Power Quality Measurement and Analysis Using Higher-Order Statistics E-Book

Olivia Florencias Oliveros

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 253

Veröffentlichungsjahr: 2022

Beschreibung

POWER QUALITY MEASUREMENT AND ANALYSIS USING HIGHER-ORDER STATISTICS Help protect your network with this important reference work on cyber security 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.

Leseprobe

Table of Contents

Cover

Title Page

Copyright Page

Dedication Page

Preface

About the Authors

Acknowledgements

Acronyms

1 Power Quality Monitoring and Higher‐Order Statistics

1.1 Introduction

1.2 Background on Power Quality

1.3 PQ Practices at the Industrial Level

1.4 A New PQ Monitoring Framework

2 HOS Measurements in the Time Domain

2.1 Introduction

2.2 Background on Power Quality

2.3 Traditional Theories of Electrical Time Domain

2.4 HOS Contribution in the PQ Field

2.5 Regulations

2.6 The Sliding Window Method for HOS Feature Extraction

2.7 PQ Index Based on HOS

2.8 Representations Used by the Time Domain

3 Event Detection Strategies Based on HOS Feature Extraction

3.1 Introduction

3.2 Detection Methods Based on HOS

3.3 Experiment Description

3.4 Flow Diagram of HOS Monitoring Strategy Focus on Detecting Short Duration Events: Detecting Amplitude, Symmetry, and Sinusoidal States

3.5 Continuous Events Characterisation Fundamental Frequency

3.6 Detection of Harmonics with HOS in the Time Domain

3.7 Conclusions

4 Measurements in the Frequency Domain

4.1 Introduction

4.2 Frequency Domain

4.3 HOS in the Frequency Domain

4.4 Harmonic Distortion

4.5 Traditional Theories of Electrical Frequency‐Domain Indicators

4.6 HOS Contribution in PQ in the Frequency Domain

5 Measurement Campaigns and Virtual Instruments

5.1 Introduction

5.2 Virtual Instrument

5.3 PQ Continuous Monitoring Based on HOS for Consumer Characterisation, Public Networks and Households

5.4 Simplified Method to Use HOS in a Continuous Monitoring Campaign

5.5 Conclusions

Appendix A: Appendix AVoltage Waveform

A.1 Theoretical Power System Waveform

Appendix B: Appendix BTime‐Domain Cumulants

Appendix C: Appendix CHOS Range for Sag Detection, 1 Cycle

Appendix D: Appendix DHOS Range for Sag Detection, 10 Cycles

References

Index

End User License Agreement

List of Tables

Preface

Table A HOS approach related to different applications.

Chapter 2

Table 2.1 Detector performance due to the signal‐to‐noise ratio.

Table 2.2 Detector performance due to the frequency sampling.

Table 2.3 Detector performance due to the number of cycles computed through...

Table 2.4 Detector performance related to the fundamental frequency fluctua...

Table 2.5 HOS vs. electrical time domain indices.

Table 2.6 HOS approach for defining PQ indices based on the waveforms in Fi...

Table 2.7 HOS ranges that summarise voltage supply variations of ±10%.

Table 2.8 Maximum values achieved by the index under different steady‐state...

Chapter 3

Table 3.1

HOS

for sag detection under voltage reference in symmetrical and...

Table 3.2 HOS for sag detection without phase‐angle jumps under voltage ref...

Table 3.3 HOS for swell detection without phase‐angle jumps under non‐symme...

Table 3.4 HOS range for sag detection including phase‐angle jump based on n...

Table 3.5 HOS range for transient detection including phase‐angle jump base...

Table 3.6 Categories and typical characteristics of the power system electr...

Table 3.7 Industrial frequency ranges according to EN 50160:2015 [13].

Table 3.8 Frequency deviations on sinusoidal and symmetric signals.

Table 3.9 HOS and PQ fluctuations for different frequency ranges: synchrono...

Table 3.10 HOS and PQ fluctuations for different frequency ranges: non‐sync...

Chapter 4

Table 4.1 Types of harmonics.

Table 4.2 Different situations of impulsive behaviour.

Table 4.3 Different number of impulsive sinusoidal cycles situation.

Table 4.4 Different number of impulsive sinusoidal cycles situation.

Chapter 5

Table 5.1 Site characterisation and data compression through the PQ index f...

Table 5.2 Site characterisation and data compression through the PQ index f...

Appendix C

Table C.1

HOS range for sag detection without phase‐angle jump based on non‐...

Appendix D

Table D.1

HOS range for sag detection including phase‐angle jumps based on n...

List of Illustrations

Chapter 1

Figure 1.1 The EN50160 rules on voltage quality until the

point of common co

...

Figure 1.2 Time‐line of

power quality

(PQ) monitoring technology evolution. ...

Figure 1.3

Power quality

(PQ) measurement chain proposed by the standard UNE...

Figure 1.4 Evolution of publications related to power systems and

smart grid

Figure 1.5 Evolution of publications related to power systems and

power qual

...

Figure 1.6 Evolution of publications related to power systems,

smart grid

(S...

Figure 1.7

Power quality

(PQ) measurements in the

smart grid

(SG) context ex...

Figure 1.8 Evolution of publications related to

higher‐order statistics

...

Chapter 2

Figure 2.1 Theoretical 50 Hz power supply and the PDF that characterises a b...

Figure 2.2 Variance vs. other electrical parameters under amplitude changes ...

Figure 2.3 PDF of the different indices and their individual ranges under di...

Figure 2.4 Evolution of the individual statistic ranges under cycle‐to‐cycle...

Figure 2.5 Evolution of the HOS trajectories for a voltage waveform that inc...

Figure 2.6 Evolution of the HOS trajectories for a voltage signal with

U

din

...

Figure 2.7 Both waveform cases, compared with the theoretical voltage.

Figure 2.8 HOS deviations of both steady‐state voltage waveforms in Figure 2...

Figure 2.9 PQ index and the PDF evolution that compute the cycle‐to‐cycle (0...

Figure 2.10 PQ index that computes simulated frequency changes and amplitude...

Figure 2.11 Bi‐dimensional HOS plane, for example variance (var) vs. kurtosi...

Figure 2.12 Fingerprint of the waveform time‐series deviation in the HOS pla...

Figure 2.13 Fingerprint of the waveform time‐series deviation in the HOS pla...

Figure 2.14 Fingerprint of the waveform time‐series deviation in the HOS pla...

Figure 2.15 One‐week monitoring of one week using the method based on HOS wi...

Chapter 3

Figure 3.1 The variance for sag detection under a voltage reference in symme...

Figure 3.2 HOS behaviour vs. changes in the reference voltage (

U

ref) accordi...

Figure 3.3 HOS range for sag and swell detection without a phase‐angle jump ...

Figure 3.4 HOS range for sag detection in Figure 3.3 without a phase‐angle j...

Figure 3.5 HOS range for swell detection in Figure 3.3 without a phase‐angle...

Figure 3.6 HOS range for sag detection including a phase‐angle jump under no...

Figure 3.7 Skewness vs. variance, sags and phase‐angle jumps regions.

Figure 3.8 Variance vs. kurtosis, sags and phase‐angle jumps regions.

Figure 3.9 Skewness vs. kurtosis, sags and phase‐angle jumps regions.

Figure 3.10 Sag 60% event in the HOS planes with the phase‐angle jumps. (a) ...

Figure 3.11 In field measurements that contain coupled transients resulting ...

Figure 3.12 Trajectories of different transients in one cycle.

Figure 3.13 Flowchart of HOS monitoring strategy focusing on detecting short...

Figure 3.14 Instantaneous frequency gap that can be detected through the sli...

Figure 3.15 Constant frequency deviations in the HOS planes.

Figure 3.16 Tracking new measurements on the background screen floor.

Figure 3.17 Flowchart of the HOS monitoring strategy focus on detecting fund...

Figure 3.18 Flow diagram that helps introduce HOS measurements as a harmonic...

Chapter 4

Figure 4.1 Effect of intermediate frequencies with and without spectral wind...

Figure 4.2 Comparison of kurtosis of different distributions.

Figure 4.3 Example of a square signal, the lowest kurtosis situation, −2 val...

Figure 4.4 Example of an impulsive situation, the highest kurtosis situation...

Figure 4.5 Example of an impulsive situation, for different numbers of ampli...

Figure 4.6 Constant amplitude sinusoidal signal and histogram.

Figure 4.7 Impulsive amplitude change sinusoidal signal and histogram.

Figure 4.8 Kurtosis for different amplitudes of an affected cycle, in one af...

Figure 4.9 Sinusoidal signal with a linear amplitude double (left) and a his...

Figure 4.10 SK of 50 Hz sinusoidal waveform, with constant amplitude and noi...

Figure 4.11 SK response for constant amplitude spectral component, with diff...

Figure 4.12 SK base oscillations (maximum and minimum values), with differen...

Figure 4.13 SK for an impulsive situation.

Figure 4.14 SK max for an impulsive situation, changing SNR.

Figure 4.15 SK for a sinusoidal signal during part of a realisation.

Figure 4.16 SK for different harmonic distortions in a power waveform.

Figure 4.17 SK for different harmonic distortions in a power waveform, under...

Figure 4.18 SK for different oscillatory transient conditions.

Figure 4.19 SK for different oscillatory transient conditions, with frequenc...

Figure 4.20 SK for a sag disturbance that starts and ends in different reali...

Figure 4.21 SK for a sag disturbance that starts and ends in the same realis...

Chapter 5

Figure 5.1 The PQ data acquisition procedure and the implementation of a PQ ...

Figure 5.2 The configuration of the virtual instrument guarantees measuremen...

Figure 5.3 The PQ control panel.

Figure 5.4 The PQ threshold panel allows monitoring of PQ behaviour in both ...

Figure 5.5 The PQ HOS statistics panel. Surveillance of HOS with standard de...

Figure 5.6 Histograms of the different weekly indices based on the CDF and t...

Figure 5.7 Representation of the PQ index time‐series along the first two we...

Figure 5.8 Different PQ monitoring strategies informing about the PQ mean ea...

Figure 5.9 Scalability of the proposed method: two singular days within the ...

Figure 5.10 The PQ 0.02 second values during 24 hours, from which different ...

Figure 5.11 Hourly trend of the index and different PQ density functions dur...

Figure 5.12 Simplified method of PQ continuous monitoring.

Figure 5.13 HOS continuous monitoring‐based procedure in the SG.

Figure 5.14 HOS continuous monitoring in a scalable proposal. A measurement ...

Guide

Cover Page

Title Page

A Practical Approach to Quantitative Validation of Patient‐Reported Outcomes

Dedication

Preface

About the Authors

Acknowledgements

Acronyms

Table of Contents

Begin Reading

Appendix A Voltage Waveform

Appendix B Time‐Domain Cumulants

Appendix C HOS Range for Sag Detection, 1 Cycle

Appendix D HOS Range for Sag Detection, 10 Cycles

References

Index

WILEY END USER LICENSE AGREEMENT

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Power Quality Measurement and Analysis Using Higher-Order Statistics

Understanding HOS Contribution on the Smart(er) Grid

Olivia Florencias‐OliverosJuan‐José González‐de‐la‐RosaJosé‐María Sierra‐FernándezManuel‐Jesús Espinosa‐GaviraAgustín Agüera‐PérezJosé‐Carlos Palomares‐Salas

University of CádizDepartment of Automation Engineering, Electronics, Architecture and Computer Networks,Research Group PAIDI‐TIC‐168. Computational lnstrumentation and Industrial Electronics (ICEI),Higher Technical School of Engineering of Algeciras (ETSIA), Spain

This edition first published 2023© 2023 John Wiley & Sons Ltd

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The right of Olivia Florencias‐Oliveros, Juan‐José González‐de‐la‐Rosa, José‐María Sierra‐Fernández, Manuel‐Jesús Espinosa‐Gavira, Agustín Agüera‐Pérez, and José‐Carlos Palomares‐Salas to be identified as the author of this work has been asserted in accordance with law.

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Library of Congress Cataloging‐in‐Publication DataNames: Florencias‐Oliveros, Olivia, author.Title: Power quality measurement and analysis using higher‐order statistics : understanding HOS contribution on the smart(er) grid / Olivia Florencias‐Oliveros [and five others].Description: Hoboken, NJ : Wiley, 2023. | Includes bibliographical  references and index.Identifiers: LCCN 2022023836 (print) | LCCN 2022023837 (ebook) | ISBN  9781119747710 (cloth) | ISBN 9781119747765 (adobe pdf) | ISBN  9781119747741 (epub)Subjects: LCSH: Electric power systems–Quality control. | Order  statistics.Classification: LCC TK1010 .F55 2023(print) | LCC TK1010(ebook) | DDC  621.31–dc23/eng/20220722LC record available at https://lccn.loc.gov/2022023836LC ebook record available at https://lccn.loc.gov/2022023837

Cover Design: WileyCover Image: © Pand P Studio/Shutterstock

To all the researchers that have inspired this work, those working to bridge the gap between signal analysis and power metering

Preface

The so‐called digital energy networks are gathering numerous elements that have emerged from different branches of Engineering and Science. Concepts such as Internet of Things (IoT), Big Data, Smart Cities, Smart Grid and Industry 4.0 all converge together with the goal of working more efficiently, and this fact inevitably leads to Power Quality (PQ) assurance. Apart from its economic losses, a bad PQ implies serious risks for machines and consequently for people. Many researchers are endeavouring to develop new analysis techniques, instruments, measurement methods and new indices and norms that match and fulfil requirements regarding the current operation of the electrical network. This book offers a compilation of the recent advances in this field. The chapters range from computing issues to technological implementations, going through event detection strategies and new indices and measurement methods that contribute significantly to the advance of PQ analysis. Experiments have been developed within the frames of research units and projects and deal with real data from industry and public buildings. Human beings have an unavoidable commitment to sustainability, which implies adapting PQ monitoring techniques to our dynamic world, defining a digital and smart concept of quality for electricity.

PQ analysis is evolving continuously, mainly due to the incessant growth and development of the smart grid (SG) and the incipient Industry 4.0, which demands quick and accurate tracking of the electrical power dynamics. Much effort has been put on two main issues. First, numerous distributed energy resources and loads provoke highly fluctuating demands that alter the ideal power delivery conditions, introducing at the same time new types of electrical disturbances. For this reason, permanent monitoring is needed in order to track this a priori unpredictable behaviour. Second and consequently, the huge amount of data (Big Data) generated by the measurement equipment during a measurement campaign is usually difficult to manage due to different causes, such as complex structures and communication protocols that hinder accessibility to storage units, and the limited possibilities of monitoring equipment, based on regulations that do not reflect the current network operation.

The introduction of new indicators in PQ is one of the main subjects of discussion in the CIRED/CIGRÉ working group; however, it is necessary to solve future challenges from new perspectives. Indeed, this book proposes to spread the use of PQ indices based on HOS from event detection up to cycle‐to‐cycle continuous monitoring, taking advantage of their most simple calculations in order to detect the effect of multiple loads acting/working together on a node for a specific length of time.

Chapter 1 introduces the State of the Art in the power quality field and will help researchers to bridge the gap between traditional methods and those applications that use HOS analysis.

Chapters 2–5 propose different and experimental approaches that have been used to validate HOS applications in monitoring the power system.

Table A summarizes the monitoring objectives that would be accomplished using HOS as part of the results of this book and according to the topics proposed in the Guideline for Selection of Monitoring Parameters. Compared with other simpler methods, such as RMS measurements, HOS are not sensitive to noise. In Chapter 3, the authors demonstrated that HOS can help to detect fundamental frequency changes in the bi‐dimensional plane and Chapter 4 introduces techniques in the frequency domain, such as spectral kurtosis.

Table A HOS approach related to different applications.

Monitoring objective

Variables

Sampling rate

Data averaging window

Reference

Compliance verification‐connections agreements/premium power contracts

Voltage sags or voltage swells

5 Hz

As specified in the contract

Chapter 3

Performance analysis

Steady‐state voltage Voltage sags and swells Highest or lowest RMS voltage per 1 (or 10 min) Fundamental frequency deviations

5 Hz

10 min averaging window 1 min averaging window

Chapter 3

Site characterization

20 kHz

Tables

Chapter 4

Chapter 5

Troubleshooting

Disturbance depending on the nature of the problem being investigated

Chapter 3

Chapter 4

Overall, here the authors summarize the last 10 years of power quality research based on HOS techniques that would be incorporated in future PQ measurement campaigns, in order to accomplish the monitoring challenges of the next generation of advanced metering infrastructure in terms of compression, as well as reporting PQ efficiently.

This book gathers new advances in techniques and procedures to describe, measure and visualize the behaviour of the electrical supply, from physical instruments to statistical signal processing (SSP) techniques and new indexes for PQ that try to go beyond traditional norms and standards. The authors are recognized experts in the field, committed to a main goal: to provide new instrumental and analytical tools to help mitigate the serious consequences of a bad PQ in our digitized society, and thus enhancing energy efficiency for a more sustainable development.

Olivia Florencias‐OliverosJuan‐José González‐de‐la‐Rosa

About the Authors

Dr Olivia Florencias‐Oliveros received a PhD degree in Energy and Sustainable Engineering in 2020 (summa cum laude) from the University of Cádiz, Spain. She is a lecturer at the University of Cádiz, in the Research Group in Computational Instrumentation and Industrial Electronics (PAIDI‐TIC168), and an IEEE Member in the Power and Energy Society and IEEE Measurement and Instrumentation Society. Her research interests include Energy Technologies to manage Energy Efficiency and Renewable Energies: smart grids, energy monitoring techniques in power systems, power quality, smart metering, computational instrumentation technologies, sensor networks, IoT in smart buildings, big data and HOS statistics.

Dr Juan‐José González‐de‐la‐Rosa received an MSc degree in Physics–Electronics in 1992 at the University of Granada, Spain and a PhD degree in Industrial Engineering in 1999 at the University of Cádiz, Spain. He has four recognitions in the field of Communication Engineering, Computation and Electronics by the Spanish Government and was also awarded a Knowledge Transfer Recognition by the Spanish Government. Furthermore, he is a Full Professor in Electronics and founder of the Research Group in Computational Instrumentation and Industrial Electronics (PAIDI‐TIC‐168). His research interests include HOS, power quality and the inclusion of computational intelligence in technologies for measurement systems.

Dr José‐María Sierra‐Fenández received a PhD degree in Industrial Engineering in 1998 at the University of Cádiz, Cádiz, Spain. He is a Lecturer at the same University in the Research Group in Computational Instrumentation and Industrial Electronics (PAIDI‐TIC‐168). His research interests include energy technologies to manage energy efficiency and renewable energies, SG, power quality, instrumentation technologies, smart metering and HOS.

Manuel‐Jesús Espinosa‐Gavira received an MS degree in 2018 at the University of Cádiz, Cádiz, Spain. He is now a PhD student in Energy and Sustainable Engineering at the University of Cádiz from 2017 and is a Member of the Research Group in Computational Instrumentation and Industrial Electronics (PAIDI‐TIC‐168). His research interests include power quality, time‐series analysis, sensor networks, meteorology applied to renewable energies and energy efficiency.

Dr Agustín Agüera‐Pérez received an MS degree in Physics in 2004 at the University of Seville, Seville, Spain and a PhD degree in Industrial Engineering in 2013 at the University of Cádiz, Cádiz, Spain. He is now a Lecturer of Electronics in the Department of Automation Engineering, Electronics, Architecture and Computer Networks at the University of Cádiz and a Researcher in the Research Group in Computational Instrumentation and Industrial Electronics (PAIDI‐TIC‐168). His research interests include energy meteorology, power quality and virtual instruments.

Dr José‐Carlos Palomares‐Salas received an MS degree in Industrial Engineering in 2008 and a PhD degree in Industrial Engineering in 2013 (summa cum laude), both at the University of Cádiz, Cádiz, Spain. Currently, he is an Associate Professor at the University of Cádiz, in the Department of Automation Engineering, Electronics, Architecture, and Computer Networks and also a Member of the Research Group in Computational Instrumentation and Industrial Electronics (PAIDI‐TIC‐168). His research interests include power quality, intelligent systems and machine learning.

Acknowledgements

The work has been carried out in the framework of the following competitive Spanish National Research Projects:

TEC2016‐77632‐C3‐3‐R‐CO – Control and Management of Isolatable NanoGrids: Smart Instruments for Solar Forecasting and Energy Monitoring (COMING‐SISEM).

PID2019‐108953RB‐C21 – Estrategias de producción conjunta para plantas fotovoltaicas: Datos operacionales energéticos y meteorológicos para sistemas fotovoltaicos (SAGPV‐EMOD).

In both projects, new techniques for power quality monitoring in the smart grid frame have been developed in the framework of the PAIDI‐ICT‐168 Research Group on Computational Instrumentation and Industrial Electronics (ICEI), founded by the Junta de Andalucía government.

During this research, a National Patent directly aligned with the method was proposed. ES2711204 Procedimiento y Sistema de Análisis de Calidad de la Energía e Índice de Claidad 2S2PQ, Caracterización de la Señal en un Punto Del Suministro Eléctrico.

In addition, researchers of our unit have been doing different four‐month research stays at Dresden University of Technology, at the Institute of Electrical and High Voltage Systems Engineering, under the supervision of Dr Jan Meyer and Dr Ana María Blanco within the Power Quality Research Group.

Acronyms

AMI

Advanced Measurement Infrastructure

CDF

Cumulative Density Function

CENELEC

European Committee for Electrotechnical Standardization

CIGRÉ

International Council of Large Electrical Networks

CIRED

International Congress of Electrical Distribution Networks

dB

Decibel

DER

Distributed Energy Resources

DFT

Discrete Fourier Transform

DSOs

Distribution system operators

EV

Electric Vehicle

FDK

Frequency Domain Kurtosis

FFT

Fast Fourier Transform

HOS

Higher‐Order Statistics

IEC

International Electrotechnical Commission

IEC‐61000‐4‐30

Paper of the IEC

IEDs

Intelligent Electronic Devices

IEEE

Institute of Electrical and Electronics Engineers

LV

Low voltage

MV

Medium voltage parameters, such as RMS (root‐mean‐square)

PDF

Probability Density Function

PMD

Power Monitoring Device (device whose main function is metering and monitoring electrical parameters)

PQ

Power Quality

PQD

Power Quality Events Detection

PQ index

Proposed PQ index based on HOS

PQI

Power Quality Instrument (instrument whose main function is to measure, monitor and/or as certain PQ parameters in power supply systems, and whose measuring methods (class A or class S) are defined in the standards

PQIDif

Standardized PQ data format adopted to make data easily compatible between devices and establish data analysis procedures

Prosumer

A consumer capable to produce energy and consume energy

PMU

Phasor Measurement Units

PV

Photovoltaic Panels

RE

Renewable Energy

RTUs

Remote Terminal Units

RVC

Rapid Voltage Change

SG

Smart Grid

SK

Spectral Kurtosis

SNR

Signal‐to‐Noise Ratio

STFT

Short Time Fourier Transform

SWM

Sliding Window Method

THD

Total Harmonic Distortion

TSOs

Transmission system operators

U

c

Nominal Supply Voltage

U

din

Supply voltage variations

U

ref

Reference voltage

U

rms

RMS of the nominal voltage

V&I

Voltage and Current waveforms

WT

Wavelet Transform

1Power Quality Monitoring and Higher‐Order Statistics: State of the Art

1.1 Introduction

The importance of power quality (PQ) monitoring is that it becomes useful when detecting variable deviations and helps to describe the network behaviour and find solutions to some problems related to a wide range of electromagnetic phenomena concerning the interaction of power systems and end‐user devices. The development of advanced monitoring solutions is essential to help utilities and end‐users to understand network behaviour in order to discriminate, under a commercial PQ contract, the pollution source between the utility and the user.

1.2 Background on Power Quality

The principle of electrotechnical systems is to carry energy from the active element, the power source, to the passive elements, associated to the electricity consumers. Energy is then transformed into another type or simply produces work, through a conversion process that depends on the nature of the technological equipment used. During this process, the behaviour of the electrical variables involved, voltages (V) and currents (I), are mutually interrelated and the system behaviour is conditioned optimal performance (see Figure 1.1).

The PQ concept was introduced to establish the requirements on which the electric voltage would be delivered to consumers' terminals. Restrictions were introduced on the method that would be used to supply power to consumers using the same connection point. Both conditions need to be accomplished on any network [1].

Figure 1.1 The EN50160 rules on voltage quality until the point of common coupling (PCC).

Source: Authors.

According to the standard specifications, supply voltages must not distort the load behaviour (quality of the supplied voltage) and consumers must comply with certain restrictions and not distort the voltage, inject harmonics in the distribution nodes or produce perturbations (quality of the end‐users). Non‐linear loads deteriorate current waveforms in a short period of time and distorted current waveforms (non‐sinusoidal) increase voltage deviation. Finally, this kind of problem could impact the voltage behaviour in shared nodes and extend the problems to other loads.

The PQ concept is still evolving, a result of the gradual increase in the system's complexity over successive decades. Even though different monitoring solutions using higher‐order statistics (HOS) have previously been proposed, there has been a need to elaborate on a compendium with a more holistic point of view that is applicable to future networks studies.

PQ phenomena consist mainly in detecting an electrical disturbance that is reflected in the power system as a waveform deviation when a sinusoidal oscillation increases and decreases their amplitude, symmetry, and waveform shape changes, mainly caused by circuit switching and the whole non‐linear devices acting with unknown dynamics. Such network behaviour could be characterised using HOS. At present there is a lack of time‐domain information in many studies because the complex solution that represents the data compression and storage challenges makes it difficult to correlate different data registers and indices. Most of the indicators that are extracted and stored come from frequency‐domain information, which has a more complex representation format than time‐domain information. In order to accomplish feature extraction, HOS can compress time‐domain data and extract waveform characteristics. According to previous experience, the HOS domain seems a convenient strategy to use in order to compress data information while avoiding the highest computation complexity.

The present work focuses on the feature extraction of waveform characteristics using the sliding window method (SWM