Wind farm layout

UPTEC ES08013

Examensarbete 20 pOktober 2008

Wind farm layouta reliability and investment analysis

Emil Eriksson

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Wind farm layout - a reliability and investmentanalysis

Emil Eriksson

Investment and maintenance costs are higher for offshore wind power compared toonshore. Also, wind turbine components offshore are subjected to higher physicalstresses compared to components onshore, due to harder winds. These strong windsoften lead to longer outage times of failed offshore components compared toonshore.

The reliability of the Swedish offshore wind farm Lillgrund is analysed in this report.The consequence of a component failure might be a smaller energy production thanexpected. This loss of energy is called expected energy not supplied (ENS)[GWh/year]. High ENS-values risks the profitability of the investment. Thus, theENS-value of Lillgrund has been calculated with a reliability analysis and is then used asinput in an investment analysis, to see how the reliability of the farm affects theinvestment proposal. Three alternative layouts, where the transformer is placed onland instead of on a platform offshore, are compared to the original layout.

The results show that all layouts have positive net present values (NPV), but there arenot that big relative differences between the NPVs of the layouts compared to thetotal investment outlay. The result shows that a transformer on land is preferablewhen the distance from farm to the shore is 7.5 km or less, while for longer distancesa platform is preferable. A sensitivity analysis shows that the NPV is most sensitive tolong outage times of the turbines, compared to long outage times for cables andtransformer. Results and views in the report are my own conclusions, based on theinput parameters used. The views are not necessarily the views of Vattenfall. Also, itis important to notice that some data have been changed because of confidentiality.However, the qualitative results and conclusions still remain the same.

Sponsor: Vattenfall ABISSN: 1650-8300, UPTEC ES08 013Examinator: Ulla TengbladÄmnesgranskare: Marcus BergHandledare: Ying He

Table of Contents Page

LIST OF ABBREVIATIONS

1 INTRODUCTION AND BACKGROUND 1

1.1 Introduction 1 1.1.1 Need for reliable power generation in offshore wind farms 1 1.1.2 Importance of reliability analyses 1 1.1.3 Relations between reliability and investments 2

2 PURPOSE AND PROBLEM FORMULATION 3

2.1 Problem statement 3 2.2 Purpose 3 2.3 Problem formulation 3 2.4 Outline of the thesis 3 2.5 Limitations of the project 4

3 THE WIND FARM AND THE NETWORK ON LAND 6

3.1 Lillgrund offshore wind farm 6 3.1.1 Geographic location of the wind farm 6 3.1.2 Technical specification and layout of the wind farm 6 3.1.3 Outer limit of the studied system 8

4 THEORY 10

4.1 Load flow 10 4.1.1 Load flow analyses 10 4.1.2 Power balance in a network 10 4.1.3 The load flow calculation 11 4.1.4 Different types of nodes for load flow calculations 12

4.2 Reliability analysis 13 4.2.1 Deterministic and probabilistic reliability criteria 13 4.2.2 Probabilistic reliability indices 13 4.2.3 Series and parallel systems 15

4.3 Investment analysis 16 4.3.1 Relations between reliability and investment costs 16 4.3.2 Internal rate of return and net present value 17 4.3.3 Capacity factor 18

5 METHOD 20

5.1 Tools for the analyses 20 5.1.1 Load flow and reliability analysis 20 5.1.2 Investment analysis 20 5.1.3 NEPLAN 20

5.2 Collecting data 21 5.2.1 Data for the load flow analysis 21 5.2.2 Data for the reliability analysis 21 5.2.3 Data for the investment analysis 21

6 ALTERNATIVE LAYOUTS OF THE WIND FARM 22

6.1 Three alternative layouts of the wind farm 22 6.1.1 Alternative one 22 6.1.2 Alternative two 22 6.1.3 Alternative three 23 6.1.4 Important assumptions made for the alternative layouts 23

6.2 A 72 kV solution 24 6.2.1 A possible future layout 24

7 IMPLEMENTATION 26

7.1 Building a model in NEPLAN 26 7.1.1 How to build a model in NEPLAN 26 7.1.2 Modelling the generators 26 7.1.3 Modelling the cables 27 7.1.4 Modelling the transformer 28 7.1.5 Other components in the wind farm 28

7.2 Reliability analysis in NEPLAN 29 7.2.1 Correct power output from the turbines 29 7.2.2 Failure rates and outage times for the reliability analysis 29 7.2.3 Maintenance operations 32 7.2.4 Sensitivity analysis 32

7.3 The investment analysis 33 7.3.1 Input for the NPV and IRR calculations 33 7.3.2 Input parameters for the cash flow calculations 34

7.4 Parameters affecting the net sellable production of the farm 36 7.4.1 Unavailability of the farm 36 7.4.2 Electrical energy losses as a function of park power output 37 7.4.3 Total electrical energy losses of the different layouts 38 7.4.4 The net sellable production from the different layouts 41

8 RESULTS 43

8.1 Result of the combined reliability and investment analysis 43 8.2 Result from the sensitivity analysis 45

9 DISCUSSION 49

9.1 The problem formulation of the report 49 9.1.1 A combined reliability and investment analysis 49

9.2 Suggestions for future studies 49

10 LIST OF REFERENCES 51

10.1 Electronic document 51 10.2 Material from the Internet 51 10.3 Literature and reports 51 10.4 Discussions 52

Appendices Number of Pages

APPENDIX 1

APPENDIX 2

Alternative layouts of the wind farm

Investment cost in more detail

3

2

List of abbreviations ENS Energy Not Supplied

IRR Internal Rate of Return

MSEK Million Swedish Kronor

NPV Net Present Value

O&M Operation and Maintenance

SAIDI System Average Interruption Duration Index

SAIFI System Average Interruption Frequency Index

VRD Vattenfall Research and Development

1 Introduction and background

1.1 Introduction

The interest for energy produced from renewable sources has grown rapidly over the last years.

Consequently, energy produced from wind power has also gained more and more interest. Wind

power, which is a relatively new technology, has developed and matured gradually the last decades,

resulting in turbines with higher rated power. Partly because of this, but also because of the fact that

there generally are stronger winds at sea compared to land, the interest in offshore wind farms has

increased. Thus, large efforts are made today to develop future offshore wind farms. The largest wind

farm in Sweden today is Lillgrund, which is an offshore wind farm in Öresund, outside the coast of

Malmö. It was in full operation in 2007 and the estimated annual energy production from the park is

0.3 TWh.

The interest of wind energy is continuing to increase worldwide and the Swedish government

proclaimed a political ambition in 2005, saying that by year 2016, the total Swedish wind energy

production should be 17 TWh per annum.

1.1.1 Need for reliable power generation in offshore wind farms

As with other forms of electricity production, there are many components in a wind farm that

all must work together at the same time. A wind farm consists mainly of a number of wind

turbines, an internal grid to connect the wind turbines, a transformer, a transmission system,

and a connection interface to the main grid. In addition to this, many electric components,

such as breakers and switches, are used in a wind farm. Offshore wind farms are exposed to a

more difficult environment than farms at land, resulting in a higher degree of loads on the

components. The difficult environmental conditions and the location at sea increase the size

of the investment costs for an offshore wind farm compared to a wind farm on land. The

operation and maintenance, O&M, costs, are also higher for offshore installations compared

to onshore alternatives. Thus, to find reliable layout of offshore wind farms is of great

importance when developing future offshore wind farms. Assessing the reliability of power

systems during the design phase has gained more interest.

1.1.2 Importance of reliability analyses

It is of great importance, both for the society and the network owner, that both the production

and the distribution of energy from a wind farm are reliable and without major disturbances.

1

Power systems contain many different components, which makes networks like wind farms

very complex when it comes to the electric configuration. An unpredicted system behavior at

one point of the system might have severe impacts at the same, or at a remote point in the

system. Therefore, it is important to investigate the probabilistic reliability properties of an

electric system when designing the layout, in order to find out how likely different

components are to fail, where in the system these components are located, for how long time

they are out of order and how severe the impact of the fault will be. To minimize both the

number of outages and the outage time, redundant capacity can be built into the system. For

example, this might be accomplished by installing an extra, parallel line between two nodes.

1.1.3 Relations between reliability and investments

There is an obvious connection between the degree of redundancy built into a system and the

investment cost for the system. Increasing the redundancy in a system is almost always done

to a higher investment cost. However, the degree of reliability is not linearly related to the

investment cost; instead, systems reliability does not usually increase as fast as the investment

costs increase. This is because of the fact that the first actions taken to increase the reliability

of one part of a system will make a bigger difference to the stability of the network than the

following actions. Investing the same amount of money once more, as with the first

redundancy built into a system, one cannot be sure that the extra effort will increase the

reliability as much as the first effort did. As an example, installing an extra line parallel to

another in a distribution system will increase the reliability for that part of the system, if the

extra line can carry the load from the first line if that one fails. But installing a second parallel

line to the first line, the degree of reliability will not increase as much as with the first parallel

line, since the probability that both the two other lines fail at the same time is relatively small.

The investment cost for the third line is nevertheless just as big as the investment cost for the

second line. Thus, there is no guarantee that the higher cost associated with a higher degree of

redundancy in a system, actually will increase the reliability of the system enough to make it

worthwhile to do the investment.

2

2 Purpose and problem formulation

2.1 Problem statement

As both onshore and offshore wind farms become more common and get higher installed power, the

energy produced by these wind farms will represent a larger amount of the total energy production. If

a wind farm cannot produce as much energy as expected, the owner of the wind farm cannot sell as

much energy as planned and will have a loss of expected income. Thus, the production of energy and

the distribution of it must be reliable. There are many different components that can fail in a wind farm

and many of these failures result in different consequences with varying severity. Changing the layout

of a wind farm will most probably change the level of both the investment cost and the reliability of

the farm. Thus, to find cost-effective and reliable layouts of wind farms is of interest when it comes to

designing future wind farms. It is important to look at different wind farm layouts and compare the

reliability and the investment between the alternatives, since it is hard to interpret the result from a

reliability calculation for a single layout without comparing it to alternatives. Thus, different layouts

must be compared in order to find a design that minimizes the investment and still has an acceptable

level of reliability.

2.2 Purpose

In view of the background, the purpose of this project is to perform quantitative wind farm layout

investment and reliability analyses based on an existing offshore wind farm. This report will use the

offshore wind farm Lillgrund outside of Malmö as a base case. The impact of alternative wind farm

layout structures on the investment costs and wind farm reliability will be investigated.

2.3 Problem formulation

The wind farm reliability is highly dependent on its electric configuration. When the amount of wind

power generation is increasing, in the case of large-scale wind farms, how should a wind farm be

designed to reduce the total investment cost while keeping the reliability of the wind farm at an

acceptable level? There may be several alternatives to place wind farm equipment. Which alternative

layout will give a reasonable level of reliability at an acceptable cost?

2.4 Outline of the thesis

Chapter 3 describes the geographic location of Lillgrund and the layout of it. A brief, technical

specification of the turbines used in the wind farm is given and the limit of the studied system is also

presented.

3

Chapter 4 explains the underlying theory used for the different parts of this report. Theory used for

load flow calculations, reliability analysis and investment analysis is given in this chapter.

Chapter 5 briefly describes the method for collecting data to the project and also how the load flow-,

reliability- and investment calculations are carried out.

In Chapter 6, the alternative layouts to be compared to the original layout are presented. Three

different designs of the farm are investigated.

Chapter 7 explains how the project is carried through. All input data needed for the different analysis

are presented here and all assumptions made in the report are also given in this chapter.

In Chapter 8, the final results from the combined reliability- and investment analysis in the project are

presented.

Finally, Chapter 9 is devoted to a discussion of the results. Suggestions for future work are also

presented in this chapter.

2.5 Limitations of the project

The outer, physical limit of the studied system is drawn at the substation in Bunkeflo, where the farm

is connected to the 138 kV network on land.

When it comes to reliability data, it is always hard to find reliable and up-to-date data. To minimize

the risk of errors origin from bad data, a sensitivity analysis will be made of the reliability analysis.

The magnetic field from the cables on land is strongly regulated and is not allowed to exceed a

maximum limit. No studies will be made in this report on how strong the field is around the 33 kV on-

shore cables in the three alternative layouts, described in Chapter 6. Also, no studies of the dynamic

electrical behaviour of these three layouts will be made

There are also some limitations in the used software. One of these limitations is that planned

maintenance of the farm cannot be included in the reliability calculations in NEPLAN. Another

limitation of NEPLAN is that a varying output power from the farm cannot be simulated. In reality,

the winds are usually stronger in winter, which leads to higher power output, but also longer repair

times when faults occur. Therefore, a constant power is used in the reliability calculations. The

4

constant power is set to correspond a capacity factor of 36.5 % (0.84 MW), which also Vattenfall

starts from when they calculate the unavailability of the farm.

It is not possible to model the turbines as PV-nodes in NEPLAN, since the load flow calculations do

not converge (see paragraph 7.1.2). Therefore, the turbines are modelled as PQ-nodes.

5

3 The wind farm and the network on land

3.1 Lillgrund offshore wind farm

3.1.1 Geographic location of the wind farm

Lillgrund offshore wind farm was built during the years 2006-2007 and was put into operation in

2007. It is located southwest of Malmö, approximately 7 km off the Swedish coast and 7 km south of

the Öresund bridge. See Figure 3-1.

Figure 3-1 Location of Lillgrund wind farm, with its export cable to Bunkeflo marked with the thin red line to the right. The Öresund bridge connecting Sweden and Denmark can also be seen in the figure as the dashed green line [7].

3.1.2 Technical specification and layout of the wind farm

The farm consists of 48 Siemens 2.3 MW Mk II turbines, all of a height of 115 meters including the

rotor. The expected annual production from the wind farm is 330 GWh, which is supposed to satisfy

the annual demand from 60 000 domestic households [2]. The turbines are pitch-regulated and

connected to a 4-pole asynchronous generator, with a voltage magnitude of 0.69 kV AC, via a

6

gearbox. A frequency converter is used to first rectify the current and then convert it into alternating

current again, now with the correct frequency compared to the network on land. The frequency

converters make it possible to vary the rotational speed of the turbines. An important detail with the

frequency converters is that they can regulate the reactive power in the wind farm. The voltage is

stepped up to 33 kV via a transformer placed at the bottom of the tower. Every turbine is then

connected to the 33 kV internal grid through a switchgear consisting of a remotely controlled circuit

breaker and disconnecting switch. This is illustrated in Figure 3-2 below, where the internal grid is

depicted with two arrows.

Figure 3-2 Illustration of how each turbine is connected to the internal 33 kV grid. The turbine and the gearbox, placed before the generator, are not pictured in the figure.

The wind farm consists of five radials, two of them with nine turbines and three of them with ten

turbines respectively. A three-core 36 kV copper cable is used to connect the turbines in the internal

grid and the cross section area of this array cable depends on how much power is flowing in it. Also,

the cables heat inside the gravity foundations, which limit their capacity to transmit power. Therefore,

cables with three different cross-section areas are used to connect the turbines. Starting from the far

end turbine of any of the five radials, the cable with the smallest cross-section area is used to connect

the first six turbines; the second cable is used for turbine seven to nine. The thickest cable is only used

in the three radials with ten turbines, to connect the tenth turbine with the offshore platform.

The five radials are all connected to an offshore platform, called W01, via a circuit breaker and a

switch. The voltage is being stepped up from 33 kV to 138 kV at the offshore transformer. The

transformer is then connected to land through a 145 kV three-core copper cable. All submarine cables

are buried on one meter depth below the bottom surface. This submarine export cable is connected to

three 145 kV single-core aluminium cables onshore, and these three single-core cables are then

connected to a switchgear station in Bunkeflo through a breaker and a switch. Like other breakers and

switches in the wind farm, these two components in Bunkeflo are also remotely controlled. There is no

breaker at the offshore platform. Because of environmental requirements, the three one-phase cables

7

on land are placed right next to each other in a triangular formation to minimize the magnetic field.

E.ON owns the 138 kV network on land and does not tolerate any reactive power exchange between

the wind farm and the network on land. The cables connecting the offshore platform with Bunkeflo

generates approximately 10 MVAr reactive power, but there is no reactor in Lillgrund to absorb it.

Instead, the transformer consumes a part of the reactive power, and the reactive power production is

also controlled through the frequency converters in the turbines.

The layout of the turbines and the platform is shown in Figure 3-3 on next page. There are cables of

three different lengths in the wind farm. The long ones, for example the one between turbines E01-

E02, are 450 meters, while the short ones (E02-F02) is 355 meters. The one diagonal cable (C05-D06)

is 570 meters long.

3.1.3 Outer limit of the studied system

The outer limit of the system studied in this report will be the substation in Bunkeflo, since it is the

reliability and the investment cost for Lillgrund that is of interest in this report. However, the

reliability of the network on land might also affect the availability of the farm. This happens if a

failure occurs in the network on land, meaning that the network on land cannot receive all power from

the wind farm. The wind farm then has to reduce its production, even if there is no fault within the

farm. Such an analysis is a bit more advanced and will not be included in this report. Instead of

modelling the network on land, an equivalent for the network on land will be modelled in Bunkeflo as

the swing bus (see Section 4.1.4).

8

A06

A01

A05

A04

A03

A02

C05

A07

D08 C08

B03

B04

B05

B06

B07 D07 C07 E07

E06 D06 C06

F05 G05

F06

B08

C01

E04 D04 C04

G03

H02

H03

H04 G04

E03

F02 G02

F03

D02 C02 B02

C03 D03

F04

B01 D01 E01

E02

Radial 1

Radial 5

Radial 4

Radial 3

Radial 2

Offshore platform

Figure 3-3 Layout of the wind farm, with its five radials and 48 turbines. All radials are connected to the offshore platform where the voltage is stepped up and the power is transported to land. A shipwreck is located on the bottom of the sea, where there is a gap in the figure (between F05 and C05).

9

4 Theory

4.1 Load flow

4.1.1 Load flow analyses

When planning and designing electric networks, it is important to know different system properties,

like loads and losses in lines for example. A load flow analysis is a tool for determining the magnitude

and phase angle of the voltage, as well as the active and reactive power entered in the network at every

bus in the system. By performing a load flow analysis at the planning and designing level, weak parts

of the system can be identified and altered before building the network in reality. A load flow analysis

is done before performing a reliability analysis on a power system, to be sure that the system is stable.

The theory of load flow can be found in [19].

4.1.2 Power balance in a network

On the left hand side in Figure 4-1, a generator G connected to a bus k generates the current IGk into

the bus and a load at the bus draws the current IDk out of the bus. On the right side of the bus, the

nodes k1 to kN are supplied with the currents Ik1 to IkN. Note that variables in bold type are complex-

valued vectors. In the equations on following pages, vectors will be marked with a line.

Figure 4-1 Description of node k , with the current IGk flowing in to the node and the currents IDk and Ik1 to IkN flowing out of it. Uk, is the bus voltage [19].

According to Kirchoff’s first law, the sum of all currents flowing in and out of any node must equal

zero. For the node k in Figure 4-1 with N neighbouring busses, this can be expressed as

∑

=

=−N

jkjDkGk III

1 (Eq. 4.1.1)

10

By conjugating and multiplying these currents by the bus voltage Uk, Kirchoff’s first law also applies

to complex power. With notation as in Figure 4-1 the expression for the complex power at a node k is:

∑=

=−N

jkjDkGk SSS

1 (Eq. 4.1.2)

where Skj is the complex power flowing in a line from the bus k to a connecting bus j. In Equation

4.1.1, the terms can be rewritten as

GkGkGk jQPS += = by the generator generated complex power

DkDkDk jQPS += = consumed complex power by the load connected to k

kjkjkj jQPS += = distributed power to bus j

The net generation of active and reactive power can be written as

∑=

=−=N

jkjDkGkGDk PPPP

1 (Eq.4.1.3)

∑=

=−=N

jkjDkGkGDk QQQQ

1 (Eq.4.1.4)

Both active power Pk and the reactive power Qk, must be in balance at every bus k, which means that the net generation of active power PGDk and reactive power QGDk must be in balance at every bus. This can easily be seen in Equation 4.1.3-4. [19]

4.1.3 The load flow calculation

The values of PGDk and QGDk, from Equation 4.1.3 and 4.1.4 are the scheduled, or predefined, values

for net active power and net reactive power respectively, entering the network at bus k. Pk, calc and

Qk, calc are the calculated net active and net reactive power being injected into the network at bus k.

These values are the actual values of active and reactive power that will be flowing in bus k in reality.

The difference in scheduled and calculated active and reactive power, ΔPk and ΔQk, can be calculated

and this difference is called the mismatch. The mismatch for the active and reactive power can be

written as

calckGDkk PPP ,−=Δ (Eq.4.1.5)

11

calckGDkk QQQ ,−=Δ (Eq.4.1.6)

The mismatch is defined as the difference between the scheduled power and the calculated power. The

software to be used in this report is called NEPLAN. The expression for the complex power mismatch

at bus k in NEPLAN is

∑=

−−=ΔN

jjkjkGDkGDkk UYUjQPS

1

** )()( (Eq.4.1.7)

where Yij is an element of the network’s admittance matrix, or Y-matrix, of the k-th row and j-th

column. A star denotes complex conjugation. Note that the sign of the power term is determined from

the direction of the currents. The expression in Equation 4.1.7 is also known as the error equation. For

solving the load flow problem, the complex voltages Ui have to be found such that ΔSk becomes zero.

Since the expression in Equation 4.1.7 is not linear, it must be solved iteratively until a convergence

criterion is reached. In this report, the Newton-Raphson method will be implemented for the load flow

calculation in NEPLAN. [1]

4.1.4 Different types of nodes for load flow calculations

The four parameters net generation of active power Pk, net generation of reactive power Qk, voltage

phase angle θk, and voltage magnitude |Uk| are used in load flow calculations. All four of them are

associated with each node k, which means that there exist a total of 4*N = 4N variables in a network

with N busses. Unfortunately, the total number of unknown variables exceeds the total number of

equations for a system. Therefore, to be able to do a load flow calculation, the number of unknown

variables must be reduced to agree with the number of equations. This is generally done by modelling

the nodes in the network in three different ways, depending on which of the four parameters

mentioned above that are known at the specific bus. Two quantities are always known at each node

and the remaining two are to be calculated.

PQ-node, or Load node. Net generated power PGDk and QGDk are known at this bus, hence the name

PQ-bus. Voltage magnitude |Uk| and voltage phase angle θk are unknown variables to be determined

through the load flow calculation. This kind of bus is most often a bus with only a load demand, but

can also be without generation and load if it is a bus where a line is connected to a transformer or a

node where transmission lines intersect.

PU-node, or Generator node. Net generated active power PGDk and voltage magnitude |Uk| are known

quantities at this bus, leaving net generated reactive power QGDk and voltage phase angle θk to be

12

calculated. As one can guess from the name, a PU-bus is usually a bus with a generator. Some sort of

voltage regulating device must be connected to the bus in order to keep a fixed voltage magnitude,

independent of the generation of reactive power. A SVC (Static VAr Compensator) can be used for

this purpose, to compensate for the additional reactive power produced at the bus.

Uθ-bus, Slack bus, or Swing bus. The phase angle θk is known here and mostly set to zero, since it

serves as a reference for the phase angles of all other bus voltages. Also, the voltage magnitude |Uk| is

known in this type of bus. Net generated active power PGDk and net generated reactive power QGDk are

unknown parameters at this location and the slack bus is also the only bus where the power is allowed

to vary. The result of this is that the swing bus will handle the system’s surplus or shortage of power,

if for example a load or a generator goes down. It is the difference in power within the network that is

called the slack and the slack bus must be a generator bus. There is only one slack bus in each system.

[19]

4.2 Reliability analysis

4.2.1 Deterministic and probabilistic reliability criteria

When electric network designers got interested in reliability issues, deterministic criteria were used.

An example of this is the (n-1) criterion. For example, a minimum number of transmission lines to a

load must be constructed in such a way, that if one line fails, the remaining lines must be able to carry

both the load they were carrying before the failure, plus the load carried by the line out of order [12].

These deterministic criteria were developed to account for failures occurring randomly, but they do not

account for probabilistic events, for example how often a certain component is expected to fail every

year, how long time it will be out of order etc. These properties of a system are of a stochastic nature

and reliability analysis should be based on techniques that respond to this behaviour [10]. In this

report, a probabilistic approach is used.

4.2.2 Probabilistic reliability indices

Two main states can be defined for an electric unit, namely up (working) and down (failed). A unit

that is in its up state will fail sooner or later, even if it will not happen for a long period of time. The

probabilistic failure frequency for a certain unit is called failure rate and is denoted by λ [1/year]. The

outage time for a unit in its failure state is denoted by μ [h/failure]. The two states for an element are

illustrated in Figure 4-2 below on next page [10].

13

Figure 4-2 Two state model for a unit, with its failure rate, λ, and outage time μ [10]

The total unavailability per year is denoted U and is simply calculated by multiplying λ and μ and

dividing by the number of hours of a year (8760) to get the value in percent per year.

8760* U μλ

= (Eq.4.2.1)

The failure rate, the outage time and the unavailability at component level take into account

neither the number of customers that are affected by the failure, nor the magnitude of the load

at failed points. Thus, different customer-oriented indices can be of interest when it comes to

reliability analysis of power systems. Three important indices are usually used for analysing

the reliability of a power system: System average interruption frequency index (SAIFI)

[interruptions/customer], System average interruption duration index (SAIDI) [minutes/

interruption] and Energy not supplied (ENS, see below) [GWh/year]. Since ENS is affected

by both failure rate and outage time, and reflects the reliability of a wind farm, it is used in

this work.

∑∑==

i

ii

NNλ

served customers ofnumber Totalonsinterrupticustomer ofnumber TotalSAIFI (Eq.4.2.2)

∑∑∑ ==

i

ii

NNU

customers ofnumber Totaldurationson interruptiCustomer

SAIDI (Eq.4.2.3)

where

λi = failure rate at load point i

Ni = number of customers at load point i

Ui = Unavailability at load point i

14

Since the degree of reliability is closely connected to economics, energy-oriented indices are also of

interest when it comes to reliability calculations. When designing a wind farm, calculations of how

much energy the farm is likely to produce per annum are carried out, in order to see the magnitude of

the annual income from selling the energy produced in the farm. Thus, it is interesting to examine how

much of this expected energy production that will not be produced, due to failures in the system. In

this report the index Energy Not Supplied (ENS) [GWh/year] is used in order to find out how much of

the supposed energy that will not be supplied to the customers [10].

∑== iUa(i)Lsuppliednot energy TotalENS (Eq.4.2.4)

where

La(i) = average energy load connected to load point i

When comparing an improved wind farm, from a reliability point of view, to another wind farm, the

ENS value will be lower. This difference in the ENS-index can easily be converted into additional

income from the extra energy produced.

4.2.3 Series and parallel systems

Components in radial distribution systems are connected in series. For a customer load connected to

any point of the system, all components between the customer and the supply point must be operating

for the customer to get his or her energy. For a system with i components in series, the average failure

rate, average outage time and average annual outage time are defined by

∑=

=n

iis

1λλ (Eq.4.2.5)

s

s

s

n

i iis

Urr

λλλ

== ∑ =1 (Eq.4.2.6)

i

n

iisss rrU ∑

=

==1

λλ (Eq.4.2.7)

where the subscript s denotes that a series system is considered.

For a system with components connected in parallel, all components must be out of service at the same

time to cause a system failure. Therefore, parallel systems differ somewhat compared to series

systems. For a system with two components in parallel, the following relations are defined for the

average failure rate, average outage time and average annual outage

15

2211

2121

1)(rr

rrp λλ

λλλ

+++

= (Eq.4.2.8)

21

21

rrrrrp +

= (Eq.4.2.9)

2121 rrrU ppp λλλ == (Eq.4.2.10)

Where the subscript p denotes that a parallel system is considered [10].

4.3 Investment analysis

4.3.1 Relations between reliability and investment costs

As mentioned in Section 4.2, the degree of reliability and the size of the investment for an electric

network are closely related. However, the relation between the investment cost and the degree of

redundancy built into the system is not linear. The first measures taken to increase the reliability

within a system can be made with a relatively small investment. However, for each extra, equally large

quantity of reliability to be added, a larger investment must be made. This is illustrated in Figure 4-3.

Figure 4-3 Degree of reliability, R, as a function of investment costs, C [10].

As one can see in Figure 4-3, ΔR does not increase at the same fast rate as the investment cost when

moving to the right in the graph. In reality this means, that for a certain degree of reliability, the costs

for making the system a little more reliable exceed the benefits of what the added reliability would

give in form of larger revenues. Thus, it is of great interest to combine the reliability analyses with an

16

investment analysis when designing a new wind farm, in order to get a layout where the costs for the

redundancy do not exceed the benefits of it [10].

4.3.2 Internal rate of return and net present value

In the phase of deciding which investment to undertake among several alternatives, the Internal rate of

return (IRR) can be used to find the most profitable option. The IRR indicates the efficiency of the

investment and mathematically, the IRR is defined as that rate of discount, which equates the present

value of the stream of net receipts with the initial investment outlay

∑= +

=n

tt

t

RS

I1

0 )1( (Eq.4.3.1)

where

St = the expected net cash receipt at the end of year t

I0 = the initial investment outlay

R = the internal rate of return

n = the project’s duration in years

Net present value (NPV) is a method to discount future cash flows into present value, for investigating

whether an investment is profitable or not. It shows the present value of future cash flows of an

investment, minus the initial investment and can be seen upon as an indicator of how much an

investment adds to the value of a firm.

01 )1(

Ik

SNPV

n

tt

t −+

= ∑=

(Eq.4.3.2)

where

k = the discount rate

If the NPV for a certain investment is calculated and greater than zero, the investment is profitable. On

the other hand, if the NPV is less than zero, the investment will not be profitable. The reason for this is

that the NPV-method discounts future cash flow into present value, and an NPV greater than zero

means that realizing the investment actually increases the present value of the capital, compared to not

realizing the investment. The same discussion holds for a negative NPV. An alternative and perhaps

more easily understood definition of the IRR is the rate of discount which equates the net present

value, NPV, of the cash flow to zero:

17

0)1( 0

1=−

+∑=

IR

Sn

tt

t (Eq.4.3.3)

Solving Equation 4.3.3 with respect to R can be tedious for a long time horizon, t, and with different St

for each year. However, a shortcut can be made by setting St to a constant value S for a project with

annuities. This gives the expression

0),(01 )1(

1 ISQIR

S Rn

n

tt =⇔=

+∑=

(Eq.4.3.4)

where Q(n,R) is the discount factor for n years and an IRR of value R. The sum on the left in Equation

4.3.4 is a geometric series. Since the investment outlay, I0, and the uniform annual receipt, S, are

known, the discount factor Q can be determined by

SI

Q Rn0

),( = (Eq. 4.3.5)

When knowing the value of Q and n, the IRR can be found in economic tables of present values.

Considering Equation 4.3.3 and 4.3.2, the NPV is equal to zero, when k = R. The IRR is always

constant and the NPV is negative for all k > R and positive for all k < R. As mentioned before, only a

project with an NPV greater than zero will be profitable and thus, R must be greater than k to accept

the project. Considering two alternative investment proposals, both with a positive NPV, the

alternative with the highest value of R will then be more profitable than the alternative with the lowest

value of R. Thus, if two or more investment alternatives have NPV greater than zero, the alternative

with the highest IRR should be chosen [18].

4.3.3 Capacity factor

One important parameter that must be considered when it comes to investment analysis of a wind farm

is the capacity factor α. Because of varying winds, maintenance and other events disturbing the energy

production in a wind farm, wind turbines cannot produce energy at rated power throughout a year. The

capacity factor is defined as the fraction of a year that a wind farm produces energy at rated power

[11] and is defined as

8760*r

a

PE

=α (Eq. 4.3.6)

18

where

Ea = Actual energy production in MWh

Pr = Rated maximum power for the wind farm in MW

19

5 Method

5.1 Tools for the analyses

5.1.1 Load flow and reliability analysis

The offshore wind farm to be investigated in this report, Lillgrund, is a rather large wind farm and its

equivalent electric network is consequently complex by nature. To make a load flow analysis and a

reliability analysis for such a network, the calculations are of course made easier by the use of a

computer and adequate software. Therefore, in this report, a software called NEPLAN will be used to

model the wind farm and to execute all load flow and reliability calculations, see Section 5.1.3.

5.1.2 Investment analysis

NEPLAN has a built-in module for investment analysis and the net present value (NPV) of different

investment alternatives can be calculated in a simplified way. In this report however, the internal rate

of return (IRR) is also of interest; instead of using NEPLAN, the investment analysis will be

performed in Microsoft Excel. The reason for this is to make it possible to choose the input parameters

for the investment calculations and make it easier to change these inputs, but it will also give a better

understanding of how the investment calculations are performed. Both the NPV and the IRR can be

calculated in a single Excel spreadsheet, where the annual cash flow and all other inputs needed for the

calculations can be defined.

5.1.3 NEPLAN

NEPLAN is used in this project since the software handles both load flow and reliability calculations.

When a model is built and a load flow calculation is performed, reliability parameters can be

addressed to all components for reliability calculations. NEPLAN is a registered trademark of BCP

Busarello + Cott + Partner Inc. It is a planning and information system for electric networks as well as

for gas and water networks. NEPLAN has built-in functions for solving all equations necessary for

load flow and reliability calculations described in Chapter 4. The results are given in a format suitable

to use in Microsoft Excel. For the load flow calculations, Newton-Raphson will be used as iteration

method. NEPLAN uses a probabilistic approach, as mentioned in Section 4.2.2, for the reliability

analysis.

20

5.2 Collecting data

5.2.1 Data for the load flow analysis

Load flow data for the wind farm are collected from reports made by Vattenfall, or from different

contractors involved in the project, like ABB and Siemens.

5.2.2 Data for the reliability analysis

The outer limit of the system, for which the reliability analyses will be performed, is drawn in

Bunkeflo where the connection between the wind farm and the 138 kV network on land is situated.

Finding reliable reliability data is hard because of many different factors. Components may be tested

experimentally in small scale, but operational field data are more commonly used in reliability

analyses and will also be used in this report. The quality of these statistical data can vary a lot,

depending on the data sources, the age of the data and how the data are processed. Because of the time

limit, the data used in this report are based on available statistics at Vattenfall Research and

Development (VRD) and the discussions with relevant persons. Also, because of the high degree of

uncertainty in reliability data, sensitivity analyses are performed within this project.

5.2.3 Data for the investment analysis

Vattenfall was involved in neither the design of Lillgrund, nor in the process of applying for permits at

Swedish authorities. Instead, Vattenfall purchased the layout of the farm with all permits belonging to

it ready, for a certain amount of money. Thus, specified economic data for the different components of

the farm are hard to find. Data for the investment analysis in this report will mainly be gathered from

different divisions within Vattenfall and suppliers of wind power components.

21

6 Alternative layouts of the wind farm

6.1 Three alternative layouts of the wind farm

6.1.1 Alternative one (A1)

In the first alternative to be investigated, called A1, the transformer is placed on land in Bunkeflo,

instead of on an offshore platform. The layout can be seen in Appendix 1 and the cable lengths can be

seen in

Table 7-2. The original five radials will be changed into six sub-radials with eight turbines in each.

The same cable dimensions as in the original layout, described in Section 3.1.2, are used in this layout.

This means that the first six conductors have a cross-section area of 95 mm2, while the last conductors

have a cross-section area of 185 mm2. The sub-radials are called 1A, 1B, 2A, 2B, 3A and 3C

respectively. 1A and 1B are connected to each other, just like 2A and 2B, and 3A and 3B, creating

three radials with 16 turbines in each. From the turbines A01, C01 and F02, three 36 kV, three-core

copper conductors connect the wind farm with the shore. The reason for using three export cables

instead of, for example, two 800 mm2 copper cables, is the problem with heating of the cables inside

the tower foundations. Onshore, each phase in the three-core copper cables are connected to a single-

core aluminium conductor leading to the transformer station now placed in Bunkeflo. The cross

section areas of the export cables are 630 mm2 for the copper cable at sea and 1000 mm2 for the

aluminium cable on land. These are the smallest cross-section areas that can be used to avoid critical

heating of the cables [27]. As for the original layout, a breaker and a switch is placed in each turbine

and also at the outgoing cables at the turbine transformer. Because of the location of the radial

breakers at the transformer, the result of a fault occurring in any of the cables between the farm and

land is that the whole radial with its 16 turbines must be shut down..

Another offshore wind farm with a similar layout as alternative A1 is Kentish Flats, in England, which

is located 8.5 km from land. This farm also has six sub-radials with turbines, connected to three 36 kV

export cables to land, where the transformer is placed. The main differences, though, are that the farm

consists of 30 Vestas V/90 turbines with a rated power of 3 MW and that the one-core cable on land is

made of copper instead of aluminium. Also, the transformer is placed more than 7 km from the shore,

instead of hardly 2 km for Lillgrund [5].

6.1.2 Alternative two (A2)

The second alternative, A2, is nearly the same as A1. The layout can be seen in Appendix 1and the

cable lengths can be seen in

22

Table 7-2. The transformer is still placed in Bunkeflo, the same cable dimensions and the same turbine

and cable layout are used. Also, the radial breakers are still located at the transformer. The main

difference from alternative A1 is that a remotely controlled breaker and disconnecting switch now also

are placed on the cables connecting turbine A01 to the two turbines next to it, namely B01 and A02.

Since A01 is the turbine where sub-radial 1A and 1B connect, anyone of the two sub-radials can be

isolated and disconnected in case of fault in a cable anywhere in the specific sub-radial. This means

that eight turbines and not 16 can be shut down in case of a cable fault within a sub-radial. The same

precaution has also been made for sub-radials 2A and 2B, and for 3A and 3B.

6.1.3 Alternative three (A3)

This alternative, A3, is an expansion of A2. The extra breakers and switches in the beginning of each

sub-radial are still there. The difference now is that switches have been placed between the fourth and

fifth turbine in radial 1A, 1B, 3A and 3B. Also, an extra cable now connects the last turbines in these

two sub-radials, that is, one cable connects turbine B08 to C08 and one connects D06 to D07. These

lines are equipped with switches in both ends. The extra switches in this layout are used to isolate

faults on cables in the radials. If there, for example, is a fault on the cable between turbine A05 and

A06 in sub-radial 1A, turbine A05 to B08 can be disconnected because of the extra switches. This

means that only four turbines have to be disconnected in case of a fault. If the same fault occurred in

alternative A1 or A2, 16 or eight turbines respectively would have to be isolated. There is no

possibility to connect the two last turbines in sub-radial 2A and 2B with an extra cable, since they are

too far from each other and other turbines are placed between them. The cable dimensions for this

layout are different from the other two alternative layouts. Since the power now can flow in both

directions in each cable in case of cable failure, only 185 and 240 mm2 cables must be used in order to

withstand the possible extra stress on the cables. If the cable dimensions from alternative A1 or A2

were used, the power production in the turbines had to be reduced when faults occur on some of the

cables and the extra redundancy would not have been utilized. The layout can be seen in Appendix 21

and the cable lengths can be seen in Table 7-2.

6.1.4 Important assumptions made for the alternative layouts

Cables are always surrounded by a magnetic field that decreases with the distance from the cable.

When laying cables on land, the allowed magnitude on the magnetic field from the cables is strongly

limited. For the original layout of Lillgrund, the restriction from the local authorities on the magnetic

field from the onshore cable was hard to obtain. Placing the single-core cables right next to each other

in a triangular formation fulfilled the restriction. No studies have been made on the magnetic field

from the 33 kV one-core onshore cables in the three alternative layouts, but it is assumed that the

restriction from the local authorities can be fulfilled.

23

For the original layout of Lillgrund, thorough studies and analyses have been made on the electrical

system of the farm. In this report, however, no dynamic studies like transient analyses have been made

in order to analyse the alternative layouts. Only load flow calculations have been performed on those

designs.

Since the turbines are placed at the same spots as in the original layout, the distances between them are

still the same. This means that the cable lengths are the same as they are today. The short distance

between two turbines is 355 meters and the long distance is 450 meters. For the few diagonal cables,

the distance is 570 meters. The cable lengths for all layouts can be found in Table 7-2 and the

alternative layouts can be found in Appendix 1.

6.2 A 72 kV solution

6.2.1 A possible future layout

33 kV is a common voltage magnitude within many offshore wind farms today. An interesting

alternative to the different layouts investigated in this report, could be a layout with a voltage

magnitude of 72 kV in the wind farm and without a platform, which would reduce this part of the

investment costs compared to the original layout of Lillgrund. The costs of cables might also be

reduced compared to alternative A1, A2 and A3, if only two export cables could be used instead of

three. However, the problem with mutual heating in the foundations has not been investigated for

72 kV cables in this report. Also, a 72 kV solution would probably get lower energy losses than a 36

kV solution, since electric losses decrease with increasing voltage.

Siemens and other turbine manufacturers just have a few, more or less standardized, technical

solutions for their turbines and today a 72 kV turbine is not one of those. For example, the existing

0.69/33 kV transformer in the turbines is an integrated part of the whole tower and a 0.69/72 kV

transformer is not. A 72 kV transformer would also, at least at present date, be larger in size than a

33 kV one. The same holds for other components like breakers and switches. All these components are

placed in the bottom of the tower, and there is limited space available for components larger than

today’s. A possible solution to this problem could be to place a container outside the bottom of the

tower where all electric components are placed. Even if a 0.69/72 kV transformer could be integrated

in an overall solution, 72 kV components are in general also more expensive than 33 kV components.

One explanation to the fact that no 72 kV turbines are available today is that there already is a high

demand on existing models. Wind power manufacturer already get many orders in the present

situation. The reason that no 72 kV wind turbines are on the market today may be because

24

manufacturers do not have enough incentives or time for developing turbines with a completely new

voltage magnitude [30].

Considering the facts above, a 72 kV layout will not be investigated further in this report. More

research and development have to be done in the area of wind power before a 72 kV wind turbine can

be reality, if it ever will.

25

7 Implementation

7.1 Building a model in NEPLAN

7.1.1 How to build a model in NEPLAN

In NEPLAN, an electric network such as a wind farm is graphically built piece by piece, by picking

the same components that exist in the real network from a list, and placing and connecting them in a

way equivalent to the real network. Small icons are used for each component and a visualization of the

wind farm with all its components is created during the build-up of the network. The software is

therefore easy to use, in a graphical meaning. In the program, parameters for load flow and reliability

calculations can be entered for each component. A small network with a generator, a transformer, a

line with a circuit breaker and a load can look as in Figure 7-1 below.

Figure 7-1 A small network consisting of a generator, a transformer, a line with a built-in circuit breaker and a load, as it looks in NEPLAN.

7.1.2 Modelling the generators

The generators at each wind turbine should, according to the theory for load flow analysis, be handled

as PV-nodes. However, when doing this in NEPLAN with 48 turbines, the iteration method will not

converge since all 48 turbines are set to regulate the magnitude of the voltage. As described in Section

3.1.2, E.ON does not accept any transport of reactive power to the net on land. Reactive power in the

farm is produced in the cables and consumed in the transformer, and in reality, the turbines regulate

the reactive power in the wind farm thanks to the frequency converters. Therefore, all turbines are

modelled as PQ-nodes in NEPLAN, with the reactive power production set to fulfil the demand from

E.ON.

Asynchronous generators combined with a frequency converter and a transformer cannot be modelled

in NEPLAN. One of the reasons for using a frequency converter in a turbine is to synchronize the

26

frequency from the asynchronous generator with the frequency in the grid on land. When looking at

the frequency in each turbine from the internal grid, the frequency is synchronous with the frequency

in the network on land. Therefore, synchronous generators will be used to model the asynchronous

generators in the wind farm.

7.1.3 Modelling the cables

In NEPLAN, all lines and cables are modelled as pi-equivalents, described in Figure 7-2 below. The

model consists of resistance R and inductance X in series and two admittances Y/2, parallel to ground

at each end of the line. The admittance Y consists of a susceptance B and a conductance G in parallel

with each other. R and X are given in Ω/km and B and G are given in μS/km.

Figure 7-2 Pi-model of a line

ABB were the cable contractor for Lillgrund and the values of R, X and C for all cables used in

Lillgrund are available. The susceptance, B, on the other hand, is calculated by

fCB π2= (Eq.6.2.1)

where f is the frequency and C is the capacitance of the line.

All of the cables in this project are modeled as pi-equivalents. Since the load flow only will be

performed in a steady state, the positive sequence values for impedance and capacitance are the only

inputs needed. Cable data for the load flow calculations for all layouts investigated in this report is

given in Table 7-1, while the total lengths of all cables are summarized in Table 7-2.

27

Location Type of cable (area [mm2])

Material Rated voltage

[kV]

Imax [A]

R, per phase [Ω/km]

X, per phase [Ω/km]

C, per phase

[μF/km]

B, per phase

[μS/km] AXLJ (1x630) Al 145 581 0.075 0.114 0.210 65.973

Land cable AXLJ (1x1000) Al 36 683 0.040 0.192 0.420 131.947FXBTV (3x400) Cu 145 624 0.086 0.128 0.167 52.465

Export cableFXCTV (3x630) Cu 36 719 0.061 0.102 0.348 109.327FXCTV (3x240) Cu 36 497 0.114 0.120 0.235 73.827FXCTV (3x185) Cu 36 438 0.143 0.128 0.200 62.832Array cable FXCTV (3x95) Cu 36 306 0.261 0.140 0.173 54.350

Table 7-1 Cable data from ABB

Land cable Export cable Array cable

Layout AXLJ

(1x630) 145 kV

AXLJ (1x1000)

36 kV

FXBTV (3x400) 145 kV

FXCTV (3x630) 36 kV

FXCTV (3x240) 36 kV

FXCTV (3x185) 36 kV

FXCTV (3x95) 36 kV

[m] [m] [m] [m] [m] [m] [m] Original 5 373 7 177 3 223 6 249 13 098Alternative 1 16 119 25 400 3 664 16 796Alternative 2 16 119 25 400 3 664 16 796Alternative 3 16 119 25 400 4 113 11 834 5 323

Table 7-2 Cable types and cable lengths for the different layouts of Lillgrund

7.1.4 Modelling the transformer

The offshore platform has a 33/138 kV transformer with a rated power of 120 MVA. It has an on-load

tap-changer to control the voltage at its 33 kV side. As mentioned earlier, E.ON owns the 138 kV

network on land and they do not allow any transport of reactive power into their network. There is no

shunt reactor in Bunkeflo, and thus the transformer must consume some of the reactive power

produced in the cables. The rated positive sequence short-circuit voltage with respect to the rated

power is 10 % in the transformer and the reactive power consumption is about 10 MVAr at rated

power. The additional reactive power in the farm will be consumed by the frequency converters, see

Section 3.1.2.

7.1.5 Other components in the wind farm

There are also protection elements like circuit breakers and switches in the wind farm, as described in

Section 3.1. Since Lillgrund is an existing wind farm, it is assumed that these elements are properly

dimensioned and will be considered as ideal elements and not overloaded during the load flow

28

calculation of the system. These elements will only be considered during the reliability analysis.

Because of that, they will not get any input data for the load flow calculation.

In NEPLAN, the slack bus will be placed where the wind farm is connected to the network on land.

This element should be seen as an equivalent for the network on land where the phase angle is zero

and the magnitude of the voltage is constant. The in- and outflow of active and reactive power will be

calculated at this bus, and the exchange of reactive power should be zero here to oblige the demands

from E.ON.

7.2 Reliability analysis in NEPLAN

7.2.1 Correct power output from the turbines

Theoretically, the maximal production of the 48 turbines in Lillgrund is 967.1 GWh per year.

However, many factors like wind climate and waking losses, for example, are affecting the annual

production in a wind farm. The estimated net sellable production from Lillgrund is 330 GWh [31].

This means that the capacity factor for the farm, α, is assumed to be 0.345. The 330 GWh includes

estimated energy losses because of unavailability and electric losses. Adding these losses again to the

330 GWh gives an energy production of 353.4 GWh per year. When Vattenfall estimated the

unavailability of Lillgrund, it was supposed to be 3.75% of these 353.4 GWh. Since Vattenfall uses the

value of 353.4 GWh as a basis when calculating the unavailability of the farm, this base value will also

be used in this report when calculating the ENS-value. A production of 353.4 GWh gives a capacity

factor of 36.5%, which will be used in this report. Of course, it does not mean that the turbines are

constantly producing energy at 36.5% of rated power throughout a year, but it is a mean power output

from the turbines over one year. However, for reliability calculations in NEPLAN, a fixed value of the

power in the generators for a whole year must be set, since real wind data cannot be imported to and

used in NEPLAN in order to vary the turbine power properly. Therefore, 36.5% of 2.3 MW, which is

0.84 MW, will be used. The ENS-value is than calculated in NEPLAN from the reliability data

combined with the fixed power in the generators. In reality, an outage in the winter can be assumed to

lead to greater energy losses than an equally long outage in the summer, since the winds that cannot be

utilized during the interruption are stronger in the winter. This kind of impact cannot be considered in

NEPLAN.

7.2.2 Failure rates and outage times for the reliability analysis

Reliability data are often associated with uncertainty and the data for the same type of components

often vary in different reports. Due to the time limit for a thorough data study, the reliability data used

in this report are based on the data available at VRD and discussions with experienced and skilled

29

people at Vattenfall Research and Development. In NEPLAN, one can specify failure rate and outage

time for long and short outages respectively. In this report, the used failure rates and outage times are

mean values of long and short outages. Also, the reliability data used are supposed to be average

values over the whole year. In reality, repair times get longer when it is too windy to go out in a

service boat and the winds are usually stronger in the winter.

All reliability data used are presented in Table 7-3 with comments. A small service boat is available at

Lillgrund. For failures in gearboxes or the transformer, for example, a special ship has to be hired

because of the large components involved. There are only eight of these ships worldwide, so there is a

risk that the waiting time for a boat will be long [8]. Also, changing a failed transformer or other large

components is strongly weather dependent and this kind of work demands many hours of continuously

fine weather. Therefore, the failure rates and the outage time in Table 7-3 might seem optimistic, but it

should be mentioned again that a sensitivity analysis will be performed. Different layouts of the farm

will be studied in this project and reliability data for these layouts are also presented in Table 7-3.

In opposite to load flow calculations, circuit breakers and disconnect switches are more important

when it comes to reliability analyses and will therefore be included in this part of the study. One

assumption though, is that elements like surge arrestors usually have a low frequency of failure,

compared to breakers and switches. Thus, they will not be included.

30

Table 7-3 Reliability data used in the report

The same reliability data used for the original layout of Lillgrund have also been used for the

components in the alternative layouts, see Chapter 6. There is one difference in reliability data that

should be mentioned however, namely the outage time for an onshore transformer, which in most

cases is shorter than the outage time for an offshore transformer. This is because repairing an offshore

transformer is strongly weather dependent compared to repairing the onshore transformer, which has

been considered for these reliability data.

Component Voltage level [kV]

Failure rate λ [f/yr],

[f/yr/km] (cables)

Outage time μ

Source and comments

Turbine 36 0.15 2 weeks

λ and μ assumed for turbine, gearbox, generator, frequency converter and 0.69/33 kV transformer connected in series [24]. All data from [9], which presents λ and μ for Swedish onshore wind turbines between 2000-2004. The trend in wind power reliability is lower failure rates and higher outage times [9]. Thus, a lower λ and a higher μ are used in this report, but the annual unavailability is the same as in [9].

36 0.03 120/12 hoursCircuit-breaker

145 0.03 120/12 hours

36 0.03 120/12 hoursDisconnectors

145 0.03 120/12 hours

Failure rate from [13] and [14], outage time from [14]. Spare parts are available as well as access to a service boat [23]. The outage time is given for Offshore/Onshore scenario. Failure rate assumed to be the same offshore and onshore, since these components are protected from rough climate [23].

36 0.004 4 weeks Sub-sea cables

145 0.004 4 weeks

Extra cables assumed to be available in Barsebäck [23]. ABB has stated an outage time off 168 hours [15], which is considered too low [24].

Transformer offshore 36/138 0.02 16 weeks

Transformer on land 0.02 12 weeks

Outage time from [13]. A ship must be hired for the offshore transformer (weather dependence). No boat needed for an onshore transformer (no weather dependence). μ for a transformer failure in Nystedt, another offshore wind farm, was four months [23] and [24].

36/138

36 0.004 1 week Cable on land 145 0.004 1 week

Shorter repair time for cables on land compared to submarine cables [25].

31

7.2.3 Maintenance operations

When performing a reliability analysis, the outage time for planned maintenance can be taken into

account for [13]. In this report, planned, annual, preventive maintenance activities will not be

considered. The reason for this is a limitation in the software. Also, preventive maintenance is

performed during summer in order to minimize the loss of produced energy. Thus, one cannot just

multiply the number of turbines and their annual mean power output with the outage time for each

turbine in order to find the ENS. The maintenance activities for Lillgrund will briefly be described

below even if they are not taken into account in the report.

In Lillgrund, turbine and transformer maintenance is performed once a year. These activities are

performed during summer, when the weather climate is most suitable for going out with the service

boat. Since the winds are lighter during summer, the reduction in energy production will be minimized

during the maintenance. Only a visual inspection and an oil test are performed during the transformer

maintenance, while the transformer is still in service. During turbine maintenance, one tower at a time

is disconnected from the radial, while all other turbines are working as usual. The service technicians

work eight to ten hours a day with one turbine and the turbine is then reconnected to the radial again

during the nights. Working this way, maintenance is performed on two turbines a week, meaning that

each turbine have a planned outage time due to maintenance of approximately 25 hours a year. It

should be noted that this time is for planned, preventive maintenance only and if some components

unexpectedly have to be changed during the maintenance, the outage time can be extended. It should

also be mentioned that Vattenfall has a five year long service contract for Lillgrund with Siemens,

saying that Siemens must compensate Vattenfall if the availability of the wind farm is lower than 90 %

the first year and lower than 95 % the following four years [34].

7.2.4 Sensitivity analysis

A sensitivity analysis is a tool for finding out how the result from the reliability analysis varies, when

changing the values of the input parameters. Thus, a sensitivity analysis is appropriate to use when

input data suffer from a high degree of uncertainty, just as the case for the reliability data in this report.

A sensitivity analysis will be performed in this report and the analysis will handle some of the

components with the longest outage times, since they give the largest contribution to the result of the

reliability analysis. The main objective for this sensitivity analysis is the uncertainty in outage time

because of delivery time for new components and bad weather conditions, when no offshore work can

be performed. Therefore, the failure rate of the different components is assumed to be the same in the

sensitivity analysis, only the outage time is altered. As for the reliability data presented in Table 7-3,

the data used in the sensitivity analysis are also thoroughly discussed with experts at Vattenfall

Research and Development [24]. The sensitivity analysis will be performed on each of the alternative

layouts. Data for the sensitivity analysis are presented in Table 7-4.

32

Component Voltage

level [kV]Failure rate [f/yr],

[f/yr/km] for cablesOutage time [weeks]

Base case

Sensitivity analysis 1

Sensitivity analysis 2

Turbine 36 0.15 2 3 4 36 0.004 4 6 8

Sub-sea cables 145 0.004 4 6 8

Transformer offshore 36/138 0.02 16 26 36 Transformer on land 36/138 0.02 12 22 32

Table 7-4 Reliability data for the sensitivity analysis

7.3 The investment analysis

7.3.1 Input for the NPV and IRR calculations

In Section 4.3, the theory for investment analysis was explained as well as the input needed to be able

to calculate the net present value (NPV) and the internal rate of return (IRR). The input parameters

needed are the initial investment outlay I0, the discount rate k, the duration of the project n, and the

annual cash flow S. The values used in this report, for the first three of these four parameters, will be

given in this section. The cash flow depends on a number of factors, all explained more thoroughly in

Section 7.3.2. It should be mentioned that the values of some parameters in Chapter 7.3 are changed

from the values used in the report handed in at Vattenfall, because of confidentiality. The qualitative

results still remain the same.

The initial investment outlay, I0, depends directly on the wind farm layout and the components that are

included. In this project, three different layouts will be compared to the present design and the same

investment costs for components in the different layouts are assumed. The alternative layouts are all

presented in more detail in Chapter 6 and detailed information of the investment costs for these layouts

can be found in Appendix 2. The total investment costs for the different layouts, however, are

summarized in Table 7-5 on next page, where also the costs for cables and the platform/transformer

station for each layout are listed. These costs are not taken directly from the real Lillgrund project, but

are collected solely for this report. It should also be noted that only costs for different components in

the wind farm have been used, and no costs for insurances of the farm etcetera have been used, since

that information was not available. The Swedish Energy Agency subsidized the project with 213

MSEK [4], but since no insurance costs have been taken into account, this subsidy will not be used in

this report, in order to cancel out the insurance costs that were not taken into account. When

calculating the NPV, the discount rate k set in advance can be described as the smallest demand on

33

return from the investor’s point of view. A lower discount rate might give a positive NPV,

theoretically meaning that an investment will be profitable. Realizing such an investment though,

might not be interesting since some risks are always involved when it comes to investments and a

company might wish to have some margins. A discount rate of k = 7 % will be used in this project and

the duration for the wind farm is set to n = 20 years. These figures will of course also be used for the

alternative layouts.

Duration, nyears

Discount rate, k

Layout Cable cost [MSEK]

Platform/ Station cost

[MSEK]

Total cost [MSEK]

Original layout 89 82 1603Alternative 1 163 7 1600Alternative 2 163 7 1602

n=20 years (all layouts)

k=7% (all layouts)

Alternative 3 169 7 1609

Table 7-5 Total investment costs for the different layouts, together with the discount rate, k, and the duration time of the project, n.

7.3.2 Input parameters for the cash flow calculations

One of the most fundamental input parameters in the cash flow calculation is of course the annual net

sellable energy production, since the annual revenues are directly related to how much energy the farm

produces each year. How the value of the annual net sellable production is determined, is presented in

more detail in Chapter 7.4. Is should once again be noted that the values of some parameters in

Chapter 7.3 differ from the values used in the report handed in at Vattenfall, because of confidentiality

matters.

The revenues from the net sellable production depend directly on electricity spot prices and prices of

green certificates. Vattenfall have made their own forecasts for future price levels of both these

parameters, but these forecasts are not used in this report. Instead, template figures for future

electricity spot and green certificate prices will be used. For this report, the assumed price level used

for 2008 is 475 SEK/MWh for the electricity spot price and 212 SEK/MWh for the price of green

certificates. These prices are then inflated with 1 % per annum until the end of the lifetime of the wind

farm, namely year 2028 [32]. There are many factors that affect the levels of certificate prices and spot

prices, for example new directives from the European Union. The daily, average spot market price for

the Nordic countries between 2008-01-01 and 2008-03-12 was 390 SEK/MWh [6], which is

considerably lower than the 470 SEK/MWh, although spot prices in winter usually are higher than

during other periods of the year. On the other hand, prices for year 2008 certificates, to be delivered in

34

March 2009, have been higher than 250 SEK/MWh for almost all of 2008 [3] [35], which is higher

than the 212 SEK/MWh used in this report. Certificates for one year are cleared on the 31st of March

the following year and that is why certificate prices for March 2009 are used. The assumed total price

of both certificates and spot for 2008 are of the same magnitude as the predictions made by Vattenfall

[35]. Therefore, this price level is used in this report. It should be stressed again that the price level for

2008 does not agree exactly with the price levels forecasted by Vattenfall. Nor does the development

of the prices used in this report, namely an increase of 1 % per year over the assumed lifetime of the

wind farm, agree with the prediction made by Vattenfall [32].

In addition to the revenues from electricity spot prices and the certificates, an environmental bonus is

also assigned to the sold electricity produced in offshore wind farms. The bonus has the form of a tax

deduction and it is the Swedish Ministry of Enterprise, Energy and Communications that makes all

decisions around it. In its present form, the deduction is not accepted by the European Union and thus,

the deduction will probably only be given until the end of year 2009. The environmental bonus is 130

SEK/MWh in 2008 and 120 SEK/MWh in 2009 [2]. It should also be mentioned that green certificates

are only obtained for the first 15 years of operation. The price levels for the first three years of

operation are presented in Table 7-6 below, together with a description of how the prices are assumed

to develop with time.

Type of revenue Price levels each year

[SEK/MWh]

Sources and comments to the price levels

2008 20092010 Spot price 475 479 484 Spot- and certificate price levels from 2008, annual Green certificate price 212 214 216 inflation rate 1 % [32]. Certificates are received 15 years.Environmental bonus 130 120 - The bonus ends in 2009 [2]Total revenues [SEK/MWh] 817 813 700

Table 7-6 Price levels used in the report

Spot prices, certificate prices and the environmental bonus can be viewed upon as factors that affect

the cash flow positively. The net cash flow also depends on other factors that affect the cash flow in a

negative way. In the model used in this report, the parameters listed in Table 7-7 on the next page are

used.

35

Item Amount Comment and source Corporate tax 28 % [32]

Depreciation time

5 years A depreciation time of five years leads to net operating losses the firstfive years. Since tax losses are carried forward, future tax expensesare reduced by applying the loss experienced in the first years [32].

O&M costs 145 SEK/MWh Annual costs throughout the lifetime of the project [21]. No distinction between offshore and onshore transformers [34]

Midlife upgrade 15 % of initial investment

Worn out components in the farm will be replaced after half thelifetime, namely in 2018. This amount is supposed to cover for unexpected expenses like new gearboxes etcetera [21].

Inflation 2.5 % Annual rate [32]

Table 7-7 Parameters for the investment analysis

7.4 Parameters affecting the net sellable production of the farm

7.4.1 Unavailability of the farm

When calculating the net sellable production of a wind farm, reductions in the maximal energy

production of the farm are made because of different losses. All losses in a wind farm of course affect

the net sellable production from it, which in turn affect the cash flow from it. The estimated

production from Lillgrund before unavailability of the farm and electric losses is 353.4 GWh. In this

value, all other losses in the farm like wake losses etcetera are included, and this is the figure used for

calculating the capacity factor used in his report, described in Section 4.3.3. The estimated net sellable

production of 330 GWh/year is calculated by first subtracting the assumed unavailability of 13.4 GWh

(3,75 %) from the 353.4 GWh and then subtract the assumed electrical energy losses of 10.2 GWh

(another 3 %) [31]. Vattenfall used these estimated figures for calculating the net sellable production

of the wind farm, during the real investment analyses. The reason for not calculating the capacity

factor in this report with the net sellable production of 330 GWh, is the fact that the unavailability

estimated by Vattenfall is calculated as a percentage of the production of 353.4 GWh and not 330

GWh. Thus, the ENS-value should be calculated on the same basis.

The assumed figures of unavailability (13.4 GWh) estimated by Vattenfall, will not be used as input

when calculating the cash flow in this project. Instead, new figures of the unavailability of the

different layouts of the wind farm are provided as a result from the reliability analysis. Starting from

the original 353.4 GWh, the annual energy losses due to the unavailability of the farm, calculated in

NEPLAN during the reliability analysis, will be subtracted. The result from these calculations will

36

then be the new figures of the production of the farm before electrical energy losses. The ENS-value

of the different layouts is shown in Table 7-8 below.

Layout ENS

[GWh]Production after unavailability, but

before electrical energy losses [GWh] Original layout 17.4 336.0 Alternative 1 16.1 337.3 Alternative 2 14.2 339.2 Alternative 3 13.3 340.1

Table 7-8 Results from the reliability calculations in NEPLAN. The ENS-value of the different layouts with the corresponding values of production before electrical energy losses can be seen.

The ENS-values in Table 7-8 are calculated with the original reliability data and not with the data to

be used in the sensitivity analysis. This is because Vattenfall's estimated unavailability of the farm is a

kind of standard assumption, just as the original reliability data are. It should be noted that the

unavailability figure estimated by Vattenfall includes interruptions for annual preventive maintenance,

while the equivalent figure from the reliability analysis performed in NEPLAN does not.

7.4.2 Electrical energy losses as a function of park power output

Energy losses in a wind farm also depend on the electric losses in the cables and the transformer in the

farm. For Lillgrund, these losses are assumed to be 3 % of the produced energy in the farm, after

losses due to unavailability. The figure of 3 %, which corresponds to 10.2 GWh, is also just an

estimate made by Vattenfall for the present layout of Lillgrund [30]. It can be viewed upon as a design

criterion, as the upper, highest allowable limit for electrical energy losses in the farm. Therefore, new

values of the electrical energy losses in the wind farm will be calculated to get a more exact figure of

the real electrical energy losses in the farm. Losses for both the present layout and the alternative

layouts will be calculated.

Electric losses in a wind farm are not constant over the year, but depend on the actual power output of

the turbines, which in turn depend on the wind speeds at the site. Therefore, load flow calculations

with varying power output have been made in NEPLAN, in order to find the electric losses for

different power outputs. Starting at rated turbine power, P = 2.3 MW, load flow calculations have been

made in ten steps down to P = 0 MW. These calculations have been performed on the models of both

the original layout and the first alternative layout, A1, to make it possible to compare the electric

losses of both the alternatives. All three alternative layouts, presented in Chapter 6, have the same

voltage level and almost the same design and they are assumed to have identical electric losses.

37

Therefore, these load flow calculations have only been performed on one of the alternative layouts,

namely alternative A1. The results from the load flow calculations are presented in Figure 7-3, where

electrical losses of the wind farm as a function of the park power output can be seen.

110,

4

99,4

88,3

77,3

66,2

55,2

44,2

33,1

22,1

11,0

0

0,5

1

1,5

2

2,5

3

Elec

tric

al lo

sses

[MW

]

Park power output [MW]

Electrical losses as a function of park power output

Original layout Transformer on land

Figure 7-3 Electric losses of the farm as a function of park power output. Losses for both the original layout of Lillgrund and Alternative A1 are presented.

Although the electric losses have been calculated in steps of 11 MW, and therefore are quite rough

estimates, it can easily be seen that the alternative layouts have larger electric losses compared to the

original layout. When the farm is running at rated power, the losses are about 75 % larger in the

alternative layouts without platform. When the turbines in the farm are running at 0.84 MW, which is

the average power output due to the capacity factor, the losses are about 60 % higher in the alternative

layouts. The losses are higher in the alternative layout since the voltage in the export cable is 33 kV

instead of 138 kV.

7.4.3 Total electrical energy losses of the different layouts

As mentioned in Section 7.4.2, power output and therefore also electric losses in a farm, depend on the

wind speed. The output power from a turbine, and hence also the electric losses, depend also on wind

direction since each turbine in a wind farm is shadowed by a different number of other turbines

depending on where the wind comes from. The annual energy production after unavailability of the

38

farm is known for the different layouts, see Figure 7-3. The total annual energy losses in Lillgrund due

to electrical energy losses, can then be calculated if the following parameters are also known

• Annual distribution of wind speeds and wind directions

• Park power output at these different wind speeds and wind directions

• Electric losses at different park power outputs

The electric losses for ten different park power outputs for Lillgrund are already known, see Figure

7-3. The other required data are also known for Lillgrund, but they are not presented at the same

intervals as the electric losses. The wind speed frequency distribution, in the form of a Weibull

distribution, shows the probability density of the wind speed. These data are presented for wind speeds

from 0 m/s to 24.5 m/s, in steps of 1 m/s. The data can easily be transformed into annual hours by

multiplying the percentage by 8760. The Weibull wind speed distribution for Lillgrund can be seen in

Figure 7-4 below [26].

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

[m/s]

[%]

Figure 7-4 Weibull wind speed frequency distribution for Lillgrund [26].

The park power output in each interval of the wind speed distribution is also known for Lillgrund. The

park power output is weighted with data of the wind directions at the site and wake losses. Vattenfall

39

has calculated the wake losses with two different programs and therefore, two different results have

been obtained. However, the values of the wake losses used in this report will be the final ones used

by Vattenfall.

By multiplying the power output from each wind speed interval with the number of hours that the

wind blows with that specific speed, the energy output for each wind speed can be calculated. The

total annual energy output from the farm is then given by adding the energy output for all wind speed

intervals. The calculated electric losses in Lillgrund, shown in Figure 7-3, are a function of the park

power output and have the unit MW. Therefore, the annual energy losses due to electrical energy

losses can be calculated in the same way as the total energy output of the farm. The electric losses

from the first load flow calculation is made for a park power output of P = 11 MW, and then in steps

of 11 MW. Therefore, losses for a park power output interval stretching from P = 5.5 MW to P = 16.5

MW are assumed to be the same as for a power output of P = 11 MW, although this is a rough

estimate. Equally, losses in an interval from 16.5 MW to 27.5 MW are assumed to be the same as for P

= 22 MW and so on, up to P = 110.4 MW. However, the park power output is given at the same

intervals as the wind speed distribution, while the electric losses are not. For example, the park power

output at 6.5 m/s is 15 MW and the park power output at 7.5 m/s is 24.2 MW. This means that the

upper limit of the first interval used for the electric losses (5.5 MW to 16.5 MW) is somewhere in the

beginning of the interval of the park power output (15 MW to 24.2 MW). A rough estimate has been

made, to be able to see how big part of this wind speed interval (6.5 m/s to 7.5m/s) that the park power

output interval (5.5-16.5 MW) represents. This is done by calculating (16.5-15)/(24.2-15), which gives

a value of 16 %. In other words, the electric losses in the farm related to a park power output from P =

5.5 MW to P = 16.5 MW, are assumed to last for 16 % of the time the wind speed is between 6.5 m/s

and 7.5 m/s and all hours of a year that the wind speed is between 3.5 m/s to 6.5 m/s and. The cut-in

wind for the farm is 3.5 m/s, which means that the farm does not produce any energy at these low

wind speeds. The same method has been used to calculate the electrical energy losses for the other

intervals as well. Because of the different intervals for the data, calculating the annual energy losses

due to electrical energy losses in this way is just a rough estimate. Nevertheless, both alternatives can

still be compared to each other.

Using the above method, the original layout of the farm is found to have electrical energy losses of

3.3 GWh per year and the alternative layouts have losses of 5.7 GWh per year, about 73 % more.

These figures are 1 % and 1.7 % respectively of the produced energy in the farm after unavailability

compared to the 3 % Vattenfall has estimated. Electric losses have been calculated in this way for all

three different layouts, but since the ENS-value does not differ that much from any of them, the same

result (5.7 GWh) was obtained for all three alternative layouts.

40

Electric losses [GWh] Layout

Estimated figure New figuresOriginal 10.2 3.3 Alternative 10.2 5.7

Table 7-9 Electric losses for the original and alternative layouts

Even if the new values of the electrical energy losses are rough estimates, they should be compared to

the estimates of 10.2 GWh that Vattenfall has used for the electrical energy losses in the present

layout. The 10.2 GWh figure is the upper limit of a design criterion from Vattenfall, used to calculate

the annual net sellable production from the farm in an economic analysis of it. The newly calculated

figures of the electrical energy losses in Lillgrund will be used as input in the investment analysis

instead of the figure estimated by Vattenfall. The same method used for calculating the production of

the farm after unavailability will be used when handling electrical energy losses. This means that the

estimated losses of 10.2 GWh in Lillgrund will first be added to the expected energy production after

unavailability. Thereafter, the losses of 3.3 GWh for the original layout and 5.7 GWh for the

alternative layouts will be subtracted in order to get the proper net sellable production of the wind

farm. There are of course no estimated figures of electric losses in the different layouts of Lillgrund,

since these designs do not exist in reality. However, the figure of 10.2 GWh will be used for these

layouts as well, since that is the largest loss accepted by Vattenfall.

7.4.4 The net sellable production from the different layouts

During the sensitivity analysis, new ENS-values are calculated for each layout, now with different

reliability input data. The ENS-values of each layout will be used in combination with the electrical

energy losses to calculate the net sellable production for all different layouts. The new value of the net

sellable production, with re-calculated figures of unavailability and electrical energy losses, will be

used as input in the cash flow calculations of the investment analysis. The net sellable production for

the different layouts in the sensitivity analysis can be seen in Table 7-10 on next page.

41

Layout Original data

Turbines Sea cables Transformer offshore/onshore

μ = 3 weeks

μ = 4 weeks

μ = 6 weeks

μ = 8 weeks

μ = 26/22 weeks

μ = 36/32 weeks

ENS-values [GWh] Original layout 17.4 20.0 22.2 18.8 20.3 20.3 23.1 Alternative 1 16.1 18.6 20.8 17.9 19.7 18.8 21.7 Alternative 2 14.2 16.8 19.1 15.6 17.0 17.1 19.9 Alternative 3 13.3 15.8 18.0 14.5 15.7 16.0 19.0

Table 7-10 ENS-values for the different layouts in the sensitivity analysis. In the second column from the left, the ENS-values for the original reliability data are presented for the different layouts. In the other columns, the ENS-values are presented where the parameter for only one component is changed. All other components are given their original reliability data for these cases. Reliability data for turbines, sea cables and the transformer are changed. For example, in the two columns under “Turbines”, the ENS-value is calculated when the outage time for turbines are changed to three and four weeks respectively.

42

8 Results

8.1 Results from the combined reliability and investment analysis

In this report, a reliability analysis of the offshore wind farm Lillgrund has been combined with an

investment analysis of the farm. The primary aim of the project has been to compare the original

layout of the farm with three alternative layouts, with respect to the reliability of the different designs.

The main difference between the original layout and the three alternatives is that the former has an

offshore platform for the transformer, while the latter alternatives have an onshore transformer. In the

case with the platform, one 138 kV export cable is used, whereas three 33 kV cables are used in the

other designs to connect the turbines in the farm with land. Different levels of redundancy are built

into the three layouts with an onshore transformer by using extra breakers, disconnectors and cables.

The four different designs of the farm do not have the same investment costs. This means that the

result from the reliability analysis alone will not be of much help when deciding which alternative to

invest in. Therefore, an investment analysis, using the results from the reliability analysis as inputs,

has been performed. The used output from the reliability analysis is the ENS-index, which tells how

much of the expected energy produced in the farm that cannot be supplied to the network on land.

Vattenfall has estimated both the unavailability of the farm and the electrical energy losses from it, but

these figures are not used. New figures for electrical energy losses have been calculated, by combining

load flow calculations and wind data with park power output from the farm. The final result of the

calculations mentioned above for all four layouts, can be seen in Table 8-1 below.

Layout ENS [GWh]

Electrical losses [GWh]

Investment cost [MSEK]

Net sellable production

[GWh]

NPV [MSEK] k = 7 %

IRR %

Original layout 17.4 3.3 1603 332.7 23.8 7.2 % Alternative 1 16.1 5.7 1600 331.8 22.5 7.2 % Alternative 2 14.2 5.7 1603 333.7 28,3 7.3 % Alternative 3 13.3 5.7 26.8 7.3 % 1609 334.6

Table 8-1 Results from the reliability and the investment analysis.

According to the results in Table 8-1, all the different layouts have positive NPV-values and are

therefore assumed to be profitable. Alternative A2 has the highest NPV, followed by Alternative A3.

From a reliability point of view, A3 is the best layout, but larger cable dimensions and two extra

cables increase the investment cost too much to make it the most profitable alternative. Even if sub-

radials 2A and 2B would be connected by an extra line in A3, which would lower the ENS-value, the

43

increased investment cost would probably cancel the extra income from the net sellable energy.

However, this is not investigated. Therefore, alternative A2 is judged to be the best alternative.

However, the NPV of the four layouts ranges from 22.5 MSEK to 28.3 MSEK. When comparing these

figures with the initial investment outlay of about 1600 MSEK for all layouts, there is really not a big

difference between the different designs.

As mentioned above, the total investment cost is almost the same for the four different layouts.

However, there are two components in the farm whose cost have major differences in the original

layout compared to the three alternatives. Firstly, the platform costs 82 MSEK, compared to the

transformer station in the alternative layouts, which costs about 7 MSEK. Also, the one export cable in

the original layout costs 4.4 MSEK/km, while the three export cables in the alternative layouts costs

12 MSEK/km together. Assuming all costs but the cost for the export cable as constant, the NPV can

be calculated for each layout as a function of the length of the export cable. It should be noted that the

export cable does not include the cables on land. New values of the ENS and the electrical energy

losses have been calculated for three different lengths of the export cable, together with new

investment costs for these lengths. These values have then been used for calculating the NPV as a

function of the length of the export cable. The results from these calculations are three new values of

the NPV for each layout and are plotted in Figure 8-1 on next page. The investment cost for cables are

linearly dependent with the length, just as the failure rate, and therefore also the ENS. Therefore, a

linear extrapolation has been made for the plotted values, also plotted in Figure 8-1.

44

NPV for the different layouts as a function of the length of the export cable

Original A1 A2 A3

-40

-20

0

20

40

60

80

0 1 2 3 4 5 6 7 8 9 10 11 12

Length [km]

NPV

[MSE

K]

Linear (Original) Linear (A1) Linear (A2) Linear (A3)

Figure 8-1 NPV for the different layouts as a function of the length of the export cable

It can be seen in Figure 8-1 that the NPV is higher for the original layout than the three alternatives

when the length of the export cable is longer than approximately 7.5 km. For export cables shorter

than 7.5 km, Alternative 2 and Alternative 3 have the highest NPV. From these results, based on the

data used and the calculations made in this report, it can be seen that an offshore platform is to prefer

when the distance from farm to land is more than 7.5 km. Otherwise, the transformer should be placed

on land. It can also be seen in Figure 8-1 that the NPV of the original layout is not that sensitive to

changes in the length of the export cable.

8.2 Results from the sensitivity analysis

The reliability data used for calculating the ENS-index for the different layouts may differ compared

to the actual reliability of the specific wind farm. Therefore, a sensitivity analysis has been performed

to see what happens with the ENS-value and the investment cost when changing the outage time for

some components. The result is presented in Table 8-2 on the next page.

45

Layout Component with new outage time

New outage time, μ [weeks]

ENS [GWh]

Investment cost

[MSEK]

Net sellable production

[GWh]

NPV [MSEK] k = 7 %

IRR %

Original data 17.4 332.7 23.8 7.2 %3 20.0 330.1 12.3 7.1 %

Turbine 4 22.2 327.9 2.5 7.0 %6 18.8 331.3 17.6 7.2 %

Sub-sea cable 8 20.3 329.8 10.9 7.1 %

26 20.3 329.8 10.9 7.1 %

Original layout

Offshore transformer 36 23.1

1603

327.0 -1.5 7.0 %Original data 16.1 331.8 22.5 7.2 %

3 18.6 329.3 11.4 7.1 %Turbine

4 20.8 327.1 1.7 7.0 %6 17.9 330.0 14.5 7.1 %

Sub-sea cable 8 19.7 328.2 6.6 7.1 %

22 18.8 329.1 10.6 7.1 %

Alternative 1

Onshore transformer 32 21.7

1600

326.2 -2.3 7.0 %Original data 14.2 333.7 28.3 7.3 %

3 16.8 331.1 16.7 7.2 %Turbine

4 19.1 328.8 6.5 7.1 %6 15.6 332.3 22.0 7.2 %

Sub-sea cable 8 17.0 330.9 15.8 7.2 %

22 17.1 330.8 15.4 7.2 %

Alternative 2

Onshore transformer 32 19.9

1603

328.0 3.0 7.0 %Original data 13.3 334.6 26.8 7.3 %

3 15.8 332.1 15.7 7.2 %Turbine

4 18.0 329.9 5.9 7.1 %6 14.5 333.4 21.5 7.2 %

Sub-sea cable 8 15.7 332.2 16.2 7.2 %

22 16.0 331.9 14.0 7.1 %

Alternative 3

Onshore transformer

1609

1.1 7.0 %32 19.1 328.8

Table 8-2 Results from the sensitivity analysis for the four different layouts.

It may be hard to interpret the resulting values of the ENS, NPV and IRR in Table 8-2, since it is not

obvious how the ENS or the NPV and IRR are changing with different outage times. Therefore, the

ENS as a function of the outage time is plotted and can be seen in Figure 8-2 on next page. Also, the

NPV as a function of the outage time for the different layouts is plotted and can be seen in Figure 8-3

on next page.

46

Resulting ENS-value of all layouts from sensitivity analysis

0,0

5,0

10,0

15,0

20,0

25,0

0 5 10 15 20 25 30 35 40

Outage time [weeks]

ENS

[GW

h]

Turbines, Original Turbines, A1 Turbines, A2

Turbines, A3 Cables, Original Cables, A1

Cables, A2 Cables, A3 Transformer, Original

Transformer, A2 Transformer, A2 Transformer, A3

Figure 8-2 The ENS-value for each layout in the sensitivity analysis.

Resulting NPV of all layouts from the sensitivity analysis

Turbines, Original Turbines, A1 Turbines, A2

Turbines, A3 Cables, Original Cables, A1

Cables, A2 Cables, A3 Transformer, Original

Transformer, A2 Transformer, A2 Transformer, A3

-5,0 0,05,0

10,015,020,025,030,0

0 5 10 15 20 25 30 35 40

Outage time [weeks]

NPV

[MSE

K]

Figure 8-3 NPV of all layouts, based on ENS-values from the sensitivity analysis.

47

It can be seen in Figure 8-2 that the ENS-values increase at a much higher rate when changing the

outage time for the turbines, compared to the sea cables and the transformer. This is because of the

high failure rate for turbines compared to sea cables and the transformer. The result is that each extra

week of outage time for the turbines will lead to a higher ENS than each extra outage week for the sea

cables or the transformer will lead to. This should imply that the NPV for the different layouts changes

in the same way, when altering the outage times for these components. This is illustrated in Figure 8-3,

where it can be seen that the outage time for the turbines affect the NPV of all the alternatives at a

much higher rate than the other two components.

48

9 Discussion

9.1 The problem formulation of the report

9.1.1 A combined reliability and investment analysis

The aim for this report was to compare different layouts of an offshore wind farm in order to find a

design with a reasonable degree of reliability that makes the investment profitable.

With the input data used in this report for the combined reliability and investment analysis, all the four

layouts investigated turned out to have a positive NPV. However, it is difficult to find reliability data

that reflect the "true" reliabilities of the components. Failures are often reported, but it is not sure that

statistics are kept of all these different failures. Especially for offshore wind power, which is a quite

new phenomenon, it is hard to find reliable reliability data. Also, most technologies suffer from a

larger number of faults when they are new, compared to after some years of operation. Thus, using this

kind of failure statistics may not give a correct picture for a time horizon of 20 years. Reliability data

used as input in this report have been taken from different reports, but the data varied considerably for

the same type of components in these reports. That is why a sensitivity analysis was carried out, in

order to see how the output from the reliability analysis varied with different reliability input data.

When it comes to economic data used in this report, the total investment cost might differ a bit from

the real investment cost, since costs for insurances have not been considered. On the other hand, the

subsidy of 213 MSEK, given by the Swedish Energy Agency, has not been taken into account. Also,

the construction of the farm started in 2006 and raw material prices have increased since then and the

cable prices used in this report come from 2008. Therefore, the investment costs of some components

in this report may be different compared to the real investment costs for Lillgrund.

9.2 Suggestions for future studies

For future reliability studies of offshore wind farms, the most important thing to do should first be to

collect reliability data of those offshore wind farms existing today, so that input data for future

reliability analyses get better. Offshore wind power has suffered from different problems, which have

lead to unexpected outages. The longer time these farms are in operation, the more data of different

failures should exist. Collecting data from these failures should not only be of interest for reliability

studies, but also for the different manufacturers. If these data are collected, the main question is if they

will be available for this kind of reliability study.

49

The electrical energy losses of 3.3 GWh and 5.7 GWh are just rough estimates, but they are still

considerably lower than the estimates Vattenfall has made. Vattenfall made this rough estimate of the

losses when calculating the net sellable energy of the wind farm before the farm was built, and the

figure was used as the highest acceptable losses. It is obvious that the real losses are lower than the

estimated figure. Thus, they could be considered when designing and evaluating future wind farm

layouts. On the other hand, Vattenfall calculated the net sellable energy from Lillgrund before the farm

was built and it is not sure that all input data needed for the load flow calculation are known at this

time of the project. Therefore, the real value of the electrical energy losses may not be possible to

calculate at that early stage in the process. Also, It is not known whether it is the best solution from an

economic point of view to estimate the electrical energy losses or to calculate them, since the latter

alternative demands larger efforts.

The network on land was not included for the reliability analysis of this report. However, the network

on land can affect the reliability of the wind farm. For example, if a failure occurs in the network on

land and the network cannot accept all energy produced in the farm, the power output of the farm has

to be lowered. A consequence of this is that the expected energy not supplied from the farm, the ENS-

value, increases, which leads to less sold energy and lower revenues. This kind of impact can be

interesting for further studies. Also, since the limit of the system in this report was drawn at the station

in Bunkeflo, no loads like domestic households or industries were considered. Thus, neither the

SAIFI- nor the SADI-index were calculated during the reliability analysis. This may be of interest for

future work.

As mentioned in Section 6.2, a 72 kV solution for wind power turbines could be of interest for future

studies, especially the technical issues for changing from 33 kV to 72 kV.

All conclusions above are based on the conditions, models and parameters used in this report. The

conclusions do not necessarily reflect the views of Vattenfall.

50

10 List of references

10.1 Electronic document

[1] BCP Busarello + Cott + Partner Inc., NEPLAN User’s Guide V5

10.2 Material from the Internet

[2] Energimyndigheten, miljöbonus, http://www.energimyndigheten.se/sv/Om-oss/Var-verksamhet/Framjande-av-vindkraft/Bygga-vindkraftverk-/Ekonomiskt-stod/Miljobonus/, 2008-03-07

[3] Energi Sverige, http://energi-sverige.se/default.aspx, 2008-03-12 [4] Fakta om Lillgrund,

http://www.vattenfall.se/www/vf_se/vf_se/518304omxva/518334vxrxv/521964aktue/522474lillg/522564vindk/index.jsp, 2008-01-15

[5] Kentish Flats Offshore wind farm, http://www.kentishflats.co.uk, 2008-01-30 [6] Nordpool, http://www.npspot.com/reports/systemprice/Post.aspx, 2008-03-12 [7] Vindkraft i Öresund – karta över sjökabel (PDF),

http://www.vattenfall.se/www/vf_se/vf_se/518304omxva/518334vxrxv/521964aktue/522474lillg/522504kartb/index.jsp, 2008-01-15

10.3 Literature and reports

[8] Baudish, R., Modelling Operation and Maintenance Costs for the offshore wind farm Horns Rev, Diploma thesis, Westsächsische Hochschule Zwickau, Identification number 19530, January 2008

[9] Bertling, L., Ribrant, J., Survey on Failures in Wind Power Systems With Focus on Swedish Wind

Power Plants During 1997-2005, IEEE Transactions on energy conversion, Vol.22, No. 1. March 2007

nd[10] Billinton, R., Allan, R. N., Reliability evaluation of power system, Plenum Press, 2 edition,

ISBN: 0-306-45259-6, 1996 [11] Boyle, G., Renewable energy, Oxford University Press, ISBN-13: 9780199261789, 2004 [12] Dahlgren, A., Lindgren, M., Söderberg, D., Design av elsystem för havsbaserade

vindkraftparker, Vindforsk projekt V-108, January 2008

51

[13] Frankén, B., STRI AB, Reliability study – Analyses of electrical system within offshore wind parks, Elforsk report, November 2007

[14] He, Y., Distribution Equipment reliability data – Tillförlitlighetsdata på komponentnivå för

eldistributionsnätet, Elforsk report 31002, September 2007 [15] He, Y., Neimane, V., Reliability evaluation of Baltic Wind Link alternatives: Summary of the

results, 2007-05-29 [16] Ingårda, L., Sjölander, J., Data assumption book BWL financial model, 2007-03-19 [17] Larsson, R., Lindgren, M., Unosson, O., Kostnadsuppskattning offshore – apparater och arbete,

2007-12-19 [18] Levy, H., Sarnat, M., Capital investment and financial decisions, Prentice Hall International

(UK) Ltd, 5th edition, ISBN: 0-13-115882-1, 1990 [19] Söder, L: Static analysis of power system, Electric Power Systems, Royal institute of

Technology, 2004

10.4 Discussions

[20] Axelsson, Urban; Vattenfall Research and Development [21] Broman, Niclas, Vattenfall PYA, Interviews, February 2008 [22] Flodérus, Arne, Vattenfall Power Consultant, 2008-01-11 [23] Hansson, Jimmy, Vattenfall PYSL, Interview 2008-01-14 [24] He, Ying, Vattenfall Research and Development, December 2007 [25] He, Ying, Vattenfall Research and Development, January 2008 [26] Kapper, Robert, Vattenfall Power Consultant, Interviews March 2008 [27] Krogh, Flemming, ABB High Voltage Cables AB, Interview 2008-01-25 [28] Liffer, Johan; ABB High Voltage Cables AB, 2007-12-20 [29] Larsson, Richard, Vattenfall Power Consultant, Interviews January 2008 [30] Larsson, Åke, Vattenfall Power Consultant, Interviews January 2008 [31] Petrini, Tobias, Vattenfall Power Consultant, Interview 2008-02-25

52

[32] Sjölander, Jonas, Vattenfall Power Consultant, Interview 2007-12-20 [33] Svensson, Mårten, Vattenfall Power Consultants, Interview 2008-01-10 [34] Svensson, Pär, Vattenfall PYS, Interviews February 2008 [35] Wetterborg, Björn, Interview 2008-02-22

53

Appendix 1

Alternative layouts of the wind farm

Alternative 1 (A1)

A06

A01

A05

A04

A03

A02

C05

A07

D08 C08

B03

B04

B05

B06

B07 D07 C07 E07

E06 D06 C06

F05 G05

F06

B08

C01

E04 D04 C04

G03

H02

H03

H04 G04

E03

F02 G02

F03

D02 C02 B02

C03

F04

B01 D01 E01

E02

Radial 1A

Radial 3A

Radial 2B

Radial 2A

Radial 1B

Radial 3B

To shore

Page 1 (3)

Alternative 2 (A2)

A06

A01

A05

A04

A03

A02

C05

A07

D08 C08

B03

B04

B05

B06

B07 D07 C07 E07

E06 D06 C06

F05 G05

F06

B08

C01

E04 D04 C04

G03

H02

H03

H04 G04

E03

F02 G02

F03

D02 C02 B02

C03 D03

F04

B01 D01 E01

E02

Radial 1A

Radial 3A

Radial 2B

Radial 2A

Radial 1B

Radial 3B

To shore

Page 2 (3)

Alternative 3 (A3)

Radial 1A

Radial 3A

Radial 2B

Radial 2A

Radial 1B

Radial 3B

To shore

A06

A01

A05

A04

A03

A02

C05

A07

D08 C08

B03

B04

B05

B06

B07 C07 E07

E06 D06 C06

F05 G05

F06

B08

C01

E04 D04

G03

H02

H03

H04 G04

E03

F02 G02

F03

D02 C02 B02

D03

F04

B01 D01 E01

E02

C04

C03

D07

Page 3 (3)

Page 1 (2)

Appendix 2

Investment costs in more detail. Original layout

Component Cable area and material

Voltage level [kV]

Price per unit [MSEK] /

[MSEK/km]

Installation price [29]

[MSEK/km]

Total length [km]

Total cost

[MSEK]Fundament [22] 6 288.0Turbine [16] 23.11 1109.3

36 0.3 15.9Breaker [17]

145 0.43 0.9 36 0.1 5.3

Disconnect switch [17] 145 0.12 0.2

3x95 mm2 Cu 36 1.15 1 13.10 28.23x185 mm2 Cu 36 1.4 1 6.25 15.03x240 mm2 Cu 36 1.7 1 3.22 8.7

Sea cables [28]

3x400 mm2 Cu 145 3.4 1 7.18 31.6Land cable [28] 3*(1x640 mm2) Al 145 0.4 0.65 5.37 5.6Transformer [33] 33/138 12 12.0Platform [17] 82 82.0 Total cost [MSEK] 1603

Alternatives 1 and 2 (A1 and A2)

Component Cable area and material

Voltage level [kV]

Price per unit

[MSEK] / [MSEK/km]

Installation price [29]

[MSEK/km]

Total length [km]

Total cost

[MSEK]

Fundament [22] 6 288Turbine [16] 23.11 1109.3

36 0.3 15.3Breaker [17]

145 0.43 0.4 36 0.1 5.1

Disconnect switch [17] 145 0.12 0.1

3x95 mm2 Cu 36 1.15 1 16.80 36.13x185 mm2 Cu 36 1.4 1 3.66 8.8Sea cables [28]

3*(3x630 mm2) Cu 36 3 1 25.40 101.6Land cable [28] 3*(1x1000 mm2) Al 36 0.39 0.65 16.12 16.7Transformer [33] 33/138 12 12Transformer station [17] 6.6 6.6 Total cost [MSEK] A1 1600 Total cost [MSEK] A2 1602

Alternative 3 (A3)

Component Cable area and material

Voltage level [kV]

Price per unit

[MSEK] / [MSEK/km]

Installation price [29]

[MSEK/km]

Total length [km]

Total cost

[MSEK]

Fundament [22] 6 288Turbine [16] 23.11 1109.3

36 0.3 17.1Breaker [17]

145 0.43 0.4 36 0.1 6.5

Disconnect switch [17] 145 0.12 0.1

3x95 mm2 Cu 36 1.15 1 5.32 11.43x185 mm2 Cu 36 1.4 1 11.83 28.43x240 mm2 Cu 36 1.7 1 4.11 11.1

Sea cables [28]

3*(3x630 mm2) Cu 36 3 1 25.40 101.6Land cable [28] 3*(1x1000 mm2) Al 36 0.39 0.65 16.12 16.7Transformer [33] 33/138 12 12Transformer station [17] 6.6 6.6 Total cost [MSEK] 1609

Page 2 (2)