ELECTRIC POWER SYSTEMS

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ELECTRIC POWERSYSTEMS

ELECTRIC POWERSYSTEMSA CONCEPTUAL INTRODUCTIONAlexandra von MeierA JOHN WILEY & SONS, INC., PUBLICATION

To my late grandfatherKarl Wilhelm Claubergwho introduced me toThe Joy of Explaining Things

&CONTENTSPrefacexiii1. The Physics of Electricity1.11.21.31.41.5Basic roductionChargePotential or VoltageGroundConductivityCurrentOhm’s law81.2.1 Resistance1.2.2 Conductance1.2.3 Insulation91011Circuit Fundamentals111.3.11.3.21.3.31.3.411121313Static ChargeElectric CircuitsVoltage DropElectric ShockResistive Heating141.4.1 Calculating Resistive Heating1.4.2 Transmission Voltage and Resistive Losses1517Electric and Magnetic The Field as a ConceptElectric FieldsMagnetic FieldsElectromagnetic InductionElectromagnetic Fields and Health EffectsElectromagnetic Radiation2. Basic Circuit Analysis2.11Modeling Circuits3030vii

viii2.22.32.4CONTENTSSeries and Parallel Circuits312.2.12.2.22.2.32.2.432333536Resistance in SeriesResistance in ParallelNetwork ReductionPractical AspectsKirchhoff’s Laws372.3.12.3.22.3.32.3.438394041Kirchhoff’s Voltage LawKirchhoff’s Current LawApplication to Simple CircuitsThe Superposition PrincipleMagnetic Circuits3. AC Power3.13.23.33.44449Alternating Current and Voltage493.1.1 Historical Notes3.1.2 Mathematical Description3.1.3 The rms .1 Definition of Electric Power3.3.2 Complex Power3.3.3 The Significance of Reactive Power666873Phasor Notation753.4.1 Phasors as Graphics3.4.2 Phasors as Exponentials3.4.3 Operations with Phasors7578804. Generators854.1The Simple Generator864.2The Synchronous Generator924.2.1 Basic Components and Functioning4.2.2 Other Design Aspects92974.3Operational Control of Synchronous e Generator: Real PowerSingle Generator: Reactive PowerMultiple Generators: Real PowerMultiple Generators: Reactive Power

CONTENTSix4.4Operating Limits1154.5The Induction Generator1184.5.1 General Characteristics4.5.2 Electromagnetic Characteristics118120Inverters1234.65. Loads1275.15.25.3Resistive LoadsMotorsElectronic Devices1281311345.4Load from the System Perspective1365.4.1 Coincident and Noncoincident Demand5.4.2 Load Profiles and Load Duration Curve137138Single- and Multiphase Connections1405.56. Transmission and Distribution6.16.26.36.46.5144System 147149150153156158Historical NotesStructural FeaturesSample DiagramTopologyLoop FlowStations and SubstationsReconfiguring the SystemThree-Phase 3164166166167Rationale for Three PhasesBalancing LoadsDelta and Wye ConnectionsPer-Phase AnalysisThree-Phase PowerD.C. TransmissionTransformers1686.3.1 General Properties6.3.2 Transformer Heating6.3.3 Delta and Wye Transformers168170172Characteristics of Power Lines1756.4.1 Conductors6.4.2 Towers, Insulators, and Other Components175179Loading1826.5.1 Thermal Limits6.5.2 Stability Limit182183

xCONTENTS6.66.7Voltage ControlProtection6.7.1 Basics of Protection and Protective Devices6.7.2 Protection Coordination7. Power Flow Analysis7.17.27.37.47.58.28.38.4195IntroductionThe Power Flow Problem7.2.1 Network Representation7.2.2 Choice of Variables7.2.3 Types of Buses7.2.4 Variables for Balancing Real Power7.2.5 Variables for Balancing Reactive Power7.2.6 The Slack Bus7.2.7 Summary of Variables195197197198201201202204205Example with Interpretation of Results2067.3.1 Six-Bus Example7.3.2 Tweaking the Case7.3.3 Conceptualizing Power Flow206210211Power Flow Equations and Solution Methods2147.4.1 Derivation of Power Flow Equations7.4.2 Solution Methods7.4.3 Decoupled Power Flow214217224Applications and Optimal Power Flow2268. System Performance8.1184188188192229Reliability2298.1.1 Measures of Reliability8.1.2 Valuation of 8.3.38.3.4234236240249The Concept of StabilitySteady-State StabilityDynamic StabilityVoltage StabilityPower Quality2508.4.1 Voltage8.4.2 Frequency8.4.3 Waveform251253255

CONTENTS9. System Operation, Management, and New Technology9.19.29.39.4xi259Operation and Control on Different Time TheScale of a CycleScale of Real-Time OperationScale of SchedulingPlanning ScaleNew geDistributed GenerationAutomationFACTSHuman s and EngineersCognitive Representations of Power SystemsOperational CriteriaImplications for Technological InnovationImplications for Restructuring292Appendix: Symbols, Units, Abbreviations, and Acronyms298Index302

&ACKNOWLEDGMENTSMany individuals and organizations have made the writing of this text possible. I amdeeply grateful to my teachers for their mentorship, inspiration, and clarity, mostespecially Gene Rochlin, Felix Wu, and Oscar Ichazo. I am also indebted to themany professionals who took the time to show me around power systems inthe field and teach me about their work. The project was supported directly andindirectly by a University of California President’s Postdoctoral Fellowship,the University of California Energy Institute (UCEI), the California EnergyCommission’s Public Interest Energy Research (PIER) program, and the CaliforniaInstitute for Energy Efficiency (CIEE). I especially thank Carl Blumstein, SeverinBorenstein, Ron Hofmann, Laurie ten Hope, and Gaymond Yee for their encouragement at various stages in the process of writing this book.I also thank all my colleagues who graciously read, discussed, and helpedimprove portions of the draft manuscript. They include Raquel Blanco, AlexFarrell, Hannah Friedman, John Galloway, Chris Greacen, Sean Greenwalt,Dianne Hawk, Nicole Hopper, Merrill Jones, Chris Marnay, Andrew McAllister,Alex McEachern, Steve Shoptaugh, Kurt von Meier, and Jim Williams. Mygratitude also extends to all others who participated in the development of thetext—particularly my students who never cease to ask insightful and challengingquestions—and to my friends and family who offered encouragement andsupport. Darcy McCormick, Thomas Harris, and Steve Shoptaugh helped prepareillustrations, Cary Berkley organized the manuscript, and Trumbull Rogersimproved it by careful editing. Of course, I am solely responsible for any errors.As an endeavor that has not, to my knowledge, been attempted before, this textis necessarily a work in progress. Suggestions from readers for improving itsaccuracy and clarity will be warmly welcomed.ALEXANDRA VON MEIERSebastopol, CaliforniaAugust 2005xv

&CHAPTER 1The Physics of Electricity1.11.1.1BASIC QUANTITIESIntroductionThis chapter describes the quantities that are essential to our understanding of electricity: charge, voltage, current, resistance, and electric and magnetic fields. Moststudents of science and engineering find it very hard to gain an intuitive appreciationof these quantities, since they are not part of the way we normally see and makesense of the world around us. Electrical phenomena have a certain mystique thatderives from the difficulty of associating them with our direct experience, but alsofrom the knowledge that they embody a potent, fundamental force of nature.Electric charge is one of the basic dimensions of physical measurement, alongwith mass, distance, time and temperature. All other units in physics can beexpressed as some combination of these five terms. Unlike the other four,however, charge is more remote from our sensory perception. While we caneasily visualize the size of an object, imagine its weight, or anticipate the durationof a process, it is difficult to conceive of “charge” as a tangible phenomenon.To be sure, electrical processes are vital to our bodies, from cell metabolism tonervous impulses, but we do not usually conceptualize these in terms of electricalquantities or forces. Our most direct and obvious experience of electricity is toreceive an electric shock. Here the presence of charge sends such a strong waveof nervous impulses through our body that it produces a distinct and unique sensation. Other firsthand encounters with electricity include hair that defiantlystands on end, a zap from a door knob, and static cling in the laundry. Yet theseexperiences hardly translate into the context of electric power, where we canwitness the effects of electricity, such as a glowing light bulb or a rotating motor,while the essential happenings take place silently and concealed within pieces ofmetal. For the most part, then, electricity remains an abstraction to us, and werely on numerical and geometric representations—aided by liberal analogies fromother areas of the physical world—to form concepts and develop an intuitionabout it.Electric Power Systems: A Conceptual Introduction, by Alexandra von MeierCopyright # 2006 John Wiley & Sons, Inc.1

21.1.2THE PHYSICS OF ELECTRICITYChargeIt was a major scientific accomplishment to integrate an understanding of electricitywith fundamental concepts about the microscopic nature of matter. Observations ofstatic electricity like those mentioned earlier were elegantly explained by BenjaminFranklin in the late 1700s as follows: There exist in nature two types of a propertycalled charge, arbitrarily labeled “positive” and “negative.” Opposite charges attracteach other, while like charges repel. When certain materials rub together, one type ofcharge can be transferred by friction and “charge up” objects that subsequently repelobjects of the same kind (hair), or attract objects of a different kind (polyester andcotton, for instance).Through a host of ingenious experiments,1 scientists arrived at a model of theatom as being composed of smaller individual particles with opposite charges,held together by their electrical attraction. Specifically, the nucleus of an atom,which constitutes the vast majority of its mass, contains protons with a positivecharge, and is enshrouded by electrons with a negative charge. The nucleus also contains neutrons, which resemble protons, except they have no charge. The electricattraction between protons and electrons just balances the electrons’ natural tendency to escape, which results from both their rapid movement, or kinetic energy,and their mutual electric repulsion. (The repulsion among protons in the nucleusis overcome by another type of force called the strong nuclear interaction, whichonly acts over very short distances.)This model explains both why most materials exhibit no obvious electrical properties, and how they can become “charged” under certain circumstances: The opposite charges carried by electrons and protons are equivalent in magnitude, and whenelectrons and protons are present in equal numbers (as they are in a normal atom),these charges “cancel” each other in terms of their effect on their environment. Thus,from the outside, the entire atom appears as if it had no charge whatsoever; it iselectrically neutral.Yet individual electrons can sometimes escape from their atoms and travel elsewhere. Friction, for instance, can cause electrons to be transferred from one materialinto another. As a result, the material with excess electrons becomes negativelycharged, and the material with a deficit of electrons becomes positively charged(since the positive charge of its protons is no longer compensated). The ability ofelectrons to

electrical engineering majors. The second category had the information I needed, but was guarded by a layer of impenetrable phasor diagrams and other symbolism that obviously required a special sort of initiation. I was extremely fortunate to have access to some of the most highly respected

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