Evaluation of wind farm layoutsStefan Lundberg

Department of Electric Power EngineeringChalmers University of Technology

S-412 96 Goteborg, SwedenEmail: stefan.lundberg@elteknik.chalmers.se

Abstract— In this paper, layouts of various large-scale windfarms, using both AC as well as DC, are investigated. The criteriain this investigation is the energy production cost. The energyproduction cost is defined as the total investment cost dividedwith the total energy production of the wind farm. To determinethe energy production and the total investment cost, loss and costmodels for the components in the wind farm are used (the mostimportant models are presented in this paper).

Of the investigated wind farm configurations, a wind farmwith series connected DC wind turbines seems to have thebest potential to give the lowest energy production cost, if thetransmission distance is longer then 10-20km.

I. INTRODUCTION

Wind energy converters are becoming larger and larger andmore and more erected in groups rather than one by one. Todaywind farms up to a size of 160 MW are being built and severalplans on 1000 MW-parks exist [1]. These larger wind farmsare mainly considered to be located out in the sea, preferablyat such a distance that they cannot be observed from the shore.The size of the wind farms has led to a problem of finding asuitable grid connection point, which is strong enough to takecare of the power from the wind farms. This leads to that inmany cases the distance between the grid connection point andthe wind farm is so long, that a DC-transmission may becomemore favorable than a conventional AC-transmission. This isfurther stressed by the fact that it is extremely difficult to getpermission to build new over-head lines, and therefore it mustbe taken into consideration that it might be necessary to useDC-cables also for the onshore transmission.

Wind farm design studies have been presented in severalpapers, for instance [2]–[9]. The most detailed study wasmade by Bauer, Haan, Meyl and Pierik [10]. In [11] someinteresting DC solutions for offshore wind farms are presentedand especially the proposal of a wind farm with wind turbinesconnected in series, is of great interest. The energy productionof various wind farms is calculated in [5], [12], [13], and in[3], [5], [13]–[15] the estimated cost of the produced electricenergy is presented. In [16] the economics of some offshorewind farms that are build and are planned to be built, arepresented.

Of importance when determining the energy capture is tohave detailed blade data as well as detailed loss models ofcomponents. Relevant blade data is not trivial to obtain, butprevious authors have most likely used the same method ashere: By not revealing the origin of the blade description, itis possible to obtain such data. Generator loss models has

for instance been presented in [14], [17], gear-box losses havebeen found in [17]. However, available loss models of existinghigh power DC/DC-converters are very crude.

Cost data is another large problem area. Here the same prin-ciple seems to be dominant: Data can be obtained providingthat the sources are not revealed. However, in [13], [15], [18]–[20] valuable cost information is given which can be utilized.

This article is based on the work presented in [21]. In [21]a detail investigation of the energy production cost of differentwind farm layouts is performed. In this paper only the mainresults from these investigations and the philosophy of thecalculation procedure are presented. The purpose of this paperis to investigate which wind farm layout that has the lowestenergy production cost and how the energy production costvaries with different circumstances.

II. THE EVALUATION

In this article the energy production cost is used to deter-mine which layout that is to prefer for a given set of boundaryconditions (transmission length, rated power, average windspeed etc.). The energy production cost is defined as thetotal investment cost of the wind farm divided with theenergy production of the wind farm. Figure 1 shows the blockdiagram over the program that is used to calculate the energyproduction cost of the different wind farm layouts. The data

Investment

costs

Loss models

Power

performance

model

Data base

System

configuration

Wind

model

Energy

production cost

Energy

production

Fig. 1. The layout of the evaluation program used to determine the bestwind farm layout.

base have all the parameters and data that is needed for thecalculations. In the system configuration block the wind farmis configured. From this the energy production is calculated,and the investment cost and finally the energy production costcan be determined.

III. WIND FARM LAYOUTS

Generally, the wind farms investigated in this work can berepresented by the sketch presented in figure 2. As seen in

WT WT WT WT

WT WT WT WT

WT WT WT WT

WT WT WT WT

collecting

point

wind farm

grid

interface

PCC

local wind turbine grid

transmission system

electro-

mechanical

drive train

voltage adjuster

wind turbine

Fig. 2. General wind farm layout.

figure 2 the wind farm consists of a number of elements,wind turbines (WT), local wind turbine grid, collecting point,transmission system, wind farm interface to the point ofcommon connection (PCC). It shall be noticed that all windturbines in this work have a voltage adjusting unit (AC orDC transformer) included in the wind turbine unit itself. Thelocal wind turbine grid connects the wind turbine units tothe collecting point. The wind turbine units are connected inparallel to radials, unless otherwise is specified in this work.In the collecting point, the voltage is increased to a levelsuitable for transmission. The energy is then transmitted tothe wind farm grid interface over the transmission system. Thewind farm grid interface adapts the voltage, frequency and thereactive power of the transmission system to the voltage level,frequency and reactive power demand of the grid in the PCC.

The size of the wind turbines has in this project beenselected to 2MW, since these turbines are available for allkinds of wind energy systems today. However, it should bepointed out that the main results of this study would mostlikely not be very different if another turbine size would havebeen selected.

This work focuses on four sizes of wind farms

• 60MW• 100MW• 160MW• 300MW

Although most wind farms today are much smaller then60MW, 60MW is used as a small wind farm here. Horns Refis one example of a 160MW offshore wind farm 14-20kmout of the west coast of Denmark [22]. It is today (2003) thelargest built sofar. No larger wind farms than 300MW is takenunder consideration in this work due to the fact that if a largerwind farm is going to be build it will probably be divided intosmaller modules, where a maximum module size of 300MWseems appropriate. Two advantages using modular building ofwind farms are, that the investment cost of the whole windfarm is spread out over a longer period and that part of theproduction can start before the whole park has been built.Another advantage of this division is that if cross connections

between the modules are made, the park can be more faulttolerate.

In this work the wind power plants will be placed in a gridwith 7 rotor diameters between the turbines in both directions.This seems to be a commonly used distance and at Horns Revthe distance used is 7 rotor diameters [22].

Of course, if the wind is mainly coming from one direction,the wind turbines can be placed closer in the direction perpen-dicular to the prevailing winds. But for the Nordic countries,wind directions from northwest to south are quit normal, whichmeans that the wind turbines should be placed with an equaldistance in all directions.

In this work, it is thus assumed that the wind turbines areput in a grid with 7 rotor diameters between. The distancefrom the column nearest the collecting point to the collectingpoint is also 7 rotor diameters, see figure 2.

Since 7 rotor diameters was used, it was possible to neglectthe wake effects. Anyway, if wake effects were taken intoaccount, it would not affect the comparison between differentwind farm configurations very much.

A. AC/AC layouts

Today the by far most common electrical system (bothtransmission and local grid system) for wind farms is AC. Inthis work, two different AC-systems are investigated, referredto as the small and the large AC wind farm. Three core cablesare used for AC transmission throughout this work.

The first configuration to be discussed is the small AC windfarm. The idea with the small AC wind farm, is that it shouldbe suitable for small wind farms with a short transmissiondistance. In the small AC wind farm, the local wind farmgrid is used both for connecting all wind turbines in a radialtogether and to transmit the generated power to the wind farmgrid interface, which is shown in figure 3. For this system the

PCC

local wind turbine grid and transmission system

WT WT WT WT

WT WT WT WT

WT WT WT WT

WT WT WT WT

collecting

point

wind farm

grid

interface

Fig. 3. The electrical system for the small AC wind farm.

cables in the local wind farm grid are assumed to be installedone and one from the wind turbines to the collecting point.From the collecting point to the wind farm grid interface, allcables are assumed to be installed together. This means thatthere is one cable installation cost per cable from the windturbines to the collecting point and only one cable installationcost for all cables from the collecting point to the wind farmgrid interface.

Let us now study a slightly different configuration, the largeAC wind farm. The large AC wind farm system is a more

traditional system, based on the general system in figure 2.This system has a local wind farm grid with a lower voltagelevel (20-30kV) connected to a transformer and a high voltagetransmission system. This system requires an offshore platformfor the transformer and switch gear, as can be seen in figure 4.Horns Rev wind farm is build according to this principle. For

WT WT WT WT

WT WT WT WT

WT WT WT WT

WT WT WT WT

collecting

point

wind farm

grid

interface

PCC

local wind turbine grid

offshore

platform

transmission system

Fig. 4. The electrical system for the large AC wind farm.

this system there is one cable installation cost per cable, dueto the fact that all cables have different routes.

B. AC/DC layout

In this system the AC transmission in figure 4 has beenreplaced with a DC transmission, this wind farm will bereferred to as the AC/DC wind farm. This type of system doesnot exist today, except for one or a few small experimentalwind farms, but it is frequently proposed when the distanceto the PCC is long, or if the AC grid that the wind farm isconnected to is weak. The system is shown in figure 5. In thissystem we have an independent local AC system in which boththe voltage and the frequency are fully controllable with theoffshore converter station. This can be utilized for a collectivevariable speed system of all wind turbines in the park. Thebenefits with this are that the aerodynamic and/or electricalefficiency can be increased, depending on the wind turbinesystem used.

WT WT WT WT

WT WT WT WT

WT WT WT WT

WT WT WT WT

collecting

point

wind farm

grid

interface

PCC

local wind turbine grid

offshore

platform

transmission systemDC

ACDC

AC

Fig. 5. The electrical system for the AC/DC wind farm.

The installation cost of the cables are the same as for thelarge AC wind farm. The two DC transmission cables, one forthe positive pole and one for the negative pole, are assumedto be installed together and therefore there is only one cableinstallation cost for these two cables.

For all DC solutions throughout this work, only transistortechnology is used. The ”classical” thyristor technology isassumed to be too large in physical size to be an attractive

technology. The transistor technology is also more attractivedue to the better controllability of the reactive power.

C. DC/DC layouts

For the pure DC wind farm, three different configurationsare investigated. Two that are based on the two layouts of theAC systems, referred to as the small DC wind farm and thelarge DC wind farm, and one configuration with the turbinesin series, as shown in [11].

The electrical system for the small DC wind farm is shownin figure 6. As can be noticed, the electrical system for the

local wind turbine grid and transmission system

WT WT WT WT

WT WT WT WT

WT WT WT WT

WT WT WT WT

collecting

point

wind farm

grid

interface

PCCDC

ACDC

DC

Fig. 6. The electrical system for the small DC wind farm.

small DC wind farm is identical to the system of the small ACwind farm. The only difference is that the transformer in thewind farm grid interface is replaced with a DC transformerand an inverter. Of course, a rectifier is needed in each windturbine. The advantage of the small DC park compared to thelarge DC park is, as for the small versus large AC park, thatit does not require an offshore platform. The installation costof the cables are assumed to be the same as for the small ACwind farm.

The configuration of the electrical system for the large DCwind farm can differ somewhat from the configuration of thelarge AC wind farm. The difference is if it requires one ortwo transformations steps to increase the DC voltage from thewind turbines to a level suitable for transmission. It is assumedthat if the DC voltage from the wind turbines is high enough(20-40kV) only one transformation step is required. But if theoutput voltage of the wind turbine is lower (5kV), two stepsare required. In figure 7 this system is presented with twoDC transformer steps. For the large DC wind farm with two

WT WT WT WT

collecting

point

wind farm

grid

interface

local wind turbine grid offshore

platform

transmission

system PCCDC

AC

DC

DC

DC

DC

WT WT WT WT

DC

DC

WT WT WT WT

DC

DC

WT WT WT WT

DC

DC

Fig. 7. The electrical system for the large DC wind farm with two DCtransformer steps.

transformation steps, all wind turbines are divided into smaller

clusters. All wind turbines within one cluster are connectedone by one to the first transformation step. The high-voltageside of the first DC transformer step are then connected to thesecond step, as can be noticed in figure 7. If only one stepis used, the wind turbines are connected in radials directlyto the second DC transformer step, similarly as for the largeAC wind farm in figure 4. For this system there is one cableinstallation cost per cable, due to the fact that all cables havedifferent routes.

In the third DC system shown in figure 8 the wind turbinesare connected in series, as mention before, in order to obtaina voltage suitable for transmission directly. This system isreferred to as the series DC wind farm. The benefit of this

AC

ACG

Low voltageHigh

voltage

wind turbine

DC

AC

WT

WT

WT

WT

wind farm

grid

interface

local wind turbine grid

transmission system

PCCDC

AC

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

WT

Local DC/DC converter

Fig. 8. DC electrical system with series connected wind turbines.

system is that it, in spite of a relatively large possible size,does not require large DC-transformers and offshore platforms.The voltage insulation in the wind turbines is taken by thetransformer in the local DC/DC converter. The drawback withthis configuration is that the DC/DC converters in the windturbines must have the capability to operate towards a veryhigh voltage. This is due to the fact that if one wind turbinedoes not feed out energy and therefore fails to hold theoutput voltage, the other turbines must compensate for thisby increasing their output voltage.

For this system, there is one cable installation cost per cable,due to the fact that all cables have different routes, as can benoticed in figure 8.

IV. AVERAGE POWER PRODUCTION

The power delivered to the PCC from the wind farm iscalculated as

PPCC = PWIND − Plosses. (1)

The aerodynamic capture, PWIND, is used in this paperas the input power to the wind farm. It is defined as thepower all turbines in the wind farm converts from the windto mechanical power on the turbines shafts. It is assumedthat for wind speeds below rated the turbine is operatedat maximum efficiency and for wind speeds over rated theturbine is operated at the rated input power. In this work animportant base assumption is that the same rated input shaftpower is used for all wind turbine systems. From the inputpower, PWIND, the losses, Plosses, that is considered in thispaper are subtracted and the output power, PPCC , is thus

obtained. The losses that are considered in this work are:

Aerodynamic lossesGear boxGenerator (AG and PM)TransformerWind turbine converterCables (AC and DC)Cable compensating inductorHVDC converterDC/DC converter

The aerodynamic losses is only considered if the usedturbine is not operated at maximum efficiency below ratedpower. This is the case for fixed speed wind turbines atlow wind speeds. The specific other losses are, of course,only considered if the wind farm layout studied includesthe specific component. The used loss models can be foundin [21].

As mentioned before, the rotor blades convert some of thekinetic energy of the wind to mechanical energy on the rotorshaft. The efficiency of this conversion depends on severalfactors such as blade profiles, pitch angle, tip speed ratio andair density. The pitch angle, β, is the angle of the bladestowards the rotational plane. If the pitch angle is low, theblades are almost perpendicular to the wind and if it is high(near 90 degrees) the blades are almost in parallel with thehub direction. The tip speed ratio, λ, is the ratio between thetip speed of the blades and the wind speed, equation 3. Theconversion from wind speed to mechanical power can in steadystate be described by [23]

Pmec =πρw3

sR2

2Cp(λ, β) (2)

λ =ωtR

ws. (3)

Where:Pmec mechanical power on the shaft [W]R rotor radius [m]ωt rotor speed [rad/s]ρ air density = 1.225 [kg/m3]ws wind speed [m/s]λ tip speed ratioβ pitch angleCp(λ, β) aerodynamic efficiency

Equation 2 is used in this article to calculate the inputpower to the wind farm, the aerodynamic capture.

To describe the variations in the wind speed over a yeara density function is used. There are several density func-tions which can be used to describe how the wind speedis distributed. The two most common are the Weibull andthe Rayleigh functions. The Rayleigh distribution, or chi-2 distribution, is a subset of the Weibull distribution. TheWeibull distribution is described by [23]

f(ws) =k

c(ws

c)k−1e−(ws/c)k

(4)

Where:f(ws) Probability densityws Wind speed > 0 [m/s]k Shape parameter > 0c Scale parameter > 0

Comparisons with measured wind speeds over the worldshow that the wind speed can be reasonably well describedby the Weibull density function if the time period is not tooshort. Periods of several weeks to a year or more is usuallyreasonably well described by the Weibull distribution but forshorter time periods the agrement is not so good [23]. In thispaper the Rayleigh distribution is used to describe the windspeed variations over a year. This distribution is obtainedif the shape parameter, k, in the Weibull distribution is putequal to 2.

The average input power can be calculated by calculate theexpectation value of the input power. The expectation valuecan be calculated as:

Pin,AV G =

∫ cutout

cutin

Pmec(ws)f(ws)dws. (5)

Where:Pin,AV G Average input power [kW]cutin Cut in wind speed =3 [m/s]cutout Cut out wind speed =25 [m/s]Pmec(ws) Input power of the wind turbine [kW]f(ws) Rayleigh distribution

Equation 5 can also be used to calculate the averageoutput power from the wind farm. By substituting the inputpower, Pmec(ws), to the output power.

V. INVESTMENT COST

A difficult task in this investigation was to obtain relevantcost data for the components, due to secrecy policies, inthe different wind farms layouts. In the list below thecomponents that is taken into consideration when thetotal investment is calculated are shown. In the list themost relevant cost data is presented, except for the windturbine, offshore platform and for the cables. The used costmodels for the other components can be found in [21].

Wind turbineWind turbine Foundation = 0.801MEURCables (AC and DC)Cable installation = 85.4EUR/m onshore

= 256EUR/m offshoreProtectionsOffshore platformTransformerCable compensating inductorHVDC converter station = 0.107EUR/WDC/DC converter = 0.107EUR/W

The cost for the structure of the offshore platform isassumed to be described with equation 6.

Cost = 2.14 + 0.0747Prated (6)

Where:Cost Structure cost for the offshore platform [MEUR]Prated Rated power of the wind farm [MW]

This cost model is for a quite sophisticated platformwith living quarters for workers, heliport, low and highvoltage switch gear, transformers and/or converters. Ofcourse, in some cases a simpler platform can be sufficient.Anyway, in this work, the cost model presented in equation 6is used for the structure of all offshore platforms in this work.

In figure 9 the cost information given for different windturbines in the range 1 to 2.5MW is shown. The costs for thewind turbines are normalized by a linear equation to 2MW.The circles in figure 9 shows the cost information used and

1 2 3 4 5 6 7 8 9 100.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

Middelgrunden→

Number

Scal

ed p

rize

[ME

UR

]Fig. 9. The cost of the wind turbines after normalizing the output power to2MW. Circles denotes the costs used, stars the costs that was not used andthe solid line the cost for a 2MW wind turbine.

the stars shows three outliers that was not used. From figure 9it can be observed that the cost of a 2MW wind turbineis approximately 1.63MEUR. The most interesting outlier infigure 9 is marked Middelgrunden and is the cost from thehome page of the Middelgrunden wind farm [24]. The costfor the 2MW wind turbine is used for all wind turbine typesin this paper. For the 2MW DC wind turbines it is assumedthat they cost the same as a 2MW AC wind turbine.

For the cable costs, AC and DC, four examples are givenin figure 10. In the figure two AC cables are presented andtwo DC cables, the circles and stars indicate the costs that wasgiven and the lines the models developed. From figure 10 itcan be noticed that the DC cables are much cheaper for thesame rating then the AC cables.

A. Energy production cost

The energy production cost is defined as how much it costto produce and deliver a unit of energy to the grid, i.e to thePCC. The energy production cost is obtained by dividing thetotal investment cost of the wind farm with the total energydelivered to the PCC. The total investment cost is calculatedassuming that the whole investment is made in the first yearand paid off during the life time of the wind farm. In addition,it is also assumed that some profit shall be made. The totalenergy that is delivered to the PCC is calculated by multiplyingthe average power delivered to the PCC with the average

0 100 200 300 400 500 600 700 8000

0.2

0.4

0.6

0.8

1

1.2

1.4

160 kVDC300 kVDC

33 kVAC

220 kVAC

Rated power [MVA]

Priz

e [M

EU

R/k

m]

Fig. 10. The cost of the AC and DC cables, circles cost information givenfor AC cables and stars for DC cables. The voltages are line to line voltages.

number of operational hours during one year multiplied withthe lifetime of the wind farm. The average power is calculatedwith equation 5. With these assumptions the energy productioncost can be calculated as in equation 7.

Ecost =Invest

Pout,AV GT

r(1 + r)N

(1 + r)N− 1

100

100 − PR

= KInvest

Pout,AV G(7)

Where:Ecost Energy production cost [EUR/kWh]Invest Investment [EUR]Pout,AV G Average output power [kW]T Average operational hour during one year [h]r Interest rate [-]N Lifetime of the wind farm [years]PR Profit in %K Constant

The life time of the wind farm is in this paper set to25 years and the average operational hours during one yearis set to 365 · 24 = 8760. In figure 11 the energy productioncost for the Horns Rev wind farm is shown for differentprofits and as function of the interest rate. According to [22]Horns Rev has a yearly production of 600 000 000kWh, anaverage wind speed of 9.7m/s and a project cost of DKK2 billion. As can be noticed from the figure 11 the energyproduction cost increases with increasing interest rate andprofit as can be expected. In this paper the interest rate is setto 7% and the profit to 10%. This gives an energy productioncost of approximately 0.043EUR/kWh, accordingly to theassumptions used in this paper. This also gives that theproduction cost gets about 138% higher then without profitand interest rate.

VI. ENERGY PRODUCTION COST OF THE SIX LAYOUTS

In this section the best configuration of each of the six windfarm layouts are compared with each other, small AC, largeAC, AC/DC, small DC, large DC and series DC. The energyproduction cost for the six investigated types of electricalsystem are normalized by the energy production cost obtained

0 1 2 3 4 5 6 7 8 9 100.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

Profit = 20%10%

5%

0%

Interest rate [%]

Ene

rgy

prod

uctio

n co

st [E

UR

/kW

h]

Fig. 11. The energy production cost for the Horns Rev wind farm for differentprofits, solid line profit = 0%, dotted =5%, dashed =10% and dash-dotted=20%. The input data is taken from [22] and the energy production cost iscalculated by (7).

for the Horns Rev wind farm, 0.043EUR/kWh. In figure 12the normalized energy production cost are shown for the sixsystems for a rated power of the wind farm of 160MW anda average wind speed of 10m/s. As can be noticed the costfound for the large AC park (The Horns Rev case, totaly 55kmtransmission length [25]) is 10% lower then the ”real” case.However, since real price information is hard to obtain andthe fact that Horns Rev was the first large offshore wind farmthe results are considered to be surprisingly good. It should bestressed that this work focuses on comparing systems ratherthen obtaining correct total costs, since this was considered tobe out of reach without having access to really good cost data.

0 20 40 60 80 100 120 140 160 180 2000.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Smal AC

Large AC

AC/DCSmal DC

Large DC

Serie DC

Transmission length [km]

Ene

rgy

prod

uctio

n co

st [p

.u.]

Fig. 12. The normalized energy production cost of the different 160MWwind farms as function of the transmission distance and at a average windspeed of 10m/s.

If the three wind farms with AC are compared, small AC(solid black), large AC (dashed) and AC/DC (dash-dotted)these results are as expected. The small AC wind farm is thebest solution for short distances, the AC/DC is best suitable forlong distances and the large AC is best in between. The smallAC wind farm is the best for short distances due to that it doesnot require an offshore platform. So the additional cost formany low voltage transmission cables is less then the cost for

the platform and the high voltage transmission cable, for shortdistances. The cost for the low voltage transmission increasesrapidly when the transmission distance increases. The breakeven point between the small and large AC system is at atransmission distance of 19km. The AC/DC system has, dueto the expensive converter stations, a high energy productioncost for short distances. Due to the fact that the cost for thetransmission cables are less for DC then for AC, see section V,the AC/DC system gets better then the large AC system fortransmission lengths over 125km.

The large DC system is better then the AC/DC system dueto that the losses in a DC wind turbine is lower then in anAC wind turbine in this work. Moreover, the cost for the localDC grid is less then the cost for the local AC grid and thelosses in the DC transformer are less then the losses in theoffshore converter station. These costs are independent of thetransmission length, but since the two systems has the sametransmission system (DC cables), the large DC wind farm willfor any transmission length be better then the AC/DC windfarm (using the assumptions made in this work).

As could be expected, the small DC wind farm is nogood solution. This is due to that it still requires a large DCtransformer and a converter station. The gain of cheaper cablesand somewhat lower losses is not enough to compensate for theexpensive DC transformer and converter station. But comparedto the large DC system it is better for short distances. Thereason is that it does not require an offshore platform.

From figure 12 it can be seen that the best wind farmsolution for a transmission length over 10km is the series DCwind farm. This is due to the fact that it does not requirean offshore platform, it has a cheaper local wind turbinegrid, DC transmission (cheaper then AC) and this system hasonly one converter station. The uncertainty which is also agreat challenge for research in the high voltage field, is howexpensive it will be to have the high voltage insulation in eachwind turbine.

It was also observed that the break even point between thesmall AC and large AC is decreasing when the wind farmsize is increased [21]. This is caused by the fact that the con-tribution to the energy production cost from the transmissionsystem decreases when the wind farm size is increased. Thedecrease is larger for the large AC wind farm then for thesmall AC wind farm. Another observation that has been madeis that the energy production cost decreases when the ratedpower of the wind farm increases.

Another parameter that strongly affects the energy produc-tion cost is the average wind speed. Figure 13 shows how theenergy production cost varies with the average wind speed.The curve is normalized by the costs at a average wind speedof 10m/s. As can be noticed from the figure 13 the costincreases rapidly if the average wind speed decreases. At aaverage wind speed of 6.5m/s the energy production cost istwice as high as at 10m/s.

4 5 6 7 8 9 10 11 12 13 140.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Average wind speed [m/s]

Ene

rgy

prod

uctio

n co

st [p

.u]

Fig. 13. Energy production cost as function of the average wind speed,normalized with the cost at a average wind speed of 10m/s.

VII. CONCLUSION

Six different types of electrical configurations of windfarms has been investigated for the energy production cost.The investigate types are

Small AC Where the local wind turbine grid is used fortransmission

Large AC Which has a low voltage grid between thewind turbines and has a central transformer onan offshore platform for increasing the voltagelevel to a level suitable for transmissionto the PCC

AC/DC Similar to the Large AC wind farm but withthe difference that the transmission ismade using DC instead of AC

Small DC Similar to the Small AC wind farm but withthe difference that the wind turbinehas a DC voltage output

Large DC Similar to the Large AC wind farm but withthe difference that the wind turbinehas a DC voltage output

Series DC Uses series connected wind turbines witha DC voltage output

The investigation is done for different rated wind farmpowers, different transmission lengths and different averagewind speeds.

The results regarding the energy production cost for the ACwind farms was as expected. The small AC wind farm wasbest for short transmission distances (up to approximately 10-20km) and the AC/DC wind farm was best for long distances(above approximately 130km). The large AC wind farm is bestin between the small AC and the AC/DC wind farm.

For the DC wind farms the results was somewhat surprising,except for the small DC wind farm, where it was found that itis not a good solution, due to the high costs of the converterstation and DC transformers. For the large DC wind farm itwas found that it is better then the AC/DC wind farm. Thisis due to that DC cables are cheaper then AC cables. Butthe reduction in the energy production cost is not so large,which results in that the large AC wind farm is still better for

shorter transmission distances. The most surprising results wasfor the series DC wind farm. This configuration shows verypromising performance. The energy production cost for theseries DC wind farm was the lowest for all the six investigatedwind farm configurations for transmission lengths over 20km.For example, for a wind farm with a rated power of 160MW,a transmission length of 80km and an average wind speedof 10m/s it was found that the series DC wind farm has anenergy production cost of 0.86p.u. The large AC has an energyproduction cost of 0.97p.u, the large DC 0.98p.u. The messagecan also be expressed as: An increased investment cost of 13%can be allowed for the series DC park before the productioncost becomes equal to the large AC park, using the input datathat was available in this work

As expected, the energy production cost was strongly de-pendent on the average wind speed. As an example, the energyproduction cost at an average wind speed of 6.5m/s was twiceas high as the cost for an average wind speed of 10m/s. It wasalso found that the energy production cost decreases when thepower of the wind farm increases.

This work has presented necessary steps to determine theenergy production cost. It should be stressed that the cost re-sults, of course, depend strongly on the cost input parameters.The aim here has been to present a determination strategy thatcan be of value for further wind farm design and cost studies.

ACKNOWLEDGMENT

This work has been carried out at the Department of ElectricPower Engineering at Chalmers University of Technology.The financial support given by the Swedish National EnergyAgency and ABB Power Technologies is gratefully acknowl-edged.

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