Power Quality Measurement and Analysis Using Higher-Order Statistics Understanding HOS contribution on the Smart(er) grid

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Power quality (PQ) in electrotechnical systems refers to a set of characteristics related to the movement of energy and the delivery of voltage to consumers in the highest standard. As electricity networks change and adapt to new technologies and concepts of energy within a future Smart Grid, it has become clear that standardized methods by which stability and accuracy of electrical service along a network are currently measured are no longer enough to solve inherent issues in service and ensure established requirements are met.

Power Quality Measurement and Analysis using Higher-Order Statistics reflects the latest information related to PQ (Power Quality) analysis solutions, particularly that related to the implementation of new quality indices in the domain of higher-order statistics (HOS). The authors—noted experts on the topic—carefully address the detection of PQ problems from two perspectives: the detection of specific events that occur on networks in isolation and continuous monitoring detection. In doing so, the authors demonstrate the use of HOS in current waveform models, enabling the characterization of different power circuit topologies and loads. This book thereby expertly explores the benefits of using HOS, bridging the gap between signal processing and power, and building a better understanding for readers.

Power Quality Measurement and Analysis using Higher-Order Statistics readers will also find:

• A unique methodology for PQ analysis through its combination of HOS and PQ monitoring
• A proposal for new measurement solutions that can be easily implemented into modern instrumentation
• The detection of PQ problems from multiple perspectives
• The use of HOS in current waveform models, which enables the characterization of different power circuit topologies and loads

Pitched at a specialized level, Power Quality Measurement and Analysis is an essential reference for researchers, academics, and industry insiders, as well as advanced students in this field.

Olivia Florencias Oliveros, PhD, is a lecturer at the University of Cádiz, Spain and is a member of the Research Group in Computational Instrumentation and Industrial Electronics.

Juan José González de la Rosa, PhD, is a senior member of the IEEE and is the main Researcher and the Founder of the Research Group in Computational Instrumental and Industrial Electronics at the University of Cádiz, Spain.

Agustín Agüera-Pérez, PhD, [missing author bio]

José-María Sierra-Fernández, PhD, [missing author bio]

José-Carlos Pakomares-Salas, PhD, [missing author bio]

Manuel-Jesús Espinosa-Gavira, [missing author bio]

University of Cádiz for all of them. Research Unit in Computational Instrumentation and Industrial Electronics. Electronics Area. Higher-Polytechnic School

POWER QUALITY MEASUREMENT AND ANALYSIS USING HIGHER-ORDER STATISTICS 1

Understanding HOS contribution on the Smart(er) Grid 1

POWER QUALITY MEASUREMENT AND ANALYSIS USING HIGHER-ORDER STATISTICS 3

Understanding HOS contribution on the Smart(er) Grid 3

LOGO 3

Contents 11

Contributors 14

Foreword 17

Acronyms 21

Acknowledgments 24

Chapter 1. Power quality monitoring and higher-order statistics. State of the Art 26

1.1 Introduction 27

1.2 Background on power quality 27

1.3 PQ Practices at the Industrial Level 33

1.4 A new PQ monitoring Framework 33

1.4.1 The Smart Grid 35

1.4.2 The Smart Grid and the Power Quality 35

1.4.3 Performance Indicators 36

1.4.4 Existing measurement and instrumentation solutions 37

1.4.5 New approach in Measurement and Instrumentation solutions in the SG 38

1.4.6 Economic Issues for PQ 39

1.4.7 Power Quality and Big Data 39

1.4.8 Signal Processing for PQ 40

1.4.9 HOS for PQ analysis 43

Chapter 2. HOS Measurements in the time domain 47

HOS Measurements in the time domain 48

2.1 Introduction 48

2.2 Background on power quality 48

2.3 Traditional theories of electrical time domain 49

2.4 HOS contribution in the PQ field 51

2.4.1 HOS indices definitions 51

2.4.2 HOS performance in signal processing 52

2.4.3 HOS versus electrical time domain indices 53

2.5 Regulations 55

2.6 The Sliding Window Method for HOS feature extraction 56

2.6.1 Amplitude Changes 57

2.6.2 Phase Angle Jumps 58

2.6.3 Fundamental Frequency 60

2.6.4 Waveform shape deviation 62

2.7 PQ index based on HOS 64

2.8 Representations used by the time-domain 67

Chapter 3. Event Detection Strategies based on HOS feature extraction 72

3.1 Introduction 73

3.2 Detection methods based in HOS 73

3.3 Experiment description 73

3.3.1 Computational Strategy 73

3.3.2 HOS for Sag Detection under Symmetrical and Sinusoidal Conditions 74

3.3.2 HOS for Sag Detection including Phase-Angle Jump based on Non-Symmetrical & Non-Sinusoidal conditions 75

3.3.2.1 HOS range for Transient detection including Phase-Angle Jump based on Non-Symmetrical & Non- Sinusoidal conditions 87

3.3 Flow Diagram of HOS monitoring strategy focus on detecting short duration events: detecting amplitude, symmetry, and sinusoidal states 87

3.4 Continuous event’s characterization fundamental frequency 90

3.4.1 Frequency deviation regions in the HOS planes 92

3.4.2 Frequency deviation regions in the HOS planes 94

3.5 Detection of Harmonics with HOS in the time domain 95

3.6 Conclusions 97

Chapter 4. Measurements in the Frequency domain 100

4.1 Introduction 101

4.2 Frequency-domain 101

4.3 HOS in Frequency-domain 102

4.3.1 Spectral Kurtosis in Power Quality 103

4.4 Harmonic distortion 103

4.4.1 Types of Harmonic distortion 104

4.4.2 Sources of Harmonic distortion 105

4.4.3 Impact of harmonic distortion over power system 105

4.5 Traditional theories of electrical frequency-domain indicators 105

4.5.1 Harmonic measure 105

4.5.2 DFT derived measures 107

4.6 HOS contribution in PQ in the frequency-domain 107

4.6.1 Spectral Kurtosis 108

4.6.2 Spectral Kurtosis basic usage 115

4.6.3 Spectral Kurtosis and Power quality 118

Chapter 5 Measurement Campaigns and Virtual Instruments 124

5.1 Introduction 125

5.2 Virtual Instrument 126

5.2.1 Measurement Analysis Framework 126

5.2.2 Experimental Strategy for PQM through a Virtual Instrument 128

5.2.3 Configuration of the Virtual Instrument 128

5.2.4 Results 131

5.3 PQ continuous monitoring based on HOS for consumers characterization, public networks and household 132

5.3.1 Measurement and Analysis Framework 132

5.3.2 Evolution of the individual statistics histograms during several weeks 133

References 149

Annex A. Voltage Waveform 1

Theoretical power system waveform 1

Annex. B. Time-domain cumulants 1

Annex. C. HOS Range for Sag Detection, one cycle 3

Annex. D. HOS Range for Sag Detection, 10 cycles 7

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