Support at the choice of solutions to the phase of preliminary design based

INTERNATIONALMechanical Engineering and Technology (IJMET), ISSN 0976 –
International Journal of JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 1, January - February (2013) © IAEME
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 1, January- February (2013), pp. 150-162 IJMET
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2012): 3.8071 (Calculated by GISI)
www.jifactor.com ©IAEME

SUPPORT AT THE CHOICE OF SOLUTIONS TO THE PHASE OF
PRELIMINARY DESIGN BASED ON RELIABILITY ANALYSIS
« APPLICATION TO GEARED-DRIVE AND DIRECT-DRIVE
WIND TURBINES »

H. Zaghar*; M. Sallaou; A. Chaâba
Department Mechanics & Structures
ENSAM, Moulay Ismail University B.P. 15290 EL Mansour, Meknes-Morocco

ABSTRACT

In the context of industrial competitiveness, taking into account the process design
throughout the product life cycle is inevitable, from the expression of the need to recycle, the
capitalization and knowledge management increasingly a target much sought after companies
because of increased knowledge. Indeed, during the approval phase and use studies and
scientific researches make have generated knowledge especially that concerning
the reliability of system components. Methods of the knowledge structuring in mechanical
design, based on functional approaches are analyzed and compared. We propose an energy
approach based on the Law of System Completeness, which decomposes a system specific
entity.
This article provides help in the choice of solutions to the phase of preliminary design
between direct-drive and geared drive wind turbine concepts, based an analytical reliability
methods. Reliability data from field surveys will be used in this study in particular the failure
rate. First, we propose a model of reliability of both existing and modified concepts, using a
decomposition of systems at a detailed level, then qualification will be carried out of the
global model is done with respect to the need expressed by the user, and which is the reason
for its existence. Such a tool is intended to help designers make decisions about the choices
inherent in comparison between these concepts.

KEYWORDS:
Preliminary design; qualification; geared and direct-drive wind turbines; reliability analysis;
quality factor.

150

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –

1. INTRODUCTION AND CONTEXT

Due of the competitive environment in electric power generation, the industry will
prefer the most productive and economic concepts of WTs, and reliable. The estimation of
these criteria will help the designer to choose among several possible configurations.
However, long-term cost analysis, including operation and maintenance (O&M), as well as
the first investment costs, would result in a better choice of WT concept. This is only possible
if the analysis included a comprehensive study of the reliability of different technologies.
This Article refers to introduce the analysis of the reliability of the preliminary design phase,
using the Markov modeling. It is expected that the method introduced in this paper will assist
in the comparison between different WT technologies from a reliability point of view. The
qualification of the global model will be conducted based on a share of an assessment
criterion that is fairly related to the need expressed by the user, and represents the reason for
its existence, and also the total cost the system.
The approach we seek to implement to provide assistance to the designer to conduct design
and exploitation of knowledge related to the product for the evaluation of different concepts
(architectures and components). This is done based on a preliminary design approach based on
the use of knowledge already capitalized [1], [2], which is based on the needs analysis and
definition of functional specifications, to generate and analyze the knowledge necessary
to result in the generation and prioritization of valid solution.
For this we propose to study geared-drive and direct-drive WT which their characteristics are
illustrated in (Table 1).
Table 1.Characteristics of the selected WT. [3] [4]

Vestas V39/500 Enercon E40
Technology Geared-drive Direct-drive
Power (kW) 500 500
Rotor diameter (m) 39 40
Rotor speed (tr/mn) 30 12-34
Control technology Pitch-regulated, Pitch-regulated,
active stall variable speed
Turbine years 804 900
considered

2. MARKOV MODELING
It is common to divide systems, from a reliability point of view, into two categories:
mission orientated and repairable. For mission-orientated systems, the first failure is the most
interesting, the probability to be in the operation state, is the most appropriate parameter to
calculate. On the other hand, for repairable systems, the availability, what the probability to
find the system in an operation state, is the most appropriate index to calculate.
A WT can be considered as a repairable system and accepting that the system operates during
his useful life, the Markov process is the best tool to study its reliability.
The failure rate function of almost all systems obeys from the bath-tube curve (Figure 1),
suggested that it is reasonable to consider that most WT components lie in the bottom of this
curve, i.e. that they have a fixed failure rate, this hypothesis to define these transition rate as
the inverse of the average duration of operation and repair. [5]

151


Burn in
λ(t)
Wear Out
Useful life

Time

Figure 1.The Bath tub curve

According to the reliability theory [6] failure and repair rate can be defined respectively as:
λ: Number of failures in a given period of time divided by total period of time the component
was operated.
1
λ= (1)
MTTF

µ : Number of repairs in a given period of time divided by total period of time the component
was being repaired.
1
µ=
MTTR (2)

In the Markov model, all states of system performance are considered. Using the transition
rates between these states could lead to the probability of residence in each state. In the
simplest form, a model with two states: running Ok and failed Ko could be considered. In
this study a simple two-state model is assumed.
A system consisting of a mechanical part and other electrical for example, could be classified
into two main categories, mechanics represented by M, and electric represented by E. So the
system could be treated as a two component system.
It is assumed that after electrical or mechanical failure, the system will be disconnected, and
failure in other parts will not occur, so the state which shows both electrical and mechanical
failure is omitted. The transition rate between state 1 and state 2 in (Figure 2) is the
aggregation of all the electrical components considered in series from the reliability point of
view. The same procedure is considered for mechanical components.

E Ko
λe λm E Ok
E Ok 2
3 M Ok 1 M Ko
M Ok
µe µm

Figure 2.Markov model of a two-component system.

Since both the mechanical and electrical problems could result in a system fault, these two
components are considered in series from the reliability point of view, so their failure and
repair rates can be combined as:

λ=λ M +λ E (3)

152


λ µ M µ E ( λ M +λ E )
µ= = (4)
 λi  µ M λ E +µ E λ M
∑ 
i  µi 

Using the frequency balance approach [6], the three-state model of (Figure 2) could be
summarized to a two-state model shown in (Figure 3).

λ
1 OK KO 2
µ
Figure 3.Markov model reduces.

To evaluate the model parameters of the reduced system reliability, and applying this method
[6] to (Figure 2) to obtain the probability, p(n), of any state, n, yields:

P(1)(λ M +λ E )=P(2)µ E +P(3)µ M
P (2 )µ E = P (1 )λ E
P (3 )µ M = P (1 )λ M
P(1)+P(2)+P(3)=1 (5)

State 1 in (Figure 3) is equivalent to state 1 in (Figure 2) and state 2 in (Figure 3) can be
deduced from aggregation of states 2 and 3 in (Figure 2), so:

µMµE
PO k (1)=P(1)= (6)
λ E µ M +λ M µ E +µ M µ E

λ E µ M +λ M µ E +λ M λ E
PKo (2)=P(2)+P(3)= (7)
λ E µ M +λ M µ E +µ M µ E

Since state 1 in both figures 2 and 3 are equivalent, their frequencies are the same, that is:

f O k (1)= f(1) ⇒ PO k (1)λ=P (1)(λ E +λ M ) (8)

Interpretation of (Figure 3) shows that the probability of the Ok state, which is identical to the
steady-state availability for this system, could be calculated as the function of this model
parameter as below:
µ
PO k ( 1 ) = (9)
λ+µ

3. DEFINITION OF COMPONENTS

The first step in a reliability study of a system is the structural and organic
decomposition into different entities constituting the system. The accuracy of such a study of
reliability depends on the depth and level of decomposition.

153


System

Entity 1 Entity 2 Entity 3

Entity 11 Entity 12 Entity 13

Figure 4.Work breakdown structures.

The (Figure 5) shows a decomposition of a geared-drive WT. Although other components are
significant in WT reliability, this paper concentrates on the following components: blade,
gearbox, generator, converter, pitch and yaw systems. The main difference between the
two concepts is gearbox, so a direct-drive WT has fewer components, the main reason for
using this concept is to eliminate the failures the gearboxes and the effects of downtime. A
comparison of reliability between these two concepts can verify this result. There is
no standard decomposition for the components of WT, but they are similar.

Level 0
Site Wind Turbine Grid
Level 1

Level 2 Processing unit power Electrical unit Control unit Support unit

Blade Low shaft Gearbox High shaft Yaw Pitch Vane

Generator Converter Cable Nacelle Tower Foundation

Figure 5.Work breakdown structures for geared-drive WT

4. ENERGY VISION

The logical organization can be useful to limit confusion or differences of
description. The law of completeness of the parties, as defined by the TRIZ method, to
distinguish for a given system, four main elements essential to achieving the required
functions [7], this law states that the realization of a function comes from the transformation
of energy (Converter), this energy is then transmitted (Transmitter), an operator then performs
the action (Operator). The law of completeness of the parties believes that a system is more
sophisticated (optimal) if it contains a control function provided by a controller component.
The control can be one, two, or all of the components.
The components must be positioned relative to a reference, which may be external to the
system to a global reference (level 0), or internal to the system to a local reference to a given
system level.

154


Input Converter C Action
Transmitter T Operator O
Energy

Controller C/C

Figure 6.Law of the completeness party [8]

As the pitch and yaw components are assumed to optimize the electrical energy production of
WT, and avoid stopping operation in unfavorable weather conditions. The function of the
pitch system in normal wind condition is to optimize the WT performance, by controlling
the pitch angle β; also the function of the yaw system is to adjust the nacelle position taking
account of the position of the WT in a wind farm, depending on the prevailing wind direction.

Input Action
Blade C Gearbox T Generator C Converter O
energy

Pitch & Yaw C/C
Figure 7.Law of the completeness party for geared WT

For the controller C/C, it is to control operation of the processing unit, depending on the speed
and direction of the wind. It is broken down into component acquisition to "take wind speed"
and a command to "stop the transmission of mechanical energy of rotation" of the processing
unit. The realization of all functions of the WT passes mainly by the transit of three functional
types of flows: [8]
As wind energy systems are complex, some techniques such as the block diagrams decompose
the system into components. These methods can be used to allocate reliability, by translating
the objective reliability of the overall system into specific objectives for components that are
easier to control.
To model the reliability of a system must analyze its performance by identifying the different
interactions between the main components. For this we use diagrams based on the energy
flows that show each component as a separate block, and these blocks and their interactions
can be combined either in series, parallel or series-parallel.
The control is performed on all components of the WT for optimizing its performance;
however, after a small failure component pitch or yaw in normal weather conditions, the WT
system is able to continue functioning in a situation non-optimal, this assumption is valid until
the failure mode affects only the pitch and/or yaw. So in this case these two components can
be considered as blocks in parallel with the other components considered, if another
component in series is affected when these two components must be connected in series. The
aggregation of the six components in series derives a simple Markov model with two states
Ok and Ko.

4.1 Geared-drive concept
The components blade, gearbox, generator and converter, can be combined in a single
transformation unit block called U with equivalent failure and repair rates, the main path
consists of U is the only path to success system independently of the parallel channels created
by the pitch and orientation systems.

155


Pitch

U

Orientation

Figure 8.Reliability block diagram of geared-drive WT

Based on diagrams of reliability established a three-component system could be considered.
As such a system to "n" components, 2n states show all possible performance states, these
states could be categorized in three states Ok, Degraded, and Ko. It is evident that only if
these three components of system are in their Ok state would result in system Ok state too.
As long as the pitch or yaw system, or both, are in their Ko state only, the WT could continue
its non-optimal performance, which is named Degraded state here. The order of the
components will respectively (blade, gearbox, generator, converter, pitch, and yaw). Any
dysfunction in one of the four components of U lead state Ko of the system WT regardless of
the state of the pitch and yaw.

4.2 Direct-drive concept
The same procedure could be conducted for direct-drive concept WT. In this type of WTs,
there is no gearbox, but the power electronic converter is fully rated, which is shown with
different block symbol, and a synchronous multi-pole generator is used, which could be
wound rotor or permanent magnet excited.
The aggregation of components in the main path could be named UD, which shows direct
transformation unit. The three-components consist of UD, pitch and yaw, would have eight-
state diagram, which could be reduced to a three-state model.
The first interpretation is that, because of a reduced number of components resulting from the
absence of the gearbox, the direct-drive concept has a better availability index than the geared
generator concept. But account must be taken of the dependency on other factors, including
generator and power electronic converter reliabilities in the two concepts. The gearbox and
partially rated converter combination should be compared with the fully rated converter in the
two concepts, as should the synchronous multi-pole generator be compared with doubly fed
induction generator.

5. CALCULATION OF TRANSITION PROBABILITIES

5.1 Modeling
For all other components of WT, a two-state model, similar to Figure 3, could be constructed
with equivalent of failure and repair rates, calculated based on their components and the type
of interconnection between these components, e.g. series or parallel. Data from the failure and
repair rates of the two WTs considered and various components were collected from European
surveys.
LWK data include failure and repair rates of major components during the study period. It
is then possible to calculate the failure and repair rates of each concept. Reliability data for
both WTs chosen are based on data from LWK, and are listed in (Table 2).

156


Table 2.Reliability data of systems considered [9], [10]

Vestas 39/500 Enercon E40
λ(f/year µ(rep./year) λ(f/year µ(rep./year)
) )
Blade 0,162 265,3 0,240 135
Gearbox 0,168 269,2 - -
Generator 0,085 170,7 0,354 143,7
Converter 0,254 508,1 0,317 430,7
Pitch 0,095 559,9 0,292 512
Yaw 0,097 436,7 0,116 348,3

The Markov graph derived from the eight states for a geared-drive WT is shown below:

Ok µU
OK U
OK P (1)
λP OK O µo
µp
λo

Degraded µp
OK U µo OK U OK U
KO P (2) K KO P (3) OK P (4)
OK O λo KO O λP KO O

µU λU
µU λU λU
Ko
KO U KO U
KO U µU
KO P (6) OK P (8)
KO P (7)
OK O KO O
KO O

λU
KO U
OK P (5)
OK O

Figure 9.State–space diagram of geared-drive WT.

5.2 Calculation procedure
If components are independent, system state probabilities can be found by the product of unit
state probabilities. If components are not independent then:
− Write an equation for each of n system states using frequency balance.
− Any n-1 equations together with can be solved to find state probabilities.
n
− ∑ Pi = 1
i= 1

Equations arranged in matrix form: The state probabilities can be obtained by solving BP = C
Where B: matrix obtained from the transpose of transition rate matrix R by replacing the
elements of an arbitrarily selected row k by 1s, R: matrix of transition rates such that its
element rij =λ ij

157


λij: constant transition rate from state i to j
P: column vector whose ith term Pi is the steady–state probability of the system being in state
i
C: column vector with kth element equal to one and other elements set to zero.
Transition matrix R:

-(λ o +λ p +λ u ) λP 0 λo λu 0 0 0
µp -(λo +λu +µo ) λo 0 0 λu 0 0
0 µo -(λ u +µo +µ p ) µp 0 0 λu 0
µo 0 λP -(µo +λp +λu ) 0 0 0 λu
µu 0 0 0 -µ u 0 0 0
0 µu 0 0 0 -µ u 0 0
0 0 µu 0 0 0 -µ u 0
0 0 0 λu 0 0 0 -λ u

• Calculating the probability of the operating state Ok:
We will calculate the determinant ∆ of the matrix B:
Calculating the probability of the operating state P୓୩ :
We put 1 in the first line of column 8 and all the other they are allowed to 0 because it
corresponds to the operating state:
∆ Ok
P O k = P1 = (10)
∆

• Calculating the probability of the degraded state:
We calculate the ∆degraded , we put 1 in rows 2, 3, 4 of the column 8 and all the others allowed it
to 0 because they correspond to the states (2, 3, 4), which are appropriate to the degraded
state.
Pd eg rad ed = P 2 + P3 + P 4
∆ degraded
Pdegraded = (11)
∆

• Calculating the probability of the failure state PKo :
There are two ways to calculate:
Or through the system is stochastic where:
PK o = 1 -PO k -Pd e g ra d e d
Or by the conventional method, the calculating determinant ∆ Ko :
We put 1 in the states which correspond to the failure states of where:

P K o = P5 + P6 + P 7 + P8
∆ Ko
PK o = (12)
∆

158


6. QUALIFICATION OF SOLUTIONS

The qualification criteria of a system are: the performance (criteria), availability and
cost. These three criteria form the main components of the quality factor of a
system defined by ISO: [11]

C r .availability
IQ= (13)
C Total

The identification of performance is achieved in Phase functional analysis, it requires an
analysis of external environments, they are expressed by the functional specification calls
"assessment criteria" level expresses the limit values. Cost is all costs incurred, depending on
the level, this cost can include the costs of use and destruction [15]. The estimation of the
performance and cost requires the development of models of system components and external
environments. The reliability of a system can be calculated by determining that of each
component that constitutes it.

6.1 The assessment criteria
The criterion for assessing the service function (converting energy aerodynamics into
electrical energy) is the energy produced per year (Epa). The power aerodynamics available
in a site per unit area, where:
1
Par =V.Pd = ρV 3 (14)
2

The site can be characterized by the frequency distribution of wind speeds over a year. It is
customary to represent this distribution by the Weibull distribution. It is a function with two
parameters k and c, the probability density function over a year, where:
K
K -1   V 
 K   V   - 
f(V )=   .  .e   C  (15)
 C   C 

k: shape parameter that characterizes the distribution of the wind, and c: scale parameter
characterizing the velocity. The available energy per year per unit area on the site is:

8760 ρ Vf 3
E pa = . . ∫ V .f(V).C p .ηg .A.dV (16)
1000 2 Vi

6.2 The cost
The cost models proposed in this study cover aspects of manufacturing and design of wind
systems. The models used are outcome studies [12], [13]. The cost of wind system is equal to
the sum of unit costs of the components that constitute it.
nc
CTE = ∑ Cci (17)
i=1
nc: number of components (for this study nc = 6 for geared-drive, 5 to direct).
Cci: Cost of component i in $.

159


• Blade
Cost 3P =3×3,1225.R 2,879 (18)

• Gearbox three stages planetary
C ost M =16,45.P 1,249 (19)

• Generator for geared-drive WT
Cost G =65.P (20)

• Generator for direct-drive WT
Cost G =219,33.P (21)

• Converter
Cost C =79.P (22)

• Pitch
Cost P =2,28(0,2106.D 2,6578 ) (23)

• Yaw
Cost o =2(0,0339.D 2,964 ) (24)

P: machine rating, D: diameter of the rotor.

7. SYNTHESES OF RESULTS

The use of failure rates and repair provided by (Table 2) of the two selected turbines
used to calculate transition probabilities of the two models derived from different concepts
considered.

Table 3.Transition probabilities of the two WTs studied.

POK PDegraded PKO

Vestas 39/500 0,91 0,0004 0,0896
Enercon E40 0,889 0,0008 0,1102

The geared-drive WT Vestas 39/500 is available as direct-drive WT Enercon E40 for this
power range.
The probability that these two concepts are in a degraded state is very small compared to other
states. And changes to the architecture of interaction between components of WTs are
required to increase the number of states in the state degraded in favor of the state Ko, and
therefore increase further system availability.

160


Table 4.Different results of the two WTs studied.
.Different

Vestas 39/500 Enercon E40
Blade($) 48489 52155
Gearbox($)
($) 38653 -
Generator ($) 32500 109665
Converter($)
($) 39500 39500
Pitch($) 8131 8697
Yaw($) 3525 3800
Total($) 170798 213817
Epa(Kwh) 7787 8192
Availability
lability 0,9104 0,8898

0.05
0.04
0.03
0.02
0.01
0
IQ
Vestas V39/500 0.0415
Enercon E40 0.0341

Figure 10.Quality factor of the two WTs considered
Quality

According to (Figure 10), the Vestas V39/500 has a better quality indicator than Enercon E40,
,
and although the latter has fewer components. Then remarkable values exceeded the
availability and quality factor for the geared-drive concept, can be a tendency of choice for
geared drive
this type of concept.

8. CONCLUSION

This study supports such a choice of solutions in this important phase in the life cycle of a
product by an analysis based on the criteria of greater weight in determining the quality of the
alysis
systems. The quality index calculated in this paper allows excluding invalid solutions
therefore not send tests on physical prototypes as solutions that are more able to succeed with
succe
the least modifications.
It is not possible to conclude definitively whether the direct-drive or geared-drive WT are the
drive
most reliable, but the proposed method of analysis shows a way to compare the two concepts
reliability point of view. The analysis indicates the importance of data reliability of
analy
components in determining the overall reliability.

161


Based on these data and models of reliability, the availability analysis of these concepts could
be made to improve the decisions, and thus help to the choice of solutions for this design
phase in order to improve future designs.
The reliability analysis of WT stresses the importance of gathering and processing reliability
data from wind farms around the world. As more reliability field data become available, more
accurate judgments could be made about different concepts, design improvements and
maintenance strategies.
The approach to the design of the gearbox was changed in recent years, after the technical
standard AGMA 6006 is introduced to the gearbox, which should improve the reliability
indices for the future of geared-drive WT. [15]

BIBLIOGRAPHIES

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préliminaire », CFM 2009, 02-03/08/2009, Marseille, France.
[3] Arabian-Hoseynabadi. H, Tavner. P.J. Oraee. H, “Reliability comparison of direct-drive and
geared drive wind turbine concepts”. Wind Energ. 2010; 13:62–73 c 2009 John Wiley & Sons,
Ltd. DOI: 10.1002/we.
[4] Vestas, GE and Enercon Data sheets. Available from manufacturer’s websites:
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Problem Solving", CRC Press, 2000.
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[9] LWK Schleswig-Holstein, Germany. (Accessed 29 June 2009): http://www.lwksh.de/cms
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[11] Spinnler. G, «Conception des machines Principes et applications». Presses Polytechniques,
Université Remands: 2001
[12] Harrison. R. Jenkins. G. “Cost Modeling of Horizontal Axis Wind Turbines”, (Phase2),
ETSU W/34/00170/REP, University of Sunderland, 1994.
[13] Fingersh. L, Hand. M, Laxson. A. Technical Report NREL/TP-500-40566 December 2006.
[14] ANSI/AGMA/AWEA 6006-A03,”Standard for Design and specification of gearboxes for
wind turbines”; Published by the American National Standards Institute.
[15] Zaghar. H, Sallaou. M, Chaaba. A, “Preliminary design support by integrating a reliability
analysis for wind turbine”, 2012,4,233-240 doi:10.4236/epe.2012. 44032 Published Online July
2012 (http:/www.SciRP.org/journal/epe)
[16] Haider M. Husen , Laith O. Maheemed and Prof. D.S. Chavan, “Enhancement Of Power
Quality In Grid-Connected Doubly Fed Wind Turbines Induction Generator” International
Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 1, 2012, pp. 182 - 196,
Published by IAEME.

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