Monitoring and Regression Based Modelling of End Winding Vibratio

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Contents
Abstract .................................................................................................................................... 1
Declaration Page ....................................................................................................................... 2
Acknowledgements ................................................................................................................... 3
Abbreviations List .................................................................................................................... 4
Table of Contents ...................................................................................................................... 6
Figures, Tables and Equations .............................................................................................. 13

Chapter 1
Project Introduction ............................................................................................................... 23

Chapter 2
Literature Review ................................................................................................................... 27
2.1 End Winding Design ...................................................................................................... 27
2.2 Online End Winding Vibration Monitoring ................................................................... 34

Chapter 3
Gas Turbine Generator End Winding Vibration ................................................................ 37
3.1The Power Station ........................................................................................................... 37
3.2 The Gas Turbine Generator ............................................................................................ 37
3.3 Gas Turbine Generator End Winding Vibration ............................................................ 38
3.4 Definition of Natural Frequency..................................................................................... 39
3.5 Static Natural Frequency Testing ................................................................................... 40
3.6 GT Generator End Winding Vibration Timeline ............................................................ 41
3.6.1 Summary of Bump Tests ......................................................................................... 41
3.6.2 Scheduled Major Outage April 2005 (AOH05) ...................................................... 42
3.6.3 Summary of 2005 Bump Test (Post Repair) ........................................................... 44
3.6.4 Scheduled Minor Outage April 2006 (AOH06) ...................................................... 45
3.6.5 Quarterly Inspection No.1 (EWV Related) July 2006 ............................................. 48
3.6.6 Quarterly Inspection No.2 (EWV Related) September 2006 .................................. 48
3.6.7 Outage for EWV Monitoring System Installation November 2006 ........................ 49
3.6.8 Scheduled Major Outage April 2007 (AOH07) ...................................................... 49
3.6.9 Forced Outage (Gas Turbine Related) October 2007 .............................................. 50
3.6.10 Scheduled Minor Outage April 2008 .................................................................... 50
3.7 Failures of Other Generators of the Same Type Due To Excessive End Winding Vibration .............. 50
3.8 The End Winding Vibration Monitoring System ........................................................... 54
3.8.1 Location of Accelerometers and Plane of Measurement ......................................... 55
3.8.2 End Winding Vibration Monitoring System Overview ........................................... 59
3.8.3 Penetration of Generator for FOA Cabling ............................................................. 60
3.8.4 Replacement of Steel Man Way Covers with Perspex ............................................ 60
3.9 Strengths and Weaknesses of the VibrosystM EWV Monitoring System ..................... 61
3.9.1 Strengths .................................................................................................................. 61
3.9.2 Weaknesses .............................................................................................................. 61
3.10 End Winding Monitoring System Improvements ......................................................... 62
3.10.1 Connection to Delphin Flight Recorder System for High Resolution Data
Recording ......................................................................................................................... 62
3.10.2 Connection to OSISOFT PI Data Acquisition System .......................................... 62

Chapter 4
Initial Data Analysis ............................................................................................................... 64
4.1 Analysis of Trend Data ................................................................................................... 64
4.2 Basic Descriptive Statistics and Correlation .................................................................. 68
4.2.1Basic Descriptive Statistics ...................................................................................... 68
4.2.2 Correlation Data ...................................................................................................... 70
4.3 Measures Taken to Reduce End Winding Vibration Levels and Setting of Alarm
Thresholds ...................................................................... 72
4.3.1 Setting of Alarm Thresholds.................................................................................... 76
4.4 Experiments Undertaken in Order to Reduce Peak End Winding Vibration Levels ..... 77
4.4.1 Peak Vibration Reduction, Option No.1. ................................................................. 78
Introduction of Excitation Limit ....................................................................................... 78
Monitoring and Regression Based Modelling of End Winding Vibration in Large Synchronous Generators
Table of Contents Page 8 David Shally
4.4.2 Peak Vibration Reduction, Option No.2. ................................................................. 82
Experiments with Generator Cooling System .................................................................. 82
4.4.3 Peak Vibration Reduction, Option No.3 .................................................................. 84
Raising of Declared Gas Turbine Minimum Stable Generation Value to160 MW
(CCGT MSG 250 MW) .................................................................................................... 84

Chapter 5
Analysis of Measured Vibration Data Post Low Tune Repair ........................................... 85
5.1 Radar Charts of Measured Vibration Pre and Post Low Tune Repair ........................... 86
5.2 Change in Maximum Recorded Vibration Values ......................................................... 89
5.3 Correlation Tables .......................................................................................................... 90
5.4 New EWV Warning and Alarm Settings applied Post LTR .......................................... 93

Chapter 6
Regression Modelling Post Low Tune Repair ...................................................................... 95
6.1 Introduction .................................................................................................................... 95
6.2 Regression Model Types Employed ............................................................................... 95
6.2.1 Simple Regression ................................................................................................... 96
6.2.2 Multiple Linear Regression ..................................................................................... 96
6.2.3 Weighted Least Squares Regression........................................................................ 97
6.2.4 LOWESS ................................................................................................................. 98
6.3 Independent/Explanatory Variables used for Model Calculation................................... 98
6.3.1 Available Plant Data for use as Independent Variables .......................................... 98
6.3.2 Independent Variables used for Regression Models ............................................... 99
6.3.3 Creation of New Explanatory Variables ................................................................ 100
6.4 Variable Selection with Large Numbers of Explanatory Variables ............................. 103
6.4.1 The All Possible Regressions Technique for Independent Variable Selection ..... 103
6.4.2 Regression Models using The Stepwise Procedure in Matlab .............................. 104
6.5 Construction Data Sets ................................................................................................. 106
6.6 Regression Model Calculation ..................................................................................... 108
6.6.1 Simple Regressions ............................................................................................... 109
6.6.2 Multiple Linear Regression Models ...................................................................... 114
6.6.2.1 TE25 Multiple Linear Regression ...................................................................... 115
6.6.2.2 TE25 MLR Using the Seven Most Significant Measured Variables ................. 117
6.7 Multiple Linear Regression Models Calculated Using the Stepwise Variable Selection Procedure .................... 118
6.7.1 EE27 Multiple Linear Regression (Stepwise Selection, Level 0) ......................... 120
6.7.2 EE27 Multiple Linear Regression (Stepwise Selection, Level 1) ......................... 123
6.7.3 EE27 Multiple Linear Regression (Stepwise Selection, Level 2) ......................... 125
6.7.4 EE27 Multiple Linear Regression (Stepwise Selection, Level 3) ......................... 127
6.7.5 EE27 Multiple Linear Regression (Stepwise Selection, Level 4) ......................... 129
6.8 Graphical Assessment of Model Predictive Capability for EE27 L0, L4 and LOWESS Model ..... 133
6.9 Assessment of Model Error Terms ............................................................................... 135
6.9.1 Residual Plots ........................................................................................................ 136
6.9.2 Model Residual -v- Model Prediction Plots .......................................................... 138
6.9.3 Residual Statistics and Distribution Fitting ........................................................... 141
6.9.3.1 EE19 L0 MLR Model Residual Statistics .......................................................... 142
6.9.3.2 EE19 L4 MLR Residual Statistics ...................................................................... 143
6.9.3.3 EE19 LOWESS Residual Statistics .................................................................... 144
6.9.4 Autocorrelation of the Residuals ........................................................................... 145
6.10 Model Validation Techniques and Selection of MLR Models for Implementation on PI ACE ........................................................................................................................... 148
6.11 Chapter Summary ....................................................................................................... 149

Chapter 7
Statistical Analysis of Generator Condition 2006 – 2011 .................................................. 151
7.1 Scattergrams ................................................................................................................. 151
7.2 Pearson Correlation Tables ........................................................................................... 154
7.3 Descriptive Statistics .................................................................................................... 156

Chapter 8
Predictive Performance of MLR And Lowess Models ...................................................... 162
8.1 2007 Multiple Linear Regression and LOWESS Non-Parametric Regression
Models ............................................................................................................................... 164
8.2 Requirements for Recalculation of Models .................................................................. 178
8.2.1 2008 Multiple Linear Regression and LOWESS Non-Parametric Regression
Models ............................................................................................................................ 178
Monitoring and Regression Based Modelling of End Winding Vibration in Large Synchronous Generators
Table of Contents Page 10 David Shally
8.2.2 2009 Multiple Linear Regression and LOWESS Non-Parametric Regression
Models ............................................................................................................................ 179
8.2.3 2009/2010 Multiple Linear Regression and LOWESS Non-Parametric
Regression Models ......................................................................................................... 180

Chapter 9
Improvement in Model Design due to Availability of Additional Independent
Variables ............................................................................................................................... 181
9.1 Construction Data for 2010 Models ............................................................................. 182
9.2 New Measured and Calculated Independent Variables Made Available for
Selection ............................................................................................................................. 182
9.3 New Model Independent Variable Arrays/Model Designations .................................. 184
9.4 Predictive Performance of New MLR and LOWESS Models ..................................... 186
9.4.1 Assessment of Models using Trend Data .............................................................. 188
9.4.2 Assessment of Models using Pearson Correlation Data ........................................ 191
9.4.3 Assessment of Models using Goodness of Fit Statistics ....................................... 194
9.5 Analysis of the Poor Performance of MLR and LOWESS Models for TE25 .............. 200

Conclusion ............................................................................................................................. 207
References/Bibliography ...................................................................................................... 211
Appendix 1
End Winding Vibration Monitoring System ...................................................................... 215
A1.1 Hardware.................................................................................................................... 215
A1.1.1 Fibre Optic Accelerometers (FOA) .................................................................... 215
A1.1.2 The PCU 100 Programmable Units .................................................................... 215
A1.1.3 Fibre Optic Accelerometer Module .................................................................... 216
A1.1.4 Analogue Output Module ................................................................................... 216
A1.2 System Installation .................................................................................................... 217

Appendix 2
GT Generator End Winding Low Tune Repair ................................................................ 220
A2.1 Requirement for Low Tune Repair of Generator End Windings .............................. 220
A2.2 Aim of Low Tune/Detune Repair of GT Generator End Windings .......................... 221
A2.2 GT Generator End Winding Low Tune/Detune Measure.......................................... 222
A2.2.1 Schedule of Repair Work ................................................................................... 222
A2.2.2 Initial Inspection ................................................................................................. 223
A2.2.3 Tangential Blocking ........................................................................................... 223
A2.2.4 Axial and Radial Decoupling of Support Ring ................................................... 223
A2.2.5 Drilling of the Support Ring ............................................................................... 225
A2.2.6 Slitting of the Support Braces ............................................................................. 225
A2.2.7 Strapping of Lower Layer Bars to the Support Ring .......................................... 226
A2.2.8 Resin Treatment of End Windings ..................................................................... 226
A2.2.9 Bump Test No.1 .................................................................................................. 227
A2.2.10 Secondary Slotting of Support Braces to Fine Tune the „Low Tune‟ Repair ... 228
A2.2.11 Bump Test No.2 ................................................................................................ 229
A2.2.12 Electrical Testing .............................................................................................. 229
A2.2.13 Final Inspection ................................................................................................ 229

Appendix 3
Regression ............................................................................................................................. 230
A3.1 Simple Linear Regression .......................................................................................... 230
A3.2 Multiple Linear Regression ....................................................................................... 231
A3.2.1 The Multiple Regression Model Equation .......................................................... 233
A3.2.2 Calculation of Coefficients ................................................................................. 233
A3.2.3 Regression Model Summary .............................................................................. 233
A3.3 Analysis of Regression Model ................................................................................... 234
A3.3.1 ANOVA Table (ANalysis Of VAriance) ............................................................. 234
A3.3.2 Parameter Information/Coefficient Table ........................................................... 235
A3.3.3 Coefficient of Determination (R2) ...................................................................... 236
A3.4 Weighted Least Squares Regression .......................................................................... 238
A3.5 Model Validation ....................................................................................................... 239
A3.5.1 Statistics for Validation of Regression Model .................................................... 240
A3.6 Prediction Error ......................................................................................................... 241
A3.6.1 Sum of Squares due to Error (SSE) .................................................................... 241
A3.6.2 Mean Squared Error (MSE) ................................................................................ 241
A3.6.3 Root Mean Squared Error (RMSEPRED) ............................................................. 242
A3.6.4 Predicted R2 (R2 PRED) .......................................................................................... 243
A3.7 Variable Selection ...................................................................................................... 244
A3.8 Regression Model Prediction ..................................................................................... 245
A3.8.1 Prediction Error Bars and Confidence Intervals. ................................................ 246
A3.8.2 Standard Error of Prediction ............................................................................... 246
A3.8.3 Root Mean Square Error of Prediction, RMSE .................................................. 248
A3.9 Interpolation and Extrapolation in Regression Modelling......................................... 249

Appendix 4
Procedure for Recalculation of MLR Models in Matlab for Implementation on PI
ACE/Process Book ................................................................................................................ 250
A4.1The Need for Recalculation of Model Coefficients .................................................... 250
A4.2 Procedure for Calculation/Recalculation and Implementation of New MLR
Model Coefficients ............................................................................................................. 251
A4.2.1 Calculation/Recalculation of MLR Models using Matlab .................................. 251
A4.2.2 Updating the Models in PI ACE ......................................................................... 257

Appendix 5
MLR and LOWESS Model Predictive Accuracy Data for 2008, 2009 and
2009/2010 Models. ................................................................................................................. 259
A5.1 2008 Multiple Linear Regression and LOWESS Non-Parametric Regression
Models ............................................................................................................................... 259
A5.2 2009 Multiple Linear Regression and LOWESS Non-Parametric Regression
Models ............................................................................................................................... 264
A5.3 2009 - 2010 Multiple Linear Regression and LOWESS Non-Parametric
Regression Models ............................................................................................................. 272

Publications ........................................................................................................................... 277
Figures, Tables and Equations

Chapter 2
Equation 2.1. The Biot-Savart Law .......................................................................................... 27
Figure 2.1 Generator End Winding .......................................................................................... 28

Chapter 3
Figure 3.1 The Gas Turbine Generator ..................................................................................... 38
Table 3.1 GT Generator Bump Test Summary ........................................................................ 42
Figure 3.2 Dusting at GT Generator TE Busbar Connections to Collector Rings at 12 O‟
Clock Position. ................................................................................................................. 43
Figure 3.3 Crack in Support Bracket No.6. .............................................................................. 46
Figure 3.4 Location of Damaged Support Brackets (Z-Profiles) ............................................. 46
Figure 3.5 Generator Following Fault to Earth at the Exciter End of the Machine due to
Excessive EWV ................................................................................................................ 51
Figure 3.6 Generator Stator End Winding following End Coil Break due to Excessive
EWV ................................................................................................................................ 53
Figure 3.7 Generator Stator Winding following End Coil Break due to Excessive EWV ....... 54
Figure 3.8 Gas Turbine Generator: Fibre Optic Accelerometer Locations on Winding
Diagram ............................................................................................................................ 57
Figure 3.9 Gas Turbine Generator: Fibre Optic Accelerometer Locations .............................. 58
Figure 3.10 GTG EWV Monitoring System Overview ............................................................ 59

Chapter 4
Figure 4.1 EE19 and EE35 Measured Vibration (Displacement), Active Power and
Reactive Power 12/12/2006 to 19/12/2006 ...................................................................... 65
Figure 4.2 TE17 and TE41 Measured Vibration (Displacement), Active Power and
Reactive Power 12/12/2006 to 19/12/2006 ...................................................................... 66
Figure 4.3 GT Generator Reactive Capability Curve ............................................................... 69
Figure 4.4 GT Generator Correlation Data for Weeks W003, W010 and W017. .................... 71
Figure 4.5 EE19 and EE35 Measured Vibration (Displacement), Active Power, Reactive
Power, Average Slot Temperature and Ambient Air Temperature
16/01/2007 to 23/01/2007 ................................................................................................. 73
Monitoring and Regression Based Modelling of End Winding Vibration in Large Synchronous Generators
Figures, Tables and Equations Page 14 David Shally
Figure 4.6 EE35 Frequency Domain Vibration Data (FFT Result) ......................................... 76
Figure 4.7 Scattergram of Measured Vibration against Reactive for End Coil TE33.
Generator Output between 225 MW and 230 MW and
Ambient Air Temperature Greater than or Equal to 4 °C. ............................................... 78
Table 4.1 R-Squared Values of Measured Vibration against Reactive Power for all End
Coils. Generator Output between 225 MW and 230 MW and
Ambient Air Temperature Greater than or Equal to 4 °C. ............................................... 79
Figure 4.8 Scattergram of Measured Vibration against Reactive Power for End Coil
TE33. ............................................................................................................................... 80
Generator Load 135 MW to 140 MW and Ambient Air Temperature Greater than or
Equal to 4 °C. ................................................................................................................... 80
Table 4.2 R-Squared Values of Measured Vibration against Reactive Power for all End
Coils. Generator Load 135 MW to 140 MW and Ambient Air Temperature
Greater than or Equal to 4 °C. .......................................................................................... 81

Chapter 5
Figure 5.1 Gas Turbine Generator (GTG) Exciter End (EE) Measured Vibration, Active
Power and Reactive Power Post Repair. 05/05/2007 to 14/05/2007. ............................... 85
Figure 5.2 Radar Diagram Showing Maximum, Minimum and Average Vibration
Amplitudes Measured at the EE of the GTG 13/03/2007 to 20/03/2007. Pre Low
Tune Repair. ..................................................................................................................... 86
Figure 5.3 Radar Diagram Showing Maximum, Minimum and Average Vibration
Amplitudes Measured at the EE of the GTG 05/05/2007 to 14/05/2007. Post Low
Tune Repair. ..................................................................................................................... 87
Figure 5.4 Radar Diagram Showing Maximum, Minimum and Average Vibration
Amplitudes Measured at the TE of the GTG 13/03/2007 to 20/03/2007. Pre Low
Tune Repair. ..................................................................................................................... 88
Figure 5.5 Radar Diagram Showing Maximum, Minimum and Average Vibration
Amplitudes Measured at the TE of the GTG 05/05/2007 to 14/05/2007. Post Low
Tune Repair. ..................................................................................................................... 88
Table 5.1 Table of Maximum Measured Vibration Values for all EE and TE
Accelerometers. Data is filtered for Average Slot Temperature between 67°C and
84°C. GTG Load 166 MW to 230 MW. ........................................................................... 89
Figure 5.6 Correlation Tables for Weeks 03, 10 and 17 (Pre Low Tune Repair) .................... 91
Monitoring and Regression Based Modelling of End Winding Vibration in Large Synchronous Generators
Figures, Tables and Equations Page 15 David Shally
Figure 5.7 Correlation Tables for Weeks 24, 25 and 30 (Post Low Tune Repair) ................... 92

Chapter 6
Table 6. 1 TE25 Simple Regression Goodness of Fit Statistics ............................................. 110
Table 6. 2 TE25 Simple Regression Analysis Of Variance ................................................... 110
Table 6. 3 TE25 Simple Regression Model Parameters ......................................................... 110
Equation 6. 1 TE25 Equation of Simple Linear Regression Model ....................................... 110
Figure 6.1 TE25 Simple Regression Measured And Predicted Vibration -v- Time .............. 112
Figure 6.2 TE25 Simple Regression Residual Plot ................................................................ 113
Figure 6. 3 TE25 Simple Regression Error Histogram .......................................................... 113
Figure 6. 4 TE25 Simple Regression Cumulative Distributions ............................................ 114
Table 6. 4 TE25 MLR Goodness of Fit Statistics .................................................................. 115
Table 6. 5 TE25 MLR Analysis of Variance .......................................................................... 115
Table 6. 6 TE25 MLR Model Parameters .............................................................................. 116
Equation 6. 2 TE25 Equation of MLR Model All 10 Plant Variables Included .................... 116
Table 6. 7 TE25 MLR Goodness of Fit Statistics (7 From 10 Selected Explanatory
Variables)....................................................................................................................... 117
Table 6. 8 TE25 MLR Analysis of Variance (7 from 10 Selected Explanatory Variables) ... 117
Table 6. 9 TE25 MLR Model Parameters (7 from 10 Selected Explanatory Variables) ....... 117
Equation 6. 3 TE25 Equation of MLR Model (7 Most Significant Explanatory Variables
Included) ......................................................................................................................... 118
Table 6. 10 EE27 Matlab Stepwise MLR L0 Goodness of Fit Statistics ............................... 120
Table 6.11 EE27 Matlab Stepwise MLR L0 Analysis Of Variance ....................................... 120
Table 6.12 EE27 Matlab Stepwise MLR L0 Model Parameters ............................................ 120
Table 6.13 EE27 L0 Correlation Table ................................................................................. 121
Figure 6. 5 Plot of EE27 MLR L0 – L4 RMSE against Stepwise Procedure Step
Number ........................................................................................................................... 122
Table 6.14 EE27 Matlab Stepwise MLR L1 Goodness of Fit Statistics ................................ 123
Table 6.15 EE27 Matlab Stepwise MLR L1 Analysis Of Variance ....................................... 123
Table 6.16 EE27 MLR L1 Model Parameters ........................................................................ 124
Table 6.17 EE27 Stepwise MLR L2 Goodness of Fit Statistics ............................................. 125
Table 6.18 EE27 MLR L2 Stepwise ANOVA Table ............................................................. 125
Table 6.19 EE27 MLR L2 Model Parameters ........................................................................ 127
Table 6.20 EE27 MLR L3 Goodness of Fit Statistics ............................................................ 127
Table 6.21 EE27 Matlab Stepwise MLR L3 Analysis Of Variance ....................................... 128
Table 6.22 EE27 Matlab Stepwise MLR L3 Model Parameters ............................................ 129
Table 6.23 EE27 Matlab Stepwise MLR L4Goodness of Fit Statistics ................................. 129
Table 6.24 EE27 Matlab Stepwise MLR L4 Analysis of Variance........................................ 130
Table 6.25 EE27 Matlab Stepwise MLR L4 Model parameters ............................................ 130
Table 6.26 EE27 MLR L4 Correlation Table ......................................................................... 131
Figure 6.6 Construction Set Data: EE27 Measured and L0 MLR Model Predicted
Vibration Levels ............................................................................................................. 133
Figure 6.7 Construction Set Data: EE27 Measured and MLR L4 Model Predicted
Vibration Levels ............................................................................................................. 134
Table 6.27 EE27 LOWESS Goodness of Fit Statistics .......................................................... 134
Figure 6.8 Construction Set Data: EE27 Measured and LOWESS Model Predicted
Vibration Levels ............................................................................................................. 135
Figure 6.9 EE19 Multiple Linear Regression L0 Residual Plot ............................................. 137
Figure 6.10 EE19 Multiple Linear Regression (MLR) L4 Residual Plot ............................... 137
Figure 6.11 EE19 Multiple Linear Regression LOWESS Model Residual Plot .................... 138
Figure 6.12 EE19 Multiple Linear Regression L0 Residuals -v- L0 Predicted EE19 ............ 139
Figure 6.13 EE19 Multiple Linear Regression Model L4 Residuals -v- L4 Predicted
EE19 ............................................................................................................................... 139
Figure 6.14 EE19 LOWESS Residuals -v- LOWESS Predicted EE19 .................................. 140
Table 6.28 EE19 L0 Error Term Statistics ............................................................................. 142
Figure 6.15 EE19 MLR L0 Residuals Histogram .................................................................. 142
Figure 6.16 EE19 MLR L0 Residuals Cumulative Distributions ........................................... 142
Table 6.29 EE19 L4 Error Term Statistics ............................................................................. 143
Figure 6.17 EE19 MLR L4 Residuals Histogram .................................................................. 143
Figure 6.18 EE19 MLR L4 Residuals Cumulative Distributions ........................................... 143
Table 6.30 EE19 LOWESS Error Term Statistics .................................................................. 144
Figure 6.19 EE19 LOWESS Residuals Histogram ................................................................ 144
Figure 6.20 EE19 LOWESS Residuals Cumulative Distributions ......................................... 144
Figure 6.21 EE19 MLR L0, L4 and LOWESS Models Autocorrelation of Error Terms ...... 145
Equation 6.4 The Durbin-Watson Statistic ............................................................................. 146
Equation 6.5 The Durbin-Watson Statistic (Alternative) ....................................................... 146
Table 6.31 EE19 Autocorrelation of Residual Vector Data ................................................... 147

Chapter 7
Figure 7.1 TE and EE EVW Scattergrams for W060063 ....................................................... 151
Figure 7.2 TE and EE EVW Scattergrams for W116119 ....................................................... 152
Figure 7.3 TE and EE EVW Scattergrams for W164167 ....................................................... 152
Figure 7.4 TE and EE EVW Scattergrams for W216219 ....................................................... 153
Table 7.1 Pearson Correlation Table for W6063 (14/01/2008 to 11/02/2008) ...................... 154
Table 7.2 Pearson Correlation Table for W116119 (02/02/2009 to 02/03/2009) .................. 154
Table 7.3 Pearson Correlation Table for W164167 (18/01/2010 to 08/02/2010) .................. 155
Table 7.4 Pearson Correlation Table for W216219 (10/01/2011 to 07/02/2011). ................. 155
Figure 7.5 TE09 Descriptive Statistics (Mean, Range, Standard Error and Standard
Deviation) 2006 to 2010. .................................................................................. 157
Table 7.5 Weekly Data Falling Within the Set Range for Descriptive Statistics
Calculations 2006 to 2010. ............................................................................................. 158
Table 7.6 Old and New Descriptive Statistics Calculation Ranges and Average Value
Calculation Intervals. ...................................................................................................... 159
Figure 7.6 TE09 Descriptive Statistics Comparison Data for (5 and 15 Minute
Averaging Interval) W154 to W171 (26/10/2009 to 08/03/2010) .......................... 160
Figure 7.7 TE09 Descriptive Statistics 15 Minute Averaging Interval with New Ranges
for Inclusion of Data W154 to W233 (26/10/2009 to 16/05/2011) ................................ 160

Chapter 8
Table 8.1 Goodness of Fit Statistics for TE09 from W032035 to W096099 for MLR
Models L0 – L4 and the LOWESS Model ..................................................................... 166
Figure 8.1 TE09 R-squared values from W032035 to W096099 for MLR L0 – L4 and
LOWESS Models ........................................................................................................... 166
Figure 8.2 TE09 Measured and MLR L0 Model Predicted Vibration for W088091
(28/07/2008 to 24/08/2008) ............................................................................................ 168
Figure 8.3 TE09 Measured and MLR L4 Model Predicted Vibration for W088091
(28/07/2008 to 24/08/2008) ............................................................................................ 168
Figure 8.4 TE09 Measured and LOWESS Model Predicted Vibration for W088091
(28/07/2008 to 24/08/2008) ............................................................................................ 169
Table 8.2 TE09 Goodness of Fit Statistics for W088091 (28/07/2008 to 24/08/2008)
MLR Interaction Levels L0 – L4 and LOWESS Models ............................................... 169
Monitoring and Regression Based Modelling of End Winding Vibration in Large Synchronous Generators
Figures, Tables and Equations Page 18 David Shally
Table 8.3 Correlation Coefficient Table for TE09 Measured against TE09 MLR and
LOWESS Model Predicted Values (W088091) ............................................................. 170
Table 8.4 Goodness of Fit Statistics for EE03 from W032035 to W096099 for MLR
Models L0 – L4 and the LOWESS Model ..................................................................... 171
Figure 8.5 EE03 R-squared values from W032035 to W096099 for MLR L0 – L4 and
LOWESS Models ........................................................................................................... 172
Figure 8.6 EE03 Measured and MLR L0 Model Predicted Vibration for W088091
(28/07/2008 to 25/08/2008) ............................................................................................ 173
Figure 8.7 EE03 Measured and MLR L4 Model Predicted Vibration for W088091
(28/07/2008 to 25/08/2008) ............................................................................................ 173
Figure 8.8 EE03 Measured and LOWESS Model Predicted Vibration for W088091
(28/07/2008 to 25/08/2008) ............................................................................................ 174
Table 8.5 EE03 Goodness of Fit Statistics for W088091
MLR Interaction Levels L0 – L4 and LOWESS Models ............................................... 174
Table 8.6 Correlation Coefficient Table for EE03 Measured against EE03 MLR and
LOWESS Model Predicted Values (W088091) ............................................................. 175
Table 8.7 Goodness of Fit Statistics for All End Coils from W032035 to W096099
(07/07/2007 to 20/10/2008) for the Best Performing MLR Models and the
LOWESS Model. ............................................................................................................ 176

Chapter 9
Table 9.1 Goodness of Fit Statistics for TE01from W195199 to W232235 for MLR
Models L0, L0FOA, L1, L1 FOA, L2 and L2 FOA as well as a LOWESS Model
with FOA Data Included in Independent Variable Data. ............................................... 187
Figure 9.1 TE09 Measured and MLR (Best L0 Models) Predicted Vibration,
Average Slot Temperature and Ambient Air Temperature W195199 (16/08/2010 to
09/09/2010). .................................................................................................................... 188
Figure 9.2 TE09 Measured and MLR (Best L1 Models) Predicted Vibration,
Average Slot Temperature and Ambient Air Temperature W195199 (16/08/2010 to
09/09/2010). .................................................................................................................... 189
Figure 9.3 TE09 Measured and MLR (Best L2 Models) Predicted Vibration,
Average Slot Temperature and Ambient Air Temperature W195199 (16/08/2010 to
09/09/2010). .................................................................................................................... 190
Monitoring and Regression Based Modelling of End Winding Vibration in Large Synchronous Generators
Figures, Tables and Equations Page 19 David Shally
Table 9.2 Pearson Correlation Table for 2010 MLR and LOWESS Model
Construction/Learning Data Measured Variables .......................................................... 191
Table 9.3 Pearson Correlation Table for W208211 (10/01/2011 to 07/02/2011)
Unfiltered. ....................................................................................................................... 192
Table 9.4 Pearson Correlation Table for W208211.
Data filtered for Average Stator Slot Temperature >60°C and Ambient
Temperature >4°C. ......................................................................................................... 193
Table 9.5 Goodness of Fit Statistics for W208211 (10/01/2011 to 07/02/2011) Filtered
and Unfiltered. ................................................................................................................ 195
Figure 9.4 TE09 Measured and MLR (Best L1 Models) Predicted Vibration, Average
Slot Temperature and Ambient Air Temperature (Unfiltered) W208211
(15/11/2010 to 11/12/2010) ............................................................................................ 196
Figure 9.5 TE09 Measured Vibration, MLR (Best L1 Models) Predicted Vibration,
Average Slot Temperature and Ambient Air Temperature for W208211.
Data Filtered for Average Stator Slot Temperature >60°C and Ambient
Temperature >4°C .......................................................................................................... 197
Table 9.6 TE09 Goodness of Fit Statistics for W208211.
Data Filtered for Average Stator Slot Temperature >60°C and Ambient
Temperature >4°C. ......................................................................................................... 198
Table 9.7 Goodness of Fit Statistics for All End Coils from W195199 to W232235 for
the Best Performing MLR and LOWESS Models.......................................................... 199
Table 9.8 Pearson Correlation Table Excerpts from 2010 Learning Data, W200203,
W208211 and W224227 for Coil Ends TE25, EE03 and TE01. .................................... 201
Figure 9.6 TE25 Measured Vibration, Active Power, Average Slot Temperature, Hot
Air Temperature, Average Cold Air Temperature and Ambient Air Temperature
for W195199 (August September 2010) ........................................................................ 203
Figure 9.7 TE25 Measured Vibration, Active Power, Average Slot Temperature, Hot
Air Temperature, Average Cold Air Temperature and Ambient Air Temperature
for W208211 (November/December 2010) .................................................................... 204
Figure 9.8 TE25 Measured Vibration, Active Power, Average Slot Temperature, Hot
Air Temperature, Average Cold Air Temperature and Ambient Air Temperature
for W208211 (November/December 2010) Data Filtered for Average Cold Air
Temperature ≥ 60°C and Ambient Air Temperature ≥ 4°C ........................................... 205
Monitoring and Regression Based Modelling of End Winding Vibration in Large Synchronous Generators
Figures, Tables and Equations Page 20 David Shally
Appendix 1
Figure A1.1 Gas Turbine Generator: Sensor Location Exciter End End-Coil Number 3
(EE03) ............................................................................................................................. 218
Figure A1.2 Gas Turbine Generator (GTG) EWV Monitoring System Protection Box B. ... 219
Figure A1.3 GTG PCU100 and BNC Connector Racks. ....................................................... 219
Figure A2.1 Axial and Radial Decoupling of Support Ring and Slitting of the Support
Brace ............................................................................................................................... 221
Appendix 2
Figure A2.2 Radial Decoupling of Support Ring from Phase Lead Connection at 12 O‟
Clock Position at the Turbine End of the GT Generator. ............................................... 224
Figure A2.3 Axial and Radial Decoupling of Support Ring from Support Bracket and
Support Brace at the Turbine End of the GT Generator. ................................................ 224
Figure A2.4 Through Holes Drilled in the Support Ring at Exciter End of the GT
Generator. Tangential Blocking Inserted During High Tune of End Winding
at AOH 2005. .................................................................................................................. 225
Figure A2.5 Strapping/Bandaging of Lower Layer End Coil Bars to Support Ring at the
EE of the GT Generator. ................................................................................................. 226
Figure A2.6 Setting of the Radial Gap Between the End Winding Support Ring and the
Support Brackets (Z-profiles) at the Exciter End of the Generator. ............................... 227
Figure A2.7 Slitting of the EE Support Bracing to the Sixth Hole Following the Initial
Bump Test. ..................................................................................................................... 228
Figure A2.8 Slitting of the TE Support Bracing to the Fifth Hole Following the Initial
Bump Test. ..................................................................................................................... 229
Appendix 3
Equation A3.1 The Simple Linear Regression Equation ........................................................ 230
Equation A3.2 The Multiple Linear Regression Equation ..................................................... 231
Equation A3.3 The Multiple Linear Regression Equation (Vector Matrix Form) ................. 231
Equation A3.4 The F-statistic ................................................................................................. 235
Equation A3.5 The t-statistic .................................................................................................. 235
Equation A3.6 The Simple Linear Regression Equation (No Constant) ................................ 236
Equation A3.7 The Multiple Linear Regression Equation (No Constant) ............................. 236
Figure A3.1 Venn Diagrams of Regression............................................................................ 238
Monitoring and Regression Based Modelling of End Winding Vibration in Large Synchronous Generators
Figures, Tables and Equations Page 21 David Shally
Equation A3.8 Prediction Error .............................................................................................. 241
Equation A3.9 Sum of Squared Error of Prediction ............................................................... 241
Equation A3.10 Mean Squared Error ..................................................................................... 241
Equation A3.11 Root Mean Squared Error ............................................................................ 242
Equation A3.12 R-squared Predicted (for Data Outside of Construction Set) ....................... 243
Equation A3.13 R-squared (Construction Set Data) .............................................................. 243
Equation A3.14 MLR Confidence Intervals ........................................................................... 246
Equation A3.15 Standard Error of Prediction (Simple Linear Regression) ........................... 247
Equation A3.16 Standard Error of Prediction (Simple Linear Regression) ........................... 247
Equation A3.17 Variance of Prediction (Multiple Regression) ............................................. 247
Equation A3.17 Variance of Prediction (Alternative) ............................................................ 248
Equation A3.18 Estimated Standard Error of Prediction ....................................................... 248
Appendix 4
Figure A4.1 Matlab Stepwise Selection GUI ......................................................................... 255
Figure A4.2 Microsoft Visual Basic/PI ACE Calculated Variable Project Page ................... 257
Appendix 5
Table A5.1 Goodness of Fit Statistics for TE09 from W084087 to W132135 for MLR
Models L0 – L4 and LOWESS ...................................................................................... 260
Figure A5.1 TE09 R-squared Values from W084087 to W132135 for MLR L0 – L4 and
LOWESS Models ........................................................................................................... 261
Figure A5.2 TE09 Measured and Model Predicted Vibration Data (MLR L0 – L4 and
LOWESS Models) for W128131 (27/04/2009 to 25/05/2009) ...................................... 262
Table A5.2 Goodness of Fit Statistics for all End Coils from W084087 to W132135 for
the Best Performing MLR Models and the LOWESS Model. ....................................... 263
Table A5.3 Goodness of Fit Statistics for TE01from W136139 to W160163 for MLR
Models L0 – L4 and LOWESS ...................................................................................... 265
Figure A5.3 TE01 Measured and Predicted Vibration for W156159 (09/11/2009 to
13/12/2009) ..................................................................................................................... 266
Table A5.4 Goodness of Fit Statistics for TE01W156159 (Unfiltered) for MLR Models
L0 – L4 and LOWESS Models using a True setting of 2 % and 6 % with
Polynomial Degree set at 2. ............................................................................................ 266
Monitoring and Regression Based Modelling of End Winding Vibration in Large Synchronous Generators
Figures, Tables and Equations Page 22 David Shally
Table A5.5 Goodness of Fit Statistics for TE01W156159 (Filtered) for MLR Models L0
– L4 and LOWESS Models using a True setting of 2 % and 6 % with Polynomial
Degree set at 2. All Data after 30/11/2009 Removed. .................. 267
Figure A5.4 TE01 Measured and Predicted Vibration for W156159 (09/11/2009 to
13/12/2009). Post Recalculation of Independent Variable Data (Average
Stator Current). ............................................................................................................... 267
Table A5.6 Goodness of Fit Statistics for TE01W156159 (Filtered) for MLR Models L0
– L4 and LOWESS Models using a True Setting of 2 %, 6 %, 10 % and 15 % with
Polynomial Degree set at 2 and a True Setting of 10 % with Polynomial Degree set
at 1. ................................................................................................................................ 268
Table A5.7 Goodness of Fit Statistics for TE01W156159 (Filtered) for MLR Models L0
– L4 and LOWESS Models using a True Setting of 2 %, 6 %, 10 % and 15 % with
Polynomial Degree set at 2 and a True Setting of 10 % with Polynomial Degree set
at 1. Data filtered for Average Slot
Temperature ≥ 60 °C and Ambient Air Temperature ≥ 6 °C. ........................................ 268
Table A5.8 Goodness of Fit Statistics for TE01W156159 (Filtered) for LOWESS
Models. True Setting of 50 % Polynomial Degree set at 2.
Data Filtered for Average Slot Temperature ≥ 60 °C and Ambient Air Temperature
≥ 6 °C. ............................................................................................................................. 269
Table A5.9 Goodness of Fit Statistics for All End Coils from W136139 to W160163 for
the Best Performing MLR Models and the LOWESS Model. ....................................... 270
Table A5.10 Goodness of Fit Statistics for TE01from W164167 to W176AOH10 for
MLR Models L0 – L4 and LOWESS ............................................................................. 273
Figure A5.5 TE09 R-Squared Values for MLR Models L0, L1, L2, L3 & L4 as well as
the LOWESS Model W164167 to W176180 (18/01/2010 to 04/05/2010
AOH 10) ......................................................................................................................... 274
Figure A5.6 TE09 RMSE Values for MLR Models L0, L1, L2, L3 & L4 as well as the
LOWESS Model W164167 to W176180 (18/01/2010 to 04/05/2010 AOH 10) ........... 274
Table A5.11 Goodness of Fit Statistics for all End-Coils from W164167 to
W176AOH10 for the Best Performing MLR Models and the LOWESS Model. .......... 275