# Condition Monitoring of Wind Turbines by Electric Signature Analysis

Condition Monitoring of Wind Turbines by Electric Signature Analysis

Condition Monitoring of Wind Turbines by Electric Signature Analysis

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Bjarke Nordent<strong>of</strong>t Madsen<br />

<strong>Condition</strong> <strong>Monitoring</strong> <strong>of</strong> <strong>Wind</strong><br />

<strong>Turbines</strong> <strong>by</strong> <strong>Electric</strong> <strong>Signature</strong><br />

<strong>Analysis</strong><br />

A cost effective alternative or a redundant<br />

option for geared wind turbines.<br />

Master’s Thesis, October 2011

<strong>Condition</strong> <strong>Monitoring</strong> <strong>of</strong> <strong>Wind</strong> <strong>Turbines</strong> <strong>by</strong> <strong>Electric</strong> <strong>Signature</strong> <strong>Analysis</strong><br />

Author:<br />

Bjarke Nordent<strong>of</strong>t Madsen<br />

Supervisor:<br />

Bogi Bech Jensen<br />

A cost effective alternative or a redundant option for geared wind turbines.<br />

Department <strong>of</strong> <strong>Electric</strong>al Engineering<br />

Centre for <strong>Electric</strong> Technology (CET)<br />

Technical University <strong>of</strong> Denmark<br />

Elektrovej 325<br />

DK-2800 Kgs. Lyng<strong>by</strong><br />

Denmark<br />

www.elektro.dtu.dk/cet<br />

Tel: (+45) 45 25 35 00<br />

Fax: (+45) 45 88 61 11<br />

E-mail: cet@elektro.dtu.dk<br />

Release date:<br />

Class:<br />

Edition:<br />

Comments:<br />

Rights:<br />

October 17 th , 2011<br />

1 (public)<br />

1. edition<br />

This report is a part <strong>of</strong> the requirements to achieve Master <strong>of</strong> Science<br />

in Engineering (MSc) at Technical University <strong>of</strong> Denmark. This report<br />

represents 30 ECTS points.<br />

© Bjarke Nordent<strong>of</strong>t Madsen, 2011

ABSTRACT<br />

During the last decade wind energy has become an important part <strong>of</strong> the electricity production<br />

throughout the world. This is mainly due to advances in wind turbine technology, and government<br />

decisions to encourage renewable power as an alternative to conventional fossil-fuelled<br />

power generation. As the amount <strong>of</strong> wind energy increases, the reliability <strong>of</strong> the wind turbine<br />

becomes crucial. A low reliability would result in an unstable energy source with poor economical<br />

performance. <strong>Monitoring</strong> the condition <strong>of</strong> vital components is a key element to keep a<br />

high reliability. At the moment this is mainly done using a condition monitoring system that<br />

monitors changes in the mechanical vibrations. Recent research has suggested that electrical<br />

signature analysis could be a cost effective alternative to vibration monitoring.<br />

In this thesis, the use <strong>of</strong> electrical signature analysis is discussed. Should it be considered as an<br />

alternative or is it more appropriate as a redundant system. The survey is based on a geared<br />

wind turbine with a squirrel cage induction generator.<br />

To support or reject the proposed alternative, the characteristic and identification <strong>of</strong> typical<br />

drive train faults are investigated. If used as an alternative it should be possible to detect the<br />

same range <strong>of</strong> faults. From the obtained results it is considered that electrical signature analysis<br />

cannot detect the same range <strong>of</strong> mechanical faults. This is mainly due to lack <strong>of</strong> multiple sensors<br />

and thus multiple monitoring signals.<br />

The steady characteristic <strong>of</strong> the generator during a fault is investigated using a 2D finite element<br />

model. Furthermore a time-harmonic simulation <strong>of</strong> the model has been conducted to investigate<br />

the sensitivity and stability <strong>of</strong> the electrical signal. It has been shown that conditions such as<br />

fault location, core saturation and pole number will affect the electrical signal.<br />

In order to verify the theoretically made observations, a small scale laboratory test has been<br />

carried out. The test demonstrates that it is possible to detect a fault at the expected harmonic<br />

frequency.<br />

Based on the results and observations made during this project, it is considered that electrical<br />

signature analysis is not appropriate as an alternative for geared wind turbines. This is based on<br />

the physical constraints in the range <strong>of</strong> fault identification, and that the electrical signal is influenced<br />

<strong>by</strong> conditions that will challenge the signal processing. It is however considered that electrical<br />

monitoring might have advantages in future gearless wind turbines with few mechanical<br />

parts.

ACKNOWLEDGEMENTS<br />

This thesis has not been made in cooperation with a company. However, during the project sessions<br />

with engineers from Dong Energy and Brüel & Kjær Vibro has been a huge inspiration to<br />

the outcome <strong>of</strong> this thesis. I would like to thank Bjarne Uhre Knudsen at Dong energy for sharing<br />

his knowledge about condition monitoring and for the guided tour in the Siemens SWT3.6-<br />

120 wind turbine at Avedøre Holme. I would also like to give my gratitude to the personal at<br />

Brüel & Kjær Vibro in Nærum, who gave me an insight in their condition monitoring system,<br />

VIBRO, and who was kind enough to listen to a short presentation <strong>of</strong> my project.<br />

Finally, I would like to thank my supervisor, Bogi Bech Jensen, for his encouragement, knowledge<br />

and support during this project.<br />

Bjarke Nordent<strong>of</strong>t Madsen<br />

i

CONTENTS<br />

Chapter 1 Introduction to <strong>Condition</strong> <strong>Monitoring</strong> ................................................. 1<br />

ii<br />

1.1 The Need for <strong>Condition</strong> <strong>Monitoring</strong> ............................................................................... 1<br />

1.2 Identifying Critical Components ..................................................................................... 5<br />

1.3 <strong>Condition</strong> <strong>Monitoring</strong> Systems ..................................................................................... 12<br />

1.4 Commercially available CMS....................................................................................... 15<br />

1.5 Chapter Conclusion ..................................................................................................... 16<br />

Chapter 2 Thesis Objectives .............................................................................. 19<br />

2.1 Problem Statement ...................................................................................................... 19<br />

2.2 Hypothesis ................................................................................................................... 20<br />

2.3 Work <strong>by</strong> Others ............................................................................................................ 25<br />

2.4 Solution Method ........................................................................................................... 25<br />

2.5 Limitations / Assumptions ............................................................................................ 26<br />

Chapter 3 The Reference <strong>Wind</strong> Turbine ............................................................ 27<br />

3.1 Introduction .................................................................................................................. 27<br />

3.2 Bearings ....................................................................................................................... 27<br />

3.3 Generator ..................................................................................................................... 30<br />

Chapter 4 Drive Train Failure Characteristics ................................................... 33<br />

4.1 Bearing Failures .......................................................................................................... 33<br />

4.2 Rotor Displacement (Eccentricity) ............................................................................... 37<br />

4.3 Air Gap Length ............................................................................................................ 43<br />

4.4 Chapter Conclusion ..................................................................................................... 44<br />

Chapter 5 Generator Characteristics ................................................................. 47<br />

5.1 Introduction .................................................................................................................. 47<br />

5.2 Analytical <strong>Analysis</strong> ....................................................................................................... 47<br />

5.3 Finite Element <strong>Analysis</strong> (FEA) ..................................................................................... 53

5.4 Relative Change and Displacement Angle .................................................................. 58<br />

5.5 Saturation Effect .......................................................................................................... 59<br />

5.6 Linearity ....................................................................................................................... 61<br />

5.7 Chapter Conclusion ..................................................................................................... 61<br />

Chapter 6 Time-Transient Simulation ................................................................. 63<br />

6.1 Introduction .................................................................................................................. 63<br />

6.2 Model Modifications and Simulation Settings .............................................................. 64<br />

6.3 Current Spectrum <strong>Analysis</strong> at No-load ........................................................................ 66<br />

6.4 Chapter Conclusion ..................................................................................................... 70<br />

Chapter 7 Small Scale Test ................................................................................. 71<br />

7.1 Introduction .................................................................................................................. 71<br />

7.2 Test Setup ................................................................................................................... 71<br />

7.3 Test Results................................................................................................................. 72<br />

7.4 Chapter Conclusion ..................................................................................................... 75<br />

Chapter 8 Conclusion .......................................................................................... 77<br />

Chapter 9 Future Work and Perspective ............................................................ 79<br />

References ............................................................................................................. 81<br />

Appendix A Design <strong>of</strong> Induction Generators ........................................................ 83<br />

A.1 Introduction .................................................................................................................. 83<br />

A.2 Step 1 – <strong>Wind</strong>ing Layout and Number <strong>of</strong> Slots ........................................................... 84<br />

A.3 Step 2 - Determinations <strong>of</strong> the Main Dimensions ........................................................ 86<br />

A.4 Step 3 - Design <strong>of</strong> Stator Slots and <strong>Wind</strong>ings ............................................................. 89<br />

A.5 Step 4 - Design <strong>of</strong> Rotor Slots and <strong>Wind</strong>ings .............................................................. 90<br />

A.6 Step 5 – Equivalent Parameter Estimation ................................................................. 92<br />

A.7 Step 5 – Performance Characteristic .......................................................................... 97<br />

A.8 Step 6 – Iteration process ........................................................................................... 99<br />

A.9 Step 7 – Verification <strong>of</strong> Design .................................................................................. 101<br />

Appendix B Pictures from Small-Scale Test ....................................................... 105<br />

Appendix C CD-ROM ............................................................................................ 107<br />

iii

Chapter 1<br />

Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

This chapter gives a brief introduction to the concept <strong>of</strong> condition monitoring <strong>of</strong> wind turbines<br />

from an economical and maintenance perspective. The recent literature within the field is reviewed<br />

and used to discuss some <strong>of</strong> the important topics. This should give a fundamental understanding<br />

before the technical concept <strong>of</strong> <strong>Electric</strong>al <strong>Signature</strong> <strong>Analysis</strong> (ESA) is elaborated.<br />

1.1 The Need for <strong>Condition</strong> <strong>Monitoring</strong><br />

The amount <strong>of</strong> wind energy in the European and international electrical grids is rapidly increasing.<br />

The target for the year 2020, set <strong>by</strong> the European <strong>Wind</strong> Energy Association, is that 14-17%<br />

<strong>of</strong> the EU‟s electricity should come from wind turbines - depending on the total demand. By the<br />

year 2030 the target is 26-35% with almost 40% coming from <strong>of</strong>fshore wind farms. This large<br />

amount <strong>of</strong> wind energy in the electrical system and the fact that wind turbines are located in<br />

remote and <strong>of</strong>fshore locations requires a high level <strong>of</strong> reliability. A low level <strong>of</strong> reliability<br />

would result in an unstable energy source. This would affect the stability <strong>of</strong> the grid and the<br />

economic performance due to unexpected operation and maintenance cost and loss in energy<br />

production. [1]<br />

Both the size and the locations <strong>of</strong> wind turbines has led to new maintenance challenges that are<br />

unique compared to traditional power producing systems:<br />

No walk around maintenance: Unlike traditionally power producing systems (coal,<br />

diesel, etc.), daily or weekly walk around maintenance checks are not feasible due<br />

to difficulty and expense <strong>of</strong> physically reaching the turbines.<br />

High maintenance cost: Maintenance cost are high due to the cost <strong>of</strong> travelling expenses<br />

to remote locations and the need for cranes or helicopters large enough to<br />

lift spare parts to the nacelle.<br />

Higher probability <strong>of</strong> faults: The mechanical elements like the gearbox, shaft and<br />

generator are designed with low weight in mind to reduce the overall weight <strong>of</strong> the<br />

nacelle. This leans towards a higher probability <strong>of</strong> stress related failures.<br />

In addition, the constant changing loads and highly variable operating conditions create high<br />

mechanical stress on the wind turbines.<br />

These factors can lead to an increased operation & maintenance (O&M) cost and a loss in the<br />

energy production. This affects the economic performance <strong>of</strong> the wind turbine or wind farm.<br />

1

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

1.1.1 Cost <strong>of</strong> Energy (COE)<br />

A commonly used terminology for evaluating the economic performance <strong>of</strong> a power producing<br />

system is the cost <strong>of</strong> energy. The cost <strong>of</strong> energy is a metric used to compare the cost <strong>of</strong> different<br />

electricity production options. From reference [3] a simplified expression is adopted from the<br />

US for estimating the cost <strong>of</strong> energy (COE) for a wind turbine system.<br />

2<br />

ICC FCRO&M COE <br />

E<br />

Where ICC is the initial capital investment cost, FCR is the annual fixed charge rate (%), E is<br />

the annual energy production (kWh) and O&M is the annual operation and maintenance cost.<br />

With the initial capital investment and the charge rate being fixed value, the O&M is a variable<br />

cost that can affect the cost <strong>of</strong> energy during the lifetime <strong>of</strong> the project. The pr<strong>of</strong>it <strong>of</strong> wind energy<br />

is highly determined <strong>by</strong> ability to control and reduce this variable cost.<br />

In a recent survey <strong>of</strong> the first <strong>of</strong>fshore wind farm expansion in the UK, the cost <strong>of</strong> energy has<br />

been compared at four wind farms from 2004-2007, [2]. The results <strong>of</strong> the survey are shown in<br />

Table 1.1, where the O&M cost is given as the percentage <strong>of</strong> the total cost <strong>of</strong> energy. In this<br />

case it is clear how poor O&M can result in low availability and a high cost <strong>of</strong> energy. The<br />

availability is the percentage <strong>of</strong> time where the turbines are able to deliver energy when requested.<br />

<strong>Wind</strong> farm Turbine Capacity Availability COE O&M<br />

North Hoyle Vestas V80 60 MW 87.7 % 67 £/MWh 22 %<br />

Scro<strong>by</strong> Sands Vestas V80 60 MW 81.0 % 67 £/MWh 16 %<br />

Kentish Flats Vestas V90 90 MW 80.4 % 67 £/MWh 16 %<br />

Barrow Vestas V90 90 MW 67.4 % 86 £/MWh 12 %<br />

Table 1.1 Comparison <strong>of</strong> four <strong>of</strong>fshore wind farms located in the UK showing the availability,<br />

cost <strong>of</strong> energy (COE) and the O&M cost as a percentage <strong>of</strong> the total COE, [2].<br />

The average cost <strong>of</strong> energy at these four <strong>of</strong>fshore wind farms is 69 £/MWh, which is noticeable<br />

higher than the average <strong>of</strong> 47 £/MWh achieved onshore in the UK. This is mainly because <strong>of</strong> a<br />

much higher availability onshore – typically between 96-99%. The average O&M cost is 18%<br />

<strong>of</strong> the total cost <strong>of</strong> energy, which furthermore is higher than the average <strong>of</strong> 12% for onshore<br />

wind turbines in the UK. It should however be mentioned that these calculation are based on<br />

early operational data where the Vestas turbines had several gearbox related problems. Compared<br />

to another EU established wind farm, Middelgrunden, located in Denmark and operational<br />

since 2001, the availability here is about 95-96 %, [4].<br />

1.1.2 <strong>Condition</strong> <strong>Monitoring</strong> as a Maintenance Strategy<br />

To understand how the performance <strong>of</strong> a wind turbine can be optimised with the use <strong>of</strong> a condition<br />

monitoring system, the different types <strong>of</strong> maintenance strategies must be investigated.<br />

Almost all industrial machinery requires maintenance during its lifetime. The maintenance can<br />

either conducted with a preventive or corrective approach. Preventive maintenance is carried out<br />

(1.1)

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

before a failure occurs, either in predetermined or condition based intervals. Corrective maintenance<br />

is carried out after a fault has occurred and is also known as the breakdown strategy. This<br />

is when you run the system until a breakdown occurs, [5]. In figure 1.1 the corrective maintenance<br />

and the two kinds <strong>of</strong> preventive maintenance are illustrated in terms <strong>of</strong> the condition <strong>of</strong> a<br />

system through time. The time used at maintenance is not illustrated, only the interval.<br />

<strong>Condition</strong> [%]<br />

Corrective maintenance<br />

(Breakdown)<br />

Scheduled<br />

corrective maintenance<br />

<strong>Condition</strong> based<br />

corrective maintenance<br />

Figure 1.1 Corrective maintenance and the two types <strong>of</strong> preventive maintenance (scheduled and condition<br />

based) strategies related with the overall condition <strong>of</strong> a system through time, [5].<br />

With the breakdown strategy, the preventive maintenance is reduced to a minimum giving the<br />

lowest number <strong>of</strong> required repairs. This would initially give the lowest operation cost. However,<br />

a breakdown is likely to occur at the highest stress level and consequential damage is likely to<br />

occur. For a wind turbine this is the period <strong>of</strong> the year with highest amount <strong>of</strong> wind, resulting in<br />

a severe production loss. In this period the accessibility might also be low and downtime could<br />

be extensive - especially at <strong>of</strong>fshore locations. Another disadvantage is that spare part logistics<br />

is very difficult.<br />

In contrast, the scheduled maintenance strategy <strong>of</strong>fer easy spare part logistics and repairs can be<br />

scheduled to periods <strong>of</strong> low wind. This reduces the downtime <strong>of</strong> the turbine and the production<br />

loss. The disadvantage is that the maintenance costs are higher compared to corrective maintenance<br />

due to the many repairs and spare parts needed.<br />

The condition based strategy <strong>of</strong>fers the possibility to use components longer, reducing the number<br />

<strong>of</strong> repairs and if early predictions are made, the repairs can be scheduled. One <strong>of</strong> the disadvantages<br />

is that additional monitoring hardware and s<strong>of</strong>tware must be added to the turbine,<br />

which increases the initial capital investment and thus the cost <strong>of</strong> energy.<br />

In table 1.2 a comparison <strong>of</strong> the three maintenance strategies is given, [5].<br />

Time<br />

3

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

4<br />

Strategy Advantages Disadvantages<br />

Corrective maintenance<br />

Preventive maintenance<br />

– Scheduled<br />

Preventive maintenance<br />

– <strong>Condition</strong><br />

based<br />

Low maintenance cost during<br />

operation.<br />

Component will be used for a<br />

maximum lifetime.<br />

Expected downtime is low<br />

(and known).<br />

Maintenance can be scheduled.<br />

Spare part logistics is easy.<br />

Components will be used for<br />

almost their full lifetime.<br />

Expected downtime is low.<br />

Spare part logistics is easier<br />

than corrective maintenance.<br />

High risk in consequential<br />

damages resulting in extensive<br />

downtimes.<br />

No maintenance scheduling is<br />

possible.<br />

Spare part logistics is complicated.<br />

Long delivery periods<br />

for spare parts are likely.<br />

Component will not be used<br />

for maximum lifetime.<br />

Maintenance cost is higher<br />

compared to corrective maintenance.<br />

Additional monitoring hardware<br />

and s<strong>of</strong>tware is required.<br />

Identifying a fault in time is<br />

difficult (threshold values are<br />

hard to determine).<br />

Only feasible for larger components.<br />

Table 1.2 Advantages and disadvantages <strong>of</strong> a corrective maintenance, scheduled preventive<br />

maintenance and condition based preventive maintenance strategy, [5].<br />

An implemented strategy will always be a combination <strong>of</strong> preventive and corrective maintenance.<br />

Some components will never be considered for preventive maintenance, as it would not<br />

be feasible compared to their reliability, stress level and expected lifetime. However, using a<br />

condition based strategy for the larger component with reliability issues can minimize maintenance<br />

cost and downtime.<br />

<strong>Condition</strong> based maintenance is relatively new for wind turbines. But, as the capacity <strong>of</strong> the<br />

single turbine increases and its location becomes even more remote, the demand to the reliability<br />

<strong>of</strong> a turbine installed today is high compared to a turbines installed 10-20 years ago.

1.2 Identifying Critical Components<br />

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

As mentioned earlier, then a condition based maintenance strategy is only feasible for certain<br />

components. A wind turbine consists <strong>of</strong> several mechanical and electrical component needed for<br />

transferring wind energy into electrical energy. It is important to look into the different types <strong>of</strong><br />

components, their failure rate and downtime consequence, before an effective condition monitoring<br />

system can be implemented.<br />

1.2.1 Categorization <strong>of</strong> Components<br />

First, the thousands <strong>of</strong> components must be categorized to make the interpretation easier. For<br />

instance, a faulty bearing within the gearbox is listed under Gearbox along with other gearbox<br />

related faults. The categorization <strong>of</strong> components has no standard form. Some operators might<br />

prefer to divide the blades and pitch system into two categories, while others prefer to have<br />

them in one. This can make comparison <strong>of</strong> operational data between operators difficult.<br />

In figure 1.2 a typical geared wind turbine is illustrated with the notation <strong>of</strong> the categories used<br />

in this report, which is based on the incident report used in the German WMEP project, [8].<br />

Sensors<br />

- anemometer<br />

- vibration switch<br />

- temperature<br />

- oil pressure switch<br />

- power sensor<br />

- revolution counter<br />

etc.<br />

Hub<br />

- hub body<br />

- pitch mechanism<br />

- pitch bearings<br />

Rotor blades<br />

- blade bolts<br />

- blade shell<br />

- aerodynamic brake<br />

Drive train<br />

- rotor bearings<br />

- drive shafts<br />

- couplings<br />

Hydraulic<br />

system<br />

- hydraulic pump<br />

- pump motor<br />

- valves<br />

- pipes/hoses<br />

Gearbox<br />

- bearings<br />

- wheels<br />

- gear shaft<br />

- sealings<br />

Mechanical<br />

brakes<br />

- brake disc<br />

- brake pads<br />

- brake shoe<br />

Generator<br />

- windings<br />

- brushes<br />

- bearings<br />

Control system<br />

- control unit<br />

- relays<br />

- mesurement cables and connections<br />

Structure<br />

- foundation<br />

- tower/tower bolts<br />

- nacelle frame<br />

- nacelle cover<br />

- ladder<br />

<strong>Electric</strong><br />

- converter<br />

- transformer<br />

- fuses / breakers<br />

- switches<br />

- cables / connections<br />

- grid<br />

Yaw system<br />

- bearings<br />

- motor<br />

- wheels and pinions<br />

Figure 1.2 Typical layout <strong>of</strong> geared wind turbine with categorization <strong>of</strong> its main components based on the<br />

incident report from the German WMEP project, [8].<br />

1.2.2 Reliability <strong>of</strong> Components<br />

The reliability <strong>of</strong> a component is the probability that it will perform as designed for a certain<br />

amount <strong>of</strong> time, [7]. Poor reliability will affect the availability or uptime <strong>of</strong> the turbine – its<br />

capability to operate when required. The availability <strong>of</strong> a modern onshore wind turbine is typically<br />

in the range <strong>of</strong> 95-98%. But, as the difference between high or low revenue might be<br />

within a few percentage <strong>of</strong> change in availability, it is important to identify the critical compo-<br />

5

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

nents that could cause low availability. A critical component is a component with a high failure<br />

rate and/or a long down time.<br />

It is <strong>of</strong>ten difficult to acquire information regarding the reliability <strong>of</strong> wind turbines and this information<br />

is <strong>of</strong>ten not published in details. The reason for this is that wind turbine manufactures<br />

rarely permit publishing failure statistics <strong>of</strong> their products, which <strong>of</strong> cause makes sense from a<br />

competitive point <strong>of</strong> view. A few databases with reliability data do exist and have been used in<br />

several surveys. In reference [6] a detailed study <strong>of</strong> these databases has been conducted and<br />

below is listed some <strong>of</strong> the larger databases in Europe.<br />

<strong>Wind</strong>stats Newsletter – Denmark and Germany (monthly, 7000 WT)<br />

<strong>Wind</strong>stats publishes operational data from wind turbines located in Denmark and Germany<br />

through <strong>Wind</strong> Power Monthly. A survey has been done using this database in reference<br />

[7], where 10 years <strong>of</strong> operational data (1994-2004) from wind turbines in Germany<br />

and Denmark was analyzed.<br />

LWK – Germany (annually, > 650 WT, closed in 2006)<br />

From 1993 to 2006 failure statistics were published containing output data and number <strong>of</strong><br />

failures <strong>of</strong> all wind turbines located in a province in the northern part <strong>of</strong> Germany<br />

(Schlleswig-Holstein).<br />

WMEP – Germany (annually, > 1500 WT, closed in 2006)<br />

Programme funded <strong>by</strong> the “250MW <strong>Wind</strong>” project in Germany. Long term operational<br />

data was collected from more than 1500 wind turbines from 1989 to 2006. It is the most<br />

comprehensive study <strong>of</strong> long-term behaviour <strong>of</strong> wind turbines worldwide.<br />

VPC – Sweden (annually, 723 WT before 2005 and 80 WT after 2005)<br />

Report published <strong>by</strong> Elforsk, providing statistical data <strong>of</strong> production and downtime data<br />

from wind turbines situated in Sweden. <strong>Monitoring</strong> range was change in 2005 due to failure<br />

reporting errors.<br />

VTT – Finland (annually, 105 WT)<br />

Report published <strong>by</strong> Elforsk, providing statistical data <strong>of</strong> production and downtime data<br />

from wind turbines situated in Sweden. <strong>Monitoring</strong> range was change in 2005 due to failure<br />

reporting errors.<br />

A lot <strong>of</strong> studies have been performed on the results stored in these databases in order to locate<br />

the most critical components. In reference [11] the failure rates from eleven different databases<br />

have been compared. The result <strong>of</strong> the comparison is given in table 1.3, showing the top-three<br />

components with the highest failure rates.<br />

6

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

Database Time Span No. <strong>of</strong> WTs Highest failure rate Location<br />

WMEP 1989-2006 1500<br />

LWK 1993-2006 241<br />

<strong>Wind</strong>stats 1995-2004 4285<br />

<strong>Wind</strong>stats 1994-2003 904<br />

VTT 2000-2004 92<br />

Elforsk 2000-2004 723<br />

EPRI 1986-1987 290<br />

NEDO 2004-2005 139<br />

Operator A 2000-2007 403<br />

Operator B 2002-2009 12<br />

Operator C 2003-2008 23<br />

1. <strong>Electric</strong>al system<br />

2. Control system<br />

3. Sensors<br />

1. <strong>Electric</strong>al system<br />

2. Rotor<br />

3. Control system<br />

1. Rotor<br />

2. <strong>Electric</strong>al system<br />

3. Sensors<br />

1. Control system<br />

2. Rotor<br />

3. Yaw System<br />

1. Hydraulics<br />

2. Rotor<br />

3. Gearbox<br />

1. <strong>Electric</strong>al system<br />

2. Hydraulics<br />

3. Sensors<br />

1. Sensors<br />

2. <strong>Electric</strong>al system<br />

3. Control system<br />

1. Sensors<br />

2. Control System<br />

3. Rotor<br />

1. Control system<br />

2. <strong>Electric</strong>al system<br />

3. Rotor<br />

1. Sensors<br />

2. Hydraulics<br />

3. <strong>Electric</strong>al system<br />

1. <strong>Electric</strong>al system<br />

2. Rotor<br />

3. Gearbox<br />

Germany<br />

Germany<br />

Germany /<br />

Denmark<br />

Germany /<br />

Denmark<br />

Finland<br />

Sweden<br />

US – California<br />

Japan<br />

Unknown<br />

Unknown<br />

Unknown<br />

Table 1.3 Comparison <strong>of</strong> the top-three components with the highest failure rates from eleven<br />

different databases, [11].<br />

Even if the results from these studies cannot be directly compared as they differ in date, duration,<br />

data collection, turbine age and turbine technology, they show similar results with a few<br />

exceptions. The electrical system has the highest failure rate in most cases, next is the control<br />

system and then sensors. Overall, the electrical related systems have a higher failure rate than<br />

the mechanical ones. Considering solely the failure rate, then the obvious choice would be to<br />

implement a condition monitoring system with focus on these systems. However, it is important<br />

to consider the downtime in relation to the failure rate. Changing a sensor or resetting a relay is<br />

less time consuming than doing repairs on a gearbox or changing a main bearing.<br />

The term downtime is a measure <strong>of</strong> the time it takes for a component to recover from a failure<br />

that brings the wind turbine to a standstill. In most cases the mean downtime would be equal to<br />

the statistical term Mean Time To Repair (MTTR). However, as the production from a wind<br />

turbine dependent on the available wind, some modern control systems measure the downtime<br />

as being the number <strong>of</strong> hours where production would have been possible. Production is only<br />

possible when the wind speed is above the threshold limit. This downtime value is important for<br />

the operators <strong>of</strong> the turbine to determine lost revenue. In this report the downtime is considered<br />

7

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

as being equal to the MTTR.<br />

In figure 1.3 and 1.4 the failure rate and the downtime are shown for the WMEP survey from<br />

Germany based on data from reference [8] and [9].<br />

8<br />

Hydraulic System<br />

Mechanical Brake<br />

Structural / Housing<br />

Germany (WMEP 1989-2006)<br />

<strong>Electric</strong><br />

Control System<br />

Sensors<br />

Yaw System<br />

Hub<br />

Generator<br />

Rotor Blades<br />

Gearbox<br />

Drive Train<br />

0.05<br />

0.13<br />

0.11<br />

0.11<br />

0.10<br />

0.10<br />

0.18<br />

0.17<br />

0.25<br />

0.23<br />

0.43<br />

0 0.1 0.2 0.3 0.4 0.5 0.6<br />

Failure rate [failures/turbine/year]<br />

Figure 1.3 Failure rates for Germany (WMEP). A total <strong>of</strong><br />

2.43 failures per turbine per year in average.<br />

0.57<br />

Structural / Housing<br />

Mechanical Brake<br />

Hydraulic System<br />

Germany (WMEP 1989-2006)<br />

<strong>Electric</strong><br />

Control System<br />

Figure 1.4 Downtimes for Germany (WMEP). Total downtime<br />

<strong>of</strong> 6.0 days per year per turbine in average.<br />

The failure rate is identical to the results given in table 1.3, where the electrical related faults<br />

were the most common. But, when taking the downtime into account, then the mechanical faults<br />

increase in severity. The gearbox has one the lowest failure rates but the longest downtime per<br />

failure, making it one the most critical components. The most critical components based on<br />

downtime per turbine per year are still the electric and control related components.<br />

To see whether this is consistent with the results from other databases, data from reference [5] is<br />

used. In this survey reliability data from Sweden (Elforsk), Finland (VTT) and Germany<br />

(WMEP) has been studied in a time period from 2000-2004. In figure 1.5 to figure 1.8 the failure<br />

rate and downtime is shown for Sweden and Finland. The results from Germany are omitted<br />

as they are the same as presented above.<br />

Hub<br />

Gearbox<br />

Generator<br />

Yaw System<br />

Sensors<br />

Rotor Blades<br />

Drive Train<br />

0.31<br />

0.29<br />

0.29<br />

0.38<br />

0.35<br />

0.49<br />

0.49<br />

0.63<br />

0.62<br />

0.59<br />

0.68<br />

0.87<br />

0 0.2 0.4 0.6 0.8 1<br />

Downtime [days/turbine/year]

Rotor Blades<br />

Hydraulic System<br />

Control System<br />

Yaw System<br />

Structural / Housing<br />

Mechanical Brake<br />

Drive Train<br />

Sweden (VPC 2000-2004)<br />

<strong>Electric</strong><br />

Sensors<br />

Gearbox<br />

Generator<br />

Other<br />

Hub<br />

0.01<br />

0.00<br />

0.00<br />

0.00<br />

0.01<br />

0.03<br />

0.02<br />

0.04<br />

0.05<br />

0.05<br />

0.05<br />

0.05<br />

Figure 1.5 Failure rates Finland (VTT). A total <strong>of</strong> 0.39<br />

failures per turbine per year in average.<br />

Figure 1.7 Failure rates for Finland (VTT). A total <strong>of</strong> 1.38<br />

failures per turbine per year in average.<br />

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

Figure 1.6 Downtimes for Sweden (VPC). Total downtime<br />

<strong>of</strong> 2.08 days per year per turbine in average.<br />

Figure 1.8 Downtimes for Finland (VTT). Total downtime<br />

<strong>of</strong> 9.88 days per year per turbine in average.<br />

The results from this survey differ from the result found using the German WMEP database. It<br />

is clear that these two countries have had longer downtimes from mechanical related faults than<br />

Germany. The gearbox and the rotor blades are among the most critical components.<br />

In table 1.4 the detailed results from the three surveys has been compared.<br />

0.07<br />

0 0.02 0.04 0.06 0.08<br />

Failure rate [failures/turbine/year]<br />

Hydraulic System<br />

Rotor Blades<br />

Yaw System<br />

Control System<br />

Structural / Housing<br />

Generator<br />

Mechanical Brake<br />

Drive Train<br />

Finland (VTT 2000-2004)<br />

Gearbox<br />

Sensors<br />

<strong>Electric</strong><br />

Other<br />

Hub<br />

0.01<br />

0.00<br />

0.04<br />

0.10<br />

0.10<br />

0.10<br />

0.09<br />

0.08<br />

0.13<br />

0.12<br />

0.11<br />

0.20<br />

0.31<br />

0 0.1 0.2 0.3 0.4<br />

Failure rate [failures/turbine/year]<br />

Control System<br />

Gearbox<br />

Rotor Blades<br />

Yaw System<br />

Sensors<br />

Other<br />

Hydraulic System<br />

<strong>Electric</strong><br />

Hub<br />

Generator<br />

Mechanical Brake<br />

Structural / Housing<br />

Drive Train<br />

Sweden (VPC 2000-2004)<br />

0.03<br />

0.03<br />

0.00<br />

0.05<br />

0.04<br />

0.11<br />

0.09<br />

0.20<br />

0.19<br />

0.30<br />

0.28<br />

0.40<br />

0.38<br />

0 0.1 0.2 0.3 0.4 0.5<br />

Downtime [days/turbine/year]<br />

Rotor Blades<br />

Hydraulic System<br />

Structural / Housing<br />

Yaw System<br />

Mechanical Brake<br />

Control System<br />

Drive Train<br />

Finland (VTT 2000-2004)<br />

Gearbox<br />

<strong>Electric</strong><br />

Generator<br />

Other<br />

Sensors<br />

Hub<br />

0.20<br />

0.17<br />

0.01<br />

0.00<br />

0.43<br />

0.41<br />

0.27<br />

0.65<br />

0.64<br />

0.64<br />

1.13<br />

2.10<br />

3.24<br />

0 1 2 3 4<br />

Downtime [days/turbine/year]<br />

9

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

10<br />

Germany Sweden Finland<br />

Failure rate 2.43 0.39 1.38 failures / turbine / year<br />

Downtime per failure 3.64 6.30 6.57 days / failure<br />

Downtime per year 2.43 2.08 9.88 days / turbine / year<br />

Top 3<br />

1. <strong>Electric</strong><br />

2. Control<br />

3. Sensors<br />

1. Gearbox<br />

2. Drive tr.<br />

3. Generator<br />

1. <strong>Electric</strong><br />

2. Control<br />

3. Hub<br />

1. <strong>Electric</strong><br />

2. Sensors<br />

3. Blades<br />

1. Drive tr.<br />

2. Yaw<br />

3. Gearbox<br />

1. Control<br />

2. Gearbox<br />

3. Blades<br />

1. Hydraulic<br />

2. Blades<br />

3. Gearbox<br />

1. Gearbox<br />

2. Blades<br />

3. Structural<br />

1. Gearbox<br />

2. Blades<br />

3. Hydraulic<br />

Distribution Elec. Mech. Elec. Mech. Elec. Mech.<br />

Failure rate 56 44 51 49 31 69<br />

Downtime 42 58 38 62 15 85<br />

failure rate<br />

downtime / failure<br />

downtime / year<br />

Table 1.4 Comparison <strong>of</strong> the reliability <strong>of</strong> wind turbines located in Germany, Sweden and Finland.<br />

Some trends can be seen between the results from Germany and Sweden. While Sweden has a<br />

lower failure rate than Germany, they suffer from long downtimes per failures giving them<br />

nearly the same amount <strong>of</strong> downtime per year. Finland seems to suffer from different problems<br />

than Germany and Sweden, and in general has a lower reliability.<br />

Conclusively, there is no clear consistency in which components that are the most critical. It<br />

depends on how the different measures are rated. Looking at the downtime per year, which can<br />

be related to the production loss over the lifespan <strong>of</strong> a turbine, the following assemblies are<br />

critical; electric, control system, gearbox and blades/hub. If a low failure rate has the highest<br />

rating, e.g. for remote <strong>of</strong>fshore locations, then sensors can be added to the list.<br />

1.2.3 Discussion <strong>of</strong> Reliability<br />

When using statistical data as in the previous section, it is important to understand conditions<br />

that can lead to poor comparison. Below is described some issues that should be considered.<br />

1.2.3.1 Age <strong>of</strong> turbine<br />

The failure rate <strong>of</strong> a wind turbine will change with time. The change in failure rate is <strong>of</strong>ten divided<br />

into three periods; an infant mortality period with decreasing failure rate, a normal life<br />

period with constant failure rate and a wear-out period with increasing failure rate. The sum <strong>of</strong><br />

the three situations is the observed failure rate.<br />

In reference [11] the reliability through time has been investigated based on the WMEP database.<br />

In the first year <strong>of</strong> operation the average failure rate was ~3.4 faults/year, decreasing to a<br />

constant level <strong>of</strong> ~2.5 faults/year after the third year. It is difficult to estimate when the failure<br />

rate increase due to wear out, since little data with this time span is available – in reference [5]<br />

there seems to be indications <strong>of</strong> an increase after the 11 th year <strong>of</strong> operation. A modern MW size<br />

wind turbine is designed be in operation for 20-25 years. In order to make the statistical data<br />

comparable, the age <strong>of</strong> the investigated wind turbines should be equal or within the period <strong>of</strong><br />

constant failure rate.<br />

%

1.2.3.2 Size <strong>of</strong> turbine<br />

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

As the rated power and size <strong>of</strong> a turbine increases the stress on components increases as well,<br />

and this could increase the failure rate. In reference [10] a comparison is made showing that<br />

wind turbines above 1.0 MW has twice the number <strong>of</strong> failures compared to wind turbines rated<br />

between 500 kW and 1.0 MW. Since the current development goes towards multi-megawatt<br />

sized turbines, the failure rate per turbine is expected to increase.<br />

1.2.3.3 Technical concept<br />

The technical concept regarding power control, speed characteristic and generator type will also<br />

affect the reliability. In reference [8] using the WMEP database the failure rate for three different<br />

concepts has been compared, see figure 1.9.<br />

Figure 1.9 Failure rate in the WMEP database (1989-2006) with respect to the technical concept. The<br />

simple Danish concept is a directly grid-connected induction generator. The advanced Danish concept has<br />

variable rotor resistance to change speed <strong>of</strong> the induction generator. The standard variable-speed turbine<br />

is fitted fully or partially converter system with a synchronous or an asynchronous generator. [8]<br />

The demand for high controllability increases the complexity <strong>of</strong> wind turbines. The trend seems<br />

to be that modern wind turbine concepts have a higher failure rate compared to older simpler<br />

concepts. This tendency is also seen in reference [11]. Here, the total failure rate related to the<br />

operational year is compared for three concepts. The results are shown in figure 1.10.<br />

Figure 1.10 Total failure rate <strong>of</strong> components per wind turbine per operational year using induction generators<br />

(simple Danish concept), synchronous generator with gear and synchronous generators with direct<br />

drive. Permanent magnet synchronous generators (PMSG) are not present. [11]<br />

These trends are important for future condition monitoring systems as the technology are moving<br />

towards gearless direct drive concepts with permanent magnet synchronous generator. The<br />

11

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

results seen in figure 1.10 suggest that removing the gearbox and replacing it with a direct<br />

driven generator increases the overall failure rate. This could be explained <strong>by</strong> a higher complexity<br />

in the power electronics and in the generator, but also that the generator is exposed to massive<br />

stress due to the high dynamic torque level when driven without a gearbox.<br />

It should be mentioned that the downtime consequences has not been compared in the surveys.<br />

1.2.3.4 Geographical location<br />

It was previously shown that Finland had a high failure rate at the blades and in the hydraulic<br />

system. This could be explained <strong>by</strong> icing on the surface <strong>of</strong> the blades that affect the shape and<br />

weight <strong>of</strong> the blade, but also affects the hydraulics controlling the pitch mechanism. These problems<br />

might not occur in Germany where the weather is warmer. This indicates that a condition<br />

monitoring system should be designed to cover a large range <strong>of</strong> faults.<br />

Another relevant issue is whether the wind turbine is located onshore or <strong>of</strong>fshore. Onshore turbines,<br />

as the ones in the WMEP survey, suffer from a large number <strong>of</strong> faults, which are easy to<br />

solve with minimum downtime, [11]. As <strong>of</strong>fshore turbine technology has been directly derived<br />

from onshore technology, similar faults are expected. Under <strong>of</strong>fshore conditions the downtime<br />

from minor faults will increase due to limited accessibility. The result is a high risk <strong>of</strong> long<br />

down time if precautions are not taken. This was the case for the UK wind farms presented at<br />

the beginning <strong>of</strong> this chapter, where the availability was reported as low as 67.4%. In the<br />

WMEP survey the average availability was about 98%. Considering this, then it becomes clear<br />

that it is a challenge to make <strong>of</strong>fshore wind turbine reliable and pr<strong>of</strong>itable. They are <strong>of</strong>ten larger<br />

in capacity, more complex and located in the most remote and inaccessible areas. The presented<br />

failure rates are mainly for onshore turbines and are considered reasonable due to short downtime.<br />

But, at <strong>of</strong>fshore these failure rates would be unacceptable.<br />

1.3 <strong>Condition</strong> <strong>Monitoring</strong> Systems<br />

One thing is to identify that wind turbines have reliability issues and that conditions based maintenance<br />

could give improvements. Another thing is actually to be able to predict whether a<br />

component is healthy or not. For this, a system is needed to detect early warning signs. The<br />

curve in figure 1.11 illustrates the development <strong>of</strong> a typical mechanical failure.<br />

12<br />

Component condition<br />

<strong>Condition</strong><br />

starts to<br />

change<br />

Vibrations<br />

Noise<br />

Heat<br />

Smoke<br />

Break down<br />

months weeks days minutes Time<br />

Figure 1.11 Typical development <strong>of</strong> a mechanical failure.<br />

To detect the change in the condition different monitoring methods exist and are widely used.<br />

But, as shown later in this section, only a few <strong>of</strong> these are being used commercially <strong>by</strong> the wind<br />

industry.

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

A condition monitoring system can be divided into three stages; collecting data, analysing data<br />

and classification. The stages are illustrated in figure 1.12.<br />

Collecting data<br />

Thermal<br />

Vibrational<br />

Debris<br />

Stress / Deformation<br />

Acoustic<br />

Current / Voltage / Power<br />

<strong>Electric</strong>al discharges<br />

etc.<br />

Analysing data<br />

Filtering<br />

Frequency-time analysis<br />

(FFT, wavelets, etc.)<br />

Identify component<br />

signatures<br />

Identify changes in<br />

signatures<br />

etc.<br />

Figure 1.12 Stages <strong>of</strong> a condition monitoring system (with examples).<br />

Classification<br />

Threshold limits from<br />

known or estimated<br />

reliability data<br />

Prediction <strong>of</strong> time until<br />

breakdown<br />

etc.<br />

In the following sections some <strong>of</strong> the proposed methods are described with focus on the ones<br />

used commercially. Each method has its advantages and disadvantages depending on its use.<br />

1.3.1 Thermal <strong>Monitoring</strong><br />

<strong>Monitoring</strong> the temperature <strong>of</strong> the observed component is one the most common methods <strong>of</strong><br />

condition monitoring. For online monitoring resistive thermal sensors (e.g. PT100) are <strong>of</strong>ten<br />

used to monitor the temperature <strong>of</strong> bearings, fluids, generator windings and similar. For mechanical<br />

components the increased friction will cause heating and for electrical fault the increased<br />

resistive power loss will cause heating. Thermography (infrared imaging) is <strong>of</strong>ten used<br />

to detect hotspot in power electronics, such as the power converter. Thermography is mainly<br />

used as <strong>of</strong>fline monitoring. [12]<br />

The advantage <strong>of</strong> thermal monitoring is that it is a reliable source as all equipment has a limited<br />

operational temperature. The disadvantage is that temperature develops slowly and is not good<br />

for early fault detection. The readings can also be influenced <strong>by</strong> the surroundings. Thermal<br />

monitoring is therefore rarely used alone, but <strong>of</strong>ten as a secondary source <strong>of</strong> information. Where<br />

the primarily source could be vibration monitoring.<br />

1.3.2 Vibration <strong>Monitoring</strong><br />

For rotating equipment vibration monitoring is <strong>of</strong>ten used to detect mechanical failures. E.g. if a<br />

bearing is worn out the shaft supported <strong>by</strong> the bearing will be <strong>of</strong>f centred. When the shaft rotates,<br />

it will now vibrate with a characteristic frequency determined <strong>by</strong> the properties <strong>of</strong> the<br />

bearing. Different types <strong>of</strong> sensors are used to detect these vibrations; in the low-frequency<br />

range position sensor are used, in the mid-frequency range velocity sensors are used and in the<br />

high frequency range accelerometers are used, [12].<br />

The data analysis is <strong>of</strong>ten a Fast Fourier Transformation (FFT) to convert the time domain signal<br />

to the frequency domain. By monitoring the amplitude at certain frequencies that can be<br />

related to certain subcomponents <strong>of</strong> the bearing, the condition <strong>of</strong> the bearing can be predicted.<br />

13

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

The advantages <strong>of</strong> vibration monitoring are that it is easy to implement in existing equipment<br />

and has a high level <strong>of</strong> interpretation, making it easy to locate the exact faulty component. For<br />

these reasons vibration monitoring is one <strong>of</strong> the most popular monitoring methods used in wind<br />

turbines. The vibration method is standardized in ISO 10816 defining positioning and use <strong>of</strong><br />

sensors. In figure 1.13 the positions used in the Siemens SWT 3.6 wind turbine are shown.<br />

14<br />

Figure 1.13 Typical vibration sensor positions in Siemens SWT 3.6 wind turbine.<br />

The disadvantage <strong>of</strong> vibration monitoring is the additional hardware and s<strong>of</strong>tware, which increases<br />

the production cost. The sensors also has difficulties at detecting low frequency faults –<br />

e.g. in the main bearing due to the low rotational speed. [12]<br />

1.3.3 Oil / Debris <strong>Monitoring</strong><br />

In equipment with lubrication or hydraulic systems such as oil for the gearbox, a debris monitoring<br />

methods can be used. The oil is pumped through the component in a closed loop system<br />

and metal debris from a cracked gearbox wheel or bearing is caught <strong>by</strong> a filter. The amount and<br />

type <strong>of</strong> metal debris can indicate the health <strong>of</strong> a component. The advantage <strong>of</strong> this method is<br />

that it is one the only methods for detecting cracks in the gearbox internals (wheels). A cracked<br />

wheel in a gearbox might not be detected <strong>by</strong> vibration monitoring or similar methods. The disadvantage<br />

<strong>of</strong> this method is that equipment for online monitoring is very expensive, so <strong>of</strong>fline<br />

monitoring in terms <strong>of</strong> oil samples is <strong>of</strong>ten used. These samples are then investigated at a lab<br />

facility, which increase the cost <strong>of</strong> in terms <strong>of</strong> labour. [12]<br />

1.3.4 Acoustic <strong>Monitoring</strong><br />

For failures characterized <strong>by</strong> high frequencies (kHz-MHz range), vibration monitoring can be<br />

insufficient. In this case acoustic monitoring can be used to detect vibrations (sounds) emitted<br />

<strong>by</strong> the component. This could be used to monitor the brush gear in a synchronous or double fed<br />

induction generator. The advantages <strong>of</strong> using acoustic monitoring are the large frequency range<br />

and the relative high signal-to-noise ratio. The disadvantage is that this method is expensive to<br />

implement and only a few types <strong>of</strong> faults are present in the high frequency range. [12]<br />

1.3.5 <strong>Electric</strong>al <strong>Monitoring</strong><br />

Gearbox low-, mid-, highspeed<br />

bearings.<br />

Main shaft<br />

bearings.<br />

Generator<br />

bearings.<br />

<strong>Electric</strong>al monitoring can be used for many purposes and for a large variety <strong>of</strong> component. It is<br />

typically used to monitor electrical components such as generators or transformers. But, it may<br />

also be used to monitor mechanical components such as bearings and gears. The source is pri-

marily current, flux or power.<br />

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

Partial discharge monitoring is <strong>of</strong>ten used to monitor insulation faults in the generator or transformer<br />

windings. Voids in the insulation will cause discharges between the conductors or<br />

ground. The discharges will cause a rapid change in the current for short period (MHz range)<br />

and hence lead to high peak voltages. Since insulation faults are rare in a wind turbine, discharges<br />

monitoring is seldom done online but periodically.<br />

A more practical use <strong>of</strong> electrical monitoring regarding rotating machines is electrical signature<br />

analysis (ESA) or machine current signature analysis (MCSA). From current measurements at<br />

the terminals, variations in the behaviour <strong>of</strong> the machine can be detected. The variations can be<br />

an unbalanced three phase load or an increase in the harmonics current. An unbalanced load<br />

could indicate a turn-to-turn shortenings <strong>of</strong> the windings. Undesired harmonics could also be<br />

present due to winding faults, but could also occur if mechanical faults are presents.<br />

The advantage <strong>of</strong> electrical monitoring is that it allows monitoring <strong>of</strong> both mechanical and electrical<br />

components. It is therefore comparable to the vibration monitoring method, but has the<br />

possibility <strong>of</strong> detecting electrical faults as well. Another advantage is that it requires fewer sensors<br />

making it a cost effective solution. The disadvantage is that it can be difficult to locate the<br />

exact faulty component. [12], [14]<br />

1.3.6 Summary<br />

In table 1.5 a summary <strong>of</strong> the described condition monitoring methods is given.<br />

Method Monitored Components Advantages Disadvantages<br />

Thermal<br />

Vibration<br />

Oil / Debris<br />

Acoustic<br />

<strong>Electric</strong>al<br />

Bearings<br />

Generator windings<br />

Bearings<br />

Gearbox<br />

Shaft<br />

Bearings<br />

Gearbox<br />

Bearings<br />

Gearbox<br />

Generator brush gear<br />

Gearbox / Bearings<br />

Generator<br />

Converter / Transformer<br />

Reliable<br />

Standardized (IEEE 814)<br />

Reliable<br />

Easy to interpret<br />

Standardized (ISO 10816)<br />

Good for gearbox internals<br />

Low and high frequency<br />

fault detection.<br />

High signal-to-noise ratio<br />

Few or no additional sensors<br />

required<br />

Large component range<br />

Influenced <strong>by</strong> surroundings<br />

Expensive hardware /<br />

s<strong>of</strong>tware<br />

Subject to sensor faults<br />

Limited component range<br />

Expensive for online use<br />

Expensive hardware /<br />

s<strong>of</strong>tware<br />

Difficult to locate fault.<br />

High signal-to-noise ratio<br />

Table 1.5 Summary <strong>of</strong> possible monitoring methods for wind turbines. [14]<br />

1.4 Commercially available CMS<br />

In reference [13] from 2010 a survey <strong>of</strong> the commercially available condition monitoring systems<br />

for wind turbines has been conducted. This survey elaborates the methods used <strong>by</strong> 20 suppliers<br />

and the conclusion is that nearly all focus on the same subassemblies, which are; blades,<br />

main bearings, gearbox internals, gearbox bearings and generator bearings. Considering the<br />

15

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

presented failure rates and downtime, presented earlier in this chapter, then the chosen components<br />

makes sense as they are among the most severe. The monitoring methods used are; 14<br />

systems are primarily based on vibration monitoring, 3 systems solely for oil debris monitoring,<br />

1 system use vibration monitoring <strong>of</strong> the blades and 2 systems uses fibre optic strain monitoring<br />

<strong>of</strong> the blades.<br />

In table 1.6 some details are given for the methods used <strong>by</strong> some the larger wind turbine manufactures.<br />

16<br />

Product<br />

Name<br />

Vibro<br />

CBM<br />

TCM<br />

<strong>Wind</strong>Con<br />

Supplier<br />

(WT manufacture)<br />

Brüel & Kjaer<br />

(Vestas)<br />

Bently Nevada<br />

(GE <strong>Wind</strong>)<br />

Gram & Juhl<br />

(Siemens)<br />

SKF<br />

(Repower)<br />

Components<br />

monitored<br />

Main bearing, gearbox,<br />

generator, nacelle.<br />

Nacelle temperature.<br />

Noise in the nacelle.<br />

Main bearing, gearbox,<br />

generator, nacelle.<br />

Optional bearing and oil<br />

temperature.<br />

Blade, main bearing,<br />

shaft, gearbox, generator,<br />

nacelle, tower.<br />

Blade, main bearing,<br />

shaft, gearbox, generator,<br />

tower, generator<br />

electrical.<br />

<strong>Monitoring</strong><br />

methods<br />

Vibration.<br />

Temperature.<br />

Accoustic.<br />

Vibration.<br />

Temperature.<br />

Vibration.<br />

Vibration.<br />

Oil debris particle<br />

counter.<br />

Table 1.6 Commercially available condition monitoring systems used <strong>by</strong> Vestas,<br />

GE <strong>Wind</strong>, Siemens and Repower. [13]<br />

<strong>Analysis</strong><br />

methods<br />

Time domain.<br />

FFT frequency<br />

domain analysis.<br />

FFT frequency<br />

domain analysis.<br />

FFT frequency<br />

domain analysis.<br />

Time domain.<br />

FFT frequency<br />

domain analysis.<br />

There seems to be little variation between the products from the suppliers as they all more or<br />

less use the same methods. None uses electrical monitoring, which could be an alternative or<br />

redundant option for the vibration system. Temperature monitoring <strong>of</strong> the generator windings<br />

and similar component is not listed as this is normally a part <strong>of</strong> the SCADA system made <strong>by</strong> the<br />

wind turbine manufacturer.<br />

1.5 Chapter Conclusion<br />

In this chapter a brief introduction to the concept <strong>of</strong> condition monitoring <strong>of</strong> wind turbines has<br />

been given. From reliability studies it has been shown that wind turbines has some critical components<br />

that affects the economical performance. Considering the failure rate alone, then faults<br />

in the electrical system, in sensors and in the control system are among the most common.<br />

However when considering the downtime due to maintenance, the mechanical faults in the drive<br />

train components such as the gearbox and the main bearings increase in severity. The downtime<br />

is an important factor as this will result in lost energy production.<br />

It is noticed that there is not a clear consistency between the reliability data taken from different<br />

sites, indicating that different circumstances affect the reliability <strong>of</strong> the wind turbines. There is a

Chapter 1 - Introduction to <strong>Condition</strong> <strong>Monitoring</strong><br />

tendency that more modern and complex turbine has a higher failure rate compared to old simpler<br />

concepts. This emphasizes the future need for predictive maintenance. Implementing a condition<br />

based monitoring strategy is an important tool for scheduling future maintenance. By<br />

planning future maintenance to periods <strong>of</strong> low wind the loss <strong>of</strong> energy production can be reduced.<br />

Presently, the commercially available condition monitoring is mainly based on vibration and<br />

temperature monitoring <strong>of</strong> the drive train component. Comparing the products from different<br />

suppliers <strong>of</strong> condition monitoring systems indicate small or no difference. Adapting a different<br />

technology such as electrical monitoring as an alternative is considered to be a competitive advantage.<br />

17

Chapter 2<br />

Thesis Objectives<br />

This chapter states the problems that are considered in this thesis. A hypothesis is presented for<br />

using the generator as the source for condition monitoring. The solution methods and project<br />

limitations are also defined.<br />

2.1 Problem Statement<br />

It became clear in chapter one, that wind turbines suffer from reliability issues that affects the<br />

reliability and economic performance. The problem was located to a few components that had a<br />

high influence on the availability <strong>of</strong> the turbine due to a combination <strong>of</strong> high failure rates and<br />

long down times. In particular wind turbines located <strong>of</strong>fshore had low availability, whereas the<br />

level onshore was more acceptable. A predictive maintenance strategy based on condition monitoring<br />

was shown to be an effective way to plan future operation and maintenance (O&M). This<br />

can limit the O&M, but more importantly repairs can be conducted in periods <strong>of</strong> low wind reducing<br />

production losses.<br />

Different condition monitoring techniques was presented in chapter one, however only a few <strong>of</strong><br />

these are used commercially. The most favourable system is based on drive train vibration<br />

analysis <strong>of</strong> the following components; main bearings, gearbox bearing, gearbox internals and<br />

generator bearings. The advantages <strong>of</strong> this system are that it is easy to locate a fault and to implement,<br />

as it is <strong>of</strong>ten done <strong>by</strong> a third party. The disadvantages are that it requires additional<br />

mechanical sensors (6-8 for a typically geared turbine) increasing the cost <strong>of</strong> the wind turbine<br />

and the possibility <strong>of</strong> sensor related faults.<br />

In this thesis a substitute or a redundancy option for the vibration based system is investigated<br />

using the generator as the source <strong>of</strong> fault detection. The setup is shown in figure 2.1.<br />

Hub<br />

Bearing<br />

gear<br />

Mechanical<br />

speed<br />

3~<br />

SCIG<br />

ωm<br />

<strong>Electric</strong><br />

signals<br />

vabc<br />

iabc<br />

Data<br />

Acquisition<br />

AC<br />

/<br />

DC<br />

Filtering<br />

Power Converter<br />

DC<br />

/<br />

AC<br />

<strong>Condition</strong> <strong>Monitoring</strong> System (CMS)<br />

Frequency<br />

<strong>Analysis</strong><br />

Figure 2.1 <strong>Electric</strong>al condition monitoring system (CMS) setup in geared wind turbine.<br />

a<br />

b<br />

c<br />

Grid /<br />

Transformer<br />

Failure<br />

Prediction<br />

19

Chapter 2 - Thesis Objectives<br />

The technical concept considered is a geared wind turbine with a squirrel cage induction generator<br />

(SCIG) and a full converter. This concept is chosen due to its popularity, especially at <strong>of</strong>fshore<br />

locations. At the terminals <strong>of</strong> the generator the voltage and current <strong>of</strong> each phase are<br />

measured. The mechanical speed ωm could also be considered. By analysing these signals in the<br />

frequency spectrum then changes caused <strong>by</strong> abnormal mechanical vibrations should be detectable.<br />

This method is known as <strong>Electric</strong>al <strong>Signature</strong> <strong>Analysis</strong> (ESA) or Machine Current <strong>Signature</strong><br />

<strong>Analysis</strong> (MCSA) and is <strong>of</strong>ten used for larger motors and generators in other industries.<br />

The advantage <strong>of</strong> this method is that it requires fewer sensors, the sensors have no moving parts,<br />

and a different source is used (electrical). This makes it a good substitute or redundant option<br />

for the mechanical vibration system.<br />

Using ESA for condition monitoring has not yet been adopted <strong>by</strong> the wind industry. For the<br />

method to be useful as an alternative it should fulfil the following requirements:<br />

20<br />

Locate origin <strong>of</strong> a failure (exactly which component needs repair).<br />

Identify the same range <strong>of</strong> failures (main bearings, gearbox bearing, some gearbox<br />

internals and generator bearings).<br />

Simple implementation and interpretation.<br />

In the given case, the generator is the source <strong>of</strong> the fault detection. The following generator<br />

related issues should be considered that could affect the electrical signal.<br />

How do conditions like core saturation affect the signal?<br />

Is there linearity between the fault degree and the measured electrical signal?<br />

2.2 Hypothesis<br />

The idea is that mechanical vibrations introduced <strong>by</strong> a failure should affect all drive train related<br />

components with frequencies characterized <strong>by</strong> their origin - including the rotor in the generator.<br />

If the rotor vibrates then the air gap distance is not identical in all positions and rotor eccentricity<br />

occurs. The change in air gap length will affect the magnetic and electrical properties <strong>of</strong> the<br />

machine. Hence, a change in air gap length will change the current magnitude and shape if the<br />

voltage is kept constant.<br />

To understand why current is a good parameter for fault detection, the simple magnetic circuit<br />

in figure 2.2 is considered. The circuit consist <strong>of</strong> a single winding with N turns and a ferromagnetic<br />

core with an air gap.

+<br />

-<br />

<strong>Wind</strong>ing,<br />

N turns<br />

i<br />

Magnetic flux lines<br />

Air gap<br />

length g<br />

Figure 2.2 Simple magnetic circuit with an air gap.<br />

Chapter 2 - Thesis Objectives<br />

Mean core length lc<br />

Air gap,<br />

permeability µ0,<br />

area Ag<br />

Magnetic core,<br />

permeability µ,<br />

area Ac<br />

The relationship between the magneto motive force mmf acting on a magnetic circuit and the<br />

magnetic field strength H is given as: [25]<br />

mmf N i H dl<br />

If the core dimensions are such that the path length <strong>of</strong> any flux line is close to the mean core<br />

length, then the line integral in equation (2.1) becomes a scalar product <strong>of</strong> the average value <strong>of</strong><br />

H and the mean core length lc.<br />

mmf N i Hc lc Hg g<br />

The relationship between the field intensity H and the magnetic flux density B is the material<br />

property µ, known as the magnetic permeability.<br />

BH If the flux is assumed uniformly distributed and air gap fringing is neglected, then the flux density<br />

can be determined from the cross sectional area and the flux in the circuit.<br />

<br />

B B <br />

c g<br />

Ac Ag<br />

Using these relations the current i in the winding can be described.<br />

lcg <br />

i´ r 0<br />

N <br />

<br />

A A<br />

c 0 g <br />

Since the permeability <strong>of</strong> the core is much greater than that <strong>of</strong> air (µr >> µ0) the current is sensitive<br />

to changes in the air gap. Typical values <strong>of</strong> µr ranges from 2,000 to 10,000 for materials<br />

used in rotating machines, where the permeability <strong>of</strong> air or free space μ0 is 4π10 -7 . If the first<br />

part in the bracket <strong>of</strong> equation (2.5) is neglected, then the current is proportional to the air gap<br />

length when the other variables are considered constant. This initially makes the current a good<br />

source for detecting variations in the air gap.<br />

The relationship between the magnetic flux linkage and the current is defined as the inductance<br />

(2.1)<br />

(2.2)<br />

(2.3)<br />

(2.4)<br />

(2.5)<br />

21

Chapter 2 - Thesis Objectives<br />

L <strong>of</strong> the winding.<br />

22<br />

N <br />

<br />

L (2.6)<br />

i i<br />

Under the assumption that the first part <strong>of</strong> equation (2.5) is negligible, then the inductance for<br />

this simple circuit can be described as:<br />

L <br />

2<br />

N 0Ag g<br />

From which it can be seen that the inductance L is inversely proportional to the air gap length.<br />

The same tendency can be seen in the magnetic circuit <strong>of</strong> the generator. In figure 2.3 and figure<br />

2.4 a six-poled squirrel cage induction generator is illustrated. In figure 2.3 the rotor is centred<br />

and in figure 2.4 the rotor is <strong>of</strong>f centred (eccentric). The red lines are the flux paths at two opposite<br />

located poles and the green circles are the related winding.<br />

Flux path<br />

<strong>Wind</strong>ing a2<br />

air gap<br />

<strong>Wind</strong>ing a1<br />

La1 = La2<br />

Figure 2.3 Six-poled SCIG with centred rotor. Inductance<br />

<strong>of</strong> winding a1 is equal to winding a2.<br />

ωr<br />

ωr<br />

Shorter air gap length<br />

=<br />

Larger inductance<br />

La1 ≠ La2<br />

(2.7)<br />

Figure 2.4 Six-poled SCIG with eccentric rotor. Inductance<br />

<strong>of</strong> winding a1 is larger than winding a2.<br />

When the rotor is centred, the inductance <strong>of</strong> winding a1 and winding a2 are equal and independent<br />

<strong>of</strong> the position <strong>of</strong> the rotor. In the case <strong>of</strong> eccentricity, it is clear that the length <strong>of</strong> the flux<br />

path and the air gap has changed. The inductances <strong>of</strong> winding a1 and winding a2 are no longer<br />

equal. The self inductance (mutual and leakage) <strong>of</strong> each winding is now a function <strong>of</strong> the position<br />

<strong>of</strong> the rotor. This change in inductance will affect the currents and voltages at the terminals<br />

<strong>of</strong> the generator making a failure detectable.<br />

In general two types <strong>of</strong> eccentricity can occur – static or dynamic. However a combination <strong>of</strong><br />

the two known as mixed eccentricity could also be present. Static and dynamic eccentricity is<br />

illustrated in figure 2.5.

Static<br />

eccentricity:<br />

rotor<br />

Dynamic<br />

eccentricity:<br />

rotor<br />

air gap<br />

stator<br />

Chapter 2 - Thesis Objectives<br />

air gap<br />

Figure 2.5 RL circuit with time changing inductance.<br />

stator<br />

Static eccentricity is when the rotor is shifted to an <strong>of</strong>f centred position and rotates in at that<br />

position. With dynamic eccentricity, the rotor is also shifted from the centre <strong>of</strong> the stator, but<br />

still rotates around the centre <strong>of</strong> the stator. The following failures are considered to cause static,<br />

dynamic or mixed rotor eccentricity:<br />

Main shaft, gearbox and generator bearings.<br />

Some gearbox internals.<br />

Misalignment between shaft, gearbox and generator.<br />

Blades (unbalanced load).<br />

The failures are the same as for the vibration system. However, misalignment and blades has<br />

been added. Misalignment <strong>of</strong> components could appear subsequently to a repair or if not<br />

mounted properly to the nacelle during installation. The blades are added since it is assumed<br />

that during a fault in the hydraulic pitch system in one <strong>of</strong> the blades, the load distribution is<br />

uneven making eccentricity possible.<br />

The fault detection is best illustrated <strong>by</strong> considering the simple RL circuit shown in figure 2.6,<br />

where R is the resistance, Lok is the inductance without a fault and Lfault is the inductance with a<br />

fault.<br />

i(t) = Imsin(ωt)<br />

R=2Ω Lok, fault<br />

Lok = 2mH<br />

Lfault = Lok[1+0.5sin(4ωt)]<br />

XL = ωL=2πf<br />

Figure 2.6 RL circuit with time changing inductance.<br />

In the normal operation the value <strong>of</strong> resistance and the inductance are constant, but in the faulty<br />

scenario the inductance oscillate with four times the grid frequency. If the current is considered<br />

regulated to a constant level <strong>by</strong> a converter, then the grid voltage can be determined as:<br />

23

Chapter 2 - Thesis Objectives<br />

24<br />

1 X L <br />

u t Im Z sint tan <br />

R (2.8)<br />

In figure 2.6 the voltage v(t) and instantaneous power p(t) is shown for the scenario without a<br />

fault and in figure 2.7 for the scenario with a fault.<br />

3<br />

2<br />

1<br />

0<br />

-1<br />

-2<br />

i(t)<br />

v(t)<br />

p(t)<br />

-3<br />

0 5 10<br />

time [ms]<br />

15 20<br />

-2<br />

i(t)<br />

v(t)<br />

p(t)<br />

-3<br />

0 5 10<br />

time [ms]<br />

15 20<br />

Figure 2.7 Scenario with no fault. Figure 2.8 Scenario with a fault.<br />

It is clear in this extreme case that in the faulty scenario the voltage differs in shape compared to<br />

the case without a fault. Due to the need <strong>of</strong> a constant current level, the voltage increases when<br />

the inductance is reduced and vice versa. Performing a Fast Fourier Transformation (FFT) <strong>of</strong> the<br />

power reveals the harmonic frequencies related to the fault.<br />

10 0<br />

10 -10<br />

10 -20<br />

10 -30<br />

p(t)<br />

0 100 200 300 400 500<br />

frequency [Hz]<br />

Figure 2.9 FFT <strong>of</strong> p(t) with no fault. Figure 2.10 FFT <strong>of</strong> p(t) with a fault.<br />

10 0<br />

3<br />

2<br />

1<br />

0<br />

-1<br />

10 -10<br />

10 -20<br />

10 -30<br />

p(t)<br />

0 100 200 300 400 500<br />

frequency [Hz]

Chapter 2 - Thesis Objectives<br />

Without constant R and L (no fault) the fundamental power component is located at 100Hz with<br />

a DC <strong>of</strong>fset at 0Hz. The introduced faulty inductance oscillates with four times the grid frequency<br />

or 200Hz. This introduces a harmonic component at 300Hz. By monitoring the change<br />

in amplitude dp/dt at this frequency the development <strong>of</strong> a fault can be monitored.<br />

fault indicator<br />

dp<br />

dt<br />

n (2.9)<br />

The same tendency is expected to be seen in the induction generator when eccentricity occurs<br />

and the inductances changes with the position <strong>of</strong> the rotor. A drive train fault (e.g. a bearing)<br />

will have its own characteristics that can be identified <strong>by</strong> the changes at certain harmonic amplitudes.<br />

2.3 Work <strong>by</strong> Others<br />

The idea <strong>of</strong> using electrical signature analysis for condition monitoring <strong>of</strong> wind turbines is not<br />

new. A lot <strong>of</strong> research has been done in last decade within this field. The general idea is that it<br />

could act as a replacement for the vibration system – a cost effective alternative. The main research<br />

has concerned the challenge <strong>of</strong> monitoring changes under variable frequency conditions,<br />

which are present with power converters. The problem is that FFT is only suitable during constant<br />

frequency conditions and require a certain time span to be accurate. In reference [20] and<br />

[21], a method using wavelet analysis has been successfully tested with unbalanced load and<br />

coil shortenings during variable frequency. Another suggested method is to use short time Fourier<br />

Transformation (STFT) as done in reference [22].<br />

It is considered that suitable solutions for detecting faults during variable frequency conditions<br />

exist. However, if electrical monitoring should be used an alternative some fundamental issue<br />

regarding fault identification and generator behaviour has not been clearly investigated.<br />

2.4 Solution Method<br />

To analyse whether the presented hypothesis is a useful solution for condition monitoring <strong>of</strong> a<br />

wind turbine, the following approach is used.<br />

Design <strong>of</strong> a simplified reference wind turbine with drive train components (bearings)<br />

and a squirrel cage induction generator. The design is based on the Siemens SWT<br />

3.6-120 <strong>of</strong>fshore wind turbine.<br />

Describe the characteristics <strong>of</strong> typical drive train bearing faults and how they are<br />

identified.<br />

The behaviour <strong>of</strong> the designed generator during eccentricity is investigated using a<br />

finite element analysis (FEA). In an earlier project <strong>by</strong> the author rotor bar faults has<br />

been studied using a qd0 reference model. To gain new knowledge a FEA is considered<br />

appropriate.<br />

Small-scale test using an induction motor with a power converter with constant V/f<br />

regulation. The motor is loaded with an unbalanced load to introduce eccentricity.<br />

25

Chapter 2 - Thesis Objectives<br />

2.5 Limitations / Assumptions<br />

The following limitations and assumptions have been taken in the process <strong>of</strong> this report.<br />

26<br />

In the design <strong>of</strong> the reference wind turbine generator thermal conditions are not<br />

considered.<br />

The eccentricity <strong>of</strong> the rotor is assumed to be constant in the axial length <strong>of</strong> the<br />

generator.<br />

The control concept <strong>of</strong> the converter is assumed to be a constant V/f regulation,<br />

which <strong>of</strong>fers a constant saturation level <strong>of</strong> the core.<br />

Frequency analysis during variable frequency is not considered as this topic has<br />

been covered <strong>by</strong> others. The analysis in this thesis is done at constant frequency.

Chapter 3<br />

The Reference <strong>Wind</strong> Turbine<br />

In this chapter a reference wind turbine is designed to be used throughout the report. Only the<br />

relevant components for this project are considered, such as the bearings and the generator.<br />

3.1 Introduction<br />

The reference wind turbine in this thesis is based on the Siemens SWT-3.6-120, which have an<br />

output power <strong>of</strong> 3.6 MW. In table 3.1 the public available specifications are given.<br />

General Information Turbine name SWT-3.6-120<br />

Manufacturer Siemens<br />

Operating Data Rated power 3,600 kW<br />

Cut-in wind speed 3-5 m/s<br />

Rated wind speed 12-13 m/s<br />

Cut-out wind speed 25 m/s<br />

Rotor Diameter 120 m<br />

Swept area 11.300 m 2<br />

Power Density 2.5 m 2 /kW<br />

Operational interval 5-13 rpm<br />

Power Regulation Type Pitch regulation with var. speed<br />

Generator Data Type Asynchronous<br />

Speed 1500 at 50 Hz (4 poles)<br />

Rated voltage 750 V<br />

Gearbox Type 3-stage planetary/helical<br />

Ratio 1:119<br />

Table 3.1 Specification for the Siemens SWT3.6-120 wind turbine, [16].<br />

The level <strong>of</strong> details is however insufficient to create an accurate model <strong>of</strong> the turbine. To model<br />

the effect <strong>of</strong> eccentricity, the specifications for the bearings and the generator must be known.<br />

This information is not publically available, so assumptions will be taken. The power converter<br />

is not considered as this survey does not concern operation at variable frequency.<br />

3.2 Bearings<br />

The purpose <strong>of</strong> a bearing is to support the axis <strong>of</strong> rotation with a low frictional surface. The<br />

drive train in the wind turbine has different types <strong>of</strong> rolling bearings depending on speed and<br />

load. For the reference turbine the electrical grid power output Pg is 3.6MW, but the load at the<br />

27

Chapter 3 - The Reference <strong>Wind</strong> Turbine<br />

drive train is higher due to loss in the transformation from mechanical to electrical power. In<br />

figure 3.1 the different stages <strong>of</strong> the power transformation is illustrated with some assumed efficiencies.<br />

28<br />

Pm<br />

ωm<br />

Gearbox<br />

ηr = 0.98<br />

Pr<br />

ωr<br />

Generator<br />

ηe = 0.97<br />

Pe<br />

ωe<br />

Converter<br />

ηc = 0.99<br />

Figure 3.1 Transformation <strong>of</strong> mechanical power to electrical power<br />

with component efficiencies.<br />

Pc<br />

ωc<br />

Transformer<br />

ηg = 0.98<br />

In this survey two bearings are considered; the main bearing rotating at the lowest speed and the<br />

gearbox bearing rotating at the highest speed. These bearings are chosen as they represent the<br />

two extremes in relation to speed and torque. The interesting power values in relation to the<br />

bearings are the power at the main shaft before the gearbox Pm and after the gearbox Pr.<br />

Pg<br />

Pm 3.90MW<br />

<br />

g c e r<br />

Pg<br />

Pr 3.83MW<br />

g c e<br />

The torque can be found using the rotational speed before and after the gearbox. The maximum<br />

speed <strong>of</strong> the main shaft is given as 13 rpm and with a gearing ratio <strong>of</strong> 1:119 the maximum speed<br />

after the gearbox is 1547 rpm. The relation between revolutions per minute and radians per second<br />

is given in equation (3.3) and the maximum torque at the two location in equation (3.4) and<br />

(3.5).<br />

2 n <br />

60<br />

Pm<br />

Tm 2.85MNm<br />

<br />

m<br />

Pr<br />

Tr 23.6kNm<br />

<br />

r<br />

The bearings at these locations should be able to support these loads, but also the mass <strong>of</strong> the<br />

system. The design process <strong>of</strong> bearings is a complicated process and irrelevant for this survey.<br />

The bearings used have been chosen from the bearing company SFK Group, which supplies<br />

bearings for a large variety <strong>of</strong> applications. [15]<br />

3.2.1 Main Bearings<br />

The main shaft in the Siemens SWT 3.6 turbine is supported <strong>by</strong> two self-aligning double spherical<br />

roller bearings, [16]. Roller bearings will carry a greater load than ball bearings <strong>of</strong> the same<br />

Pg<br />

ωg<br />

(3.1)<br />

(3.2)<br />

(3.3)<br />

(3.4)<br />

(3.5)

Chapter 3 - The Reference <strong>Wind</strong> Turbine<br />

size because <strong>of</strong> the larger contact area. The spherical elements have the advantage <strong>of</strong> increasing<br />

the contact area as the load increases, which insures alignment and low friction.<br />

To simplify the determination <strong>of</strong> the fault characteristic in chapter four, the bearing in this survey<br />

will be assumed to be a simple ball bearing. From the SFK online catalogue a ball bearing is<br />

chosen with the layout shown in figure 3.2.<br />

Db<br />

Di<br />

Inner<br />

racetrack<br />

Outer<br />

racetrack Ball<br />

θb<br />

Cage<br />

Dc<br />

Figure 3.2 Power transformation in the wind turbine.<br />

The geometrical specifications <strong>of</strong> the bearing are given in table 3.2.<br />

Inner<br />

diameter<br />

Outer<br />

diameter<br />

Ball<br />

diameter<br />

Cage<br />

diameter<br />

Number<br />

<strong>of</strong> balls<br />

β<br />

Do<br />

Contact<br />

angle<br />

D i D o D b D c N b β θ b<br />

Ball<br />

angle<br />

800 mm 1130 mm 143.5 mm 968 mm 27 40° 13.3°<br />

Table 3.2 Specifications for the low speed ball bearing (SKF – BA1B311745).<br />

Only the parameters needed to determine the characteristic frequency <strong>of</strong> the bearing are given.<br />

The chosen bearing is able to support a static load <strong>of</strong> about 3MNm.<br />

3.2.2 Gearbox Bearings<br />

The purpose <strong>of</strong> the gearbox is to transform the slow high-torque rotation <strong>of</strong> the turbine into a<br />

high speed low-torque rotation that can be connected to the generator. The gearbox used in the<br />

reference turbine is a three stage planetary/Helical with a gearing ratio <strong>of</strong> 1:119. In figure 3.3<br />

this type <strong>of</strong> gearbox is illustrated.<br />

29

Chapter 3 - The Reference <strong>Wind</strong> Turbine<br />

30<br />

Low-speed<br />

roller bearing.<br />

Figure 3.3 Two stage planetary gearbox with one spur gear (three stages), www.nke.ak.<br />

The first two stages use the planetary gearing and is characterised <strong>by</strong> a low gear ratio and high<br />

torque. The third and final stage is a spur gear with high gear ratio and low torque. This design<br />

is <strong>of</strong>ten chosen as it can be made compact and lightweight. The total number <strong>of</strong> bearings in this<br />

configuration is about fifteen. In this survey only the high speed ball bearing is being considered<br />

as mentioned earlier. A ball bearing is chosen from the SFK online catalogue with the specifications<br />

given in table 3.3.<br />

Inner<br />

diameter<br />

Outer<br />

diameter<br />

Ball<br />

diameter<br />

Cage<br />

diameter<br />

Number<br />

<strong>of</strong> balls<br />

Contact<br />

angle<br />

D i D o D b D c N b β θ b<br />

Ball<br />

angle<br />

95 mm 250 mm 57.5 mm 172.5 mm 10 36° 36°<br />

Table 3.3 Specifications for the high speed ball bearing (SKF - 7419 CBM).<br />

The chosen bearing is able to support a static load <strong>of</strong> about 25kNm.<br />

3.3 Generator<br />

The generator is the main component in this analysis as it is the source <strong>of</strong> the fault detection, so<br />

an accurate finite element model (FEM) is needed. The required output power Pe from the generator<br />

can be calculated from the efficiencies shown in figure 3.1<br />

Pg<br />

Pe 3.71MW<br />

<br />

g c<br />

Stage 1<br />

Stage 2<br />

Stage 3<br />

The design process <strong>of</strong> a generator is extensive and for this reason the detailed process is located<br />

in appendix A. The design process consists <strong>of</strong> an analytical iterative process with validation<br />

using a finite element analysis.<br />

In figure 3.4 the first pole <strong>of</strong> the designed four poled induction generator is shown.<br />

High-speed<br />

ball bearing.<br />

(3.6)

Stator slot<br />

wedge<br />

Rotor bar<br />

Rotor core<br />

Shaft<br />

A-<br />

A-<br />

Chapter 3 - The Reference <strong>Wind</strong> Turbine<br />

Figure 3.4 Finite element model <strong>of</strong> the designed reference generator showing the first pole.<br />

The stator has 48 slots with a two layer fully pitched winding configuration distributed over four<br />

slots. Each winding has eight turns and are connected in parallel to increase the number <strong>of</strong> turns<br />

per slot, which initially is small due to low terminal voltage (750V). The shape <strong>of</strong> the stator<br />

slots is squared to allow insertion <strong>of</strong> preformed coils with a high fill factor (60%). Each slot is<br />

closed with a slot wedge to keep the windings in place. The wedges are made <strong>of</strong> a low relative<br />

permeability material (µr ≈ 2-5). The rotor has 44 bars with a trapezoidal shape to keep the tooth<br />

width constant to avoid saturation. The rotor bars and end rings are made <strong>of</strong> aluminium to increase<br />

the rotor resistance and the slip value.<br />

In table 3.4 the main dimensions <strong>of</strong> the generator are given.<br />

B+<br />

B+<br />

B+<br />

B+<br />

C-<br />

Parameter Value Unit Description<br />

Dsi 731.0 mm Stator inner diameter<br />

Dso 1250.0 mm Stator outer diameter<br />

Dri 372.0 mm Rotor inner diameter<br />

Dro 727.8 mm Rotor outer diameter<br />

L 994.0 mm Length <strong>of</strong> stator core<br />

g 1.6 mm Air gap length<br />

Stator slot<br />

(double layer)<br />

Mr 2058.9 Kg Mass <strong>of</strong> rotor (core + bars + end rings)<br />

Ms 6429.7 Kg Mass <strong>of</strong> stator (core + windings)<br />

Table 3.4 The main dimensions <strong>of</strong> the designed reference generator.<br />

Stator core<br />

The generator is designed with low mass in mind since it is to be used in a wind turbine, where<br />

weight is important. This means that the electric loading is high (56kA/m), which requires active<br />

cooling <strong>of</strong> the machine (air or liquid).<br />

C-<br />

C-<br />

C-<br />

A+<br />

A+<br />

31

Chapter 3 - The Reference <strong>Wind</strong> Turbine<br />

In table 3.5 and in table 3.6 the equivalent parameters and the performance at maximum load are<br />

shown.<br />

32<br />

Parameter Value Unit Description<br />

R1 0.59 mΩ Stator winding resistance<br />

R ´ 2 0.79 mΩ Rotor cage resistance<br />

Rc 4.92 Ω Core loss resistance<br />

X1 8.92 mΩ Stator winding leakage reactance<br />

X ´ 2 5.86 mΩ Rotor cage leakage reactance<br />

Xm 519.08 mΩ Mutual reactance<br />

Table 3.5 Estimated equivalent parameters for the reference generator at 50Hz.<br />

Parameter Value Unit Description<br />

Imax 3066.8 A Maximum phase current (RMS)<br />

s -0.55 % Slip at Imax<br />

Pe 3744 kW Power output at Imax<br />

η 96.0 % Efficiency at Imax (core loss included)<br />

PF -0.94 Power factor at Imax<br />

Table 3.6 Performance <strong>of</strong> the reference generator at maximum load.<br />

The design has been optimized to have high efficiency and power factor. The efficiency <strong>of</strong> 96%<br />

includes core loss. With a power factor <strong>of</strong> -0.94 the power converter should have a rating <strong>of</strong><br />

about 4 MVA.<br />

In figure 3.5 and 3.6 the flux density and the flux contours are shown at a single pole under noload<br />

and full-load conditions, respectively.<br />

Figure 3.5 Flux contour and density<br />

at no-load (Iph = 819.2A).<br />

Figure 3.6 Flux contour and density<br />

at full-load (Iph = 3066.8A).

Chapter 4<br />

Drive Train Failure Characteristics<br />

This chapter describes the characteristic <strong>of</strong> failures in bearings. These characteristics are important<br />

to understand how faults can be identified. The rotor displacement during a fault is also<br />

investigated for use in the finite element analysis <strong>of</strong> the generator inductances in chapter five.<br />

4.1 Bearing Failures<br />

A bearing consist <strong>of</strong> three major components; the inner racetrack, the outer racetrack and the<br />

rotating elements. During operation these components will deteriorate over time and ideally the<br />

deterioration will be equally distributed over the entire contact surfaces <strong>of</strong> the bearing. This is<br />

referred to as normal wear or fatigue. During high dynamic stress situations it is however more<br />

likely that flaking will occur. Flaking is when a chunk <strong>of</strong> the bearing material has broken loose<br />

and forms a small cavity. This is referred to as a bearing fault. The two concepts are illustrated<br />

in figure 4.1.<br />

Flaking<br />

Distributed wear<br />

Figure 4.1 Bearing wear (distributed) and bearing flaking (cavity). [17]<br />

In this report the two types <strong>of</strong> incidents are distinguished from each other as they have different<br />

characteristics.<br />

4.1.1 Characteristic Frequencies <strong>of</strong> a Bearing (Fault ID)<br />

When a failure is present in one <strong>of</strong> the subcomponents <strong>of</strong> the bearing it will occur with a certain<br />

interval or characteristic frequency. If these frequencies are unique, they can be used to identify<br />

the bearing – hence locate the fault.<br />

There are five basic motions that are used to describe the dynamics <strong>of</strong> a bearing and each <strong>of</strong><br />

33

Chapter 4 - Drive Train Failure Characteristics<br />

these motions has a corresponding frequency. The five frequencies are denoted the shaft angular<br />

frequency ωs, the fundamental cage frequency ωc, the ball pass inner racetrack frequency ωbpi,<br />

the ball pass outer racetrack frequency ωbpo and the ball frequency ωb. These five frequencies<br />

are illustrated in figure 4.2. [18]<br />

34<br />

ωb<br />

ωc<br />

ωs<br />

vor<br />

vc<br />

vir<br />

ωbpi ωbpo<br />

Figure 4.2 Typical layout <strong>of</strong> geared wind turbine with categorization <strong>of</strong> its main components.<br />

The angular frequency <strong>of</strong> the shaft ωs is the speed <strong>of</strong> the wind turbine rotor, gear or generator<br />

and the known variable. The other angular frequencies must be described in terms <strong>of</strong> this frequency.<br />

In figure 4.2 vir, vc and vor, represent the tangential linear velocity <strong>of</strong> the inner racetrack,<br />

the ball centre and the outer racetrack, respectively. Db is the ball diameter, Dc is the bearing<br />

cage diameter and β is the contact angle <strong>of</strong> the bearing.<br />

The relation between angular frequency ω, ordinary frequency f and the tangential linear velocity<br />

v is given in equation (4.1), where r is the radius to the centre <strong>of</strong> rotation.<br />

v<br />

2 f <br />

r<br />

The fundamental cage angular frequency is related to the motion <strong>of</strong> the cage. It can be derived<br />

from the linear velocity <strong>of</strong> a point in the cage vc, which is the mean linear velocity <strong>of</strong> the inner<br />

racetrack and the outer racetrack.<br />

Dc<br />

β<br />

Db<br />

(4.1)<br />

vc vir vor1virvor c<br />

(4.2)<br />

r 2 r D<br />

c c c<br />

In terms <strong>of</strong> the angular frequency, the velocity <strong>of</strong> the inner racetrack and the outer racetrack can<br />

be written as:<br />

ir ir ir ir c b<br />

or or or or c b<br />

cos / 2<br />

v r r D <br />

cos / 2<br />

v r r D <br />

The fundamental rotational cage frequency is then:<br />

(4.3)

c<br />

<br />

D<br />

ir ir or or<br />

c<br />

1 Dc Db cos Dc Db<br />

cos <br />

ir or<br />

D 2 2 <br />

c<br />

Chapter 4 - Drive Train Failure Characteristics<br />

In a motor or generator configuration, the out racetrack can be assumed stationary (ωor = 0),<br />

since it is locked in place <strong>by</strong> an external casing, while the inner racetrack is rotating at the speed<br />

<strong>of</strong> the shaft (ωir = ωs).<br />

1 Db<br />

cos <br />

c s 1<br />

2<br />

Dc<br />

<br />

<br />

<br />

The ball pass inner racetrack frequency ωbpi indicate the rate at which a ball passes a point on<br />

the inner racetrack. The frequency is determined <strong>by</strong> the number <strong>of</strong> balls Nb and the difference<br />

between the fundamental cage frequency ωc and the inner racetrack frequency ωir, which is<br />

equal with the shaft frequency in the given case (ωir = ωs).<br />

N <br />

bpi b c s<br />

1 Db<br />

cos<br />

<br />

Nb<br />

s1s 2 Dc<br />

<br />

N b Dbcos<br />

s 1 2 Dc<br />

<br />

In the same way the ball pass outer racetrack frequency ωbpo is defined as the rate at which a<br />

ball passes a point on the outer racetrack. The frequency is determined <strong>by</strong> the number <strong>of</strong> balls<br />

Nb and the difference between the cage frequency ωc and the outer racetrack frequency ωor,<br />

which is zero in the given case (ωor = 0).<br />

N 0<br />

bpo b c<br />

1 Db<br />

cos<br />

<br />

Nbs1<br />

2 Dc<br />

<br />

N b Dbcos<br />

<br />

s 1 2 Dc<br />

<br />

The ball angular frequency ωb is the rate <strong>of</strong> rotation <strong>of</strong> a ball about its own axis. This frequency<br />

can be obtained from the difference between the cage frequency and the inner or outer frequency,<br />

and the radii relationship. The radii relationship can be thought <strong>of</strong> as the “gear” ratio.<br />

(4.4)<br />

(4.5)<br />

(4.6)<br />

(4.7)<br />

35

Chapter 4 - Drive Train Failure Characteristics<br />

36<br />

r r<br />

<br />

<br />

ir or<br />

b ir c<br />

rb or c<br />

rb<br />

r D cos<br />

/ 2<br />

1 Db<br />

cos c b<br />

0s1 2 D r<br />

2 2<br />

D c Db<br />

cos <br />

s 12 2 Db Dc<br />

<br />

c b<br />

Frequency studies have shown that when defects occur in a bearing, the defects will generate<br />

some <strong>of</strong> the above mentioned frequencies in the vibration signals. If the defective area is large<br />

harmonics <strong>of</strong> these frequencies will also be present, [18] and [19].<br />

For the reference wind turbine the two bearings will have the characteristics frequencies given<br />

in table 4.1. Here presented in ordinary frequency.<br />

Bearing<br />

Shaft<br />

speed<br />

Shaft<br />

frequency<br />

Ball pass inner<br />

frequency<br />

Ball pass outer<br />

frequency<br />

Ball<br />

frequency<br />

n f s f bpi f bpo f b<br />

high speed 1547 rpm 25.8 Hz 163.7 Hz 94.2 Hz 35.9 Hz<br />

low speed 13 rpm 0.2 Hz 3.3 Hz 2.6 Hz 0.7 Hz<br />

Table 4.1 Characteristic frequencies (fault IDs) for bearings in the reference wind turbine.<br />

For the two chosen bearings the fault IDs are unique, which makes it possible to identify the<br />

two bearings in the vibration or electrical frequency spectrum. In the electrical frequency spectrum<br />

an incident in the bearing should also produce additional frequencies fi,k in the stator current.<br />

In reference [19] this has been shown to have the following relationship.<br />

(4.8)<br />

fi, k fe k f f f f fbpi, fbpo,2 fb<br />

(4.9)<br />

Where fe is the electrical stator supply frequency, ff is one <strong>of</strong> the characteristic frequencies and k<br />

is an integer value (k = 1,2,3...). Twice the ball frequency is used as it is likely that if a ball has<br />

a defect, it will touch both inner and outer racetrack during one rotation.<br />

If two identical bearings were chosen and rotated at the same speed, their IDs are no longer<br />

unique. When using vibration monitoring, the difference in amplitude measured at the two different<br />

bearings can be used to identify and locate a fault. This is possible since multiple vibration<br />

sensors are used. But, for electrical monitoring this would not be possible since only one<br />

sensor is used (the generator).

4.2 Rotor Displacement (Eccentricity)<br />

Chapter 4 - Drive Train Failure Characteristics<br />

In the previous section, the characteristic frequencies <strong>of</strong> a ball bearing have been derived. To<br />

investigate the influence on the inductances <strong>of</strong> the generator during faults, the rotor displacement<br />

and the resulting air gap length must be described. When the rotor is displaced, it is eccentric<br />

positioned compared to the stator. Three types <strong>of</strong> eccentricity can occur as mentioned in<br />

chapter two; static, dynamic and mixed eccentricity.<br />

In figure 4.3 the geometrical configuration for a general rotor displacement is illustrated, where<br />

Rsi is the inner stator radius, Rro is the outer rotor radius, rd is the displacement vector, θd is the<br />

displacement angle and θr is the rotor angle.<br />

Rsi<br />

stator<br />

rotor Rro<br />

Figure 4.3 Geometrical configuration <strong>of</strong> rotor with displacement vector rd.<br />

It should be mentioned that the following considerations suppose a uniform air gap length in the<br />

axial direction <strong>of</strong> the machine, as mentioned in the assumptions <strong>of</strong> the project objectives. This<br />

allows the problem to be considered as a two-dimensional case and simplifies the calculations.<br />

However, this simplifying assumption is probably not verified in most practical cases, but is<br />

only considered to affect the amplitude at the characteristic frequencies.<br />

4.2.1 Misalignment (Static Eccentricity)<br />

In the case <strong>of</strong> misaligned components, the rotor displacement does not depend on the position <strong>of</strong><br />

the rotor nor does it depend on a failure frequency. This is a case <strong>of</strong> static eccentricity. It is<br />

statically locked in an <strong>of</strong>f centred position. The displacement vector rd <strong>of</strong> the rotor can be describes<br />

<strong>by</strong> its components a and b using the displacement angle.<br />

cos sin <br />

d 0 s d d 0 s d<br />

y<br />

a<br />

rd<br />

θd<br />

a g b g (4.10)<br />

where δs denote the degree <strong>of</strong> static eccentricity with respect to the uniform air gap length g0.<br />

The uniform air gap length is equal to, g0 = Rsi - Rro.<br />

b<br />

θr<br />

x<br />

37

Chapter 4 - Drive Train Failure Characteristics<br />

4.2.2 Bearing Failures (dynamic eccentricity)<br />

In case <strong>of</strong> a fault in the bearing, the rotor displacement depends on the position <strong>of</strong> the rotor and<br />

the failure rate frequency. This is a case <strong>of</strong> dynamic eccentricity. The length <strong>of</strong> the displacement<br />

vector rd depends on the failure rate frequency and the position <strong>of</strong> the rotor θr. For a large defective<br />

area the change in length can be assumed to a continuous function that follows a sinusoidal<br />

tendency. If the defective area is small the change is no longer continuous, but rather an impulse.<br />

These two concepts are illustrated in figure 4.4 and figure 4.5 for a fault in the inner racetrack<br />

<strong>of</strong> the bearing.<br />

38<br />

|rd|<br />

θ<br />

Large<br />

defective area<br />

θ 2θ 3θ<br />

Bearing<br />

ball<br />

Figure 4.4 Large defective area – continuous<br />

function.<br />

θr<br />

|rd|<br />

θ<br />

Small<br />

defective area<br />

θ 2θ 3θ<br />

Bearing<br />

ball<br />

Figure 4.5 Small defective area – impulse<br />

function.<br />

If the defective area is large, the displacement <strong>of</strong> the rotor is always changing. When one ball<br />

leaves the defective area, the next ball enters. But, if the defective area is small, the rotor is only<br />

displaced at the very instance when the ball passes the defective area. In all other positions the<br />

rotor is centred and the displacement is zero. Related to the development <strong>of</strong> a fault, it can be<br />

assumed that at the early stage, the defective area is small. As the fault become more severe the<br />

defective area becomes larger. To simulate a fault at an early stage, which is important for early<br />

fault detection, the displacement <strong>of</strong> the rotor should be done with the small defective area.<br />

The displacement <strong>of</strong> the rotor can in the case <strong>of</strong> a small defective area be described using the<br />

Dirac delta function as done in [19]. In equation (4.11) the criteria for the Dirac delta function δ<br />

is given.<br />

<br />

<br />

<br />

,<br />

x 0<br />

xdx1x 0,<br />

x 0<br />

θr<br />

(4.11)<br />

For all other value than x = 0 the integral <strong>of</strong> δ(x) is zero. If x = θr – θf, then when the rotor θr is<br />

located at the fault location θf, the integral <strong>of</strong> δ(x) is one. This would result in single unit impulse<br />

at each fault location, which in reference [19] is used to investigate the air gap change at<br />

the fault location. This is however not considered to represent the actual shape <strong>of</strong> the defective<br />

area. Instead an exponential function is used in this project, which also is one when θr – θf = 0,<br />

but has a slope before and after. The function to adjust the shape <strong>of</strong> the displacement vector is

shown in equation (4.12) in terms <strong>of</strong> the rotor position.<br />

<br />

2<br />

( rkf )<br />

Chapter 4 - Drive Train Failure Characteristics<br />

2<br />

w2 (4.12)<br />

r g e<br />

d r 0 d<br />

<br />

k1<br />

Where k is the value that satisfies the condition θr – kθf = 0, so that the first fault incident is at k<br />

= 1, the second at k = 2 and so forth. θw is the angular width <strong>of</strong> the defective area.<br />

The angle between each fault incident θf can be found from the characteristic failure frequencies<br />

(ωf = ωbpi, ωbpo or ωb) described in section 4.1.<br />

ngsng2s fngstf (4.13)<br />

f <br />

f f<br />

Where ng represent the gear ratio between the location <strong>of</strong> the bearing and the rotor in the generator.<br />

If the bearing is located at the high speed side <strong>of</strong> the gearbox then ng = 1 and if the bearing<br />

is located at the low speed side then ng = 119.<br />

The components a and b for the displacement vector can then be described as:<br />

<br />

r<br />

brg0d cos e<br />

<br />

<br />

n <br />

g k 1<br />

<br />

r<br />

arg0d sin e<br />

<br />

<br />

n <br />

g k 1<br />

2<br />

( rkf )<br />

2<br />

w2 2<br />

( rkf )<br />

2<br />

w2 (4.14)<br />

Where θr/ng represents the displacement angle θd. The displacement vector will move at a speed<br />

determined <strong>by</strong> the speed at the fault location.<br />

4.2.2.1 Inner Racetrack Failure<br />

In figure 4.6 and 4.7, the rotor displacement is shown for an inner racetrack fault in the low<br />

speed main bearing. Figure 4.6 shows the polar plot <strong>of</strong> the displacement vector and figure 4.6<br />

shows the magnitude in terms <strong>of</strong> the rotor position. The following values are used: g0 = 1.6 mm,<br />

δd = 0.5, ng = 119, θf = 2850° and θw = θb / 2 = 6.67°. The width <strong>of</strong> the defective area θw is chosen<br />

as half the value <strong>of</strong> the angle between two balls in the bearing θb.<br />

39

Chapter 4 - Drive Train Failure Characteristics<br />

40<br />

0.5<br />

Figure 4.6 Polar plot <strong>of</strong> the displacement vector<br />

during an inner racetrack fault in the low speed<br />

bearing in relation to the displacement angle θd.<br />

Figure 4.7 Magnitude <strong>of</strong> the displacement vector<br />

during an inner racetrack fault in the low speed<br />

bearing in relation to the rotor position θr.<br />

Due to the large gear ratio the rotor is eccentric for about two rotations since the effective width<br />

<strong>of</strong> the fault at the rotor is 119 times the width at the fault location. An important observation is<br />

that since the angle between incidents is 2850°, the fault is only present at about every 8 th rotation<br />

<strong>of</strong> the rotor. In a four poled machine this equal to 16 electrical periods at 50Hz.This can<br />

make the fault detection difficult, as the fault is not continuously present in the electrical signal.<br />

In figure 4.8 and 4.9 the rotor displacement is shown for an inner racetrack fault in the high<br />

speed gearbox bearing. The following values are used: g0 = 1.6 mm, δd = 0.5, ng = 1, θf = 56.7°<br />

and θw = θb / 2 = 18°.<br />

|r r | [mm]<br />

|r r | [mm]<br />

150<br />

210<br />

120<br />

240<br />

90<br />

270<br />

Figure 4.8 Polar plot <strong>of</strong> the displacement vector<br />

during an inner racetrack fault in the high speed<br />

bearing in relation to the displacement angle θd.<br />

1<br />

60<br />

300<br />

30<br />

180 0<br />

150<br />

210<br />

Displacement angle d [deg]<br />

120<br />

240<br />

90<br />

1<br />

0.5<br />

60<br />

330<br />

30<br />

180 0<br />

270<br />

300<br />

Displacement angle d [deg]<br />

330<br />

|r r | [mm]<br />

|r r | [mm]<br />

1.6<br />

1.4<br />

1.2<br />

1<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

0<br />

0 1000 2000 3000 4000<br />

Rotor position [deg]<br />

r<br />

1.6<br />

1.4<br />

1.2<br />

1<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

0<br />

0 100 200 300<br />

Rotor position [deg]<br />

r<br />

Figure 4.9 Magnitude <strong>of</strong> the displacement vector<br />

during an inner racetrack fault in the high speed<br />

bearing in relation to the rotor position θr.

Chapter 4 - Drive Train Failure Characteristics<br />

Since the bearing is rotating with the speed <strong>of</strong> the rotor, the number <strong>of</strong> incidents is larger than at<br />

a fault in the low speed bearing. This makes the detection easier as the fault is continuously<br />

present in the electric signal. But, as the angle between incidents θf divided <strong>by</strong> 360° (one rotation)<br />

is not an integer value, the displacement will not occur at the same location. This means<br />

that the generator must be independent on the fault location to get a reliable reading.<br />

4.2.2.2 Outer Racetrack Failure<br />

In figure 4.10 and 4.11 the rotor displacement for the low speed main shaft bearing and the high<br />

speed gearbox bearing is shown in case <strong>of</strong> an outer race track failure, respectively. The polar<br />

plot is omitted in this case.<br />

|r r | [mm]<br />

1.6<br />

1.4<br />

1.2<br />

1<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

0<br />

0 1000 2000 3000 4000<br />

Rotor position [deg]<br />

r<br />

Figure 4.10 Magnitude <strong>of</strong> the displacement vector<br />

during an outer racetrack fault in the low speed bearing<br />

in relation to the rotor position θr.<br />

Figure 4.11 Magnitude <strong>of</strong> the displacement vector<br />

during an outer racetrack fault in the high speed<br />

bearing in relation to the rotor position θr.<br />

As the circumference <strong>of</strong> the outer racetrack is larger, the failure rate frequency is lower resulting<br />

in fewer incidents per rotation.<br />

4.2.2.3 Ball Failure<br />

0<br />

0 100 200 300<br />

Rotor position [deg]<br />

r<br />

In figure 4.12 and 4.13 the rotor displacement for the low speed main shaft bearing and the high<br />

speed gearbox bearing is shown in case <strong>of</strong> a ball failure, respectively.<br />

|r r | [mm]<br />

1.6<br />

1.4<br />

1.2<br />

1<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

41

Chapter 4 - Drive Train Failure Characteristics<br />

|r r | [mm]<br />

42<br />

1.6<br />

1.4<br />

1.2<br />

1<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

0<br />

0 5000 10000 15000<br />

Rotor position [deg]<br />

r<br />

Figure 4.12 Magnitude <strong>of</strong> the displacement vector<br />

during a ball fault in the low speed bearing in<br />

relation to the rotor position θr.<br />

Figure 4.13 Magnitude <strong>of</strong> the displacement vector<br />

during a ball fault in the high speed bearing<br />

in relation to the rotor position θr.<br />

A fault in a ball will have the lowest failure rate frequency <strong>of</strong> the three described cases and the<br />

angle between faults is then extensive. For the low speed main shaft bearing this means that the<br />

fault is only present after 36 rotor rotations. If the balls are arranged so that the defective area<br />

touch both the inner and outer racetrack during one rotation then failure rate is twice the presented<br />

values. This would be the case for roller type bearing or ball bearings with a 0° attack<br />

angle.<br />

4.2.3 Combined Failures (mixed eccentricity)<br />

If different failure types are present, e.g. misalignment and a bearing fault, then a combination<br />

<strong>of</strong> static and dynamic eccentricity will be present. This type <strong>of</strong> eccentricity is called mixed eccentricity.<br />

By combining equation (4.10) and equation (4.14) a case <strong>of</strong> mixed eccentricity can be<br />

described as, where the degree <strong>of</strong> static eccentricity occur in the direction <strong>of</strong> component a.<br />

<br />

2<br />

<br />

( rkf )<br />

<br />

2<br />

<br />

r<br />

w2 a r g0 s d cos e<br />

<br />

<br />

<br />

n <br />

g k 1<br />

<br />

<br />

<br />

r<br />

brg0d sin e<br />

<br />

<br />

n <br />

g k 1<br />

<br />

2<br />

( rkf )<br />

2<br />

w2 (4.15)<br />

To avoid that the rotor rubs against the stator then the degree <strong>of</strong> eccentricity must be less than<br />

one, δs + δd < 1.<br />

4.2.4 Bearing Wear (dynamic eccentricity)<br />

0<br />

0 100 200 300 400<br />

Rotor position [deg]<br />

r<br />

In the introduction to this chapter it was mentioned that bearings failures are distinguished from<br />

the normal distributed wear <strong>of</strong> a bearing. A bearing is designed from a statistical point <strong>of</strong> view<br />

|r r | [mm]<br />

1.6<br />

1.4<br />

1.2<br />

1<br />

0.8<br />

0.6<br />

0.4<br />

0.2

Chapter 4 - Drive Train Failure Characteristics<br />

to last for certain amount <strong>of</strong> time. In the ideal case the fatigue <strong>of</strong> the bearing is equally distributed<br />

between the two racetracks and the balls. In this case the displacement <strong>of</strong> the rotor is constant<br />

in an <strong>of</strong>f centred position and does not oscillate as in case <strong>of</strong> the small defective area. This<br />

is a traditional case <strong>of</strong> dynamic eccentricity as illustrated in figure 4.14.<br />

|rd|<br />

Degree <strong>of</strong><br />

fatigue<br />

θ<br />

θ 2θ 3θ<br />

Figure 4.14 Distributed bearing wear (fatigue) in a ball bearing.<br />

The components <strong>of</strong> the displacement vector can be described as:<br />

r<br />

arg0d cos <br />

<br />

n <br />

g <br />

r<br />

brg0d sin <br />

<br />

<br />

n <br />

g <br />

θr<br />

(4.16)<br />

Since the rotor displacement does not depend on a characteristic frequency <strong>of</strong> the bearing, it will<br />

be impossible to determine the exact bearing causing the displacement if rotating at the same<br />

speed (at same gear ratio ng). It is however possible to determine at which speed stage the fault<br />

is located.<br />

4.3 Air Gap Length<br />

In the previous sections, the displacement <strong>of</strong> the rotor during different cases <strong>of</strong> eccentricity has<br />

been studied. The displacement is important when doing finite element simulations, but for analytical<br />

studies the air gap length is more useful. During eccentricity, the air gap length is no<br />

longer uniform in the circumference <strong>of</strong> the machine. It will change with the degree <strong>of</strong> eccentricity<br />

and the position <strong>of</strong> the rotor in the case <strong>of</strong> dynamic eccentricity. During static eccentricity<br />

the air gap length is independent on the position <strong>of</strong> the rotor.<br />

The air gap length at uniform conditions is the difference between the inner circumference <strong>of</strong><br />

the stator and the outer circumference <strong>of</strong> the rotor. The inner circumference <strong>of</strong> the stator and the<br />

outer circumference <strong>of</strong> the rotor can be described in terms <strong>of</strong> x and y components, where θm is<br />

43

Chapter 4 - Drive Train Failure Characteristics<br />

the mechanical angle <strong>of</strong> the circumference.<br />

44<br />

<br />

x R cos y R sin<br />

(4.17)<br />

si si m si si m<br />

<br />

x R cos y R sin<br />

(4.18)<br />

ro ro m ro ro m<br />

By applying the displacement components (a, b) to the coordinates <strong>of</strong> the outer circumference <strong>of</strong><br />

the rotor then the air gap length g can then be described in terms <strong>of</strong> the mechanical angle θm and<br />

the rotor position θr.<br />

g<br />

, <br />

m r<br />

<br />

2<br />

xsi m xro m ar<br />

ysi m ( yro m b r <br />

( ...<br />

2<br />

(4.19)<br />

To illustrate the use <strong>of</strong> equation (4.19) a case <strong>of</strong> static eccentricity is shown in figure 4.15. In<br />

this case the rotor is displaced at θd = 0° with 50% eccentricity. The uniform air gap length is g0<br />

= 1.6mm.<br />

Air gap length g [mm]<br />

2.5<br />

2<br />

1.5<br />

1<br />

0.5<br />

0 50 100 150 200 250 300 350<br />

Mechanical angle [deg]<br />

m<br />

Figure 4.15 Change in air gap length in the circumference <strong>of</strong> the generator during 50%<br />

static eccentricity at 0°.<br />

The air gap length at 0° is reduced to 0.8mm and increased to 2.4mm at 180°, which is expected<br />

when the rotor is moved in the direction <strong>of</strong> component a located at 0°.<br />

4.4 Chapter Conclusion<br />

50% static ecc.<br />

0% static ecc.<br />

In this chapter the characteristics bearings failure has been described. In relation to condition<br />

monitoring it is important to identify the exact defective component in order to perform effective<br />

maintenance. A fault in a bearing will cause a mechanical vibration with a characteristic<br />

frequency that can be related to an incident in the inner racetrack, outer racetrack or in the balls.<br />

In condition monitoring these frequencies are known as the bearing signature or ID, and <strong>by</strong><br />

monitoring the amplitude at these frequencies the development <strong>of</strong> a fault can be observed. The<br />

frequencies will both be present in the mechanical vibration spectrum and in the electrical spec-

Chapter 4 - Drive Train Failure Characteristics<br />

trum. An important observation is that if two identical bearing are used and rotated and the same<br />

speed, then they will have the same signature. The main shaft in a typical wind turbine is <strong>of</strong>ten<br />

supported <strong>by</strong> two main bearings, and it is likely that these would be identical. In this case it<br />

would not be possible to identify the faulty bearing using ESA due to similar signatures. This<br />

would be possible with vibration monitoring <strong>by</strong> comparing the amplitude measured at the sensors<br />

located at each bearing.<br />

In the analysis a distinction was made between bearing wear and bearing faults; wear is the<br />

slowly and distributed degradation <strong>of</strong> the bearing, a fault is the small cracks / flakes. As the<br />

distributed wear will not have a characteristic frequency, then it will not be possible to locate<br />

the exact worn out bearing if rotated at the same speed.<br />

Another important observation is that due to the high gear ratio, the fault frequency <strong>of</strong> the low<br />

speed bearing is very low. During a fault in a bearing rotating at low speed it will not be continuously<br />

present in the electrical signal. This is considered to be a difficult challenge for the<br />

signal processing.<br />

These physical constraints and challenges limit the use <strong>of</strong> ESA in condition monitoring as a<br />

replacement for the vibration based system.<br />

45

Chapter 5<br />

Generator Characteristics<br />

In this chapter the characteristics <strong>of</strong> the generator is investigated during eccentricity. A simplified<br />

analytical analysis <strong>of</strong> the change in machine inductances is compared to a finite element<br />

analysis.<br />

5.1 Introduction<br />

When the rotor is displaced, the air gap length becomes non-uniform. In the hypothesis in chapter<br />

two it was shown that the self inductance is inversely proportional to the air gap length,<br />

when the mmf drop <strong>of</strong> the core is neglected. This is <strong>of</strong>ten a reasonable assumption as the permeability<br />

<strong>of</strong> the core is much greater than that <strong>of</strong> air (µr >> µ0). However in a real case the influence<br />

<strong>of</strong> the core must be considered. By including this factor the actual sensitivity <strong>of</strong> the generator<br />

can be investigated.<br />

5.2 Analytical <strong>Analysis</strong><br />

From the geometry <strong>of</strong> reference generator shown in figure 5.1, the magnetic properties <strong>of</strong> the<br />

machine are investigated. The red arrowed lines illustrate the flux paths.<br />

dscb<br />

hst<br />

g<br />

hrt<br />

drcb<br />

135°<br />

90°<br />

A1<br />

Air gap area per pole, Ag<br />

-45°<br />

A1<br />

<strong>Wind</strong>ing a,1<br />

Figure 5.1 Geometry <strong>of</strong> the reference generator used in the analytical analysis.<br />

In table 5.1 the dimensions used throughout this section are given.<br />

0°<br />

47

Chapter 5 - Generator Characteristics<br />

48<br />

Parameter Value Unit Description<br />

Dsi 731.0 mm Stator inner diameter<br />

Dso 1250.0 mm Stator outer diameter<br />

Dri 372.0 mm Rotor inner diameter<br />

L 994.0 mm Length <strong>of</strong> stator core<br />

g0 1.6 mm Uniform air gap length<br />

dscb 164.7 mm Stator core back depth<br />

drcb 106.6 mm Rotor core back depth<br />

hst 95 mm Stator teeth height<br />

hrt 71 mm Rotor teeth height<br />

μr 3000 Relative permeability <strong>of</strong> iron core<br />

Table 5.1 Values <strong>of</strong> the parameters shown figure 5.1.<br />

5.2.1 Equivalent Circuit (Reluctance Network)<br />

Magnetic field problems involving components such as current coils, ferromagnetic cores and<br />

air gaps can be solved as magnetic circuits. Here, the analogues magnetic quantities to the corresponding<br />

electric quantities are used in an electric circuit. In figure 5.2 the magnetic circuit <strong>of</strong><br />

winding a,1 and the related core section is presented. A lumped approach is used, so that all<br />

stator teeth reluctances at one pole are lumped together, and so forth. The air gap reluctances are<br />

lumped into three parts, so that one part accounts for the send path (0°-90°) and one for each<br />

return path (-45°-0° and 90°-135°).<br />

2 st<br />

scb<br />

Na,n·Ia,n<br />

an<br />

,<br />

scb<br />

st 2 st<br />

g1, n<br />

g1, n<br />

g1,<br />

n<br />

2 rt<br />

rcb<br />

rt<br />

rcb<br />

Figure 5.2 Equivalent magnetic circuit <strong>of</strong> phase winding a,n.<br />

2 rt<br />

scb is the stator core back reluctance, st is the stator teeth reluctance, g is the air gap reluctance,<br />

rt is the rotor teeth reluctance and rcb is the rotor core back reluctance. If core satura-

Chapter 5 - Generator Characteristics<br />

tion is neglected (µr is constant) then the core related reluctances are constant during eccentricity.<br />

The stator core back reluctance scb is determined as:<br />

lscb<br />

scb A<br />

0<br />

r scb<br />

where the stator core back length lscb and the area Ascb is found as:<br />

(5.1)<br />

1<br />

lscb Dso dscb Ascb dscb L<br />

p (5.2)<br />

The stator teeth reluctance st and rotor teeth reluctance rt are determined as:<br />

h<br />

A <br />

st<br />

st<br />

0rAst st<br />

h<br />

A <br />

rt<br />

rt<br />

0rArt rt<br />

For simplification then the total teeth area is chosen to be half the air gap area, which is a common<br />

choice in machine design. The rotor core back reluctance rcb is determined as:<br />

lrcb<br />

rcb A<br />

0<br />

r rcb<br />

where the rotor core back length lrcb and the area Arcb is found as:<br />

A<br />

g<br />

2<br />

A<br />

g<br />

2<br />

(5.3)<br />

(5.4)<br />

(5.5)<br />

1<br />

lrcb Dri drcb Arcb drcb L<br />

p (5.6)<br />

The air gap reluctances will change during rotor eccentricity, so to determine the reluctance the<br />

mean air gap length must determined at each angle and for each winding. For winding n <strong>of</strong><br />

phase a the mean air gap length can be determined at the three locations using the air gap length<br />

function found in chapter four - equation (4.19).<br />

n360<br />

p<br />

p<br />

g g , <br />

d<br />

360<br />

1, n r m r m<br />

(5.7)<br />

n1360 p<br />

360 n0.5<br />

<br />

p<br />

2<br />

p<br />

g g , <br />

d<br />

(5.8)<br />

1,<br />

n r m r m<br />

360 n360<br />

p<br />

360 n1<br />

<br />

p<br />

2<br />

p<br />

g g , <br />

d<br />

360<br />

1,<br />

n r m r m<br />

(5.9)<br />

n1.5360 p<br />

49

Chapter 5 - Generator Characteristics<br />

The reluctance at the three positions is then:<br />

50<br />

<br />

g<br />

1<br />

A D g L<br />

<br />

1, n r<br />

g1, n<br />

0<br />

Ag g<br />

p<br />

si 0<br />

g<br />

<br />

<br />

1,<br />

n r<br />

g1, n 1 0<br />

2 Ag<br />

g<br />

<br />

<br />

1,<br />

n r<br />

g1, n 1 0<br />

2 Ag<br />

(5.10)<br />

(5.11)<br />

(5.12)<br />

The total reluctance a,n <strong>of</strong> the given circuit can be determined <strong>by</strong> considering the three parallel<br />

branches.<br />

scb st g 1,<br />

n rt rcb <br />

<br />

1<br />

...<br />

scb 2stg1, n 2rtrcb<br />

1<br />

1<br />

<br />

2 2 ...<br />

<br />

<br />

<br />

<br />

a, n st g1, n rt<br />

1<br />

<br />

<br />

<br />

From the total reluctance and the mmf the magnetic flux a,n can be determined.<br />

<br />

an ,<br />

N I<br />

<br />

<br />

a, n a, n<br />

an ,<br />

The inductance <strong>of</strong> a winding is defined as the ratio <strong>of</strong> magnetic flux linkage Φ to current I.<br />

(5.13)<br />

(5.14)<br />

N <br />

L (5.15)<br />

I I<br />

In terms <strong>of</strong> the total reluctance the self-inductance can be found as:<br />

L<br />

an ,<br />

2<br />

Na, n a, n Na, n Na, n Ia,<br />

n Na,<br />

n<br />

<br />

I I (5.16)<br />

a, n a, n a, n a, n<br />

The self-inductance inductance <strong>of</strong> winding a,n can now be estimated. Since the windings for the<br />

reference machine are coupled in parallel this must be taken into account to determine the selfinductance<br />

<strong>of</strong> phase a, La,par.<br />

L<br />

a, par<br />

n1 an , <br />

1<br />

p<br />

1 <br />

<br />

<br />

(5.17)<br />

L <br />

Other machines could be coupled in series and to evaluate the difference between the two methods,<br />

equation (5.18) is used for the series connected windings. In this case the number <strong>of</strong> turns<br />

should be adjusted. The reference machine has eight turns per winding, which if coupled in<br />

parallel also is eight turns per phase. But 32 turns if coupled in series, so the number <strong>of</strong> turns per

winding must be adjusted to get a proper comparison.<br />

p<br />

a, ser a, n<br />

n1<br />

Chapter 5 - Generator Characteristics<br />

L L<br />

(5.18)<br />

From the derived equation it is now possible described the sensitivity <strong>of</strong> the self-inductance <strong>of</strong><br />

phase a during eccentricity. If the self-inductance <strong>of</strong> phase b and c should be estimated, the calculation<br />

<strong>of</strong> the mean air gap length would have to be shifted <strong>by</strong> 30° for phase c and 60° for<br />

phase b (if a four poled machine is used). This analytical analysis is however based on phase a.<br />

5.2.2 Relative Change in Self-Inductance (Sensitivity)<br />

To find the sensitivity <strong>of</strong> the inductance when eccentricity occur a simple misalignment is considered.<br />

In case <strong>of</strong> a misalignment the rotor is shifted to a static <strong>of</strong>f centred position and the air<br />

gap length is time independent. This will make the interpretation <strong>of</strong> the results easier. The displacement<br />

components a and b for misalignment was derived in equation (4.10).<br />

cos sin<br />

<br />

a g b g (5.19)<br />

d 0 s d d 0 s d<br />

Where g0 is the uniform air gap length, δs is the degree <strong>of</strong> displacement and θd is the displacement<br />

angle. First, the relation between the displacement angle and the relative change is investigated<br />

for the self-inductance <strong>of</strong> phase a, as shown in figure 5.3. The magnetic flux path for<br />

winding a,(n = 1:4) is located at 45°, 135°, 225° and 315°.<br />

L a ( s = 0.5) / L a ( s = 0)<br />

1.05<br />

1.04<br />

1.03<br />

1.02<br />

1.01<br />

1<br />

0.99<br />

0.98<br />

0.97<br />

0.96<br />

parallel<br />

serial<br />

0.95<br />

0 45 90 135 180 225 270 315 360<br />

Rotor displacement angle <br />

d<br />

Figure 5.3 Six-poled SCIG with centred rotor. Inductance <strong>of</strong> winding a1 is equal to winding a2.<br />

The relative change is small compared to the large degree <strong>of</strong> eccentricity. With the air gap<br />

length reduced <strong>by</strong> 50%, the change is only 2-3%. The inductance is increasing when connected<br />

in serial and decreasing when connected in parallel. This makes sense as serial connected inductances<br />

are most sensitive to the largest inductance, where parallel connected inductances are<br />

most sensitive to the smallest inductance.<br />

In table 5.2 the relative change in the inductance <strong>of</strong> winding n <strong>of</strong> phase a is given.<br />

51

Chapter 5 - Generator Characteristics<br />

52<br />

ΔLa,1 ΔLa,2 ΔLa,3 ΔLa,4 ΔLa θd<br />

Parallel 1.222 1.222 0.809 0.809 0.974 90°<br />

Serial 1.399 0.979 0.756 0.979 1.028 45°<br />

Table 5.2 Relatively change in inductance <strong>of</strong> coil a,n at 50% eccentricity.<br />

The change is large when considering a single winding, but when combined the change is small<br />

as they tend to cancels each other out.<br />

In figure 5.3 it also noticed that the relative change is not independent <strong>of</strong> the angle <strong>of</strong> displacement<br />

– it oscillates. This is an important observation as it could lead incorrect readings <strong>of</strong> the<br />

degree <strong>of</strong> eccentricity at certain positions. These oscillations are reduced as the numbers <strong>of</strong><br />

poles are increased as shown in figure 5.4, where the relative change has been calculated for an<br />

increasing pole numbers.<br />

L a ( s = 0.5) / L a ( s = 0)<br />

1.07<br />

1.06<br />

1.05<br />

1.04<br />

1.03<br />

1.02<br />

1.01<br />

1<br />

0.99<br />

0.98<br />

p = 4<br />

0.97<br />

p = 6<br />

0.96<br />

p = 10<br />

0.95<br />

0.94<br />

p = 20<br />

0 45 90 135 180 225 270 315 360<br />

Rotor displacement angle <br />

d<br />

Figure 5.4 Relatively change in inductance with increasing number <strong>of</strong> poles.<br />

Increasing the number <strong>of</strong> poles reduces the oscillations and at high pole a number they are removed.<br />

Another important observation is that the relative change is increased. This indicates<br />

that multi-poled machines could be more sensitive to eccentricity and that the readings are more<br />

reliable.<br />

5.2.3 Leakage and Mutual Inductance<br />

Until now only the self-inductance <strong>of</strong> a winding has been considered. The self-inductance however<br />

consists <strong>of</strong> a leakage part Lla and a mutual part Lma.<br />

La Lma Lla<br />

(5.20)<br />

The mutual inductance represents the flux that links the stator and the rotor circuit, where leakage<br />

represents all other fluxes. In the equivalent circuit, the leakage reluctance has not been<br />

included as only the flux passing the air gap has been described. The investigated selfinductance<br />

is actually a representation <strong>of</strong> the mutual inductance.

Chapter 5 - Generator Characteristics<br />

The leakage inductance <strong>of</strong> a winding can be difficult to determine as it consist <strong>of</strong> many subcomponents.<br />

In the design process <strong>of</strong> the reference generator in appendix A, the estimated leakage<br />

inductance is based on slot leakage, zig zag leakage and end turn leakage.<br />

Lla Lsl Lzzl Lel<br />

(5.21)<br />

The three components are illustrated in figure 5.5.<br />

Stator<br />

slot<br />

Air gap<br />

Rotor<br />

slot<br />

Stator slot<br />

leakage flux<br />

Mutual<br />

flux<br />

Rotor slot<br />

leakage flux<br />

End turn<br />

leakage flux<br />

Figure 5.5 – From the left: slot leakage, zigzag leakage and end turn leakage.<br />

The slot leakage and the end turn leakage do not depend on the length <strong>of</strong> the air gap, but the zig<br />

zag leakage does in some degree. In the design process the following equation is used to estimate<br />

the stator zig zag leakage inductance. [26]<br />

2 2<br />

ss a k<br />

st e<br />

<br />

p a 1 a 1 k <br />

Lzzl Lma 1 2 <br />

<br />

2 12 Nss 2k <br />

<br />

g<br />

<br />

w g<br />

(5.22)<br />

Where Nss is the number <strong>of</strong> stator slots, τss is the stator slot pitch, wst is the stator tooth width and<br />

ge is the effective air gap length. This equation is only a rough estimate for machines with uniform<br />

air gaps. If k is assumed constant then the zig zag leakage is proportional to the change in<br />

the mutual inductance. But, since the zig zag leakage only accounts for about 6% <strong>of</strong> the total<br />

leakage inductance Lal for the reference machine, then a 3% change in mutual inductance will<br />

only affect the leakage inductance <strong>by</strong> about 0.2%.<br />

The actual change in the leakage inductance will be investigated during the finite element analysis<br />

<strong>of</strong> the machine, as this is considered to give better results.<br />

5.3 Finite Element <strong>Analysis</strong> (FEA)<br />

In order to verify the analytical obtained results and to do further analysis, a finite element analysis<br />

<strong>of</strong> the reference generator is performed. The s<strong>of</strong>tware tool used is MagNet <strong>by</strong> Infolytica.<br />

53

Chapter 5 - Generator Characteristics<br />

5.3.1 Simulation Settings<br />

To obtain a proper accuracy <strong>of</strong> the simulations while keeping the calculation time low, the grid<br />

<strong>of</strong> finite element model has been separated into four regions. These four regions are illustrated<br />

in figure 5.6.<br />

Region 2<br />

Region 4<br />

54<br />

Figure 5.6 Grid regions used in finite element model.<br />

The grid in region one and region four covers the outer part <strong>of</strong> the stator and the inner part <strong>of</strong> the<br />

rotor and is chosen to be a coarse grid. The default grid is used in these two regions. Region two<br />

covers the area surrounding the stator and rotor teeth. The grid in this region has been adjusted<br />

with a curvature angle <strong>of</strong> 1° to increase the accuracy. The third region cover the air gap <strong>of</strong> the<br />

machine and has been adjusted to a maximum element size <strong>of</strong> 1mm. This insures accurate results<br />

during eccentricity.<br />

For a proper value <strong>of</strong> the leakage inductance including all subcomponents (slot, zigzag and end<br />

turn) a 3D FE model is required. However, since the calculation <strong>of</strong> 3D models is time consuming,<br />

it would be an advantage to use 2D where possible. The slot and air gap related components<br />

can both be found using a 2D model, and since the end turn leakage is independent on the<br />

air gap length, as shown in the previous section, a 2D model is considered sufficient.<br />

5.3.2 Stator Leakage Inductance<br />

To determine the leakage inductance in the FE analysis, the model is fitted so that it does not<br />

allow any flux to link the rotor bars and end rings. In MagNet this can be done <strong>by</strong> applying a<br />

perfect conducting material (σ →∞) to the rotor bars. For a conductor with infinite conductivity<br />

no internal electric field (E) can be maintained which leads to the condition that B = 0. In other<br />

words the flux produced <strong>by</strong> the stator coils is repelled <strong>by</strong> the perfect conductive rotor cage. The<br />

resulting flux linkage measured in the FE analysis is then an expression <strong>of</strong> the leakage flux.<br />

L<br />

1<br />

1<br />

<br />

i<br />

1<br />

Region 1<br />

Region 3<br />

(5.23)<br />

The current level for i1 is the magnetizing or no-load current. The no-load current is determined<br />

at zero slip (s = 0) and <strong>by</strong> use <strong>of</strong> the estimated equivalent parameters.

I<br />

0<br />

V<br />

<br />

R X R X<br />

1 ph<br />

1 c || m<br />

750 V / 3<br />

819.2A<br />

5.9m 8.92m 519.08m<br />

Chapter 5 - Generator Characteristics<br />

(5.24)<br />

Later in this chapter the effect <strong>of</strong> increasing the load and here<strong>by</strong> the saturation <strong>of</strong> the generator<br />

is investigated.<br />

In figure 5.7 the resulting flux contour is plotted for a single pole with the rotor bar material as<br />

perfect conductive.<br />

Figure 5.7 Finite element model with rotor bars fitted with perfect conductive material.<br />

In figure 5.8 the resulting leakage reactance is shown when rotating the rotor two rotor slots<br />

(16.36°). The solid lines are the leakage inductance with no eccentricity and the dotted lines are<br />

with 50% static eccentricity (δs = 0.5) at θd = 90°.<br />

Stator leakage inductance [H]<br />

x 10<br />

7.5<br />

-5<br />

7<br />

6.5<br />

6<br />

5.5<br />

5<br />

4.5<br />

4<br />

3.5<br />

0 2 4 6 8 10 12 14 16<br />

Rotor position [deg]<br />

r<br />

L1a( s = 0)<br />

L1a( s = 0.5)<br />

L1b( s = 0)<br />

L1b( s = 0.5)<br />

L1c( s = 0)<br />

L1c( s = 0.5)<br />

Figure 5.8 Stator leakage inductance at 0% eccentricity (solid line) and at 50%<br />

eccentricity (dotted line).<br />

55

Chapter 5 - Generator Characteristics<br />

The oscillating tendency is due to the slotting effect, which means that the flux linkage is dependent<br />

on the position <strong>of</strong> the rotor. With 50% eccentricity the increased is about 3%.<br />

5.3.3 Rotor Leakage Inductance<br />

The same approach as for the stator leakage inductance is used to determine the rotor leakage<br />

inductance. The stator slots are fitted with perfect conductive material, so that the flux produced<br />

<strong>by</strong> the rotor cage is repelled <strong>by</strong> the stator windings. The leakage inductance is then estimated as:<br />

56<br />

L<br />

<br />

2<br />

2 (5.25)<br />

i2<br />

The maximum rotor current i2 can be found from the stator current and the transformations factor<br />

from stator to rotor side.<br />

m Nk 1 1 w1<br />

I2 I1 m2 N2kw2 380.9577 819.2A855A 440.51 (5.26)<br />

Where m1 is the number <strong>of</strong> stator phases, N1 is the number <strong>of</strong> stator turns, kw1 is the stator winding<br />

factor, m2 is the number <strong>of</strong> rotor phases, N2 is the number <strong>of</strong> rotor turns (0.5 for squirrel<br />

cage) and kw2 is the rotor winding factor (1 for squirrel cage). These values have been calculated<br />

during the design process in appendix A.<br />

The current for bar n (Ib,n) can be found from the electrical angle α between each bar. The details<br />

are given in appendix A, section A.6.2.<br />

p<br />

<br />

<br />

16.36 Ibn , I2cosn 0.5<br />

(5.27)<br />

Nrs<br />

In figure 5.9 the resulting flux contour is plotted for a single pole with the stator slot material as<br />

perfect conductive.<br />

Figure 5.9 Finite element model with stator slots fitted with perfect conductive material.

Chapter 5 - Generator Characteristics<br />

The resulting leakage reactance is shown in figure 5.10 when rotating the rotor two stator slots<br />

(15°). The solid lines represents the leakage inductance with no eccentricity and the dashed lines<br />

are with 50% static eccentricity (δs = 0.5) at θd = 90°.<br />

Rotor leakage inductance [H]<br />

x 10-5<br />

3.75<br />

3.5<br />

3.25<br />

3<br />

2.75<br />

2.5<br />

2.25<br />

2<br />

1.75<br />

1.5<br />

0 2 4 6 8 10 12 14<br />

Rotor position [deg]<br />

r<br />

Figure 5.10 Rotor leakage inductance at 0% eccentricity (solid line) and at 50%<br />

eccentricity (dotted line).<br />

Similar to the stator leakage inductance, the rotor leakage inductance is increased about 3% at<br />

the peak value.<br />

5.3.4 Stator Self and Mutual Inductances<br />

In the analytical analysis only the self- and mutual inductance <strong>of</strong> a single phase was considered,<br />

but in the actual case one must consider the mutual inductance between each phase. The complete<br />

inductances for the stator L1 can be described in matrix form as:<br />

LaaLbaLca L<br />

<br />

L L L<br />

<br />

1 <br />

ab bb cb <br />

LacLbcL cc <br />

The diagonal elements represent the self inductance and the <strong>of</strong>f diagonal elements represent the<br />

mutual inductances. The inductances <strong>of</strong> the first column are found with ib = ic = 0A.<br />

a b c<br />

aa<br />

ia ab<br />

ia ac<br />

ia<br />

L2( s = 0)<br />

L2( s = 0.5)<br />

(5.28)<br />

<br />

L L L (5.29)<br />

The inductances <strong>of</strong> the second and third column are found with ia = ic = 0A and ia = ib = 0A,<br />

respectively.<br />

In figure 5.11 and in figure 5.12 the stator self-inductances and the mutual inductances are<br />

shown. The inductance matrix is symmetrical about the diagonal, so only the lower triangular<br />

elements are shown (i.e. Lab = Lba). The solid lines represents the leakage inductance with no<br />

eccentricity and the dotted lines are with 50% static eccentricity (δs = 0.5) at θd = 90°.<br />

57

Chapter 5 - Generator Characteristics<br />

58<br />

Stator mutual inductance [H]<br />

Stator mutual inductance [H]<br />

x 10-3<br />

2.55<br />

2.5<br />

2.45<br />

2.4<br />

2.35<br />

2.3<br />

2.25<br />

0 2 4 6 8 10 12 14 16<br />

Rotor position [deg]<br />

r<br />

x 10-3<br />

-0.6<br />

-0.7<br />

-0.8<br />

-0.9<br />

-1<br />

-1.1<br />

-1.2<br />

-1.3<br />

Figure 5.11 Stator self inductances at 0% eccentricity (solid line) and at 50%<br />

eccentricity (dotted line).<br />

-1.4<br />

0 2 4 6 8 10 12 14 16<br />

Rotor position [deg]<br />

r<br />

Figure 5.12 Stator mutual inductances at 0% eccentricity (solid line) and at 50%<br />

eccentricity (dotted line).<br />

The self- and mutual inductances has a more constant change during eccentricity and is less<br />

influenced <strong>by</strong> the rotor position. The self inductances are decreased <strong>by</strong> about 2-3% which is<br />

close the analytical found estimate. The mutual inductances are increasing, but the change is<br />

larger – about 3-5%. The mutual inductances are represented <strong>by</strong> a negative value, since the flux<br />

linkage is negative compared to flux generated in winding a.<br />

5.4 Relative Change and Displacement Angle<br />

Laa( s = 0)<br />

Laa( s = 0.5)<br />

Lbb( s = 0)<br />

Lbb( s = 0.5)<br />

Lcc( s = 0)<br />

Lcc( s = 0.5)<br />

Lab( s = 0)<br />

Lab( s = 0.5)<br />

Lac( s = 0)<br />

Lac( s = 0.5)<br />

Lbc( s = 0)<br />

Lbc( s = 0.5)<br />

In the analytical analysis it was shown that the relative change in the inductance was depending<br />

on the displacement angle. The same analysis has been performed with the finite element model.<br />

The peak value at 4.09° for stator self- and leakage inductance is used, and the peak value at<br />

3.75° for the rotor leakage inductance. The results are shown in figure 5.13.

Relative change [p.u.]<br />

1.05<br />

1.04<br />

1.03<br />

1.02<br />

1.01<br />

1<br />

0.99<br />

0.98<br />

0.97<br />

0 45 90 135 180 225 270 315 360<br />

Displacement angle [deg]<br />

d<br />

Chapter 5 - Generator Characteristics<br />

Figure 5.13 Relatively change in inductances as a function <strong>of</strong> the displacement angle.<br />

The relative change <strong>of</strong> the self-inductance is close to the analytically estimated result for the<br />

parallel connected windings. It peaks at the cross over point between two windings, which for<br />

phase winding a is located at 0°, 90°, 180° and 270°. Oscillations are also seen in the stator and<br />

rotor leakage inductance with less uniformity.<br />

5.5 Saturation Effect<br />

Until now the characteristic <strong>of</strong> the generator during eccentricity has been investigated at no-load<br />

current. But, as the field strength H increases, the flux density B in the core increases until saturation<br />

is reached. The relation between H and B is represented <strong>by</strong> the magnetizing or hysteresis<br />

curve. The magnetizing curve for the core material used in the reference generator is shown in<br />

figure 5.14 along with the relative permeability (red curve).<br />

Flux density B [T]<br />

2<br />

1.5<br />

1<br />

0.5<br />

Saturated<br />

region<br />

Figure 5.14 Magnetizing curve and relative permeability <strong>of</strong> core iron in reference generator.<br />

Since the inductance <strong>of</strong> a winding is defined as the ratio <strong>of</strong> magnetic flux linkage to current,<br />

then the inductance will drop as the core is saturated. In the saturated region, the inductance is<br />

L1a<br />

L2<br />

Laa<br />

Laa est.<br />

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2<br />

x 10 4<br />

0<br />

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2<br />

x 10 4<br />

0<br />

Field strength H [A/m]<br />

2000<br />

1500<br />

1000<br />

500<br />

Relative permeability [u/u 0 ]<br />

59

Chapter 5 - Generator Characteristics<br />

less influenced <strong>by</strong> small changes in the flux density. As eccentricity is detected <strong>by</strong> small variations<br />

in the flux density, then it is expected that relative change decreases as the core saturates.<br />

In figure 5.15 and 5.16, the inductances and the relative change are shown at 50% eccentricity<br />

while increasing the current from 1A to 3200A.<br />

60<br />

Leakage inductance L 1a ,L 2 [H]<br />

7.5<br />

7<br />

6.5<br />

6<br />

5.5<br />

5<br />

4.5<br />

4<br />

3.5<br />

x 10-5<br />

3<br />

0 500 1000 1500 2000 2500 3000<br />

Stator phase current [A]<br />

Figure 5.15 Inductances at 0% eccentricity (solid line) and with 50% eccentricity (dashed lines)<br />

as a function <strong>of</strong> the phase current.<br />

Relative change [p.u.]<br />

1.05<br />

1.04<br />

1.03<br />

1.02<br />

1.01<br />

1<br />

0.99<br />

0.98<br />

L1a( s = 0)<br />

L1a( s = 0.5)<br />

L2( s = 0)<br />

L2( s = 0.5)<br />

Laa( s = 0)<br />

Laa( s = 0.5)<br />

L1a( s = 0.5)<br />

L2( s = 0.5)<br />

Laa( s = 0.5)<br />

0.97<br />

0 500 1000 1500 2000 2500 3000<br />

Stator phase current [A]<br />

Figure 5.16 Relatively change in inductances as a function <strong>of</strong> the phase current.<br />

x 10<br />

3<br />

-3<br />

The saturation level <strong>of</strong> the core clearly has influence on the relatively change in the inductance<br />

values. The change decreases with saturation as expected. This makes it difficult to classify the<br />

same fault during different load condition. In a wind turbine with a full converter, it is likely<br />

that a constant V/f regulation is used to keep a constant saturation level. In this case it is easier<br />

to classify the same fault. But, if the saturation level is chosen high to reduce size and weight <strong>of</strong><br />

the generator, then the relative change is small.<br />

2.8<br />

2.6<br />

2.4<br />

2.2<br />

2<br />

1.8<br />

1.6<br />

1.4<br />

1.2<br />

1<br />

Self inductance L aa [H]

5.6 Linearity<br />

Chapter 5 - Generator Characteristics<br />

In order to relate relative change in the inductances to the degree <strong>of</strong> the mechanical fault (eccentricity)<br />

a proportional or linear relation would be preferable. This will make the electrical signal<br />

analysis easier. In figure 5.17 the relative change is shown when varying the degree <strong>of</strong> eccentricity<br />

from 0 to 50%. The estimated result using the reluctance network is also shown for the<br />

self-inductance (red dashed line).<br />

Relative change [p.u.]<br />

1.05<br />

1.04<br />

1.03<br />

1.02<br />

1.01<br />

1<br />

0.99<br />

0.98<br />

L1a<br />

L2<br />

Laa<br />

Laa est.<br />

0.97<br />

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5<br />

Degree <strong>of</strong> static eccentricity [p.u.]<br />

s<br />

Figure 5.17 Relatively change in inductances as a function <strong>of</strong> the degree <strong>of</strong> static eccentricity.<br />

It is seen that there is no proportionality or linearity between the degree <strong>of</strong> eccentricity and the<br />

relative change in the inductance values. This will make it difficult to monitor the development<br />

<strong>of</strong> a fault if the machine characteristics are unknown.<br />

5.7 Chapter Conclusion<br />

In this chapter the characteristics <strong>of</strong> the generator inductances during eccentricity has been investigated.<br />

The purpose was to uncover conditions that should be taken into account if ESA<br />

should be used as a reliable conditions monitoring system.<br />

By use <strong>of</strong> analytical and finite element analysis it has been illustrated that the relative change in<br />

the inductances are low compared to the degree <strong>of</strong> eccentricity. It is therefore considered to be<br />

difficult to locate small early stage faults. It was also seen that the inductances are influenced <strong>by</strong><br />

the fault displacement angle and the saturation level, and that linearity between the degree <strong>of</strong><br />

eccentricity and the relative change was not present. To account for these conditions precise<br />

knowledge <strong>of</strong> the monitored generator is required. This will make the system complicated to<br />

adapt for types <strong>of</strong> wind turbine generators.<br />

Note: In this chapter the analytically found parameters have been used to estimate the no-load<br />

current. This was not the original idea. Since there is a small different between the analytically<br />

and the finite element found parameter in appendix A. The actual no-load current is smaller –<br />

about 710A. This should result in the same characteristics, but with smaller relative change.<br />

61

Chapter 6<br />

Time-Transient Simulation<br />

In chapter five a static finite element analysis was conducted. In this chapter a time transient<br />

simulations is used to analyse the behaviour <strong>of</strong> the generator during dynamic eccentricity. This<br />

should illustrate how a fault can be detected.<br />

6.1 Introduction<br />

MagNet <strong>of</strong>fers the possibility <strong>of</strong> performing time transient simulation with motion components<br />

such as the rotor in an electrical machine. By performing simulations with rotor motions it<br />

should be possible detect changes in electrical signals due to variations in inductances. Ideally,<br />

it would have been interesting to simulate the early stage bearing faults with the exponential<br />

function derived in chapter four. But, MagNet has some limitations to motions components –<br />

they can either have a rotary motion or a linear motion in one direction. Since the exponential<br />

function requires both a rotary motion and a linear motion in two directions, it is not possible to<br />

use this function. It is however possible to simulate simple dynamic eccentricity where the rotor<br />

is statically shifted from the center <strong>of</strong> the stator while rotating. This type <strong>of</strong> eccentricity occurs<br />

at distributed bearing wear and an expression for the components <strong>of</strong> the displacement vector<br />

was derived in equation (4.16), and shown below.<br />

cos sin <br />

a g b g (6.1)<br />

r 0 d r r 0 d r<br />

It is only possible to rotate the displacement vector with the same speed as the rotor (θd = θr),<br />

which could illustrate a worn out generator bearing. In figure 6.1 the motion component is illustrated.<br />

Stator<br />

ωr<br />

a<br />

b<br />

ωr<br />

Rotor<br />

(motion component)<br />

Center <strong>of</strong> rotation<br />

Figure 6.1 Displaced motion component used to simulate dynamic eccentricity in MagNet.<br />

With this type <strong>of</strong> motion the inductances are constantly changing with the position <strong>of</strong> the rotor<br />

and as a result frequency components related the rate <strong>of</strong> change should be present in the electri-<br />

63

Chapter 6 - Time-Transient Simulation<br />

cal frequency spectrum. In reference [23] it has been shown that the frequency components will<br />

appear as side-band components to the fundamental electrical frequency fe given as:<br />

64<br />

s<br />

21<br />

fecc,k fe k fr fr fe<br />

(6.2)<br />

p<br />

Where fr is the mechanical rotational frequency <strong>of</strong> the rotor, determined <strong>by</strong> the slip and the<br />

number <strong>of</strong> poles in the generator. For the four poled reference generator at no-load (s = 0) the<br />

components are expected at k<br />

6.2 Model Modifications and Simulation Settings<br />

To perform time transient simulations modification has been made to model used in the static<br />

analysis. The modifications are explained in this section.<br />

6.2.1 Rotor Skew<br />

The simulations are done in 2D to reduced simulation time. Since the skew effect <strong>of</strong> the rotor<br />

cannot be taken into account in a 2D simulation, the slotting effect using the static model would<br />

be too significant. The slotting effect will cause high harmonic currents due to the large changes<br />

in the flux density in the air gap, when the rotor slot passes the stator tooth. To reduce the slotting<br />

effect, the rotor slots have been redesigned for the transient model. In figure 6.2 the slot<br />

layout used in the two models is shown.<br />

Figure 6.2 Rotor slot layout in static model (left) and transient model (right).<br />

With the new design it has been possible to reduce the slotting effect to an acceptable level. It<br />

should be mentioned that the design changes increases the leakage reactance and the mutual<br />

inductance. This will result in a different no-load current compared to the one used in the static<br />

model, and the relative change during eccentricity might be different. This is considered acceptable<br />

as the main goal is to show that eccentricity will introduce frequency components.<br />

6.2.2 <strong>Electric</strong>al Circuit<br />

In order to perform time transient calculations the stator and rotor coils must be connected in an<br />

electrical circuit. In figure 6.3 the electrical circuit is shown for stator phase a and for a small<br />

part <strong>of</strong> the rotor cage.

R27<br />

5.6455e-007<br />

R28<br />

5.6455e-007<br />

V1<br />

PWL<br />

Rotor_coil_1<br />

T1 T2<br />

Rotor_coil_2<br />

T1 T2<br />

R101<br />

0.00059<br />

R13<br />

5.6455e-007<br />

R14<br />

5.6455e-007<br />

Chapter 6 - Time-Transient Simulation<br />

Figure 6.3 <strong>Electric</strong>al circuit for a single stator phase (top) and for a part <strong>of</strong> the rotor cage (bottom).<br />

Resistor R1-R4 has been added to account for the end winding resistance, which is not present<br />

in the 2D model. The same has been done in the rotor cage, where R27 for instance represent<br />

the end ring section between rotor coil 1 and 2. R101 is added to account for the increase in<br />

leakage and mutual inductance. The end turn leakage inductance has been neglected, since it is<br />

small and not considered to affect the results. The conductivity and cross sectional area has been<br />

changed, so the resistances match the values found in Appendix A.<br />

6.2.3 Voltage and Time Settings<br />

R1<br />

0.001088<br />

R2<br />

0.001088<br />

R3<br />

0.001088<br />

R4<br />

0.001088<br />

phase_a_1<br />

T1 T2<br />

phase_a_2<br />

T1 T2<br />

phase_a_3<br />

T1 T2<br />

phase_a_4<br />

T1 T2<br />

Rotor_coil_44<br />

T1 T2<br />

Rotor_coil_43<br />

T1 T2<br />

The generator is mainly inductive with a small resistance and can be considered as an RL circuit.<br />

Due to the large inductance a huge magnetizing current is drawn as the voltage source is<br />

switched on. This will cause a long transient period and a displacement <strong>of</strong> the currents before<br />

steady state is reached. Since the generator is to be analyzed at steady state it would be a time<br />

advantages to reduce the transient period. Adding a progressive voltage source, that slowly increases<br />

the voltage from min. to max. in 200ms, can reduce the transient period. The effect is<br />

shown in figure 6.4 for a single phase current using normal and progressive voltage development.<br />

R78<br />

5.6455e-007<br />

R77<br />

5.6455e-007<br />

R100<br />

5.6455e-007<br />

R99<br />

5.6455e-007<br />

65

Chapter 6 - Time-Transient Simulation<br />

66<br />

Stator phase current [A]<br />

x 104<br />

1<br />

0<br />

-1<br />

-2<br />

-3<br />

-4<br />

progressive<br />

-5<br />

0 50 100 150<br />

Time [ms]<br />

200 250 300<br />

Figure 6.4 Current transients using normal and progressive voltage development.<br />

The transient period is reduced but still long. To reduce calculation time, different time steps<br />

have been used. In table 6.2 the time steps are given.<br />

0-700ms 700-800ms 800-900ms<br />

time step 1ms 0.5ms 0.1ms<br />

Table 6.1 Time step used in transient model.<br />

In the last time period from 800 to 900 ms the last 80ms is used in the spectrum analysis. During<br />

80ms or four electrical periods at 50Hz, the rotor has moved one rotation at no-load. The<br />

total amount <strong>of</strong> steps is 1900 and with a simulation time <strong>of</strong> 30-60 seconds per step, the total<br />

simulation time is between 16 and 32 hours. This is achieved with the default grid in MagNet.<br />

Simulations done with eccentricity tend to be more time demanding due to the finer mesh in the<br />

small air gap regions. The long simulation time is one <strong>of</strong> the downsides <strong>of</strong> using finite element<br />

analysis for time based simulations.<br />

The initial idea was to investigate the behaviour during different conditions, such as the degree<br />

<strong>of</strong> saturation and eccentricity. But, due to the long simulation time only a few simulation has<br />

been made to illustrate that it is possible to detect eccentricity with spectrum analysis.<br />

6.3 Current Spectrum <strong>Analysis</strong> at No-load<br />

In figure 6.5 the current is shown at no-load with no eccentricity and with 50% dynamic eccentricity.<br />

The rotor is kept at a constant speed <strong>of</strong> 1500 rpm throughout the simulation.<br />

normal

Stator phase current I a [A]<br />

600<br />

400<br />

200<br />

0<br />

-200<br />

-400<br />

Chapter 6 - Time-Transient Simulation<br />

-600<br />

0 0.01 0.02 0.03 0.04<br />

Time [s]<br />

0.05 0.06 0.07 0.08<br />

Figure 6.5 Stator current Ia at no-load with 0% eccentricity and at 50% eccentricity.<br />

The high frequency oscillation in the current is a result <strong>of</strong> the slotting effect. Even with the rotor<br />

slot redesigned they are still present. The slotting effect introduces harmonic currents determined<br />

<strong>by</strong> the number <strong>of</strong> rotor bars. The m‟th harmonic slot frequency component fslot,m depend<br />

on the number <strong>of</strong> rotor bars Nrs, the slip s and the fundamental electrical frequency fe and can be<br />

calculated as shown in equation (6.3). [23]<br />

<br />

2Nrs 1s<br />

<br />

f mf p <br />

slot ,m e<br />

<br />

2 48 1 0 <br />

fslot , 1 150Hz1150Hz 4 <br />

In figure 6.6 the Fast Fourier transform (FFT) is shown for the current with no eccentricity in a<br />

frequency range <strong>of</strong> 0-2000Hz. The current signal has been extended in time to increase the frequency<br />

interval. This is done <strong>by</strong> repeating the signal shown in figure 6.5.<br />

Relative Magnitude [dB]<br />

0<br />

-50<br />

-100<br />

Fundament frequency<br />

component – 50Hz<br />

Slot frequency<br />

component<br />

1150Hz<br />

Figure 6.6 FFT <strong>of</strong> stator current Ia with 0% eccentricity, Ia1 = 423A.<br />

0% ecc.<br />

50% ecc.<br />

-150<br />

0 200 400 600 800 1000 1200 1400 1600 1800 2000<br />

Frequency [Hz]<br />

(6.3)<br />

67

Chapter 6 - Time-Transient Simulation<br />

Since the slot related frequency component is located at a relatively high frequency, it is not<br />

considered to influence the frequency components introduced <strong>by</strong> eccentricity. These should be<br />

located near the fundament frequency component. In figure 6.7 the FFT is shown for the two<br />

currents from 0-150Hz.<br />

68<br />

Relative Magnitude [dB]<br />

Relative Magnitude [dB]<br />

0<br />

-10<br />

-20<br />

-30<br />

-40<br />

-50<br />

-60<br />

-70<br />

-80<br />

0 25 50 75<br />

Frequency [Hz]<br />

100 125 150<br />

0<br />

-10<br />

-20<br />

-30<br />

-40<br />

-50<br />

-60<br />

-70<br />

fe - fr<br />

fe + fr<br />

Figure 6.7 FFT <strong>of</strong> Stator current Ia at no-load with 0% eccentricity and at 50% eccentricity.<br />

With 50% eccentricity two small side band are present at the fe ± fr components. The change is<br />

small, but noticeable. At fe + fr (75Hz) the current is increase from -65dB to -56.2dB and at fe - fr<br />

(25Hz) the current is increase from -62dB to -54.55dB. The second and third frequency components<br />

are not considered to be related to eccentricity as they exist in both currents.<br />

6.3.1 Signal stability (Oscillating effects)<br />

fe + 2fr<br />

fe + 3fr<br />

0% ecc.<br />

50% ecc.<br />

-80<br />

0 25 50 75<br />

Frequency [Hz]<br />

100 125 150<br />

To get a reliable indication <strong>of</strong> the degree <strong>of</strong> eccentricity a stable current signal is required. This<br />

is important if the condition monitoring system should be able to predict the development <strong>of</strong> a<br />

fault. By applying a band pass filter with a window <strong>of</strong> ±2Hz the stability <strong>of</strong> the fundamental<br />

current and the two eccentric frequencies has been studied. The result is shown in figure 6.8.

Stator phase current [A]<br />

Stator phase current [A]<br />

Stator phase current [A]<br />

-50<br />

-100<br />

-150<br />

-200<br />

-250<br />

-300<br />

-350<br />

-400<br />

-450<br />

0<br />

50<br />

450<br />

400<br />

350<br />

300<br />

250<br />

200<br />

150<br />

100<br />

Chapter 6 - Time-Transient Simulation<br />

50Hz component<br />

19.5 19.55 19.6 19.65 19.7 19.75<br />

Time [s]<br />

19.8 19.85 19.9 19.95 20<br />

0.6<br />

0.5<br />

0.4<br />

0.3<br />

0.2<br />

0.1<br />

0<br />

-0.1<br />

-0.2<br />

-0.3<br />

-0.4<br />

-0.5<br />

-0.6<br />

25Hz component<br />

-0.7<br />

19.5 19.55 19.6 19.65 19.7 19.75<br />

Time [s]<br />

19.8 19.85 19.9 19.95 20<br />

0.8<br />

0.7<br />

0.6<br />

0.5<br />

0.4<br />

0.3<br />

0.2<br />

0.1<br />

0<br />

-0.1<br />

-0.2<br />

-0.3<br />

-0.4<br />

-0.5<br />

-0.6<br />

-0.7<br />

75Hz component<br />

-0.8<br />

19.5 19.55 19.6 19.65 19.7 19.75<br />

Time [s]<br />

19.8 19.85 19.9 19.95 20<br />

Figure 6.8 Band pass filtered fundamental current (top) and the two eccentric components (fe ± fr). The<br />

filter window is ±2Hz at the related frequency.<br />

The fundament current (50Hz) and the low frequency eccentric current (25Hz) seem unaffected<br />

<strong>by</strong> oscillations. However a small DC <strong>of</strong>fset seems to be present, which could indicate that the<br />

69

Chapter 6 - Time-Transient Simulation<br />

signals are still affected <strong>by</strong> the transient period. The high frequency eccentric component (75Hz)<br />

does have an oscillating tendency. The amplitude has a small 25Hz oscillation, which is equal to<br />

the mechanical speed <strong>of</strong> the rotor. This indicates that the observation made using static model in<br />

chapter five is valid. The inductances and hence the currents depends on the displacement angle<br />

<strong>of</strong> the rotor.<br />

6.4 Chapter Conclusion<br />

The purpose <strong>of</strong> the time transient simulation was to show that it is possible to detect eccentricity<br />

using current spectrum analysis and that the frequency components would appear according to<br />

theory. A Simulation made at no-load with 50% eccentricity has shown the frequency components<br />

occur as sidebands to the fundament current. The amplitude is however very small, only<br />

0.15% <strong>of</strong> the fundamental current. This could lead to a poor signal to noise ratio when used in<br />

practice.<br />

Using a band pass filter the stability <strong>of</strong> the introduced eccentric components has been investigated.<br />

It has been shown that oscillating tendencies are present in the high frequency component,<br />

which is assumed to be caused <strong>by</strong> change in the rotor displacement angle. This verifies the<br />

observation made in chapter five. If the components are oscillating, it can be difficult to get a<br />

reliable signal for the condition monitoring system.<br />

The original idea was to simulate the model under various load and eccentricity conditions, but<br />

due to the long simulations time and other problems, only two useful simulations has been<br />

made. Some <strong>of</strong> the problems encountered during the simulation process are given below:<br />

- If the grid in the air gap is too large then eccentricity is not detected. But if the grid is too<br />

small, the calculation time is extensive.<br />

- Since the analyzed signal is only recorded for 80ms, it is extended to increase the frequency<br />

interval <strong>of</strong> the FFT. Extending the signal can lead to undesired signals (artifacts) in the<br />

spectrum analysis. Artifacts can occur if the start point and end point <strong>of</strong> the signal does not<br />

match in time or value. Then the reconstructed signal is not an accurate representation <strong>of</strong><br />

the original signal. An example <strong>of</strong> a signal containing artifacts is shown below. The artifacts<br />

can be identified <strong>by</strong> the constant frequency interval. These artifacts can lead to incorrect<br />

results as they are present at the same frequencies, where the eccentricity components<br />

are expected.<br />

70<br />

Relative Magnitude [dB]<br />

0<br />

-10<br />

-20<br />

-30<br />

-40<br />

-50<br />

-60<br />

-70<br />

Artifacts<br />

-80<br />

0 25 50 75<br />

Frequency [Hz]<br />

100 125 150

Chapter 7<br />

Small Scale Test<br />

In this chapter the results from a small scale test on an induction machine are presented. The<br />

purpose <strong>of</strong> this test is to verify some <strong>of</strong> the observations made in the previous chapters.<br />

7.1 Introduction<br />

To verify the generator characteristics found using the finite element model a small scale test<br />

has been carried out. The test is done <strong>by</strong> running an induction motor with an eccentric located<br />

mass. This creates centrifugal forces acting on the mass, causing the rotor to be displaced while<br />

rotating (dynamic eccentricity). The degree <strong>of</strong> eccentricity is changed <strong>by</strong> varying the centrifugal<br />

force.<br />

The test should verify;<br />

That it is possible to force eccentricity to an induction machine considered to be<br />

in good / normal condition.<br />

That dynamic eccentricity will introduce frequencies according to theory and<br />

simulated results.<br />

7.2 Test Setup<br />

The test setup consists <strong>of</strong> an induction machine fitted with a variable eccentric load, a power<br />

converter for voltage/frequency control and an oscilloscope for measurements. The complete<br />

setup is shown in figure 7.1 with apparatus connections and specifications. Pictures from the<br />

actual setup are located in appendix B.<br />

V/f control<br />

Spitzenberger<br />

DM 150000/PAS<br />

AC/DC Mains<br />

Simulation<br />

Oscilioscope<br />

Tektronix TDS 2014B<br />

Ch. 1: Va Ch. 2: Ia<br />

Ch. 3: Ib Ch. 4: Ic<br />

Fs = 5000 Hz<br />

(sample frequency)<br />

Figure 7.1 Complete setup used in small scale eccentricity test.<br />

A close up <strong>of</strong> the eccentricity tool fitted to the machine is illustrated in figure 7.2.<br />

Induction Machine<br />

ASEA M160M<br />

p = 4 P2 = 11kW<br />

Vn = 380V In = 23A<br />

PF = 0.83 (delta con.)<br />

Eccentricity tool<br />

71

Chapter 7 - Small Scale Test<br />

72<br />

Motor mount<br />

Thread<br />

Angular velocity, ωr<br />

Adjustable length, R1 (75mm-120mm)<br />

Figure 7.2 Tool used to simulate dynamic eccentricity.<br />

Rotating mass, M1 (0.65kg)<br />

Centrifugal force, F1<br />

The tool consists <strong>of</strong> a rotating mass M1 made <strong>of</strong> aluminum with a weight <strong>of</strong> 0.65kg. The mass is<br />

connected to the machine <strong>by</strong> a thread so the displacement length R1 can be varied. When rotating,<br />

a force F1 will act on the mass in the radial direction and if large enough, the rotor is displaced.<br />

The force is known as the centrifugal force, given as:<br />

2<br />

2<br />

<br />

F 1 r ,R1 M1 R1 r r<br />

nr<br />

(7.1)<br />

60<br />

The force can be varied <strong>by</strong> changing the speed <strong>of</strong> the rotor ωr or the displacement length R1. The<br />

force is sensitive to changes in speed since squared, while it is linear proportional to the displacement<br />

length.<br />

7.3 Test Results<br />

The test has been performed at 10Hz, 15Hz and 20Hz and <strong>by</strong> adjusting the length from 75mm to<br />

120mm. Due to high mechanical vibrations, the maximum frequency was chosen as 20Hz. At<br />

20Hz and 120mm mass displacement the force acting on the machine is about 300N. The voltage<br />

and currents are measured with a sampling frequency <strong>of</strong> 5000Hz and for at least four periods.<br />

In four electrical periods the four poled machine has completed one mechanical rotation.<br />

7.3.1 Spectrum <strong>Analysis</strong> <strong>of</strong> Stator Current<br />

During eccentricity harmonic components should reveal around the current fundamental frequency.<br />

As for the simulated results the harmonic frequencies are calculated as:<br />

s<br />

21<br />

fecc,k fe k fr fr fe<br />

(7.2)<br />

p<br />

The induction machine is running at no-load condition except for the inertial load <strong>of</strong> the eccentricity<br />

tool. The slip can be assumed to be close to zero (s = 0).<br />

In figure 7.3 the stator current is shown at 20Hz with R1 = 0 and R1 = 120mm. This should<br />

represent the machine with no eccentricity and with maximum eccentricity.

Stator phase current I a [A]<br />

20<br />

15<br />

10<br />

5<br />

0<br />

-5<br />

-10<br />

-15<br />

Figure 7.3 Stator current Ia at 20Hz with R1 = 0mm and R1 = 120mm.<br />

Chapter 7 - Small Scale Test<br />

R 1 = 0mm<br />

R 1 = 120mm<br />

-20<br />

0 0.02 0.04 0.06 0.08 0.1<br />

Time [s]<br />

0.12 0.14 0.16 0.18 0.2<br />

In figure 7.4 the two signals are presented in the frequency domain <strong>by</strong> applying FFT.<br />

Relative Magnitude [dB]<br />

Relative Magnitude [dB]<br />

0<br />

-10<br />

-20<br />

-30<br />

-40<br />

-50<br />

-60<br />

-70<br />

R 1 = 0mm<br />

-80<br />

0 10 20 30<br />

Frequency [Hz]<br />

40 50 60<br />

0<br />

-10<br />

-20<br />

-30<br />

-40<br />

-50<br />

-60<br />

-70<br />

fe - fr<br />

fe + fr<br />

fe + 2fr<br />

fe + 3fr<br />

R 1 = 120mm<br />

-80<br />

0 10 20 30<br />

Frequency [Hz]<br />

40 50 60<br />

Figure 7.4 FFT <strong>of</strong> Stator current Ia with R1 = 0mm (top) and R1 = 120mm (bottom).<br />

73

Chapter 7 - Small Scale Test<br />

From the current spectrum the frequency components that can be related to the dynamic eccentricity<br />

are present. The largest change is seen at the fe + fr component where the amplitude is<br />

increase from -58.9 dB to -36.5dB.<br />

To see if there is a linear relation between the applied force and the amplitude at the presented<br />

frequency components a series test have be conducted. In table 7.1 the amplitudes under different<br />

load conditions are presented.<br />

74<br />

Fc fe - fr fe + fr fe + 2fr fe + 3fr<br />

0.0 -54.6 -58.9 -57.5 -35.3<br />

77.0 -39.8 -37.3 - -<br />

173.2 -36.7 -39.6 - -<br />

192.5 -41.0 -40.6 -55.3 -35.6<br />

218.1 -39.1 -40.2 -55.7 -35.3<br />

243.8 -39.7 -39.6 -55.5 -35.0<br />

269.4 -37.8 -38.3 -56.8 -35.6<br />

295.1 -38.6 -38.7 -62.7 -35.6<br />

307.9 -35.5 -36.5 -58.0 -36.0<br />

Table 7.1 Characteristic component amplitudes at various loads.<br />

The frequency components at fe ± fr increase as expected, but the third and second related components<br />

seem unaffected. Since these components already exist in the machine without the eccentricity<br />

tool added, they could be caused <strong>by</strong> other defects. Like static eccentricity.<br />

In figure 7.5 the linear magnitude <strong>of</strong> the first components are illustrated.<br />

Relative current [A]<br />

0.02<br />

0.015<br />

0.01<br />

0.005<br />

f e - f r<br />

f e + f r<br />

0<br />

0 50 100 150 200 250 300 350<br />

Centrifugal Force F [N]<br />

c<br />

Figure 7.5 linear magnitude <strong>of</strong> components fe ± fr<br />

There does not seem to be a clear linear relation between the applied force and the amplitude <strong>of</strong><br />

the first components. This could be an issue when relating the degree <strong>of</strong> a mechanical fault a<br />

change in the current. Further analysis is required to understand this tendency.

7.3.2 Signal stability (Oscillating effects)<br />

Chapter 7 - Small Scale Test<br />

As done for the simulated results a band pass filter is used to isolated the fundamental and the<br />

eccentric current component (fe + fr).<br />

Stator phase current [A]<br />

Stator phase current [A]<br />

20<br />

15<br />

10<br />

5<br />

0<br />

-5<br />

-10<br />

-15<br />

-20<br />

19 19.1 19.2 19.3 19.4 19.5<br />

Time [s]<br />

19.6 19.7 19.8 19.9 20<br />

0.3<br />

0.2<br />

0.1<br />

0<br />

-0.1<br />

-0.2<br />

19 19.1 19.2 19.3 19.4 19.5<br />

Time [s]<br />

19.6 19.7 19.8 19.9 20<br />

Figure 7.6 Band pass filtered fundamental current (top) and the eccentric component (fe + fr). The filter<br />

window is ±2Hz at the related frequency.<br />

The fundamental current has little or no oscillations, while the eccentric frequency component is<br />

oscillating. The oscillating frequency is lower than the result found in the in the simulated result<br />

in chapter six. The frequency is about 1Hz and since the rotor is rotating 10Hz, this does not<br />

verify the idea that it depends on the rotor displacement angle. Other conditions could be causing<br />

the oscillations. The slip might not be constant in at positions, which would cause variations<br />

in the current. The machine might also have some degree <strong>of</strong> static eccentricity that affects that<br />

affect the result. These pheromones have not been further investigated.<br />

7.4 Chapter Conclusion<br />

The purpose <strong>of</strong> the small-scale test was to illustrate that it is possible to add eccentricity to an<br />

electrical machine considered to be in good condition. During various eccentric loads it has<br />

75

Chapter 7 - Small Scale Test<br />

been shown that frequency components related to the eccentricity are present in the current<br />

spectrum. At maximum eccentric load the magnitude <strong>of</strong> the largest eccentric component is about<br />

1% <strong>of</strong> the fundamental current value. This is larger than the value found at 50% eccentricity in<br />

the simulated results, which were about 0.15%. Since it is unlikely that the degree <strong>of</strong> eccentricity<br />

in the small scale test is 50%, it is assumed that the design used in the test machine makes it<br />

more sensitive to eccentricity. In chapter five it was also shown that relative change was depending<br />

on the current level <strong>of</strong> the machine (saturation). Due to the small slip that is present due<br />

to friction, the motor is not rotating at ideal synchronous speed and the measured current is actually<br />

higher than the ideal no-load current. The saturation level <strong>of</strong> the machine might be in the<br />

area where it is most sensitive to change in the air gap. In order to verify this tendency a larger<br />

test should have been conducted with the possible to change the load and speed <strong>of</strong> the machine.<br />

76

Chapter 8<br />

Conclusion<br />

The purpose <strong>of</strong> this thesis has been to investigate conditions that could support the idea <strong>of</strong> using<br />

electrical signature analysis as an alternative to vibration monitoring, or if it is more suitable as<br />

a redundant option.<br />

The demand for a reliable condition monitoring system exists. In a reliability study it was<br />

shown that even with the advances made in wind turbine technology, modern wind turbines still<br />

suffer from low availability. As the wind turbine become larger and more complex, the failure<br />

rate increases. This especially affects performance at <strong>of</strong>fshore wind turbines due to their remote<br />

location. Presently, the most popular <strong>of</strong>fshore wind turbine concept is a geared turbine with a<br />

full or partial power converter. It has been shown that the drive train components in these turbines<br />

are very critical. The most common method for monitoring these components is <strong>by</strong> vibration<br />

analysis. The downside <strong>of</strong> this system is that it requires up to eight sensors, which increases<br />

cost and the possibility <strong>of</strong> sensor related faults. As an alternative, electrical signature analysis<br />

(ESA) has been suggested since this method requires fewer sensors.<br />

If electrical signature analysis should be considered as an alternative, it should be able to locate<br />

and detect the same range <strong>of</strong> faults as the vibration system. By studying the characteristics <strong>of</strong><br />

faults in bearings, it has been shown that ESA has some physical constraints and some challenges<br />

regarding fault detection. Since the fault identification is based on the characteristic frequencies<br />

<strong>of</strong> the bearing, it is not possible distinguish two identical bearings from each other if<br />

rotated at the same speed. This is possible with vibration analysis since multiple sensors are<br />

used, so the difference in amplitude at the two sensors can be used to locate the fault.<br />

It has also been shown that detecting small fault in a low speed bearing will be a challenge,<br />

since the fault is not continuously present in the electrical signal. This is considered a challenge<br />

for the signal processing, but not a constraint.<br />

To study conditions that affect the reliability <strong>of</strong> the electrical signal measured at the generator<br />

terminal, a finite element model has been designed. The model is based on the Siemens SWT-<br />

3.6MW wind turbine due to its popularity at <strong>of</strong>fshore locations. Through a static analysis <strong>of</strong> the<br />

inductances model, it has been shown that the relative change depends on several conditions.<br />

These conditions should be accounted for to get a reliable indication <strong>of</strong> the actual degree <strong>of</strong><br />

eccentricity. For low poled machines the relative change varies with the rotor displacement angle.<br />

The result is that the same fault would appear more severe in some position compared to<br />

other. The relative change is also depending on the saturation level <strong>of</strong> the generator. It tends to<br />

decrease as the core is saturated – this makes sense as a saturated core is less sensitive to small<br />

changes in the flux density. Since a converter based wind turbine is likely to have a constant<br />

voltage / frequency regulation to keep the saturation level constant, the relative change is constant<br />

at various loads. This is positive in relation the reliability <strong>of</strong> the electrical signal. But, if<br />

machine is kept at a high saturation level, which is likely to reduce the weight <strong>of</strong> the generator,<br />

77

Chapter 8 - Conclusion<br />

then the relative change is very small. This indicates that it could be difficult to detect small<br />

early stage faults. During the analysis it has also been shown that the relative change is not linear<br />

or proportion to the degree <strong>of</strong> eccentricity. This is downside as the signal processing system<br />

would have know to characteristics <strong>of</strong> the monitored generator in order to relate the measured<br />

signal to the severity <strong>of</strong> a fault.<br />

During a time-transient simulation <strong>of</strong> the finite element model, it has been verified that it is<br />

possible to measure a change in the current signal during eccentricity. The change is however<br />

small – about 0.15% <strong>of</strong> the fundamental current at 50% eccentricity. Oscillating tendencies are<br />

noted in the signal, which verifies that the relative change depends on the rotor position.<br />

A small scale test on an induction motor with an unbalanced load has verified that it is possible<br />

to introduce and measure eccentricity to a machine considered in good condition. During eccentricity,<br />

changes in the current signal were measured at the same frequency components as in the<br />

simulated model. The change was larger – about 1% <strong>of</strong> the fundamental current.<br />

Based on the mentioned circumstances then electrical signature analysis is not considered to be<br />

a suitable alternative to vibration monitoring in geared wind turbines. One thing is to be able to<br />

measure a change in the electrical signal, but another is actually to relate the change to the severity<br />

<strong>of</strong> a fault and to predict the future outcome. This requires extensive study and information<br />

<strong>of</strong> the involved generator, which would make the system impractical to implement.<br />

78

Chapter 9<br />

Future Work and Perspective<br />

Is electrical signature analysis not useful as a condition monitoring system wind turbines, or<br />

does it have some future perspective. The current trend in wind turbine design is gearless designs<br />

with permanent magnet generators. In figure 9.1 a typical gearless design is illustrated.<br />

Bearings<br />

Rotor<br />

Magnets<br />

Stator<br />

Converter Grid<br />

Figure 9.1 Typical gearless wind turbine with permanent magnet generator.<br />

In this configuration the number <strong>of</strong> drive train components is reduced to a minimum. The general<br />

idea is that this should increase the reliability <strong>of</strong> the wind turbine. But, as permanent magnet<br />

generators are more complex in their design compared to induction generators, they can be<br />

assumed to be less reliable. This emphasise that there is a future demand for a condition monitoring<br />

system capable to detect generator faults. In this case electrical signature analysis might<br />

be suitable, as most faults will occur in the electrical system. An instigation <strong>of</strong> the following<br />

types <strong>of</strong> incidents is considered important for future work:<br />

Faults in the main bearings, so the need for a vibration system can be removed.<br />

Generator related faults, such as demagnetization and coil shortenings.<br />

Converter and transformer faults.<br />

79

REFERENCES<br />

[1] The European <strong>Wind</strong> Energy Association, 2010, <strong>Wind</strong> Energy Factsheets - Statistics and Targets.<br />

[2] Yeng Y., Tavner P. J., “Early operational experience <strong>of</strong> UK round 1 <strong>of</strong>fshore wind farms”,<br />

2010<br />

[3] Walford C. A., “<strong>Wind</strong> Turbine Reliability: Understanding and Minimizing <strong>Wind</strong> Turbine Operation<br />

and Maintenance Costs”, 2006.<br />

[4] Larsen J. H. M., „Experiences from Middelgrunden 40 MW Offshore <strong>Wind</strong> Farm‟, Copenhagen<br />

<strong>of</strong>fshore wind conference, 2005.<br />

[5] Ribrant J., "Reliability performance and maintenance - a survey <strong>of</strong> failure in wind power systems"<br />

M.Sc. dissertation, Dept. Elec. Eng., Univ., KTH, Sweden, 2006.<br />

[6] Elforsk, “RAMS-database for <strong>Wind</strong> <strong>Turbines</strong>, Elforsk”, 2010.<br />

[7] Tavner P. J., Xiang J. and Spinato F., “Reliability analysis for wind turbines. <strong>Wind</strong> Energy”,<br />

2007.<br />

[8] Faulstich S., Hahn B. and Tavner P. J., “<strong>Wind</strong> turbine downtime and its importance for <strong>of</strong>fshore<br />

deployment”, 2010.<br />

[9] Faulstich S., Durstewitz M., Hahn B., Knorr K., Rohrig K., “<strong>Wind</strong>energie Report Deutschland<br />

2008”, Institut für solare Energieversorgungstechnik (Hrsg.), Kassel, 2008.<br />

[10] Faulstich S., Hahn B. and Lyding P., “<strong>Electric</strong>al subassemblies <strong>of</strong> wind turbines – a substantial<br />

risk for the availability”, In Proc. <strong>of</strong> European <strong>Wind</strong> Energy Conference 2010, Warsaw, Poland,<br />

2010.<br />

[11] Echavarria E., Hahn B., van Bussel G.J.W., Tomiyama T., “Reliability <strong>of</strong> <strong>Wind</strong> Turbine Technology<br />

Through Time‟, Journal <strong>of</strong> Solar Energy Engineering, Aug. 2008 Vol. 130 / 031005-1.<br />

[12] Hameed Z., Hong Y. S., Cho Y. M., Ahn S. H., and Song, C. K., “<strong>Condition</strong> monitoring and<br />

fault detection <strong>of</strong> wind turbines and related algorithms: A review” 2009.<br />

[13] Crabtree C. J., „Survey <strong>of</strong> Commercially Available <strong>Condition</strong> <strong>Monitoring</strong> Systems for <strong>Wind</strong><br />

<strong>Turbines</strong>‟, 2010, Revision: 5<br />

[14] Lu B., “A Review <strong>of</strong> Recent Advances in <strong>Wind</strong> Turbine <strong>Condition</strong> <strong>Monitoring</strong> and Fault Diagnosis”,<br />

2009.<br />

[15] SKF, Online Product Catalogue: http://www.vsm.skf.com/en-UK/OnlineCatalogue.aspx<br />

81

References<br />

[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<br />

[17] SKF, “Bearing failures and their causes”, 2010.<br />

[18] B. Li, M. Chow, Y. Tipsuwan, and J. Hung, “Neural-network-based motor rolling bearing fault<br />

diagnosis”, IEEE Trans. Ind. Electron., vol. 47, no. 5, pp. 1060–1069, Oct. 2000.<br />

[19] Blödt M., Granjon P., Raison B. and Rostaing G., “Models for Bearing Damage Detection in<br />

Induction Motors using stator current monitoring”, IEEE Trans. Ind. Electron., vol. 55, no. 4,<br />

pp. 1813–1822, April 2008.<br />

[20] Yang W., Tavner P. J., Crabtree C. J., “Cost-effective <strong>Condition</strong> <strong>Monitoring</strong> for <strong>Wind</strong> <strong>Turbines</strong>”,<br />

2010.<br />

[21] Yang W., Tavner P. J., Wilkinson M., ”<strong>Wind</strong> Turbine <strong>Condition</strong> <strong>Monitoring</strong> and Fault dianosis<br />

Using both Mechanical and <strong>Electric</strong>al <strong>Signature</strong>s”, 2008.<br />

[22] Djurovic S., Williamson S., “<strong>Condition</strong> <strong>Monitoring</strong> Artifacts for Detecting <strong>Wind</strong>ing Faults in<br />

<strong>Wind</strong> <strong>Turbines</strong> DFIG”, 2009.<br />

[23] Faiz Z., Ibrahimi B.M., Akin B., Toliyat H.A., “Dynamic analysis <strong>of</strong> mixed eccentricity at<br />

various operating points and scrutiny <strong>of</strong> related indices for induction motors”, 2009.<br />

[24] Boldea I., Tutelea L., “<strong>Electric</strong> Machines – Steady State, Transients and Design with Matlab”,<br />

2010, ISBN: 978-1-4200-5572.<br />

[25] Fitzgerald A. E., “<strong>Electric</strong> Machinery”, sixth edition, 2003, ISBN: 0-07-366009-4.<br />

[26] Boldea I., Nasar S., “The Induction Machine Handbook”, first edition, CRC Press Inc, 2001,<br />

ISBN: 978-0849300042.<br />

82

Appendix A<br />

Design <strong>of</strong> Induction Generators<br />

In this appendix the design process <strong>of</strong> the reference generator is described. The methodology<br />

used is an analytical approach verified <strong>by</strong> a numerical Finite Element <strong>Analysis</strong> (FEA).<br />

A.1 Introduction<br />

A.1.1 Generator Specifications<br />

In table A.1 the performance requirements are given for the generator. The rated output power<br />

<strong>of</strong> the generator is not known for the SWT 3.6-120 wind turbine, but can roughly be estimated<br />

considering a converter efficiency <strong>of</strong> 99% and a transformer efficiency <strong>of</strong> 98% then the rated<br />

output power is 3,710 kW. The efficiency <strong>of</strong> the generator is estimated to minimum <strong>of</strong> 97% and<br />

the power factor to 0.93. With a power factor <strong>of</strong> 0.93 at rated power the power rating <strong>of</strong> the fullscale<br />

converter is about 4,000 kVA, which is considered realistic.<br />

Parameter Value Unit Description<br />

Pn 3710 kW Rated Power output<br />

n 1500 Rpm Nominal speed (50Hz)<br />

Vn 750 V Rated voltage (RMS line voltage)<br />

m1 3 Number <strong>of</strong> phases<br />

p 4 Number <strong>of</strong> poles<br />

η 0.97 Efficiency at Pn (min value)<br />

cos(υ) 0.93 Power factor at Pn (min value)<br />

Table A.1 The initial performance requirements for reference generator.<br />

A.1.2 Design Procedure<br />

The design <strong>of</strong> an induction machine can be divided into the following steps:<br />

1. <strong>Wind</strong>ing layout and number <strong>of</strong> slots.<br />

2. Determination <strong>of</strong> the main dimensions.<br />

3. Design <strong>of</strong> the stator winding.<br />

4. Design <strong>of</strong> the rotor winding.<br />

5. Parameter estimation.<br />

6. Analytical iteration process – find optimum design.<br />

7. Numerical verification <strong>of</strong> the design (FE).<br />

In the following sections these steps are explained and then used in a Matlab script to determine<br />

a useful generator design based on some chosen design variables.<br />

83

Appendix A - Design <strong>of</strong> Induction Generators<br />

A.2 Step 1 – <strong>Wind</strong>ing Layout and Number <strong>of</strong> Slots<br />

Finding the number <strong>of</strong> stator slots Nss is the first step to in the slot dimensioning.<br />

84<br />

N S m p<br />

ss<br />

1 1<br />

(A.1)<br />

Where S1 is the chosen number <strong>of</strong> stator slots per phase per pole, m is the number <strong>of</strong> phases and<br />

p is the number <strong>of</strong> poles. The value <strong>of</strong> S1 has several considerations; it affects the angle that a<br />

winding can be pitched, it <strong>of</strong>fers the opportunity to distribute a winding over several slots, it<br />

should be large enough to support windings and slot closure. For machines with few pole pairs<br />

an integer value between 2 and 6 is <strong>of</strong>ten chosen. In reference [24] the following relation between<br />

the number <strong>of</strong> stator slots and rotor slots are given for two pole pairs.<br />

Pole pairs S1 Number <strong>of</strong> rotor slots<br />

2 2 16 18 20 30 33 34 35 36<br />

3 24 28 30 32 34 45 48<br />

4 30 36 40 44 57 59<br />

5 36 42 48 50 70 72 74<br />

6 42 48 54 56 60 61 62 68 76 82 86 90<br />

Table A.2 Suitable stator and rotor slot combinations for a machine with two pole pairs.<br />

To find a good solution that suppress the space harmonics related to the mmf distribution, the<br />

winding factor Kw is calculated for each value <strong>of</strong> S1. The winding factor is determined <strong>by</strong> the<br />

distribution factor Kd and the pitch factor Kp, given as:<br />

K K K<br />

wn dn pn<br />

n S1<br />

<br />

<br />

sin / 2<br />

np Kdn Kpncos<br />

<br />

S1sin n<br />

/ 2 2 <br />

(A.2)<br />

Where n represents the n´th harmonic, γ is the electric angular displacement between slots and<br />

θp is the pitch angle. The angular displacement and the pitch angle are determined as:<br />

180<br />

n<br />

<br />

<br />

m S<br />

1 1<br />

p p<br />

(A.3)<br />

With np being the number <strong>of</strong> slots pitched (integer value). In table A.3 Kdn and Kpn is calculated<br />

for n = 1:15 submitting the even harmonics as they will cancels, and with np = 1.

Distribution factor Kdn<br />

Appendix A - Design <strong>of</strong> Induction Generators<br />

S1 γ 1 3 5 7 9 11 13 15<br />

1 60 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000<br />

2 30 0.966 0.707 0.259 -0.259 -0.707 -0.966 -0.966 -0.707<br />

3 20 0.960 0.667 0.218 -0.177 -0.333 -0.177 0.218 0.667<br />

4 15 0.958 0.653 0.205 -0.158 -0.271 -0.126 0.126 0.271<br />

5 12 0.957 0.647 0.200 -0.149 -0.247 -0.109 0.102 0.200<br />

6 10 0.956 0.644 0.197 -0.145 -0.236 -0.102 0.092 0.173<br />

Pitch factor Kpn<br />

S1 θp 1 3 5 7 9 11 13 15<br />

1 60 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000<br />

2 30 0.966 0.707 0.259 -0.259 -0.707 -0.966 -0.966 -0.707<br />

3 20 0.985 0.866 0.643 0.342 0.000 -0.342 -0.643 -0.866<br />

4 15 0.991 0.924 0.793 0.609 0.383 0.131 -0.131 -0.383<br />

5 12 0.995 0.951 0.866 0.743 0.588 0.407 0.208 0.000<br />

6 10 0.996 0.966 0.906 0.819 0.707 0.574 0.423 0.259<br />

Table A.3 Distribution factor and pitch factor for uneven harmonics when pitched one slot.<br />

If the machine is not connected to neutral then the third related harmonics (3, 9, 15) cannot exist.<br />

In table A.4 the resulting winding factor is calculated without the third related harmonics.<br />

<strong>Wind</strong>ing factor Kwn<br />

S1 1 5 7 11 13<br />

1 1.000 1.000 1.000 1.000 1.000 2.236 2.236 2.236<br />

2 0.933 0.067 0.067 0.933 0.933 1.619 1.693 1.713<br />

3 0.945 0.140 -0.061 0.061 -0.140 0.969 1.023 1.425<br />

4 0.949 0.163 -0.096 -0.016 -0.016 0.968 0.996 1.420<br />

5 0.951 0.173 -0.111 -0.045 0.021 0.975 0.989 1.581<br />

6 0.953 0.179 -0.119 -0.058 0.039 0.979 0.986 1.730<br />

Table A.4 Resulting winding factor with third related harmonics.<br />

From the resulting winding factor it would be preferable to chose 3 slots per phase per slots or<br />

above, and pitch the winding one slot. However the effect <strong>of</strong> pitching has minor influence on<br />

the harmonic levels in this case, since the third related harmonics cannot exists.<br />

Based on these considerations, the machine in the given case is chosen to have S1 = 4 with fully<br />

pitched windings. The number <strong>of</strong> stator slot Nss is then 48. The winding layout is illustrated in<br />

figure A.2 for the first two coils <strong>of</strong> phase A. The configuration is a two layer arrangement to<br />

give the possibility <strong>of</strong> pitching the windings.<br />

85

Appendix A - Design <strong>of</strong> Induction Generators<br />

86<br />

A A A A C’ C’ C’ C’ B B B B<br />

A A A A<br />

43<br />

44<br />

mmfA<br />

A’ A’ A’ A’<br />

C’ C’ C’ C’ B B B B A’ A’ A’ A’<br />

C C<br />

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24<br />

C<br />

C C C B’<br />

C C<br />

Figure A.2 Two layer fully pitched winding arrangement and resulting mmf for phase A.<br />

B’<br />

B’<br />

B’<br />

B’<br />

B’<br />

B’<br />

B’<br />

A<br />

A<br />

A<br />

A<br />

A<br />

A<br />

A<br />

A<br />

25 26<br />

The green curve is the resulting mmfA when distributed over four slots. The coils are left open,<br />

but can either be connected in series or in parallel.<br />

If the efficiency is low a pitched solution could be chosen. In figure A.3 the slot layout is shown<br />

where the same winding setup is pitched one slot (7.5°).<br />

A A A A C’ C’ C’ C’ B B B B<br />

A A A<br />

43<br />

44<br />

A’ A’ A’ A’<br />

C’ C’ C’ C’ B B B B A’ A’ A’ A’<br />

C C<br />

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24<br />

C<br />

C C C B’<br />

C C<br />

Figure A.3 Two layer winding arrangement when short pitched one slot length.<br />

A.3 Step 2 - Determinations <strong>of</strong> the Main Dimensions<br />

B’<br />

B’<br />

B’<br />

B’<br />

B’<br />

B’<br />

B’<br />

A<br />

A<br />

A<br />

A<br />

A<br />

A<br />

A<br />

A<br />

C’<br />

25 26<br />

The main dimensions <strong>of</strong> the machines are shown in figure A.4. They are the outer stator diameter<br />

Dso, the inner stator diameter Dsi, the outer rotor diameter Dro, the inner rotor diameter Dri<br />

and the length <strong>of</strong> the machine L.

hsy<br />

hry<br />

Dri<br />

Dro<br />

Dsi<br />

Dso<br />

Figure A.4 Main dimension <strong>of</strong> an induction machine.<br />

Appendix A - Design <strong>of</strong> Induction Generators<br />

The length and inner stator diameter can be determined from the output equation, which can be<br />

described <strong>by</strong> considering the induced RMS voltage <strong>of</strong> an entire phase winding. [24]<br />

2 <br />

E f k ˆ<br />

wN1p 2<br />

p n 2<br />

2<br />

ˆ Dsi<br />

<br />

Kw1N1<br />

Bg L<br />

120 p n <br />

2 k ˆ<br />

w1N1BgDsiL<br />

60 <br />

L<br />

(A.4)<br />

Where p is number <strong>of</strong> poles, n is the rotor speed (rpm), L is the active stator core length and Bg<br />

is the peak air gap flux density.<br />

If q is defined as the specific electric loading (Ampere-conductors/meter), then it can found<br />

from the phase current Iph. The electric loading is typically in the range <strong>of</strong> 30.000-100.000 A/m<br />

for larger machines.<br />

<br />

2 3N<br />

D<br />

q I I q <br />

D 6N<br />

1<br />

ph<br />

si<br />

ph<br />

The apparent power Sn <strong>of</strong> the machine can be written as:<br />

Pn<br />

S 3<br />

I E<br />

cos<br />

n ph ph<br />

Combining the three equations and solving for Dsi and L gives the following solution:<br />

si<br />

1<br />

(A.5)<br />

(A.6)<br />

87

Appendix A - Design <strong>of</strong> Induction Generators<br />

88<br />

Dsi q n <br />

3 2<br />

ˆ <br />

Sn Kw1N1BgDsi<br />

L <br />

6 N1<br />

60 <br />

2<br />

q n K ˆ<br />

2<br />

w1Bg Dsi L<br />

2 60<br />

2 60S 2<br />

n<br />

Dsi L 2<br />

q n K ˆ<br />

w1Bg (A.7)<br />

This equation relates the dimensions <strong>of</strong> the machine to its power rating, and is in general known<br />

as the output equation. To determine Dsi and L a relation c0 is defined between the length and<br />

the pole pitch τp.<br />

L D<br />

c0 where p <br />

<br />

p<br />

p<br />

si<br />

(A.8)<br />

c0 is also referred to as the shape factor and is typically chosen in a range <strong>of</strong> 0.5-3.0. The diameter<br />

Dsi can then be determined as:<br />

D<br />

si<br />

<br />

3<br />

2 60 S p<br />

n<br />

3<br />

q n K ˆ<br />

w1Bg c0<br />

The machine length and pole pitch can be then be found using equation (A.8).<br />

(A.9)<br />

The length <strong>of</strong> the stator yoke hsy and the rotor yoke hry can be determined from the desired flux<br />

densities, the stator diameter and the number <strong>of</strong> poles.<br />

h<br />

h<br />

sy<br />

ry<br />

Bˆ D<br />

<br />

Bˆ<br />

p<br />

g si<br />

sy<br />

Bˆ D<br />

<br />

Bˆ<br />

p<br />

g si<br />

ry<br />

(A.10)<br />

The required air gap length g <strong>of</strong> the machine can be estimated from the rated power given in<br />

kilo-Watts. [24]<br />

<br />

g <br />

<br />

0.1 0.2 3 Pn if p 2<br />

0.10.13Pnif p 4<br />

The outer diameter <strong>of</strong> the rotor Dro is then:<br />

D D 2<br />

g<br />

ro si<br />

(A.11)<br />

(A.12)<br />

The inner diameter <strong>of</strong> the rotor and the outer diameter <strong>of</strong> stator will depend on the chosen slot<br />

layout. This is described in step two and three.

Appendix A - Design <strong>of</strong> Induction Generators<br />

A.4 Step 3 - Design <strong>of</strong> Stator Slots and <strong>Wind</strong>ings<br />

For large machines an open rectangular shaped slot is <strong>of</strong>ten used for the stator. The advantage <strong>of</strong><br />

an open slot is that preformed coils can be inserted with a high copper fill factor. In figure A.5<br />

the rectangular open slot is illustrated.<br />

hsy stator yoke<br />

teeth<br />

wssc<br />

wss<br />

usable<br />

slot<br />

area<br />

Slot closure<br />

air gap<br />

Figure A.5 Stator slots and teeth layout (rectangular shaped slots).<br />

To keep the preformed coils in place a slot closure to secure the coil. The material used for the<br />

slot closure should be <strong>of</strong> low permeability to reduced leakage flux. A material like steel with a<br />

relatively permeability <strong>of</strong> 100 (µ/µ0) could be used, but <strong>of</strong>ten a composite material is chosen.<br />

Custom made epoxy glass fibre with iron powder could be used. In this case the relative permeability<br />

can be as low as 3-4 (µ/µ0). The slot closure height and tap width is estimated as:<br />

hss<br />

hssc<br />

wst<br />

0.10 0.20<br />

w round w h round h <br />

ssc ss sc ss<br />

(A.13)<br />

Where round represent the closest integer value (e.g. 1.23mm = 1mm). The stator slot pitch τss<br />

and the teeth width wst can then be found as:<br />

D<br />

Bˆ<br />

si<br />

g<br />

ss wst<br />

ss (A.14)<br />

N Bˆ<br />

ss st<br />

Bst is the chosen flux density in the stator teeth. The maximum width wss <strong>of</strong> the stator slot is<br />

then:<br />

w w ss ss st<br />

The depth <strong>of</strong> the stator slots hss are obtained from the required copper area Ascu.<br />

I D<br />

A I <br />

<br />

ts si<br />

scu<br />

Js ts<br />

q Nss<br />

(A.15)<br />

(A.16)<br />

Where Its is the total RMS ampere turn per slot and Js is current density. For an air cooled winding<br />

the current density is typically chosen as 2-3 A/mm 2 . The stator slot area Ass is found from<br />

the chosen fill factor Ksf and the slot height hss can then be found.<br />

89

Appendix A - Design <strong>of</strong> Induction Generators<br />

90<br />

A A<br />

A h <br />

scu ss<br />

ss<br />

Ksf ss<br />

wss<br />

(A.17)<br />

The fill factor for a preformed winding can be up to 60-70%, where it for a wound winding<br />

might be 40-50%. The outer diameter <strong>of</strong> the stator Dso can now be calculated.<br />

Dso Dsi hss hssc hsy<br />

(A.18)<br />

With the geometry <strong>of</strong> the stator in place the number <strong>of</strong> turns per phase N1 can be estimated using<br />

equation (A.4) with the assumption that Vph = Eph.<br />

N<br />

<br />

V<br />

ph<br />

1<br />

2 f k ˆ<br />

wp Where ˆ p represents the flux per pole found as:<br />

ˆ 2<br />

ˆ<br />

p Bg p L<br />

<br />

The number <strong>of</strong> turns per slot Nsc is equal to:<br />

N<br />

N a<br />

p S n<br />

1<br />

sc <br />

1 <br />

L<br />

(A.19)<br />

(A.20)<br />

(A.21)<br />

Where a is the number <strong>of</strong> parallel paths and nL is the number <strong>of</strong> winding layers. Nsc is rounded<br />

<strong>of</strong> the closest integer value and then N1 is recalculated.<br />

A.5 Step 4 - Design <strong>of</strong> Rotor Slots and <strong>Wind</strong>ings<br />

In large induction machines the rotor bars are primarily made <strong>of</strong> copper and in some cases<br />

bronze. The shape <strong>of</strong> slot is for smaller machines <strong>of</strong>ten chosen with thoughts on the assembly<br />

process. In larger machines the shape <strong>of</strong> the bars is designed to meet special requirements such<br />

as starting torque. Deep bars as single or double cage arrangements will increase the starting<br />

torque due to current displacement (increase in rotor AC resistance).<br />

For the reference generator a trapezoidal shaped slot is chosen so that the teeth are rectangular,<br />

see figure A.6. The height <strong>of</strong> the slot opening hrso is chosen to be 2.0mm. The number <strong>of</strong> rotor<br />

slots Nrs can evaluated in terms <strong>of</strong> the harmonics as done for the number <strong>of</strong> stator slots. This is<br />

however neglected and Nrs = 48 slots are chosen, which according to reference [24] is a suitable<br />

value when S1 = 4, also shown see table A.2.

otor bar<br />

rotor yoke<br />

wrt<br />

wrs1<br />

hrs rotor bar<br />

wrs2<br />

Appendix A - Design <strong>of</strong> Induction Generators<br />

hrso<br />

teeth<br />

air gap<br />

rotor bar<br />

Figure A.6 Rotor slots and teeth layout (trapezoidal shaped slots).<br />

Now, the rotor slot pitch τrs and the rotor tooth width wrt can be found.<br />

D<br />

Bˆ<br />

ro<br />

g<br />

rs wrt<br />

rs (A.22)<br />

N Bˆ<br />

rs rt<br />

The maximum rotor slot top width wrs is then:<br />

w w<br />

(A.23)<br />

rs1 rs rt<br />

To determine the required copper area the current in each rotor bar Ib must be estimated. This<br />

can be done <strong>by</strong> considering the chosen electric loading <strong>of</strong> the machine q1. Using this method<br />

instead <strong>of</strong> comparing the stator mmf to the rotor mmf as <strong>of</strong>ten done will allow the iteration process<br />

to focus on the electric loading <strong>of</strong> the machine. [24]<br />

I<br />

b<br />

D<br />

cos qN si<br />

rs<br />

hry<br />

(A.24)<br />

The power factor cosυ accounts for the fact that a part <strong>of</strong> the stator current is used for magnetization.<br />

The area <strong>of</strong> one bar Ab can then be determined as done for the stator winding.<br />

Ib<br />

Ab<br />

<br />

J<br />

r<br />

(A.25)<br />

Where Js is current density in the rotor bars, which for an air cooled winding typically, is chosen<br />

between 2-3 A/mm 2 . From the required copper area the area <strong>of</strong> one slot Ars is found using the<br />

fill factor Krf. The fill factor in a squirrel caged rotor will be close to one – in this report it is<br />

selected as 0.95.<br />

A<br />

A<br />

b<br />

rs (A.26)<br />

Krf<br />

The bottom width wrs2 and the height hrs <strong>of</strong> the trapezoidal shaped slot is found using equation x<br />

and Y. An iterative process is used for variable hrs until Ars,new

Appendix A - Design <strong>of</strong> Induction Generators<br />

92<br />

D h h <br />

2 0.5 ro rs rso<br />

rs2 rt<br />

w w<br />

(A.27)<br />

Nrs<br />

A<br />

<br />

h w w<br />

rs rs1 rs2<br />

rs, new (A.28)<br />

2<br />

Note: In the finite element model the rotor slots has been reshaped with round ends to give better<br />

flux distribution.<br />

To determine the dimensions <strong>of</strong> the end ring, the end ring current Ie is required. [24]<br />

I<br />

e<br />

Ib<br />

<br />

p <br />

2 sin <br />

2Nrs <br />

The cross sectional area <strong>of</strong> the end ring Ae and length le is then:<br />

I A<br />

A l <br />

e e<br />

e<br />

Jr e<br />

hrs hrso<br />

<br />

(A.29)<br />

(A.30)<br />

The height <strong>of</strong> the end ring is chosen to be the height <strong>of</strong> the rotor slots hrs plus the height <strong>of</strong> the<br />

rotor slot opening hrso.<br />

A.6 Step 5 – Equivalent Parameter Estimation<br />

The equivalent parameters are shown in the equivalent circuit diagram presented in figure A.7.<br />

V1<br />

I1<br />

R1 L1 L´2<br />

E1<br />

Rc<br />

I2<br />

Lm<br />

R´2<br />

s<br />

Figure A.7 Single phase equivalent circuit <strong>of</strong> the induction machine.<br />

Where R1 is the resistance in the stator windings, X1 is the leakage reactance <strong>of</strong> the stator windings,<br />

Rc represent the iron loss in the core, Xm is the magnetizing reactance (mutual), X ’ 2 is the<br />

leakage reactance <strong>of</strong> the rotor windings and R ’ 2/s is the resistance <strong>of</strong> the rotor windings and s is<br />

the slip. In the diagram the rotor parameters has been referred to the stator side, which is the<br />

reason for the notation X ’ 2 instead <strong>of</strong> X2.<br />

A.6.1 Stator Resistance - R1<br />

The resistance <strong>of</strong> the stator conductor R1 is determined <strong>by</strong> the length lcon, the conductor cross<br />

sectional area Acon and the conductivity σ <strong>of</strong> the material used.

lconAscu R1 Acon<br />

A <br />

N / S<br />

con sc<br />

Appendix A - Design <strong>of</strong> Induction Generators<br />

1<br />

(A.31)<br />

where Nsc/S1 is the number <strong>of</strong> turns per slot. The length <strong>of</strong> the conductor can be determined <strong>by</strong><br />

considering the chosen geometry, see figure A.8.<br />

Dend = Dsi +hss + hssc<br />

The end turn length can be found as:<br />

l<br />

Dend<br />

let<br />

θp<br />

let = end turn length<br />

θp = pitch angle<br />

Figure A.8 Geometry used to estimate stator conductor length.<br />

DendDend 1.3 <br />

p 2 <br />

et p<br />

(A.32)<br />

where the factor <strong>of</strong> 1.3 accounts for bend at the end turn. The total conductor length lcon is then:<br />

<br />

l 2<br />

N L l<br />

con 1 et<br />

A.6.2 Rotor Resistance - R ’ 2<br />

(A.33)<br />

The resistance <strong>of</strong> the squirrel cage rotor is determined <strong>by</strong> the bar resistance Rb and end ring resistance<br />

Re. Where Rb represents one bar resistance and Re represents the resistance <strong>of</strong> one end<br />

ring segment. As for the stator resistance these are found from the cross sectional area, the conductor<br />

length and the conductivity for the material.<br />

R<br />

b<br />

lb<br />

<br />

A<br />

b<br />

li<br />

Re<br />

<br />

A<br />

e<br />

(A.34)<br />

(A.35)<br />

Where lb is the length <strong>of</strong> one bar and li is the length on one end ring segment. The length <strong>of</strong> one<br />

bar lb would initially be equal to the machine length but if the rotor is skewed, the actual length<br />

becomes larger.<br />

93

Appendix A - Design <strong>of</strong> Induction Generators<br />

The length between two rotor slots or bars is equal to the length <strong>of</strong> the end ring segment li. The<br />

length li can be determined <strong>by</strong> the mean diameter <strong>of</strong> the rotor slots Drs divided be the number <strong>of</strong><br />

rotor slots Nrs.<br />

94<br />

Drs Dro hrs hrso<br />

D<br />

li<br />

<br />

N<br />

rs<br />

rs<br />

(A.36)<br />

(A.37)<br />

The length <strong>of</strong> one bar lb taken the skew factor Ks into account can found using stator slot pitch<br />

τss and the assumption that it is straight for the small segment.<br />

2<br />

l l K <br />

b<br />

2<br />

m s ss<br />

(A.38)<br />

Normally for squirrel cage rotors the rotor bars are skewed <strong>by</strong> one slot pitch to account for harmonic<br />

<strong>by</strong> the slotting <strong>of</strong> the stator.<br />

To find the equivalent per phase resistance seen from the stator side, the conservation <strong>of</strong> energy<br />

can be used. To find the energy or power dissipation the current distribution in the rotor must be<br />

described. The number <strong>of</strong> phases in the rotor is equal to the number <strong>of</strong> bars per pole pair and the<br />

electrical angle α between each phase can be determined <strong>by</strong> the pole pairs and the number <strong>of</strong><br />

phases (m2 = Nrs).<br />

p<br />

<br />

N<br />

rs<br />

(A.39)<br />

If the number <strong>of</strong> rotor bars is sufficiently high then the current in the end rings can be considered<br />

sinusoidal. In figure A.9 the current distribution in the rotor is illustrated.<br />

0 π/p 2π/p<br />

Current in end<br />

ring<br />

[Rad]<br />

[Rad]<br />

0<br />

α<br />

π/p 2π/p<br />

Current in bars<br />

Figure A.9 Bar current and end ring current a squirrel cage rotor.<br />

The RMS value <strong>of</strong> the current running in the end rings Ie can be found from the rotor bar current<br />

Ib and the electric angle α. [26]

I<br />

e<br />

Ib<br />

<br />

p <br />

2 sin <br />

2Nrs <br />

Appendix A - Design <strong>of</strong> Induction Generators<br />

(A.40)<br />

The conversation <strong>of</strong> energy can now be written in terms <strong>of</strong> the energy dissipated in the bars and<br />

end rings, compared to the energy equation using the per phase resistance R2. These two must be<br />

equal.<br />

2<br />

2 2 2 m2I2 Nrs Ib Rb Nrs Ie Re R<br />

p<br />

By substituting equation (A.40) into equation (A.41) the following relation can be written.<br />

<br />

<br />

R 2 mI N I R R<br />

2<br />

2 e 2 2<br />

rs b b <br />

2 p <br />

p<br />

<br />

<br />

4 sin<br />

<br />

2 N <br />

rs <br />

Since Nrs = m2 then Ib = 2I2/p which means that the per phase rotor resistance can be found as:<br />

<br />

<br />

R<br />

R R <br />

<br />

2<br />

e<br />

<br />

<br />

b<br />

2 p <br />

4 sin<br />

<br />

<br />

2 N <br />

rs <br />

The rotor resistance referred to the stator side R ‟ 2 is:<br />

m Nk R R<br />

m N k<br />

2 2<br />

'<br />

2 2 1<br />

2 <br />

1<br />

2<br />

2 <br />

w1<br />

2<br />

w2<br />

2<br />

2<br />

(A.41)<br />

(A.42)<br />

(A.43)<br />

(A.44)<br />

In the case <strong>of</strong> a squirrel cage rotor the number <strong>of</strong> phase is equal to the number <strong>of</strong> slot (Nrs = m2),<br />

the number <strong>of</strong> turns N2 = ½ and the winding factor Kw2 = 1.<br />

A.6.3 Magnetizing Inductance - Lm<br />

The magnetizing inductance is a representation <strong>of</strong> the flux that links both the stator and the rotor<br />

– the leakage reactances represent all other fluxes. The magnetizing reactance is given as:<br />

Lm<br />

<br />

<br />

m I<br />

m<br />

(A.45)<br />

It depends on the flux linkage ψm and the magnetizing current Im. In reference [26] the following<br />

solution is given for the unsaturated magnetizing inductance. This will be used in the analytical<br />

design process and later a more accurate inductance is determined using FEA.<br />

95

Appendix A - Design <strong>of</strong> Induction Generators<br />

96<br />

L<br />

m0<br />

2<br />

2<br />

1 1<br />

3LDsi0Nkw <br />

p g e<br />

(A.46)<br />

It is important to understand that Lm will change as the core saturates. In this equation the effective<br />

air gap ge length is used that account for rotor and stator slotting. The effective air gap is<br />

found using the Carter coefficient, Kcs and Kcr.<br />

K<br />

cs<br />

ss <br />

g/2<br />

ss<br />

wss <br />

2 <br />

g<br />

<br />

<br />

w<br />

52 g<br />

2<br />

ss<br />

(A.47)<br />

The carter coefficient is calculated for both stator Kcs and rotor Kcr, so that the effective air gap<br />

is equal to:<br />

ge g Kcs Kcr<br />

(A.48)<br />

A.6.4 Stator Leakage inductance – L1<br />

The estimated leakage flux in this report consists <strong>of</strong> slot leakage, zig zag leakage and end turn<br />

leakage. The stator slot leakage inductance Lssl is found as, [26].<br />

L<br />

ssl<br />

2<br />

0N1 Ls<br />

(A.49)<br />

N<br />

ss<br />

Where λs is the geometrical slot permeance that for a rectangular shape is:<br />

h h<br />

s <br />

3<br />

w w<br />

ss ssc<br />

ss ss<br />

The stator zigzag leakage can also be estimated, [26].<br />

2 2<br />

1 1 <br />

p a a k <br />

LszlLm 1 2 <br />

<br />

2 12 Nss 2k<br />

<br />

<br />

g<br />

<br />

w g<br />

ss a k<br />

st e<br />

The end turn leakage depends on the winding layout, but can roughly be estimated as:<br />

2<br />

35 . m1N1 Dsi<br />

Lel K 2 6<br />

p .<br />

p 10<br />

03<br />

(A.50)<br />

(A.51)<br />

(A.52)

Appendix A - Design <strong>of</strong> Induction Generators<br />

This value is split equally between the rotor and stator leakage inductance. The total stator leakage<br />

inductance is then equal to:<br />

Lel<br />

L1 Lssl Lszl<br />

(A.53)<br />

2<br />

A.6.5 Rotor Leakage inductance – L ’ 2<br />

The rotor slot leakage inductance Lssl and zig zag leakage Lrzzl is found as, [26]<br />

L<br />

rsl<br />

2<br />

0N2 Lr<br />

(A.54)<br />

N<br />

rs<br />

h h<br />

r <br />

3<br />

w w<br />

rs rso<br />

rs rs<br />

2 2<br />

<br />

2<br />

Nss<br />

2 2<br />

ss rs<br />

1 1 <br />

p a a k <br />

LrzlLm <br />

<br />

2 12 NN2k <br />

g<br />

<br />

w g<br />

rs a k<br />

rt e<br />

The total rotor leakage inductance L ’ 2 referred to the stator side is then:<br />

L<br />

m Nk L L<br />

L<br />

<br />

2 2<br />

' 1 1 w1 2 2 2 <br />

m2 N2kw2 rsl rzl el<br />

2<br />

(A.55)<br />

(A.56)<br />

(A.57)<br />

Only the slot leakage inductance should be transferred as the zig zag and end turn leakage inductances<br />

are referred to the stator side.<br />

A.7 Step 5 – Performance Characteristic<br />

To evaluate the design, the performance characteristics such as current, power and efficiency<br />

must be calculated. The equivalent circuit shown earlier in figure A.6 is used.<br />

To simplify the core loss resistance is neglected and the impedances are described as:<br />

<br />

' ' '<br />

Z1 R1 jX1 Z2 s R2 / s jX 2 Zm jX m<br />

(A.58)<br />

The current stator current I1 and rotor current I’2 in terms <strong>of</strong> the slip:<br />

<br />

I s<br />

<br />

V<br />

Z Z s<br />

1<br />

Z1<br />

<br />

1<br />

m <br />

m <br />

'<br />

2<br />

'<br />

2<br />

<br />

<br />

Z Z s<br />

(A.59)<br />

97

Appendix A - Design <strong>of</strong> Induction Generators<br />

98<br />

<br />

I s<br />

<br />

<br />

V ZIs (A.60)<br />

'<br />

1 1 1<br />

2 '<br />

Z2s The efficiency <strong>of</strong> any device is the ratio <strong>of</strong> the input and the output power.<br />

P<br />

P<br />

out (A.61)<br />

in<br />

The complex power S for a three phase induction machine can be found using the phase voltage<br />

V1 and current I1.<br />

*<br />

3<br />

S3 s V1 I1 s<br />

(A.62)<br />

The real part <strong>of</strong> 3 S corresponds to the electrical output power Pout. (if generator)<br />

out<br />

<br />

<br />

P s P s real S s<br />

3 3<br />

(A.63)<br />

The mechanical power Pmech or input power Pin is given as:<br />

'<br />

'<br />

2 R2<br />

Pin s Pmech s 3I2s1 s<br />

(A.64)<br />

s<br />

The power factor PF or cos(υ) is defined as the ratio <strong>of</strong> the real power and the apparent power.<br />

<br />

cos <br />

PF s s<br />

<br />

<br />

P s<br />

3<br />

(A.65)<br />

S s<br />

3<br />

The relation between the mechanical power Pmech in equation (A.64) and the mechanical torque<br />

Tmech is determined <strong>by</strong> the rotational speed <strong>of</strong> the machine ωmech.<br />

'<br />

'<br />

2 R2<br />

Pmech s Tmech s mech s 3I2s1 s<br />

(A.66)<br />

s<br />

The mechanical speed related to the synchronous speed ωsync,<br />

1 s<br />

mech sync<br />

(A.67)<br />

and ωsync is determined <strong>by</strong> the supply frequency f and the number <strong>of</strong> poles p.<br />

120 f 4 f<br />

sync2 <br />

60 p p<br />

The mechanical torque can now be determined in relation the synchronous speed and the slip.<br />

Pmech Pmech 1<br />

R<br />

Tmech s 3<br />

I2 s <br />

s <br />

<br />

s<br />

1 <br />

mech sync sync<br />

'<br />

'<br />

2<br />

2<br />

(A.68)<br />

(A.69)

Appendix A - Design <strong>of</strong> Induction Generators<br />

To evaluate if the generator meets its minimum requirements, the maximum operation point<br />

should be known. This is at the slip value were the current is equal to the maximum permitted<br />

current in the stator winding I1max.<br />

I1,max Js Acon a1<br />

(A.70)<br />

Since the calculation <strong>of</strong> the motor performance is done in Matlab a simple IF statement can be<br />

used to compare the calculated current with the maximum current.<br />

Another important performance characteristic is the total mass <strong>of</strong> the generator. The total can be<br />

calculated from the dimensions determined in step 2-4. The mass <strong>of</strong> the stator core Msc is:<br />

2 2<br />

DsoDsi sc ssssfe M N A L<br />

2 2 <br />

The mass <strong>of</strong> the stator windings Msw,<br />

sw 1 con scu cu<br />

(A.71)<br />

M m l A <br />

(A.72)<br />

The mass <strong>of</strong> the rotor core Mrc,<br />

2 2<br />

DroDri rc rsrsfe M N A L<br />

2 2 <br />

The mass <strong>of</strong> the rotor bars and end rings Mrw,<br />

2<br />

(A.73)<br />

Mrw NrsAbDrohrshrsoAe alu(A.74)<br />

The total active mass is the sum <strong>of</strong> the four elements (housing and shaft is neglected).<br />

A.8 Step 6 – Iteration process<br />

The design parameters given in table A.5 are used to find the optimum design using a Matlab<br />

script that performs the iterative process. The script is located at the CD-ROM in appendix C.<br />

Some <strong>of</strong> the design variables have been found using sub iterations such as the shape factor,<br />

number <strong>of</strong> parallel paths for the stator winding and the material used for the rotor bars. The optimum<br />

shape factor with an electric loading <strong>of</strong> 56 kA/m was found to be 2.2 be comparing the<br />

possible output power. The number <strong>of</strong> parallel paths was chosen to four to increase the number<br />

<strong>of</strong> turns per coil, which is low due to the relatively low terminal voltage <strong>of</strong> 750V. To increase<br />

the maximum slip value, which is proportional to the rotor resistance, aluminium was chosen<br />

for the rotor bars and end rings<br />

Parameter Value Unit Description<br />

q 56 kA/m <strong>Electric</strong> loading<br />

c0 2.2 Shape factor<br />

nL 2 Number <strong>of</strong> stator winding layers<br />

np 4 Number <strong>of</strong> parallel paths<br />

99

Appendix A - Design <strong>of</strong> Induction Generators<br />

100<br />

Bg 0.7 T Air gap flux density (peak)<br />

Bst 1.2 T Stator tooth flux density (peak)<br />

Bsy 1.0 T Stator yoke flux density (peak)<br />

Brt 1.1 T Rotor tooth flux density (peak)<br />

Bry 1.2 T Rotor yoke flux density (peak)<br />

Js 3 A/mm 2 Stator winding current density<br />

Jr 3 A/mm 2 Rotor winding current density<br />

g 1.6 mm Air gap length<br />

Ks 1 Rotor bar skew factor<br />

Ksf 0.6 Stator slot fill factor<br />

Krf 0.95 Rotor slot fill factor<br />

Nss 48 Number <strong>of</strong> stator slots<br />

Nrs 44 Number <strong>of</strong> rotor slots / bars<br />

σcu 59.6 MS/m Conductivity at 20°C<br />

αcu 0.0039 K -1 Temperature Coefficient<br />

σalu 32.2 MS/m Conductivity at 20°C<br />

αalu 0.0039 K -1 Temperature Coefficient<br />

ρfe 7800 Kg/m 3 Mass density <strong>of</strong> iron<br />

ρcu 8900 Kg/m 3 Mass density <strong>of</strong> copper<br />

ρalu 2700 Kg/m 3 Mass density <strong>of</strong> aluminium<br />

Table A.5 Chosen design parameters for the reference generator.<br />

In table A.6 the resulting main geometrical properties are listed for the machine.<br />

Parameter Value Unit Description<br />

Dsi 731.0 mm Stator inner diameter<br />

Dso 1250.0 mm Stator outer diameter<br />

Dri 372.0 mm Rotor inner diameter<br />

Dro 727.8 mm Rotor outer diameter<br />

L 994.0 mm Length <strong>of</strong> stator core<br />

N1 8 turns Number <strong>of</strong> turns per coil per phase<br />

Mr 2058.9 Kg Mass <strong>of</strong> rotor (core + bars + end rings)<br />

Ms 6429.7 Kg Mass <strong>of</strong> stator (core + windings)<br />

Table A.6 Main geometrical properties for the reference generator.<br />

The analytically estimated equivalent parameters for this design are given in table A.7 and the<br />

performance at maximum load is given in table A.8.

Parameter Value Unit Description<br />

R1 0.59 mΩ Stator winding resistance<br />

R ´ 2 0.79 mΩ Rotor referred resistance<br />

Appendix A - Design <strong>of</strong> Induction Generators<br />

X1 8.92 mΩ Stator winding leakage reactance<br />

X ´ 2 5.86 mΩ Rotor referred leakage reactance<br />

Xm 519.08 mΩ Mutual reactance<br />

Table A.7 Analytically estimated equivalent parameters for the reference generator at 50Hz.<br />

Parameter Value Unit Description<br />

Imax 3064.5 A Maximum phase current (RMS)<br />

s 0.55 % Slip<br />

Pe 3732 kW <strong>Electric</strong>al power output<br />

η 99.0 % Efficiency (core loss not included)<br />

PF -0.94 Power factor<br />

Table A.8 Performance <strong>of</strong> the reference generator at maximum load based<br />

on analytically found parameters.<br />

A.9 Step 7 – Verification <strong>of</strong> Design<br />

To verify the analytical found design, a numerical analysis <strong>of</strong> the generator is performed using<br />

the finite element tool MagNet <strong>by</strong> Infolytica. In this finite element model the stator leakage<br />

reactance, the rotor leakage reactance, the mutual reactance and the core loss can be determined.<br />

The approach is the same as used in chapter four, so it will not be explained in details in this<br />

appendix.<br />

A.9.1 Stator leakage reactance - X1<br />

The stator leakage reactance is found at the maximum phase current <strong>of</strong> 3065A. In figure A.10<br />

the resulting leakage reactance is shown when rotating the rotor one rotor slot (8.18°).<br />

Stator Leakage Reactance [ohm]<br />

0.016<br />

0.015<br />

0.014<br />

0.013<br />

0.012<br />

0.011<br />

0.01<br />

0.009<br />

0.008<br />

0 1 2 3 4 5 6 7 8<br />

Rotor position [deg]<br />

Figure A.10 The stator leakage reactance at 50Hz when rotating the rotor one rotor slot (8.18°).<br />

X 1a<br />

X 1b<br />

X 1c<br />

101

Appendix A - Design <strong>of</strong> Induction Generators<br />

The mean value is 11.1mΩ and this is without the end-turn leakage as the simulation is done in<br />

2D. Compared to the analytically found leakage reactance <strong>of</strong> 8.92mΩ, the FE found value is<br />

higher. This is expected as more leakage contribution are including in the FE analysis compared<br />

to the analytically found value. The FE analysis also includes the effect <strong>of</strong> having stator wedges.<br />

A.9.2 Rotor leakage reactance - X2<br />

The equivalent rotor current I ’ 2 can be found as:<br />

102<br />

m Nk I I <br />

m N k<br />

' 1 1 w1<br />

2 1<br />

2 2 w2<br />

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).<br />

p 4<br />

16.36<br />

N 44<br />

rs<br />

'<br />

bn , 2<br />

<br />

I I cos n 0.5<br />

(A.75)<br />

(A.76)<br />

In figure A.11 the resulting rotor leakage reactance is shown when rotating the rotor one stator<br />

slot (7.5°).<br />

Rotor Leakage Reactance [ohm]<br />

x 10-3<br />

8<br />

7<br />

6<br />

5<br />

4<br />

3<br />

0 1 2 3 4 5 6 7<br />

Rotor position [deg]<br />

Figure A.11 The rotor leakage reactance at 50Hz when rotating the rotor one stator slot (7.5°).<br />

The mean leakage reactance is 5.1mΩ without the end turn contribution. The analytical estimated<br />

reactance is 5.86mΩ with end turn leakage.<br />

A.9.3 Mutual Reactance - Xm<br />

The mutual reactance Xm can be estimated using the magnetizing current Im or no-load current I0<br />

at s = 0.<br />

X 2

I<br />

0<br />

V<br />

<br />

R X R X<br />

1 ph<br />

1 c || m<br />

750 V / 3<br />

819.2A<br />

5.9m 8.92m 519.08m<br />

Appendix A - Design <strong>of</strong> Induction Generators<br />

(A.77)<br />

In figure A.12 the resulting mutual reactance is shown when rotating the rotor one rotor slot<br />

(8.18°).<br />

Mutual Reactance [ohm]<br />

0.63<br />

0.62<br />

0.61<br />

0.6<br />

0.59<br />

0.58<br />

0.57<br />

0 1 2 3 4 5 6 7 8<br />

Rotor position [deg]<br />

Figure A.12 The mutual reactance at 50Hz when rotating the rotor one rotor slot (8.18°)<br />

The mean value <strong>of</strong> the mutual reactance <strong>of</strong> phase wind a is 592mΩ.<br />

A.9.4 Core Loss and Core Resistance - Rc<br />

The core loss resistance can be found from the core loss and the back EMF voltage E1. The back<br />

EMF voltage E1 at no-load can be found as:<br />

E V Z I<br />

1 1 1 0<br />

750V<br />

8.94m 1123.8A 423V<br />

3<br />

The core loss resistance Rc can then found using the core loss Pc. (Pc = 109.1kW)<br />

R<br />

c<br />

(A.78)<br />

2 2<br />

3E13423V 4.92<br />

(A.79)<br />

P 109.1kW<br />

c<br />

A.9.5 Updated Performance Characteristics<br />

In figure A.13 and A.14 the performance <strong>of</strong> the generator using the finite element estimated<br />

parameters is plotted. In table A9 the performance at maximum operation is given.<br />

X ma<br />

X mb<br />

X mc<br />

103

Appendix A - Design <strong>of</strong> Induction Generators<br />

Figure A.13 Efficiency, power factor, electrical power and mechanical power for the reference generator.<br />

104<br />

[W]<br />

[Nm, A]<br />

1.5<br />

1<br />

0.5<br />

0<br />

-0.5<br />

x 107<br />

-1<br />

Efficiency<br />

Pow er Factor<br />

-0.6<br />

Elec. pow er<br />

Mech. pow er<br />

-0.8<br />

-1.5<br />

-1<br />

1400 1420 1440 1460 1480 1500<br />

Speed [rpm]<br />

1520 1540 1560 1580 1600<br />

8<br />

6<br />

4<br />

2<br />

0<br />

-2<br />

x 104<br />

-0.4<br />

-4<br />

Torque<br />

-0.6<br />

-6<br />

Efficiency<br />

Pow er Factor<br />

Current<br />

-0.8<br />

-8<br />

-1<br />

1400 1420 1440 1460 1480 1500<br />

Speed [rpm]<br />

1520 1540 1560 1580 1600<br />

Figure A.14 Torque, efficiency, power factor and current (magnitude) for the reference generator.<br />

Parameter Value Unit Description<br />

Imax 3066.8 A Maximum phase current (RMS)<br />

s -0.55 % Slip at Imax<br />

Pe 3744 kW Power output at Imax<br />

η 96.0 % Efficiency at Imax (core loss included)<br />

PF -0.94 Power factor at Imax<br />

Table A.9 Updated performance characteristics <strong>of</strong> the reference generator<br />

using the finite element found parameter<br />

1<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

0<br />

-0.2<br />

-0.4<br />

1<br />

0.8<br />

0.6<br />

0.4<br />

0.2<br />

0<br />

-0.2

Appendix B<br />

Pictures from Small-Scale Test<br />

Figure B.1 Pictures from small Scale test setup. (Motor stand, converter and eccentricity tool).<br />

105

106

Appendix C<br />

CD-ROM<br />

The following is located at the CD-ROM.<br />

- PDF version <strong>of</strong> the report.<br />

- Matlab and MatchCad script files.<br />

- MagNet static and motion model.<br />

107

www.elektro.dtu.dk/cet<br />

Department <strong>of</strong> <strong>Electric</strong>al Engineering<br />

Centre for <strong>Electric</strong> Technology (CET)<br />

Technical University <strong>of</strong> Denmark<br />

Elektrovej 325<br />

DK-2800 Kgs. Lyng<strong>by</strong><br />

Denmark<br />

Tel: (+45) 45 25 35 00<br />

Fax: (+45) 45 88 61 11<br />

E-mail: cet@elektro.dtu.dk