Quantitative Risk Assessment of Wave Energy Technology

TVE-MFE 18 001, UPTEC E 18 003

Examensarbete 30 hp Februari 2018

Quantitative Risk Assessment of Wave Energy Technology

Emil Ericsson

Eric Gregorson

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

Quantitative Risk Assessment of Wave Energy Technology

Emil Ericsson, Eric Gregorson

European Commission (2011) aims to reduce the greenhouse gas emissions by 85-95% by 2050 in comparison to 1990’s levels. Wave energy could be an important step to archiving this goal. This report aims to develop a quantitative risk assessment for the Uppsala University's wave energy converter. Failure rates have been collected from various databases and reports and have been processed accordingly in order to implement them in the risk analysis. CAPEX, OPEX and possible downtime windows have been estimated. A fault tree analysis (FTA) has estimated the total unavailability, unreliability and downtime. Furthermore an economical assessment model using Monte Carlo and the unreliability data from the FTA has been developed, estimating the expected LCOE and OPEX/WEC for parks consisting of 20, 100, and 200 WECs (wave energy converters). The result show that the O-ring seal has the largest impact on both the unavailability, and the economy of the OPEX/WEC. Second biggest contributor is the translator bearing failure. The study also shows

that the CAPEX cost has to be reduced to make the LCOE competitive in comparison to other renewable sources. A comparison between the system unavailability and unreliability has also been done in terms of

different component parameters.

TVE-MFE 18 001, UPTEC E 18 003

Examinator: Juan de Santiago, Tomas Nyberg Ämnesgranskare: Jens Engström

Handledare: Malin Göteman

Acknowledgement

First of all, we would like to thank our supervisor Malin Göteman for the guidance, help and support during the work of our master thesis. We would also like to thank our subject reviewer Jens Engström for additional assistance.

Furthermore we would like to thank Marcus Berg for the help regarding Markov chains

and Monte Carlo simulations.

Contents

1. Introduction 1

1.1. Uppsala University’s Wave Power Project . . . . 1

1.2. Risk assessment . . . . 2

1.3. Division of labour . . . . 4

2. Technical Overview 5 2.1. The Linear Generator . . . . 6

2.2. End Stop Springs . . . . 7

2.3. Subsystems . . . . 8

3. Methodology 10 3.1. Failure rates . . . . 10

3.1.1. Constraints . . . . 10

3.1.2. Base failure rates . . . . 10

3.1.3. Failure rate adjustments . . . . 12

3.1.4. Processing the data . . . . 17

3.1.5. Failure rates in the power absorbing subsystem . . . . 18

3.2. Unavailability . . . 20

3.2.1. Repair rate . . . 20

3.2.2. Unavailability for constant failure rates . . . . 21

3.2.3. Fault tree analysis (FTA) . . . 23

3.2.4. Sensitivity analysis for the uncertainty . . . 25

3.3. Unreliability and other analysis methods . . . 25

3.3.1. Unreliability of the L12 WEC . . . 26

3.3.2. Frequency and CFI . . . 27

3.4. Non-constant failure rates . . . 27

3.5. Definition of investigated economical parameters . . . 29

3.5.1. LCOE and OPEX assumptions . . . 30

3.6. Power and Energy Assumption . . . . 31

3.7. Capex estimation . . . 32

3.7.1. Large-scale production . . . 33

3.7.2. Replacing WECs . . . 35

3.8. Failure costs and delay time . . . 36

3.9. Economical assessment model . . . 39

3.9.1. Kernel Density Estimation (KDE) . . . 40

3.9.2. Highest Density Interval (HDI) . . . . 41

4. Results 42

4.1. Final failure rates . . . 42

4.2. Fault tree of the WEC . . . 43

4.2.1. Delimitation of failure rate sources . . . 46

4.3. Sensitivity analysis . . . 48

4.4. Economical assessment model . . . 54

4.4.1. Original CAPEX . . . 55

4.4.2. Large-scale CAPEX . . . 58

4.4.3. Sensitivity Analysis . . . . 61

5. Discussion 63 5.1. Technical assessment . . . 63

5.1.1. The issues concerning the failure rates in this thesis . . . 63

5.1.2. The fault tree . . . 64

5.1.3. The sensitivity analysis . . . 65

5.2. Economical assessment model . . . 66

5.2.1. Original CAPEX . . . 66

5.2.2. Large-scale production . . . 67

5.2.3. Sensitivity analysis . . . 68

5.3. Concluding remarks . . . 69

5.4. Future work . . . 70

Bibliography 71

Appendices 76

A. Table of environments 77

B. Isograph gates and events 78

C. The fault tree 80

D. Unreliability with sensitivity factors 84

Abbreviations and Nomenclature

List of Abbreviations

CAPEX Capital expense

CFI Conditional failure intensity FTD Fault tree diagram

HDI Highest density interval LCOE Levelized cost of electricity MTTF Mean time to failure MTTR Mean time to repair NPV Net present value OPEX Operating expense PA Point absorber

PMLG Permanent magnet linear generator PTO Power take-off

PV Present value

TDT Total system downtime WEC Wave energy converter

Nomenclature

β Shape parameter

η Scale parameter

γ Location parameter

γ

Additional adjustment factor

λ Failure rate

µ Repair rate

π

Data source uncertainty factor π

Environmental adjustment factor π

Failure mode factor

A Availability

a

Intercept parameter

E Event

F Unreliability

N

Cycles to failure

Q Unavailability

R Reliability

s Stress

T System lifetime

w Component failure frequency

1. Introduction

European Commission (2011) aims to reduce the greenhouse gas emissions by 85–95%

by 2050 in comparison to 1990’s levels. An important step in obtaining this goal is by increasing the use of renewable energy sources. Clément et al. (2002) estimates that 10% of the world’s electricity consumption can be covered by the use of wave energy technology. The same authors further conclude the presence of over 1000 different wave energy technologies.

Despite the large existence of different wave energy technologies, there are still only small- scale wave power operations (Levitan, 2014). One of the biggest constrains is to make a simple cost-efficient construction, yet making a device sturdy enough for the harsh ocean climate. IEA and NEA (2015) calculates the overnight cost for windpower to be around 2.6 times larger offshore in comparison to onshore.

1.1. Uppsala University’s Wave Power Project

In 2002 Uppsala University (UU) began its research and wave power development "The Lysekil project" (Kamf, 2017; Sjökvist, 2017). Four years later, the first wave energy converter (WEC) prototype, L1, was finished and deployed at the Lysekil test site. Lysekil is a locality situated approximately 100 km north-west of the Swedish city Gothenburg.

The wave energy converter (WEC) is of the type point absorber (PA), meaning it uses a buoy for the power take-off (PTO) while the generator is placed on the seabed. Ocean wave’s power increases by the wave height squared, resulting that storms will produce huge forces. UU’s solution is thus to place the WEC’s most vital parts on the seabed for protection (Parwal et al., n.d.). The housing is mounted to a seabed on a concrete foundation, with no further need of anchoring.

UU’s WEC uses a linear generator, which simplifies the mechanical system. Parwal et al.

(n.d.) explains that this setup potentially can reduce the need for maintenance.

Figure 1.1.: Uppsala University’s wave energy converter.

1.2. Risk assessment

Risk can generally be defined as a probability that a certain undesired event will occur.

Rausand (2014) describes risk as an answer to a set of three questions: 1. What can go wrong? 2.How probable is it? 3.What are the consequences? Rausand (2011) states that risks are in general greater now compared to a few decades ago due to various modern phenomena such as the rapid technological expansions and the increasing complexity of the technology to accommodate the increasing demand for better products. Risks arise from potential hazards, i.e. sources of danger, in a system and these are the causes of the undesired events, i.e. failures in this case. A potential hazard for a WEC could for instance be large waves as a result of a storm. Rausand (2011) suggests that identification of hazards can be done by acknowledging the fact that a lot of hazards are related to different forms of energy such as corrosive energy, mechanical energy, electrical energy etc. The potential hazards need to be identified before analysis and evaluation of the failures can be implemented to determine the probabilities and impact of the risks.

Although some books and articles, e.g. Reij and van Schothorst (2000), defines risk

assessment as an integrated part of risk analysis contrary to, e.g. Vinnem (2014), where

risk analysis is an integrated part of risk assessment, the overall step-by-step procedure

is mostly still the same. This thesis will have the same definition of risk assessment as

Vinnem (2014) and Rausand (2011) as this terminology is commonly used in the offshore

industry. The risk analysis and the risk evaluation constitutes the main parts of a risk assessment and this process is illustrated in figure 1.2. Furthermore, if monitoring of how the risks changes over time combined with measures to decrease the risks are added to the process, it is defined as a Risk Management ( Rausand, 2011).

The risk assessment can be done either qualitatively or quantitatively and this is explained more in detail by Burtonshaw-Gunn (2009). The qualitative risk assessment focuses on prioritizing the identified risks by probability of occurrence and severity of impact which are then ranked with a pre-defined scale, e.g. very low to very high. These two properties can be combined in a so called risk matrix to assess the severity of the identified risks, often distinguished with different colors, e.g. red for extreme risk. The reason for this type of assessment could stem from incapability to cope with all included risks due to insufficient amount of resources and an extensive list of various risks.

The quantitative risk assessment seeks to analyze the probabilities and impacts numeri- cally yielding more exact values for the risks and thus, allows a more precise evaluation of the economic consequences. It is often a follow-up assessment done as a consequence of the qualitative risk assessment which highlights the risks that requires further inves- tigation. The importance of this type of assessment is emphasized by Vinnem (2014).

The quantitative risk assessment should also include a sensitivity analysis in which the uncertainties of the input data is considered. The basic idea of a sensitivity analysis is to investigate how a change of an input parameter influences the output data.

Figure 1.2.: Risk assessment process by Vinnem (2014)

1.3. Division of labour

This report will be divided into two parts; (1) WEC System, and (2) Economical assess- ment, where (1) is written by Eric Gregorson and (2) by Emil Ericsson.

Both of the authors have contributed to the introduction, as well as the sections 5.3 and 5.4. Below the sections for the different parts are listed.

• WEC System includes the following sections::

– Technical Overview

– Method: 3.1, 3.2, 3.3, and 3.4.

– Results: 4.1, 4.2 and 4.3.

– Discussion: 5.1

• Economical assessment includes sections:

– Method: 3.5, 3.6, 3.7, 3.8, and 3.9.

– Results: 4.4.

– Discussion: 5.2

2. Technical Overview

The incoming sea waves causes the buoy of the WEC to oscillate. A connection line composed by a stranded steel wire is attached between the buoy and a translator. The movement of the buoy is thereby transferred by the connection line to the translator and thus forces it to move in the same manner. This is the dynamic process that constitutes the absorption of kinetic energy from the waves.

There is a line guidance funnel mounted on top of the steel housing in which the generator

is located and can be seen in figure 1.1. The purpose of this funnel is to absorb the forces

originating from the surge motions of the waves that causes the buoy to be horizontally

displaced and thus protecting the piston sealing in which the connection line is lead

through (Rahm, 2010). Inside the steel housing there is also an upper end stop spring

located above the translator and a lower end stop spring located below the translator in

case of high wave amplitudes. It should be noted that figure 1.1 depicts an older version

of the WEC. The most important difference is the retracting springs which is not a part

of the latest WEC model (L12). The purpose of the retracting springs was to amplify

the descending force of the translator, though in the L12 model only the gravitational

force of the translator is used. The extracted wave energy is then converted to electricity

by the generator and processed through power electronics to enable grid connection. A

simple overview of the conversion steps along with most of the important acting forces is

graphically illustrated in figure 2.1.

Figure 2.1.: Energy conversion system for Uppsala University’s WEC.

2.1. The Linear Generator

Instead of a conventional rotating generator, a directly driven three-phase linear generator

is used for the WEC, and the vertical linear motion in the system makes the choice of a

linear generator rather implicit. It comprises two main components, namely a translator,

which is the linear generator’s equivalent of a rotor, and a stator. The translator is

essentially a metallic pipe with attached permanent ferrite magnets to generate magnetic

flux which is then confined to the laminated steel core of the stator. The translator

oscillates vertically relative to the enclosing stator and this process induces electric voltage

in the stator windings according to Faraday’s law of induction. The air gap between the

translator and the stator is maintained using four equidistant columns of wheels mounted

on the inside of the steel housing walls on which the translator moves (Lejerskog et al.,

2015). If a load is connected to the generator an electric current will also flow through

the stator windings and a certain amount of power is extracted.

The PMLG is, albeit bulky and expensive, simple, robust and has a higher expected efficiency compared to other alternatives for the same WEC category, i.e. point absorbers, according to Polinder et al. (2007). An example could be a hydraulic system which is utilized by the Pelamis WEC where the immense forces present in this technique warrants this type pf PTO, but this technique is not considered to be a PA.

The fact that the PMLG is directly driven, i.e. no secondary conversion such as a turbine or a gearbox is required, combined with the small number of mechanical parts in the PMLG compared to other energy conversion methods, attains its simplicity. Although this makes it less prone to failures and maintenance requirements, it incurs the necessity of a more complex electrical system. The necessity of a more complex electrical system, which is explained more in detail by Rahm et al. (2010), stems from the irregular motion of the sea waves that causes the output voltage to vary in both amplitude and frequency.

Moreover, as the translator alters direction vertically once every wavelength, so will the order of the three phases. This makes direct connection to the grid impracticable and thus, the electrical power must be rectified and then converted into AC with a steady amplitude and frequency. This process is illustraded in figure 2.1.

2.2. End Stop Springs

The end stop springs will absorb a possible excessive force exerting from the translator in both vertical directions. If a wave peak is high enough the end stop springs will be compressed by the translator, damping the motion which averts a possible impact of the translator on the end stops inside the steel housing and thereby limits the stroke length.

The stroke length is defined as the distance the translator can move from its neutral position in the ascending and descending directions allowing the electromechanical field phenomena to arise. The stroke length can be divided into a free stroke length and a total stroke length. The free stroke length is represented by the translator’s potential vertical alignment without compressing the end stop spring whereas the total stroke length is the translator’s potential vertical alignment when the end stop spring is fully compressed.

This phenomenon can be seen in figure 2.2. An infinite stroke length combined with an infinitely high stator would, albeit impossible to practically implement, allow full utilization of the waves in terms of energy absorption and thus, exhibit the ideal case.

However, the slight increase of harnessed wave energy for a very large stroke length would

not warrant the neglection of a stroke length restriction due to the significant cost increase

incurred by the necessary increase of the generator size.

Figure 2.2.: Illustration of the stroke length for the WEC by Sjökvist and Göteman (2017).

2.3. Subsystems

The WEC can be divided in three different subsystems: the Power absorbing subsystem, the Structural subsystem and the Power take-off subsystem (PTO). This is illustrated in figure 2.3. The one sided black arrows indicate that two components are connected to each other, e.g. the shackle is connected to the chain. The two sided arrows indicate an interaction between two components, e.g. the translator can interact with an end stop spring. The one sided yellow arrows indicate a subsystem cross-over connection between two components, e.g. the stator is mounted on the interior casing walls. The dashed lines can be translated: the larger block comprises the smaller block, e.g. the stator core comprises thin silicon steel sheets. The end stop springs are connected on the top side and the bottom side inside the casing, however this connection is excluded in figure 2.3 to avoid an extensive amount of arrows and thus facilitate comprehension of the illustrated system.

The power absorbing subsystem is represented as the device that absorbs the kinetic energy provided by the sea waves before it is processed by the linear generator. The connection line and the buoy are the two important components in this subsystem, though the chain and the shackle are included to make the illustrated system more detailed and for the sake of the risk assessment.

The structural subsystem contains the exterior components used for protection and load

resistance along with the foundation on which the WEC is attached to. It can be argued whether if the component named as piston in figure 2.3 should be a part of the structural subsystem or the power absorbing subsystem, though the authors deemed the whole system more apparent if this component is included in the latter. The piston is the component sliding through the o-ring seal, which isolates the generator from the sea water, and is attached between the connection line and the translator.

The PTO subsystem is the prerequisite apparatus for the conversion from mechanical energy to electrical energy which can also be understood from figure 2.1. The main components are the translator and the stator which constitutes the generator. The wheels are also included in this subsystem as this is the bearing system that enables the relative movement between the translator and the stator.

Figure 2.3.: Component block diagram with three different sub-systems.

3. Methodology

3.1. Failure rates

Failure rate, most commonly denoted with a λ, is defined as the number of times a component or system will fail per unit of time and can be calculated using equation 3.1 where MTTF = Mean Time To Failure (derivation of this equation can be found in section 3.3). It is sometimes wrongly interpreted as a probability of failure but should rather be perceived as an intensity or frequency of failure. The failure rate is predominantly measured in failures per year or in failures per million hours due to the small numbers they generally exhibit. If e.g. a failure rate for a component is 0.05 per year, then that component is expected to fail once for every twentieth year.

λ = 1

M T T F (3.1)

3.1.1. Constraints

Base failure rates with decent quality are in general hard to obtain as these are found in databases that are often kept confidential or due to lack of actual measured component failure data, which is also mentioned by Thies et al. (2009). The failure rates available for the general public are therefore in many cases generic and not directly applicable for an intended component. Another issue is the fact that essentially all failure rates that are accessible to the general public are regarded as constant, i.e. do not vary over time. They might also include impertinent failure modes, which is defined as the manner in which a component or system fails, or do not include the sufficient amount of failure modes for the intended component. Furthermore, the span between the largest found failure rate and the lowest for one single component could be of a considerable extent.

3.1.2. Base failure rates

Base failure rates are in this thesis defined as the initial failure rates obtained directly

from various databases and reports. Table 3.1 presents base failure rates in failures per

year used for this thesis. They are not based on the L12 WEC design and thus, cannot be

directly applied. The different amount of base failure rates for each component in table

3.1 is due to varying difficulty in gathering of these failure rates.

The most commonly used database to obtain base failure rates is SINTEF industrial management (2002) in this thesis as this is considered to be a reliable source of offshore data. There is a wide range of failure data in this database including maximum, minimum and mean failure rates together with corresponding standard deviations. However, only mean failure rates have been collected and this database is mostly used for the electric generator and the casing as relevant failure rates for the other components could not be found here. There are several different failure modes for each component in SINTEF industrial management (2002) and the challenge is to obtain those which are most relevant for the L12 WEC as this database is primarily used for the offshore oil and gas industry.

The failure data for e.g. generators concerns conventional rotating generators and thus, many of the listed failure modes are impertinent for a PMLG, e.g. fail to start on demand or fail to synchronize. The one failure mode for the PMLG considered in this thesis is generator short circuit. The failure data for the casing was obtained from vessels in this database, e.g. vessels of coalescers and flash drums. The most relevant failure modes have been selected to the author’s best ability, however this data is subject to uncertainties considering the differences in design and application of these components.

The level of quality and uncertainty of the different sources for the base failure rates in

table 3.1 vary to a great extent. Some of these failure rates are obtained from established

reliability databases such as SINTEF industrial management (2002) and Reliability In-

formation Analysis Center et al. (1991) while others are obtained from scientific reports

and articles.

Table 3.1.: Base failure rates obtained from various sources Component λ

[

]

Casing 0.8116

0.0010

0.0270

0.0100

0.0480

0.0410

Translator wheels 0.0229

1.9000

0.0040

0.0088

0.0110

0.1753

0.2190

0.0600

0.1490

0.0027

0.0025

0.0036

Electric generator 1.5900

0.0830

0.0430

0.0100

0.0244

0.0240

0.0800

0.0440

0.0350

0.0438

0.1647

O-ring seal 0.2190

0.0570

0.7800

0.0028

0.3700

0.0700

Steel stranded rope 0.0013

a This failure rate is based on a WEC similar to the one being researched by Uppsala University and calculated with Telcordia III (Cretu et al.,2016).

b This failure rate is based on a Pelamis WEC and obtained from (Rinaldi et al., 2016) which in turn refers to (Thies et al.,2009).

c This failure rate is obtained from (SINTEF industrial management,2002).

d This failure rate is based on a ball bearing system (Active Power,2008).

e This failure rate is found in Appendix C.2 in (Thies,2012) which in turn refers to (Reliability Infor- mation Analysis Center et al., 1995).

f This failure rate is found in Table 6 in (Ambuehl et al., 2014) which in turn refers to (Arabian- Hoseynabadi et al., 2010).

g This failure rate is obtained from (Smith, 2005) and is based on the famous database FARADIP.THREE.

h This failure rate is obtained from (Failure Rate Estimates for Mechanical Components, n.d.) which is a calculated average value based on a Weibull distribution.

i This failure rate is obtained from (Reliability Information Analysis Center et al.,1991).

j This failure rate is found in Table 3 in (Thies et al.,2009) which in turn refers to (SINTEF industrial management,1997).

k This failure rate is found in Appendix C.2 in (Thies,2012) which in turn refers to (Green and Bourne, 1978).

l This failure rate is found in Appendix C.2 in (Thies,2012) which in turn refers to (SINTEF industrial management,1997).

3.1.3. Failure rate adjustments

As mentioned in subsection 3.1.2, most of the failure rates in table 3.1 cannot be directly

applied in the risk assessment as these components are different from the corresponding

components in the WEC examined in this thesis in terms of design, operation, environ-

ment, the amount of stress etc. This necessitates adjustments of the base failure rates in

order to make them more applicable for the L12 WEC. Thies et al. (2009) presents a pro-

cedure derived from Department of Defense (1991) which is used in this thesis where the

base failure rate is multiplied with a set of different adjustment factors. The adjustment

of a component failure rate (λ

) from a base failure rate (λ

) is calculated according

to equation 3.2 where π

represents the environmental factor, π

represents the failure

mode factor, π

represents the data source uncertainty factor and γ

is an additional

factor to compensate for any other potential differences such as a new design or a safety

factor. This failure rate adjustment method is merely an approximate approach as it is hard to predict exactly how the failure rates are affected in practice by a new design and new operational conditions which is also emphasized by Thies et al. (2009).

An involved safety factor can be expected when there is a risk of e.g. environmental pollution or loss of human lives which demands a higher reliability. These types of conse- quences are not relevant for the prevailing WEC and the failure rates would therefore be higher should they be obtained from such a source. Burr and Cheatham (1995) explains how different structures and devices have different safety factors. The failure rates ac- quired from SINTEF industrial management (2002) are the ones affected by this as these failure rates are based on the offshore oil and gas industry. It is unclear what exact safety factor should be used for this case, though in this thesis the safety factor will assume a value of two which is generally the case for buildings and pressurized fuselages.

λ

= λ

· π

· π

· π

· γ

(3.2)

A new operational environment can affect a component failure rate both negatively and positively depending on the base failure rate. As the offshore environments are harsh in comparison to most other environments the failure rates are predominantly adjusted with an environmental factor equal to or greater than one in this thesis. Table 3.2 presents conversion factors between different environments and can be used to obtain an environ- mental adjustment factor. The seven characteristic environmental factors, e.g. G

= 0.38, used in table 3.2 to calculate the conversion factor are based on the environmental factors provided by Department of Defense (1991), though recalculated by Thies et al. (2009) to make them applicable for WECs as they are originally intended for electronic equipment.

It is therefore essential to know the original environment in which the base failure rate was procured. Explanations for each environment are found in appendix A.

Table 3.2.: Matrix for environmental adjustment factors π

by Thies (2012); Thies et al.

(2009).

Base failure rate environment

G

G

G

N

N

N

N

Factor 0.38 2.50 4.20 4.00 5.70 6.30 4.00 Environment

Ground, benign G

0.38 1.00 0.15 0.09 0.10 0.07 0.06 0.10 Ground, fixed G

2.50 6.58 1.00 0.60 0.63 0.44 0.40 0.63 Ground, mobile G

4.20 11.05 1.68 1.00 1.05 0.74 0.67 1.05 Naval, sheltered N

4.00 10.53 1.60 0.95 1.00 0.70 0.63 1.00 Naval, unsheltered N

5.70 15.00 2.28 1.36 1.43 1.00 0.90 1.43 Naval, undersea N

6.30 16.58 2.52 1.50 1.58

1.11 1.00 1.58 Naval, submarine N

4.00 10.53 1.60 0.95 1.00 0.70 0.63 1.00

a If e.g. a component has a base failure rate based on a naval sheltered environment and it requires adjustment for use in a naval undersea environment, then this is the factor that should be applied to the base failure rate for a correct adjustment (6.30/4.00).

Debray et al. (2004) presents a table (table 3.3) containing failure mode adjustment factors used in process safety management. Only Inaccessible for inspection and Exposed to mechanical damage are used in this thesis. It can be argued whether if the failure mode Corrosion should be used or not as the sea water is a source of corrosion. However, this is already accounted for in the environmental adjustment factor for marine application (Thies et al., 2009).

Table 3.3.: Failure mode adjustment factors π

from Debray et al. (2004) Adjustment factors

Failure rate influences Instruments Valves

Corrosion 1.07 1.14

Erosion 1.14 1.28

Fouling, plugging 1.07 1.14

Pulsating flow 1.14 1.07

Temperature extremes 1.07 1.07

Vibration 1.42 1.21

Corrosive atmosphere 1.21 1.21

Dirty atmosphere 1.07 1.07

High temperature/humidity 1.07 1.07

Exposed to mechanical damage 1.07 1.07

Inaccessible for inspection 1.07 1.07

The data source uncertainty factor, π

accounts for the uncertainty of the failure rate as it is often obtained from sources with generic failure rates or failure rates that are not based on the component that which is subject for adjustments. Hence, the data source uncertainty factor is supposed to account for the difference between the theoretical predicted failure rate and the actual failure rate. Thies (2012) refers to a study where predicted failure rates for electrical, mechanical and electronic equipment were compared to actual field data failure rates. The factor that differs the predicted failure rate from the actual failure rate was no greater than two in a majority of the cases in this study. In the light of this, most of the data source uncertainty factors in the adjustment calculations of this thesis uses a factor of two which is a rather crude assumption as it is very difficult to predict how this factor would agree with the actual failure rates of the L12 WEC.

Table 3.4 - 3.7 and 3.9 presents all adjustment calculations for the base failure rates in table 3.1 using table 3.2 - 3.3 combined with data source uncertainty factors and additional adjustment factors. An empty table cell can be regarded as having the value of one for the adjustment calculation.

The failure rate n = 1 in table 3.4 is procured by Cretu et al. (2016) using a reliability prediction model called Telcordia III. Telcordia III is used to statistically predict failure rates for electronic equipment and additional adjustments would therefore be excessive in this case.

The additional adjustment factor of three for the failure rate n = 2 in table 3.4 is highly

uncertain as this is a factor solely based on judgment from the author. The tall casing

is, albeit placed on the seabed and thus protected against direct harsh wave conditions, subjected to a bending strain originating from the surge motions of the buoy that causes horizontal forces (Ekergård et al., 2013; Ulvgård, 2017) and is illustrated in figure 3.1.

This, combined with the fact that the base failure rate related to this adjustment is considerably lower compared to the other obtained base failure rates for the casing, is the reason for this adjustment. The failure rate is originally already adjusted by Thies et al.

(2009) and the conceived additional adjustment factor is of a great magnitude and thus, failure mode and data source uncertainty factors are not included here.

Table 3.4.: Adjusted failure rates for the WEC casing n λ

π

π

π

γ

Resulting λ

1 0.8116 0.8116

2 0.0010 1.11 3

0.0033

3 0.0270 1.00 1.07

2 2

0.1200

4 0.0100 1.00 1.07

2 2

0.0458

5 0.0480 1.58 1.07

2 2

0.3470

6 0.0410 1.58 1.07

2 2

0.2970

a This factor is applied to compensate for the less robust casing of L12 com- pared to a Pelamis and the likely increased stress experienced by it.

b This base failure rate is obtained from (SINTEF industrial management, 2002) and thus, an additional factor of 2 is applied to compensate for the safety factor involved in this failure rate.

c This value has a small rounding or calculation error.

Figure 3.1.: Forces applied on the WEC casing by (Ekergård et al., 2013)

It is unclear what the original environment was for failure rate n = 2 in table 3.5 as the author did not have access to Reliability Information Analysis Center et al. (1995).

Numerically, the closest failure rate for the bearing in the previous version Reliability

Information Analysis Center et al. (1991) was based on a ground mobile environment and

thus, the environmental adjustment factor is set to be the conversion from a ground,

mobile environment to a naval, submarine environment. The author concluded that a

data source uncertainty factor would be excessive in this case as the failure rate already is of an extreme magnitude. The small errors in table 3.5 have no true effect on the final result in table 4.1. All the base failure rates in this table are procured from actual bearings and are therefore adjusted with an additional adjustment factor of 1.5 as the L12 WEC instead utilizes columns of rubber wheels for the bearing system.

Table 3.5.: Adjusted failure rates for the translator bearings (wheels)

n λ

π

π

π

γ

Resulting λ

1 0.0229 1.60 1.07

2 1.5

0.1260

2 1.9000 0.95 1.07

1.5

3.1000

3 0.0040 1.60 1.07

2 1.5

0.0225

4 0.0088 1.60 1.07

2 1.5

0.0480

5 0.0110 1.60 1.07

2 1.5

0.0600

6 0.1753 1.60 1.07

2 1.5

0.9630

7 0.2190 1.60 1.07

2 1.5

1.2000

8 0.0600 0.63 1.07

2 1.5

0.1300

9 0.1490 0.63 1.07

2 1.5

0.3220

10 0.0027 10.53 1.07

2 1.5

0.0980

11 0.0025 1.60 1.07

2 1.5

0.0137

12 0.0036 1.00 1.07

2 1.5

× 2

0.0250

a The base failure rate is based on bearings and not common wheels, hence a factor of 1.5 is applied to compensate for this.

b This base failure rate is obtained from (SINTEF industrial management,2002) and thus, an additional factor of 2 is applied to compensate for the safety factor involved in this failure rate.

c This value has a small rounding or calculation error.

Table 3.6.: Adjusted failure rates for the generator

n λ

π

π

π

γ

Resulting λ

1 1.5900 2 0.5

1.5900

2 0.0830 1.60 1.07

2 0.3080

3 0.0430 1.00 1.07

2 0.1030

4 0.0100 1.00 1.07

2 2

0.0460

5 0.0244 1.00 1.07

2 2

0.1120

6 0.0240 1.00 1.07

2 2

0.1100

7 0.0800 1.00 1.07

2 2

0.3640

8 0.0440 1.00 1.07

2 2

0.2060

9 0.0350 1.00 1.07

2 2

0.1590

10 0.0438 1.60 1.07

2 0.1590

11 0.1647 1.00 1.07

2 2

0.7540

a This base failure rate is assumed to include an excessive amount of failure modes in relation to the generator failure modes relevant to this thesis. Be- cause of this and the considerable high base failure rate compared the other obtained generator failure rates a factor of 0.5 is applied.

b This base failure rate is obtained from (SINTEF industrial management, 2002) and thus, an additional factor of 2 is applied to compensate for the safety factor involved in this failure rate.

c This factor is applied due to the fact that this failure rate originates from (SINTEF industrial management, 1997) and thus, an additional factor of 2 is applied to compensate for the safety factor involved in this failure rate.

d This value has a small rounding or calculation error.

Table 3.7.: Adjusted failure rates for the o-ring seal n λ

π

π

π

γ

Resulting λ

1 0.2190 1.5 1.07

1.7

0.6390

2 0.0570 1.5 1.07

1.7

0.1660

3 0.7800 1.5 1.07

1.7

2.2770

4 0.0028 2.52 1.07

2 0.0160

5 0.3700 2.52 1.07

1.7

1.8150

6 0.0700 2 0.1400

a The slightly lower data source uncertainty factor is due to the author’s esti- mation that this base failure rate is somewhat more applicable to the WEC.

b This value has a small rounding or calculation error.

3.1.4. Processing the data

There are more than one adjusted failure rate for each component which can be seen in tables 3.4 - 3.7 and 3.9. This warrants some form of processing of these failure rates to ob- tain a single value for each component. Smith (2005) describes two different approaches:

Arithmetic mean, which is calculated using equation 3.3, and Geometric mean, which is

calculated using equation 3.4. The amount of failure rates included in the calculation is

denoted n for both equations. The geometric mean is more preferable when the span is large between the maximum and minimum failure rate as the arithmetic mean tends to be closer to the maximum value in this case. The geometric mean should be used if the failure rates differ with a factor greater than ten according to Smith (2005). For exam- ple: consider the failure rates λ

= 0.001, λ

= 0.005 and λ

= 0.8. The arithmetic mean would be equal to 0.289 whereas the geometric mean would be equal to 0.016 and thus, yielding a more central and equitable value. The largest difference between the lowest and highest failure rate is found in table 3.4 and differs with a factor of approximately 246 while the smallest difference between the lowest and highest failure rate is found in table 3.6 and differs with a factor of approximately 35 and thus, the geometric mean should be used in this case. The final failure rates calculated using equation 3.4 is presented in table 4.1.

n

X

i

λ

n (3.3)

(

n

Y

i

λ

)

(3.4)

3.1.5. Failure rates in the power absorbing subsystem

The power absorbing subsystem contains the buoy, the shackle, the chain and the connec- tion line, as can be seen in figure 2.3. The reason why the failure rates in this subsystem have not yet been discussed is that the gathering of these failure rates have been done in a slightly different way, mostly due to scarce available failure data for the including components. To obtain these failure rates, the fatigue life of a component is assessed using an S-N curve where the magnitude of stress is ploted as a function of number of cycles to failure illustrated in figure 3.2. The number of cycles to failure (N

) can be obtained from an S-N curve using equation 3.5 which is explained by Det Norske Veritas (2011). The intercept parameter (a

) and the negative slope of the curve (m) for different curve parameters can be found within the tables of Det Norske Veritas (2011). Det Norske Veritas (2010) suggests one of these curve parameters for calculation of fatigue life for long term mooring shackles yielding a value for a

and m. The stress ranges (s) used in table 3.8 are merely suppositions and should not be interpreted as definitive values. The finite element method can be used for definitive stress values.

log(N

) = log(a

) − m · log(s) (3.5)

Figure 3.2.: S-N curve for steel wire ropes and chains by Det Norske Veritas (2010).

The failure rates presented in table 3.8 are calculated by assuming an average wave period of five seconds and using equation 3.6 to calculate the amount of cycles the WEC is performing during one year (N

) and equation 3.7 to calculate the failure rate for a specific number of cycles to failure (N

).

N

= Time in one year

Average wave period ≈ 6.31 × 10

(3.6)

λ

= 1

Ntf

NW EC

(3.7)

Table 3.8.: Calculated cycles to failure and failure rates according to equation 3.5.

Component log(a

) m s [MPa] Cycles N

λ

Shackle 17.146 5 60 1.803 · 10

0.034900

Chain 10.778 3 10 0.600 · 10

0.100000

Steel rope 14.53 4 10 339.625 · 10

0.000186

One base failure rate for the steel stranded rope could be found in Reliability Information

Analysis Center et al. (1991) in addition to the failure rate calculated from the S-N curve

as can be seen in table 3.1. Table 3.9 presents the adjustments for this component. The failure rate from the S-N curve has an environmental adjustment factor of one as Det Norske Veritas (2010) states that the S-N curves for the steel stranded ropes are based on the assumption that they are protected against the corrosive effect of the sea water. This is the case for the L12 WEC as the steel stranded rope is coated. The usual failure mode and data source uncertainty factors are also applied to remain consistent in relation to the adjustment calculations for the other components and also because of the considerably higher failure rate from Reliability Information Analysis Center et al. (1991). To adjust the failure rate for the shackle and for the chain would not make much sense as these are solely based on supposed stress levels and do not have a base failure rate reference as in the case for the steel stranded rope.

Table 3.9.: Adjusted failure rates for the steel stranded rope

λ

π

π

π

γ

Resulting λ

0.0013 16.58 1.07

2 0.04935

0.000186 1.00 1.07

2 0.00043

3.2. Unavailability

Availability is defined as “the ability of an item (under combined aspects of its reliability, maintainability, and maintenance support) to perform its required function at a stated instant of time or over a stated period of time (IEC 60050-191, 1990)” (Rausand, 2011).

Unavailability opposes availability and thus describes the inability to do the same. It is the proportion of time that which a component or system is non-operational so if e.g. a system has a mean unavailability of 0.001 after one year, then that system is non-operational for 0.001 × 8765 = 8.765 hours during that time. Unavailability and unreliability are closely related and both aspects are discussed in this thesis. However, the focus lies on unavailability as this is the property closest related to the cost incurred by the failures in the system.

3.2.1. Repair rate

Repair rate is an important parameter in the calculation of unavailability and describes not only the amount of time which is required for active repair of a component, but also the respond time. In other words, the repair rate represents the amount of time the system is not running due to a malfunction. It can therefore have a great impact on a WEC as it may be inaccessible for a large portion of the year due to harsh weather conditions. The repair rate is calculated using equation 3.8 where MTTR = Mean Time To Repair, i.e.

the downtime of the component. If e.g. a component is non-operational for ten days the

repair rate per year would be calculated as 1/(10/365) = 36.5. Therefore, a less amount

of time that the component is non-operational would result in a higher repair rate. The

impact of the repair rate on a component unavailability can be seen in figure 3.4.

µ = 1

M T T R (3.8)

3.2.2. Unavailability for constant failure rates

Unavailability is in this thesis regarded as constant over the component lifetime since constant failure rates are used. This means that all components in the system are regarded as good as new after a repair. However, this is a simplified view on the problem as failure rates in practice tend to vary in time, which will be further discussed in section 3.4.

Unavailability for constant failure rates can be calculated according to equation 3.9 and would yield the unavailability for either one of the including components of the WEC in this case. This equation can be simplified to equation 3.10 as the component lifetime t increases or as the sum of the failure rate and the repair rate increases. This can be defined, in addition to the previous stated definition, as the probability that the component is non-operational at time t (Rausand, 2011). In figure 3.3 a comparison between these two equations are presented illustrating the validity of equation 3.10 for different repair rates and assuming a component lifetime of t = 1 and a failure rate of λ = 0.1. The same case for varying failure rate is not presented as µ  λ for a vast majority of repairable components and systems. As implied in subsection 3.2.1, the highest amount of time to repair a component corresponds to the lowest repair rate, and the lowest repair rate used in this thesis is µ = 11.1 which can be seen in figure 4.1. Furthermore, the system lifetime of the WEC is assumed to be 20 years and thus, equation 3.10 is a very good approximation for a component unavailability in this case. Figure 3.4 illustrates the effect of the component lifetime for µ = 1, µ = 0, and µ = 24.3 where the latter represents the failure mode, generator short circuit, of the fault tree in figure 4.1. They are divided in three different graphs due to the large scale differences. The important thing to note here is that the component unavailability reaches its steady-state region early even for reasonably low repair rates. The steady-state region is reached in figure 3.3 when both line plots are fully merged. Equation 3.10 can be converted to equation 3.11 if one wishes to calculate the unavailability using the system uptime and downtime rather than using failure rate and repair rate.

Q(t) = λ

λ + µ (1 − e

) (3.9)

Q ≈ λ

λ + µ , (λ + µ)t >> 1 (3.10)

Q ≈ M T T R

M T T F + M T T R (3.11)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Repair rate

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Unavailability [Q]

Unavailability for different repair rates

Definitive unavailability Approximate unavailability

Figure 3.3.: Comparison of equation 3.9 and equation 3.10 for t = 1.

0 1 2 3 4 5

Time [years]

0.000 0.100 0.200

Unavailability [Q]

Q(t) for repair rate = 1, failure rate = 0.213

0 5 10 15 20

Time [years]

0.000 0.500 1.000

Unavailability [Q]

Q(t) for repair rate = 0, failure rate = 0.213

0 0.5 1 1.5 2

Time [years]

0.000 0.005 0.010

Unavailability [Q]

Q(t) for repair rate = 24.3, failure rate = 0.213

Figure 3.4.: Unavailability as a function of time for different repair rates.

3.2.3. Fault tree analysis (FTA)

The total unavailability of the WEC system is assessed in the software Isograph Reliability Workbench using the FTA module and it is within the help contents of this software that equations 3.1, 3.8 - 3.10 can be found. With an FTA, one can determine the probability or frequency for predetermined consequences in a system and find out the causes of these consequences. The FTA dates back to 1962 when a safety evaluation of a ballistic missile control system was performed by Bell Telephone Laboratories (Rausand, 2011).

Before an FTA can be performed, an FTD needs to be established. The FTD comprises

logic gates and events in a top-down logic order, i.e. the final failure state known as the top event is positioned at the top of the tree and branching down in various gates and events. The procedure is deductive which means that one starts by determining the final state and from there conceive the possible causes of this top event. The next step after determination of the top event would thereby be to determine the intermediate events that lead directly to the top event and then determine the events that lead to these intermediate events closest to the top event and so on. When the FTD is complete, the initial events are assigned with failure and repair data to enable the FTA. The complete FTA for the L12 WEC unavailability is illustrated in figure 4.1. The assigned failure rates (FR) are collected from table 4.1 and the assigned repair rates (RR) are collected and calculated from table 3.14. The only gate type existing within this fault tree is the OR-gate as the initial failures are independent. For the OR-gate it is sufficient if either one of the inputs to the gate is true, while for e.g. the AND-gate all inputs must be true simultaneously for the output to be true. The three intermidiate OR-gates before the top event can be represented by the subsystem division in figure 2.3 where the failure event buoy breaks free is related to the power absorbing subsystem, generator flooded is related to the structural subsystem and generator failure is related to the PTO subsystem. Hence, all the basic events in the fault tree have corresponding components that can be located within the three different subsystems in figure 2.3.

The eighth initial event in the fault tree named end stop spring failure is part of the FTD but not part of the FTA. It is a potential failure mode but would not in practice be considered as severe as the other failure modes. The parallel structure of the OR-gates in the fault tree would however cause the severity of this failure mode to be equal to the other failure modes should it be included in the FTA. As the end stop springs are an important part of the WEC, the solution is thus to include the corresponding failure mode in the FTD as an undeveloped event. An undeveloped event in the FTD is defined as “an event that is not examined further because information is unavailable or because its consequence is insignificant” (Rausand, 2011). The different available gates and initial events in Isograph can be viewed in appendix B.

Isograph performs the statistical calculations for the FTA in figure 4.1 according to equa- tion 3.13 for three input events and equation 3.14 for two input events. The general form for n events is represented by equation 3.12 where Q(E

+ E

+ . . . + E

) equals the un- availability Q for n events E ( Isograph Inc, 2015). These equations can also be converted to equation 3.15. Note that they are only valid for OR-gates as this is the only gate type used in this thesis.

Q(E

+ E

+ . . . + E

) =

n

X

i=1

Q(E

) −

n−1

X

i=1 n

X

j=i+1



Q(E

)Q(E

)

+ . . . (−1)

Q(E

)Q(E

) . . . Q(E

)

(3.12)

Q(E

+ E

+ E

) = Q(E

) + Q(E

) + Q(E

)

− Q(E

∩ E

) − Q(E

∩ E

)

− Q(E

∩ E

) + Q(E

∩ E

∩ E

) (3.13)

Q(E

+ E

) = Q(E

) + Q(E

) − Q(E

∩ E

) (3.14)

Q(E

+ E

+ ...E

) = 1 −

n

Y

i=1

(1 − Q(E

)) (3.15)

Equation 3.16 and 3.17 can be found within the help contents of Isograph where TDT is the total system downtime and T is the system lifetime.

TDT =

Z T 0

Q(t)dt (3.16)

Mean unavailability = Q

= TDT

T (3.17)

3.2.4. Sensitivity analysis for the uncertainty

Rausand (2011) defines sensitivity analysis as an “analysis that examines how the results of a calculation or model vary as individual assumptions are changed (AS/NZS 4360, 1995)”. When performing a sensitivity analysis for an FTA one monitors the change of the top event as a result of an input parameter change. It is a procedure to somewhat assess the uncertainty of the results. There are two types of uncertainty that can generally be defined as aleatory uncertainty, which is related to randomness and natural variation, and epistemic uncertainty, which is related to lack of knowledge. For the failure rates it is mainly the epistemic uncertainty that has a great impact on the results in this thesis. The sensitivity analysis of the result is conducted in MATLAB 2017B and Isograph Reliability Workbench and is presented in section 4.3. The parameter changes in this case are the final failure rates, the data source uncertainty factor π

, and MTTR.

3.3. Unreliability and other analysis methods

Reliability is defined as “the ability of an item to perform a required function, under given

environmental and operational conditions and for a stated period of time” (Rausand,

2011). Unreliability opposes reliability and thus describes the inability to do the same.

When regarding the quantitative aspect of unreliability, it is the probability that an item cannot perform a required function, i.e. the probability that a component or system has experienced its first failure at time t. The reliability function R(t) for constant failure rates, which yields the probability of success, is calculated according to equation 3.18 (Thies, 2012) and the unreliability is therefore calculated according to equation 3.19.

When comparing equation 3.9 with equation 3.19 it is easy to see that unreliability equals unavailability when µ = 0 which is the case for non-repairable components. An example of this case can be seen in figure 3.4. Furthermore, the reliability can be integrated to yield mean time to fail which is proven by equation 3.20.

R(t) = e

(3.18)

F (t) = 1 − e

(3.19)

Z ∞ 0

R(t)dt = 1

λ = MTTF (3.20)

As failure rates are regarded as constant in this thesis, the amount of time between failures is exponentially distributed. The number of failures that is occurring to time t is therefore following a homogeneous Poisson process. The unreliability function (equation 3.19) is also called the distribution function ( Thies, 2012) and by taking the derivative of this function one can obtain the probability density function for a component or system lifetime t. This derivation is seen in equation 3.21. As an example, the probability density function for the translator bearings (wheels) is illustrated in figure 3.5 with the same assigned failure rate as in the fault tree (figure 4.1).

f (t) = dF (t)

dt = λe

(3.21)

Equation 3.22 proves that the failure rate can be obtained by dividing the probability density function (equation 3.21) with the reliability function (equation 3.18):

f (t)

R(t) = λe

e

= λ (3.22)

3.3.1. Unreliability of the L12 WEC

The unreliability of the system is, like the unavailability, assessed using the fault tree mod-

ule in the Isograph Reliability Workbench software. The complete FTA for the L12 WEC

unreliability is illustrated in figure 4.2 and has the same statistical procedure (equation

3.13 and 3.14 or equation 3.15) but calculated using unreliability (F) instead of unavail- ability (Q).

0 2 4 6 8 10 12 14 16 18 20

Time[years]

0 0.1 0.2 0.3 0.4 0.5 0.6

pdf

Probability density function (translator bearings)

Figure 3.5.: Probability density function for the translator bearings (wheels).

3.3.2. Frequency and CFI

Two other perspectives of the results in the fault tree is viewing the frequency or the conditional failure intensity (CFI). These can be viewed in appendix C in figures C.3 - C.4. The frequency w can be calculated according to equation 3.23 and yields the component failure frequency, i.e. the number of actual times a component fails when the unavailability is taken into account. If e.g. a component has a failure rate of λ = 3 per year and an unavailability of Q= 0.7, the component cannot fail with an average of three times per year as it will be unavailable 70% of the time and will thus have a component failure frequency of 3(1 − 0.7) = 0.9.

The CFI assumes that the component has survived to the time t. It can in figure C.4 be regarded as the failure rates of the gates.

w = λ(1 − Q) (3.23)

3.4. Non-constant failure rates

A more realistic view on the reliability problem is to regard the failure rates as non-

constant over the lifetime of a component or a system. The characteristics of non-constant

failure rates can be described with a so called bathtub curve. The bathtub curve can be