A Consistent Rule for Selecting Roots in Cubic Equations of State

Pergamon Microelectron. Reliab., Vol. 35, Nos 9-10, pp. 1285-1307, 1995

Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved

0026-2714/95 $9.50+.00

RELIABILITY ANALYSIS IN WIND TURBINE ENGINEERING

A.J. Seebregts 1, L.W.M.M. Rademakers 1, and B.A. van den Horn 1

Abstract Wind turbines are being designed in accordance with deterministic design rules. As wind turbines increase in size and power, these rules may not be adequate to ascertain a safe and well balanced design. Wind turbine industry can take advantage of the safety and reliability practices in e.g. aerospace, nuclear and offshore industry. These practices include System Reliability (such as FMECA, Event Sequence Analysis and Fault Tree Analysis) and Structural Reliability methods. The approach to introduce Probabilistic Safety Assessment (PSA) which incorporates these reliability methods into wind turbine engineering will be described. By means of two recent case studies, the applicability, benefits, and limitations of these methods will be illustrated.

1 .Introduction

Wind turbines are being designed in accordance with deterministic design

rules, e.g. [Van Hulle, 1991, IEC, 1992, Stare et al., 1991, RISO, 1992,

Germanisher Lloyd, 1993]. These rules concern the design of main

components e.g. blades, hub, and tower, and the design of safety

systems. As wind turbines increase in size and power, these rules may

not be adequate to ascertain a safe and well balanced design. They

neither facilitate the quantification of the degree of conservatism in the

applied safety margins nor explicitly address the reliability and safety of

the wind turbine. While in the past, small wind turbines could be

developed with trial and error, this approach seems not adequate for the

development of large wind turbines. A failure of a large wind turbine may

have severe consequences. The approach of trial and error is also not

adequate for mass produced wind turbines. Numerous design

modifications realized after installation appear to be very expensive for

Netherlands Energy Research Foundation ECN, P.O. Box 1, NL- 1755 ZG Petten, The Netherlands

1285

1286 A.J. Seebregts et at.

manufacturers. For the development of large or mass produced wind

turbines, analytical and systematic tools to improve safety and reliability

become more and more important. Even with the additional costs of a

PSA, it is expected that the cost benefit ratio of such an analytical and

systematical approach is better than the traditional trial and error

approach.

Furthermore, the local and national authorities ask more and more for an

evaluation of the safety and risks of industrial activities. In the

Netherlands for instance, this evaluation should include a quantitative

judgement of safety and risk. Criteria for safety and risks are defined in

[VROM, 1990]. For the siting of new wind turbine parks, the safety and

risk should be evaluated also, as part of a so called 'Environmental Impact

Report' [MER Commission, 1993]. Moreover, on a competitive market,

utilities will easier choose wind turbine designs for which a safety and

risk analysis has been performed, as an advantage compared to those for

which no such analyses have been performed.

Thus, the application of PSA seems inevitable to assess the risk of wind

turbines or wind turbine parks. In the past, several reliability analyses

have been performed for wind turbines with a limited scope. Applied

methods were FMEA [USDOE, 1979, Bollmeier, 1981], Fault Trees

[Petersen et al., 1990], and environmental risk assessment (conditional

upon blade failure) [Montgomerie, 1982, Turner, 1986]. The PSA

methodology outlined here integrates these and other methods to enable

a more complete assessment of a wind turbine design.

2. Development phases for introduction of psa

To introduce the PSA methods into wind turbine engineering,

following development phases have been or are to be carried out:

the

Reliability analysis 1287

Phase 1 : Development of Methodology

The feasibility of reliability based methods in wind turbine engineering has

recently been demonstrated in the project 'PSA of Wind Turbines'

[Rademakers et al., 1992, 1993], carried out under a joint contract of

NOVEM (Netherlands Agency for Energy and Environment) and the CEC

DG-XII (Commission of the European Communities DG XII for Science,

Research, and Development), see section 3.1.

Phase 2: Verification of Methodology

ECN is presently performing a project called 'Reliability Analysis and

Design Review of the NEWECS-45'. The NEWECS-45 wind turbine is the

only 1 MW machine installed in the Netherlands. It is equipped with two

lightweight glass fibre reinforced plastic rotor blades, an integrated drive

train and a soft tower design. Furthermore, the machine has some unique

control features, namely fast blade pitch adjustment and variable rotor

speed. The machine is in operation since 1985. During the first period of

operation, a measurement program has been performed, so the system

performance and characteristics are known. Furthermore, operating

experience is documented in log books and failure registration forms over

the full period. The availability, and thus the actual energy production,

appears to stay far behind the preliminary estimates, due to technical

troubles. One objective of the study is to increase the availability, to

assess the reliability of important components, and to reduce the

maintenance costs. The other objective is to refine and improve the

methodology for PSA of wind turbines. This project will be finished in

1994.

Phase 3: Technology Transfer

The groups that can benefit from the PSA methods are designers and

manufactures of wind turbines, utilities, and certifying bodies. In wind

turbine industry, the knowledge about these methods is now mostly

1288 A.J. Seebregts et al.

present at research institutes. The best way to transfer knowledge is by

means of case studies tailored to the specific interests and needs of the

different groups. In the Netherlands, case studies are planned on the

short term. ECN has recently performed an analysis of an American wind

turbine, the AOC 15/50 [Carter et el., 1993], see section 3.2.

Phase 4: Development of Guidelines, Standards, and Criteria

ECN wil l take initiatives to introduce the PSA methods in the national and

international wind turbine standards. These methods should be used to

further underpin the currently used safety factors, to detail the

requirements for wind turbine safety, and the design of safety systems.

The development of guidelines, standards, and criteria will be done in

close cooperation with other international research institutes and

manufacturers.

3. Methodology and examples

3.1 LW 15/75 Case Study

The methodology has been applied on a mass produced, medium size

wind turbine, the LAGERWEY LW 15/75 design [Rademakers et el.,

1993], see Fig. 1. It describes how to assess the safety, reliability, and

availability in a more integrated and quantitative way, very much

structured analogously to PSAs for Nuclear Power Plants [IAEA, 1992].

The case study has focused on safety and availability mainly. The extent

to which the methodology can be implemented in the current design

practices on the short term and the areas that require further research

have also been indicated. The subsequent tasks and are briefly discussed

below.

Task 1: Description of System Design and Operation

Before starting a detailed analysis of a wind turbine, it is necessary for

the reliability analyst(s) to become familiar with the specific wind turbine.

Reliabil i ty analysis 1289

, 101 I t l

[. Rotor

2. Blades

3. Gcazbox

4. Generator

5. Yaw ruolor

6. Wind vane 7. Nacelle 8. Step 9. Tower

tO. Worm geart~x of yaw drive

Figure 1- Main components of the LW 15/75

This should result in a detailed description of the system design and

operation, including maintenance, test and inspection procedures, and

design modifications. State Diagrams and Event Trees have been used to

explain the control and safety actions.

The Lagerwey LW 15/75 wind turbine is equipped with an upwind, two

bladed rotor that has a diameter of 15.6 m. The rated electrical power of

75 kW is produced with an asynchronous generator at wind speeds

between 3 and 30 m/s. The power control is realized by pitch control of

the blades towards feather position in combination with a variable rotor

speed. This power control method requires a fairly complex electrical


system, which is tuned with the passive blade pitch control mechanism.

It is recommended by the manufacturer to shut-down the turbine

manually at wind speeds over 30 m/s by yawing the nacelle such that the

rotor is at 150 degrees towards the wind direction. The nacelle is placed

on a steel tower of a length that can be either 24, 30 or 36 meter. In

order to ensure safe operation the wind turbine is equipped with two

independent and diverse safety systems, viz. a passive blade pitching

mechanism, and a yaw mechanism.

Generally, the control systems of the LW 15/75 have to keep the wind

turbine within its design limits during normal operation and to ensure

electrical energy is generated and supplied to the grid in an efficient

manner. In case of a failure or in case of abnormal external conditions,

the control systems in combination with the safety systems have also to

keep the turbine within its design envelope to prevent damage or unsafe

operation. For a clear description of the wind turbine operation, a State

Diagram has been made. A distinction has been made between

Operational (O), Transitional (T), and Damaged (D) Modes. The State

Diagram enables a clear presentation for the relationships between the

different wind turbines modes (or states), see Fig. 2.

The safety systems of the LW 15/75 will be activated in case of the

following events: an overspeed situation, excessive vibration, overload of

the generator, loss of load, too high inverter temperature, and abnormal

cable twist which have all been considered in the case study. In case of a

normal shut-down (T4), the nacelle will be yawed out of the wind; the

yaw motor is activated by the grid. In case of an emergency shut-down

(TS), the yaw motor is powered directly by the generator. This happens

for instance during grid failure (S5).

Task 2: FMECA

From the FMECA, a set of critical component failures and initiating events

has been derived. This survey has been used to check the measures the


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l Figure 2: State Diagram of the LW 15/75.

manufacturer has taken to prevent these failures and events from

happening or to reduce the likelihood. Since Lagerwey has a long term ex-

perience with this type of turbine, most of the preventive measures

conceived during the FMECA had already been realized, either as a design

modification, or by changing the maintenance procedures.

Task 3: Event Sequence Analysis and System Modelling

The event sequence analysis involved safety actions leading to

unavailability of the wind turbine. The analysis has focused on the


operational modes 'Idling', 02, and 'Energy Production', O3, and on the

transitional modes 'Normal Shutdown', T4, and 'Emergency Shutdown',

T5. These modes are the most important with respect to the

unavailability and safety of the wind turbines. For the event sequence

analysis and system modelling, techniques have been used like event

trees, see Fig. 3, and fault trees, respectively.

From the qualitative analyses, unbalances were found in the design of

safety systems. Excessive vibration had the lowest level of defence, viz.

a single failure.

Task 4: Data Collection and Parameter Estimation

Maintenance and failure data have been derived partially from

maintenance sheets, audits, and logbooks. In addition, generic data

contained in reliability data handbooks, European, and American wind

turbine databases, and engineering judgment have been used to finally

arrive at the parameters required for the quantification process (see next

task) and to compare the specific LW 15/75 failure data with. The

operational data have been derived from logbooks, measurements, and

function tests. The data of 11 turbines have been collected and analyzed,

representing operational experience of about 26 years. Limitations

showed up in the current practices of data collection. Not all types of

data required for reliability purposes have been recorded. Despite these

shortcomings, both useful qualitative and quantitative information has

been derived from the available operational experience. In general, the

component failure frequencies of the LW 15/75 compared favourably to

the reported generic wind turbine data.

Task 5: System Reliability Quantification

The fault trees and event trees developed in Task 3 have been quantified

with the failure rates, initiating event frequencies, and downtimes,

estimated in Task 4. Estimates have been obtained of safety system


unavailabilities and wind turbine unavailability. Components contributing

to the safety system unavailabilities have been ranked according to their

importance in order to identify possibly weak points in the LW 15/75

design, to highlight unbalances, and to indicate effective areas for

improvement. The end states of the event trees have been quantified by

multiplying the probabilities of the successive events, see Table 1 and

Fig. 3.

Table 1: Initiating Events and Frequencies of End States

Initiating Event Frequency [/yr]

Frequency End State [/yr]

Shutdown Not Shutdown Not Shutdown No Damage Partial Damage Severe Damage

$10verspeed 0.65 6.5E-1

$2 Excessive Vibration 0.95 9.3E-1

$3 Inverter Temperature 0.038 3.8E-2

$4 Inverter Control 0.23 2.2E-1

$5 Grid Failures 3.12 2.98

$6 Generator Overload 0.42 4.0E-1

Total 5.408 5.21

3.2E-3

2.3E-2

4.7E-4 4.2E-6

1.1E-2 9.6E-5

1.4E-1 1.2E-3

2.3E-2 2.1E-4

0.17 0.028

Yaw System

Pitch Control System

End State:

$5. Grid failures (3.12/yr)

StlCC~k~

I (0.956)

failm~

(0.9911)

I (0.044)

(0.0089)

Figure 3: S5 event tree quantification

S-ND (3.0 ~)

NS-PD (0.14/yr.)

NS.SD (0.0012/yr)


The results show an estimated severe damage frequency of 1 per 35

wind turbine operating years. Partial damage with no safety implications

occurs approximately once in 6 years. Successful shut-downs occur 5

times per year. Especially failure of the detection units (e.g. tachometer

and vibration detection) contribute to the damage frequencies. This is

because there is no redundancy in these components.

Task 6: Structural Reliability

The possible application of probabilistic techniques for the assessment of

the structural integrity of wind turbine components has been investigated.

For the structural reliability analysis, four levels can be identified [de

Kraker et al.]:

• Level O: A deterministic analysis based on fixed data, a deterministic

(high) load, a deterministic (low) strength, and an 'overall-safety' factor.

• Level I: Intended for routine design use. For each stochastic variable, a

certain unfavourable value is chosen, the so-called characteristic value,

usually based on a 5% confidence limit. In addition, a set of partial safety

factors is applied, which establish the margin between load and strength

for the various cases to be considered. This approach is yet commonly

used in wind engineering.

• Level I1: An approximative analysis based on the so-called 'f irst

order/second moment' principle. Briefly, what it amounts to is that only

the mean value and the standard deviation of each stochastic variable are

taken into account, linearization being applied when necessary. Level II

approximations are used to provide a basis for Level I procedures. Level II

studies aim to underpin the partial safety factor of a Level I analysis as

soundly as possible. Moreover, they are used for special and important

structures for which an above-normal standard of reliability is considered

essential, e.g. offshore structures.

• Level II1: Comprises complete and exact analyses using analytical or

numerical procedures or Monte Carlo simulations. Level III analyses


generally demand too much computational effort to be practical for

dealing with major problems due to the large number of stochastic

variables to be considered. The scope for applying them exists mainly in

verifying and complementing Level II approximations.

To demonstrate structural reliability applications on wind turbines, fatigue

failure of the tower foot has been selected. Normally, only the stochastic

nature of the wind speed is incorporated in a deterministic fatigue

analysis. A probabilistic analysis provides a manner to deal with the

stochastic behaviour of the most important problem variables more

realistically than with the use of prescribed safety factors. The procedure

for a probabilistic fatigue analysis of the tower foot is based on

[Karadeniz et al., 1984, Ang and Tang, 19841. A reliability function Z

must be selected in a deterministic way as to establish that Z < 0

corresponds to fatigue failure and Z >_ 0 to non-failure, and the limit state

is given by Z = 0. Z is related to the Miner sum D and Z = 1 - D has

been chosen. After the distributions are selected and the reliability

function is defined, the failure integral must be calculated. The most

accurate computational procedure for the probabilistic fatigue analysis is

presented in Fig. 4.

load structure material properties (wind) (wind turbine) (fatigue)

~ b a s ~ l e s

D

Figure 4: Determination D and the fatigue failure probability.


When the influence of the uncertainties in load, geometry and material

properties are considered, it is possible to make a frequency table for D.

This can be achieved by the combination of every possible value of the

basic variables in the calculation of D. Subsequently, a distribution of D

has to be selected and the statistical parameters have to be determined.

The probability of fatigue failure can be expressed as

and can be determined for the IogC-value associated wi th a line in the

WShler-diagram. A normal distribution is selected for IogC in

correspondence wi th off-shore industry. However, it is practically not

possible to evaluate the frequency table for D, because the load

calculations wi th SWIFT [Winkelaar, 1992] and PHATAS-II [Lindenburg,

1992] are too t ime-consuming. Therefore, the failure integral (1) is

approximated wi th the Mean Value Approach (MVA), which is a simple

application of a Level II method.

In a general formulation for MVA, the reliability function is a funct ion of

the problem variables including a number of stochastic variables here

given the designation X1, )(2 ..... X,. The stochastic variables are assumed

to be uncorrelated, mutually independent and normally distributed wi th

known mean values/1,- and standard deviations a;. When Z is linearized in

the mean values of the stochastic variables, the mean value #z and the

standard deviation az of Z can then be approximated by the expressions

~/Z =Z(~ /1 ,/J2, • • " ,/Jn ) = 1 -D (Pl ,P2, • • • ,P,) = 1 -Po (2)

az = az (p l ,gz . . . . . p,)ai i .1

The partial derivatives in (3) cannot be determined analytically and are


therefore numerically approached

az ~ Z(/zl ,#2,... ,p;+o;, . . . ,p , ) -#z = .bZ~ (4)

In this particular case, the partial derivatives in (3) can be approximated

by _ a z ~ D(IJ1 , I J 2 , . . . , I J i + o ' i , . . . , P , ) - P o = A D i (5)

a Xi a i (>,

The standard deviation of Z is then given by

Oz = i ;-' (6)

and the reliability index B can be written as

= __Pz = 1 - P o

az I ; (71 (AD;)2

=1

Now, the failure

derived

probability of the welding in the tower foot can be

P~ = q)N(-B ) (8)

where (I)N is the standard normal cumulative distribution function. For

positive # it appears that the larger p, the larger the safety. The

importance factors a7 are defined by the squares of the direction cosines

of # and can be expressed as: = (~Oi)2 (9}

var Z

They are a measure for the percentage of variability due to each random

variable.


A selection has been made of wind parameters, wind turbine parameters,

and fatigue parameters which are considered to be stochastical instead of

fixed and deterministic. Table 2 lists the parameter means and standard

deviations, which have been derived from measurements or based on

engineering judgment.

Tabel 2: Stochastic variables and results

i Designation xl Pi ai (a/p) i

1 Turbulence alU~o 19.28 % 1 % 0.052 intensity

2 1st tower f,~., 0.97 Hz 0.049 Hz 0.050 e i g e n f r e q u e n c y

3 maximum lift C~,,= 1.60 0.04 0.024 coefficient

4 torsion spring Mp,=h,,= 730 Nm 50 Nm 0.068

5 load level Model 1.0 0.125 0.125 uncertainties

6 wall thickness t,,= 10 mm 0.5 mm 0.050

7 constant of S-N logo 12.511 0.207 0.017 c u r v e

8 annual average U,,, 7.28 m/s 0.728 m/s 0.100 wind speed

i Po + L~9i EO, =

1 0.2225 0.0009

2 0.1818 0.0001

3 O.1770 0.0003

4 0.2081 0.0002

5 0.2748 0.0067

6 0.2235 0.0009

7 0.3109 0.0139

8 0.3124 0.0142

Po = 0.1930

Pz = 0.8070

a z = 0.1929

/9 = 4.18

Pc = 1.4E-5

The importance factors are displayed in Fig. 5.

It appeared that the fatigue coefficient IogC and the average annual wind

speed Uo., are by far the most important sources of variability, followed


by the model uncertainties.

o/r.~,, 2.3% model uncertainties

log C

37.3%

18.0%

4

_-_ _~_ _ _ " - ~ _ |

~ 0.6% M~m~,(4) 0.7% C,._. (3)

38.3% 0.3% f,,,, (2)

u= 2.s% t . (l)

Figure 5: Importance factors obtained with MVA

Summarizing, MVA in addition to the currently used deterministic design

rules gives qualitative insights in the uncertainties of the fatigue damage

calculations. MVA appeared to have limitations, but a further application

of probabilistic design techniques is strongly recommended. The speed of

the load calculation codes and the probabilistic techniques need to be

improved for actual implementation in the design and certification

process.

However, the process of identifying components, failure modes, and a list

of uncertain parameters for each combination is expected to be more

troublesome and time-consuming than the actual calculational procedure.

The first emphasis should therefore be on this initial step, because it also

affects the results of the current deterministic structural analyses. In

addition, Monte Carlo procedures, in particular Latin Hypercube Sampling

(LHS) [Imam, 1984], is worthwhile investigating. Although perhaps time-

consuming, this procedure has advantages compared to Level II methods

like MVA, viz.:

- parameters can be varied simultaneously and correlations can be

HR 35 :9 /10 -G


taken into account;

- PF can be derived directly and is not dependent of a (non-robust)

definition of Z; and

- no assumptions are needed on the normality of parameter or PF

distributions.

For more details, see [Rademakers, 1993] or [Van den Horn, 1993].

Task 7: Interpretation and Discussions of the Results

It has been concluded that there are unbalances in the safety systems

design. Excessive vibration of the nacelle had the lowest level of defence

(only the yaw system) and contributed the most to the severe damage

frequency. If safety is to be improved, modifications can best be focused

on the improvement of the detection units. A strong improvement of the

wind turbine availability can be made by, under certain conditions,

automatic resetting, which causes the downtimes to decrease. The

presented estimates for the safety system unavailabilities, the wind

turbine unavailability, and the damage frequencies should be considered

as approximate values because of the data and modelling uncertainties.

The results are based on assumptions which depend on certain external

conditions, as given by the site of the wind turbine, and operating

procedures. These assumptions may be different for other sites. The

event tree and fault tree models can be easily recalculated for those sites,

if site specific data is available. Sensitivity analyses have been performed

to show the robustness of the conclusions.

The system reliability analysis results are valid for the so-called 'useful

life' period where failures are random and component failure rates are

more or less constant. Reported gross failures (from other than the 1 1

units) which have resulted in hazardous situations appeared to be caused

not by random failures during the useful life period, but were mostly the

result of unexpected situations not foreseen in the design stage.

Especially, activation of the yaw mechanism at high wind speeds was

Reliability analysis, 1301

found to be critical. In early designs, this situation led to excessive

vibrations and high loads. The phenomena causing these effects were not

known in the design phase. A load and operation monitoring programme

together with the analysis of more load situations are strongly

recommended to gain more insights in the dynamic behaviour of the

turbine and to reduce the occurrence of these failures. To improve the

safety at high wind speeds, it is recommended to enhance the yaw

mechanism or to add an extra safety device. Otherwise, it is

recommended to install an anemometer that causes automatic shut-down

at lower wind speed.

3.2 AOC 15/50 Case Study

Atlantic Orient Corporation (AOC, USA) is presently developing the AOC

15/50 wind turbine. This turbine is derived from an existing mass

produced wind turbine, the ENERTECH 44. Based on experienced failures

of this design, AOC has conceived design modifications to enhance the

structural integrity, to improve the reliability and to reduce the

maintenance costs. This update led to some unique and innovative

features, viz. an integrated gearbox design, the tip brake design, and the

procedures for normal and emergency shut down. Since the AOC 15/50

is at the very end of the design phase and at the beginning of the testing

phase, ECN has performed a qualitative reliability analysis in close

co-operation with personnel of AOC [Carter et al., 1993]. In addition, the

safety systems have been assessed qualitatively. Tasks 1, 2, and 3 have

been performed. The major part of the analysis consisted of an FMECA of

the improved and innovative components and systems. The transitional

modes, e.g. start up, normal shut down, and emergency shut down, have

been analyzed with event trees to determine possible critical items in

these event sequences. The analyses are yet not finished so only partly

results can be given here. The FMECA:

- estimated the likelihood, and thus the criticality, of failure modes

1302 A. J. Seebregts et al.

of innovative components rather high. Reliability demonstration

testing and prototype testing must prove that the actual likelihood

of a failure mode is lower than the first estimate; and

indicated that no active protection system had to be installed to

prevent excessive cable twist. This is required by e.g. the Dutch

certification criteria [Stam et al., 1991]. From the reported failures

of the similar ENERTECH 44 design, it appeared that the likelihood

of cable twist is very low, which could be underpinned from

reliability demonstration testing of the power cable. Furthermore,

no effect with a high severity could be conceived. The criticality of

this failure mode was thus rather low.

lead to unsafe

In addition to the FMECA, the event tree analyses:

- did not identify any single failure that could

operation of the turbine; and

- completed the list with load situations

situations presented in the current

appeared to be too generic for this specific turbine.

and showed that load

deterministic standards

4. Uncertainties and acceptance

in areas where new techniques are introduced, people must be convinced

of the added value of the new methodology. E.g., for Psa for nuclear

power plants [hirschberg, 1992], there is sometimes criticism on the

usefulness of these techniques because of the uncertainties. For wind

turbine application, similar uncertainties exist. The most important

insights provided by a psa are engineering ones, i.e., those related to the

identification of potential design weaknesses. In many cases, once such

insights have been obtained the value of the predicted frequencies

involved becomes less important. Such 'relative' results of psas are

usually not undermined by the numerical uncertainties involved.

Moreover, it should be noted that one of the strengths of psa is to show

the limitations and uncertainties that still exist. One rarely observes this in


the standard deterministic analyses. In addition, the systematic nature of

the process already leads to valuable insights and a better understanding

of the design just by doing the exercise. Of course, the (numerical)

results of psas should also be used with caution both in the design,

regulatory and certification process. Probabilistic analyses applied for

regulatory and certification purposes have been introduced in other indus-

tries after a period of familiarization and obtaining experience. For wind

turbine industry, requirements should also not be hastened, and the

emphasis should first be on the qualitative analyses.

5. Conclusions and recommendations

based on the experiences of the Iw 15/75 and aoc 15/50 case studies,

the following conclusions can be drawn on the methodology:

feasibility

the short term benefits of system reliability analysis (thorough system

description, state diagrams, fmeca, event tree and fault tree analysis)

have been proven. Probabilistic analyses constitute a necessary

supplement to the existing deterministic analyses and design rules in

order to achieve a more balanced and safe design. Qualitative analysis

methods can and should be applied immediately.

Limitations

in addition to deterministic analyses, probabilistic analysis techniques are

not the only means to further enhance safety and reliability. There is still

a fundamental lack of knowledge of physical phenomena in wind turbine

engineering that may cause hazardous situations, e.g. excessive

vibrations. Even when these phenomena are known, quite often they

cannot be adequately modelled with the current computer codes. It is

therefore highly recommended to perform analyses of additional load

situations during the design stage and to use measurement, test and


monitoring programmes during the early operational phase of a wind

turbine. The results of these programmes can be used for updating the

design process.

Data collection and analysis

in view of limitations in the current practices of data collection, priority

must be given to a systematic collection of data, not only concerning

maintenance and failure data (component failures, downtimes, failure

causes, etc.) but also concerning operational data (external conditions,

starts and stops, etc.). Computerized data collection systems are

recommended to prevent these time-consuming, partly manual efforts.

Qualitative insights and trends can be derived very easily. On the longer

term, reliability data for quantitative analyses (e.g. optimizing

maintenance procedures) can be obtained. Each manufacturer must set

up his own data collection system, preferably computerized. Such a data

base can play an important role in the planning of maintenance and for

the improvement of reliability and availability of the considered wind

turbine. A central data base with accidents and incidents must be

maintained to assess the safety and risks for the environment, to adjust

the rules for siting, and to sharpen the current design rules.

Certification

on a short term, the certification institutes can especially benefit from

qualitative analysis methods. The systematic approach and presentation,

e.g. state diagrams and event trees enable a direct insight in the

operation of the considered wind turbine. Fmecas performed by the

designers provide a survey of critical events which the certification

institutes can review during the certification process. At this moment, the

critical events are often conceived by the certification institutes

themselves in a more or less unstructured way. They should therefore ask

at least for the results of an fmeca. In addition, quantification of the


safety system unavailabilities will be necessary for evaluating safety

concepts that differ from the deterministic safety concept as described in

the dutch certification criteria.

Safe operation of a wind turbine is not only determined by its design and

manufacturing process but also by the operating, maintenance and

inspection procedures. These procedures are considered in the

certification process but only in a limited fashion. During the operating

phase of a wind turbine, no check is made to see if these procedures are

applied correctly and to see if the wind turbine is in a 'healthy' state. In

the certification process, more attention should be paid to these

procedures, preferably by asking for checklists and using reliability

analysis techniques.

Structural reliability

although the demonstrated mva for the structural reliability analysis of

mechanical components appeared to have limitations, a further

application of probabilistic design techniques is strongly recommended.

The application of the mva in addition to the currently used deterministic

design rules gives qualitative insights in the uncertainties of the fatigue

damage calculations. Fruitful discussions in wind turbine industry which

must lead to a wider acceptance and introduction of probabilistic design

techniques can be generated only if these techniques are wider applied,

parallel to the improvement of the methodology and the identification and

quantification of uncertain parameters. In the near future, more advanced

probabilistic techniques should be used to further underpin or adjust the

currently used safety factors.

References Ang, A.H.S., Tang, W.H.: Probability Concepts in Engineering Planning and Design, Vo/ I1: Decision, Risk en Reliability. J. Wiley & Sons, 1984.

Bollmeier, W.S.: Applying Reliability Analysis to Small Wind Systems. Proc. 5th Biennal Wind Energy Conf. and Workshop, Washington,

1306

October 5-7, 1981.

A. J, Seebregts eta/ .

Carter, J., Johnson, B., Rademakers, L., and Sherwin, B.: Failure Modes and Effects Analysis of the AOC 15/50 Wind Turbine. Proc. AWEA Wind- power '93 Conf. San Fransisco, 13-16 July 1993.

Germanisher Lloyd: Rules and Regulations, I V - Non Marine Technology, Part 1 Wind Energy: Regulation for the Certification of Wind Energy Conversion Systems. 1993.

Hirschberg, S.: Prospects of Probabilistic Safety Assessment. Nuclear Safety, Vol. 33, No. 3, 1992.

IAEA: Procedures for Conducting Probabilistic Safety Assessments of Nuclear Power Plants (Level 1). Safety Series No. 50-P-4, Vienna, 1992.

IEC Standard: Safety of Wind Turbine Generator Systems. Draft document, IEC TC 88, 1992.

Imam, R.L, M.J. Shortencarier: A Fortran 77 Program arts User's Guide for the Generation of Latin Hypercube and Random Samples for Use with Computer Models. NUREG/CR-3624, March 1984.

Karadeniz, H., van Manen, S., Vrouwenvelder, A.: Probabilistic Reliability Analysis for the Fatigue Limit State of OH-shore Structures. Bulletin Tech- nique du Bureau Veritas, July 1984.

de Kraker, A., Tichler, J., Vrouwenvelder, A.: Safety, Reliability and Service Life of Structures. TNO Building and Metal Research.

Lindenburg, C. and Hendriks, H.B.: PHATAS-II: Program for Horizontal Axis Wind Turbine Analysis and Simulation version II, User's Manual. ECN-C--92-020, April 1992.

MER Commission: Advies voor Richtlijnen voor de Inhoud van het Milieu- effectrapport Windmolenpark Groningen. (In Dutch), Commission for Environmental Impact Reporting, March 29, 1993, The Netherlands.

Montgomerie, B.: Horizontal Axis Wind Turbine Blade Failure, Blade Fragment Six Degrees of Freedom Trajectory, Site Risk Level Prediction. Proc. Int. Symp. on Wind Energy Systems, Stockholm, September 21-24, 1982.

Petersen, K.E., et al.: Reliability of Smaller Wind Turbines. (in Danish) RISO-M-2872, May 1990.

Reliability unulvsis 1307

Rademakers, L. et al: Reliability Analysis Methods for Wind Turbines; Task 1 of the Project: Probabilistic Safety Assessment for Wind Turbines. ECN-C--92-018, June 1992.

Rademakers, L. et al: Methodology for Probabilistic Safety Assessments of Wind Turbines - Demonstrated by a Case Study of the LAGERWEY LW 15/'75 Design. ECN-C--93-010, March 1993.

RISO: Technisk Grundlag for Typegodkendelse og Certificering af Vindmoller i Danmark. (In Danish), July 1992.

Stam, W.J. et al: Regulations for the Type-certification of Wind Turbines: Technical Criteria. ECN-91--001, February 1991.

Turner, D.M.: A Monte Carlo Method for Determining the Risk Presented by Wind Turbine Blade Failures. Wind Engineering, Vol. 11, No. 1, 1986.

USDOE: MOD-2 Failure Mode and Effect Analysis. NASA CR-159632, July 1979.

VROM: Premises for Risk ManagemenC Annex to the Dutch National Environmental Policy Plan "to Choose or to Lose'. Ministery of Housing, Physical Planning and Environment (VROM), The Netherlands, VROM 00197/4-90, 1990.

Van den Horn, B.A, Rademakers, L.: Reliability Analysis for the Load- Carrying Parts of Horizontal Axis Wind Turbines. Proc. 6th Int. Conf. on Structural Safety and Reliability, Innsbruck, 9-13 August 1993.

Van Hulle, J.L. (ed.): Recommendations for a European Wind Turbine Design Standard: Load Cases and Loads. CEC Contract Number XVIII7030/ETDI8912, Final Report, April 1991.

Winkelaar, D.: SWIFT: Program for Three-Dimensional Wind Simulation; Part 1: Model Description and Program Verification. ECN-R--92-013, December 1992.

A Consistent Rule for Selecting Roots in Cubic Equations of State

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