Power Quality in Power Systems, Electrical Machines, and Power-Electronic Drives

By Ewald F. Fuchs and Mohammad A. S. Masoum

Power Quality in Power Systems, Electrical Machines, and Power-Electronic Drives uses current research and engineering practices, guidelines, standards, and regulations for engineering professionals and students interested in solving power quality problems in a cost effective, reliable, and safe manner within the context of renewable energy systems.

The book contains chapters that address power quality across diverse facets of electric energy engineering, including AC and DC transmission and distribution lines; end-user applications such as electric machines, transformers, inductors, capacitors, wind power, and photovoltaic power plants; and variable-speed, variable-torque power-electronic drives. The book covers nonsinusoidal waveshapes, voltage disturbances, harmonic losses, aging and lifetime reductions, single-time events such as voltage dips, and the effects of variable-speed drives controlled by PWM converters.

The book also reviews a corpus of techniques to mitigate power-quality problems, such as the optimal design of renewable energy storage devices (including lithium-ion batteries and fuel cells for automobiles serving as energy storage), and the optimal design of nonlinear loads for simultaneous efficiency and power quality.

• Provides theoretical and practical insights into power-quality problems related to future, smart grid, renewable, hybrid electric power systems, electric machines, and variable-speed, variable-torque power-electronic drives
• Contains a highly varied corpus of practical applications drawn from current international practice
• Designed as a self-study tool with end-of-chapter problems and solutions designed to build understanding
• Includes very highly referenced chapters that enable readers to save time and money in the research discovery process for critical research articles, regulatory standards, and guidelines

• Language: English
• Publisher: Academic Press
• Release date: Feb 13, 2023
• ISBN: 9780128178577

Ewald F. Fuchs

Professor Ewald Fuchs is a fellow of IEEE, his research interests are the effects of harmonics on power system components, variable-speed drives for improvement of industrial processes, conducted jointly with Unique Mobility, National Renewable Energy Labs, EPRI, Martin Marietta, and Teltech.

Book preview

9780128178577_FC

Power Quality in Power Systems, Electrical Machines, and Power-Electronic Drives

Third Edition

Ewald F. Fuchs

Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO, United States

Mohammad A.S. Masoum

Engineering Department, Utah Valley University (UVU), Orem, UT, United States

Table of Contents

Cover

Title page

Copyright

Preface

1: Past and future electric energy systems

2: Renewable hybrid energy system developments

References

Acknowledgments

References

The climate dilemma

References

Summary overview of chapters

Chapter 1: Introduction to power quality

Abstract

1.1: Definition of power quality

1.2: Causes of disturbances in power systems

1.3: Classification of power quality issues

1.4: Formulations and measures used for power quality

1.5: Effects of poor power quality on power system devices

1.6: Standards and guidelines referring to power quality

1.7: Harmonic modeling philosophies

1.8: Power quality improvement techniques

1.9: Summary

1.10: Problems

References

Additional bibliography

Chapter 2: Harmonic models of transformers

Abstract

2.1: Sinusoidal (linear) modeling of transformers

2.2: Harmonic losses in transformers

2.3: Derating of single-phase transformers

2.4: Nonlinear harmonic models of transformers

2.5: Ferroresonance of power transformers

2.6: Effects of solar-geomagnetic disturbances on power systems and transformers

2.7: Grounding

2.8: Measurement of derating of three-phase transformers

2.9: Summary

2.10: Problems

References

Additional Bibliography

Chapter 3: Modeling and analysis of induction machines

Abstract

3.1: Complete sinusoidal equivalent circuit of a three-phase induction machine

3.2: Magnetic fields of three-phase machines for the calculation of inductive machine parameters

3.3: Steady-state stability of a three-phase induction machine

3.4: Spatial (space) harmonics of a three-phase induction machine

3.5: Time harmonics of a three-phase induction machine

3.6: Fundamental and harmonic torques of an induction machine

3.7: Measurement results for three- and single-phase induction machines

3.8: Inter- and subharmonic torques of three-phase induction machines

3.9: Interaction of space and time harmonics of three-phase induction machines

3.10: Conclusions concerning induction machine harmonics

3.11: Voltage-stress winding failures of AC motors fed by variable-frequency, voltage- and current-source PWM inverters

3.12: Nonlinear harmonic models of three-phase induction machines

3.13: Static and dynamic rotor eccentricity of three-phase induction machines

3.14: Operation of three-phase machines within a single-phase power system

3.15: Classification of three-phase induction machines

3.16: Summary

3.17: Problems

References

Additional bibliography

Chapter 4: Modeling and analysis of synchronous machines

Abstract

4.1: Sinusoidal state-space modeling of a synchronous machine in the time domain

4.2: Steady-state, transient, and subtransient operation

4.3: Harmonic modeling of a synchronous machine

4.4: Discretization errors of numerical solutions

4.5: Operating point-dependent reactances under saturated magnetic field conditions

4.6: Summary

4.7: Problems

References

Additional bibliography

Chapter 5: Performance of power-electronic drives with respect to speed and torque

Abstract

5.1: Closed-form and numerical-solution techniques for variable-speed, variable-torque drives, and review of circuit approximations suitable for numerical solutions

5.2: Three-phase distribution system supplying energy to lithium-ion batteries via rectifiers

5.3: Three-phase permanent-magnet generator supplying energy to lead-acid battery via rectifier

5.4: Speed and torque control of drives consisting of three-phase induction machine connected to current-controlled, voltage-source inverter

5.5: Speed and torque control of brushless-DC machine or permanent-magnet machine fed/supplied by inverter for either motor or generator operation

5.6: Control of speed and torque for three-phase synchronous motor/machine fed/supplied by either lithium-ion battery or fuel cell via inverter for either motor or generator operation

5.7: Performance issues with batteries, fuel cells, and combustion engines

5.8: Summary

References

Chapter 6: Interaction of harmonics with capacitors

Abstract

6.1: Application of capacitors to power-factor correction

6.2: Application of capacitors to reactive power compensation

6.3: Application of capacitors to harmonic filtering

6.4: Power quality problems associated with capacitors

6.5: Frequency and capacitance scanning

6.6: Harmonic constraints for capacitors

6.7: Equivalent circuits of capacitors

6.8: Summary

6.9: Problems

References

Chapter 7: Lifetime reduction of transformers and induction machines

Abstract

7.1: Rationale for relying on the worst-case conditions

7.2: Elevated temperature rise due to voltage harmonics

7.3: Weighted-harmonic factors

7.4: Exponents of weighted-harmonic factors

7.5: Additional losses or temperature rises versus weighted-harmonic factors

7.6: Arrhenius plots

7.7: Reaction rate equation

7.8: Decrease of lifetime due to an additional temperature rise

7.9: Reduction of lifetime of components with activation energy E = 1.1 eV due to harmonics of the terminal voltage within residential or commercial utility systems

7.10: Possible limits for harmonic voltages

7.11: Probabilistic and time-varying nature of harmonics

7.12: The cost of harmonics

7.13: Temperature as a function of time

7.14: Various operating modes of rotating machines

7.15: Summary

7.16: Problems

References

Chapter 8: Power system modeling under nonsinusoidal operating conditions

Abstract

8.1: Overview of a modern power system

8.2: Power system matrices

8.3: Fundamental power flow

8.4: Newton-based harmonic power flow

8.5: Classification of harmonic power flow techniques

8.6: Summary

8.7: Problems

References

Chapter 9: Impact of poor power quality on reliability, relaying, and security

Abstract

9.1: Reliability indices

9.2: Degradation of reliability and security due to poor power quality

9.3: Tools for detecting poor power quality

9.4: Tools for improving reliability and security

9.5: Load shedding and load management

9.6: Energy-storage methods

9.7: Matching the operation of intermittent renewable power plants with energy storage

9.8: Summary

9.9: Problems

References

Additional bibliography

Chapter 10: The roles of filters in power systems and unified power quality conditioners

Abstract

10.1: Types of nonlinear loads

10.2: Classification of filters employed in power systems

10.3: Passive filters as used in power systems

10.4: Active filters

10.5: Hybrid power filters

10.6: Block diagram of active filters

10.7: Control of filters

10.8: Compensation devices at fundamental and harmonic frequencies

10.9: Unified power quality conditioner (UPQC)

10.10: The UPQC control system

10.11: UPQC control using the Park (dqo) transformation

10.12: UPQC control based on the instantaneous real and imaginary power theory

10.13: Performance of the UPQC

10.14: Summary

References

Chapter 11: Optimal placement and sizing of shunt capacitor banks in the presence of harmonics

Abstract

11.1: Reactive power compensation

11.2: Common types of distribution shunt capacitor banks

11.3: Classification of capacitor allocation techniques for sinusoidal operating conditions

11.4: Optimal placement and sizing of shunt capacitor banks in the presence of harmonics

11.5: Summary

References

Chapter 12: Power quality solutions for renewable energy systems

Abstract

12.1: Energy conservation and efficiency

12.2: Photovoltaic and thermal solar (power) systems

12.3: Horizontal and vertical-axes wind power (WP) plants

12.4: Complementary control of renewable plants with energy storage plants [144]

12.5: AC transmission lines vs DC lines

12.6: Fast-charging stations for electric cars

12.7: Off-shore renewable plants

12.8: Metering

12.9: Other renewable energy plants

12.10: Production of automotive fuel from wind, water, and CO2

12.11: Water efficiency

12.12: Village with 2600 inhabitants achieves energy independence

12.13: Reduction of lifetime as a function of temperature

12.14: Paralleling of two power systems

12.15: The TEXAS synchrophasor network

12.16: Summary

12.17: Problems

References

Glossary of symbols, abbreviations, and acronyms

Appendices

Appendix 1: Sampling techniques

Appendix 2: Program list for Fourier analysis (Chapter 2, reference 81)

Appendix 3: Equipment for tests

Appendix 4: Measurement error of powers

Index

Copyright

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Preface

This book is intended for graduate students and professionals working in the fields of power systems, renewable energy, such as wind and photovoltaics, and storage devices, such as batteries and fuel cells, including the design of electric power-electronic drives. The main objective of this book is to design components that meet acceptable power quality standards.

1: Past and future electric energy systems

Edison’s Pearl Street direct-current (DC) power station in Manhattan, NYC, opened in 1882 [1], was the first central power plant in the United States, providing electric power only to clients in the immediate vicinity, due to its low voltage and very high current, which had to be transmitted in buried DC very-large-cross-section cables to limit ohmic losses. The voltage was controlled within the fenced-in power station. This power station was able to function due to the invention of the mechanical commutator, on which DC machines are based, converting the AC current/voltage of the rotor to direct current/voltage at the terminals of the DC generator employing carbon brushes.

On the other hand, Tesla favored—with his invention of the two-phase rotating field [2]—an alternating current (AC) central fenced-in power station with voltage and frequency control. Electricity conduction is based on endowed electrons capable of useful work, as explained by Franck [3] in his Nobel Prize acceptance speech. Power generation at this time was mainly based on coal-fired and hydropower plants. Power quality played a subordinate role because only a few mercury rectifiers and inverters were employed within the central and distribution power system environment.

The invention of the semiconductor p-n junction [4], along with the development of rectifiers [5] and inverters [6], led Hingorani [7] to believe that all endowed electrons pass at least once through power-electronic components within the power system. The development of light-emitting-diode (LED) lights [8] and variable-speed drives, such as brushless DC machines (inverter-fed AC machines) [9], confirm Hingorani’s prediction. Thus, modern power systems with a high penetration of power-electronic components came about, relying mostly on wind, photovoltaic, solar thermal, and nuclear power plants, as discussed in the next section. This, in turn, created an increased need to investigate power quality due to source- and load-generated harmonics and transients—while on the other hand, an efficiency increase is achieved.

2: Renewable hybrid energy system developments

Fig. 1 shows a future smart interconnected power and load system where control and dispatch centers combine the advantages of DC transmission [1]—no stability problems—with those of AC transmission [2], where high voltages with low currents permit very efficient energy transmission. The combination of DC and AC components leads to a renewable electric hybrid power and distribution system.

Fig. 1

Fig. 1 Basic elements of a future, smart, renewable hybrid electric power system.

While in a central power station—either DC or AC—the manufacturing of electric power [9] occurs within a fenced-in area, in future or smart and hybrid power systems the manufacturing occurs within the entire system due to photovoltaic DC generation on individual houses, wind AC generation on farmlands or oceans, and temporary DC energy storage in batteries, such as automobile batteries or within family houses, etc. The development of the Texas Synchrophasor Network [10] permits control of distant renewable energy power plants if Dunkelflaute [11] occurs locally. Aging properties during the lifetime of any device [12] lead to decreased generation of electric equipment; see Fig. 2 for the photovoltaic DC system resulting in ≈ 1% energy output decrease per year. The disadvantage of rectifiers and inverters leads—without filtering—to the generation of integer and noninteger voltage and current harmonics, resulting in power quality problems: premature aging, mechanical and electric maloperations, and impact on under- and over-frequency operation [13].

Fig. 2

Fig. 2 Measured decrease of the PV module output power generation EI year [kWh] for 8 years from 2014 to 2021.

The strategy of combining locally operated smart power systems [14] with large-scale hybrid power systems, as shown in Fig. 1, may lead to further development of future power systems. The development of many small-scale renewable power sources requires increased water consumption [15,16] within manufacturing facilities for cooling and production of power plants, e.g., biogas and nuclear, semiconductors, batteries, and other small-scale power equipment. Per capita water consumption in Germany is 120 L per day, and virtual water consumption also occurs: as examples, one cup of coffee requires ≈ 130 L for growing coffee trees and the harvesting of coffee beans in countries with warm climates; and the production of 1 kg of beef requires ≈ 15,400 L for the growing of cattle feed, cleaning stables, and operating slaughtering houses. This is to say that in addition to providing sufficient renewable electric power, the provision of clean water will pose a tremendous challenge for mankind.

Key features

•Provides theoretical and practical insight into power quality problems related to power systems, electric machines, and power-electronic drives.

•Contains 148 practical application (example) problems with solutions.

•Includes 140 practical application problems posed at the end of chapters whose solutions are presented in the Instructor Manual, which is available from the publisher upon request.

•Comprises 1024 references—mostly journal and conference papers as well as national and international standards and guidelines.

References

[1] Jenkins R.V., Nier K.A. A record for invention: Thomas Edison and his papers. IEEE Trans. Educ. 1984;27(4).

[2] Nikola Tesla 1857–1943. Proc. IRE. 1943;31(5):194. doi:10.1109/JRPROC.1943.230030.

[3] Franck J. Transformation of Kinetic Energy of Free Electrons Into Excitation Energy of Atoms by Impacts. Nobel Price Lecture 1925.79–108. https://www.nobelprize.org/prizes/physics/1925/franck/biographical.

[4]The Editors of Encyclopedia Britannica. Conductors, Insulators, and Semiconductors, https://www.britannica.com/technology/semiconductor-diode.

[5]Edison Tech Center. Mercury Arc Rectifiers, https://edisontechcenter.org/MercArcRectifiers.html.

[6] Rissik H. Mercury-Arc Current Converters. 1941 Pitman.

[7] Hingorani N.G. Future role of power electronics in power systems. In: Proceedings of International Symposium on Power Semiconductor Devices and IC's: ISPSD '95, Yokohama, Japan; 1995:13–15. doi:10.1109/ISPSD.1995.515001.

[8]https://www.energy.gov/energysaver/save-electricity-and-fuel/lighting-choices-save-you-money/how-energy-efficient-light.

[9] Fuchs E.F., Fuchs H.A. Introduction to Energy, Renewable Energy and Electrical Engineering: Essentials for Engineering Science (STEM) Professionals and Students. Hardcover New York, NY: John Wiley & Sons; 2021.

[10]https://web.ecs.baylor.edu/faculty/grady/_2017_Texas_Synchrophasor_Network_Reports_for_2017_Updated_171027.pdf.

[11]https://www.welt.de/wirtschaft/article191195983/Energiewende-Das-droht-uns-in-der-kalten-Dunkelflaute.html.

[12] Dixon R.R. Thermal aging predictions from an Arrhenius plot with only one data point. IEEE Trans. Electr. Insul. 1980;E1-15(4):331.

[13] Fuller J.F., Fuchs E.F., Roesler D.J. Influence of harmonics on power system distribution protection. IEEE Trans. Power Deliv. 1988;TPWRD-3(2):546–554 (PES/IEEE Prize Paper Award 1989).

[14]https://www.springer.com/de/book/9783319304250.

[15]water footprint , org/Vereinigung Deutscher Gewaesserschutz e.v. und kfW.

[16] menschen im blickpunkt. Das Magazin des Muenchener Roten Kreuzes, Maerz. 2022. https://www.brk-muenchen.de/aktuell/menschen-im-blickpunkt/.

Acknowledgments

The authors wish to express their appreciation to their wives Wendy and Roshanak for their help in shaping and proofreading the manuscript. In particular, the encouragement and support of Dipl.-Ing. Dietrich J. Roesler, formerly with the US Department of Energy, Washington, DC, who was one of the first professionals to initiate the research on photovoltaic power plants [1] as part of the DOE mission, is greatly appreciated. Lastly, the work on numerical field calculation [2] initiated by the late Professor Edward A. Erdelyi is reflected in a part of this book.

References

[1] Dugan R.C., Jewell W.T., Roesler D.J. Harmonics and reactive power from line-commutated inverters in proposed photovoltaic subdivision. ID: 6637722; DOE Report Contract Number W-7405-ENG-2 1983.

[2] Trutt F.C., Erdelyi E.A., Jackson R.F. The non-linear potential equation and its numerical solution for highly saturated electrical machines. IEEE Trans. Aerospace. 1963;1(2):430–440.

Ewald F. Fuchs, Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO, United States

Mohammad A.S. Masoum, Department of Engineering, Utah Valley University, Orem, UT, United States

The climate dilemma

This book explains and discusses suitable components for limiting global temperature increase to 1.5°C by 2050 on a worldwide basis, although some countries (e.g., in Europe) have the ambition to reach this goal by 2035. The tools instrumental for reaching this temperature limit are renewable energy generated by wind-power and photovoltaic plants, as well as hydro and geothermal power, and energy-storage devices such as fuel cells, batteries, and stored hydrogen, which can be changed through methanation [1], for example, to fuel airplanes. The methanation reactions of COx were first discovered by Sabatier and Senderens in 1902. The colorless, pungent gas ammonia composed of nitrogen and hydrogen (NH3) was first prepared by English physical scientist Joseph Priestley in 1774, and its exact composition was determined by French chemist Claude-Louis Berthollet in 1785. Ammonia [2] is a flexible fuel for ships, has an energy density by volume almost 30% higher than that of liquid hydrogen, and is easier to distribute and store.

Nuclear power plants will contribute substantially to the goal of limiting climate change, although the storage of spent nuclear waste is contentious and problematic. It is interesting to note that nuclear fuel is man-made through enrichment process, and it does not occur in nature except in the form of uranium, which cannot be used in nuclear plants. The use of oil, natural gas, and coal must be minimized by relying on heat pumps for heating and cooling. Both CO2 generation and—even worse—methane, escaping permafrost due to global warming as well as drilling/fracking process and use [3], speed up climate change. Exacerbating climate change is the maldistribution of water and temperatures experienced on a worldwide basis [4].

In short, the technological tools are available to limit climate change and adapt to its consequences; however, technology cannot prevent climate change if humankind does not change its habits and psychological attitudes. Unfortunately, climate change is related to social dilemmas in which people must choose between their short-term own self-interest and the longer-term interest of the entire population [5]. To mitigate climate change, one can point to two important psychological changes required:

(1)People need to recognize their individual impact on the climate.

(2)There is conflict between self-interest and collective human interests, which creates the dilemma between short-term and longer-term human interest.

How should people change their lifestyles? One important health aspect is self-propulsion (e.g., walking, bicycling). Change purchasing habits by relying mostly on locally grown food and manufactured goods. Avoid pollution of land and oceans by not using plastic containers and packaging. Reduce use of chemicals during daily life, which will improve ground- and waste-water quality. Prevent the destruction of natural habitats (e.g., rain forest) and enhance survival of wildlife (e.g., bees, insects) by providing sufficient food supplies, enabling them to pollinate crops for human and animal consumption.

A recent book [6] details the consequences (e.g., increased temperature, floods, extreme dryness, lack of rain, tornadoes, high winds), best emission scenarios for CO2, the present state of conventional and renewable energy sources, and excessive electricity consumption which can neither be supplied by electric power plants, renewable plants or electric energy storage plants in any form as those fed by biogas or hydrogen. Although great progress has been made with the invention of the pn junction [7] as used in computers and LED lighting, it must be pointed out that a single cell phone requiring transmission towers consumes as much power as one standard-sized refrigerator. This is to say, technology cannot solve the climate change dilemma if the psychological attitude of the human race does not change accordingly.

References

[1] Rönsch S., Schneider J., Matthischke S., Schlüter M., Götz M., Lefebvre J., Prabhakaran P., Bajohr S. Review on methanation – from fundamentals to current projects. Fuel. 2016;166:276–296. doi:10.1016/j.fuel.2015.10.111.

[2] Priestley J. Experiments and Observations on Different Kinds of Air. second ed.; 163–177. 1775;vol. 1 Part 2, § 1: Observations on Alkaline Air. London, England.

[3]Methane Releases From Arctic Shelf May Be Much Larger and Faster Than Anticipated (Press release). National Science Foundation (NSF). March 10, 2010. Archived from the original on August 1, 2018. Retrieved 6 April 2018.

[4]https://www.nature.com/articles/s41893-021-00846-9

[5] Arnold J., et al. Work Psychology: Understanding Human Behaviour in the Workplace. Pearson Education; 2005.

[6] Fuchs E.F., Fuchs H.A. Introduction to Energy, Renewable Energy and Electrical Engineering, Essentials for Engineering Science (STEM) Professionals and Students. Wiley; 2021.

[7] Sedra A.S., Smith K.C. Microelectronic Circuits. fourth ed. New York/Oxford: Oxford University Press; 1998.

Summary overview of chapters

This textbook leads the way for power and energy development by introducing students and professionals to the design of renewable, reliable, and efficient components and their operation within modern interconnected power and distribution systems. It accommodates the paralleling/synchronization of smart AC and DC local distribution systems resulting in a hybrid system: Such an approach increases the power quality, reliability, and efficacy and efficiency of the electric energy system. Extensive deployment of power-electronic components such as rectifiers and inverters within the power and distribution system increases efficiency of generation, transmission, and use—although with increase in harmonics power quality may decrease if power-electronic devices and filters are not judiciously applied. The combination of AC and DC systems including DC transmission lines leads to a smart and hybrid power supply system.

Chapter 1 defines power quality and reviews causes of disturbances within a hybrid power system. It addresses steady-state and transient power quality phenomena and measures for power quality formulation. It discusses IEEE and international IEC standards and guidelines referring to power quality and its improvement techniques and tools such as specialty transformers, harmonic filters, surge suppressors, APLCS, and UPQCs. Chapters 2–4 introduce fundamental and harmonic models of transformers, induction machines, and synchronous machines, respectively. Chapter 5 presents power-electronic circuits such as rectifiers and inverters that are extensively applied to electric drives including nonideal lithium-ion battery and polymer electrolyte membrane (PEM) fuel cell: Electric automobiles can be used as storage for electric energy and can assist in voltage control within distribution systems by providing or consuming active and reactive powers. The charging of electric lithium-ion batteries is best if three-phase systems are available. Single-phase systems at low 120/240 V require a 100 kWh battery long charging time. Chapter 6 details the behavior of capacitors under the influence of harmonics and defines their harmonic constraints. In Chapter 7, Arrhenius plots are the basis for determining the lifetime of transformers and induction machines exposed to harmonics. In Chapter 8, the Newton-Raphson technique is used for the modeling and analysis of fundamental and harmonic operations of interconnected power systems. In Chapter 9, the impact of poor power quality on reliability, relaying, and security presents an important challenge to the operation of power and distribution systems: Passive and active filters can improve poor power quality phenomena as addressed in Chapter 10. In Chapter 11, the optimal energy-efficient, secure power systems operation can be achieved by proper sizing of capacitor allocation to permit sinusoidal operation. The use of unified power quality conditioner (UPQC) can assist in this effort. Analytical methods, numerical programming, heuristic and artificial intelligence (AI) such as genetic algorithms, simulated annealing, artificial neural networks, fuzzy set theory, graph search algorithm, particle swarm algorithm, and tabu search are powerful approaches for the optimal energy-efficient operation of smart power and distribution systems. Chapter 12 reviews and applies energy conservation and efficiency based on ground-water heat pumps, photovoltaic and thermal solar plants, fuel cells as well as wind power (WP) plants including storage plants based on hydro, batteries, fuel cells, and compressed air. Assisting in this effort are pulse-width-modulated (PWM) rectifiers and current-controlled, voltage-source inverters. This chapter concludes with recommendations for hydrogen generation through electrolysis and methanation of hydrogen for airplanes, buses, trains, ships, and automobiles.

Appendices 1, 2, 3, and 4 provide sampling techniques, Fourier analysis program, transformer banks including rectifier and inverter data used for experiments within the book, powers including nameplate data of single-and three-phase transformers as used in obtaining measurements, and measurement error formulas, respectively.

Chapter 1: Introduction to power quality

Abstract

This chapter defines power quality and presents the most important national (IEEE) and international (IEC) standards with regard to harmonics and transient phenomena as they occur in an interconnected power system consisting of transformers, electric machines, rectifiers, inverters, and control equipment. Causes of disturbances, classification of power quality issues, and the effect of poor power quality due to harmonics and voltage, current, and power transients are discussed. Various closed-form and discrete harmonic modeling approaches for simulation techniques and some circuits for power quality improvements are presented. Measurements are applied to components exposed to harmonics and transients supplement theoretical analyses. Harmonic current and voltage generation and response of detailed distribution feeders are investigated. It is anticipated that the increased use of nonlinear circuit elements exacerbates harmonic problems. There is a tradeoff between energy efficiency and decrease of power quality. The question is to which level one can permit power quality to decrease.

Keywords

Power quality standards; Interconnected power system; Causes of disturbances; Classification of power quality issues; Effects of poor power quality; Harmonic voltages and currents; Power transients; Closed-form and discrete modeling techniques; Power quality improvement; Measurements of harmonic effects; Tradeoff between energy efficiency and power quality

The subject of power quality is very broad by nature. It covers all aspects of power system engineering, from transmission and distribution level analyses to end-user problems. Therefore, electric power quality has become the concern of utilities, end users, architects, and civil engineers as well as manufacturers. These professionals must work together in developing solutions to power quality problems:

•Electric utility managers and designers must build and operate systems that take into account the interaction between customer facilities and power system. Electric utilities must understand the sensitivity of the end-use equipment to the quality of voltage.

•Customers must learn to respect the rights of their neighbors and control the quality of their nonlinear loads. Studies show that the best and the most efficient solution to power quality problems is to control them at their source. Customers can perform this by careful selection and control of their nonlinear loads and by taking appropriate actions to control and mitigate single-time disturbances and harmonics before connecting their loads to the power system.

•Architects and civil engineers must design buildings to minimize the susceptibility and vulnerability of electrical components to power quality problems.

•Manufacturers and equipment engineers must design devices that are compatible with the power system. This might mean a lower level of harmonic generation or less sensitivity to voltage distortions.

•Engineers must be able to devise ride-through capabilities of distributed generators (e.g., wind and solar generating plants).

This chapter introduces the subject of electric power quality. After a brief definition of power quality and its causes, detailed classification of the subject is presented. The formulations and measures used for power quality are explained, and the impacts of poor power quality on power system and end-use devices such as appliances are mentioned. A section is presented addressing the most important IEEE [1] and IEC [2] standards referring to power quality. The remainder of this chapter introduces issues that will be covered in the following chapters, including modeling and mitigation techniques for power quality phenomena in electric machines and power systems. This chapter contains nine application examples and ends with a summary.

1.1: Definition of power quality

Electric power quality has become an important part of power systems and electric machines. The subject has attracted the attention of many universities and industries, and a number of books have been published in this exciting and relatively new field [3–12].

Despite important papers, articles, and books published in the area of electric power quality, its definition has not been universally agreed upon. However, nearly everybody accepts that it is a very important aspect of power systems and electric machinery with direct impacts on efficiency, security, and reliability. Various sources use the term power quality with different meaning. It is used synonymously with supply reliability, service quality, voltage quality, current quality, quality of supply, and quality of consumption.

Judging by the different definitions, power quality is generally meant to express the quality of voltage and/or the quality of current and can be defined as: the measure, analysis, and improvement of the bus voltage to maintain a sinusoidal waveform at rated voltage and frequency. This definition includes all momentary and steady-state phenomena.

1.2: Causes of disturbances in power systems

Although a significant literature on power quality is now available, most engineers, facility managers, and consumers remain unclear as to what constitutes a power quality problem. Furthermore, due to the power system impedance, any current (or voltage) harmonic will result in the generation and propagation of voltage (or current) harmonics and affects the entire power system. Fig. 1.1 illustrates the impact of current harmonics generated by a nonlinear load on a typical power system with linear loads.

Fig. 1.1

Fig. 1.1 Propagation of harmonics (generated by a nonlinear load) in power systems.

What are the origins of the power quality problem? Some references [9] divide the distortion sources into three categories: small and predictable (e.g., residential consumers generating harmonics), large and random (e.g., arc furnaces producing voltage fluctuations and flicker), and large and predictable (e.g., static converters of smelters and high-voltage DC transmission causing characteristic and uncharacteristic harmonics as well as harmonic instability). However, the likely answers to the question are these: unpredictable events, the electric utility, the customer, and the manufacturer.

1.2.1: Unpredictable events

Both electric utilities and end users agree that more than 60% of power quality problems are generated by natural and unpredictable events [6]. Some of these include faults, lightning surge propagation, resonance, ferroresonance, and geomagnetically induced currents (GICs) due to solar flares [13]. These events are considered to be utility-related problems.

1.2.2: The electric utility

There are three main sources of poor power quality related to utilities:

•The point of supply generation. Although synchronous machines generate nearly perfect sinusoidal voltages (harmonic content less than 3%), there are power quality problems originating at generating plants which are mainly due to maintenance activity, planning, capacity and expansion constraints, scheduling, events leading to forced outages, and load transferring from one substation to another.

•The transmission system. Relatively few power quality problems originate in the transmission system. Typical power quality problems originating in the transmission system are galloping (under high-wind conditions resulting in supply interruptions and/or random voltage variations), lightning (resulting in a spike or transient overvoltage), insulator flashover, voltage dips (due to faults), interruptions (due to planned outages by utility), transient overvoltages (generated by capacitor and/or inductor switching, and lightning), transformer energizing (resulting in inrush currents that are rich in harmonic components), improper operation of voltage regulation devices (which can lead to long-duration voltage variations), slow voltage variations (due to a long-term variation of the load caused by the continuous switching of devices and load), flexible AC transmission system (FACTS) devices [14] and high-voltage DC (HVDC) systems [15], corona [16], power line carrier signals [17], broadband power line (BPL) communications [18], and electromagnetic fields (EMFs) [19].

•The distribution system. Typical power quality problems originating in the distribution system are voltage dips, spikes, and interruptions, transient overvoltages, transformer energizing, improper operation of voltage regulation devices, slow voltage variations, power line carrier signals, BPL, and EMFs.

1.2.3: The customer

Customer loads generate a considerable portion of power quality problems in today's power systems. Some end-user-related problems are harmonics (generated by nonlinear loads such as power electronic devices and equipment, renewable energy sources, FACTS devices, adjustable-speed drives, uninterruptible power supplies (UPS), fax machines, laser printers, computers, fluorescent lights, and light-emitting diode (LED) lights), poor power factor (due to highly inductive loads such as induction motors and air-conditioning units), flicker (generated by arc furnaces [20]), transients (mostly generated inside a facility due to device switching, electrostatic discharge, and arcing), improper grounding (causing most reported customer problems), frequency variations (when secondary and backup power sources, such as diesel engine and turbine generators, are used), misapplication of technology, wiring regulations, and other relevant standards.

1.2.4: Manufacturing regulations

There are two main sources of poor power quality related to manufacturing regulations:

•Standards. The lack of standards for testing, certification, sale, purchase, installation, and use of electronic equipment and appliances is a major cause of power quality problems.

•Equipment sensitivity. The proliferation of sensitive electronic equipment and appliances is one of the main reasons for the increase of power quality problems. The design characteristics of these devices, including computer-based equipment, have increased the incompatibility of a wide variety of these devices with the electrical environment [21].

Power quality therefore must necessarily be tackled from three fronts, namely:

•The utility must design, maintain, and operate the power system while minimizing power quality problems.

•The end user must employ proper wiring, system grounding practices, and state-of-the-art electronic devices.

•The manufacturer must design electronic devices that keep electrical environmental disturbances to a minimum and that are immune to anomalies of the power supply line.

1.3: Classification of power quality issues

To solve power quality problems it is necessary to understand and classify this relatively complicated subject. This section is based on the power quality classification and information from Refs. [6, 9].

There are different classifications for power quality issues, each using a specific property to categorize the problem. Some of them classify the events as steady-state and non–steady-state phenomena. In some regulations (e.g., ANSI C84.1 [22]), the most important factor is the duration of the event. Other guidelines (e.g., IEEE-519) use the wave shape (duration and magnitude) of each event to classify power quality problems. Other standards (e.g., IEC) use the frequency range of the event for the classification.

For example, IEC 61000-2-5 uses the frequency range and divides the problems into three main categories: low frequency (< 9 kHz), high frequency (> 9 kHz), and electrostatic discharge phenomena. In addition, each frequency range is divided into radiated and conducted disturbances. Table 1.1 shows the principal phenomena causing electromagnetic disturbances according to IEC classifications [9]. All these phenomena are considered to be power quality issues; however, the two conducted categories are more frequently addressed by the industry.

Table 1.1

The magnitude and duration of events can be used to classify power quality events, as shown in Fig. 1.2. In the magnitude–duration plot, there are nine different parts [11]. Various standards give different names to events in these parts. The voltage magnitude is split into three regions:

•interruption: voltage magnitude is zero,

•undervoltage: voltage magnitude is below its nominal value, and

•overvoltage: voltage magnitude is above its nominal value.

Fig. 1.2

Fig. 1.2 Magnitude-duration plot for classification of power quality events [11] .

The duration of these events is split into four regions: very short, short, long, and very long. The borders in this plot are somewhat arbitrary and the user can set them according to the standard that is used.

IEEE standards use several additional terms (as compared with IEC terminology) to classify power quality events. Table 1.2 provides information about categories and characteristics of electromagnetic phenomena defined by IEEE-1159 [23]. These categories are briefly introduced in the remaining parts of this section.

Table 1.2

1.3.1: Transients

Power system transients are undesirable, fast- and short-duration events that produce distortions. Their characteristics and waveforms depend on the mechanism of generation and the network parameters (e.g., resistance, inductance, and capacitance) at the point of interest. Surge is often considered synonymous with transient.

Transients can be classified with their many characteristic components such as amplitude, duration, rise time, frequency of ringing polarity, energy delivery capability, amplitude spectral density, and frequency of occurrence. Transients are usually classified into two categories: impulsive and oscillatory (Table 1.2).

An impulsive transient is a sudden frequency change in the steady-state condition of voltage, current, or both that is unidirectional in polarity (Fig. 1.3). The most common cause of impulsive transients is a lightning current surge. Impulsive transients can excite the natural frequency of the system.

Fig. 1.3

Fig. 1.3 Impulsive transient current caused by lightning strike, result of PSpice simulation.

An oscillatory transient is a sudden frequency change in the steady-state condition of voltage, current, or both that includes both positive and negative polarity values. Oscillatory transients occur for different reasons in power systems such as appliance switching, capacitor bank switching (Fig. 1.4), fast-acting overcurrent protective devices, and ferroresonance (Fig. 1.5).

Fig. 1.4

Fig. 1.4 Low-frequency oscillatory transient caused by capacitor bank energization.

Fig. 1.5

Fig. 1.5 Low-frequency oscillatory transient caused by ferroresonance of a transformer at no load, result of Mathematica simulation.

1.3.2: Short-duration voltage variations

This category encompasses the IEC category of voltage dips and short interruptions. According to the IEEE-1159 classification, there are three different types of short-duration events (Table 1.2): instantaneous, momentary, and temporary. Each category is divided into interruption, sag, and swell. Principal cases of short-duration voltage variations are fault conditions, large load energization, and loose connections.

Interruption. Interruption occurs when the supply voltage (or load current) decreases to less than 0.1 pu for less than 1 min, as shown in Fig. 1.6. Some causes of interruption are equipment failures, control malfunction, and blown fuse or breaker opening.

Fig. 1.6

Fig. 1.6 Momentary interruptions due to a fault.

The difference between long (or sustained) interruption and interruption is that in the former the supply is restored manually, but during the latter the supply is restored automatically. Interruption is usually measured by its duration. For example, according to the European standard EN-50160 [24]:

•a short interruption is up to 3 min and

•a long interruption is longer than 3 min.

However, based on the standard IEEE-1250 [25]:

•An instantaneous interruption is between 0.5 and 30 cycles.

•A momentary interruption is between 30 cycles and 2 s.

•A temporary interruption is between 2 s and 2 min.

•A sustained interruption is longer than 2 min.

Sags (Dips). Sags are short-duration reductions in the rms voltage between 0.1 and 0.9 pu, as shown in Fig. 1.7. There is no clear definition for the duration of sag, but it is usually between 0.5 cycles and 1 min. Voltage sags are usually caused by:

•energization of heavy loads (e.g., arc furnace),

•starting of large induction motors,

•single line-to-ground faults, and

•load transferring from one power source to another.

Fig. 1.7

Fig. 1.7 Voltage sag caused by a single line-to-ground (SLG) fault.

Each of these cases may cause a sag with a special (magnitude and duration) characteristic. For example, if a device is sensitive to voltage sag of 25%, it will be affected by induction motor starting [11]. Sags are main reasons for malfunctions of electrical low-voltage devices. Uninterruptible power supply (UPS) or power conditioners are mostly used to prevent voltage sags.

Swells. The increase of voltage magnitude between 1.1 and 1.8 pu is called swell, as shown in Fig. 1.8. The most accepted duration of a swell is from 0.5 cycles to 1 min [7]. Swells are not as common as sags and their main causes are:

•switching off of a large load,

•energizing a capacitor bank, or

•voltage increase of the unfaulted phases during a single line-to-ground fault [10].

Fig. 1.8

Fig. 1.8 Instantaneous voltage swell caused by a single line-to-ground fault.

In some textbooks the term momentary overvoltage is used as a synonym for the term swell. As in the case of sags, UPS or power conditioners are typical solutions to limit the effect of swell [10].

1.3.3: Long-duration voltage variations

According to standards (e.g., IEEE-1159, ANSI-C84.1), the deviation of the rms value of voltage from the nominal value for longer than 1 min is called long-duration voltage variation. The main causes of long-duration voltage variations are load variations and system switching operations. IEEE-1159 divides these events into three categories (Table 1.2): sustained interruption, undervoltage, and overvoltage.

Sustained interruption. Sustained (or long) interruption is the most severe and the oldest power quality event at which voltage drops to zero and does not return automatically. According to the IEC definition, the duration of sustained interruption is more than 3 min; but based on the IEEE definition the duration is more than 1 min. The number and duration of long interruptions are very important characteristics in measuring the ability of a power system to deliver service to customers. The most important causes of sustained interruptions are:

•fault occurrence in a part of power systems with no redundancy or with the redundant part out of operation,

•an incorrect intervention of a protective relay leading to a component outage, or

•scheduled (or planned) interruption in a low-voltage network with no redundancy.

Undervoltage. The undervoltage condition occurs when the rms voltage decreases to 0.8–0.9 pu for more than 1 min.

Overvoltage. Overvoltage is defined as an increase in the rms voltage to 1.1–1.2 pu for more than 1 min. There are three types of overvoltages:

•overvoltages generated by an insulation fault, ferroresonance, faults with the alternator regulator, tap changer transformer, or overcompensation;

•lightning overvoltages; and

•switching overvoltages produced by rapid modifications in the network structure such as opening of protective devices or the switching on of capacitive circuits.

1.3.4: Voltage imbalance

When voltages of a three-phase system are not identical in magnitude and/or the phase differences between them are not exactly 120 degrees, voltage imbalance occurs [10]. There are two ways to calculate the degree of imbalance:

•divide the maximum deviation from the average of three-phase voltages by the average of three-phase voltages or

•compute the ratio of the negative- (or zero-) sequence component to the positive-sequence component [7].

The main causes of voltage imbalance in power systems are:

•unbalanced single-phase loading in a three-phase system,

•overhead transmission lines that are not transposed,

•blown fuses in one phase of a three-phase capacitor bank, and

•severe voltage imbalance (e.g., > 5%), which can result from single phasing conditions.

1.3.5: Waveform distortion

A steady-state deviation from a sine wave of power frequency is called waveform distortion [7]. There are five primary types of waveform distortions: DC offset, harmonics, interharmonics, notching, and electric noise. A Fourier series is usually used to analyze the nonsinusoidal waveform.

DC offset. The presence of a DC current and/or voltage component in an AC system is called DC offset [7]. Main causes of DC offset in power systems are:

•employment of rectifiers and other electronic switching devices and

•geomagnetic disturbances [6,7,13] causing GICs.

The main detrimental effects of DC offset in alternating networks are:

•half-cycle saturation of transformer core [26–28],

•generation of even harmonics [26] in addition to odd harmonics [29,30],

•additional heating in appliances leading to a decrease of the lifetime of transformers [31–36], rotating machines, and electromagnetic devices, and

•electrolytic erosion of grounding electrodes and other connectors.

Fig. 1.9A shows strong half-cycle saturation in a transformer due to DC magnetization and the influence of the tank, and Fig. 1.9B exhibits less half-cycle saturation due to DC magnetization and the absence of any tank. One concludes that to suppress DC currents due to rectifiers and geomagnetically induced currents, three-limb transformers with a relatively large air gap between core and tank should be used.

Fig. 1.9Fig. 1.9

Fig. 1.9 Measured voltages and currents at balanced DC bias current I DC   =  − 2 A for a 2.3 kVA three-limb transformer (A) at full load with tank (note the strong half-cycle saturation) and (B) at full load without tank (note the reduced half-cycle saturation) [27] . Dividing the ordinate values by 2.36 and 203 the voltages in volts and the currents in amperes are obtained, respectively.

Harmonics. Harmonics are sinusoidal voltages or currents with frequencies that are integer multiples of the power system (fundamental) frequency (usually, f = 50 or 60 Hz). For example, the frequency of the hth harmonic is (hf). Periodic nonsinusoidal waveforms can be subjected to Fourier series and can be decomposed into the sum of fundamental component and harmonics. Main sources of harmonics in power systems are:

•industrial nonlinear loads (Fig. 1.10) such as power electronic equipment, for example, drives (Fig. 1.10A), rectifiers (Fig. 1.10B and C), inverters, or loads generating electric arcs, for example, arc furnaces, welding machines, and lighting and

Fig. 1.10 (A) Computed electronic switch ( upper graph ) and motor ( lower graph ) currents of an adjustable-speed brushless DC motor drive for a phase angle of Θ = 0 degree [29]. (B) Voltage notching caused by a three-phase rectifier for a firing angle of α = 50 degree, result of PSpice simulation. Top: phase current; second from top: line-to-line voltage of rectifier; third from top: line-to-line voltages of infinite bus; bottom: DC output voltage of rectifier. (C) Voltage notching caused by a three-phase rectifier with interphase reactor for a firing angle of α = 0 degree, result of PSpice simulation. Waveshapes with notches: line-to-line voltages of rectifier, vab and vab′being the line-to-line voltages of the two voltage systems; sinusoidal waveshape: line-to-line voltage of infinite bus vAB.

•residential loads with switch-mode power supplies such as television sets, computers (Fig. 1.11), and fluorescent and energy-saving lamps.

Fig. 1.11 Measured current wave shape of state-of-the-art personal computer (PC) (many periods) [45].

Some detrimental effects of harmonics are:

•maloperation of control devices,

•additional losses in capacitors, transformers, and rotating machines,

•additional noise from motors and other apparatus,

•telephone interference, and

•causing parallel and series resonance frequencies (due to the power factor correction capacitor and cable capacitance), resulting in voltage amplification even at a remote location from the distorting load.

Recommended solutions to reduce and control harmonics are applications of high-pulse rectification, passive, active, and hybrid filters, and custom power devices such as active-power line conditioners (APLCs) and unified power quality conditioners (UPQCs).

Interharmonics. Interharmonics are discussed in Section 1.4.1. Their frequencies are not integer multiples of the fundamental frequency.

Notching. A periodic voltage disturbance caused by line-commutated thyristor circuits is called notching. The notching appears in the line voltage waveform during normal operation of power electronic devices when the current commutates from one phase to another. During this notching period, there exists a momentary short-circuit between the two commutating phases, reducing the line voltage; the voltage reduction is limited only by the system impedance.

Notching is repetitive and can be characterized by its frequency spectrum (Fig. 1.10B and C). The frequency of this spectrum is quite high. Usually it is not possible to measure it with equipment normally used for harmonic analysis. Notches can impose extra stress on the insulation of transformers, generators, and sensitive measuring equipment.

Notching can be characterized by the following properties:

•Notch depth: average depth of the line voltage notch from the sinusoidal waveform at the fundamental frequency;

•Notch width: the duration of the commutation process;

•Notch area: the product of notch depth and width; and

•Notch position: where the notch occurs on the sinusoidal waveform.

Some standards (e.g., IEEE-519) set limits for notch depth and duration (with respect to the system impedance and load current) in terms of the notch depth, the total harmonic distortion THDv of supply voltage, and the notch area for different supply systems.

Electric noise. Electric noise is defined as unwanted electrical signals with broadband spectral content lower than 200 kHz [37] superimposed on the power system voltage or current in phase conductors, or found on neutral conductors or signal lines. Electric noise may result from faulty connections in transmission or distribution systems, arc furnaces, electrical furnaces, power electronic devices, control circuits, welding equipment, loads with solid-state rectifiers, improper grounding, turning off capacitor banks, adjustable-speed drives, corona, and broadband power line (BPL) communication circuits. The problem can be mitigated by using filters, line conditioners, and dedicated lines or transformers. Electric noise impacts electronic devices such as microcomputers and programmable controllers.

1.3.6: Voltage fluctuation and flicker

Voltage fluctuations are systemic variations of the voltage envelope or random voltage changes, the magnitude of which does not normally exceed specified voltage ranges (e.g., 0.9–1.1 pu as defined by ANSI C84.1-1982) [22,38]. Voltage fluctuations are divided into two categories:

•step-voltage changes, regular or irregular in time and

•cyclic or random voltage changes produced by variations in the load impedances.

Voltage fluctuations degrade the performance of the equipment and cause instability of the internal voltages and currents of electronic equipment. However, voltage fluctuations less than 10% do not affect electronic equipment. The main causes of voltage fluctuation are pulsed-power output, resistance welders, start-up of drives, arc furnaces, drives with rapidly changing loads, and rolling mills.

Flicker. Flicker (Fig. 1.12) has been described as continuous and rapid variations in the load current magnitude which causes voltage variations. The term flicker is derived from the impact of the voltage fluctuation on lamps such that they are perceived to flicker by the human eye. This may be caused by an arc furnace, one of the most common causes of the voltage fluctuations in utility transmission and distribution systems.

Fig. 1.12

Fig. 1.12 Voltage flicker caused by arc furnace operation.

1.3.7: Power–frequency variations

The deviation of the power system fundamental frequency from its specified nominal value (e.g., 50 or 60 Hz) is defined as power frequency variation [39]. If the balance between generation and demand (load) is not maintained, the frequency of the power system will deviate because of changes in the rotational speed of electromechanical generators. The amount of deviation and its duration of the frequency depend on the load characteristics and response of the generation control system to load changes. Faults of the power transmission system can also cause frequency variations outside of the accepted range for normal steady-state operation of the power system.

1.4: Formulations and measures used for power quality

This section briefly introduces some of the most commonly used formulations and measures of electric power quality as used in this book and as defined in standard documents. Main sources for power quality terminologies are IEEE Std 100 [40], IEC Std 61000-1-1, and CENELEC Std EN 50160 [24,41]. Appendix C of Ref. [11] presents a fine survey of power quality definitions.

1.4.1: Harmonics

Nonsinusoidal current and voltage waveforms (Figs. 1.13–1.20) occur in today's power systems due to equipment with nonlinear characteristics such as transformers, rotating electric machines, FACTS devices, power electronics components (e.g., rectifiers, triacs, thyristors, and diodes with capacitor smoothing, which are used extensively in PCs, audio, and video equipment), switch-mode power supplies, compact fluorescent lamps, induction furnaces, adjustable AC and DC drives, arc furnaces, welding tools, renewable energy sources, and HVDC networks. The main effects of harmonics are maloperation of control devices, telephone interferences, additional line losses (at fundamental and harmonic frequencies), and decreased lifetime and increased losses in utility equipment (e.g., transformers, rotating machines, and capacitor banks) and customer devices.

Fig. 1.13

Fig. 1.13 Measured wave shapes of single-phase induction motor fed by thyristor/triac controller at rated operation [42].

Fig. 1.14

Fig. 1.14 Measured wave shapes of three-phase induction motor fed by thyristor/triac controller at rated operation [42] .

Fig. 1.15

Fig. 1.15 Measured wave shapes of 4.5 kVA three-phase transformer feeding full-wave rectifier [43].

Fig. 1.16

Fig. 1.16 Calculated current of brushless DC motor in full-on mode at rated operation [29] .

Fig. 1.17

Fig. 1.17 Calculated current of brushless DC motor in PWM mode at rated operation [29] .

Fig. 1.18

Fig. 1.18 Measured wave shapes of 15 kVA three-phase transformer feeding resonant rectifier [43] .

Fig. 1.19

Fig. 1.19 Measured wave shapes of 15 kVA three-phase transformer fed by PWM inverter [43] .

Fig. 1.20

Fig. 1.20 (A) Measured current and (B) measured current spectrum of 20 kW/25 kVA wind-power plant supplying power via inverter into the 240 V three-phase distribution system at rated load [44].

The periodic nonsinusoidal waveforms can be formulated in terms of Fourier series. Each term in the Fourier series is called the harmonic component of the distorted waveform. The frequency of harmonics are integer multiples of the fundamental frequency. Therefore, nonsinusoidal voltage and current waveforms can be defined as

si1_e

   (1.1a)

si2_e

   (1.1b)

where ωo is the fundamental frequency, h is the harmonic order, and Vrms(h), Irms(h), αh, and βh are the rms amplitude values and phase shifts of voltage and current for the hth harmonic.

Even and odd harmonics of a nonsinusoidal function correspond to even (e.g., 2, 4, 6, 8, …) and odd (e.g., 3, 5, 7, 9, …) components of its Fourier series. Harmonics of order 1 and 0 are assigned to the fundamental frequency and the DC component of the waveform, respectively. When both positive and negative half-cycles of the waveform have identical shapes, the wave shape has half-wave symmetry and the Fourier series contains only odd harmonics. This is the usual case with voltages and currents of power systems. The presence of even harmonics is often a clue that there is something wrong (e.g., imperfect gating of electronic switches [42]), either with the load equipment or with the transducer used to make the measurement. There are notable exceptions to this such as half-wave rectifiers, arc furnaces (with random arcs), and the presence of GICs in power systems [27].

1.4.1.1: Triplen harmonics

Triplen harmonics (Fig. 1.21) are the odd multiples of the third harmonic (h = 3, 9, 15, 21, …). These harmonic orders become an important issue for grounded-wye systems with current flowing in the neutral line of a wye configuration. Two typical problems are overloading of the neutral conductor and telephone interference.

Fig. 1.21

Fig. 1.21 Input current to personal computer with dominant third harmonic [45] .

For a system of perfectly balanced three-phase nonsinusoidal loads, fundamental current components in the neutral are zero. The third harmonic neutral currents are three times the third-harmonic phase currents because they coincide in phase or time.

Transformer winding connections have a significant impact on the flow of triplen harmonic currents caused by three-phase nonlinear loads. For the grounded wye-delta transformer, the triplen harmonic currents enter the wye side and since they are in phase, they add in the neutral. The delta winding provides ampere-turn balance so that they can flow in the delta, but they remain trapped in the delta and are absent in the line currents of the delta side of the transformer. This type of transformer connection is the most commonly employed in utility distribution substations with the delta winding connected to the transmission feeder. Using grounded-wye windings on both sides of the transformer allows balanced triplen harmonics to flow unimpeded from the low-voltage system to the high-voltage system. They will be present in equal proportion on both sides of a transformer.

1.4.1.2: Subharmonics

Subharmonics have frequencies below the fundamental frequency. There are rarely subharmonics in power systems. However, due to the fast control of electronic power supplies of computers, inter- and subharmonics are generated in the input current (Fig. 1.11) [45]. Resonance between the harmonic currents or voltages with the power system (series) capacitance and inductance may cause subharmonics, called subsynchronous resonance [46]. They may be generated when a system is highly inductive (such as an arc furnace during start-up) or when the power system contains large capacitor banks for power factor correction or filtering.

1.4.1.3: Interharmonics

The frequency of interharmonics are not integer multiples of the fundamental frequency. Interharmonics appear as discrete frequencies or as a band spectrum. Main sources of interharmonic waveforms are static frequency converters, cycloconverters, induction motors, arcing devices, and computers. Interharmonics cause flicker, low-frequency torques [32], additional temperature rise in induction machines [33,34], and malfunctioning of protective (under-frequency) relays [35]. Interharmonics have been included in a number of guidelines such as the IEC 61000-4-7 [36] and the IEEE-519. However, many important related issues, such as the range of frequencies, should be addressed in revised guidelines.

1.4.1.4: Characteristic and uncharacteristic harmonics

The harmonics of orders 12k + 1 (positive sequence) and 12k – 1 (negative sequence) are called characteristic and uncharacteristic harmonics, respectively. The amplitudes of these harmonics are inversely proportional to the harmonic order. Filters are used to reduce characteristic harmonics of large power converters. When the AC system is weak [47] and the operation is not perfectly symmetrical, uncharacteristic harmonics appear. It is not economical to reduce uncharacteristic harmonics with filters; therefore, even a small injection of these harmonic currents can, via parallel resonant conditions, produce very large voltage distortion levels.

1.4.1.5: Positive-, negative-, and zero-sequence harmonics [48]

Assuming a positive-phase (abc) sequence balanced three-phase power system, the expressions for the fundamental currents are

si3_e    (1.2)

The negative displacement angles indicate that the fundamental phasors rotate clockwise in the space–time plane.

For the third harmonic (zero-sequence) currents,

si4_e

   (1.3)

These equations show that the third harmonic phasors are in phase and have zero displacement angles between them. The third harmonic currents are known as zero-sequence harmonics.

The expressions for the fifth harmonic currents are

si5_e

   (1.4)

Note that displacement angles are positive; therefore, the phase sequence of this harmonic is counterclockwise, and opposite to that of the fundamental. The fifth harmonic currents are known as negative-sequence harmonics.