Condition Monitoring of Wind Turbines by Electric Signature Analysis

Bjarke Nordentoft Madsen
Condition Monitoring of Wind
Turbines by Electric Signature
Analysis
A cost effective alternative or a redundant
option for geared wind turbines.
Master’s Thesis, October 2011

Condition Monitoring of Wind Turbines by Electric Signature Analysis
Author:
Bjarke Nordentoft Madsen
Supervisor:
Bogi Bech Jensen
A cost effective alternative or a redundant option for geared wind turbines.
Department of Electrical Engineering
Centre for Electric Technology (CET)
Technical University of Denmark
Elektrovej 325
DK-2800 Kgs. Lyngby
Denmark
www.elektro.dtu.dk/cet
Tel: (+45) 45 25 35 00
Fax: (+45) 45 88 61 11
E-mail: cet@elektro.dtu.dk
Release date:
Class:
Edition:
Comments:
Rights:
October 17 th , 2011
1 (public)
1. edition
This report is a part of the requirements to achieve Master of Science
in Engineering (MSc) at Technical University of Denmark. This report
represents 30 ECTS points.
© Bjarke Nordentoft Madsen, 2011

ABSTRACT
During the last decade wind energy has become an important part of the electricity production
throughout the world. This is mainly due to advances in wind turbine technology, and government
decisions to encourage renewable power as an alternative to conventional fossil-fuelled
power generation. As the amount of wind energy increases, the reliability of the wind turbine
becomes crucial. A low reliability would result in an unstable energy source with poor economical
performance. Monitoring the condition of vital components is a key element to keep a
high reliability. At the moment this is mainly done using a condition monitoring system that
monitors changes in the mechanical vibrations. Recent research has suggested that electrical
signature analysis could be a cost effective alternative to vibration monitoring.
In this thesis, the use of electrical signature analysis is discussed. Should it be considered as an
alternative or is it more appropriate as a redundant system. The survey is based on a geared
wind turbine with a squirrel cage induction generator.
To support or reject the proposed alternative, the characteristic and identification of typical
drive train faults are investigated. If used as an alternative it should be possible to detect the
same range of faults. From the obtained results it is considered that electrical signature analysis
cannot detect the same range of mechanical faults. This is mainly due to lack of multiple sensors
and thus multiple monitoring signals.
The steady characteristic of the generator during a fault is investigated using a 2D finite element
model. Furthermore a time-harmonic simulation of the model has been conducted to investigate
the sensitivity and stability of the electrical signal. It has been shown that conditions such as
fault location, core saturation and pole number will affect the electrical signal.
In order to verify the theoretically made observations, a small scale laboratory test has been
carried out. The test demonstrates that it is possible to detect a fault at the expected harmonic
frequency.
Based on the results and observations made during this project, it is considered that electrical
signature analysis is not appropriate as an alternative for geared wind turbines. This is based on
the physical constraints in the range of fault identification, and that the electrical signal is influenced
by conditions that will challenge the signal processing. It is however considered that electrical
monitoring might have advantages in future gearless wind turbines with few mechanical
parts.

ACKNOWLEDGEMENTS
This thesis has not been made in cooperation with a company. However, during the project sessions
with engineers from Dong Energy and Brüel & Kjær Vibro has been a huge inspiration to
the outcome of this thesis. I would like to thank Bjarne Uhre Knudsen at Dong energy for sharing
his knowledge about condition monitoring and for the guided tour in the Siemens SWT3.6-
120 wind turbine at Avedøre Holme. I would also like to give my gratitude to the personal at
Brüel & Kjær Vibro in Nærum, who gave me an insight in their condition monitoring system,
VIBRO, and who was kind enough to listen to a short presentation of my project.
Finally, I would like to thank my supervisor, Bogi Bech Jensen, for his encouragement, knowledge
and support during this project.
Bjarke Nordentoft Madsen
i

CONTENTS
Chapter 1 Introduction to Condition Monitoring ................................................. 1
ii
1.1 The Need for Condition Monitoring ............................................................................... 1
1.2 Identifying Critical Components ..................................................................................... 5
1.3 Condition Monitoring Systems ..................................................................................... 12
1.4 Commercially available CMS....................................................................................... 15
1.5 Chapter Conclusion ..................................................................................................... 16
Chapter 2 Thesis Objectives .............................................................................. 19
2.1 Problem Statement ...................................................................................................... 19
2.2 Hypothesis ................................................................................................................... 20
2.3 Work by Others ............................................................................................................ 25
2.4 Solution Method ........................................................................................................... 25
2.5 Limitations / Assumptions ............................................................................................ 26
Chapter 3 The Reference Wind Turbine ............................................................ 27
3.1 Introduction .................................................................................................................. 27
3.2 Bearings ....................................................................................................................... 27
3.3 Generator ..................................................................................................................... 30
Chapter 4 Drive Train Failure Characteristics ................................................... 33
4.1 Bearing Failures .......................................................................................................... 33
4.2 Rotor Displacement (Eccentricity) ............................................................................... 37
4.3 Air Gap Length ............................................................................................................ 43
4.4 Chapter Conclusion ..................................................................................................... 44
Chapter 5 Generator Characteristics ................................................................. 47
5.1 Introduction .................................................................................................................. 47
5.2 Analytical Analysis ....................................................................................................... 47
5.3 Finite Element Analysis (FEA) ..................................................................................... 53

5.4 Relative Change and Displacement Angle .................................................................. 58
5.5 Saturation Effect .......................................................................................................... 59
5.6 Linearity ....................................................................................................................... 61
5.7 Chapter Conclusion ..................................................................................................... 61
Chapter 6 Time-Transient Simulation ................................................................. 63
6.1 Introduction .................................................................................................................. 63
6.2 Model Modifications and Simulation Settings .............................................................. 64
6.3 Current Spectrum Analysis at No-load ........................................................................ 66
6.4 Chapter Conclusion ..................................................................................................... 70
Chapter 7 Small Scale Test ................................................................................. 71
7.1 Introduction .................................................................................................................. 71
7.2 Test Setup ................................................................................................................... 71
7.3 Test Results................................................................................................................. 72
7.4 Chapter Conclusion ..................................................................................................... 75
Chapter 8 Conclusion .......................................................................................... 77
Chapter 9 Future Work and Perspective ............................................................ 79
References ............................................................................................................. 81
Appendix A Design of Induction Generators ........................................................ 83
A.1 Introduction .................................................................................................................. 83
A.2 Step 1 – Winding Layout and Number of Slots ........................................................... 84
A.3 Step 2 - Determinations of the Main Dimensions ........................................................ 86
A.4 Step 3 - Design of Stator Slots and Windings ............................................................. 89
A.5 Step 4 - Design of Rotor Slots and Windings .............................................................. 90
A.6 Step 5 – Equivalent Parameter Estimation ................................................................. 92
A.7 Step 5 – Performance Characteristic .......................................................................... 97
A.8 Step 6 – Iteration process ........................................................................................... 99
A.9 Step 7 – Verification of Design .................................................................................. 101
Appendix B Pictures from Small-Scale Test ....................................................... 105
Appendix C CD-ROM ............................................................................................ 107
iii

Chapter 1
Introduction to Condition Monitoring
This chapter gives a brief introduction to the concept of condition monitoring of wind turbines
from an economical and maintenance perspective. The recent literature within the field is reviewed
and used to discuss some of the important topics. This should give a fundamental understanding
before the technical concept of Electrical Signature Analysis (ESA) is elaborated.
1.1 The Need for Condition Monitoring
The amount of wind energy in the European and international electrical grids is rapidly increasing.
The target for the year 2020, set by the European Wind Energy Association, is that 14-17%
of the EU‟s electricity should come from wind turbines - depending on the total demand. By the
year 2030 the target is 26-35% with almost 40% coming from offshore wind farms. This large
amount of wind energy in the electrical system and the fact that wind turbines are located in
remote and offshore locations requires a high level of reliability. A low level of reliability
would result in an unstable energy source. This would affect the stability of the grid and the
economic performance due to unexpected operation and maintenance cost and loss in energy
production. [1]
Both the size and the locations of wind turbines has led to new maintenance challenges that are
unique compared to traditional power producing systems:
No walk around maintenance: Unlike traditionally power producing systems (coal,
diesel, etc.), daily or weekly walk around maintenance checks are not feasible due
to difficulty and expense of physically reaching the turbines.
High maintenance cost: Maintenance cost are high due to the cost of travelling expenses
to remote locations and the need for cranes or helicopters large enough to
lift spare parts to the nacelle.
Higher probability of faults: The mechanical elements like the gearbox, shaft and
generator are designed with low weight in mind to reduce the overall weight of the
nacelle. This leans towards a higher probability of stress related failures.
In addition, the constant changing loads and highly variable operating conditions create high
mechanical stress on the wind turbines.
These factors can lead to an increased operation & maintenance (O&M) cost and a loss in the
energy production. This affects the economic performance of the wind turbine or wind farm.
1

Chapter 1 - Introduction to Condition Monitoring
1.1.1 Cost of Energy (COE)
A commonly used terminology for evaluating the economic performance of a power producing
system is the cost of energy. The cost of energy is a metric used to compare the cost of different
electricity production options. From reference [3] a simplified expression is adopted from the
US for estimating the cost of energy (COE) for a wind turbine system.
2
ICC FCRO&M COE
E
Where ICC is the initial capital investment cost, FCR is the annual fixed charge rate (%), E is
the annual energy production (kWh) and O&M is the annual operation and maintenance cost.
With the initial capital investment and the charge rate being fixed value, the O&M is a variable
cost that can affect the cost of energy during the lifetime of the project. The profit of wind energy
is highly determined by ability to control and reduce this variable cost.
In a recent survey of the first offshore wind farm expansion in the UK, the cost of energy has
been compared at four wind farms from 2004-2007, [2]. The results of the survey are shown in
Table 1.1, where the O&M cost is given as the percentage of the total cost of energy. In this
case it is clear how poor O&M can result in low availability and a high cost of energy. The
availability is the percentage of time where the turbines are able to deliver energy when requested.
Wind farm Turbine Capacity Availability COE O&M
North Hoyle Vestas V80 60 MW 87.7 % 67 £/MWh 22 %
Scroby Sands Vestas V80 60 MW 81.0 % 67 £/MWh 16 %
Kentish Flats Vestas V90 90 MW 80.4 % 67 £/MWh 16 %
Barrow Vestas V90 90 MW 67.4 % 86 £/MWh 12 %
Table 1.1 Comparison of four offshore wind farms located in the UK showing the availability,
cost of energy (COE) and the O&M cost as a percentage of the total COE, [2].
The average cost of energy at these four offshore wind farms is 69 £/MWh, which is noticeable
higher than the average of 47 £/MWh achieved onshore in the UK. This is mainly because of a
much higher availability onshore – typically between 96-99%. The average O&M cost is 18%
of the total cost of energy, which furthermore is higher than the average of 12% for onshore
wind turbines in the UK. It should however be mentioned that these calculation are based on
early operational data where the Vestas turbines had several gearbox related problems. Compared
to another EU established wind farm, Middelgrunden, located in Denmark and operational
since 2001, the availability here is about 95-96 %, [4].
1.1.2 Condition Monitoring as a Maintenance Strategy
To understand how the performance of a wind turbine can be optimised with the use of a condition
monitoring system, the different types of maintenance strategies must be investigated.
Almost all industrial machinery requires maintenance during its lifetime. The maintenance can
either conducted with a preventive or corrective approach. Preventive maintenance is carried out
(1.1)

Chapter 1 - Introduction to Condition Monitoring
before a failure occurs, either in predetermined or condition based intervals. Corrective maintenance
is carried out after a fault has occurred and is also known as the breakdown strategy. This
is when you run the system until a breakdown occurs, [5]. In figure 1.1 the corrective maintenance
and the two kinds of preventive maintenance are illustrated in terms of the condition of a
system through time. The time used at maintenance is not illustrated, only the interval.
Condition [%]
Corrective maintenance
(Breakdown)
Scheduled
corrective maintenance
Condition based
corrective maintenance
Figure 1.1 Corrective maintenance and the two types of preventive maintenance (scheduled and condition
based) strategies related with the overall condition of a system through time, [5].
With the breakdown strategy, the preventive maintenance is reduced to a minimum giving the
lowest number of required repairs. This would initially give the lowest operation cost. However,
a breakdown is likely to occur at the highest stress level and consequential damage is likely to
occur. For a wind turbine this is the period of the year with highest amount of wind, resulting in
a severe production loss. In this period the accessibility might also be low and downtime could
be extensive - especially at offshore locations. Another disadvantage is that spare part logistics
is very difficult.
In contrast, the scheduled maintenance strategy offer easy spare part logistics and repairs can be
scheduled to periods of low wind. This reduces the downtime of the turbine and the production
loss. The disadvantage is that the maintenance costs are higher compared to corrective maintenance
due to the many repairs and spare parts needed.
The condition based strategy offers the possibility to use components longer, reducing the number
of repairs and if early predictions are made, the repairs can be scheduled. One of the disadvantages
is that additional monitoring hardware and software must be added to the turbine,
which increases the initial capital investment and thus the cost of energy.
In table 1.2 a comparison of the three maintenance strategies is given, [5].
Time
3

Chapter 1 - Introduction to Condition Monitoring
4
Strategy Advantages Disadvantages
Corrective maintenance
Preventive maintenance
– Scheduled
Preventive maintenance
– Condition
based
Low maintenance cost during
operation.
Component will be used for a
maximum lifetime.
Expected downtime is low
(and known).
Maintenance can be scheduled.
Spare part logistics is easy.
Components will be used for
almost their full lifetime.
Expected downtime is low.
Spare part logistics is easier
than corrective maintenance.
High risk in consequential
damages resulting in extensive
downtimes.
No maintenance scheduling is
possible.
Spare part logistics is complicated.
Long delivery periods
for spare parts are likely.
Component will not be used
for maximum lifetime.
Maintenance cost is higher
compared to corrective maintenance.
Additional monitoring hardware
and software is required.
Identifying a fault in time is
difficult (threshold values are
hard to determine).
Only feasible for larger components.
Table 1.2 Advantages and disadvantages of a corrective maintenance, scheduled preventive
maintenance and condition based preventive maintenance strategy, [5].
An implemented strategy will always be a combination of preventive and corrective maintenance.
Some components will never be considered for preventive maintenance, as it would not
be feasible compared to their reliability, stress level and expected lifetime. However, using a
condition based strategy for the larger component with reliability issues can minimize maintenance
cost and downtime.
Condition based maintenance is relatively new for wind turbines. But, as the capacity of the
single turbine increases and its location becomes even more remote, the demand to the reliability
of a turbine installed today is high compared to a turbines installed 10-20 years ago.

1.2 Identifying Critical Components
Chapter 1 - Introduction to Condition Monitoring
As mentioned earlier, then a condition based maintenance strategy is only feasible for certain
components. A wind turbine consists of several mechanical and electrical component needed for
transferring wind energy into electrical energy. It is important to look into the different types of
components, their failure rate and downtime consequence, before an effective condition monitoring
system can be implemented.
1.2.1 Categorization of Components
First, the thousands of components must be categorized to make the interpretation easier. For
instance, a faulty bearing within the gearbox is listed under Gearbox along with other gearbox
related faults. The categorization of components has no standard form. Some operators might
prefer to divide the blades and pitch system into two categories, while others prefer to have
them in one. This can make comparison of operational data between operators difficult.
In figure 1.2 a typical geared wind turbine is illustrated with the notation of the categories used
in this report, which is based on the incident report used in the German WMEP project, [8].
Sensors
- anemometer
- vibration switch
- temperature
- oil pressure switch
- power sensor
- revolution counter
etc.
Hub
- hub body
- pitch mechanism
- pitch bearings
Rotor blades
- blade bolts
- blade shell
- aerodynamic brake
Drive train
- rotor bearings
- drive shafts
- couplings
Hydraulic
system
- hydraulic pump
- pump motor
- valves
- pipes/hoses
Gearbox
- bearings
- wheels
- gear shaft
- sealings
Mechanical
brakes
- brake disc
- brake pads
- brake shoe
Generator
- windings
- brushes
- bearings
Control system
- control unit
- relays
- mesurement cables and connections
Structure
- foundation
- tower/tower bolts
- nacelle frame
- nacelle cover
- ladder
Electric
- converter
- transformer
- fuses / breakers
- switches
- cables / connections
- grid
Yaw system
- bearings
- motor
- wheels and pinions
Figure 1.2 Typical layout of geared wind turbine with categorization of its main components based on the
incident report from the German WMEP project, [8].
1.2.2 Reliability of Components
The reliability of a component is the probability that it will perform as designed for a certain
amount of time, [7]. Poor reliability will affect the availability or uptime of the turbine – its
capability to operate when required. The availability of a modern onshore wind turbine is typically
in the range of 95-98%. But, as the difference between high or low revenue might be
within a few percentage of change in availability, it is important to identify the critical compo-
5

Chapter 1 - Introduction to Condition Monitoring
nents that could cause low availability. A critical component is a component with a high failure
rate and/or a long down time.
It is often difficult to acquire information regarding the reliability of wind turbines and this information
is often not published in details. The reason for this is that wind turbine manufactures
rarely permit publishing failure statistics of their products, which of cause makes sense from a
competitive point of view. A few databases with reliability data do exist and have been used in
several surveys. In reference [6] a detailed study of these databases has been conducted and
below is listed some of the larger databases in Europe.
Windstats Newsletter – Denmark and Germany (monthly, 7000 WT)
Windstats publishes operational data from wind turbines located in Denmark and Germany
through Wind Power Monthly. A survey has been done using this database in reference
[7], where 10 years of operational data (1994-2004) from wind turbines in Germany
and Denmark was analyzed.
LWK – Germany (annually, > 650 WT, closed in 2006)
From 1993 to 2006 failure statistics were published containing output data and number of
failures of all wind turbines located in a province in the northern part of Germany
(Schlleswig-Holstein).
WMEP – Germany (annually, > 1500 WT, closed in 2006)
Programme funded by the “250MW Wind” project in Germany. Long term operational
data was collected from more than 1500 wind turbines from 1989 to 2006. It is the most
comprehensive study of long-term behaviour of wind turbines worldwide.
VPC – Sweden (annually, 723 WT before 2005 and 80 WT after 2005)
Report published by Elforsk, providing statistical data of production and downtime data
from wind turbines situated in Sweden. Monitoring range was change in 2005 due to failure
reporting errors.
VTT – Finland (annually, 105 WT)
Report published by Elforsk, providing statistical data of production and downtime data
from wind turbines situated in Sweden. Monitoring range was change in 2005 due to failure
reporting errors.
A lot of studies have been performed on the results stored in these databases in order to locate
the most critical components. In reference [11] the failure rates from eleven different databases
have been compared. The result of the comparison is given in table 1.3, showing the top-three
components with the highest failure rates.
6

Chapter 1 - Introduction to Condition Monitoring
Database Time Span No. of WTs Highest failure rate Location
WMEP 1989-2006 1500
LWK 1993-2006 241
Windstats 1995-2004 4285
Windstats 1994-2003 904
VTT 2000-2004 92
Elforsk 2000-2004 723
EPRI 1986-1987 290
NEDO 2004-2005 139
Operator A 2000-2007 403
Operator B 2002-2009 12
Operator C 2003-2008 23
1. Electrical system
2. Control system
3. Sensors
1. Electrical system
2. Rotor
3. Control system
1. Rotor
2. Electrical system
3. Sensors
1. Control system
2. Rotor
3. Yaw System
1. Hydraulics
2. Rotor
3. Gearbox
1. Electrical system
2. Hydraulics
3. Sensors
1. Sensors
2. Electrical system
3. Control system
1. Sensors
2. Control System
3. Rotor
1. Control system
2. Electrical system
3. Rotor
1. Sensors
2. Hydraulics
3. Electrical system
1. Electrical system
2. Rotor
3. Gearbox
Germany
Germany
Germany /
Denmark
Germany /
Denmark
Finland
Sweden
US – California
Japan
Unknown
Unknown
Unknown
Table 1.3 Comparison of the top-three components with the highest failure rates from eleven
different databases, [11].
Even if the results from these studies cannot be directly compared as they differ in date, duration,
data collection, turbine age and turbine technology, they show similar results with a few
exceptions. The electrical system has the highest failure rate in most cases, next is the control
system and then sensors. Overall, the electrical related systems have a higher failure rate than
the mechanical ones. Considering solely the failure rate, then the obvious choice would be to
implement a condition monitoring system with focus on these systems. However, it is important
to consider the downtime in relation to the failure rate. Changing a sensor or resetting a relay is
less time consuming than doing repairs on a gearbox or changing a main bearing.
The term downtime is a measure of the time it takes for a component to recover from a failure
that brings the wind turbine to a standstill. In most cases the mean downtime would be equal to
the statistical term Mean Time To Repair (MTTR). However, as the production from a wind
turbine dependent on the available wind, some modern control systems measure the downtime
as being the number of hours where production would have been possible. Production is only
possible when the wind speed is above the threshold limit. This downtime value is important for
the operators of the turbine to determine lost revenue. In this report the downtime is considered
7

Chapter 1 - Introduction to Condition Monitoring
as being equal to the MTTR.
In figure 1.3 and 1.4 the failure rate and the downtime are shown for the WMEP survey from
Germany based on data from reference [8] and [9].
8
Hydraulic System
Mechanical Brake
Structural / Housing
Germany (WMEP 1989-2006)
Electric
Control System
Sensors
Yaw System
Hub
Generator
Rotor Blades
Gearbox
Drive Train
0.05
0.13
0.11
0.11
0.10
0.10
0.18
0.17
0.25
0.23
0.43
0 0.1 0.2 0.3 0.4 0.5 0.6
Failure rate [failures/turbine/year]
Figure 1.3 Failure rates for Germany (WMEP). A total of
2.43 failures per turbine per year in average.
0.57
Structural / Housing
Mechanical Brake
Hydraulic System
Germany (WMEP 1989-2006)
Electric
Control System
Figure 1.4 Downtimes for Germany (WMEP). Total downtime
of 6.0 days per year per turbine in average.
The failure rate is identical to the results given in table 1.3, where the electrical related faults
were the most common. But, when taking the downtime into account, then the mechanical faults
increase in severity. The gearbox has one the lowest failure rates but the longest downtime per
failure, making it one the most critical components. The most critical components based on
downtime per turbine per year are still the electric and control related components.
To see whether this is consistent with the results from other databases, data from reference [5] is
used. In this survey reliability data from Sweden (Elforsk), Finland (VTT) and Germany
(WMEP) has been studied in a time period from 2000-2004. In figure 1.5 to figure 1.8 the failure
rate and downtime is shown for Sweden and Finland. The results from Germany are omitted
as they are the same as presented above.
Hub
Gearbox
Generator
Yaw System
Sensors
Rotor Blades
Drive Train
0.31
0.29
0.29
0.38
0.35
0.49
0.49
0.63
0.62
0.59
0.68
0.87
0 0.2 0.4 0.6 0.8 1
Downtime [days/turbine/year]

Rotor Blades
Hydraulic System
Control System
Yaw System
Structural / Housing
Mechanical Brake
Drive Train
Sweden (VPC 2000-2004)
Electric
Sensors
Gearbox
Generator
Other
Hub
0.01
0.00
0.00
0.00
0.01
0.03
0.02
0.04
0.05
0.05
0.05
0.05
Figure 1.5 Failure rates Finland (VTT). A total of 0.39
failures per turbine per year in average.
Figure 1.7 Failure rates for Finland (VTT). A total of 1.38
failures per turbine per year in average.
Chapter 1 - Introduction to Condition Monitoring
Figure 1.6 Downtimes for Sweden (VPC). Total downtime
of 2.08 days per year per turbine in average.
Figure 1.8 Downtimes for Finland (VTT). Total downtime
of 9.88 days per year per turbine in average.
The results from this survey differ from the result found using the German WMEP database. It
is clear that these two countries have had longer downtimes from mechanical related faults than
Germany. The gearbox and the rotor blades are among the most critical components.
In table 1.4 the detailed results from the three surveys has been compared.
0.07
0 0.02 0.04 0.06 0.08
Failure rate [failures/turbine/year]
Hydraulic System
Rotor Blades
Yaw System
Control System
Structural / Housing
Generator
Mechanical Brake
Drive Train
Finland (VTT 2000-2004)
Gearbox
Sensors
Electric
Other
Hub
0.01
0.00
0.04
0.10
0.10
0.10
0.09
0.08
0.13
0.12
0.11
0.20
0.31
0 0.1 0.2 0.3 0.4
Failure rate [failures/turbine/year]
Control System
Gearbox
Rotor Blades
Yaw System
Sensors
Other
Hydraulic System
Electric
Hub
Generator
Mechanical Brake
Structural / Housing
Drive Train
Sweden (VPC 2000-2004)
0.03
0.03
0.00
0.05
0.04
0.11
0.09
0.20
0.19
0.30
0.28
0.40
0.38
0 0.1 0.2 0.3 0.4 0.5
Downtime [days/turbine/year]
Rotor Blades
Hydraulic System
Structural / Housing
Yaw System
Mechanical Brake
Control System
Drive Train
Finland (VTT 2000-2004)
Gearbox
Electric
Generator
Other
Sensors
Hub
0.20
0.17
0.01
0.00
0.43
0.41
0.27
0.65
0.64
0.64
1.13
2.10
3.24
0 1 2 3 4
Downtime [days/turbine/year]
9

Chapter 1 - Introduction to Condition Monitoring
10
Germany Sweden Finland
Failure rate 2.43 0.39 1.38 failures / turbine / year
Downtime per failure 3.64 6.30 6.57 days / failure
Downtime per year 2.43 2.08 9.88 days / turbine / year
Top 3
1. Electric
2. Control
3. Sensors
1. Gearbox
2. Drive tr.
3. Generator
1. Electric
2. Control
3. Hub
1. Electric
2. Sensors
3. Blades
1. Drive tr.
2. Yaw
3. Gearbox
1. Control
2. Gearbox
3. Blades
1. Hydraulic
2. Blades
3. Gearbox
1. Gearbox
2. Blades
3. Structural
1. Gearbox
2. Blades
3. Hydraulic
Distribution Elec. Mech. Elec. Mech. Elec. Mech.
Failure rate 56 44 51 49 31 69
Downtime 42 58 38 62 15 85
failure rate
downtime / failure
downtime / year
Table 1.4 Comparison of the reliability of wind turbines located in Germany, Sweden and Finland.
Some trends can be seen between the results from Germany and Sweden. While Sweden has a
lower failure rate than Germany, they suffer from long downtimes per failures giving them
nearly the same amount of downtime per year. Finland seems to suffer from different problems
than Germany and Sweden, and in general has a lower reliability.
Conclusively, there is no clear consistency in which components that are the most critical. It
depends on how the different measures are rated. Looking at the downtime per year, which can
be related to the production loss over the lifespan of a turbine, the following assemblies are
critical; electric, control system, gearbox and blades/hub. If a low failure rate has the highest
rating, e.g. for remote offshore locations, then sensors can be added to the list.
1.2.3 Discussion of Reliability
When using statistical data as in the previous section, it is important to understand conditions
that can lead to poor comparison. Below is described some issues that should be considered.
1.2.3.1 Age of turbine
The failure rate of a wind turbine will change with time. The change in failure rate is often divided
into three periods; an infant mortality period with decreasing failure rate, a normal life
period with constant failure rate and a wear-out period with increasing failure rate. The sum of
the three situations is the observed failure rate.
In reference [11] the reliability through time has been investigated based on the WMEP database.
In the first year of operation the average failure rate was ~3.4 faults/year, decreasing to a
constant level of ~2.5 faults/year after the third year. It is difficult to estimate when the failure
rate increase due to wear out, since little data with this time span is available – in reference [5]
there seems to be indications of an increase after the 11 th year of operation. A modern MW size
wind turbine is designed be in operation for 20-25 years. In order to make the statistical data
comparable, the age of the investigated wind turbines should be equal or within the period of
constant failure rate.
%

1.2.3.2 Size of turbine
Chapter 1 - Introduction to Condition Monitoring
As the rated power and size of a turbine increases the stress on components increases as well,
and this could increase the failure rate. In reference [10] a comparison is made showing that
wind turbines above 1.0 MW has twice the number of failures compared to wind turbines rated
between 500 kW and 1.0 MW. Since the current development goes towards multi-megawatt
sized turbines, the failure rate per turbine is expected to increase.
1.2.3.3 Technical concept
The technical concept regarding power control, speed characteristic and generator type will also
affect the reliability. In reference [8] using the WMEP database the failure rate for three different
concepts has been compared, see figure 1.9.
Figure 1.9 Failure rate in the WMEP database (1989-2006) with respect to the technical concept. The
simple Danish concept is a directly grid-connected induction generator. The advanced Danish concept has
variable rotor resistance to change speed of the induction generator. The standard variable-speed turbine
is fitted fully or partially converter system with a synchronous or an asynchronous generator. [8]
The demand for high controllability increases the complexity of wind turbines. The trend seems
to be that modern wind turbine concepts have a higher failure rate compared to older simpler
concepts. This tendency is also seen in reference [11]. Here, the total failure rate related to the
operational year is compared for three concepts. The results are shown in figure 1.10.
Figure 1.10 Total failure rate of components per wind turbine per operational year using induction generators
(simple Danish concept), synchronous generator with gear and synchronous generators with direct
drive. Permanent magnet synchronous generators (PMSG) are not present. [11]
These trends are important for future condition monitoring systems as the technology are moving
towards gearless direct drive concepts with permanent magnet synchronous generator. The
11

Chapter 1 - Introduction to Condition Monitoring
results seen in figure 1.10 suggest that removing the gearbox and replacing it with a direct
driven generator increases the overall failure rate. This could be explained by a higher complexity
in the power electronics and in the generator, but also that the generator is exposed to massive
stress due to the high dynamic torque level when driven without a gearbox.
It should be mentioned that the downtime consequences has not been compared in the surveys.
1.2.3.4 Geographical location
It was previously shown that Finland had a high failure rate at the blades and in the hydraulic
system. This could be explained by icing on the surface of the blades that affect the shape and
weight of the blade, but also affects the hydraulics controlling the pitch mechanism. These problems
might not occur in Germany where the weather is warmer. This indicates that a condition
monitoring system should be designed to cover a large range of faults.
Another relevant issue is whether the wind turbine is located onshore or offshore. Onshore turbines,
as the ones in the WMEP survey, suffer from a large number of faults, which are easy to
solve with minimum downtime, [11]. As offshore turbine technology has been directly derived
from onshore technology, similar faults are expected. Under offshore conditions the downtime
from minor faults will increase due to limited accessibility. The result is a high risk of long
down time if precautions are not taken. This was the case for the UK wind farms presented at
the beginning of this chapter, where the availability was reported as low as 67.4%. In the
WMEP survey the average availability was about 98%. Considering this, then it becomes clear
that it is a challenge to make offshore wind turbine reliable and profitable. They are often larger
in capacity, more complex and located in the most remote and inaccessible areas. The presented
failure rates are mainly for onshore turbines and are considered reasonable due to short downtime.
But, at offshore these failure rates would be unacceptable.
1.3 Condition Monitoring Systems
One thing is to identify that wind turbines have reliability issues and that conditions based maintenance
could give improvements. Another thing is actually to be able to predict whether a
component is healthy or not. For this, a system is needed to detect early warning signs. The
curve in figure 1.11 illustrates the development of a typical mechanical failure.
12
Component condition
Condition
starts to
change
Vibrations
Noise
Heat
Smoke
Break down
months weeks days minutes Time
Figure 1.11 Typical development of a mechanical failure.
To detect the change in the condition different monitoring methods exist and are widely used.
But, as shown later in this section, only a few of these are being used commercially by the wind
industry.

Chapter 1 - Introduction to Condition Monitoring
A condition monitoring system can be divided into three stages; collecting data, analysing data
and classification. The stages are illustrated in figure 1.12.
Collecting data
Thermal
Vibrational
Debris
Stress / Deformation
Acoustic
Current / Voltage / Power
Electrical discharges
etc.
Analysing data
Filtering
Frequency-time analysis
(FFT, wavelets, etc.)
Identify component
signatures
Identify changes in
signatures
etc.
Figure 1.12 Stages of a condition monitoring system (with examples).
Classification
Threshold limits from
known or estimated
reliability data
Prediction of time until
breakdown
etc.
In the following sections some of the proposed methods are described with focus on the ones
used commercially. Each method has its advantages and disadvantages depending on its use.
1.3.1 Thermal Monitoring
Monitoring the temperature of the observed component is one the most common methods of
condition monitoring. For online monitoring resistive thermal sensors (e.g. PT100) are often
used to monitor the temperature of bearings, fluids, generator windings and similar. For mechanical
components the increased friction will cause heating and for electrical fault the increased
resistive power loss will cause heating. Thermography (infrared imaging) is often used
to detect hotspot in power electronics, such as the power converter. Thermography is mainly
used as offline monitoring. [12]
The advantage of thermal monitoring is that it is a reliable source as all equipment has a limited
operational temperature. The disadvantage is that temperature develops slowly and is not good
for early fault detection. The readings can also be influenced by the surroundings. Thermal
monitoring is therefore rarely used alone, but often as a secondary source of information. Where
the primarily source could be vibration monitoring.
1.3.2 Vibration Monitoring
For rotating equipment vibration monitoring is often used to detect mechanical failures. E.g. if a
bearing is worn out the shaft supported by the bearing will be off centred. When the shaft rotates,
it will now vibrate with a characteristic frequency determined by the properties of the
bearing. Different types of sensors are used to detect these vibrations; in the low-frequency
range position sensor are used, in the mid-frequency range velocity sensors are used and in the
high frequency range accelerometers are used, [12].
The data analysis is often a Fast Fourier Transformation (FFT) to convert the time domain signal
to the frequency domain. By monitoring the amplitude at certain frequencies that can be
related to certain subcomponents of the bearing, the condition of the bearing can be predicted.
13

Chapter 1 - Introduction to Condition Monitoring
The advantages of vibration monitoring are that it is easy to implement in existing equipment
and has a high level of interpretation, making it easy to locate the exact faulty component. For
these reasons vibration monitoring is one of the most popular monitoring methods used in wind
turbines. The vibration method is standardized in ISO 10816 defining positioning and use of
sensors. In figure 1.13 the positions used in the Siemens SWT 3.6 wind turbine are shown.
14
Figure 1.13 Typical vibration sensor positions in Siemens SWT 3.6 wind turbine.
The disadvantage of vibration monitoring is the additional hardware and software, which increases
the production cost. The sensors also has difficulties at detecting low frequency faults –
e.g. in the main bearing due to the low rotational speed. [12]
1.3.3 Oil / Debris Monitoring
In equipment with lubrication or hydraulic systems such as oil for the gearbox, a debris monitoring
methods can be used. The oil is pumped through the component in a closed loop system
and metal debris from a cracked gearbox wheel or bearing is caught by a filter. The amount and
type of metal debris can indicate the health of a component. The advantage of this method is
that it is one the only methods for detecting cracks in the gearbox internals (wheels). A cracked
wheel in a gearbox might not be detected by vibration monitoring or similar methods. The disadvantage
of this method is that equipment for online monitoring is very expensive, so offline
monitoring in terms of oil samples is often used. These samples are then investigated at a lab
facility, which increase the cost of in terms of labour. [12]
1.3.4 Acoustic Monitoring
For failures characterized by high frequencies (kHz-MHz range), vibration monitoring can be
insufficient. In this case acoustic monitoring can be used to detect vibrations (sounds) emitted
by the component. This could be used to monitor the brush gear in a synchronous or double fed
induction generator. The advantages of using acoustic monitoring are the large frequency range
and the relative high signal-to-noise ratio. The disadvantage is that this method is expensive to
implement and only a few types of faults are present in the high frequency range. [12]
1.3.5 Electrical Monitoring
Gearbox low-, mid-, highspeed
bearings.
Main shaft
bearings.
Generator
bearings.
Electrical monitoring can be used for many purposes and for a large variety of component. It is
typically used to monitor electrical components such as generators or transformers. But, it may
also be used to monitor mechanical components such as bearings and gears. The source is pri-

marily current, flux or power.
Chapter 1 - Introduction to Condition Monitoring
Partial discharge monitoring is often used to monitor insulation faults in the generator or transformer
windings. Voids in the insulation will cause discharges between the conductors or
ground. The discharges will cause a rapid change in the current for short period (MHz range)
and hence lead to high peak voltages. Since insulation faults are rare in a wind turbine, discharges
monitoring is seldom done online but periodically.
A more practical use of electrical monitoring regarding rotating machines is electrical signature
analysis (ESA) or machine current signature analysis (MCSA). From current measurements at
the terminals, variations in the behaviour of the machine can be detected. The variations can be
an unbalanced three phase load or an increase in the harmonics current. An unbalanced load
could indicate a turn-to-turn shortenings of the windings. Undesired harmonics could also be
present due to winding faults, but could also occur if mechanical faults are presents.
The advantage of electrical monitoring is that it allows monitoring of both mechanical and electrical
components. It is therefore comparable to the vibration monitoring method, but has the
possibility of detecting electrical faults as well. Another advantage is that it requires fewer sensors
making it a cost effective solution. The disadvantage is that it can be difficult to locate the
exact faulty component. [12], [14]
1.3.6 Summary
In table 1.5 a summary of the described condition monitoring methods is given.
Method Monitored Components Advantages Disadvantages
Thermal
Vibration
Oil / Debris
Acoustic
Electrical
Bearings
Generator windings
Bearings
Gearbox
Shaft
Bearings
Gearbox
Bearings
Gearbox
Generator brush gear
Gearbox / Bearings
Generator
Converter / Transformer
Reliable
Standardized (IEEE 814)
Reliable
Easy to interpret
Standardized (ISO 10816)
Good for gearbox internals
Low and high frequency
fault detection.
High signal-to-noise ratio
Few or no additional sensors
required
Large component range
Influenced by surroundings
Expensive hardware /
software
Subject to sensor faults
Limited component range
Expensive for online use
Expensive hardware /
software
Difficult to locate fault.
High signal-to-noise ratio
Table 1.5 Summary of possible monitoring methods for wind turbines. [14]
1.4 Commercially available CMS
In reference [13] from 2010 a survey of the commercially available condition monitoring systems
for wind turbines has been conducted. This survey elaborates the methods used by 20 suppliers
and the conclusion is that nearly all focus on the same subassemblies, which are; blades,
main bearings, gearbox internals, gearbox bearings and generator bearings. Considering the
15

Chapter 1 - Introduction to Condition Monitoring
presented failure rates and downtime, presented earlier in this chapter, then the chosen components
makes sense as they are among the most severe. The monitoring methods used are; 14
systems are primarily based on vibration monitoring, 3 systems solely for oil debris monitoring,
1 system use vibration monitoring of the blades and 2 systems uses fibre optic strain monitoring
of the blades.
In table 1.6 some details are given for the methods used by some the larger wind turbine manufactures.
16
Product
Name
Vibro
CBM
TCM
WindCon
Supplier
(WT manufacture)
Brüel & Kjaer
(Vestas)
Bently Nevada
(GE Wind)
Gram & Juhl
(Siemens)
SKF
(Repower)
Components
monitored
Main bearing, gearbox,
generator, nacelle.
Nacelle temperature.
Noise in the nacelle.
Main bearing, gearbox,
generator, nacelle.
Optional bearing and oil
temperature.
Blade, main bearing,
shaft, gearbox, generator,
nacelle, tower.
Blade, main bearing,
shaft, gearbox, generator,
tower, generator
electrical.
Monitoring
methods
Vibration.
Temperature.
Accoustic.
Vibration.
Temperature.
Vibration.
Vibration.
Oil debris particle
counter.
Table 1.6 Commercially available condition monitoring systems used by Vestas,
GE Wind, Siemens and Repower. [13]
Analysis
methods
Time domain.
FFT frequency
domain analysis.
FFT frequency
domain analysis.
FFT frequency
domain analysis.
Time domain.
FFT frequency
domain analysis.
There seems to be little variation between the products from the suppliers as they all more or
less use the same methods. None uses electrical monitoring, which could be an alternative or
redundant option for the vibration system. Temperature monitoring of the generator windings
and similar component is not listed as this is normally a part of the SCADA system made by the
wind turbine manufacturer.
1.5 Chapter Conclusion
In this chapter a brief introduction to the concept of condition monitoring of wind turbines has
been given. From reliability studies it has been shown that wind turbines has some critical components
that affects the economical performance. Considering the failure rate alone, then faults
in the electrical system, in sensors and in the control system are among the most common.
However when considering the downtime due to maintenance, the mechanical faults in the drive
train components such as the gearbox and the main bearings increase in severity. The downtime
is an important factor as this will result in lost energy production.
It is noticed that there is not a clear consistency between the reliability data taken from different
sites, indicating that different circumstances affect the reliability of the wind turbines. There is a

Chapter 1 - Introduction to Condition Monitoring
tendency that more modern and complex turbine has a higher failure rate compared to old simpler
concepts. This emphasizes the future need for predictive maintenance. Implementing a condition
based monitoring strategy is an important tool for scheduling future maintenance. By
planning future maintenance to periods of low wind the loss of energy production can be reduced.
Presently, the commercially available condition monitoring is mainly based on vibration and
temperature monitoring of the drive train component. Comparing the products from different
suppliers of condition monitoring systems indicate small or no difference. Adapting a different
technology such as electrical monitoring as an alternative is considered to be a competitive advantage.
17

Chapter 2
Thesis Objectives
This chapter states the problems that are considered in this thesis. A hypothesis is presented for
using the generator as the source for condition monitoring. The solution methods and project
limitations are also defined.
2.1 Problem Statement
It became clear in chapter one, that wind turbines suffer from reliability issues that affects the
reliability and economic performance. The problem was located to a few components that had a
high influence on the availability of the turbine due to a combination of high failure rates and
long down times. In particular wind turbines located offshore had low availability, whereas the
level onshore was more acceptable. A predictive maintenance strategy based on condition monitoring
was shown to be an effective way to plan future operation and maintenance (O&M). This
can limit the O&M, but more importantly repairs can be conducted in periods of low wind reducing
production losses.
Different condition monitoring techniques was presented in chapter one, however only a few of
these are used commercially. The most favourable system is based on drive train vibration
analysis of the following components; main bearings, gearbox bearing, gearbox internals and
generator bearings. The advantages of this system are that it is easy to locate a fault and to implement,
as it is often done by a third party. The disadvantages are that it requires additional
mechanical sensors (6-8 for a typically geared turbine) increasing the cost of the wind turbine
and the possibility of sensor related faults.
In this thesis a substitute or a redundancy option for the vibration based system is investigated
using the generator as the source of fault detection. The setup is shown in figure 2.1.
Hub
Bearing
gear
Mechanical
speed
3~
SCIG
ωm
Electric
signals
vabc
iabc
Data
Acquisition
AC
/
DC
Filtering
Power Converter
DC
/
AC
Condition Monitoring System (CMS)
Frequency
Analysis
Figure 2.1 Electrical condition monitoring system (CMS) setup in geared wind turbine.
a
b
c
Grid /
Transformer
Failure
Prediction
19

Chapter 2 - Thesis Objectives
The technical concept considered is a geared wind turbine with a squirrel cage induction generator
(SCIG) and a full converter. This concept is chosen due to its popularity, especially at offshore
locations. At the terminals of the generator the voltage and current of each phase are
measured. The mechanical speed ωm could also be considered. By analysing these signals in the
frequency spectrum then changes caused by abnormal mechanical vibrations should be detectable.
This method is known as Electrical Signature Analysis (ESA) or Machine Current Signature
Analysis (MCSA) and is often used for larger motors and generators in other industries.
The advantage of this method is that it requires fewer sensors, the sensors have no moving parts,
and a different source is used (electrical). This makes it a good substitute or redundant option
for the mechanical vibration system.
Using ESA for condition monitoring has not yet been adopted by the wind industry. For the
method to be useful as an alternative it should fulfil the following requirements:
20
Locate origin of a failure (exactly which component needs repair).
Identify the same range of failures (main bearings, gearbox bearing, some gearbox
internals and generator bearings).
Simple implementation and interpretation.
In the given case, the generator is the source of the fault detection. The following generator
related issues should be considered that could affect the electrical signal.
How do conditions like core saturation affect the signal?
Is there linearity between the fault degree and the measured electrical signal?
2.2 Hypothesis
The idea is that mechanical vibrations introduced by a failure should affect all drive train related
components with frequencies characterized by their origin - including the rotor in the generator.
If the rotor vibrates then the air gap distance is not identical in all positions and rotor eccentricity
occurs. The change in air gap length will affect the magnetic and electrical properties of the
machine. Hence, a change in air gap length will change the current magnitude and shape if the
voltage is kept constant.
To understand why current is a good parameter for fault detection, the simple magnetic circuit
in figure 2.2 is considered. The circuit consist of a single winding with N turns and a ferromagnetic
core with an air gap.

+
-
Winding,
N turns
i
Magnetic flux lines
Air gap
length g
Figure 2.2 Simple magnetic circuit with an air gap.
Chapter 2 - Thesis Objectives
Mean core length lc
Air gap,
permeability µ0,
area Ag
Magnetic core,
permeability µ,
area Ac
The relationship between the magneto motive force mmf acting on a magnetic circuit and the
magnetic field strength H is given as: [25]
mmf N i H dl
If the core dimensions are such that the path length of any flux line is close to the mean core
length, then the line integral in equation (2.1) becomes a scalar product of the average value of
H and the mean core length lc.
mmf N i Hc lc Hg g
The relationship between the field intensity H and the magnetic flux density B is the material
property µ, known as the magnetic permeability.
BH If the flux is assumed uniformly distributed and air gap fringing is neglected, then the flux density
can be determined from the cross sectional area and the flux in the circuit.
B B
c g
Ac Ag
Using these relations the current i in the winding can be described.
lcg
i´ r 0
N
A A
c 0 g
Since the permeability of the core is much greater than that of air (µr >> µ0) the current is sensitive
to changes in the air gap. Typical values of µr ranges from 2,000 to 10,000 for materials
used in rotating machines, where the permeability of air or free space μ0 is 4π10 -7 . If the first
part in the bracket of equation (2.5) is neglected, then the current is proportional to the air gap
length when the other variables are considered constant. This initially makes the current a good
source for detecting variations in the air gap.
The relationship between the magnetic flux linkage and the current is defined as the inductance
(2.1)
(2.2)
(2.3)
(2.4)
(2.5)
21

Chapter 2 - Thesis Objectives
L of the winding.
22
N
L (2.6)
i i
Under the assumption that the first part of equation (2.5) is negligible, then the inductance for
this simple circuit can be described as:
L
2
N 0Ag g
From which it can be seen that the inductance L is inversely proportional to the air gap length.
The same tendency can be seen in the magnetic circuit of the generator. In figure 2.3 and figure
2.4 a six-poled squirrel cage induction generator is illustrated. In figure 2.3 the rotor is centred
and in figure 2.4 the rotor is off centred (eccentric). The red lines are the flux paths at two opposite
located poles and the green circles are the related winding.
Flux path
Winding a2
air gap
Winding a1
La1 = La2
Figure 2.3 Six-poled SCIG with centred rotor. Inductance
of winding a1 is equal to winding a2.
ωr
ωr
Shorter air gap length
=
Larger inductance
La1 ≠ La2
(2.7)
Figure 2.4 Six-poled SCIG with eccentric rotor. Inductance
of winding a1 is larger than winding a2.
When the rotor is centred, the inductance of winding a1 and winding a2 are equal and independent
of the position of the rotor. In the case of eccentricity, it is clear that the length of the flux
path and the air gap has changed. The inductances of winding a1 and winding a2 are no longer
equal. The self inductance (mutual and leakage) of each winding is now a function of the position
of the rotor. This change in inductance will affect the currents and voltages at the terminals
of the generator making a failure detectable.
In general two types of eccentricity can occur – static or dynamic. However a combination of
the two known as mixed eccentricity could also be present. Static and dynamic eccentricity is
illustrated in figure 2.5.

Static
eccentricity:
rotor
Dynamic
eccentricity:
rotor
air gap
stator
Chapter 2 - Thesis Objectives
air gap
Figure 2.5 RL circuit with time changing inductance.
stator
Static eccentricity is when the rotor is shifted to an off centred position and rotates in at that
position. With dynamic eccentricity, the rotor is also shifted from the centre of the stator, but
still rotates around the centre of the stator. The following failures are considered to cause static,
dynamic or mixed rotor eccentricity:
Main shaft, gearbox and generator bearings.
Some gearbox internals.
Misalignment between shaft, gearbox and generator.
Blades (unbalanced load).
The failures are the same as for the vibration system. However, misalignment and blades has
been added. Misalignment of components could appear subsequently to a repair or if not
mounted properly to the nacelle during installation. The blades are added since it is assumed
that during a fault in the hydraulic pitch system in one of the blades, the load distribution is
uneven making eccentricity possible.
The fault detection is best illustrated by considering the simple RL circuit shown in figure 2.6,
where R is the resistance, Lok is the inductance without a fault and Lfault is the inductance with a
fault.
i(t) = Imsin(ωt)
R=2Ω Lok, fault
Lok = 2mH
Lfault = Lok[1+0.5sin(4ωt)]
XL = ωL=2πf
Figure 2.6 RL circuit with time changing inductance.
In the normal operation the value of resistance and the inductance are constant, but in the faulty
scenario the inductance oscillate with four times the grid frequency. If the current is considered
regulated to a constant level by a converter, then the grid voltage can be determined as:
23

Chapter 2 - Thesis Objectives
24
1 X L
u t Im Z sint tan
R (2.8)
In figure 2.6 the voltage v(t) and instantaneous power p(t) is shown for the scenario without a
fault and in figure 2.7 for the scenario with a fault.
3
2
1
0
-1
-2
i(t)
v(t)
p(t)
-3
0 5 10
time [ms]
15 20
-2
i(t)
v(t)
p(t)
-3
0 5 10
time [ms]
15 20
Figure 2.7 Scenario with no fault. Figure 2.8 Scenario with a fault.
It is clear in this extreme case that in the faulty scenario the voltage differs in shape compared to
the case without a fault. Due to the need of a constant current level, the voltage increases when
the inductance is reduced and vice versa. Performing a Fast Fourier Transformation (FFT) of the
power reveals the harmonic frequencies related to the fault.
10 0
10 -10
10 -20
10 -30
p(t)
0 100 200 300 400 500
frequency [Hz]
Figure 2.9 FFT of p(t) with no fault. Figure 2.10 FFT of p(t) with a fault.
10 0
3
2
1
0
-1
10 -10
10 -20
10 -30
p(t)
0 100 200 300 400 500
frequency [Hz]

Chapter 2 - Thesis Objectives
Without constant R and L (no fault) the fundamental power component is located at 100Hz with
a DC offset at 0Hz. The introduced faulty inductance oscillates with four times the grid frequency
or 200Hz. This introduces a harmonic component at 300Hz. By monitoring the change
in amplitude dp/dt at this frequency the development of a fault can be monitored.
fault indicator
dp
dt
n (2.9)
The same tendency is expected to be seen in the induction generator when eccentricity occurs
and the inductances changes with the position of the rotor. A drive train fault (e.g. a bearing)
will have its own characteristics that can be identified by the changes at certain harmonic amplitudes.
2.3 Work by Others
The idea of using electrical signature analysis for condition monitoring of wind turbines is not
new. A lot of research has been done in last decade within this field. The general idea is that it
could act as a replacement for the vibration system – a cost effective alternative. The main research
has concerned the challenge of monitoring changes under variable frequency conditions,
which are present with power converters. The problem is that FFT is only suitable during constant
frequency conditions and require a certain time span to be accurate. In reference [20] and
[21], a method using wavelet analysis has been successfully tested with unbalanced load and
coil shortenings during variable frequency. Another suggested method is to use short time Fourier
Transformation (STFT) as done in reference [22].
It is considered that suitable solutions for detecting faults during variable frequency conditions
exist. However, if electrical monitoring should be used an alternative some fundamental issue
regarding fault identification and generator behaviour has not been clearly investigated.
2.4 Solution Method
To analyse whether the presented hypothesis is a useful solution for condition monitoring of a
wind turbine, the following approach is used.
Design of a simplified reference wind turbine with drive train components (bearings)
and a squirrel cage induction generator. The design is based on the Siemens SWT
3.6-120 offshore wind turbine.
Describe the characteristics of typical drive train bearing faults and how they are
identified.
The behaviour of the designed generator during eccentricity is investigated using a
finite element analysis (FEA). In an earlier project by the author rotor bar faults has
been studied using a qd0 reference model. To gain new knowledge a FEA is considered
appropriate.
Small-scale test using an induction motor with a power converter with constant V/f
regulation. The motor is loaded with an unbalanced load to introduce eccentricity.
25

Chapter 2 - Thesis Objectives
2.5 Limitations / Assumptions
The following limitations and assumptions have been taken in the process of this report.
26
In the design of the reference wind turbine generator thermal conditions are not
considered.
The eccentricity of the rotor is assumed to be constant in the axial length of the
generator.
The control concept of the converter is assumed to be a constant V/f regulation,
which offers a constant saturation level of the core.
Frequency analysis during variable frequency is not considered as this topic has
been covered by others. The analysis in this thesis is done at constant frequency.

Chapter 3
The Reference Wind Turbine
In this chapter a reference wind turbine is designed to be used throughout the report. Only the
relevant components for this project are considered, such as the bearings and the generator.
3.1 Introduction
The reference wind turbine in this thesis is based on the Siemens SWT-3.6-120, which have an
output power of 3.6 MW. In table 3.1 the public available specifications are given.
General Information Turbine name SWT-3.6-120
Manufacturer Siemens
Operating Data Rated power 3,600 kW
Cut-in wind speed 3-5 m/s
Rated wind speed 12-13 m/s
Cut-out wind speed 25 m/s
Rotor Diameter 120 m
Swept area 11.300 m 2
Power Density 2.5 m 2 /kW
Operational interval 5-13 rpm
Power Regulation Type Pitch regulation with var. speed
Generator Data Type Asynchronous
Speed 1500 at 50 Hz (4 poles)
Rated voltage 750 V
Gearbox Type 3-stage planetary/helical
Ratio 1:119
Table 3.1 Specification for the Siemens SWT3.6-120 wind turbine, [16].
The level of details is however insufficient to create an accurate model of the turbine. To model
the effect of eccentricity, the specifications for the bearings and the generator must be known.
This information is not publically available, so assumptions will be taken. The power converter
is not considered as this survey does not concern operation at variable frequency.
3.2 Bearings
The purpose of a bearing is to support the axis of rotation with a low frictional surface. The
drive train in the wind turbine has different types of rolling bearings depending on speed and
load. For the reference turbine the electrical grid power output Pg is 3.6MW, but the load at the
27

Chapter 3 - The Reference Wind Turbine
drive train is higher due to loss in the transformation from mechanical to electrical power. In
figure 3.1 the different stages of the power transformation is illustrated with some assumed efficiencies.
28
Pm
ωm
Gearbox
ηr = 0.98
Pr
ωr
Generator
ηe = 0.97
Pe
ωe
Converter
ηc = 0.99
Figure 3.1 Transformation of mechanical power to electrical power
with component efficiencies.
Pc
ωc
Transformer
ηg = 0.98
In this survey two bearings are considered; the main bearing rotating at the lowest speed and the
gearbox bearing rotating at the highest speed. These bearings are chosen as they represent the
two extremes in relation to speed and torque. The interesting power values in relation to the
bearings are the power at the main shaft before the gearbox Pm and after the gearbox Pr.
Pg
Pm 3.90MW
g c e r
Pg
Pr 3.83MW
g c e
The torque can be found using the rotational speed before and after the gearbox. The maximum
speed of the main shaft is given as 13 rpm and with a gearing ratio of 1:119 the maximum speed
after the gearbox is 1547 rpm. The relation between revolutions per minute and radians per second
is given in equation (3.3) and the maximum torque at the two location in equation (3.4) and
(3.5).
2 n
60
Pm
Tm 2.85MNm
m
Pr
Tr 23.6kNm
r
The bearings at these locations should be able to support these loads, but also the mass of the
system. The design process of bearings is a complicated process and irrelevant for this survey.
The bearings used have been chosen from the bearing company SFK Group, which supplies
bearings for a large variety of applications. [15]
3.2.1 Main Bearings
The main shaft in the Siemens SWT 3.6 turbine is supported by two self-aligning double spherical
roller bearings, [16]. Roller bearings will carry a greater load than ball bearings of the same
Pg
ωg
(3.1)
(3.2)
(3.3)
(3.4)
(3.5)

Chapter 3 - The Reference Wind Turbine
size because of the larger contact area. The spherical elements have the advantage of increasing
the contact area as the load increases, which insures alignment and low friction.
To simplify the determination of the fault characteristic in chapter four, the bearing in this survey
will be assumed to be a simple ball bearing. From the SFK online catalogue a ball bearing is
chosen with the layout shown in figure 3.2.
Db
Di
Inner
racetrack
Outer
racetrack Ball
θb
Cage
Dc
Figure 3.2 Power transformation in the wind turbine.
The geometrical specifications of the bearing are given in table 3.2.
Inner
diameter
Outer
diameter
Ball
diameter
Cage
diameter
Number
of balls
β
Do
Contact
angle
D i D o D b D c N b β θ b
Ball
angle
800 mm 1130 mm 143.5 mm 968 mm 27 40° 13.3°
Table 3.2 Specifications for the low speed ball bearing (SKF – BA1B311745).
Only the parameters needed to determine the characteristic frequency of the bearing are given.
The chosen bearing is able to support a static load of about 3MNm.
3.2.2 Gearbox Bearings
The purpose of the gearbox is to transform the slow high-torque rotation of the turbine into a
high speed low-torque rotation that can be connected to the generator. The gearbox used in the
reference turbine is a three stage planetary/Helical with a gearing ratio of 1:119. In figure 3.3
this type of gearbox is illustrated.
29

Chapter 3 - The Reference Wind Turbine
30
Low-speed
roller bearing.
Figure 3.3 Two stage planetary gearbox with one spur gear (three stages), www.nke.ak.
The first two stages use the planetary gearing and is characterised by a low gear ratio and high
torque. The third and final stage is a spur gear with high gear ratio and low torque. This design
is often chosen as it can be made compact and lightweight. The total number of bearings in this
configuration is about fifteen. In this survey only the high speed ball bearing is being considered
as mentioned earlier. A ball bearing is chosen from the SFK online catalogue with the specifications
given in table 3.3.
Inner
diameter
Outer
diameter
Ball
diameter
Cage
diameter
Number
of balls
Contact
angle
D i D o D b D c N b β θ b
Ball
angle
95 mm 250 mm 57.5 mm 172.5 mm 10 36° 36°
Table 3.3 Specifications for the high speed ball bearing (SKF - 7419 CBM).
The chosen bearing is able to support a static load of about 25kNm.
3.3 Generator
The generator is the main component in this analysis as it is the source of the fault detection, so
an accurate finite element model (FEM) is needed. The required output power Pe from the generator
can be calculated from the efficiencies shown in figure 3.1
Pg
Pe 3.71MW
g c
Stage 1
Stage 2
Stage 3
The design process of a generator is extensive and for this reason the detailed process is located
in appendix A. The design process consists of an analytical iterative process with validation
using a finite element analysis.
In figure 3.4 the first pole of the designed four poled induction generator is shown.
High-speed
ball bearing.
(3.6)

Stator slot
wedge
Rotor bar
Rotor core
Shaft
A-
A-
Chapter 3 - The Reference Wind Turbine
Figure 3.4 Finite element model of the designed reference generator showing the first pole.
The stator has 48 slots with a two layer fully pitched winding configuration distributed over four
slots. Each winding has eight turns and are connected in parallel to increase the number of turns
per slot, which initially is small due to low terminal voltage (750V). The shape of the stator
slots is squared to allow insertion of preformed coils with a high fill factor (60%). Each slot is
closed with a slot wedge to keep the windings in place. The wedges are made of a low relative
permeability material (µr ≈ 2-5). The rotor has 44 bars with a trapezoidal shape to keep the tooth
width constant to avoid saturation. The rotor bars and end rings are made of aluminium to increase
the rotor resistance and the slip value.
In table 3.4 the main dimensions of the generator are given.
B+
B+
B+
B+
C-
Parameter Value Unit Description
Dsi 731.0 mm Stator inner diameter
Dso 1250.0 mm Stator outer diameter
Dri 372.0 mm Rotor inner diameter
Dro 727.8 mm Rotor outer diameter
L 994.0 mm Length of stator core
g 1.6 mm Air gap length
Stator slot
(double layer)
Mr 2058.9 Kg Mass of rotor (core + bars + end rings)
Ms 6429.7 Kg Mass of stator (core + windings)
Table 3.4 The main dimensions of the designed reference generator.
Stator core
The generator is designed with low mass in mind since it is to be used in a wind turbine, where
weight is important. This means that the electric loading is high (56kA/m), which requires active
cooling of the machine (air or liquid).
C-
C-
C-
A+
A+
31

Chapter 3 - The Reference Wind Turbine
In table 3.5 and in table 3.6 the equivalent parameters and the performance at maximum load are
shown.
32
Parameter Value Unit Description
R1 0.59 mΩ Stator winding resistance
R ´ 2 0.79 mΩ Rotor cage resistance
Rc 4.92 Ω Core loss resistance
X1 8.92 mΩ Stator winding leakage reactance
X ´ 2 5.86 mΩ Rotor cage leakage reactance
Xm 519.08 mΩ Mutual reactance
Table 3.5 Estimated equivalent parameters for the reference generator at 50Hz.
Parameter Value Unit Description
Imax 3066.8 A Maximum phase current (RMS)
s -0.55 % Slip at Imax
Pe 3744 kW Power output at Imax
η 96.0 % Efficiency at Imax (core loss included)
PF -0.94 Power factor at Imax
Table 3.6 Performance of the reference generator at maximum load.
The design has been optimized to have high efficiency and power factor. The efficiency of 96%
includes core loss. With a power factor of -0.94 the power converter should have a rating of
about 4 MVA.
In figure 3.5 and 3.6 the flux density and the flux contours are shown at a single pole under noload
and full-load conditions, respectively.
Figure 3.5 Flux contour and density
at no-load (Iph = 819.2A).
Figure 3.6 Flux contour and density
at full-load (Iph = 3066.8A).

Chapter 4
Drive Train Failure Characteristics
This chapter describes the characteristic of failures in bearings. These characteristics are important
to understand how faults can be identified. The rotor displacement during a fault is also
investigated for use in the finite element analysis of the generator inductances in chapter five.
4.1 Bearing Failures
A bearing consist of three major components; the inner racetrack, the outer racetrack and the
rotating elements. During operation these components will deteriorate over time and ideally the
deterioration will be equally distributed over the entire contact surfaces of the bearing. This is
referred to as normal wear or fatigue. During high dynamic stress situations it is however more
likely that flaking will occur. Flaking is when a chunk of the bearing material has broken loose
and forms a small cavity. This is referred to as a bearing fault. The two concepts are illustrated
in figure 4.1.
Flaking
Distributed wear
Figure 4.1 Bearing wear (distributed) and bearing flaking (cavity). [17]
In this report the two types of incidents are distinguished from each other as they have different
characteristics.
4.1.1 Characteristic Frequencies of a Bearing (Fault ID)
When a failure is present in one of the subcomponents of the bearing it will occur with a certain
interval or characteristic frequency. If these frequencies are unique, they can be used to identify
the bearing – hence locate the fault.
There are five basic motions that are used to describe the dynamics of a bearing and each of
33

Chapter 4 - Drive Train Failure Characteristics
these motions has a corresponding frequency. The five frequencies are denoted the shaft angular
frequency ωs, the fundamental cage frequency ωc, the ball pass inner racetrack frequency ωbpi,
the ball pass outer racetrack frequency ωbpo and the ball frequency ωb. These five frequencies
are illustrated in figure 4.2. [18]
34
ωb
ωc
ωs
vor
vc
vir
ωbpi ωbpo
Figure 4.2 Typical layout of geared wind turbine with categorization of its main components.
The angular frequency of the shaft ωs is the speed of the wind turbine rotor, gear or generator
and the known variable. The other angular frequencies must be described in terms of this frequency.
In figure 4.2 vir, vc and vor, represent the tangential linear velocity of the inner racetrack,
the ball centre and the outer racetrack, respectively. Db is the ball diameter, Dc is the bearing
cage diameter and β is the contact angle of the bearing.
The relation between angular frequency ω, ordinary frequency f and the tangential linear velocity
v is given in equation (4.1), where r is the radius to the centre of rotation.
v
2 f
r
The fundamental cage angular frequency is related to the motion of the cage. It can be derived
from the linear velocity of a point in the cage vc, which is the mean linear velocity of the inner
racetrack and the outer racetrack.
Dc
β
Db
(4.1)
vc vir vor1virvor c
(4.2)
r 2 r D
c c c
In terms of the angular frequency, the velocity of the inner racetrack and the outer racetrack can
be written as:
ir ir ir ir c b
or or or or c b
cos / 2
v r r D
cos / 2
v r r D
The fundamental rotational cage frequency is then:
(4.3)

c
D
ir ir or or
c
1 Dc Db cos Dc Db
cos
ir or
D 2 2
c
Chapter 4 - Drive Train Failure Characteristics
In a motor or generator configuration, the out racetrack can be assumed stationary (ωor = 0),
since it is locked in place by an external casing, while the inner racetrack is rotating at the speed
of the shaft (ωir = ωs).
1 Db
cos
c s 1
2
Dc
The ball pass inner racetrack frequency ωbpi indicate the rate at which a ball passes a point on
the inner racetrack. The frequency is determined by the number of balls Nb and the difference
between the fundamental cage frequency ωc and the inner racetrack frequency ωir, which is
equal with the shaft frequency in the given case (ωir = ωs).
N
bpi b c s
1 Db
cos
Nb
s1s 2 Dc
N b Dbcos
s 1 2 Dc
In the same way the ball pass outer racetrack frequency ωbpo is defined as the rate at which a
ball passes a point on the outer racetrack. The frequency is determined by the number of balls
Nb and the difference between the cage frequency ωc and the outer racetrack frequency ωor,
which is zero in the given case (ωor = 0).
N 0
bpo b c
1 Db
cos
Nbs1
2 Dc
N b Dbcos
s 1 2 Dc
The ball angular frequency ωb is the rate of rotation of a ball about its own axis. This frequency
can be obtained from the difference between the cage frequency and the inner or outer frequency,
and the radii relationship. The radii relationship can be thought of as the “gear” ratio.
(4.4)
(4.5)
(4.6)
(4.7)
35

Chapter 4 - Drive Train Failure Characteristics
36
r r
ir or
b ir c
rb or c
rb
r D cos
/ 2
1 Db
cos c b
0s1 2 D r
2 2
D c Db
cos
s 12 2 Db Dc
c b
Frequency studies have shown that when defects occur in a bearing, the defects will generate
some of the above mentioned frequencies in the vibration signals. If the defective area is large
harmonics of these frequencies will also be present, [18] and [19].
For the reference wind turbine the two bearings will have the characteristics frequencies given
in table 4.1. Here presented in ordinary frequency.
Bearing
Shaft
speed
Shaft
frequency
Ball pass inner
frequency
Ball pass outer
frequency
Ball
frequency
n f s f bpi f bpo f b
high speed 1547 rpm 25.8 Hz 163.7 Hz 94.2 Hz 35.9 Hz
low speed 13 rpm 0.2 Hz 3.3 Hz 2.6 Hz 0.7 Hz
Table 4.1 Characteristic frequencies (fault IDs) for bearings in the reference wind turbine.
For the two chosen bearings the fault IDs are unique, which makes it possible to identify the
two bearings in the vibration or electrical frequency spectrum. In the electrical frequency spectrum
an incident in the bearing should also produce additional frequencies fi,k in the stator current.
In reference [19] this has been shown to have the following relationship.
(4.8)
fi, k fe k f f f f fbpi, fbpo,2 fb
(4.9)
Where fe is the electrical stator supply frequency, ff is one of the characteristic frequencies and k
is an integer value (k = 1,2,3...). Twice the ball frequency is used as it is likely that if a ball has
a defect, it will touch both inner and outer racetrack during one rotation.
If two identical bearings were chosen and rotated at the same speed, their IDs are no longer
unique. When using vibration monitoring, the difference in amplitude measured at the two different
bearings can be used to identify and locate a fault. This is possible since multiple vibration
sensors are used. But, for electrical monitoring this would not be possible since only one
sensor is used (the generator).

4.2 Rotor Displacement (Eccentricity)
Chapter 4 - Drive Train Failure Characteristics
In the previous section, the characteristic frequencies of a ball bearing have been derived. To
investigate the influence on the inductances of the generator during faults, the rotor displacement
and the resulting air gap length must be described. When the rotor is displaced, it is eccentric
positioned compared to the stator. Three types of eccentricity can occur as mentioned in
chapter two; static, dynamic and mixed eccentricity.
In figure 4.3 the geometrical configuration for a general rotor displacement is illustrated, where
Rsi is the inner stator radius, Rro is the outer rotor radius, rd is the displacement vector, θd is the
displacement angle and θr is the rotor angle.
Rsi
stator
rotor Rro
Figure 4.3 Geometrical configuration of rotor with displacement vector rd.
It should be mentioned that the following considerations suppose a uniform air gap length in the
axial direction of the machine, as mentioned in the assumptions of the project objectives. This
allows the problem to be considered as a two-dimensional case and simplifies the calculations.
However, this simplifying assumption is probably not verified in most practical cases, but is
only considered to affect the amplitude at the characteristic frequencies.
4.2.1 Misalignment (Static Eccentricity)
In the case of misaligned components, the rotor displacement does not depend on the position of
the rotor nor does it depend on a failure frequency. This is a case of static eccentricity. It is
statically locked in an off centred position. The displacement vector rd of the rotor can be describes
by its components a and b using the displacement angle.
cos sin
d 0 s d d 0 s d
y
a
rd
θd
a g b g (4.10)
where δs denote the degree of static eccentricity with respect to the uniform air gap length g0.
The uniform air gap length is equal to, g0 = Rsi - Rro.
b
θr
x
37

Chapter 4 - Drive Train Failure Characteristics
4.2.2 Bearing Failures (dynamic eccentricity)
In case of a fault in the bearing, the rotor displacement depends on the position of the rotor and
the failure rate frequency. This is a case of dynamic eccentricity. The length of the displacement
vector rd depends on the failure rate frequency and the position of the rotor θr. For a large defective
area the change in length can be assumed to a continuous function that follows a sinusoidal
tendency. If the defective area is small the change is no longer continuous, but rather an impulse.
These two concepts are illustrated in figure 4.4 and figure 4.5 for a fault in the inner racetrack
of the bearing.
38
|rd|
θ
Large
defective area
θ 2θ 3θ
Bearing
ball
Figure 4.4 Large defective area – continuous
function.
θr
|rd|
θ
Small
defective area
θ 2θ 3θ
Bearing
ball
Figure 4.5 Small defective area – impulse
function.
If the defective area is large, the displacement of the rotor is always changing. When one ball
leaves the defective area, the next ball enters. But, if the defective area is small, the rotor is only
displaced at the very instance when the ball passes the defective area. In all other positions the
rotor is centred and the displacement is zero. Related to the development of a fault, it can be
assumed that at the early stage, the defective area is small. As the fault become more severe the
defective area becomes larger. To simulate a fault at an early stage, which is important for early
fault detection, the displacement of the rotor should be done with the small defective area.
The displacement of the rotor can in the case of a small defective area be described using the
Dirac delta function as done in [19]. In equation (4.11) the criteria for the Dirac delta function δ
is given.
,
x 0
xdx1x 0,
x 0
θr
(4.11)
For all other value than x = 0 the integral of δ(x) is zero. If x = θr – θf, then when the rotor θr is
located at the fault location θf, the integral of δ(x) is one. This would result in single unit impulse
at each fault location, which in reference [19] is used to investigate the air gap change at
the fault location. This is however not considered to represent the actual shape of the defective
area. Instead an exponential function is used in this project, which also is one when θr – θf = 0,
but has a slope before and after. The function to adjust the shape of the displacement vector is

shown in equation (4.12) in terms of the rotor position.
2
( rkf )
Chapter 4 - Drive Train Failure Characteristics
2
w2 (4.12)
r g e
d r 0 d
k1
Where k is the value that satisfies the condition θr – kθf = 0, so that the first fault incident is at k
= 1, the second at k = 2 and so forth. θw is the angular width of the defective area.
The angle between each fault incident θf can be found from the characteristic failure frequencies
(ωf = ωbpi, ωbpo or ωb) described in section 4.1.
ngsng2s fngstf (4.13)
f
f f
Where ng represent the gear ratio between the location of the bearing and the rotor in the generator.
If the bearing is located at the high speed side of the gearbox then ng = 1 and if the bearing
is located at the low speed side then ng = 119.
The components a and b for the displacement vector can then be described as:
r
brg0d cos e
n
g k 1
r
arg0d sin e
n
g k 1
2
( rkf )
2
w2 2
( rkf )
2
w2 (4.14)
Where θr/ng represents the displacement angle θd. The displacement vector will move at a speed
determined by the speed at the fault location.
4.2.2.1 Inner Racetrack Failure
In figure 4.6 and 4.7, the rotor displacement is shown for an inner racetrack fault in the low
speed main bearing. Figure 4.6 shows the polar plot of the displacement vector and figure 4.6
shows the magnitude in terms of the rotor position. The following values are used: g0 = 1.6 mm,
δd = 0.5, ng = 119, θf = 2850° and θw = θb / 2 = 6.67°. The width of the defective area θw is chosen
as half the value of the angle between two balls in the bearing θb.
39

Chapter 4 - Drive Train Failure Characteristics
40
0.5
Figure 4.6 Polar plot of the displacement vector
during an inner racetrack fault in the low speed
bearing in relation to the displacement angle θd.
Figure 4.7 Magnitude of the displacement vector
during an inner racetrack fault in the low speed
bearing in relation to the rotor position θr.
Due to the large gear ratio the rotor is eccentric for about two rotations since the effective width
of the fault at the rotor is 119 times the width at the fault location. An important observation is
that since the angle between incidents is 2850°, the fault is only present at about every 8 th rotation
of the rotor. In a four poled machine this equal to 16 electrical periods at 50Hz.This can
make the fault detection difficult, as the fault is not continuously present in the electrical signal.
In figure 4.8 and 4.9 the rotor displacement is shown for an inner racetrack fault in the high
speed gearbox bearing. The following values are used: g0 = 1.6 mm, δd = 0.5, ng = 1, θf = 56.7°
and θw = θb / 2 = 18°.
|r r | [mm]
|r r | [mm]
150
210
120
240
90
270
Figure 4.8 Polar plot of the displacement vector
during an inner racetrack fault in the high speed
bearing in relation to the displacement angle θd.
1
60
300
30
180 0
150
210
Displacement angle d [deg]
120
240
90
1
0.5
60
330
30
180 0
270
300
Displacement angle d [deg]
330
|r r | [mm]
|r r | [mm]
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 1000 2000 3000 4000
Rotor position [deg]
r
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 100 200 300
Rotor position [deg]
r
Figure 4.9 Magnitude of the displacement vector
during an inner racetrack fault in the high speed
bearing in relation to the rotor position θr.

Chapter 4 - Drive Train Failure Characteristics
Since the bearing is rotating with the speed of the rotor, the number of incidents is larger than at
a fault in the low speed bearing. This makes the detection easier as the fault is continuously
present in the electric signal. But, as the angle between incidents θf divided by 360° (one rotation)
is not an integer value, the displacement will not occur at the same location. This means
that the generator must be independent on the fault location to get a reliable reading.
4.2.2.2 Outer Racetrack Failure
In figure 4.10 and 4.11 the rotor displacement for the low speed main shaft bearing and the high
speed gearbox bearing is shown in case of an outer race track failure, respectively. The polar
plot is omitted in this case.
|r r | [mm]
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 1000 2000 3000 4000
Rotor position [deg]
r
Figure 4.10 Magnitude of the displacement vector
during an outer racetrack fault in the low speed bearing
in relation to the rotor position θr.
Figure 4.11 Magnitude of the displacement vector
during an outer racetrack fault in the high speed
bearing in relation to the rotor position θr.
As the circumference of the outer racetrack is larger, the failure rate frequency is lower resulting
in fewer incidents per rotation.
4.2.2.3 Ball Failure
0
0 100 200 300
Rotor position [deg]
r
In figure 4.12 and 4.13 the rotor displacement for the low speed main shaft bearing and the high
speed gearbox bearing is shown in case of a ball failure, respectively.
|r r | [mm]
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
41

Chapter 4 - Drive Train Failure Characteristics
|r r | [mm]
42
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0 5000 10000 15000
Rotor position [deg]
r
Figure 4.12 Magnitude of the displacement vector
during a ball fault in the low speed bearing in
relation to the rotor position θr.
Figure 4.13 Magnitude of the displacement vector
during a ball fault in the high speed bearing
in relation to the rotor position θr.
A fault in a ball will have the lowest failure rate frequency of the three described cases and the
angle between faults is then extensive. For the low speed main shaft bearing this means that the
fault is only present after 36 rotor rotations. If the balls are arranged so that the defective area
touch both the inner and outer racetrack during one rotation then failure rate is twice the presented
values. This would be the case for roller type bearing or ball bearings with a 0° attack
angle.
4.2.3 Combined Failures (mixed eccentricity)
If different failure types are present, e.g. misalignment and a bearing fault, then a combination
of static and dynamic eccentricity will be present. This type of eccentricity is called mixed eccentricity.
By combining equation (4.10) and equation (4.14) a case of mixed eccentricity can be
described as, where the degree of static eccentricity occur in the direction of component a.
2
( rkf )
2
r
w2 a r g0 s d cos e
n
g k 1
r
brg0d sin e
n
g k 1
2
( rkf )
2
w2 (4.15)
To avoid that the rotor rubs against the stator then the degree of eccentricity must be less than
one, δs + δd < 1.
4.2.4 Bearing Wear (dynamic eccentricity)
0
0 100 200 300 400
Rotor position [deg]
r
In the introduction to this chapter it was mentioned that bearings failures are distinguished from
the normal distributed wear of a bearing. A bearing is designed from a statistical point of view
|r r | [mm]
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2

Chapter 4 - Drive Train Failure Characteristics
to last for certain amount of time. In the ideal case the fatigue of the bearing is equally distributed
between the two racetracks and the balls. In this case the displacement of the rotor is constant
in an off centred position and does not oscillate as in case of the small defective area. This
is a traditional case of dynamic eccentricity as illustrated in figure 4.14.
|rd|
Degree of
fatigue
θ
θ 2θ 3θ
Figure 4.14 Distributed bearing wear (fatigue) in a ball bearing.
The components of the displacement vector can be described as:
r
arg0d cos
n
g
r
brg0d sin
n
g
θr
(4.16)
Since the rotor displacement does not depend on a characteristic frequency of the bearing, it will
be impossible to determine the exact bearing causing the displacement if rotating at the same
speed (at same gear ratio ng). It is however possible to determine at which speed stage the fault
is located.
4.3 Air Gap Length
In the previous sections, the displacement of the rotor during different cases of eccentricity has
been studied. The displacement is important when doing finite element simulations, but for analytical
studies the air gap length is more useful. During eccentricity, the air gap length is no
longer uniform in the circumference of the machine. It will change with the degree of eccentricity
and the position of the rotor in the case of dynamic eccentricity. During static eccentricity
the air gap length is independent on the position of the rotor.
The air gap length at uniform conditions is the difference between the inner circumference of
the stator and the outer circumference of the rotor. The inner circumference of the stator and the
outer circumference of the rotor can be described in terms of x and y components, where θm is
43

Chapter 4 - Drive Train Failure Characteristics
the mechanical angle of the circumference.
44
x R cos y R sin
(4.17)
si si m si si m
x R cos y R sin
(4.18)
ro ro m ro ro m
By applying the displacement components (a, b) to the coordinates of the outer circumference of
the rotor then the air gap length g can then be described in terms of the mechanical angle θm and
the rotor position θr.
g
,
m r
2
xsi m xro m ar
ysi m ( yro m b r
( ...
2
(4.19)
To illustrate the use of equation (4.19) a case of static eccentricity is shown in figure 4.15. In
this case the rotor is displaced at θd = 0° with 50% eccentricity. The uniform air gap length is g0
= 1.6mm.
Air gap length g [mm]
2.5
2
1.5
1
0.5
0 50 100 150 200 250 300 350
Mechanical angle [deg]
m
Figure 4.15 Change in air gap length in the circumference of the generator during 50%
static eccentricity at 0°.
The air gap length at 0° is reduced to 0.8mm and increased to 2.4mm at 180°, which is expected
when the rotor is moved in the direction of component a located at 0°.
4.4 Chapter Conclusion
50% static ecc.
0% static ecc.
In this chapter the characteristics bearings failure has been described. In relation to condition
monitoring it is important to identify the exact defective component in order to perform effective
maintenance. A fault in a bearing will cause a mechanical vibration with a characteristic
frequency that can be related to an incident in the inner racetrack, outer racetrack or in the balls.
In condition monitoring these frequencies are known as the bearing signature or ID, and by
monitoring the amplitude at these frequencies the development of a fault can be observed. The
frequencies will both be present in the mechanical vibration spectrum and in the electrical spec-

Chapter 4 - Drive Train Failure Characteristics
trum. An important observation is that if two identical bearing are used and rotated and the same
speed, then they will have the same signature. The main shaft in a typical wind turbine is often
supported by two main bearings, and it is likely that these would be identical. In this case it
would not be possible to identify the faulty bearing using ESA due to similar signatures. This
would be possible with vibration monitoring by comparing the amplitude measured at the sensors
located at each bearing.
In the analysis a distinction was made between bearing wear and bearing faults; wear is the
slowly and distributed degradation of the bearing, a fault is the small cracks / flakes. As the
distributed wear will not have a characteristic frequency, then it will not be possible to locate
the exact worn out bearing if rotated at the same speed.
Another important observation is that due to the high gear ratio, the fault frequency of the low
speed bearing is very low. During a fault in a bearing rotating at low speed it will not be continuously
present in the electrical signal. This is considered to be a difficult challenge for the
signal processing.
These physical constraints and challenges limit the use of ESA in condition monitoring as a
replacement for the vibration based system.
45

Chapter 5
Generator Characteristics
In this chapter the characteristics of the generator is investigated during eccentricity. A simplified
analytical analysis of the change in machine inductances is compared to a finite element
analysis.
5.1 Introduction
When the rotor is displaced, the air gap length becomes non-uniform. In the hypothesis in chapter
two it was shown that the self inductance is inversely proportional to the air gap length,
when the mmf drop of the core is neglected. This is often a reasonable assumption as the permeability
of the core is much greater than that of air (µr >> µ0). However in a real case the influence
of the core must be considered. By including this factor the actual sensitivity of the generator
can be investigated.
5.2 Analytical Analysis
From the geometry of reference generator shown in figure 5.1, the magnetic properties of the
machine are investigated. The red arrowed lines illustrate the flux paths.
dscb
hst
g
hrt
drcb
135°
90°
A1
Air gap area per pole, Ag
-45°
A1
Winding a,1
Figure 5.1 Geometry of the reference generator used in the analytical analysis.
In table 5.1 the dimensions used throughout this section are given.
0°
47

Chapter 5 - Generator Characteristics
48
Parameter Value Unit Description
Dsi 731.0 mm Stator inner diameter
Dso 1250.0 mm Stator outer diameter
Dri 372.0 mm Rotor inner diameter
L 994.0 mm Length of stator core
g0 1.6 mm Uniform air gap length
dscb 164.7 mm Stator core back depth
drcb 106.6 mm Rotor core back depth
hst 95 mm Stator teeth height
hrt 71 mm Rotor teeth height
μr 3000 Relative permeability of iron core
Table 5.1 Values of the parameters shown figure 5.1.
5.2.1 Equivalent Circuit (Reluctance Network)
Magnetic field problems involving components such as current coils, ferromagnetic cores and
air gaps can be solved as magnetic circuits. Here, the analogues magnetic quantities to the corresponding
electric quantities are used in an electric circuit. In figure 5.2 the magnetic circuit of
winding a,1 and the related core section is presented. A lumped approach is used, so that all
stator teeth reluctances at one pole are lumped together, and so forth. The air gap reluctances are
lumped into three parts, so that one part accounts for the send path (0°-90°) and one for each
return path (-45°-0° and 90°-135°).
2 st
scb
Na,n·Ia,n
an
,
scb
st 2 st
g1, n
g1, n
g1,
n
2 rt
rcb
rt
rcb
Figure 5.2 Equivalent magnetic circuit of phase winding a,n.
2 rt
scb is the stator core back reluctance, st is the stator teeth reluctance, g is the air gap reluctance,
rt is the rotor teeth reluctance and rcb is the rotor core back reluctance. If core satura-

Chapter 5 - Generator Characteristics
tion is neglected (µr is constant) then the core related reluctances are constant during eccentricity.
The stator core back reluctance scb is determined as:
lscb
scb A
0
r scb
where the stator core back length lscb and the area Ascb is found as:
(5.1)
1
lscb Dso dscb Ascb dscb L
p (5.2)
The stator teeth reluctance st and rotor teeth reluctance rt are determined as:
h
A
st
st
0rAst st
h
A
rt
rt
0rArt rt
For simplification then the total teeth area is chosen to be half the air gap area, which is a common
choice in machine design. The rotor core back reluctance rcb is determined as:
lrcb
rcb A
0
r rcb
where the rotor core back length lrcb and the area Arcb is found as:
A
g
2
A
g
2
(5.3)
(5.4)
(5.5)
1
lrcb Dri drcb Arcb drcb L
p (5.6)
The air gap reluctances will change during rotor eccentricity, so to determine the reluctance the
mean air gap length must determined at each angle and for each winding. For winding n of
phase a the mean air gap length can be determined at the three locations using the air gap length
function found in chapter four - equation (4.19).
n360
p
p
g g ,
d
360
1, n r m r m
(5.7)
n1360 p
360 n0.5
p
2
p
g g ,
d
(5.8)
1,
n r m r m
360 n360
p
360 n1
p
2
p
g g ,
d
360
1,
n r m r m
(5.9)
n1.5360 p
49

Chapter 5 - Generator Characteristics
The reluctance at the three positions is then:
50
g
1
A D g L
1, n r
g1, n
0
Ag g
p
si 0
g
1,
n r
g1, n 1 0
2 Ag
g
1,
n r
g1, n 1 0
2 Ag
(5.10)
(5.11)
(5.12)
The total reluctance a,n of the given circuit can be determined by considering the three parallel
branches.
scb st g 1,
n rt rcb
1
...
scb 2stg1, n 2rtrcb
1
1
2 2 ...
a, n st g1, n rt
1
From the total reluctance and the mmf the magnetic flux a,n can be determined.
an ,
N I
a, n a, n
an ,
The inductance of a winding is defined as the ratio of magnetic flux linkage Φ to current I.
(5.13)
(5.14)
N
L (5.15)
I I
In terms of the total reluctance the self-inductance can be found as:
L
an ,
2
Na, n a, n Na, n Na, n Ia,
n Na,
n
I I (5.16)
a, n a, n a, n a, n
The self-inductance inductance of winding a,n can now be estimated. Since the windings for the
reference machine are coupled in parallel this must be taken into account to determine the selfinductance
of phase a, La,par.
L
a, par
n1 an ,
1
p
1
(5.17)
L
Other machines could be coupled in series and to evaluate the difference between the two methods,
equation (5.18) is used for the series connected windings. In this case the number of turns
should be adjusted. The reference machine has eight turns per winding, which if coupled in
parallel also is eight turns per phase. But 32 turns if coupled in series, so the number of turns per

winding must be adjusted to get a proper comparison.
p
a, ser a, n
n1
Chapter 5 - Generator Characteristics
L L
(5.18)
From the derived equation it is now possible described the sensitivity of the self-inductance of
phase a during eccentricity. If the self-inductance of phase b and c should be estimated, the calculation
of the mean air gap length would have to be shifted by 30° for phase c and 60° for
phase b (if a four poled machine is used). This analytical analysis is however based on phase a.
5.2.2 Relative Change in Self-Inductance (Sensitivity)
To find the sensitivity of the inductance when eccentricity occur a simple misalignment is considered.
In case of a misalignment the rotor is shifted to a static off centred position and the air
gap length is time independent. This will make the interpretation of the results easier. The displacement
components a and b for misalignment was derived in equation (4.10).
cos sin
a g b g (5.19)
d 0 s d d 0 s d
Where g0 is the uniform air gap length, δs is the degree of displacement and θd is the displacement
angle. First, the relation between the displacement angle and the relative change is investigated
for the self-inductance of phase a, as shown in figure 5.3. The magnetic flux path for
winding a,(n = 1:4) is located at 45°, 135°, 225° and 315°.
L a ( s = 0.5) / L a ( s = 0)
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.96
parallel
serial
0.95
0 45 90 135 180 225 270 315 360
Rotor displacement angle
d
Figure 5.3 Six-poled SCIG with centred rotor. Inductance of winding a1 is equal to winding a2.
The relative change is small compared to the large degree of eccentricity. With the air gap
length reduced by 50%, the change is only 2-3%. The inductance is increasing when connected
in serial and decreasing when connected in parallel. This makes sense as serial connected inductances
are most sensitive to the largest inductance, where parallel connected inductances are
most sensitive to the smallest inductance.
In table 5.2 the relative change in the inductance of winding n of phase a is given.
51

Chapter 5 - Generator Characteristics
52
ΔLa,1 ΔLa,2 ΔLa,3 ΔLa,4 ΔLa θd
Parallel 1.222 1.222 0.809 0.809 0.974 90°
Serial 1.399 0.979 0.756 0.979 1.028 45°
Table 5.2 Relatively change in inductance of coil a,n at 50% eccentricity.
The change is large when considering a single winding, but when combined the change is small
as they tend to cancels each other out.
In figure 5.3 it also noticed that the relative change is not independent of the angle of displacement
– it oscillates. This is an important observation as it could lead incorrect readings of the
degree of eccentricity at certain positions. These oscillations are reduced as the numbers of
poles are increased as shown in figure 5.4, where the relative change has been calculated for an
increasing pole numbers.
L a ( s = 0.5) / L a ( s = 0)
1.07
1.06
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
p = 4
0.97
p = 6
0.96
p = 10
0.95
0.94
p = 20
0 45 90 135 180 225 270 315 360
Rotor displacement angle
d
Figure 5.4 Relatively change in inductance with increasing number of poles.
Increasing the number of poles reduces the oscillations and at high pole a number they are removed.
Another important observation is that the relative change is increased. This indicates
that multi-poled machines could be more sensitive to eccentricity and that the readings are more
reliable.
5.2.3 Leakage and Mutual Inductance
Until now only the self-inductance of a winding has been considered. The self-inductance however
consists of a leakage part Lla and a mutual part Lma.
La Lma Lla
(5.20)
The mutual inductance represents the flux that links the stator and the rotor circuit, where leakage
represents all other fluxes. In the equivalent circuit, the leakage reluctance has not been
included as only the flux passing the air gap has been described. The investigated selfinductance
is actually a representation of the mutual inductance.

Chapter 5 - Generator Characteristics
The leakage inductance of a winding can be difficult to determine as it consist of many subcomponents.
In the design process of the reference generator in appendix A, the estimated leakage
inductance is based on slot leakage, zig zag leakage and end turn leakage.
Lla Lsl Lzzl Lel
(5.21)
The three components are illustrated in figure 5.5.
Stator
slot
Air gap
Rotor
slot
Stator slot
leakage flux
Mutual
flux
Rotor slot
leakage flux
End turn
leakage flux
Figure 5.5 – From the left: slot leakage, zigzag leakage and end turn leakage.
The slot leakage and the end turn leakage do not depend on the length of the air gap, but the zig
zag leakage does in some degree. In the design process the following equation is used to estimate
the stator zig zag leakage inductance. [26]
2 2
ss a k
st e
p a 1 a 1 k
Lzzl Lma 1 2
2 12 Nss 2k
g
w g
(5.22)
Where Nss is the number of stator slots, τss is the stator slot pitch, wst is the stator tooth width and
ge is the effective air gap length. This equation is only a rough estimate for machines with uniform
air gaps. If k is assumed constant then the zig zag leakage is proportional to the change in
the mutual inductance. But, since the zig zag leakage only accounts for about 6% of the total
leakage inductance Lal for the reference machine, then a 3% change in mutual inductance will
only affect the leakage inductance by about 0.2%.
The actual change in the leakage inductance will be investigated during the finite element analysis
of the machine, as this is considered to give better results.
5.3 Finite Element Analysis (FEA)
In order to verify the analytical obtained results and to do further analysis, a finite element analysis
of the reference generator is performed. The software tool used is MagNet by Infolytica.
53

Chapter 5 - Generator Characteristics
5.3.1 Simulation Settings
To obtain a proper accuracy of the simulations while keeping the calculation time low, the grid
of finite element model has been separated into four regions. These four regions are illustrated
in figure 5.6.
Region 2
Region 4
54
Figure 5.6 Grid regions used in finite element model.
The grid in region one and region four covers the outer part of the stator and the inner part of the
rotor and is chosen to be a coarse grid. The default grid is used in these two regions. Region two
covers the area surrounding the stator and rotor teeth. The grid in this region has been adjusted
with a curvature angle of 1° to increase the accuracy. The third region cover the air gap of the
machine and has been adjusted to a maximum element size of 1mm. This insures accurate results
during eccentricity.
For a proper value of the leakage inductance including all subcomponents (slot, zigzag and end
turn) a 3D FE model is required. However, since the calculation of 3D models is time consuming,
it would be an advantage to use 2D where possible. The slot and air gap related components
can both be found using a 2D model, and since the end turn leakage is independent on the
air gap length, as shown in the previous section, a 2D model is considered sufficient.
5.3.2 Stator Leakage Inductance
To determine the leakage inductance in the FE analysis, the model is fitted so that it does not
allow any flux to link the rotor bars and end rings. In MagNet this can be done by applying a
perfect conducting material (σ →∞) to the rotor bars. For a conductor with infinite conductivity
no internal electric field (E) can be maintained which leads to the condition that B = 0. In other
words the flux produced by the stator coils is repelled by the perfect conductive rotor cage. The
resulting flux linkage measured in the FE analysis is then an expression of the leakage flux.
L
1
1
i
1
Region 1
Region 3
(5.23)
The current level for i1 is the magnetizing or no-load current. The no-load current is determined
at zero slip (s = 0) and by use of the estimated equivalent parameters.

I
0
V
R X R X
1 ph
1 c || m
750 V / 3
819.2A
5.9m 8.92m 519.08m
Chapter 5 - Generator Characteristics
(5.24)
Later in this chapter the effect of increasing the load and hereby the saturation of the generator
is investigated.
In figure 5.7 the resulting flux contour is plotted for a single pole with the rotor bar material as
perfect conductive.
Figure 5.7 Finite element model with rotor bars fitted with perfect conductive material.
In figure 5.8 the resulting leakage reactance is shown when rotating the rotor two rotor slots
(16.36°). The solid lines are the leakage inductance with no eccentricity and the dotted lines are
with 50% static eccentricity (δs = 0.5) at θd = 90°.
Stator leakage inductance [H]
x 10
7.5
-5
7
6.5
6
5.5
5
4.5
4
3.5
0 2 4 6 8 10 12 14 16
Rotor position [deg]
r
L1a( s = 0)
L1a( s = 0.5)
L1b( s = 0)
L1b( s = 0.5)
L1c( s = 0)
L1c( s = 0.5)
Figure 5.8 Stator leakage inductance at 0% eccentricity (solid line) and at 50%
eccentricity (dotted line).
55

Chapter 5 - Generator Characteristics
The oscillating tendency is due to the slotting effect, which means that the flux linkage is dependent
on the position of the rotor. With 50% eccentricity the increased is about 3%.
5.3.3 Rotor Leakage Inductance
The same approach as for the stator leakage inductance is used to determine the rotor leakage
inductance. The stator slots are fitted with perfect conductive material, so that the flux produced
by the rotor cage is repelled by the stator windings. The leakage inductance is then estimated as:
56
L
2
2 (5.25)
i2
The maximum rotor current i2 can be found from the stator current and the transformations factor
from stator to rotor side.
m Nk 1 1 w1
I2 I1 m2 N2kw2 380.9577 819.2A855A 440.51 (5.26)
Where m1 is the number of stator phases, N1 is the number of stator turns, kw1 is the stator winding
factor, m2 is the number of rotor phases, N2 is the number of rotor turns (0.5 for squirrel
cage) and kw2 is the rotor winding factor (1 for squirrel cage). These values have been calculated
during the design process in appendix A.
The current for bar n (Ib,n) can be found from the electrical angle α between each bar. The details
are given in appendix A, section A.6.2.
p
16.36 Ibn , I2cosn 0.5
(5.27)
Nrs
In figure 5.9 the resulting flux contour is plotted for a single pole with the stator slot material as
perfect conductive.
Figure 5.9 Finite element model with stator slots fitted with perfect conductive material.

Chapter 5 - Generator Characteristics
The resulting leakage reactance is shown in figure 5.10 when rotating the rotor two stator slots
(15°). The solid lines represents the leakage inductance with no eccentricity and the dashed lines
are with 50% static eccentricity (δs = 0.5) at θd = 90°.
Rotor leakage inductance [H]
x 10-5
3.75
3.5
3.25
3
2.75
2.5
2.25
2
1.75
1.5
0 2 4 6 8 10 12 14
Rotor position [deg]
r
Figure 5.10 Rotor leakage inductance at 0% eccentricity (solid line) and at 50%
eccentricity (dotted line).
Similar to the stator leakage inductance, the rotor leakage inductance is increased about 3% at
the peak value.
5.3.4 Stator Self and Mutual Inductances
In the analytical analysis only the self- and mutual inductance of a single phase was considered,
but in the actual case one must consider the mutual inductance between each phase. The complete
inductances for the stator L1 can be described in matrix form as:
LaaLbaLca L
L L L
1
ab bb cb
LacLbcL cc
The diagonal elements represent the self inductance and the off diagonal elements represent the
mutual inductances. The inductances of the first column are found with ib = ic = 0A.
a b c
aa
ia ab
ia ac
ia
L2( s = 0)
L2( s = 0.5)
(5.28)
L L L (5.29)
The inductances of the second and third column are found with ia = ic = 0A and ia = ib = 0A,
respectively.
In figure 5.11 and in figure 5.12 the stator self-inductances and the mutual inductances are
shown. The inductance matrix is symmetrical about the diagonal, so only the lower triangular
elements are shown (i.e. Lab = Lba). The solid lines represents the leakage inductance with no
eccentricity and the dotted lines are with 50% static eccentricity (δs = 0.5) at θd = 90°.
57

Chapter 5 - Generator Characteristics
58
Stator mutual inductance [H]
Stator mutual inductance [H]
x 10-3
2.55
2.5
2.45
2.4
2.35
2.3
2.25
0 2 4 6 8 10 12 14 16
Rotor position [deg]
r
x 10-3
-0.6
-0.7
-0.8
-0.9
-1
-1.1
-1.2
-1.3
Figure 5.11 Stator self inductances at 0% eccentricity (solid line) and at 50%
eccentricity (dotted line).
-1.4
0 2 4 6 8 10 12 14 16
Rotor position [deg]
r
Figure 5.12 Stator mutual inductances at 0% eccentricity (solid line) and at 50%
eccentricity (dotted line).
The self- and mutual inductances has a more constant change during eccentricity and is less
influenced by the rotor position. The self inductances are decreased by about 2-3% which is
close the analytical found estimate. The mutual inductances are increasing, but the change is
larger – about 3-5%. The mutual inductances are represented by a negative value, since the flux
linkage is negative compared to flux generated in winding a.
5.4 Relative Change and Displacement Angle
Laa( s = 0)
Laa( s = 0.5)
Lbb( s = 0)
Lbb( s = 0.5)
Lcc( s = 0)
Lcc( s = 0.5)
Lab( s = 0)
Lab( s = 0.5)
Lac( s = 0)
Lac( s = 0.5)
Lbc( s = 0)
Lbc( s = 0.5)
In the analytical analysis it was shown that the relative change in the inductance was depending
on the displacement angle. The same analysis has been performed with the finite element model.
The peak value at 4.09° for stator self- and leakage inductance is used, and the peak value at
3.75° for the rotor leakage inductance. The results are shown in figure 5.13.

Relative change [p.u.]
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0 45 90 135 180 225 270 315 360
Displacement angle [deg]
d
Chapter 5 - Generator Characteristics
Figure 5.13 Relatively change in inductances as a function of the displacement angle.
The relative change of the self-inductance is close to the analytically estimated result for the
parallel connected windings. It peaks at the cross over point between two windings, which for
phase winding a is located at 0°, 90°, 180° and 270°. Oscillations are also seen in the stator and
rotor leakage inductance with less uniformity.
5.5 Saturation Effect
Until now the characteristic of the generator during eccentricity has been investigated at no-load
current. But, as the field strength H increases, the flux density B in the core increases until saturation
is reached. The relation between H and B is represented by the magnetizing or hysteresis
curve. The magnetizing curve for the core material used in the reference generator is shown in
figure 5.14 along with the relative permeability (red curve).
Flux density B [T]
2
1.5
1
0.5
Saturated
region
Figure 5.14 Magnetizing curve and relative permeability of core iron in reference generator.
Since the inductance of a winding is defined as the ratio of magnetic flux linkage to current,
then the inductance will drop as the core is saturated. In the saturated region, the inductance is
L1a
L2
Laa
Laa est.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 10 4
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 10 4
0
Field strength H [A/m]
2000
1500
1000
500
Relative permeability [u/u 0 ]
59

Chapter 5 - Generator Characteristics
less influenced by small changes in the flux density. As eccentricity is detected by small variations
in the flux density, then it is expected that relative change decreases as the core saturates.
In figure 5.15 and 5.16, the inductances and the relative change are shown at 50% eccentricity
while increasing the current from 1A to 3200A.
60
Leakage inductance L 1a ,L 2 [H]
7.5
7
6.5
6
5.5
5
4.5
4
3.5
x 10-5
3
0 500 1000 1500 2000 2500 3000
Stator phase current [A]
Figure 5.15 Inductances at 0% eccentricity (solid line) and with 50% eccentricity (dashed lines)
as a function of the phase current.
Relative change [p.u.]
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
L1a( s = 0)
L1a( s = 0.5)
L2( s = 0)
L2( s = 0.5)
Laa( s = 0)
Laa( s = 0.5)
L1a( s = 0.5)
L2( s = 0.5)
Laa( s = 0.5)
0.97
0 500 1000 1500 2000 2500 3000
Stator phase current [A]
Figure 5.16 Relatively change in inductances as a function of the phase current.
x 10
3
-3
The saturation level of the core clearly has influence on the relatively change in the inductance
values. The change decreases with saturation as expected. This makes it difficult to classify the
same fault during different load condition. In a wind turbine with a full converter, it is likely
that a constant V/f regulation is used to keep a constant saturation level. In this case it is easier
to classify the same fault. But, if the saturation level is chosen high to reduce size and weight of
the generator, then the relative change is small.
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
Self inductance L aa [H]

5.6 Linearity
Chapter 5 - Generator Characteristics
In order to relate relative change in the inductances to the degree of the mechanical fault (eccentricity)
a proportional or linear relation would be preferable. This will make the electrical signal
analysis easier. In figure 5.17 the relative change is shown when varying the degree of eccentricity
from 0 to 50%. The estimated result using the reluctance network is also shown for the
self-inductance (red dashed line).
Relative change [p.u.]
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
L1a
L2
Laa
Laa est.
0.97
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Degree of static eccentricity [p.u.]
s
Figure 5.17 Relatively change in inductances as a function of the degree of static eccentricity.
It is seen that there is no proportionality or linearity between the degree of eccentricity and the
relative change in the inductance values. This will make it difficult to monitor the development
of a fault if the machine characteristics are unknown.
5.7 Chapter Conclusion
In this chapter the characteristics of the generator inductances during eccentricity has been investigated.
The purpose was to uncover conditions that should be taken into account if ESA
should be used as a reliable conditions monitoring system.
By use of analytical and finite element analysis it has been illustrated that the relative change in
the inductances are low compared to the degree of eccentricity. It is therefore considered to be
difficult to locate small early stage faults. It was also seen that the inductances are influenced by
the fault displacement angle and the saturation level, and that linearity between the degree of
eccentricity and the relative change was not present. To account for these conditions precise
knowledge of the monitored generator is required. This will make the system complicated to
adapt for types of wind turbine generators.
Note: In this chapter the analytically found parameters have been used to estimate the no-load
current. This was not the original idea. Since there is a small different between the analytically
and the finite element found parameter in appendix A. The actual no-load current is smaller –
about 710A. This should result in the same characteristics, but with smaller relative change.
61

Chapter 6
Time-Transient Simulation
In chapter five a static finite element analysis was conducted. In this chapter a time transient
simulations is used to analyse the behaviour of the generator during dynamic eccentricity. This
should illustrate how a fault can be detected.
6.1 Introduction
MagNet offers the possibility of performing time transient simulation with motion components
such as the rotor in an electrical machine. By performing simulations with rotor motions it
should be possible detect changes in electrical signals due to variations in inductances. Ideally,
it would have been interesting to simulate the early stage bearing faults with the exponential
function derived in chapter four. But, MagNet has some limitations to motions components –
they can either have a rotary motion or a linear motion in one direction. Since the exponential
function requires both a rotary motion and a linear motion in two directions, it is not possible to
use this function. It is however possible to simulate simple dynamic eccentricity where the rotor
is statically shifted from the center of the stator while rotating. This type of eccentricity occurs
at distributed bearing wear and an expression for the components of the displacement vector
was derived in equation (4.16), and shown below.
cos sin
a g b g (6.1)
r 0 d r r 0 d r
It is only possible to rotate the displacement vector with the same speed as the rotor (θd = θr),
which could illustrate a worn out generator bearing. In figure 6.1 the motion component is illustrated.
Stator
ωr
a
b
ωr
Rotor
(motion component)
Center of rotation
Figure 6.1 Displaced motion component used to simulate dynamic eccentricity in MagNet.
With this type of motion the inductances are constantly changing with the position of the rotor
and as a result frequency components related the rate of change should be present in the electri-
63

Chapter 6 - Time-Transient Simulation
cal frequency spectrum. In reference [23] it has been shown that the frequency components will
appear as side-band components to the fundamental electrical frequency fe given as:
64
s
21
fecc,k fe k fr fr fe
(6.2)
p
Where fr is the mechanical rotational frequency of the rotor, determined by the slip and the
number of poles in the generator. For the four poled reference generator at no-load (s = 0) the
components are expected at k
6.2 Model Modifications and Simulation Settings
To perform time transient simulations modification has been made to model used in the static
analysis. The modifications are explained in this section.
6.2.1 Rotor Skew
The simulations are done in 2D to reduced simulation time. Since the skew effect of the rotor
cannot be taken into account in a 2D simulation, the slotting effect using the static model would
be too significant. The slotting effect will cause high harmonic currents due to the large changes
in the flux density in the air gap, when the rotor slot passes the stator tooth. To reduce the slotting
effect, the rotor slots have been redesigned for the transient model. In figure 6.2 the slot
layout used in the two models is shown.
Figure 6.2 Rotor slot layout in static model (left) and transient model (right).
With the new design it has been possible to reduce the slotting effect to an acceptable level. It
should be mentioned that the design changes increases the leakage reactance and the mutual
inductance. This will result in a different no-load current compared to the one used in the static
model, and the relative change during eccentricity might be different. This is considered acceptable
as the main goal is to show that eccentricity will introduce frequency components.
6.2.2 Electrical Circuit
In order to perform time transient calculations the stator and rotor coils must be connected in an
electrical circuit. In figure 6.3 the electrical circuit is shown for stator phase a and for a small
part of the rotor cage.

R27
5.6455e-007
R28
5.6455e-007
V1
PWL
Rotor_coil_1
T1 T2
Rotor_coil_2
T1 T2
R101
0.00059
R13
5.6455e-007
R14
5.6455e-007
Chapter 6 - Time-Transient Simulation
Figure 6.3 Electrical circuit for a single stator phase (top) and for a part of the rotor cage (bottom).
Resistor R1-R4 has been added to account for the end winding resistance, which is not present
in the 2D model. The same has been done in the rotor cage, where R27 for instance represent
the end ring section between rotor coil 1 and 2. R101 is added to account for the increase in
leakage and mutual inductance. The end turn leakage inductance has been neglected, since it is
small and not considered to affect the results. The conductivity and cross sectional area has been
changed, so the resistances match the values found in Appendix A.
6.2.3 Voltage and Time Settings
R1
0.001088
R2
0.001088
R3
0.001088
R4
0.001088
phase_a_1
T1 T2
phase_a_2
T1 T2
phase_a_3
T1 T2
phase_a_4
T1 T2
Rotor_coil_44
T1 T2
Rotor_coil_43
T1 T2
The generator is mainly inductive with a small resistance and can be considered as an RL circuit.
Due to the large inductance a huge magnetizing current is drawn as the voltage source is
switched on. This will cause a long transient period and a displacement of the currents before
steady state is reached. Since the generator is to be analyzed at steady state it would be a time
advantages to reduce the transient period. Adding a progressive voltage source, that slowly increases
the voltage from min. to max. in 200ms, can reduce the transient period. The effect is
shown in figure 6.4 for a single phase current using normal and progressive voltage development.
R78
5.6455e-007
R77
5.6455e-007
R100
5.6455e-007
R99
5.6455e-007
65

Chapter 6 - Time-Transient Simulation
66
Stator phase current [A]
x 104
1
0
-1
-2
-3
-4
progressive
-5
0 50 100 150
Time [ms]
200 250 300
Figure 6.4 Current transients using normal and progressive voltage development.
The transient period is reduced but still long. To reduce calculation time, different time steps
have been used. In table 6.2 the time steps are given.
0-700ms 700-800ms 800-900ms
time step 1ms 0.5ms 0.1ms
Table 6.1 Time step used in transient model.
In the last time period from 800 to 900 ms the last 80ms is used in the spectrum analysis. During
80ms or four electrical periods at 50Hz, the rotor has moved one rotation at no-load. The
total amount of steps is 1900 and with a simulation time of 30-60 seconds per step, the total
simulation time is between 16 and 32 hours. This is achieved with the default grid in MagNet.
Simulations done with eccentricity tend to be more time demanding due to the finer mesh in the
small air gap regions. The long simulation time is one of the downsides of using finite element
analysis for time based simulations.
The initial idea was to investigate the behaviour during different conditions, such as the degree
of saturation and eccentricity. But, due to the long simulation time only a few simulation has
been made to illustrate that it is possible to detect eccentricity with spectrum analysis.
6.3 Current Spectrum Analysis at No-load
In figure 6.5 the current is shown at no-load with no eccentricity and with 50% dynamic eccentricity.
The rotor is kept at a constant speed of 1500 rpm throughout the simulation.
normal

Stator phase current I a [A]
600
400
200
0
-200
-400
Chapter 6 - Time-Transient Simulation
-600
0 0.01 0.02 0.03 0.04
Time [s]
0.05 0.06 0.07 0.08
Figure 6.5 Stator current Ia at no-load with 0% eccentricity and at 50% eccentricity.
The high frequency oscillation in the current is a result of the slotting effect. Even with the rotor
slot redesigned they are still present. The slotting effect introduces harmonic currents determined
by the number of rotor bars. The m‟th harmonic slot frequency component fslot,m depend
on the number of rotor bars Nrs, the slip s and the fundamental electrical frequency fe and can be
calculated as shown in equation (6.3). [23]
2Nrs 1s
f mf p
slot ,m e
2 48 1 0
fslot , 1 150Hz1150Hz 4
In figure 6.6 the Fast Fourier transform (FFT) is shown for the current with no eccentricity in a
frequency range of 0-2000Hz. The current signal has been extended in time to increase the frequency
interval. This is done by repeating the signal shown in figure 6.5.
Relative Magnitude [dB]
0
-50
-100
Fundament frequency
component – 50Hz
Slot frequency
component
1150Hz
Figure 6.6 FFT of stator current Ia with 0% eccentricity, Ia1 = 423A.
0% ecc.
50% ecc.
-150
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Frequency [Hz]
(6.3)
67

Chapter 6 - Time-Transient Simulation
Since the slot related frequency component is located at a relatively high frequency, it is not
considered to influence the frequency components introduced by eccentricity. These should be
located near the fundament frequency component. In figure 6.7 the FFT is shown for the two
currents from 0-150Hz.
68
Relative Magnitude [dB]
Relative Magnitude [dB]
0
-10
-20
-30
-40
-50
-60
-70
-80
0 25 50 75
Frequency [Hz]
100 125 150
0
-10
-20
-30
-40
-50
-60
-70
fe - fr
fe + fr
Figure 6.7 FFT of Stator current Ia at no-load with 0% eccentricity and at 50% eccentricity.
With 50% eccentricity two small side band are present at the fe ± fr components. The change is
small, but noticeable. At fe + fr (75Hz) the current is increase from -65dB to -56.2dB and at fe - fr
(25Hz) the current is increase from -62dB to -54.55dB. The second and third frequency components
are not considered to be related to eccentricity as they exist in both currents.
6.3.1 Signal stability (Oscillating effects)
fe + 2fr
fe + 3fr
0% ecc.
50% ecc.
-80
0 25 50 75
Frequency [Hz]
100 125 150
To get a reliable indication of the degree of eccentricity a stable current signal is required. This
is important if the condition monitoring system should be able to predict the development of a
fault. By applying a band pass filter with a window of ±2Hz the stability of the fundamental
current and the two eccentric frequencies has been studied. The result is shown in figure 6.8.

Stator phase current [A]
Stator phase current [A]
Stator phase current [A]
-50
-100
-150
-200
-250
-300
-350
-400
-450
0
50
450
400
350
300
250
200
150
100
Chapter 6 - Time-Transient Simulation
50Hz component
19.5 19.55 19.6 19.65 19.7 19.75
Time [s]
19.8 19.85 19.9 19.95 20
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
25Hz component
-0.7
19.5 19.55 19.6 19.65 19.7 19.75
Time [s]
19.8 19.85 19.9 19.95 20
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
75Hz component
-0.8
19.5 19.55 19.6 19.65 19.7 19.75
Time [s]
19.8 19.85 19.9 19.95 20
Figure 6.8 Band pass filtered fundamental current (top) and the two eccentric components (fe ± fr). The
filter window is ±2Hz at the related frequency.
The fundament current (50Hz) and the low frequency eccentric current (25Hz) seem unaffected
by oscillations. However a small DC offset seems to be present, which could indicate that the
69

Chapter 6 - Time-Transient Simulation
signals are still affected by the transient period. The high frequency eccentric component (75Hz)
does have an oscillating tendency. The amplitude has a small 25Hz oscillation, which is equal to
the mechanical speed of the rotor. This indicates that the observation made using static model in
chapter five is valid. The inductances and hence the currents depends on the displacement angle
of the rotor.
6.4 Chapter Conclusion
The purpose of the time transient simulation was to show that it is possible to detect eccentricity
using current spectrum analysis and that the frequency components would appear according to
theory. A Simulation made at no-load with 50% eccentricity has shown the frequency components
occur as sidebands to the fundament current. The amplitude is however very small, only
0.15% of the fundamental current. This could lead to a poor signal to noise ratio when used in
practice.
Using a band pass filter the stability of the introduced eccentric components has been investigated.
It has been shown that oscillating tendencies are present in the high frequency component,
which is assumed to be caused by change in the rotor displacement angle. This verifies the
observation made in chapter five. If the components are oscillating, it can be difficult to get a
reliable signal for the condition monitoring system.
The original idea was to simulate the model under various load and eccentricity conditions, but
due to the long simulations time and other problems, only two useful simulations has been
made. Some of the problems encountered during the simulation process are given below:
- If the grid in the air gap is too large then eccentricity is not detected. But if the grid is too
small, the calculation time is extensive.
- Since the analyzed signal is only recorded for 80ms, it is extended to increase the frequency
interval of the FFT. Extending the signal can lead to undesired signals (artifacts) in the
spectrum analysis. Artifacts can occur if the start point and end point of the signal does not
match in time or value. Then the reconstructed signal is not an accurate representation of
the original signal. An example of a signal containing artifacts is shown below. The artifacts
can be identified by the constant frequency interval. These artifacts can lead to incorrect
results as they are present at the same frequencies, where the eccentricity components
are expected.
70
Relative Magnitude [dB]
0
-10
-20
-30
-40
-50
-60
-70
Artifacts
-80
0 25 50 75
Frequency [Hz]
100 125 150

Chapter 7
Small Scale Test
In this chapter the results from a small scale test on an induction machine are presented. The
purpose of this test is to verify some of the observations made in the previous chapters.
7.1 Introduction
To verify the generator characteristics found using the finite element model a small scale test
has been carried out. The test is done by running an induction motor with an eccentric located
mass. This creates centrifugal forces acting on the mass, causing the rotor to be displaced while
rotating (dynamic eccentricity). The degree of eccentricity is changed by varying the centrifugal
force.
The test should verify;
That it is possible to force eccentricity to an induction machine considered to be
in good / normal condition.
That dynamic eccentricity will introduce frequencies according to theory and
simulated results.
7.2 Test Setup
The test setup consists of an induction machine fitted with a variable eccentric load, a power
converter for voltage/frequency control and an oscilloscope for measurements. The complete
setup is shown in figure 7.1 with apparatus connections and specifications. Pictures from the
actual setup are located in appendix B.
V/f control
Spitzenberger
DM 150000/PAS
AC/DC Mains
Simulation
Oscilioscope
Tektronix TDS 2014B
Ch. 1: Va Ch. 2: Ia
Ch. 3: Ib Ch. 4: Ic
Fs = 5000 Hz
(sample frequency)
Figure 7.1 Complete setup used in small scale eccentricity test.
A close up of the eccentricity tool fitted to the machine is illustrated in figure 7.2.
Induction Machine
ASEA M160M
p = 4 P2 = 11kW
Vn = 380V In = 23A
PF = 0.83 (delta con.)
Eccentricity tool
71

Chapter 7 - Small Scale Test
72
Motor mount
Thread
Angular velocity, ωr
Adjustable length, R1 (75mm-120mm)
Figure 7.2 Tool used to simulate dynamic eccentricity.
Rotating mass, M1 (0.65kg)
Centrifugal force, F1
The tool consists of a rotating mass M1 made of aluminum with a weight of 0.65kg. The mass is
connected to the machine by a thread so the displacement length R1 can be varied. When rotating,
a force F1 will act on the mass in the radial direction and if large enough, the rotor is displaced.
The force is known as the centrifugal force, given as:
2
2
F 1 r ,R1 M1 R1 r r
nr
(7.1)
60
The force can be varied by changing the speed of the rotor ωr or the displacement length R1. The
force is sensitive to changes in speed since squared, while it is linear proportional to the displacement
length.
7.3 Test Results
The test has been performed at 10Hz, 15Hz and 20Hz and by adjusting the length from 75mm to
120mm. Due to high mechanical vibrations, the maximum frequency was chosen as 20Hz. At
20Hz and 120mm mass displacement the force acting on the machine is about 300N. The voltage
and currents are measured with a sampling frequency of 5000Hz and for at least four periods.
In four electrical periods the four poled machine has completed one mechanical rotation.
7.3.1 Spectrum Analysis of Stator Current
During eccentricity harmonic components should reveal around the current fundamental frequency.
As for the simulated results the harmonic frequencies are calculated as:
s
21
fecc,k fe k fr fr fe
(7.2)
p
The induction machine is running at no-load condition except for the inertial load of the eccentricity
tool. The slip can be assumed to be close to zero (s = 0).
In figure 7.3 the stator current is shown at 20Hz with R1 = 0 and R1 = 120mm. This should
represent the machine with no eccentricity and with maximum eccentricity.

Stator phase current I a [A]
20
15
10
5
0
-5
-10
-15
Figure 7.3 Stator current Ia at 20Hz with R1 = 0mm and R1 = 120mm.
Chapter 7 - Small Scale Test
R 1 = 0mm
R 1 = 120mm
-20
0 0.02 0.04 0.06 0.08 0.1
Time [s]
0.12 0.14 0.16 0.18 0.2
In figure 7.4 the two signals are presented in the frequency domain by applying FFT.
Relative Magnitude [dB]
Relative Magnitude [dB]
0
-10
-20
-30
-40
-50
-60
-70
R 1 = 0mm
-80
0 10 20 30
Frequency [Hz]
40 50 60
0
-10
-20
-30
-40
-50
-60
-70
fe - fr
fe + fr
fe + 2fr
fe + 3fr
R 1 = 120mm
-80
0 10 20 30
Frequency [Hz]
40 50 60
Figure 7.4 FFT of Stator current Ia with R1 = 0mm (top) and R1 = 120mm (bottom).
73

Chapter 7 - Small Scale Test
From the current spectrum the frequency components that can be related to the dynamic eccentricity
are present. The largest change is seen at the fe + fr component where the amplitude is
increase from -58.9 dB to -36.5dB.
To see if there is a linear relation between the applied force and the amplitude at the presented
frequency components a series test have be conducted. In table 7.1 the amplitudes under different
load conditions are presented.
74
Fc fe - fr fe + fr fe + 2fr fe + 3fr
0.0 -54.6 -58.9 -57.5 -35.3
77.0 -39.8 -37.3 - -
173.2 -36.7 -39.6 - -
192.5 -41.0 -40.6 -55.3 -35.6
218.1 -39.1 -40.2 -55.7 -35.3
243.8 -39.7 -39.6 -55.5 -35.0
269.4 -37.8 -38.3 -56.8 -35.6
295.1 -38.6 -38.7 -62.7 -35.6
307.9 -35.5 -36.5 -58.0 -36.0
Table 7.1 Characteristic component amplitudes at various loads.
The frequency components at fe ± fr increase as expected, but the third and second related components
seem unaffected. Since these components already exist in the machine without the eccentricity
tool added, they could be caused by other defects. Like static eccentricity.
In figure 7.5 the linear magnitude of the first components are illustrated.
Relative current [A]
0.02
0.015
0.01
0.005
f e - f r
f e + f r
0
0 50 100 150 200 250 300 350
Centrifugal Force F [N]
c
Figure 7.5 linear magnitude of components fe ± fr
There does not seem to be a clear linear relation between the applied force and the amplitude of
the first components. This could be an issue when relating the degree of a mechanical fault a
change in the current. Further analysis is required to understand this tendency.

7.3.2 Signal stability (Oscillating effects)
Chapter 7 - Small Scale Test
As done for the simulated results a band pass filter is used to isolated the fundamental and the
eccentric current component (fe + fr).
Stator phase current [A]
Stator phase current [A]
20
15
10
5
0
-5
-10
-15
-20
19 19.1 19.2 19.3 19.4 19.5
Time [s]
19.6 19.7 19.8 19.9 20
0.3
0.2
0.1
0
-0.1
-0.2
19 19.1 19.2 19.3 19.4 19.5
Time [s]
19.6 19.7 19.8 19.9 20
Figure 7.6 Band pass filtered fundamental current (top) and the eccentric component (fe + fr). The filter
window is ±2Hz at the related frequency.
The fundamental current has little or no oscillations, while the eccentric frequency component is
oscillating. The oscillating frequency is lower than the result found in the in the simulated result
in chapter six. The frequency is about 1Hz and since the rotor is rotating 10Hz, this does not
verify the idea that it depends on the rotor displacement angle. Other conditions could be causing
the oscillations. The slip might not be constant in at positions, which would cause variations
in the current. The machine might also have some degree of static eccentricity that affects that
affect the result. These pheromones have not been further investigated.
7.4 Chapter Conclusion
The purpose of the small-scale test was to illustrate that it is possible to add eccentricity to an
electrical machine considered to be in good condition. During various eccentric loads it has
75

Chapter 7 - Small Scale Test
been shown that frequency components related to the eccentricity are present in the current
spectrum. At maximum eccentric load the magnitude of the largest eccentric component is about
1% of the fundamental current value. This is larger than the value found at 50% eccentricity in
the simulated results, which were about 0.15%. Since it is unlikely that the degree of eccentricity
in the small scale test is 50%, it is assumed that the design used in the test machine makes it
more sensitive to eccentricity. In chapter five it was also shown that relative change was depending
on the current level of the machine (saturation). Due to the small slip that is present due
to friction, the motor is not rotating at ideal synchronous speed and the measured current is actually
higher than the ideal no-load current. The saturation level of the machine might be in the
area where it is most sensitive to change in the air gap. In order to verify this tendency a larger
test should have been conducted with the possible to change the load and speed of the machine.
76

Chapter 8
Conclusion
The purpose of this thesis has been to investigate conditions that could support the idea of using
electrical signature analysis as an alternative to vibration monitoring, or if it is more suitable as
a redundant option.
The demand for a reliable condition monitoring system exists. In a reliability study it was
shown that even with the advances made in wind turbine technology, modern wind turbines still
suffer from low availability. As the wind turbine become larger and more complex, the failure
rate increases. This especially affects performance at offshore wind turbines due to their remote
location. Presently, the most popular offshore wind turbine concept is a geared turbine with a
full or partial power converter. It has been shown that the drive train components in these turbines
are very critical. The most common method for monitoring these components is by vibration
analysis. The downside of this system is that it requires up to eight sensors, which increases
cost and the possibility of sensor related faults. As an alternative, electrical signature analysis
(ESA) has been suggested since this method requires fewer sensors.
If electrical signature analysis should be considered as an alternative, it should be able to locate
and detect the same range of faults as the vibration system. By studying the characteristics of
faults in bearings, it has been shown that ESA has some physical constraints and some challenges
regarding fault detection. Since the fault identification is based on the characteristic frequencies
of the bearing, it is not possible distinguish two identical bearings from each other if
rotated at the same speed. This is possible with vibration analysis since multiple sensors are
used, so the difference in amplitude at the two sensors can be used to locate the fault.
It has also been shown that detecting small fault in a low speed bearing will be a challenge,
since the fault is not continuously present in the electrical signal. This is considered a challenge
for the signal processing, but not a constraint.
To study conditions that affect the reliability of the electrical signal measured at the generator
terminal, a finite element model has been designed. The model is based on the Siemens SWT-
3.6MW wind turbine due to its popularity at offshore locations. Through a static analysis of the
inductances model, it has been shown that the relative change depends on several conditions.
These conditions should be accounted for to get a reliable indication of the actual degree of
eccentricity. For low poled machines the relative change varies with the rotor displacement angle.
The result is that the same fault would appear more severe in some position compared to
other. The relative change is also depending on the saturation level of the generator. It tends to
decrease as the core is saturated – this makes sense as a saturated core is less sensitive to small
changes in the flux density. Since a converter based wind turbine is likely to have a constant
voltage / frequency regulation to keep the saturation level constant, the relative change is constant
at various loads. This is positive in relation the reliability of the electrical signal. But, if
machine is kept at a high saturation level, which is likely to reduce the weight of the generator,
77

Chapter 8 - Conclusion
then the relative change is very small. This indicates that it could be difficult to detect small
early stage faults. During the analysis it has also been shown that the relative change is not linear
or proportion to the degree of eccentricity. This is downside as the signal processing system
would have know to characteristics of the monitored generator in order to relate the measured
signal to the severity of a fault.
During a time-transient simulation of the finite element model, it has been verified that it is
possible to measure a change in the current signal during eccentricity. The change is however
small – about 0.15% of the fundamental current at 50% eccentricity. Oscillating tendencies are
noted in the signal, which verifies that the relative change depends on the rotor position.
A small scale test on an induction motor with an unbalanced load has verified that it is possible
to introduce and measure eccentricity to a machine considered in good condition. During eccentricity,
changes in the current signal were measured at the same frequency components as in the
simulated model. The change was larger – about 1% of the fundamental current.
Based on the mentioned circumstances then electrical signature analysis is not considered to be
a suitable alternative to vibration monitoring in geared wind turbines. One thing is to be able to
measure a change in the electrical signal, but another is actually to relate the change to the severity
of a fault and to predict the future outcome. This requires extensive study and information
of the involved generator, which would make the system impractical to implement.
78

Chapter 9
Future Work and Perspective
Is electrical signature analysis not useful as a condition monitoring system wind turbines, or
does it have some future perspective. The current trend in wind turbine design is gearless designs
with permanent magnet generators. In figure 9.1 a typical gearless design is illustrated.
Bearings
Rotor
Magnets
Stator
Converter Grid
Figure 9.1 Typical gearless wind turbine with permanent magnet generator.
In this configuration the number of drive train components is reduced to a minimum. The general
idea is that this should increase the reliability of the wind turbine. But, as permanent magnet
generators are more complex in their design compared to induction generators, they can be
assumed to be less reliable. This emphasise that there is a future demand for a condition monitoring
system capable to detect generator faults. In this case electrical signature analysis might
be suitable, as most faults will occur in the electrical system. An instigation of the following
types of incidents is considered important for future work:
Faults in the main bearings, so the need for a vibration system can be removed.
Generator related faults, such as demagnetization and coil shortenings.
Converter and transformer faults.
79

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offshore wind conference, 2005.
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M.Sc. dissertation, Dept. Elec. Eng., Univ., KTH, Sweden, 2006.
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[7] Tavner P. J., Xiang J. and Spinato F., “Reliability analysis for wind turbines. Wind Energy”,
2007.
[8] Faulstich S., Hahn B. and Tavner P. J., “Wind turbine downtime and its importance for offshore
deployment”, 2010.
[9] Faulstich S., Durstewitz M., Hahn B., Knorr K., Rohrig K., “Windenergie Report Deutschland
2008”, Institut für solare Energieversorgungstechnik (Hrsg.), Kassel, 2008.
[10] Faulstich S., Hahn B. and Lyding P., “Electrical subassemblies of wind turbines – a substantial
risk for the availability”, In Proc. of European Wind Energy Conference 2010, Warsaw, Poland,
2010.
[11] Echavarria E., Hahn B., van Bussel G.J.W., Tomiyama T., “Reliability of Wind Turbine Technology
Through Time‟, Journal of Solar Energy Engineering, Aug. 2008 Vol. 130 / 031005-1.
[12] Hameed Z., Hong Y. S., Cho Y. M., Ahn S. H., and Song, C. K., “Condition monitoring and
fault detection of wind turbines and related algorithms: A review” 2009.
[13] Crabtree C. J., „Survey of Commercially Available Condition Monitoring Systems for Wind
Turbines‟, 2010, Revision: 5
[14] Lu B., “A Review of Recent Advances in Wind Turbine Condition Monitoring and Fault Diagnosis”,
2009.
[15] SKF, Online Product Catalogue: http://www.vsm.skf.com/en-UK/OnlineCatalogue.aspx
81

References
[16] Siemens, SWT 3.6-120 wind turbine datasheet: http://www.energy.siemens.com/us/en/powergeneration/renewables/wind-power/wind-turbines/swt-3-6-120.htm
[17] SKF, “Bearing failures and their causes”, 2010.
[18] B. Li, M. Chow, Y. Tipsuwan, and J. Hung, “Neural-network-based motor rolling bearing fault
diagnosis”, IEEE Trans. Ind. Electron., vol. 47, no. 5, pp. 1060–1069, Oct. 2000.
[19] Blödt M., Granjon P., Raison B. and Rostaing G., “Models for Bearing Damage Detection in
Induction Motors using stator current monitoring”, IEEE Trans. Ind. Electron., vol. 55, no. 4,
pp. 1813–1822, April 2008.
[20] Yang W., Tavner P. J., Crabtree C. J., “Cost-effective Condition Monitoring for Wind Turbines”,
2010.
[21] Yang W., Tavner P. J., Wilkinson M., ”Wind Turbine Condition Monitoring and Fault dianosis
Using both Mechanical and Electrical Signatures”, 2008.
[22] Djurovic S., Williamson S., “Condition Monitoring Artifacts for Detecting Winding Faults in
Wind Turbines DFIG”, 2009.
[23] Faiz Z., Ibrahimi B.M., Akin B., Toliyat H.A., “Dynamic analysis of mixed eccentricity at
various operating points and scrutiny of related indices for induction motors”, 2009.
[24] Boldea I., Tutelea L., “Electric Machines – Steady State, Transients and Design with Matlab”,
2010, ISBN: 978-1-4200-5572.
[25] Fitzgerald A. E., “Electric Machinery”, sixth edition, 2003, ISBN: 0-07-366009-4.
[26] Boldea I., Nasar S., “The Induction Machine Handbook”, first edition, CRC Press Inc, 2001,
ISBN: 978-0849300042.
82

Appendix A
Design of Induction Generators
In this appendix the design process of the reference generator is described. The methodology
used is an analytical approach verified by a numerical Finite Element Analysis (FEA).
A.1 Introduction
A.1.1 Generator Specifications
In table A.1 the performance requirements are given for the generator. The rated output power
of the generator is not known for the SWT 3.6-120 wind turbine, but can roughly be estimated
considering a converter efficiency of 99% and a transformer efficiency of 98% then the rated
output power is 3,710 kW. The efficiency of the generator is estimated to minimum of 97% and
the power factor to 0.93. With a power factor of 0.93 at rated power the power rating of the fullscale
converter is about 4,000 kVA, which is considered realistic.
Parameter Value Unit Description
Pn 3710 kW Rated Power output
n 1500 Rpm Nominal speed (50Hz)
Vn 750 V Rated voltage (RMS line voltage)
m1 3 Number of phases
p 4 Number of poles
η 0.97 Efficiency at Pn (min value)
cos(υ) 0.93 Power factor at Pn (min value)
Table A.1 The initial performance requirements for reference generator.
A.1.2 Design Procedure
The design of an induction machine can be divided into the following steps:
1. Winding layout and number of slots.
2. Determination of the main dimensions.
3. Design of the stator winding.
4. Design of the rotor winding.
5. Parameter estimation.
6. Analytical iteration process – find optimum design.
7. Numerical verification of the design (FE).
In the following sections these steps are explained and then used in a Matlab script to determine
a useful generator design based on some chosen design variables.
83

Appendix A - Design of Induction Generators
A.2 Step 1 – Winding Layout and Number of Slots
Finding the number of stator slots Nss is the first step to in the slot dimensioning.
84
N S m p
ss
1 1
(A.1)
Where S1 is the chosen number of stator slots per phase per pole, m is the number of phases and
p is the number of poles. The value of S1 has several considerations; it affects the angle that a
winding can be pitched, it offers the opportunity to distribute a winding over several slots, it
should be large enough to support windings and slot closure. For machines with few pole pairs
an integer value between 2 and 6 is often chosen. In reference [24] the following relation between
the number of stator slots and rotor slots are given for two pole pairs.
Pole pairs S1 Number of rotor slots
2 2 16 18 20 30 33 34 35 36
3 24 28 30 32 34 45 48
4 30 36 40 44 57 59
5 36 42 48 50 70 72 74
6 42 48 54 56 60 61 62 68 76 82 86 90
Table A.2 Suitable stator and rotor slot combinations for a machine with two pole pairs.
To find a good solution that suppress the space harmonics related to the mmf distribution, the
winding factor Kw is calculated for each value of S1. The winding factor is determined by the
distribution factor Kd and the pitch factor Kp, given as:
K K K
wn dn pn
n S1
sin / 2
np Kdn Kpncos
S1sin n
/ 2 2
(A.2)
Where n represents the n´th harmonic, γ is the electric angular displacement between slots and
θp is the pitch angle. The angular displacement and the pitch angle are determined as:
180
n
m S
1 1
p p
(A.3)
With np being the number of slots pitched (integer value). In table A.3 Kdn and Kpn is calculated
for n = 1:15 submitting the even harmonics as they will cancels, and with np = 1.

Distribution factor Kdn
Appendix A - Design of Induction Generators
S1 γ 1 3 5 7 9 11 13 15
1 60 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2 30 0.966 0.707 0.259 -0.259 -0.707 -0.966 -0.966 -0.707
3 20 0.960 0.667 0.218 -0.177 -0.333 -0.177 0.218 0.667
4 15 0.958 0.653 0.205 -0.158 -0.271 -0.126 0.126 0.271
5 12 0.957 0.647 0.200 -0.149 -0.247 -0.109 0.102 0.200
6 10 0.956 0.644 0.197 -0.145 -0.236 -0.102 0.092 0.173
Pitch factor Kpn
S1 θp 1 3 5 7 9 11 13 15
1 60 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2 30 0.966 0.707 0.259 -0.259 -0.707 -0.966 -0.966 -0.707
3 20 0.985 0.866 0.643 0.342 0.000 -0.342 -0.643 -0.866
4 15 0.991 0.924 0.793 0.609 0.383 0.131 -0.131 -0.383
5 12 0.995 0.951 0.866 0.743 0.588 0.407 0.208 0.000
6 10 0.996 0.966 0.906 0.819 0.707 0.574 0.423 0.259
Table A.3 Distribution factor and pitch factor for uneven harmonics when pitched one slot.
If the machine is not connected to neutral then the third related harmonics (3, 9, 15) cannot exist.
In table A.4 the resulting winding factor is calculated without the third related harmonics.
Winding factor Kwn
S1 1 5 7 11 13
1 1.000 1.000 1.000 1.000 1.000 2.236 2.236 2.236
2 0.933 0.067 0.067 0.933 0.933 1.619 1.693 1.713
3 0.945 0.140 -0.061 0.061 -0.140 0.969 1.023 1.425
4 0.949 0.163 -0.096 -0.016 -0.016 0.968 0.996 1.420
5 0.951 0.173 -0.111 -0.045 0.021 0.975 0.989 1.581
6 0.953 0.179 -0.119 -0.058 0.039 0.979 0.986 1.730
Table A.4 Resulting winding factor with third related harmonics.
From the resulting winding factor it would be preferable to chose 3 slots per phase per slots or
above, and pitch the winding one slot. However the effect of pitching has minor influence on
the harmonic levels in this case, since the third related harmonics cannot exists.
Based on these considerations, the machine in the given case is chosen to have S1 = 4 with fully
pitched windings. The number of stator slot Nss is then 48. The winding layout is illustrated in
figure A.2 for the first two coils of phase A. The configuration is a two layer arrangement to
give the possibility of pitching the windings.
85

Appendix A - Design of Induction Generators
86
A A A A C’ C’ C’ C’ B B B B
A A A A
43
44
mmfA
A’ A’ A’ A’
C’ C’ C’ C’ B B B B A’ A’ A’ A’
C C
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
C
C C C B’
C C
Figure A.2 Two layer fully pitched winding arrangement and resulting mmf for phase A.
B’
B’
B’
B’
B’
B’
B’
A
A
A
A
A
A
A
A
25 26
The green curve is the resulting mmfA when distributed over four slots. The coils are left open,
but can either be connected in series or in parallel.
If the efficiency is low a pitched solution could be chosen. In figure A.3 the slot layout is shown
where the same winding setup is pitched one slot (7.5°).
A A A A C’ C’ C’ C’ B B B B
A A A
43
44
A’ A’ A’ A’
C’ C’ C’ C’ B B B B A’ A’ A’ A’
C C
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
C
C C C B’
C C
Figure A.3 Two layer winding arrangement when short pitched one slot length.
A.3 Step 2 - Determinations of the Main Dimensions
B’
B’
B’
B’
B’
B’
B’
A
A
A
A
A
A
A
A
C’
25 26
The main dimensions of the machines are shown in figure A.4. They are the outer stator diameter
Dso, the inner stator diameter Dsi, the outer rotor diameter Dro, the inner rotor diameter Dri
and the length of the machine L.

hsy
hry
Dri
Dro
Dsi
Dso
Figure A.4 Main dimension of an induction machine.
Appendix A - Design of Induction Generators
The length and inner stator diameter can be determined from the output equation, which can be
described by considering the induced RMS voltage of an entire phase winding. [24]
2
E f k ˆ
wN1p 2
p n 2
2
ˆ Dsi
Kw1N1
Bg L
120 p n
2 k ˆ
w1N1BgDsiL
60
L
(A.4)
Where p is number of poles, n is the rotor speed (rpm), L is the active stator core length and Bg
is the peak air gap flux density.
If q is defined as the specific electric loading (Ampere-conductors/meter), then it can found
from the phase current Iph. The electric loading is typically in the range of 30.000-100.000 A/m
for larger machines.
2 3N
D
q I I q
D 6N
1
ph
si
ph
The apparent power Sn of the machine can be written as:
Pn
S 3
I E
cos
n ph ph
Combining the three equations and solving for Dsi and L gives the following solution:
si
1
(A.5)
(A.6)
87

Appendix A - Design of Induction Generators
88
Dsi q n
3 2
ˆ
Sn Kw1N1BgDsi
L
6 N1
60
2
q n K ˆ
2
w1Bg Dsi L
2 60
2 60S 2
n
Dsi L 2
q n K ˆ
w1Bg (A.7)
This equation relates the dimensions of the machine to its power rating, and is in general known
as the output equation. To determine Dsi and L a relation c0 is defined between the length and
the pole pitch τp.
L D
c0 where p
p
p
si
(A.8)
c0 is also referred to as the shape factor and is typically chosen in a range of 0.5-3.0. The diameter
Dsi can then be determined as:
D
si
3
2 60 S p
n
3
q n K ˆ
w1Bg c0
The machine length and pole pitch can be then be found using equation (A.8).
(A.9)
The length of the stator yoke hsy and the rotor yoke hry can be determined from the desired flux
densities, the stator diameter and the number of poles.
h
h
sy
ry
Bˆ D
Bˆ
p
g si
sy
Bˆ D
Bˆ
p
g si
ry
(A.10)
The required air gap length g of the machine can be estimated from the rated power given in
kilo-Watts. [24]
g
0.1 0.2 3 Pn if p 2
0.10.13Pnif p 4
The outer diameter of the rotor Dro is then:
D D 2
g
ro si
(A.11)
(A.12)
The inner diameter of the rotor and the outer diameter of stator will depend on the chosen slot
layout. This is described in step two and three.

Appendix A - Design of Induction Generators
A.4 Step 3 - Design of Stator Slots and Windings
For large machines an open rectangular shaped slot is often used for the stator. The advantage of
an open slot is that preformed coils can be inserted with a high copper fill factor. In figure A.5
the rectangular open slot is illustrated.
hsy stator yoke
teeth
wssc
wss
usable
slot
area
Slot closure
air gap
Figure A.5 Stator slots and teeth layout (rectangular shaped slots).
To keep the preformed coils in place a slot closure to secure the coil. The material used for the
slot closure should be of low permeability to reduced leakage flux. A material like steel with a
relatively permeability of 100 (µ/µ0) could be used, but often a composite material is chosen.
Custom made epoxy glass fibre with iron powder could be used. In this case the relative permeability
can be as low as 3-4 (µ/µ0). The slot closure height and tap width is estimated as:
hss
hssc
wst
0.10 0.20
w round w h round h
ssc ss sc ss
(A.13)
Where round represent the closest integer value (e.g. 1.23mm = 1mm). The stator slot pitch τss
and the teeth width wst can then be found as:
D
Bˆ
si
g
ss wst
ss (A.14)
N Bˆ
ss st
Bst is the chosen flux density in the stator teeth. The maximum width wss of the stator slot is
then:
w w ss ss st
The depth of the stator slots hss are obtained from the required copper area Ascu.
I D
A I
ts si
scu
Js ts
q Nss
(A.15)
(A.16)
Where Its is the total RMS ampere turn per slot and Js is current density. For an air cooled winding
the current density is typically chosen as 2-3 A/mm 2 . The stator slot area Ass is found from
the chosen fill factor Ksf and the slot height hss can then be found.
89

Appendix A - Design of Induction Generators
90
A A
A h
scu ss
ss
Ksf ss
wss
(A.17)
The fill factor for a preformed winding can be up to 60-70%, where it for a wound winding
might be 40-50%. The outer diameter of the stator Dso can now be calculated.
Dso Dsi hss hssc hsy
(A.18)
With the geometry of the stator in place the number of turns per phase N1 can be estimated using
equation (A.4) with the assumption that Vph = Eph.
N
V
ph
1
2 f k ˆ
wp Where ˆ p represents the flux per pole found as:
ˆ 2
ˆ
p Bg p L
The number of turns per slot Nsc is equal to:
N
N a
p S n
1
sc
1
L
(A.19)
(A.20)
(A.21)
Where a is the number of parallel paths and nL is the number of winding layers. Nsc is rounded
of the closest integer value and then N1 is recalculated.
A.5 Step 4 - Design of Rotor Slots and Windings
In large induction machines the rotor bars are primarily made of copper and in some cases
bronze. The shape of slot is for smaller machines often chosen with thoughts on the assembly
process. In larger machines the shape of the bars is designed to meet special requirements such
as starting torque. Deep bars as single or double cage arrangements will increase the starting
torque due to current displacement (increase in rotor AC resistance).
For the reference generator a trapezoidal shaped slot is chosen so that the teeth are rectangular,
see figure A.6. The height of the slot opening hrso is chosen to be 2.0mm. The number of rotor
slots Nrs can evaluated in terms of the harmonics as done for the number of stator slots. This is
however neglected and Nrs = 48 slots are chosen, which according to reference [24] is a suitable
value when S1 = 4, also shown see table A.2.

otor bar
rotor yoke
wrt
wrs1
hrs rotor bar
wrs2
Appendix A - Design of Induction Generators
hrso
teeth
air gap
rotor bar
Figure A.6 Rotor slots and teeth layout (trapezoidal shaped slots).
Now, the rotor slot pitch τrs and the rotor tooth width wrt can be found.
D
Bˆ
ro
g
rs wrt
rs (A.22)
N Bˆ
rs rt
The maximum rotor slot top width wrs is then:
w w
(A.23)
rs1 rs rt
To determine the required copper area the current in each rotor bar Ib must be estimated. This
can be done by considering the chosen electric loading of the machine q1. Using this method
instead of comparing the stator mmf to the rotor mmf as often done will allow the iteration process
to focus on the electric loading of the machine. [24]
I
b
D
cos qN si
rs
hry
(A.24)
The power factor cosυ accounts for the fact that a part of the stator current is used for magnetization.
The area of one bar Ab can then be determined as done for the stator winding.
Ib
Ab
J
r
(A.25)
Where Js is current density in the rotor bars, which for an air cooled winding typically, is chosen
between 2-3 A/mm 2 . From the required copper area the area of one slot Ars is found using the
fill factor Krf. The fill factor in a squirrel caged rotor will be close to one – in this report it is
selected as 0.95.
A
A
b
rs (A.26)
Krf
The bottom width wrs2 and the height hrs of the trapezoidal shaped slot is found using equation x
and Y. An iterative process is used for variable hrs until Ars,new

Appendix A - Design of Induction Generators
92
D h h
2 0.5 ro rs rso
rs2 rt
w w
(A.27)
Nrs
A
h w w
rs rs1 rs2
rs, new (A.28)
2
Note: In the finite element model the rotor slots has been reshaped with round ends to give better
flux distribution.
To determine the dimensions of the end ring, the end ring current Ie is required. [24]
I
e
Ib
p
2 sin
2Nrs
The cross sectional area of the end ring Ae and length le is then:
I A
A l
e e
e
Jr e
hrs hrso
(A.29)
(A.30)
The height of the end ring is chosen to be the height of the rotor slots hrs plus the height of the
rotor slot opening hrso.
A.6 Step 5 – Equivalent Parameter Estimation
The equivalent parameters are shown in the equivalent circuit diagram presented in figure A.7.
V1
I1
R1 L1 L´2
E1
Rc
I2
Lm
R´2
s
Figure A.7 Single phase equivalent circuit of the induction machine.
Where R1 is the resistance in the stator windings, X1 is the leakage reactance of the stator windings,
Rc represent the iron loss in the core, Xm is the magnetizing reactance (mutual), X ’ 2 is the
leakage reactance of the rotor windings and R ’ 2/s is the resistance of the rotor windings and s is
the slip. In the diagram the rotor parameters has been referred to the stator side, which is the
reason for the notation X ’ 2 instead of X2.
A.6.1 Stator Resistance - R1
The resistance of the stator conductor R1 is determined by the length lcon, the conductor cross
sectional area Acon and the conductivity σ of the material used.

lconAscu R1 Acon
A
N / S
con sc
Appendix A - Design of Induction Generators
1
(A.31)
where Nsc/S1 is the number of turns per slot. The length of the conductor can be determined by
considering the chosen geometry, see figure A.8.
Dend = Dsi +hss + hssc
The end turn length can be found as:
l
Dend
let
θp
let = end turn length
θp = pitch angle
Figure A.8 Geometry used to estimate stator conductor length.
DendDend 1.3
p 2
et p
(A.32)
where the factor of 1.3 accounts for bend at the end turn. The total conductor length lcon is then:
l 2
N L l
con 1 et
A.6.2 Rotor Resistance - R ’ 2
(A.33)
The resistance of the squirrel cage rotor is determined by the bar resistance Rb and end ring resistance
Re. Where Rb represents one bar resistance and Re represents the resistance of one end
ring segment. As for the stator resistance these are found from the cross sectional area, the conductor
length and the conductivity for the material.
R
b
lb
A
b
li
Re
A
e
(A.34)
(A.35)
Where lb is the length of one bar and li is the length on one end ring segment. The length of one
bar lb would initially be equal to the machine length but if the rotor is skewed, the actual length
becomes larger.
93

Appendix A - Design of Induction Generators
The length between two rotor slots or bars is equal to the length of the end ring segment li. The
length li can be determined by the mean diameter of the rotor slots Drs divided be the number of
rotor slots Nrs.
94
Drs Dro hrs hrso
D
li
N
rs
rs
(A.36)
(A.37)
The length of one bar lb taken the skew factor Ks into account can found using stator slot pitch
τss and the assumption that it is straight for the small segment.
2
l l K
b
2
m s ss
(A.38)
Normally for squirrel cage rotors the rotor bars are skewed by one slot pitch to account for harmonic
by the slotting of the stator.
To find the equivalent per phase resistance seen from the stator side, the conservation of energy
can be used. To find the energy or power dissipation the current distribution in the rotor must be
described. The number of phases in the rotor is equal to the number of bars per pole pair and the
electrical angle α between each phase can be determined by the pole pairs and the number of
phases (m2 = Nrs).
p
N
rs
(A.39)
If the number of rotor bars is sufficiently high then the current in the end rings can be considered
sinusoidal. In figure A.9 the current distribution in the rotor is illustrated.
0 π/p 2π/p
Current in end
ring
[Rad]
[Rad]
0
α
π/p 2π/p
Current in bars
Figure A.9 Bar current and end ring current a squirrel cage rotor.
The RMS value of the current running in the end rings Ie can be found from the rotor bar current
Ib and the electric angle α. [26]

I
e
Ib
p
2 sin
2Nrs
Appendix A - Design of Induction Generators
(A.40)
The conversation of energy can now be written in terms of the energy dissipated in the bars and
end rings, compared to the energy equation using the per phase resistance R2. These two must be
equal.
2
2 2 2 m2I2 Nrs Ib Rb Nrs Ie Re R
p
By substituting equation (A.40) into equation (A.41) the following relation can be written.
R 2 mI N I R R
2
2 e 2 2
rs b b
2 p
p
4 sin
2 N
rs
Since Nrs = m2 then Ib = 2I2/p which means that the per phase rotor resistance can be found as:
R
R R
2
e
b
2 p
4 sin
2 N
rs
The rotor resistance referred to the stator side R ‟ 2 is:
m Nk R R
m N k
2 2
'
2 2 1
2
1
2
2
w1
2
w2
2
2
(A.41)
(A.42)
(A.43)
(A.44)
In the case of a squirrel cage rotor the number of phase is equal to the number of slot (Nrs = m2),
the number of turns N2 = ½ and the winding factor Kw2 = 1.
A.6.3 Magnetizing Inductance - Lm
The magnetizing inductance is a representation of the flux that links both the stator and the rotor
– the leakage reactances represent all other fluxes. The magnetizing reactance is given as:
Lm
m I
m
(A.45)
It depends on the flux linkage ψm and the magnetizing current Im. In reference [26] the following
solution is given for the unsaturated magnetizing inductance. This will be used in the analytical
design process and later a more accurate inductance is determined using FEA.
95

Appendix A - Design of Induction Generators
96
L
m0
2
2
1 1
3LDsi0Nkw
p g e
(A.46)
It is important to understand that Lm will change as the core saturates. In this equation the effective
air gap ge length is used that account for rotor and stator slotting. The effective air gap is
found using the Carter coefficient, Kcs and Kcr.
K
cs
ss
g/2
ss
wss
2
g
w
52 g
2
ss
(A.47)
The carter coefficient is calculated for both stator Kcs and rotor Kcr, so that the effective air gap
is equal to:
ge g Kcs Kcr
(A.48)
A.6.4 Stator Leakage inductance – L1
The estimated leakage flux in this report consists of slot leakage, zig zag leakage and end turn
leakage. The stator slot leakage inductance Lssl is found as, [26].
L
ssl
2
0N1 Ls
(A.49)
N
ss
Where λs is the geometrical slot permeance that for a rectangular shape is:
h h
s
3
w w
ss ssc
ss ss
The stator zigzag leakage can also be estimated, [26].
2 2
1 1
p a a k
LszlLm 1 2
2 12 Nss 2k
g
w g
ss a k
st e
The end turn leakage depends on the winding layout, but can roughly be estimated as:
2
35 . m1N1 Dsi
Lel K 2 6
p .
p 10
03
(A.50)
(A.51)
(A.52)

Appendix A - Design of Induction Generators
This value is split equally between the rotor and stator leakage inductance. The total stator leakage
inductance is then equal to:
Lel
L1 Lssl Lszl
(A.53)
2
A.6.5 Rotor Leakage inductance – L ’ 2
The rotor slot leakage inductance Lssl and zig zag leakage Lrzzl is found as, [26]
L
rsl
2
0N2 Lr
(A.54)
N
rs
h h
r
3
w w
rs rso
rs rs
2 2
2
Nss
2 2
ss rs
1 1
p a a k
LrzlLm
2 12 NN2k
g
w g
rs a k
rt e
The total rotor leakage inductance L ’ 2 referred to the stator side is then:
L
m Nk L L
L
2 2
' 1 1 w1 2 2 2
m2 N2kw2 rsl rzl el
2
(A.55)
(A.56)
(A.57)
Only the slot leakage inductance should be transferred as the zig zag and end turn leakage inductances
are referred to the stator side.
A.7 Step 5 – Performance Characteristic
To evaluate the design, the performance characteristics such as current, power and efficiency
must be calculated. The equivalent circuit shown earlier in figure A.6 is used.
To simplify the core loss resistance is neglected and the impedances are described as:
' ' '
Z1 R1 jX1 Z2 s R2 / s jX 2 Zm jX m
(A.58)
The current stator current I1 and rotor current I’2 in terms of the slip:
I s
V
Z Z s
1
Z1
1
m
m
'
2
'
2
Z Z s
(A.59)
97

Appendix A - Design of Induction Generators
98
I s
V ZIs (A.60)
'
1 1 1
2 '
Z2s The efficiency of any device is the ratio of the input and the output power.
P
P
out (A.61)
in
The complex power S for a three phase induction machine can be found using the phase voltage
V1 and current I1.
*
3
S3 s V1 I1 s
(A.62)
The real part of 3 S corresponds to the electrical output power Pout. (if generator)
out
P s P s real S s
3 3
(A.63)
The mechanical power Pmech or input power Pin is given as:
'
'
2 R2
Pin s Pmech s 3I2s1 s
(A.64)
s
The power factor PF or cos(υ) is defined as the ratio of the real power and the apparent power.
cos
PF s s
P s
3
(A.65)
S s
3
The relation between the mechanical power Pmech in equation (A.64) and the mechanical torque
Tmech is determined by the rotational speed of the machine ωmech.
'
'
2 R2
Pmech s Tmech s mech s 3I2s1 s
(A.66)
s
The mechanical speed related to the synchronous speed ωsync,
1 s
mech sync
(A.67)
and ωsync is determined by the supply frequency f and the number of poles p.
120 f 4 f
sync2
60 p p
The mechanical torque can now be determined in relation the synchronous speed and the slip.
Pmech Pmech 1
R
Tmech s 3
I2 s
s
s
1
mech sync sync
'
'
2
2
(A.68)
(A.69)

Appendix A - Design of Induction Generators
To evaluate if the generator meets its minimum requirements, the maximum operation point
should be known. This is at the slip value were the current is equal to the maximum permitted
current in the stator winding I1max.
I1,max Js Acon a1
(A.70)
Since the calculation of the motor performance is done in Matlab a simple IF statement can be
used to compare the calculated current with the maximum current.
Another important performance characteristic is the total mass of the generator. The total can be
calculated from the dimensions determined in step 2-4. The mass of the stator core Msc is:
2 2
DsoDsi sc ssssfe M N A L
2 2
The mass of the stator windings Msw,
sw 1 con scu cu
(A.71)
M m l A
(A.72)
The mass of the rotor core Mrc,
2 2
DroDri rc rsrsfe M N A L
2 2
The mass of the rotor bars and end rings Mrw,
2
(A.73)
Mrw NrsAbDrohrshrsoAe alu(A.74)
The total active mass is the sum of the four elements (housing and shaft is neglected).
A.8 Step 6 – Iteration process
The design parameters given in table A.5 are used to find the optimum design using a Matlab
script that performs the iterative process. The script is located at the CD-ROM in appendix C.
Some of the design variables have been found using sub iterations such as the shape factor,
number of parallel paths for the stator winding and the material used for the rotor bars. The optimum
shape factor with an electric loading of 56 kA/m was found to be 2.2 be comparing the
possible output power. The number of parallel paths was chosen to four to increase the number
of turns per coil, which is low due to the relatively low terminal voltage of 750V. To increase
the maximum slip value, which is proportional to the rotor resistance, aluminium was chosen
for the rotor bars and end rings
Parameter Value Unit Description
q 56 kA/m Electric loading
c0 2.2 Shape factor
nL 2 Number of stator winding layers
np 4 Number of parallel paths
99

Appendix A - Design of Induction Generators
100
Bg 0.7 T Air gap flux density (peak)
Bst 1.2 T Stator tooth flux density (peak)
Bsy 1.0 T Stator yoke flux density (peak)
Brt 1.1 T Rotor tooth flux density (peak)
Bry 1.2 T Rotor yoke flux density (peak)
Js 3 A/mm 2 Stator winding current density
Jr 3 A/mm 2 Rotor winding current density
g 1.6 mm Air gap length
Ks 1 Rotor bar skew factor
Ksf 0.6 Stator slot fill factor
Krf 0.95 Rotor slot fill factor
Nss 48 Number of stator slots
Nrs 44 Number of rotor slots / bars
σcu 59.6 MS/m Conductivity at 20°C
αcu 0.0039 K -1 Temperature Coefficient
σalu 32.2 MS/m Conductivity at 20°C
αalu 0.0039 K -1 Temperature Coefficient
ρfe 7800 Kg/m 3 Mass density of iron
ρcu 8900 Kg/m 3 Mass density of copper
ρalu 2700 Kg/m 3 Mass density of aluminium
Table A.5 Chosen design parameters for the reference generator.
In table A.6 the resulting main geometrical properties are listed for the machine.
Parameter Value Unit Description
Dsi 731.0 mm Stator inner diameter
Dso 1250.0 mm Stator outer diameter
Dri 372.0 mm Rotor inner diameter
Dro 727.8 mm Rotor outer diameter
L 994.0 mm Length of stator core
N1 8 turns Number of turns per coil per phase
Mr 2058.9 Kg Mass of rotor (core + bars + end rings)
Ms 6429.7 Kg Mass of stator (core + windings)
Table A.6 Main geometrical properties for the reference generator.
The analytically estimated equivalent parameters for this design are given in table A.7 and the
performance at maximum load is given in table A.8.

Parameter Value Unit Description
R1 0.59 mΩ Stator winding resistance
R ´ 2 0.79 mΩ Rotor referred resistance
Appendix A - Design of Induction Generators
X1 8.92 mΩ Stator winding leakage reactance
X ´ 2 5.86 mΩ Rotor referred leakage reactance
Xm 519.08 mΩ Mutual reactance
Table A.7 Analytically estimated equivalent parameters for the reference generator at 50Hz.
Parameter Value Unit Description
Imax 3064.5 A Maximum phase current (RMS)
s 0.55 % Slip
Pe 3732 kW Electrical power output
η 99.0 % Efficiency (core loss not included)
PF -0.94 Power factor
Table A.8 Performance of the reference generator at maximum load based
on analytically found parameters.
A.9 Step 7 – Verification of Design
To verify the analytical found design, a numerical analysis of the generator is performed using
the finite element tool MagNet by Infolytica. In this finite element model the stator leakage
reactance, the rotor leakage reactance, the mutual reactance and the core loss can be determined.
The approach is the same as used in chapter four, so it will not be explained in details in this
appendix.
A.9.1 Stator leakage reactance - X1
The stator leakage reactance is found at the maximum phase current of 3065A. In figure A.10
the resulting leakage reactance is shown when rotating the rotor one rotor slot (8.18°).
Stator Leakage Reactance [ohm]
0.016
0.015
0.014
0.013
0.012
0.011
0.01
0.009
0.008
0 1 2 3 4 5 6 7 8
Rotor position [deg]
Figure A.10 The stator leakage reactance at 50Hz when rotating the rotor one rotor slot (8.18°).
X 1a
X 1b
X 1c
101

Appendix A - Design of Induction Generators
The mean value is 11.1mΩ and this is without the end-turn leakage as the simulation is done in
2D. Compared to the analytically found leakage reactance of 8.92mΩ, the FE found value is
higher. This is expected as more leakage contribution are including in the FE analysis compared
to the analytically found value. The FE analysis also includes the effect of having stator wedges.
A.9.2 Rotor leakage reactance - X2
The equivalent rotor current I ’ 2 can be found as:
102
m Nk I I
m N k
' 1 1 w1
2 1
2 2 w2
380.9577 3064.5A3201.7A 44 0.51 The current for bar Ib,n can be found from the electrical angle α given in equation (A.39).
p 4
16.36
N 44
rs
'
bn , 2
I I cos n 0.5
(A.75)
(A.76)
In figure A.11 the resulting rotor leakage reactance is shown when rotating the rotor one stator
slot (7.5°).
Rotor Leakage Reactance [ohm]
x 10-3
8
7
6
5
4
3
0 1 2 3 4 5 6 7
Rotor position [deg]
Figure A.11 The rotor leakage reactance at 50Hz when rotating the rotor one stator slot (7.5°).
The mean leakage reactance is 5.1mΩ without the end turn contribution. The analytical estimated
reactance is 5.86mΩ with end turn leakage.
A.9.3 Mutual Reactance - Xm
The mutual reactance Xm can be estimated using the magnetizing current Im or no-load current I0
at s = 0.
X 2

I
0
V
R X R X
1 ph
1 c || m
750 V / 3
819.2A
5.9m 8.92m 519.08m
Appendix A - Design of Induction Generators
(A.77)
In figure A.12 the resulting mutual reactance is shown when rotating the rotor one rotor slot
(8.18°).
Mutual Reactance [ohm]
0.63
0.62
0.61
0.6
0.59
0.58
0.57
0 1 2 3 4 5 6 7 8
Rotor position [deg]
Figure A.12 The mutual reactance at 50Hz when rotating the rotor one rotor slot (8.18°)
The mean value of the mutual reactance of phase wind a is 592mΩ.
A.9.4 Core Loss and Core Resistance - Rc
The core loss resistance can be found from the core loss and the back EMF voltage E1. The back
EMF voltage E1 at no-load can be found as:
E V Z I
1 1 1 0
750V
8.94m 1123.8A 423V
3
The core loss resistance Rc can then found using the core loss Pc. (Pc = 109.1kW)
R
c
(A.78)
2 2
3E13423V 4.92
(A.79)
P 109.1kW
c
A.9.5 Updated Performance Characteristics
In figure A.13 and A.14 the performance of the generator using the finite element estimated
parameters is plotted. In table A9 the performance at maximum operation is given.
X ma
X mb
X mc
103

Appendix A - Design of Induction Generators
Figure A.13 Efficiency, power factor, electrical power and mechanical power for the reference generator.
104
[W]
[Nm, A]
1.5
1
0.5
0
-0.5
x 107
-1
Efficiency
Pow er Factor
-0.6
Elec. pow er
Mech. pow er
-0.8
-1.5
-1
1400 1420 1440 1460 1480 1500
Speed [rpm]
1520 1540 1560 1580 1600
8
6
4
2
0
-2
x 104
-0.4
-4
Torque
-0.6
-6
Efficiency
Pow er Factor
Current
-0.8
-8
-1
1400 1420 1440 1460 1480 1500
Speed [rpm]
1520 1540 1560 1580 1600
Figure A.14 Torque, efficiency, power factor and current (magnitude) for the reference generator.
Parameter Value Unit Description
Imax 3066.8 A Maximum phase current (RMS)
s -0.55 % Slip at Imax
Pe 3744 kW Power output at Imax
η 96.0 % Efficiency at Imax (core loss included)
PF -0.94 Power factor at Imax
Table A.9 Updated performance characteristics of the reference generator
using the finite element found parameter
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4
1
0.8
0.6
0.4
0.2
0
-0.2

Appendix B
Pictures from Small-Scale Test
Figure B.1 Pictures from small Scale test setup. (Motor stand, converter and eccentricity tool).
105

106

Appendix C
CD-ROM
The following is located at the CD-ROM.
- PDF version of the report.
- Matlab and MatchCad script files.
- MagNet static and motion model.
107

www.elektro.dtu.dk/cet
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Centre for Electric Technology (CET)
Technical University of Denmark
Elektrovej 325
DK-2800 Kgs. Lyngby
Denmark
Tel: (+45) 45 25 35 00
Fax: (+45) 45 88 61 11
E-mail: cet@elektro.dtu.dk