Wind farm layout: a reliability and investment analysis

UPTEC ES08013

Examensarbete 20 p Oktober 2008

Wind farm layout

a 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 investment analysis

Emil Eriksson

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

onshore.

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 than expected. This loss of energy is called expected energy not supplied (ENS)

[GWh/year]. High ENS-values risks the profitability of the investment. Thus, the ENS-value of Lillgrund has been calculated with a reliability analysis and is then used as input in an investment analysis, to see how the reliability of the farm affects the investment proposal. Three alternative layouts, where the transformer is placed on land 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 are not that big relative differences between the NPVs of the layouts compared to the total investment outlay. The result shows that a transformer on land is preferable when the distance from farm to the shore is 7.5 km or less, while for longer distances a platform is preferable. A sensitivity analysis shows that the NPV is most sensitive to long outage times of the turbines, compared to long outage times for cables and transformer. Results and views in the report are my own conclusions, based on the input parameters used. The views are not necessarily the views of Vattenfall. Also, it is important to notice that some data have been changed because of confidentiality.

However, the qualitative results and conclusions still remain the same.

Sponsor: Vattenfall AB

ISSN: 1650-8300, UPTEC ES08 013 Examinator: Ulla Tengblad

Ämnesgranskare: Marcus Berg Handledare: Ying He

Table of Contents

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

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.

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 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

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

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.

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

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

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).

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).

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 I_Gk 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 k_N are supplied with the currents I_k1 to I_kN. 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

j kj Dk

Gk I I

I

1

(Eq. 4.1.1)

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

j kj Dk

Gk S S

S

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

Gk

Gk PGk jQ

S = + = by the generator generated complex power

Dk

Dk PDk jQ

S = + = consumed complex power by the load connected to k

kj

kj

P

jQ

S = +

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

∑

=

−

= ^N

j kj Dk

Gk

GDk P P P

P

1

(Eq.4.1.3)

∑

=

−

= ^N

j kj Dk

Gk

GDk Q Q Q

Q

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 P_GDk and reactive power Q_GDk 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. P_{k, 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

calc k GDk

k

P P

P = −

Δ

calc k GDk

k

Q Q

Q = −

Δ

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

∑

−

−

=

Δ ^N

j kj j

k GDk GDk

k P jQ U Y U

S

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 U_i have to be found such that ΔS_k 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 P_k, net generation of reactive power Q_k, 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 |U_k| 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 P_GDk and voltage magnitude |U_k| are known quantities at this bus, leaving net generated reactive power QGDk and voltage phase angle θk to be

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 P_GDk and net generated reactive power Q_GDk 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

].

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 λ * μ

=

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 i i

N

λ

customers of

number Total

ons interrupti customer

of number Total

SAIFI (Eq.4.2.2)

∑ ∑

∑

=

i i i

N N U customers

of number Total

durations on

interrupti Customer

SAIDI (Eq.4.2.3)

where

λi = failure rate at load point i

N_i = number of customers at load point i Ui = Unavailability at load point i

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].

∑

=

=Totalenergy not supplied L_a(i)U_i

ENS (Eq.4.2.4)

where

L_a(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

∑

=

i i

s 1

λ

λ

s s s

n i i i s

r U

r λ λ

λ =

= ∑

i n

i i

s s

s

r r

U ∑

=

=

=

1

λ

λ

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

2 2 1 1

2 1 2 1

1

) (

r r

r r

p

λ λ

λ λ λ

+ +

= + (Eq.4.2.8)

2 1

2 1

r r

r r_p r

= + (Eq.4.2.9)

2 1 2

1

r r

r

U

= λ

= λ λ

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

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

t t

t

R I S

1

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.

0

1 (1 ) I

k NPV ⁿ S

t t

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:

) 0 1

( ⁰

1

= + −

∑

R I S

n

t t

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 S_t 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 ) , ( 0

1 (1 )

1 I SQ I

S ⁿ R _nR

t t = ⇔ =

∑

=

(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

S

Q_(n,R) = I⁰ (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

P

= E

α

where

Ea = Actual energy production in MWh

P_r = Rated maximum power for the wind farm in MW

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.

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.

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

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.

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

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.

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

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

fC

B = 2 π

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.

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 0.420 131.947 FXBTV (3x400) Cu 145 624 0.086 0.128 0.167 52.465 Export cable

FXCTV (3x630) Cu 36 719 0.061 0.102 0.348 109.327 FXCTV (3x240) Cu 36 497 0.114 0.120 0.235 73.827 FXCTV (3x185) Cu 36 438 0.143 0.128 0.200 62.832 Array 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 13 098

Alternative 1 16 119 25 400 3 664 16 796

Alternative 2 16 119 25 400 3 664 16 796

Alternative 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

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

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.