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Degree project in

Cost estimation of wind farms internalgrids

ERIKA NORD

Stockholm, Sweden 201X

XR-EE-ES 2011:017

Electric Power Systems

Second Level,

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Cost estimation of wind farms internal grids

ERIKA NORD

Masters Thesis at KTH School of Electrical Engineering

Supervisor: Camille Hamon

Examiner: Mikael AmelinComissioned by Vattenfall Power Consultant AB

Supervisor: Mikael Eklund

TRITA xxx yyyy-nn

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Abstract

When establishing new wind farms there are a lot of dif-ferent stakeholders that have different demands and ambi-tions. The local grid in a wind farm constitutes of about 10% of the total investment cost and therefore it is of impor-tance that it is optimized both regarding losses and costs.

In a wind farm project a system analysis is ordered thatsummarizes information such as cable layout, electric dataand losses. A drawback is that this analysis is given in alater part of the project, when most decisions already havebeen made due to permits. If the analysis shows that thereare unnecessarily high losses in the system it can be too

late to make changes.The aim of this Masters thesis project is to develop a

method that makes the essential calculations so that an es-timation of losses and its costs together with the investmentcosts can be made at an early stage.

The first part of the thesis consisted of developing aprogram using this method with the requests above to, inthe next stage, compare the results the method acquireswith a reference system analysis of an existing wind farm.From this comparison conclusions were made whether themethod is usable and in which ways it resembles and differsfrom the more advanced method used in a program today.

The results show that the method makes a good esti-mation of losses. Deviations between the developed methodand the reference analysis are due to that different ap-proaches are made when calculating certain losses and alsothe depth of the calculations. Furthermore there is no de-scription of how precise the calculations in the referencereport were made so approximations can be a source of er-ror. The conclusion is that this method can be used toget an early estimation of the losses and the correspondingcosts of the local grid.

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Sammanfattning

Vid byggnation av nya vindkraftparker finns det mnga in-tressenter som har olika krav och ml. Det interna elntet ien vindkraftpark utgr ungefr 10 % av den totala invester-ingskostnaden och drfr r det viktigt att det interna el-ntet kan optimeras frlust- och kostnadsmssigt. I ett vin-dkraftparksprojekt genomfrs en elsystemstudie som sam-manfattar information s som kabelntslayout, elektriskdata samt frluster. En nackdel r att denna studie till-

handahlls en bra bit in i ett projekt, d de flesta beslutenredan r tagna baserat p tillstnd. Visar systemstudientill exempel p ondigt stora frluster i systemet kan detvara fr sent att ndra.

Detta examensarbete syftar till att ta fram en metodsom skall gra de vsentliga berkningarna s att en upp-skattning om frluster och dess kostnader tillsammans medinvesteringskostnader kan gras redan i ett tidigt stadium.

Frsta delen av examensarbetet bestod av att framstl-la ett program dr denna metod anvnds med ovanstendenskeml fr att sedan i nsta steg jmfra resultaten meto-den erhller med en referensstudie som gjorts fr en exis-terande vindkraftpark. Utifrn denna jmfrelse skulle slut-satser dras om programmet som baseras p metoden r an-vndbart och p vilka stt det liknar och skiljer sig frnmetoden som det mer avancerade programmet anvnderidag.

Resultaten visar att den hr metoden gr en bra es-timering av frluster. Skillnader mellan den framtagna meto-den och referensstudien beror p olika tillvgagngsstt iframtagningen av vissa frluster samt hur detaljerade vissaberkningar r gjorda. Dessutom finns det ingen beskrivn-ing av hur noggranna berkningarna i referensstudien rgjorda s approximationer kan vara en felklla. Slutsatsenr att metoden kan anvndas fr att gra en tidig estimer-

ing av frluster och de kostnader som r relaterade till dessafrluster fr ett internt elnt i en vindkraftpark.

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Contents

Contents

List of Tables

List of Figures

List of Symbols

List of Abbreviations

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Layout of the report . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Dimensioning of cables 52.1 Choosing cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Trefoil and flat formation . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Choice of conductor . . . . . . . . . . . . . . . . . . . . . . . 62.1.3 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.4 Reactance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.5 Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Losses in cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Conductor losses . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Dielectric losses . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.3 Sheath losses . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.4 Reactive losses . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.5 Voltage drop . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Bonding of metallic screens . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Both-ends bonding . . . . . . . . . . . . . . . . . . . . . . . . 112.3.2 Single-point bonding . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.3 Cross-bonding . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Rating factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

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2.4.1 Temperature in the ground relative to temperature in the con-

ductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.2 Thermal resistivity of ground . . . . . . . . . . . . . . . . . . 152.4.3 Laying depth of cables . . . . . . . . . . . . . . . . . . . . . . 152.4.4 Cables installed in pipes . . . . . . . . . . . . . . . . . . . . . 162.4.5 Distance between cable groups . . . . . . . . . . . . . . . . . 16

2.5 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Wind turbines 193.1 Wind distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1.1 Rayleigh distribution . . . . . . . . . . . . . . . . . . . . . . . 203.1.2 Weibull distribution . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Power curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3 Energy output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.4 Losses in wind farms . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.5 Losses in wind turbines . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.5.1 No-load losses . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.5.2 Full-load losses . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.6 Losses in local grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.7 Costs of the transmission systems . . . . . . . . . . . . . . . . . . . . 28

3.7.1 Cost of losses . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.7.2 Material costs . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4 Method 294.1 Starting assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2 Calculating production . . . . . . . . . . . . . . . . . . . . . . . . . . 304.3 Dimensioning cables . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.4 Calculating losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.4.1 Cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.4.2 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.5 Calculating costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5 Case study 355.1 The test system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2 The PSS/E study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.3.1 Theoretical comparison . . . . . . . . . . . . . . . . . . . . . 365.3.2 Actual comparison . . . . . . . . . . . . . . . . . . . . . . . . 37

6 Conclusions and future work 39

Bibliography 41

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List of Tables

2.1 XLPE cable data for different aluminium conductor areas . . . . . . . . 82.2 Comparison between flat- and trefoil formation . . . . . . . . . . . . . . 142.3 Rating factors for ground temperature . . . . . . . . . . . . . . . . . . . 152.4 Rating factors for thermal resistivity of ground . . . . . . . . . . . . . . 152.5 Rating factors for laying depth . . . . . . . . . . . . . . . . . . . . . . . 162.6 Rating factors for groups of cables in the ground . . . . . . . . . . . . . 16

5.1 Comparison between the developed software results and the PSS/E study 38

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List of Figures

2.1 Cable construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Trefoil formation and flat formation . . . . . . . . . . . . . . . . . . . . 62.3 Both-ends bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Single-point bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 Cross-bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.6 The induced voltages in a cable with three phases . . . . . . . . . . . . 13

3.1 Layout of a wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2 Rayleigh wind distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3 Weibull distribution with different shape parameter values . . . . . . . . 223.4 Power curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.5 The change in power curves with increasing/decreasing air density . . . 243.6 Wake effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.7 Layout of a wind farm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.1 Layout of the test system wind farm . . . . . . . . . . . . . . . . . . . . 36

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List of Symbols

RAC AC resistance of the cable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7RDC D C r e s i s t a n c e o f t h e c a b l e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

ys Skin effect factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7yp Proximity effect factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7xs Skin effect factor variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7ks Skin effect factor coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7T Resistivity of conductor material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7A Area of conductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7xp Prox imity effect factor v ariable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7kp Proximity effect factor coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7dc Diameter of the conductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7s Distance between conductor axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7XL Inductive reactance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Angular velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8L Inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8C Capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Relative permittivity of insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

ro R a d i u s o f i n s u l a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8ri Radius of conductor screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Pl O h m i c l o s s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9I R a t e d c u r r e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9tan() Lossfactor of insulation material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Pd Dielectric losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Psh S h e a t h l o s s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Is S h e a t h c u r r e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Rs Sheath resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Xm Mutual reactance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Ql Reactive losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 0S Apparent power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10U Voltage drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Z Cable impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10UL1 Induced voltage in cable, first phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12UL2 Induced voltage in cable, second phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12UL3 Induced voltage in cable, third phase .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

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Uires R e s i d u a l v o l t a g e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2

pr Rayleigh distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20pw Weibull distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20v Wind velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20vav Average wind velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 0kw Shape parameter of Weibull distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Aw Scale parameter of Weibull distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Air density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Awind Cros s s ectional area of the wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21E E n e r g y o u t p u t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3T Period of time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23hi Probability of occurrence of wind velocity i . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Pi Power generated at wind velocity i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23n Number of wind turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27U Rated voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Elnoload E n e r g y l o s s w i t h o u t l o a d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6P0 P o w e r w i t h o u t l o a d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 6Elload Energy loss with load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Pload Power with load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Sn Apparent power of the transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

U t i l i z a t i o n t i m e o f l o s s e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7Cw Capacity factor of a wind turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27cos() P o w e r f a c t o r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 7

Clcable Price of losses in cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Expected electricity price for losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Cltrans Price of los s es in trans formers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28Pmax Maximum rated power of wind turbine .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27

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List of Abbreviations

V P C Vattenfall Power Consultant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2PSS/E Power System Simulator for Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

AC Alternating Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7P EX Cross-Linked Polyethelene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

DC D i r e c t C u r r e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7XLPE Cross-Linked Polyethelene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Emf Electro Motive Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9m/s Meters Per Second . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19CAD C o m p u t e r - A i d e d D e s i g n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 9

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Acknowledgements

First, I would like to thank Bengt Gransson at Vattenfall Power Consultant ABwho gave me the opportunity to do this thesis project and to my supervisor at VPC,

Mikael Eklund, for the valuable guidance and interest in my work.Furthermore, I am very thankful towards my supervisor at the Royal Institute

of Technology, Camille Hamon, for the advice and support throughout the wholeproject and towards my examiner, Mikael Amelin, who helped me improve my work.

Finally, I would like to express my deepest gratitude to my family for alwaysbelieving in me.

ErikaStockholm, June 2011

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Chapter 1

Introduction

1.1 Background

Wind power has been used for at least 5,5 thousand years by humans to propelsailing ships and run wind mills for mechanical power. However it was not untilabout 30 years ago that the modern wind power industry began, when the companyVestas began to manufacture wind turbines. It was then the production of windturbines started in Denmark. Those turbines were rather small compared with theones that are available today and had capacities of 20-30 kW. Today the capacityhas increased greatly and a wind turbine can be able to deliver up to 7,5 MW but

the commonly used produce around 2-3 MW.A wind farm is used to produce electric power and can consist of two turbines

to over a thousand. These wind farms can both be located onshore or offshore. Theadvantages with wind energy is that it is one of the cleanest ways to produce energyand that it can be used to either supply electricity to a near located household orto the transmission grid so that the electricity is used elsewhere. The downsidesare that it is expensive, takes up a lot of space and is rather complicated to build,in terms of permits and regulations. The power system in a wind farm consists ofmedium voltage cables which are connected between the individual turbines and toa substation that connects the grid to the high voltage electric power transmissiongrid.

When planning to build a wind farm the design of the local power grid is asubstantial part of the process. The cost for the power system in a wind farm isapproximately 10% [8] of the total investment cost. Furthermore it resides costsdue to losses, interruptions and maintenance during the lifetime of the wind farm.The losses are approximately only 2-3 % [8] of the energy production, but it shouldbe taken into account that these losses will occur during the whole lifetime of thewind farm and will therefore generate large costs.

When designing a power system for a wind farm both local and general param-eters have to be considered. The understanding of the consequences of the choice ofvoltage level and the cost for the losses related to that choice is however relatively

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CHAPTER 1. INTRODUCTION

low in the wind power industry. Vattenfall Power Consultant (VPC) decided that

it could be the foundation of a masters thesis to investigate and develop a methodwhich can be used to build a program that shows the losses and the costs for a windfarm. The reason is mainly to get a comprehension about these aspects at an earlystage in the project and to be able to influence other stakeholders.

1.2 Objective

The purpose of this project is to analyse the internal grid of a wind farm by creating

a simplified method and to compare it with the more advanced method used todayin a program called PSS/E. The method will then be used to assess the cost of theinternal grid of a wind farm. The method must be adaptable to changes in pricesfor materials, structural methods, placement of the farm and electrical conditions.By studying the parameters individually and in relation to each other conclusionscan be drawn and developed into a program that generates the total cost of buildinga wind farm.

The concerned people at Vattenfall Power Consultant are supposed to be ableto quickly get an overview of the costs for the power system of a wind farm at anupstart of a new project and be able to see how much losses the wind farm willgenerate during its lifetime and what is causing them.

Today it exists a method used in a program called PSS/E. It calculates thelosses but not the costs. Additionally it makes power flow calculations and dynamicsimulations. This program is however very time consuming and has an unwieldyenvironment.

The expectation of the developed method is that the corporate promoter willget an early comprehension regarding costs, mainly regarding the losses that occurin wind power systems so that the grids can be designed optimally. This is usuallya non-trivial matter where it is easy to build an opinion early on regarding buildingcosts but not what kind of impact on the losses this will lead to and this is perceivedto be a common problem in this line of business.

1.3 Method

This method is to be used by people with more or less knowledge in power systemsso it has to be methodical and relatively easy to follow. By using the informationavailable early in a projects stage a method will be developed to obtain the lossesand costs for the internal grid in a wind farm. Then the losses and costs for aninternal grid are calculated using this method and compared to a theoretical windfarm that VPC has analysed with a more advanced computation method in PSS/E.

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1.4. LAYOUT OF THE REPORT

1.4 Layout of the report

The first chapters, 2 and 3, give the reader the theory behind the calculations inthe method. Then the procedure of making the calculations is explained in chapter4 and finally the comparison with a test case is evaluated in chapter 5.

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Chapter 2

Dimensioning of cables

Power cables consist of a number of layers with different materials. Innermost isthe conductor, where the current flows, followed by the inner semi-conducting layer,which is there to prevent air-filled cavities between the conductor and the insulationso that less electrical discharges occur. Then there is the insulation that inhibits themagnetic field from the conductor, the outer semi-conducting layer which has thesame use as the inner layer. The metallic screen is an earthed layer which conductsleakage currents if needed and the non-metallic outer sheath is a flame resistant andmoist repellent layer. Finally the cable is surrounded by an armour to protect thecable from external forces. An example of how a cable can be constructed is seenin figure 2.1.

Figure 2.1. Cable construction [3]

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CHAPTER 2. DIMENSIONING OF CABLES

Figure 2.2. Trefoil formation and flat formation

2.1 Choosing cables

2.1.1 Trefoil and flat formation

There are single-phase cables and there are three-phase cables. A three-phase sys-tem can therefore either be built by three single-phase cables or one three-phasecable. The three cables in a three-phase circuit can be placed in different forma-tions. The two typical formations are trefoil (triangular) and flat formations, seefigure 2.2. The choice between the two depends on factors like bonding method,which will be explained in a later section, conductor area and available space forinstallation.

2.1.2 Choice of conductor

When deciding which conductor to use the first choice is between copper and alu-minium. Thereafter it is decided how the conductor should be composed, if it shouldbe a solid wire or stranded wire and which shape it should have.

For conductors with a cross sectional area less than 16 mm2 copper is used. Thecopper is produced through an electrolytic process, has a purity of 99.9 % but ithas a high density of 8.89 kg/dm3 and is much more expensive than aluminium.For conductor areas larger than 25 mm2 aluminium is usually chosen since it hasa purity of 99.5 %, 61 % of the conductivity of copper but only 30 % of coppers

density, i.e. 2.70 kg/dm3. When building offshore it used to be cables consistingof copper that was mainly installed due to that it is heavier and has less corrosionrisk. Today aluminium is more often considered even when building offshore sincethose cables also have water immune layers and it lowers the price of the investment[2].

Solid wires consist of one piece of metal wire. Stranded wires are composed ofa bundle of small-gauge wires to make a larger conductor. A benefit with strandedwires are that they are more flexible but they are also more expensive than solidwires of the same total cross-sectional area. Solid wires provide mechanical stur-diness and protection against environment due to that they have relatively less

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2.1. CHOOSING CABLES

surface area that are exposed to attacks by corrosives. Hence stranded wires are

used whenever ease of bending or repeated bending are required.

2.1.3 Resistance

The AC resistance RAC of a cable consists of the DC resistance RDC , the skineffect factor ys , and the proximity effect factor yp as seen in (2.1).

RAC = RDC(1 + ys + yp) /km (2.1)

The DC resistance, RDC, is dependent on the conductor area, A, and the resistivityof the conductor material per unit length, T, and is computed as below.

RDC = TA

/km, (2.2)

The resistivity T in (2.2) changes depending on which temperature the PEX, an-other name for Cross-Linked Polyethelene, insulation should be able to withstand.In the method developed in this thesis the PEX insulation is chosen to withstandtemperatures up to 65 or 90 Celsius. Since the resistivity at 20 Celsius is 20=28.2 mm2/km for aluminium and it increases with 0.4 % per degree, the resistivity at65 Celsius is 65=33.3 mm

2/km and at 90 Celsius it is 90=36.1 mm2/km.

The resistivity for copper at 65 Celsius is 65=19.8 mm2/km and for 90 Celsius

it is 90=21.5 mm2/km.

The skin effect factor is given by

ys =x4s

192 + 0.8x4s, (2.3)

and

x2s =8f

RDC 107 ks, (2.4)

where f is the frequency of the current and the coefficient ks is equal to 1 since thecables used in this project are presumed to be round or sector shaped.

The proximity effect factor for three-core cables or three single-core cables isgiven by

yp =x4p

192 + 0, 8x4p

dcs

2 0, 312dcs

2+

1, 18x4p

192+0,8x4p+ 0, 27

, (2.5)

and

x2p =8f

RDC 107 kp (2.6)

where f is the frequency of the current, dc the diameter of the conductor, s thedistance between conductor axes and the coefficient kp is equal to 0.8 for the samereasons as for ks [1].

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2.1.4 Reactance

A cable consists of both inductive and capacitive reactance, although the capacitivereactance often is so small that it is not included in calculations. The inductivereactance functions in series with the conductor whilst the capacitive reactancefunctions between conductor and ground. The inductive reactance can be obtainedfrom (2.7).

XL = L /km, (2.7)

where = 2f, f is the frequency in Hz and L the inductance in H/km

2.1.5 Capacitance

A cable can be seen as a capacitor, where the conductor is one of the electrodesand the metallic sheath is the other. The insulation corresponds to the capacitorsdielectric. For a cable where every phase is screened individually the calculation ofthe capacitance is as follows

C =

18 lnrori

F/km, (2.8)where is the relative permittivity of the insulation and is dimensionless, ro is theexternal diameter of the insulation and ri is the diameter of the conductor, includingthe screen. The relative permittivity for Cross-Linked Polyethelene cables (XLPEcables) is = 2.3.

The specific data for the resistance, reactance and capacitance for different con-ductor areas are shown in table 2.1.

Table 2.1. XLPE cable data for different aluminium conductor areas

Conductor area [mm2] R [/km] XL [/km] C [F/km]

95 0.38 0.11 0.22150 0.24 0.10 0.26240 0.15 0.09 0.31400 0.09 0.13 0.18630 0.06 0.12 0.21

2.2 Losses in cables

2.2.1 Conductor losses

When electric current runs through a cable a power is dissipated in the conductor.This power is proportional to the current squared and directly proportional to theconductor resistance. It is very important to consider these losses when dimension-ing cable connections to ensure that the cable does not overheat so that the cables

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2.2. LOSSES IN CABLES

life span decreases and to prevent massive costs that come with large energy losses.

The losses are calculated according to (2.9).

Pl = I2 RAC W/km, (2.9)

where RAC is the AC resistance of the conductor and I is the current. This equationwill be further developed later in this report when more theory has been explained.

2.2.2 Dielectric losses

The insulation becomes heated from the losses that the load current causes. Tocalculate the dielectric losses the loss factor of the insulation material, tan(), must

be known. This loss factor partly depends on the voltage and the temperature, butmainly it is a material property. The losses are calculated according to the formula:

Pd = U2 C tan() W/km, (2.10)

where U is the rated voltage and tan() is the loss factor of the insulation material.As seen in (2.10) the dielectric losses are proportional to the voltage squared. Thecables used in this project have un-filled PEX insulation and a loss factor tan()equal to 0.3 103 [3].

2.2.3 Sheath lossesIn a cable that is used for AC an electromotive force (emf) is created in the metallicsheath and in the surrounding cables sheaths. This emf can cause two types oflosses.

Eddy currents Conductor currents in the perimeter of the sheath induceeddy currents. These currents decrease with increasing cable length and normallythe eddy current losses are so small relative to the conductor losses that they areneglected.

Circulating currents Circulating currents that are driven by the inducedemf are created if closed sheath circuits are utilized. These sheath circuits generateloops in which the currents can flow. The magnitudes of these currents depend onthe sheath resistances Rs, length of cables and conductor current. These sheathlosses are

Psh = I2s Rs = I

2 Rs

X2mR2s + X

2m

W/km, (2.11)

where I is the conductor current, Is the sheath current, Rs the sheath resistanceand Xm the mutual reactance [12].

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2.2.4 Reactive losses

Reactive power is the non-working power caused by the magnetizing current and isrequired to operate and sustain the magnetism in the load. Reactive power requiredby inductive loads increases the amount of apparent power, S , in the distributionsystem. The increase in reactive and apparent power causes the power factor todecrease. Just as there is active/ohmic losses there are reactive losses which arecalculated according to (4.5).

Ql = I2 XL VAr/km (2.12)

The current can be expressed as

I = PU cos A, (2.13)

so that

Ql =

P

U cos

2 XL VAr/km (2.14)

2.2.5 Voltage drop

The resistance and reactance will generate a voltage drop over the cable. Thevoltage drop is increased with increasing cable length but is reduced with increasingconductor area. In low voltage circuits with long transmission distances the voltage

drop affects the dimensioning. To calculate the voltage drop the following equationcan be used for three phase systems.

U =I Z L

U cos 100% =

P (R cos + XL sin ) L

U2 cos 100%, (2.15)

where P is the transferred power, Z is the cable impedance, L is the length of thecable, R is the conductor resistance, XL is the reactance, U the rated voltage andcos() the power factor of the load.

The voltage drop is supposed to be maintained within a specific range andaccording to Svensk Elstandard SS-EN 61000-2-2 the changes in the voltage areunder normal circumstances limited to 3 % of the nominal voltage. Causes of

voltage drop could be voltage dips, over tones or transients. The consequences offast voltage changes are shifts in the light intensity, for example in a light bulb, andhigh stress on the mechanical part of the electric drive system. When the voltagechanges exceed about 2 % of the rated voltage the effects can be visually noticed.

2.3 Bonding of metallic screens

Bonding is the industrial word for connecting electrical equipment so that theyacquire the same potential. This is desirable due to that no static sparking canoccur between objects with the same potential.

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2.3. BONDING OF METALLIC SCREENS

Figure 2.3. Both-ends bonding [3]

The power losses in a cable circuit are, as stated previously, dependent on thecurrents flowing in the metallic sheaths of the cables. Therefore by reducing oreliminating the metallic sheath currents through different methods of bonding, itis possible to increase the load current carrying capacity, the so-called ampacity.The ampacity is the maximum amount of electrical current which a cable can carrybefore sustaining immediate or progressive deterioration.The three most common bonding methods are the following.

2.3.1 Both-ends bonding

If the arrangements are such that the cable sheaths provide path for circulatingcurrents at normal conditions the system is both ends bonded, see figure 2.3. Thiscirculating current causes losses in the screen, which reduce the cables currentcarrying capacity. These losses are smaller for cables in trefoil formation than inflat formation. The circulating currents are usually much greater than the eddycurrents. Therefore the eddy currents can be ignored when dealing with sheathsthat have both points grounded.

2.3.2 Single-point bondingIf the arrangements are such that the cable sheaths provide no path for the flow ofcirculating currents or external fault currents the system is single point bonded, seefigure 2.4. This is the simplest form of special bonding. The sheaths of the threecable sections are connected and grounded at one point only along their length. Atall other points, there will be an induced voltage between sheath and ground thatwill be at its maximum at the farthest point from the ground bond. The sheathsmust therefore be adequately insulated from ground. Since there is no closed sheathcircuit, except through the sheath voltage limiter, the current does not normallyflow longitudinally along the sheaths and no sheath circulation current loss occurs.

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Figure 2.4. Single-point bonding [3]

Voltage limiters provide effective protection for personnel and equipment and itlimits occurring shock-hazard voltages to safe values.

This type of bonding can only be utilized for limited route lengths, usually lessthan 500 meters, since the voltage becomes very high at the farthest point for longercables which causes high magnetic fields and may cause arcing in the insulation,but in general the accepted screen voltage potential limits the length.

2.3.3 Cross-bonding

If the arrangements are such that the circuit provides electrically continuous sheathruns from grounded termination to grounded termination but with the sheathsso sectionalized and cross-connected in order to eliminate the sheath circulatingcurrents the system is cross-bonded, see figure 2.5. In that case, a voltage willbe induced between screen and ground, but no significant current will flow. Themaximum induced voltage will appear at the link boxes where the cross bondingtakes place. The cable length is divided into three approximately equal sections.Each of the three alternating magnetic fields induces a voltage, UL1, UL2 and UL3,with a phase shift of 120 in the cable shields. Ideally, the vectorial addition of the

induced voltages results in Uires 0, see figure 2.6.In practice, the cable length and the laying conditions will vary, resulting in a

small residual voltage and a negligible current. Since there is no current flow, thereare practically no losses in the screen. The total of the three voltages is zero, thus theends of the three sections can be grounded. This method permits a cable current-carrying capacity as high as with single-point bonding but longer route lengths thanthe latter. It requires screen separation and additional link boxes. Link boxes areprovided to affect the cross bonding, give the ability to isolate the sheaths fromground for jacket integrity tests, and to house the sheath voltage limiters.

Depending on which bonding method that is chosen different cable formations

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2.3. BONDING OF METALLIC SCREENS

Figure 2.5. Cross-bonding [3]

Figure 2.6. The induced voltages in a cable with three phases

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are preferable, as mentioned earlier. Table 2.2 shows a comparison between the two

cable formations and which one that is preferable for the different bonding methods.

Table 2.2. Comparison between flat- and trefoil formation [11]

Trefoil forma-tion

Flat formation

Price Less expensive More expensive

Space Requires lessspace

Requires morespace

Single-point bonding More losses Less losses

Cross bonding More losses Less losses

Both-ends bonding Less losses More losses

Symmetry Symmetric,same reac-tance betweencables

Unsymmetrical,uneven currentdistribution

2.4 Rating factors

Rating factor is a factor by which the rated current can be multiplied to determineits absolute maximum measurable current. The rated current which is obtainedfrom data sheets compiled by manufacturers are a value under certain conditions.These conditions are ground temperature, thermal resistivity, laying depth of thecable, distance between cable groups and if the cable is installed in a pipe.The rating factors below are valid for XLPE cables, both on land and in sea.

2.4.1 Temperature in the ground relative to temperature in theconductor

The cooling effect from the ground decreases with increasing depth of cables, i.e.the grounds thermal resistance increases with depth and the cables ampacity de-creases. Therefore adjustments have to be made depending on which maximumconductor temperature that is chosen according to table 2.3. The maximum con-ductor temperature is the maximal temperature at which the insulation aroundthe conductor can retain its shape and properties under a longer period of time.Different cables can withstand different temperatures due to different insulations.

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2.4. RATING FACTORS

Table 2.3. Rating factors for ground temperature [3]

Conductor Ground Temp. CTemp. C 10 15 20 25 30 35 40 45

90 1.07 1.04 1 0.96 0.93 0.89 0.84 0.8065 1.11 1.05 1 0.94 0.88 0.82 0.74 0.66

2.4.2 Thermal resistivity of ground

It is not normally necessary to devote too much attention to ground thermal resis-

tivity unless there is an immediate danger that the soil will dry out. Therefore inSweden the thermal resistivity of the ground is normally set to be 1 and in somecases 0.7 if the environment are more like a swamp. A frame of reference can beseen in table 2.4.

Table 2.4. Rating factors for thermal resistivity of ground [12]

Thermal resistivity[W/km]

Rating factor Soil conditions Weather conditions

0.7 1.14 Very moist Continuously moist1 1.00 Moist Regular rainfall2 0.74 Dry Seldom rains3 0.61 Very dry Little or no rain

2.4.3 Laying depth of cables

When installing cables in the ground the first thing that has to be done is to dig ashaft where the cable/cables will lie. The bottom layer consists of sand on which

the cable is put and then the area around the cable is filled also with sand. Ontop of this layer a warning strip is put that states the presence of a high voltagecable underneath in case an excavating machine happens to dig near the cable.Then the shaft is filled with earth, another warning strip is put on top and finallycompleted with a layer of the environmental substance uppermost. Normally cablesare installed at a depth of 0.5 to 1 meter. However, since wind farms are built insuch remote locations it is more common to put the cables on a laying depth of 0.3m. This is a consideration between price and likeliness that external forces woulddamage the cable. A table of the rating factors at different laying depths can beseen in table 2.5.

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Table 2.5. Rating factors for laying depth [3]

Laying depth [m] Rating factor

0.3 1.160.5 1.100.7 1.050.9 1.01

1.00 1.001.20 0.981.50 0.95

2.4.4 Cables installed in pipes

An advantage of putting cables into pipes is that it is done simultaneously with thecompletion of the roads so that the cables can be put in place at an arbitrary timeafterwards. Furthermore a damaged cable can be easily pulled out if an openingis near by. On the other hand, when installing cables in pipes it is surrounded bystatic air that inhibits the heat transportation. Thus, there has to be a rating factorof 0.9 multiplied to the adjusted current rating when cables are installed in pipes.

2.4.5 Distance between cable groups

When several cables are put in one shaft they will all contribute to the heating ofthe ground. Therefore, it is not recommendable to have two layers of cables on topof each other due to the substantially decreased cooling effect of the cables. Therating factors in table 2.6 are referring to the distance between trefoil formationsor flat formations and not the distance between each phase.

Table 2.6. Rating factors for groups of cables in the ground [3]

Distance between Number of groups

groups [mm] 1 2 3 4 5

100 1 0.76 0.67 0.59 0.55200 1 0.81 0.71 0.65 0.61400 1 0.85 0.77 0.72 0.69600 1 0.88 0.81 0.77 0.74800 1 0.90 0.84 0.81 0.79

2000 1 0.96 0.93 0.92 0.91

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2.5. CHAPTER SUMMARY

2.5 Chapter summary

In this chapter the importance of dimensioning the cables correctly in a grid isemphasized. The choice of cable is dependent on bonding method, the power ittransfers, the amount of losses in the cable and rating factors. The choice of bond-ing method has a large impact on whether flat- or trefoil formation is chosen. Theamount of power that the cable is supposed to transfer decides how large cross-sectional area the conductor has to have and consequently which material the con-ductor should be made of. The amount of losses that occur in the cable can be areason, if they are too large, to increase the size of the conductor if the costs forthe losses over-weigh the costs for a larger cable. Finally the rating factors, whichmostly depend on the surrounding area, can have an influence on whether a larger

or a smaller cable should be used. For instance if the surroundings are favourableto the cable and actually increase its ampacity, perhaps a cable with a smaller con-ductor area will do whilst if the surroundings are unfavourable and the ampacity ofthe cable is decreased, perhaps a cable with a larger conductor area should be used.

These pros and cons can be more and less important to different stakeholdersdepending on which situation they are in. For some stakeholders the instant cost(investment cost) is the most important one to hold down and for others the costduring the life-cycle (cost of losses) has to be weighed against the investment cost.

The following chapter will describe the wind turbines impact on the energyproduction and the losses in the cables.

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Chapter 3

Wind turbines

Wind turbines convert kinetic energy to mechanical energy and an example of howthey can be constructed is seen in figure 3.1. They can have different layouts, mostones have gear boxes in the nacelle, but since the gear box is the most commonreason to technical failure there are also turbines produced without. The horizontalaxis turbines are made of three components; the rotor component, the generatorcomponent and the structural support component. In figure 3.1 the procedure ofmaking electricity in a wind turbine is demonstrated. When wind blows over theblades (1) it causes them to rotate. Inside the nacelle (11) the gearbox (6) connectsthe low-speed shaft (5) to the high-speed shaft (12) and can change the rotationalspeed so that it is suitable for the generator (7) which produces electricity. The

controller (8) starts up the turbine at wind speeds of about 3 m/s (meters persecond) and shuts off the turbine at about 25 m/s. Most turbines do not operateat wind speeds above 25 m/s since they might be damaged by the high winds.

One method to control the rotor speed and keep the rotor from turning in highwind speeds is to pitch out (3) the blades of the wind to let the air flow throughthe blades and prevent the buoyant force that otherwise helps the blades to rotate.Another method to control the rotor speed is to stall control the wind turbine. On astall-regulated wind turbine, the blades are locked in place and do not adjust duringoperation. Instead the blades are designed and shaped to increasingly "stall" theblades angle of attack with the wind to both maximize power output and protectthe turbine from excessive wind speeds. The yaw drive (13) is used to keep the

rotor facing into the wind as the wind direction changes and the yaw motor (14)powers the yaw drive.

3.1 Wind distribution

In order to calculate the power output from a wind turbine it is necessary to knowthe wind distribution in the planned turbine location. There are general methodsfor calculating the probability for wind at different wind speeds such as Rayleighand Weibull, although in the method developed in this thesis the wind distribution

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CHAPTER 3. WIND TURBINES

Figure 3.1. Layout of a wind turbine [5]

is assumed to be known to some extent, explained later. An example of a wind

distribution can be seen in figure 3.2. If the measured wind distribution is notknown but an average wind speed at the location is known a standard Rayleighdistribution can be used.

3.1.1 Rayleigh distribution

The Rayleigh probability density function is

pr(v) =

2

v

v2ave

4

vvav

2

, (3.1)

where v is the investigated wind speed and vav is the average wind speed at the

location of interest. An example of a Rayleigh distribution is seen in figure 3.2.

3.1.2 Weibull distribution

If the Rayleigh function is not satisfactory the Weibull function may be appliedinstead. This function is depending on two parameters; a scale parameter Aw anda shape parameter k. If k is equal to 2 the curve becomes a Rayleigh distribution.The Weibull probability density function is

pw(v) =k

Aw

v

Aw

k1e

vAw

k, (3.2)

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3.2. POWER CURVE

Figure 3.2. Rayleigh wind distribution

where v is the investigated wind speed, k > 0 is the shape parameter and Aw > 0is the scale parameter. Weibull distributions depending on what value the shapeparameter has is seen in figure 3.3.

3.2 Power curve

Another requirement for calculating the energy output of the wind turbine over agiven time period is to know the amount of power a certain wind class produces.How much power a certain wind class produces is dependent on what value the airdensity in the surrounding has which can be seen from (3.3).

Pwind =1

2Awindv

3 W, (3.3)

where is the air density, Awind the cross sectional area of the wind and v thevelocity of the wind. The developed method will assume that the client has chosena wind turbine so that the power curve for that specific turbine is known. Anexample of a power curve can be seen in figure 3.4 and the following expressionscan be found in it.

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Figure 3.3. Weibull distribution with different shape parameter values

Cut-in speed is the wind speed at which a wind turbine begins to producepower.

Cut-out speed is the wind speed at which the turbine is shut down to preventthe rotor and drive train machinery from being damaged. Pitch control can be usedto gradually decrease the power output to zero with increasing wind speed.

Rated output speed is the wind speed at which the rated power is achieved.

Rated output power is the installed capacity.

When the air density changes the power curve shifts to the right if the air den-sity is lower and to the left if it is higher but the rated power does not change. Anillustration of this is seen in figure 3.5.

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3.3. ENERGY OUTPUT

Figure 3.4. Power curve

3.3 Energy output

When the power curve and the wind distribution are known the energy outputduring a given time period can be calculated according to equation (3.4).

E =ji=0

hiPiT Wh, (3.4)

where hi is the probability of wind at wind speed i from the wind distribution, Pithe power generated at wind speed i from the power curve, T the time period and

j the number of wind speed classes.

3.4 Losses in wind farms

The overall production of a wind farm can be limited by several factors that makethe wind turbine produce less power than what it is capable of. Such losses areexplained below.

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Figure 3.5. The change in power curves with increasing/decreasing air density

Wake effect Wind turbines extract energy from the wind and downstreamthere is a wake from each wind turbine, where wind speed is reduced. The flowproceeds downstream and the wake spreads and recovers towards free stream con-ditions. This affects the wind turbines behind and therefore wind turbines in farmsare usually spaced 5 to 9 rotor diameters apart in the prevailing wind direction and3 to 5 rotor diameters from one another in the direction perpendicular to that inorder to avoid too much turbulence around the turbines downstream. The totalloss from the wake effect for 5 to 10 turbines is typically around 5 % or less [14].A figure of wake effect is seen in figure 3.6 where v0 is the wind speed at the firstrotor, v the wind speed x meters behind the rotor, u the undisturbed wind speedin front of the rotor and R the radius of the rotor.

Turbine availability The average turbine availability of a wind farm repre-sents, as a percentage, a factor that needs to be applied to the energy output toaccount for availability losses. These losses are associated with the amount of timethe turbines are unavailable to produce electricity. These times can be caused bymechanical failure and the related repairs, routine maintenance or external causes

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3.5. LOSSES IN WIND TURBINES

Figure 3.6. Wake effect [14]

such as lightning strikes and ice accumulation. Modern wind turbines have an avail-ability of more than 98 % [4], which is a very high value in comparison with forexample nuclear power plants, which have an availability around 80 %.

Environmental In certain conditions, dirt can form on the blades or, overtime, the surface of the blades may degrade. Extremes of weather may affect theenergy production such as ice building up on wind turbines and also the growthor felling of nearby trees. The air density, mentioned earlier, is dependent on theenvironment since it changes with variances in temperature and humidity.

The wind turbines in a wind farm are often located on so called radials. Theseradials come together at a transformer station that transforms the voltage to thevoltage level that the transmission grid which the farm is connected to has. Fromthis transformer station the export cables transfer the produced energy out to the

transmission grid. Figure 3.7 demonstrates this.

3.5 Losses in wind turbines

The wind turbines also lose power in the gear box, the generator, the controlleramongst other components but these losses are generally included in the powercurve. However the losses in the transformer that connects the wind turbine to thegrid has to be considered separately. The losses in the transformer depend on theload current and can be expressed in two ways, no-load or full-load loss.

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Figure 3.7. Layout of a wind farm

3.5.1 No-load losses

No-load losses are caused by the magnetizing current needed to energize the coreof the transformer and are present the entire time the transformer is powered on,regardless of whether there is any load or not. The calculation of the no-load energylosses, Elnoload , for a given time period T when the secondary winding is madeopen-circuit is done as:

Elnoload = P0 T Wh, (3.5)

where P0 is the power without load, normally this data is given and T is a period

of time.

3.5.2 Full-load losses

The coil losses, commonly referred to as load losses, are caused by the windingimpedance and vary according to the loading on the transformer. The equation forthe energy losses with full load, Elload, for one year is

Elload = Pload

S

Sn

2 Wh, (3.6)

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3.6. LOSSES IN LOCAL GRID

where Pload is the power of the transformer with load, S is the apparent power of the

turbine/turbines, Sn the apparent power of the transformer and the calculatedutilization time of losses [7].

This is a simplified method due to the lack of information that is known at theearly stages of a project. The utilization time of losses itself is an estimation ofhow many hours multiplied with the maximum load that correspond to the actualamount of energy that the transformer loses during a longer period. It is a sourceof uncertainty since the measured wind velocities that the production is calculatedwith, (3.3), has an uncertainty of about 2 to 4 % [6] due to measuring problems andinterferences.

The utilization time of losses is calculated according to

=ji=0

Pi

Pmax

2 hi

8760 h, (3.7)

where Pmax is the maximum power of the wind turbine.The capacity factor of a wind turbine Cw is the ratio of the actual output of a

wind turbine during a period of time and its potential output if it had operated atfull capacity the entire time.

Cw =E

Pmax 8760, (3.8)

where E is obtained from (3.4).

3.6 Losses in local grid

There are transformers in the grid as well and the losses that occur by them arecalculated using (4.7) and (4.6) too. Furthermore there are the cable losses thatwere explained in section 2.2. Equation (2.9), the conductor losses in the cables,can now be extended with more precise information about how it is calculated. Thecurrent flowing in the cable for a given wind speed i can be expressed as

Ii =n Pi

U

cos

A, (3.9)

where hi is the probability of wind at wind speed i, Pi the power generated at windspeed i, n is the number of wind turbines the cable is connected to, U is the ratedvoltage and cos() is the power factor. This leads to an expression for the conductorlosses that is

Pl = I2 RAC =

ji=0

n Pi

U cos

2 RAC hi W/km, (3.10)

where RAC is obtained from (2.1).

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3.7 Costs of the transmission systems

In general, the higher the voltage level is, the more expensive the electricity equip-ments are. In return the power capacity increases and the losses decreases dra-matically. Furthermore it is more expensive to establish power grids offshore thanonshore. That is a result of the more complex materials that is used along with thefact that there are significantly less installing ships to use. In addition to that theinstallation of the wind farm must be adjusted to weather conditions.

3.7.1 Cost of losses

When calculating the price that comes with losses in the cables the computed ohmic

power loss Pl (3.10), the dielectric loss Pd (2.10) and the sheath loss Psh (2.11) isused together with an expected electricity price for losses, .

Cl = (Pl + Pd + Psh) T SEK (3.11)

Almost the same formula is used when calculating the costs of losses for the trans-formers from (4.7) and (4.6).

Cltrans = (Elload + Elnoload) SEK (3.12)

3.7.2 Material costs

The prices for cables and other material such as transformers and stations are ob-tained from an annually upgraded website that Svensk Energi distributes, cataloguesP1 and P2, [9],[10].

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Chapter 4

Method

The methods purpose is, as mentioned earlier, to get an early comprehension aboutthe amount of losses in the internal grid and to be able to make changes to reducethese losses without having to spend much time on the process. This method isiterative and enables the person using this method to go back to a previous calcu-lation step when a partial result is obtained and change certain values to see if theamount of losses and costs increase or decrease.

4.1 Starting assumptions

The first step in this method is to obtain a layout of the electrical grid in the windfarm so that the conditions, the facts which can not be changed such as location ofthe wind turbines and transformer stations, are known. The process of deciding thelayout of the internal grid is normally not written in stone, hence the method canbe used to evaluate if changes should be made in the first draft. The first draft ofthe layout is made with a method called CAD, Computer-Aided Design, but howthat process works is beyond the scope of this thesis, so the assumption is now madethat the first draft of the layout is done.

To begin with the voltage level of the internal grid is determined, but can be

altered later if the first choice is not satisfactory. The voltage levels that can bechosen are 12 kV, 24 kV or 36 kV. Then it can be necessary to choose another voltagelevel when transporting the produced energy of the wind farm to the connectingpoint in the transmission grid. If the distance to the connecting point is long thenit will be of importance from a loss perspective to have a higher voltage level onthis transport cable. In general the decision is at first made roughly according to athumb rule. If the wind farm consists of 4 to 10 MW installed capacity the voltagelevel of the transport cable can be 24 kV. Furthermore if there is 10 to 40 MWinstalled capacity, 52-72.5 kV should be used and if there is 40 to 100 MW, 145 kVis best suited. Higher voltages are seldom used, instead several cables are used in

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CHAPTER 4. METHOD

parallel.

If the amount of turbines are in between two regions it should be consideredto test two different voltages. This is because there are certain advantages anddisadvantages with increasing and decreasing the voltage level. A higher voltagelevel enables more power to flow on each cable, hence an increasing number ofturbines can be put on the same radial. Additionally the losses are reduced withincreasing voltage level. On the other hand, the cables get more expensive thehigher voltage level that is used, therefore two alternatives should be consideredwhen hesitant.

When the voltage level is decided the power factor has to be determined. Mostwind turbines have the goal of maintaining the power factor at 1. If the chosen windturbine has that control, choose cos equal to 1. However, if there is information

that says that the power factor should be lower, use that value.

4.2 Calculating production

As mentioned in the theory chapter the power curve is assumed to be known sincethe specific turbine has been chosen. If however the power curve, the production ofthe turbine for each wind velocity, is not known (3.3) can be used given that theinformation required in that formula is known.

The wind distribution can either consist of measured values for the specific sitethat is chosen, which is the most accurate approach, or with the general methods.If only an average wind speed is known for the site the Rayleigh method, (3.1), orthe Weibull method, (3.2), should be used. In the Rayleigh method the averagewind speed, vav is simply used at each wind speed. In the Weibull method a shapeparameter k is chosen to decide the shape of the distribution. Furthermore a scaleparameter A, corresponding to an average wind at the site, is used.

The information about the power curve and the wind distribution can nowcontribute to calculating the produced energy for each wind speed and a summationof that energy for one turbine through the equation

E =ji=0

hiPiT Wh, (4.1)

with hi being the values from the wind distribution and Pi the values from thepower curve.

Since the energy production is now known and the maximum power that thewind turbine can produce of course is known too, these values can be used to geta notion of how large the turbines capacity factor is with (3.8) and how manyhours the turbine would have to go at maximum power to achieve its annual energyproduction, the capacity factor according to (3.8) multiplied with the amount ofhours in a year.

If there is a desire to rectify the total energy production by considering lossesfrom wake effect and availability these factors are simply multiplied with the ob-

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4.3. DIMENSIONING CABLES

tained energy production. If no advanced wind analysis program are at hand, the

wake effect can be considered a general value for the total production loss and doesnot have to be specified for each turbine. So if one turbine has 10 % production lossand another one has 2 % production loss, make an estimation of how much the windfarm as a whole loses and rectify the production. The same applies for availability.Wind turbines do not have exactly the same percentile availability since they can besubjected to different problems, external or electrical. This means that an averagevalue of all the turbines availabilities can be multiplied with the production to geta more probable value.

4.3 Dimensioning cables

Looking at the layout of the internal grid the cable lengths between each turbineare specified and probably also a suggestion of how large the conductors crosssectional area should be. Start with the recommended thickness and if the resultsin this step show relatively higher losses in some cables, perhaps a larger cableshould be considered.

To begin with, use the manufacturers data sheet for the cables used and locatethe cable that is chosen. Check what the manufacturer suggests that the ratedcurrent is for the thickness and for the bonding method used. Which bondingmethod that should be used can be determined by choosing the method that appliesbest for the specific case, evaluated in section 2.3. The most common method to

use is the single-point bonding due to that it is the cheapest method, materiallyspeaking, and one of the safest together with cross bonding. Then simply use Ohmslaw to double check whether the current that the layout has suggested is below themaximum according to

I =Pmax n

U cos A, (4.2)

where Pmax is the maximum power of the turbine, n the number of turbines installedon that cable, U the rated voltage and cos the power factor.

If this current turns out to be larger than the rated current, either removea turbine from this radial or choose a larger cable and do the calculation again.Although, if the obtained current is just slightly over the rated current or under,

the decision should be further investigated using rating factors.Calculating rating factors is a way to really dig deeper into what amount of

ampacity the cable can have, depending on where it is placed. Information aboutlocation, which depth the cables are going to be placed and other factors are gradedin section 2.4 in this report. Apply the factors for this specific location and nowcheck again if the actual current capacity has changed. Perhaps a cables rated cur-rent has increased or decreased, depending on the environment, and no alterationshave to be done. If there still are overloads in certain cables, increase the cablessize.An example of how the current is altered is if a cable with an insulation that is

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CHAPTER 4. METHOD

supposed to be able to handle temperatures up to 65 Celsius, table 2.3, lies alone

in a moist ground environment of 15

Celsius, table 2.4, 0.5 meter below the surface,table 2.5, and in a pipe, section 2.4.4. The actual current becomes

Actual current = Current 1.14 1.05 1.10 0.9 = Current 1.185 A (4.3)

This shows that during these circumstances the cable is able to take 18.5 % morecurrent than what the manufacturers data sheet says.

4.4 Calculating losses

4.4.1 Cables

When the production is obtained and the cables dimensions are decided the lossescan be calculated. Use the formula for the AC resistance, (2.1) by specifying theformation and size of the cable. The losses for this certain cable are obtained with

Pl = I2 RAC =

ji=0

n Pi

U cos

2 hi RAC W/km (4.4)

This needs to be done for all cable sections in the layout. When the loss calculationsfor the cables are completed an inspection of the results are in order. If any lossvalue is significantly higher than the others the easiest way to improve this is to

choose a larger cable for that particular length, more expensive material but reducedlosses. These ohmic losses are significantly higher than the dielectric and the sheathlosses, but if thoroughness is required, use (2.10) and (2.11) to calculate them andadd to the ohmic losses. These losses will however not affect the choice of cablesize.

If the power factor was chosen to be equal to 1 then the reactive losses does notexist, but if the power factor was less than 1 the equation below is used to obtainthese losses

Ql =ji=0

n Pi

U cos

2 hi XL VAr/km (4.5)

where the inductive reactance is obtained by finding the cables inductance in the

manufacturers data sheet.

4.4.2 Transformers

Then the transformer losses are to be calculated. These losses are often not possibleto change since they are dependent on the size of the transformer, which is usuallydimensioned correctly. They often contribute to the largest amount of losses in theinternal grid so it is important that they are included in loss calculations.

The required information to be able to compute these losses is the maximalapparent power of the turbine S, the apparent power of the transformer Sn, the

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4.5. CALCULATING COSTS

power with load, Pload, and the power without load, P0. All these values are obtained

from the manufacturer.This information is then used in the equations

Elload = Pload

S

Sn

2 Wh, (4.6)

andElnoload = P0 T Wh, (4.7)

as stated earlier in the report. Perform these calculations both for the transformersat each wind turbine as well as for any park transformers that may be situated inthe internal grid.

Now the losses for the internal grid are calculated. As stated earlier the trans-former losses are high and there is not much that can be done to decrease them, ifnot reducing the capacity of the whole wind farm.

4.5 Calculating costs

The final step of this method is to calculate the costs for losses and the used material.The optimized losses are used in equations

Cl = (Pl + Pd + Psh) T SEK (4.8)

and Cltrans = (Elload + Elnoload) SEK (4.9)

The only question mark in these equations is . The expected electricity price forlosses, , can be obtained at a trading site for electricity such as NordPool [13].Depending on which voltage level that was chosen for the internal grid the costs forthe material are going to differ rather much. The material cost for different voltagelevels should always be examined since they could be the reason to change or staywith a certain voltage level. This is the chance to compare the prices to the voltagelevels. For example if the chosen voltage at first was 24 kV that generally meansless expensive material costs but larger costs for losses. If 36 kV was to be chosenperhaps the sum of the cost for those losses, since they are significantly lower, and

the material price are below the price for 24 kV. In many cases this is the case.Additionally, although beyond the scope of this report, tariff costs for supplying

the transmission grid with new electricity are often higher the lower voltage levelthat is supplied to the grid.

The prices of components are obtained from Svensk Energi, [9], [10]. This sitehas prices for whole packages, such as a transformer stations including labour ex-penses and digging costs, to prices for specific components, such as single cablecompartment.

The same components but for different voltage levels naturally have differentprices and therefore it is more expensive with higher voltage equipment.

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CHAPTER 4. METHOD

The substance of this chapter is that neither material costs nor cost of losses

can be considered separately. The optimal price for an internal grid in a wind farmis reached when these two factors are compared to each other.

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Chapter 5

Case study

The aim of this masters thesis was to develop a method that calculated the lossesof the internal grid in a wind farm and its costs so that this information could beacquired at an early stage in wind farm projects. In this chapter the developedmethod is applied to a test system and compared to a method that also has madecalculations for this test system.

5.1 The test system

The test system used to evaluate the developed method is a site that consists of 15turbines with 34,5 MW installed capacity and an internal grid of 24 kV, which isconnected to a 145 kV transmission grid. The cables have conductor areas of 240mm2 and 95 mm2 and the insulation is supposed to be able to withstand heat up to65 Celsius. It has one transformer station in the internal grid that transforms thevoltage from 24 kV to 145 kV and 15 transformers in the towers that transform thevoltage from 0,69 kV to 24 kV. The layout of the wind farm is seen in figure 5.1.

5.2 The PSS/E study

A study was used as a reference to confirm whether the developed method is a goodmodel for calculating losses and their costs. This study was made in PSS/E todescribe the conditions for connecting a wind farm, both from the connecting gridsperspective and the electrical layouts.

PSS/E is a software tool used for simulating, analysing and optimizing electricaltransmission networks and provides probabilistic and dynamic modelling features.The information that this analysis provides is first and foremost a voltage profile, thefault current contribution, flicker emission and harmonics. Furthermore the reportfrom this study contains information about grid layout, maximum transmissionlosses, dimensioning of cables and reactive power compensation.

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CHAPTER 5. CASE STUDY

Figure 5.1. Layout of the test system wind farm

5.3 Comparison

5.3.1 Theoretical comparison

The method in PSS/E only calculates maximum losses, the losses that occur atmaximum production, and not the actual losses. The maximum losses multipliedwith the utilization time of losses, need to be calculated by hand afterwards. Hence,PSS/E does not really have an equivalent method to the one developed in this thesis.Therefore the developed method arranged in a software is the fastest way to make

the calculations for losses.PSS/E should be used when more advanced calculations are required to ob-

tain information such as power flow and to perform dynamic simulations. Thetwo methods can therefore be seen as complementing each other. The developedmethod in this report can be used early in a wind farm project to be able to makeessential decisions about layout and dimensioning whilst PSS/E can be used laterwhen a permit is approved to make detailed power flow calculations and dynamicsimulations.

The execution times of these two methods are also a factor that makes a dif-ference. The method developed in this thesis can for an untrained person take

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5.3. COMPARISON

approximately up to one hour. A person with routine can perform the assumptions

and the calculations within a half hour. When requesting a study made in PSS/E onthe other hand, the deliverance time can take up to several weeks, a very uncertainfactor when dealing with projects that has tight deadlines.

As pointed out earlier in this report, the analysis of the losses and its costs in aprocess today is made relatively late. There is a reason for this. The informationabout components and performance of the components is very inadequate at anearly stage of a project. That causes a certain dilemma since it is early in theproject the losses need to be considered.

This method is therefore built on the fact that there is not very detailed informa-tion at the time the method is used and could truthfully lead to slightly less precisecalculations. On the other hand, the experience in the industry is that an approxi-

mation is better than not analysing the losses at all, and without a comprehensionlet a site be permitted with essential flaws.

The turbine transformer losses in the developed method are an approximationsince the specific information about the transformers are not known at the earlystage when these calculations are to be performed. The developed methods calcu-lations are based on the apparent power of the turbine and the transformer togetherwith the full-load power of the transformer. The PSS/E study probably had moreinformation such as the transformers impedance and thus a more exact value.

Furthermore the accuracy of the calculations in the PSS/E study is not knownso some difference can be due to that man-made approximations have been made.

5.3.2 Actual comparison

In table 5.1 a selection from a comparison of production and losses of the samesystem can be seen.

To examine if the developed method is something that can be used in realprojects a comparison with a PSS/E study was made. Some values differ betweenthe results from the developed method and the PSS/E study.

The deviation in cable losses is probably due to that the PSS/E study did notinclude dielectric and sheath losses when calculating the maximum losses in thecables.

The differing values in produced energy could be that the study used a general

model for a wind distribution, which is not as precise as having the real measuredwind distribution that was used in the developed method. The table shows thatthe losses stand for 1,6 % of the produced energy in this wind farm. It should betaken into consideration that the park transformer losses were not calculated in thePSS/E study. If they are added the total percentage of losses increases to 2,0 % ofthe total production, which is in the range of 2-3 % that was stated earlier in thereport.

The difference in total losses between the developed program and the PSS/Estudy is 30 MWh/year without the park transformer included and 469 MWh/yearwith the park transformer included, which approximately corresponds to 60 re-

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CHAPTER 5. CASE STUDY

Table 5.1. Comparison between the developed software results and the PSS/E study

Developedsoftware

PSS/Estudy

Produced energy [GWh/year] 110 113Utilization time of losses [h/year] 2368 2370Export cable losses [MWh/year] 351 344Local grid cable losses [MWh/year] 414 405Turbine transformer losses (noload) [MWh/year] 342 342Turbine transformer losses (load) [MWh/year] 653 639

Total losses [MWh/year] 1760

1.6%

1730

1.5%Park transformer losses (noload) [MWh/year] 175 N/APark transformer losses (load) [MWh/year] 264 N/A

Total losses [MWh/year] 21992.0%

17301.5%

spectively 235 kSEK/year. The fact that the developed method makes a higherestimation of losses is obviously something that a client is not thrilled about. Onthe other hand it may be better to over-estimate, if the program does that, so thatthe client can be pleasantly surprised later when the losses turn out to be a bit less,

than the other way around. However, the fact is that the clients often do not reflecton this matter called losses. With this developed program the cost of losses duringa year and a life time of a wind farm can easily be shown and hopefully increasethe knowledge of its importance.

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Chapter 6

Conclusions and future work

This masters thesis was about developing a method that would calculate losses andthe costs relating to those losses for the internal grid in wind farms. The losses andthe relating costs are shown to be dependent on the dimensioning of the cables andthe amount of energy obtained from the wind turbines.

The method has proven to be a relatively accurate model and a good estimatorof losses. It can be of guidance in the early stages of a project to get an overallestimation of losses and their costs. The method is iterative and enables the personusing this method to go back to a previous calculation step when a partial result isobtained and change so that the results get more appealing.

The calculated losses are dependent on which cable that is used, material and

formation, which wind turbine model that is chosen, power curve, and where thesite is located, which is reflected in the wind distribution.

The choices of choosing the right cables and voltage levels for an internal grid ina wind farm are however not black and white. The important part of this methodis the relation between costs of material and losses. Although the material costs arethe ones subjected to a client initially, and also something that they often react to,it is important to weigh these costs against the cost of losses.

The costs of losses are present during the whole life cycle of a wind farm andtherefore it is crucial to dimension cables optimally to reduce these losses to thegreatest extent. Additionally it is important to emphasize that this is a cost thatin the worst case exceeds the material cost if the choice to bargain on the size of

the cable is made.Compared with the already existing program PSS/E the developed method re-

quires much less time to obtain results and calculates the costs for all losses in theinternal grid.

This method allows VPC to get an estimation of losses and its costs at an ear-lier stage than what they get today. It also makes VPC more able to recommendchanges in a project before the decisions are made.

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CHAPTER 6. CONCLUSIONS AND FUTURE WORK

This masters thesis led to a project employment at VPC where this method is

to be taken into use to give clients an estimation of costs for building and runninga wind farm. The method can therefore be further developed into optimizing thecosts of a wind farm. One thing that can increase the width of the method is ifthe making of the first layout is included more. The layout which usually is madein CAD can definitely be optimized by choosing appropriate paths, not over highhills or around cities, and perhaps by laying cables together for longer routes tominimize costs for digging shafts. Every meter of cable that is saved, saves a lotof losses over the years. The method in this report already has the cable lengthsdecided when obtaining a first draft of the layout, and it shall be pointed out thatthis layout is a very important part of the work when establishing an electrical gridfor a wind farm.

Furthermore the effect of wake losses and availability can be developed if a methodfor specifying what wake effect each turbine has in the farm along with their avail-ability is created. It would generate a more accurate energy production and thusmore accurate values of the losses.Another thing that can be added is the impact of tariffs. Tariffs are taken from elec-tricity companies when new wind farms are built, due to the increasing load in thegrid. On the other hand these companies can also give a refund if the wind farmssupplied electricity reduces the losses that would occur if the electricity otherwisewould have to be taken from a location farther away. T

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