Electromagnetic Analysis and Condition Monitoring of Synchronous Generators

Cover
Title Page
Copyright
Contents
Author Biographies
Preface
Chapter 1 Introduction
1.1 Introduction to Condition Monitoring of Electric Machines
1.2 Importance of Synchronous Generators
1.3 Economic Aspects and Advantages
1.4 Intention of the Book
References
Chapter 2 Operation Principles, Structure, and Design of Synchronous Generators
2.1 Introduction
2.1.1 Rotating Magnetic Field of a Three‐Phase Synchronous Machine
2.2 History of Synchronous Generators
2.2.1 Advancement History of Synchronous Generators
2.2.1.1 Up to the Year 1970
2.2.1.2 Changes in the 1970s
2.2.1.3 Developments in the 1980s
2.2.1.4 Developments in the 1990s
2.2.1.5 Developments After 2000
2.3 Types and Constructions of Synchronous Machines
2.3.1 Non‐salient or Round Rotor
2.3.2 Salient‐Pole Rotor
2.3.3 Synchronous Generators with Different Field Locations
2.3.4 Different Schemes of Excitation Systems for Synchronous Generators
2.3.4.1 DC Excitation
2.3.4.2 Static Excitation System
2.3.4.3 Brushless Excitation System
2.4 Voltage Equation and Rated Power of the Synchronous Generator
2.5 Synchronous Generator Model Parameters
2.6 Different Operating Modes of Synchronous Machines
2.7 Damper Bars in Synchronous Generators
2.8 Losses and Efficiency in Synchronous Generators
2.9 High‐Voltage Synchronous Generators
2.10 Preliminary Design Considerations
2.10.1 Output Equations
2.10.2 Selecting Specific Magnetic Loading
2.10.3 Selecting Specific Electric Loading
2.10.4 Relationship between L and D
2.10.4.1 Salient‐Pole Generators
2.10.4.2 Turbo‐generators
2.10.4.3 Short Circuit Ratio
2.10.5 Air Gap Length
2.11 Stator Design Considerations
2.11.1 Stator Core Outer Diameter
2.11.2 Leakage Reactance
2.11.3 Stator Winding
2.11.3.1 Double‐Layer Winding
2.11.3.2 Stator Winding Resistance
2.11.3.3 Eddy Current Losses in Conductors
2.11.3.4 Eddy Current Loss Estimation
2.11.3.5 Number of Slots
2.11.3.6 Number of Turns per Phase
2.11.3.7 Conductor Cross‐section
2.11.3.8 Single‐turn Bar Winding
2.11.3.9 Multi‐turn Windings
2.11.3.10 Stator Winding Type Comparison
2.11.3.11 Winding and Slot Insulation
2.11.3.12 Stator Slot Dimensions
2.11.4 Rotor Design of a Salient Pole Synchronous Generator
2.11.4.1 Pole Shape
2.11.4.2 Pole Dimensions
2.11.4.3 Copper Losses of Field Windings
2.11.4.4 Rotor Core Depth
2.11.4.5 Ampere‐Turns of the No‐Load Field
2.11.5 Design of the Rotor of Round‐Rotor Synchronous Generators
2.11.6 Rotor Winding Design
2.11.7 Synchronous Generator Excitation System Design Issues
2.12 Summary
References
Chapter 3 Transformed Models and Parameter Identification of Synchronous Generators
3.1 Introduction
3.2 Multi‐Phase Synchronous Generator Modeling Based on Park Equations
3.2.1 Two‐Phase Synchronous Generators
3.2.2 Three‐Phase Synchronous Generators
3.2.3 Six‐Phase Synchronous Generators
3.3 Mathematical Modeling
3.3.1 Optimal Observer with Kalman Filters
3.4 Parameter Estimation Algorithms
3.4.1 Offline Parameter Estimation Techniques
3.4.1.1 Frequency Domain‐Based Methods
3.4.1.2 Time Domain‐Based Methods
3.4.1.3 Finite Element Methods
3.4.1.4 An Example of Offline Parameter Estimation Using the DC Standstill Test
3.4.2 Online Parameter Estimation Techniques
3.4.2.1 Numerical Methods
3.4.2.2 Observer‐Based Methods
3.4.2.3 Artificial Intelligence (AI)‐Based Methods
3.4.2.4 An Example of Online Parameter Estimation Using the Affine Projection Algorithm
3.5 Parameter Accuracy Increments by Considering Saturation
3.6 Fault Detection Based on Parameter Deviation
3.6.1 Principle of the Method
3.7 Summary
References
Chapter 4 Introduction to Different Types of Faults in Synchronous Generators
4.1 Reasons for Condition Monitoring of Synchronous Generators
4.2 Different Faults in Synchronous Generators
4.3 Main Factors Leading to Electrical Machine Damage
4.4 Major Destruction Factors of Stator Winding
4.4.1 Thermal Stress
4.4.2 Electrical Stress
4.4.3 Mechanical Stresses
4.4.4 Ambient Stress
4.5 Common Faults in Stator Winding
4.6 Rotor Field Winding Fault
4.7 Eccentricity Faults
4.8 Misalignment Faults
4.9 Damper Winding Fault
4.10 Summary
References
Chapter 5 Laboratory Scale Implementation
5.1 Introduction
5.2 Salient Pole Synchronous Generator
5.3 Induction Motor
5.4 Gearbox
5.5 Converter
5.6 Rotor Magnetization Unit
5.7 DC Power Supply
5.8 Local Passive Load
5.9 Sensors
5.9.1 Hall‐Effect Sensors
5.9.2 Search Coil
5.9.3 Accelerometer
5.9.4 Voltage Transformer
5.9.5 Current Transformer
5.10 Data Acquisition
5.11 Fault Implementation
5.11.1 Stator Short Circuit Fault
5.11.2 Inter‐Turn Short Circuit Fault in a Rotor Field Winding
5.11.3 Eccentricity Fault
5.11.4 Misalignment Fault
5.11.5 Broken Damper Bar Fault
5.12 Noise Considerations
5.13 Summary
References
Chapter 6 Analytical Modeling Based on Wave and Permeance Method
6.1 Introduction
6.2 Eccentricity Fault Definition
6.3 The Air Gap Magnetic Field
6.4 The Electromotive Force in Stator Terminals
6.5 The Stator Current
6.6 Force Density and Unbalanced Magnetic Pull
6.7 Stator Slotting Effects
6.8 Magnetic Saturation Effects
6.9 The Mixed Eccentricity Fault
6.10 The Air Gap Magnetic Field
6.11 Induced Electromotive Force in Stator Terminals
6.12 Force Density and Unbalanced Magnetic Pull
6.13 Short Circuit Modeling
6.14 Air Gap Permeance Under a Short Circuit Fault
6.15 Force Density and Unbalanced Magnetic Pull under a Rotor Inter‐turn Short Circuit Fault
6.16 Summary
References
Chapter 7 Analytical Modeling Based on Winding Function Methods
7.1 Introduction
7.2 History and Usage of the WFM
7.3 Winding Function Modeling of a Synchronous Generator
7.4 Mutual Inductance Calculation Between the Stator Phases
7.4.1 Turn Function of Winding Phase B
7.4.2 The Modified Winding Function of Phase A
7.4.3 The Inverse Air Gap Function
7.5 The Mutual Inductance Between the Stator and Rotor
7.5.1 The Mutual Inductance Between the Stator Phase Winding and Rotor Field Winding
7.5.2 The Mutual Inductance of the Stator Phase Winding and Rotor Damper Winding
7.6 The Self Inductance of the Rotor
7.6.1 The Self Inductance of the Rotor Field Winding
7.6.2 The Self Inductance of the Rotor Damper Winding
7.6.3 The Mutual Inductance Between the Rotor Field Winding and Damper Winding in the d‐Axis
7.6.4 The Mutual Inductance Between the Rotor Field Winding and Damper Winding in the q‐Axis
7.7 Derivative Forms of Synchronous Generator Inductances
7.7.1 Derivative Form of Stator Mutual Inductance
7.7.2 Derivative Form of Stator and Rotor Mutual Inductance
7.7.3 Dynamic Equations Governing the Synchronous Machines
7.8 A Practical Case Study
7.8.1 Parameter Identification
7.8.1.1 Resistance of the Stator Phase Winding
7.8.1.2 Rotor Field Winding Resistance
7.8.1.3 The Direct Axis (d) Reactance
7.8.1.4 Sub‐transient Reactance of the Direct Axis
7.8.1.5 Number of Turns of Rotor Field Windings
7.8.1.6 Transient Direct Axis Reactance
7.8.1.7 Number of d‐Axis Damper Winding Turns
7.9 Healthy Case Simulation
7.9.1 Stator and Rotor Winding Function
7.9.2 Stator Phase Windings Mutual Inductances
7.9.3 Mutual Inductance Between Stator and Rotor Windings
7.9.3.1 Mutual Inductance Between Stator Phase Windings and Rotor Field Windings
7.9.3.2 Mutual Inductance Between Stator Phase Windings and Damper Windings
7.9.4 Dynamic Model Simulation in the Healthy Case
7.10 Faulty Case Simulation
7.10.1 Turn Functions and Inductances
7.10.2 Dynamic Model Simulation in the Faulty Case
7.11 Algorithm for Determination of the Magnetic Saturation Factor
7.11.1 Algorithm
7.11.2 Excitation Field Factors Plot
7.11.3 Magnetic Equivalent Circuit Modeling Under the No‐Load Condition
7.12 Eccentricity Fault Modeling Considering Magnetic Saturation Under Load Variations
7.12.1 Calculation of Inverse Air Gap Length by Considering the Saturation Effect
7.12.2 The Air Gap Length Calculation in the Presence of the Eccentricity Fault
7.12.3 Mutual and Self Inductance Calculations under an Eccentricity Fault
7.13 Dynamic Modeling under an Eccentricity Fault
7.14 Summary
References
Chapter 8 Finite Element Modeling of a Synchronous Generator
8.1 Introduction
8.2 Electromagnetic Field Computation
8.3 Eddy Current and Core Loss Considerations
8.4 Material Modeling
8.5 Band Object, Motion Setup, and Boundary Conditions
8.6 Mesh Consideration
8.7 Time Steps and Simulation Run Time
8.8 Transient and Steady‐State Modeling
8.9 No‐Load and On‐Load Modeling
8.10 2D and 3D FEM
8.11 3D‐FE Equations of the Synchronous Generator
8.12 Modeling of the Stator and Rotor Windings of the Generator and Its Load
8.12.1 Modeling Movement of Movable Parts and Electromechanical Connections
8.13 Air Gap Magnetic Field Measurements
8.14 Stray Flux Measurements
8.15 Eccentricity Fault Modeling
8.16 Stator and Rotor Short Circuit Fault
8.16.1 Phase‐to‐Earth Fault
8.16.2 Phase‐to‐Phase Fault
8.16.3 Inter‐turn Fault
8.16.4 Inter‐turn Fault in Field Windings of the Synchronous Generator
8.17 Broken Damper Bar Modeling
8.18 Summary
References
Chapter 9 Thermal Analysis of Synchronous Generators
9.1 Introduction
9.2 Overview of Thermal Modeling and Analysis
9.3 Thermal Modeling and Analyzing Synchronous Generators
9.3.1 Analytical Method
9.3.1.1 Heat Conduction
9.3.1.2 Heat Convection
9.3.1.3 Heat Radiation
9.3.2 Synchronous Generator Loss Calculation
9.3.3 Numerical Methods
9.4 Modeling and Analysis of Faulty Synchronous Generators
9.4.1 Reasons for Faults in Synchronous Generators
9.4.1.1 Single‐Phase Open‐Circuit Fault
9.4.1.2 Conversion of Three‐Phase to Two‐Phase
9.4.1.3 Three‐Phase Short Circuit Fault
9.5 Summary
References
Chapter 10 Signal Processing
10.1 Introduction
10.2 Signal
10.3 Fast Fourier Transform
10.4 Fast Fourier Transform with an Adjusted Sampling Frequency
10.5 Short‐Time Fourier Transform
10.6 Continuous Wavelet Transform
10.7 Discrete Wavelet Transform
10.7.1 Wavelet Energies
10.7.2 Wavelet Entropy
10.8 Hilbert–Huang Transform
10.8.1 Hilbert Transform
10.8.2 Empirical Mode Decomposition
10.9 Time Series Data Mining
10.10 Spectral Kurtosis and Kurtogram
10.10.1 Kurtosis
10.10.2 Spectral Kurtosis
10.10.3 Kurtogram
10.11 Noise
10.11.1 Various Types of Noise
10.11.2 Sources of Noise in Industry
10.11.3 Noise Recognition
10.11.4 Noise Effect on FFT
10.11.5 Noise Effect on the STFT
10.11.6 Noise Effect on CWT
10.11.7 Noise Effect on DWT
10.11.8 Noise Effect on TSDM
10.12 Summary
References
Chapter 11 Electromagnetic Signature Analysis of Electrical Faults
11.1 Introduction
11.2 General Introduction to Short Circuit Fault Detection Methods in Synchronous Machines
11.3 Stator Short Circuit Fault Types
11.3.1 Stator Unbalanced Phases
11.3.2 Single‐Phase Fault to Ground
11.3.3 Phase‐to‐Phase Fault
11.3.4 Turn‐to‐Turn Short Circuit Fault
11.4 Synchronous Generator Stator Fault Effects
11.5 Fault Diagnosis Methods in the Stator Winding
11.5.1 Invasive Methods
11.5.1.1 Thermal Analysis
11.5.1.2 Vibration Analysis
11.5.1.3 Acoustic Noise Analysis
11.5.1.4 Partial Discharge Analysis
11.5.1.5 Output Gas Analysis
11.5.1.6 Impulse Test
11.5.1.7 Air Gap Magnetic Field Monitoring
11.5.2 Non‐invasive Methods
11.5.2.1 Field Current Signature Analysis
11.5.2.2 Stator Winding Currents
11.5.2.3 Current Park Vector
11.5.2.4 Rotor Current
11.5.2.5 Using the Negative Sequence Current of the Stator
11.5.2.6 The Injected Negative Sequence Current
11.5.2.7 Second Component of Current in the q‐Axis
11.5.2.8 Stator Terminal Voltage
11.5.2.9 Voltage Sequences
11.5.2.10 Impedance Sequence
11.5.2.11 Instantaneous Power Index
11.5.2.12 Analysis of Transient Operation of the Salient Pole Synchronous Generator
11.5.2.13 Stray Magnetic Field
11.5.2.14 Axial Leakage Flux
11.6 Stator Short Circuit Fault Detection of Brushless Synchronous Machines
11.7 Stator Short Circuit Fault Detection of Powerformers
11.8 Stator Short Circuit Fault Detection of Turbo‐generators
11.8.1 The Inter‐turn Fault Detection Algorithm of the Stator Winding
11.8.1.1 Circuit Analysis
11.8.1.2 Turn‐to‐Turn Fault
11.8.1.3 Factors Affecting the Proposed Index
11.8.1.4 External Phase‐to‐Phase Fault
11.8.1.5 Internal Phase‐to‐Phase Fault
11.8.1.6 Turn‐to‐Turn Fault Detection Algorithm
11.8.1.7 Increasing the Gradient of the Current
11.8.1.8 Current Category Determination
11.8.1.9 Calculating the Difference Between Two Currents
11.8.2 Algorithm Applications
11.8.2.1 Single‐Phase to Ground Fault
11.8.2.2 Inter‐Turn Fault
11.8.2.3 Internal Phase‐to‐Phase Fault
11.8.2.4 External Phase‐to‐Phase Fault
11.8.2.5 Transformer Inrush Current
11.8.2.6 Performance of the Proposed Algorithm in the Face of Various Types of Faults
11.9 Inter‐Turn Short Circuit Fault in Rotor Field Winding
11.9.1 Introduction
11.9.2 Invasive Method
11.9.2.1 Airgap Magnetic Field
11.9.2.2 Polar Diagram
11.9.2.3 Application of the Frequency Spectrum in the Inter‐turns Short Circuit Fault Using the Air Gap Magnetic Field
11.9.3 Non‐invasive Methods
11.9.3.1 The Stator and Rotor Current
11.9.3.2 Stator Voltage
11.9.3.3 Rotor Coil Impedance Index
11.9.3.4 Electromagnetic Power Index
11.9.3.5 Generator Capability Curve
11.9.3.6 Shaft Flux
11.9.3.7 Stray Magnetic Field
11.10 Summary
References
Chapter 12 Electromagnetic Signature Analysis of Mechanical Faults
12.1 Introduction
12.2 Eccentricity Faults
12.2.1 Invasive Detection Methods
12.2.1.1 Air Gap Magnetic Field
12.2.1.2 Frequency Analysis of the Air Gap Magnetic Field
12.2.1.3 Spectral Kurtosis
12.2.2 Non‐invasive Detection Methods
12.2.2.1 Inductance Variation Index
12.2.2.2 Harmonics of the Stator Current
12.2.2.3 Harmonics of the Open‐Circuit Voltage of the Stator Winding
12.2.2.4 Analysis of the Space Vector Loci of the Electromotive Force
12.2.2.5 The Harmonic Component in the Current of the Rotor Field Winding
12.2.2.6 Stator Split‐Phase Current
12.2.2.7 Stator Voltage Subharmonics Index
12.2.2.8 Shaft Voltage
12.2.2.9 Stray Magnetic Field
12.3 Stator Core Fault
12.3.1 Introduction
12.3.2 Core Loss
12.3.3 Rated Flux
12.3.4 EL‐CID Method
12.4 Broken Damper Bar Fault
12.4.1 Introduction
12.4.2 Single‐Phase Rotation Test
12.4.3 Air Gap Magnetic Field
12.4.4 Stray Magnetic Field Monitoring
12.4.5 Stator Current
12.4.6 Rotor Field Winding Voltage
12.5 Summary
References
Chapter 13 Vibration Monitoring
13.1 Introduction
13.2 Condition Monitoring Using Vibration
13.3 Vibration in Salient‐Pole Synchronous Generators
13.4 Introduction to Utilized Terms in Vibration Analysis
13.4.1 Time Harmonics
13.4.2 Spatial Harmonics
13.4.3 Mode Number and Deformation
13.4.4 Resonance
13.5 Force and Vibration Analysis
13.5.1 Modal Analysis
13.5.2 Analysis of a Healthy Generator
13.5.2.1 Time‐Domain Distributions of the Magnetic Field
13.5.2.2 Spatial‐Domain Distributions of the Magnetic Field
13.5.2.3 Mechanical Analysis
13.5.3 Analysis of a Synchronous Generator under an Interturn Short Circuit Fault
13.5.3.1 Time‐Domain Distributions of the Magnetic Field
13.5.3.2 Spatial Domain Distributions of the Magnetic Field
13.5.3.3 Mechanical Analysis
13.5.4 Analysis of a Synchronous Generator under Static Eccentricity
13.5.4.1 Time‐Domain Distributions of a Magnetic Field
13.5.4.2 Spatial‐Domain Distributions of the Magnetic Field
13.5.4.3 Mechanical Analysis
13.5.5 Load Effect
13.5.6 Comparison of Fault Impacts on the Magnetic and Vibration Signatures
13.6 Summary
References
Chapter 14 Application of Machine Learning in Fault Detection
14.1 Introduction
14.2 Supervised Learning
14.2.1 Feature Extraction and Selection
14.2.1.1 Time Series Feature Extraction Based on Scalable Hypothesis Tests (TSFRESH)
14.2.2 Data Set Balancing
14.2.3 Training and Testing
14.2.4 Evaluation Metrics
14.3 Ensemble Learners
14.4 Logistic Regression
14.5 K‐Nearest Neighbors
14.6 Support Vector Machine
14.7 Decision Tree Learning
14.8 Random Forest
14.9 Boosted Trees
14.10 Gradient Boost Decision Trees
14.11 Artificial Neural Network
14.11.1 Perceptron
14.11.2 Multi‐Layer Perceptron
14.11.3 Activation Function
14.11.4 Training
14.12 Other Artificial Neural Networks
14.13 Real Case Application
14.13.1 Data Pre‐processing
14.13.2 Feature Extraction
14.13.2.1 Fast Fourier Transform
14.13.2.2 DWT Wavelet Energies
14.13.2.3 TSFRESH
14.13.3 Exploratory Data Analysis
14.13.4 Feature Selection
14.13.4.1 Random Forest Feature Selection
14.13.4.2 Time Series Feature Extraction Based on Scalable Hypothesis Tests (TSFRESH)
14.13.4.3 Summary of Feature Selection
14.13.5 Fault Detection
14.13.5.1 Initial Hyper‐parameter Choices
14.13.5.2 Metrics
14.13.5.3 Cross‐Validation
14.13.5.4 Standardization
14.13.5.5 Results
14.13.6 Feature Selection and Reduction Performance
14.13.7 Hyper‐parameter Optimization and Selection
14.13.8 Stacking Classifiers
14.13.9 Final Classifier
14.13.9.1 Feature Usefulness
14.13.9.2 Fault Severity Assessment
14.13.10 Data Management and Pre‐processing
14.13.11 Feature Extraction and Importance
14.13.12 Feature Selection and Target Leakage
14.13.13 Classifier Selection
14.13.14 Performance
14.13.15 Real‐World Validity
14.13.16 Real‐World Applicability
14.13.17 Anomaly Detection
14.13.18 Simulated Data Generation
14.14 Summary
References
Chapter 15 Insulation Defect Monitoring
15.1 Introduction
15.2 History and Advantages of Using Partial Discharge Techniques
15.3 Electrical Machine Fault Generation Factors
15.4 Rotating Machine Insulation System
15.4.1 Rotor Insulation System
15.4.2 Stator Insulation System
15.5 PD Types in Rotating Machines
15.5.1 Internal Discharge
15.5.1.1 Internal Void
15.5.1.2 Internal Delamination
15.5.1.3 Delamination Between the Conductor and Insulation
15.5.1.4 Electrical Treeing
15.5.2 Slot Discharges
15.5.3 Discharges in the End Winding
15.5.3.1 Surface Discharge
15.5.3.2 Conductive Particles
15.5.3.3 Phase‐to‐Phase Discharge
15.5.4 Arcing and Sparking
15.5.4.1 Arcing at Broken Conductors
15.5.4.2 Vibration Sparking
15.6 Risk Assessment of Different Partial Discharge Faults
15.7 Frequency Characteristics of Current Pulses
15.8 Measurement of PD Signals
15.9 Online Measurements of PD in Rotating Electrical Machines
15.9.1 Electrical Measurement of Partial Discharge
15.9.1.1 Capacitive Coupling Method
15.9.1.2 Implement Capacitive Coupler Method
15.9.1.3 Current Transformer
15.9.1.4 Antenna Monitoring Method
15.9.2 Acoustic Measurement of PD
15.9.3 Chemical Measurement of PD
15.9.4 Visual Inspection and Optical Measurement of PD
15.10 Summary
References
Chapter 16 Noise Rejection Methods and Data Interpretation
16.1 Introduction
16.2 Noise Rejection in Online Measurement
16.3 Noise Sources in Generators
16.4 Different Methods for Denoising
16.4.1 Restricting the Frequency Range
16.4.2 Pulse Shape Analysis
16.4.3 Noise Rejection by Propagation Time
16.4.4 Residue of Two Channel Signals
16.4.5 Gating
16.4.6 Three‐Phase Amplitude Relation Diagram (3PARD)
16.4.7 Current Signal Features
16.4.8 Noise Rejection Using Fourier Transform
16.4.8.1 Principles of Noise Rejection Using Fourier Transform
16.4.9 Denoising Using Wavelet Transform
16.5 Data Interpretation
16.5.1 Data Interpretation in the Low‐Frequency Range
16.5.2 Data Interpretation in VHF and UHF Measurements
16.5.3 Data Interpretation Based on Artificial Intelligence
16.6 Separating PD Sources
16.7 Summary
References
Index
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