf

SimWindDir

Other

Power Flow

No

Transportation

DCPF

ACPF

Point-to-Point

Electrical Losses

Exact

Quadratic

No

Other

Linear

Reliability

NoDeter

Probabilistic

1


1) Radial topology


VOLUME XXX 2019 7







minsumiisinN

sumjisinNw

|T |sumt=1

utsumk=1


subject to

sumiisinN

|T |sumt=1

utsumk=1


sumiisinN

|T |sumt=1

utsumk=1


iisinNw

|T |sumt=1

utsumk=1


forallj isinNw


|T |sumt=1

utsumk=1




MILP

minsumiisinN

sumjisinNw

|T |sumt=1


8 VOLUME XXX 2019














No No No [48]


fij minussum

iisinNw


sumiisinN

|T |sumt=1


|T |sumt=1



|T |sumt=1








sumiisinN

sumjisinNw

|T |sumt=1

utsumk=1








VOLUME XXX 2019 9













10 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019








2 VOLUME XXX 2019







75 23 2018

London Array 630 175x36MW 55 25 2013

Gemini 600 150x4MW 110 36 2017






Macrositing

Micrositing


ControlProtOper

OWiFDO(Inputs)

OWiFDO(Outputs)

1






Static rated sizing







1



VOLUME XXX 2019 3








4 VOLUME XXX 2019






Which topology


WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

OSS

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

Which objective

Length(L)

Invt(I)

Invt+Reliab(IR)

Invt+Losses(IL)



1






1




VOLUME XXX 2019 5







Heuristics







Metaheuristics







GlobalOptimization








34

GA

25

BIP+MILP

19

Heuristics

8

PSO

4

MIQP

4

MINLP

4

ACO

2 SA

1





Math Form

LI

IL

IRIRL

1



6 VOLUME XXX 2019





Wake EffectsOther

VertexPacking


CFD

No

Wind Stochasticity

Deter

SampWind pdf

Sim Wind

SampWindDir

pdf

SimWindDir

Other

Power Flow

No

Transportation

DCPF

ACPF

Point-to-Point

Electrical Losses

Exact

Quadratic

No

Other

Linear

Reliability

NoDeter

Probabilistic

1


1) Radial topology


VOLUME XXX 2019 7







minsumiisinN

sumjisinNw

|T |sumt=1

utsumk=1


subject to

sumiisinN

|T |sumt=1

utsumk=1


sumiisinN

|T |sumt=1

utsumk=1


iisinNw

|T |sumt=1

utsumk=1


forallj isinNw


|T |sumt=1

utsumk=1




MILP

minsumiisinN

sumjisinNw

|T |sumt=1


8 VOLUME XXX 2019














No No No [48]


fij minussum

iisinNw


sumiisinN

|T |sumt=1


|T |sumt=1



|T |sumt=1








sumiisinN

sumjisinNw

|T |sumt=1

utsumk=1








VOLUME XXX 2019 9













10 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019







75 23 2018

London Array 630 175x36MW 55 25 2013

Gemini 600 150x4MW 110 36 2017






Macrositing

Micrositing


ControlProtOper

OWiFDO(Inputs)

OWiFDO(Outputs)

1






Static rated sizing







1



VOLUME XXX 2019 3








4 VOLUME XXX 2019






Which topology


WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

OSS

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

Which objective

Length(L)

Invt(I)

Invt+Reliab(IR)

Invt+Losses(IL)



1






1




VOLUME XXX 2019 5







Heuristics







Metaheuristics







GlobalOptimization








34

GA

25

BIP+MILP

19

Heuristics

8

PSO

4

MIQP

4

MINLP

4

ACO

2 SA

1





Math Form

LI

IL

IRIRL

1



6 VOLUME XXX 2019





Wake EffectsOther

VertexPacking


CFD

No

Wind Stochasticity

Deter

SampWind pdf

Sim Wind

SampWindDir

pdf

SimWindDir

Other

Power Flow

No

Transportation

DCPF

ACPF

Point-to-Point

Electrical Losses

Exact

Quadratic

No

Other

Linear

Reliability

NoDeter

Probabilistic

1


1) Radial topology


VOLUME XXX 2019 7







minsumiisinN

sumjisinNw

|T |sumt=1

utsumk=1


subject to

sumiisinN

|T |sumt=1

utsumk=1


sumiisinN

|T |sumt=1

utsumk=1


iisinNw

|T |sumt=1

utsumk=1


forallj isinNw


|T |sumt=1

utsumk=1




MILP

minsumiisinN

sumjisinNw

|T |sumt=1


8 VOLUME XXX 2019














No No No [48]


fij minussum

iisinNw


sumiisinN

|T |sumt=1


|T |sumt=1



|T |sumt=1








sumiisinN

sumjisinNw

|T |sumt=1

utsumk=1








VOLUME XXX 2019 9













10 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019








4 VOLUME XXX 2019






Which topology


WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

OSS

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

Which objective

Length(L)

Invt(I)

Invt+Reliab(IR)

Invt+Losses(IL)



1






1




VOLUME XXX 2019 5







Heuristics







Metaheuristics







GlobalOptimization








34

GA

25

BIP+MILP

19

Heuristics

8

PSO

4

MIQP

4

MINLP

4

ACO

2 SA

1





Math Form

LI

IL

IRIRL

1



6 VOLUME XXX 2019





Wake EffectsOther

VertexPacking


CFD

No

Wind Stochasticity

Deter

SampWind pdf

Sim Wind

SampWindDir

pdf

SimWindDir

Other

Power Flow

No

Transportation

DCPF

ACPF

Point-to-Point

Electrical Losses

Exact

Quadratic

No

Other

Linear

Reliability

NoDeter

Probabilistic

1


1) Radial topology


VOLUME XXX 2019 7







minsumiisinN

sumjisinNw

|T |sumt=1

utsumk=1


subject to

sumiisinN

|T |sumt=1

utsumk=1


sumiisinN

|T |sumt=1

utsumk=1


iisinNw

|T |sumt=1

utsumk=1


forallj isinNw


|T |sumt=1

utsumk=1




MILP

minsumiisinN

sumjisinNw

|T |sumt=1


8 VOLUME XXX 2019














No No No [48]


fij minussum

iisinNw


sumiisinN

|T |sumt=1


|T |sumt=1



|T |sumt=1








sumiisinN

sumjisinNw

|T |sumt=1

utsumk=1








VOLUME XXX 2019 9













10 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019






Which topology


WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

OSS

WT

OSS

WT

WT

WT

WT

OSS

WT

WT

WT

WT

WT

WT

WT

Which objective

Length(L)

Invt(I)

Invt+Reliab(IR)

Invt+Losses(IL)



1






1




VOLUME XXX 2019 5







Heuristics







Metaheuristics







GlobalOptimization








34

GA

25

BIP+MILP

19

Heuristics

8

PSO

4

MIQP

4

MINLP

4

ACO

2 SA

1





Math Form

LI

IL

IRIRL

1



6 VOLUME XXX 2019





Wake EffectsOther

VertexPacking


CFD

No

Wind Stochasticity

Deter

SampWind pdf

Sim Wind

SampWindDir

pdf

SimWindDir

Other

Power Flow

No

Transportation

DCPF

ACPF

Point-to-Point

Electrical Losses

Exact

Quadratic

No

Other

Linear

Reliability

NoDeter

Probabilistic

1


1) Radial topology


VOLUME XXX 2019 7







minsumiisinN

sumjisinNw

|T |sumt=1

utsumk=1


subject to

sumiisinN

|T |sumt=1

utsumk=1


sumiisinN

|T |sumt=1

utsumk=1


iisinNw

|T |sumt=1

utsumk=1


forallj isinNw


|T |sumt=1

utsumk=1




MILP

minsumiisinN

sumjisinNw

|T |sumt=1


8 VOLUME XXX 2019














No No No [48]


fij minussum

iisinNw


sumiisinN

|T |sumt=1


|T |sumt=1



|T |sumt=1








sumiisinN

sumjisinNw

|T |sumt=1

utsumk=1








VOLUME XXX 2019 9













10 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019







Heuristics







Metaheuristics







GlobalOptimization








34

GA

25

BIP+MILP

19

Heuristics

8

PSO

4

MIQP

4

MINLP

4

ACO

2 SA

1





Math Form

LI

IL

IRIRL

1



6 VOLUME XXX 2019





Wake EffectsOther

VertexPacking


CFD

No

Wind Stochasticity

Deter

SampWind pdf

Sim Wind

SampWindDir

pdf

SimWindDir

Other

Power Flow

No

Transportation

DCPF

ACPF

Point-to-Point

Electrical Losses

Exact

Quadratic

No

Other

Linear

Reliability

NoDeter

Probabilistic

1


1) Radial topology


VOLUME XXX 2019 7







minsumiisinN

sumjisinNw

|T |sumt=1

utsumk=1


subject to

sumiisinN

|T |sumt=1

utsumk=1


sumiisinN

|T |sumt=1

utsumk=1


iisinNw

|T |sumt=1

utsumk=1


forallj isinNw


|T |sumt=1

utsumk=1




MILP

minsumiisinN

sumjisinNw

|T |sumt=1


8 VOLUME XXX 2019














No No No [48]


fij minussum

iisinNw


sumiisinN

|T |sumt=1


|T |sumt=1



|T |sumt=1








sumiisinN

sumjisinNw

|T |sumt=1

utsumk=1








VOLUME XXX 2019 9













10 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019





Wake EffectsOther

VertexPacking


CFD

No

Wind Stochasticity

Deter

SampWind pdf

Sim Wind

SampWindDir

pdf

SimWindDir

Other

Power Flow

No

Transportation

DCPF

ACPF

Point-to-Point

Electrical Losses

Exact

Quadratic

No

Other

Linear

Reliability

NoDeter

Probabilistic

1


1) Radial topology


VOLUME XXX 2019 7







minsumiisinN

sumjisinNw

|T |sumt=1

utsumk=1


subject to

sumiisinN

|T |sumt=1

utsumk=1


sumiisinN

|T |sumt=1

utsumk=1


iisinNw

|T |sumt=1

utsumk=1


forallj isinNw


|T |sumt=1

utsumk=1




MILP

minsumiisinN

sumjisinNw

|T |sumt=1


8 VOLUME XXX 2019














No No No [48]


fij minussum

iisinNw


sumiisinN

|T |sumt=1


|T |sumt=1



|T |sumt=1








sumiisinN

sumjisinNw

|T |sumt=1

utsumk=1








VOLUME XXX 2019 9













10 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019







minsumiisinN

sumjisinNw

|T |sumt=1

utsumk=1


subject to

sumiisinN

|T |sumt=1

utsumk=1


sumiisinN

|T |sumt=1

utsumk=1


iisinNw

|T |sumt=1

utsumk=1


forallj isinNw


|T |sumt=1

utsumk=1




MILP

minsumiisinN

sumjisinNw

|T |sumt=1


8 VOLUME XXX 2019














No No No [48]


fij minussum

iisinNw


sumiisinN

|T |sumt=1


|T |sumt=1



|T |sumt=1








sumiisinN

sumjisinNw

|T |sumt=1

utsumk=1








VOLUME XXX 2019 9













10 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019














No No No [48]


fij minussum

iisinNw


sumiisinN

|T |sumt=1


|T |sumt=1



|T |sumt=1








sumiisinN

sumjisinNw

|T |sumt=1

utsumk=1








VOLUME XXX 2019 9













10 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019













10 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019










No [56]


















hop-indexed


No [54]




No No No [43]



No No No [52]

No No No [53]

No No No [60]




No No No [59]

No No No [63]

No No No [54]

No No No [45]




VOLUME XXX 2019 11








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019








12 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019







VOLUME XXX 2019 13
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019
















































14 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019

















































VOLUME XXX 2019 15













16 VOLUME XXX 2019













16 VOLUME XXX 2019

electrical cable optimization in offshore wind farms -a review · danish waters of lolland in the...

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