ELECTRIC POWER SYSTEMS CONTENTS 1. The Physics of Electricity_________________________________ 1 1.1 Basic Quantities _________________________________1 1.1.1 Introduction _________________________________1 1.1.2 Charge _________________________________2 1.1.3 Potential or Voltage _________________________________3 1.1.4 Ground _________________________________5 1.1.5 Conductivity _________________________________5 1.1.6 Current _________________________________6 1.2 Ohm’s law _________________________________8 1.2.1 Resistance _________________________________9 1.2.2 Conductance _________________________________10 1.2.3 Insulation _________________________________11 1.3 Circuit Fundamentals _________________________________11 1.3.1 Static Charge _________________________________11 1.3.2 Electric Circuits _________________________________12 1.3.3 Voltage Drop _________________________________13 1.3.4 Electric Shock _________________________________13 1.4 Resistive Heating _________________________________14 1.4.1 Calculating Resistive Heating _________________________________15 1.4.2 Transmission Voltage and Resistive Losses _________________________________17 1.5 Electric and Magnetic Fields _________________________________18 1.5.1 The Field as a Concept _________________________________18 1.5.2 Electric Fields _________________________________19 1.5.3 Magnetic Fields _________________________________21 1.5.4 Electromagnetic Induction _________________________________24 1.5.5 Electromagnetic Fields and Health Effects _________________________________25 1.5.6 Electromagnetic Radiation _________________________________26 2. Basic Circuit Analysis _________________________________30 2.1 Modeling Circuits _________________________________30 2.2 Series and Parallel Circuits _________________________________31 2.2.1 Resistance in Series _________________________________32 2.2.2 Resistance in Parallel _________________________________33 2.2.3 Network Reduction _________________________________35 2.2.4 Practical Aspects _________________________________36 2.3 Kirchhoff’s Laws _________________________________37 2.3.1 Kirchhoff’s Voltage Law _________________________________38 2.3.2 Kirchhoff’s Current Law _________________________________39 2.3.3 Application to Simple Circuits _________________________________40 2.3.4 The Superposition Principle _________________________________41 2.4 Magnetic Circuits _________________________________44 3. AC Power _________________________________49 3.1 Alternating Current and Voltage _________________________________49 3.1.1 Historical Notes _________________________________49 3.1.2 Mathematical Description _________________________________50 3.1.3 The rms Value _________________________________53 3.2 Reactance _________________________________55 3.2.1 Inductance _________________________________55 3.2.2 Capacitance _________________________________58 3.2.3 Impedance _________________________________64 3.2.4 Admittance _________________________________64 3.3 Power _________________________________66 3.3.1 Definition of Electric Power _________________________________66 3.3.2 Complex Power _________________________________68 3.3.3 The Significance of Reactive Power _________________________________73 3.4 Phasor Notation _________________________________75 3.4.1 Phasors as Graphics _________________________________75 3.4.2 Phasors as Exponentials _________________________________78 3.4.3 Operations with Phasors _________________________________80 4. Generators _________________________________85 4.1 The Simple Generator _________________________________86 4.2 The Synchronous Generator _________________________________92 4.2.1 Basic Components and Functioning _________________________________92 4.2.2 Other Design Aspects _________________________________97 4.3 Operational Control of Synchronous Generators _________________________________100 4.3.1 Single Generator: Real Power _________________________________100 4.3.2 Single Generator: Reactive Power _________________________________101 4.3.3 Multiple Generators: Real Power _________________________________107 4.3.4 Multiple Generators: Reactive Power _________________________________112 4.4 Operating Limits _________________________________115 4.5 The Induction Generator _________________________________118 4.5.1 General Characteristics _________________________________118 4.5.2 Electromagnetic Characteristics _________________________________120 4.6 Inverters _________________________________123 5. Loads _________________________________127 5.1 Resistive Loads _________________________________128 5.2 Motors _________________________________131 5.3 Electronic Devices _________________________________134 5.4 Load from the System Perspective _________________________________136 5.4.1 Coincident and Noncoincident Demand _________________________________137 5.4.2 Load Profiles and Load Duration Curve _________________________________138 5.5 Single- and Multiphase Connections _________________________________140 6. Transmission and Distribution _________________________________144 6.1 System Structure _________________________________144 6.1.1 Historical Notes _________________________________144 6.1.2 Structural Features _________________________________147 6.1.3 Sample Diagram _________________________________149 6.1.4 Topology _________________________________150 6.1.5 Loop Flow _________________________________153 6.1.6 Stations and Substations_________________________________ 156 6.1.7 Reconfiguring the System _________________________________158 6.2 Three-Phase Transmission _________________________________159 6.2.1 Rationale for Three Phases _________________________________160 6.2.2 Balancing Loads _________________________________163 6.2.3 Delta and Wye Connections _________________________________164 6.2.4 Per-Phase Analysis _________________________________166 6.2.5 Three-Phase Power _________________________________166 6.2.6 D.C. Transmission _________________________________167 6.3 Transformers _________________________________168 6.3.1 General Properties _________________________________168 6.3.2 Transformer Heating _________________________________170 6.3.3 Delta and Wye Transformers _________________________________172 6.4 Characteristics of Power Lines _________________________________175 6.4.1 Conductors _________________________________175 6.4.2 Towers, Insulators, and Other Components _________________________________179 6.5 Loading _________________________________182 6.5.1 Thermal Limits _________________________________182 6.5.2 Stability Limit _________________________________183 6.6 Voltage Control _________________________________184 6.7 Protection _________________________________188 6.7.1 Basics of Protection and Protective Devices _________________________________188 6.7.2 Protection Coordination _________________________________192 7. Power Flow Analysis_________________________________ 195 7.1 Introduction _________________________________195 7.2 The Power Flow Problem _________________________________197 7.2.1 Network Representation _________________________________197 7.2.2 Choice of Variables _________________________________198 7.2.3 Types of Buses _________________________________201 7.2.4 Variables for Balancing Real Power _________________________________201 7.2.5 Variables for Balancing Reactive Power _________________________________202 7.2.6 The Slack Bus _________________________________204 7.2.7 Summary of Variables _________________________________205 7.3 Example with Interpretation of Results _________________________________206 7.3.1 Six-Bus Example _________________________________206 7.3.2 Tweaking the Case _________________________________210 7.3.3 Conceptualizing Power Flow _________________________________211 7.4 Power Flow Equations and Solution Methods _________________________________214 7.4.1 Derivation of Power Flow Equations _________________________________214 7.4.2 Solution Methods _________________________________217 7.4.3 Decoupled Power Flow _________________________________224 7.5 Applications and Optimal Power Flow_________________________________ 226 8. System Performance _________________________________229 8.1 Reliability _________________________________229 8.1.1 Measures of Reliability _________________________________229 8.1.2 Valuation of Reliability _________________________________231 8.2 Security _________________________________233 8.3 Stability _________________________________234 8.3.1 The Concept of Stability _________________________________234 8.3.2 Steady-State Stability _________________________________236 8.3.3 Dynamic Stability _________________________________240 8.3.4 Voltage Stability _________________________________249 8.4 Power Quality _________________________________250 8.4.1 Voltage _________________________________251 8.4.2 Frequency _________________________________253 8.4.3 Waveform _________________________________255 9. System Operation, Management, and New Technology _________________________________259 9.1 Operation and Control on Different Time Scales _________________________________260 9.1.1 The Scale of a Cycle _________________________________261 9.1.2 The Scale of Real-Time Operation_________________________________ 262 9.1.3 The Scale of Scheduling _________________________________264 9.1.4 The Planning Scale _________________________________267 9.2 New Technology _________________________________268 9.2.1 Storage _________________________________268 9.2.2 Distributed Generation _________________________________271 9.2.3 Automation_________________________________ 278 9.2.4 FACTS _________________________________280 9.3 Human Factors _________________________________281 9.3.1 Operators and Engineers _________________________________281 9.3.2 Cognitive Representations of Power Systems _________________________________282 9.3.3 Operational Criteria _________________________________285 9.3.4 Implications for Technological Innovation _________________________________291 9.4 Implications for Restructuring _________________________________292 Appendix: Symbols, Units, Abbreviations, and Acronyms _________________________________298 Index_________________________________ 302
ELECTRIC POWER SYSTEMS
CONTENTS
1. The Physics of Electricity_________________________________ 1
1.1 Basic Quantities _________________________________1
1.1.1 Introduction _________________________________1
1.1.2 Charge _________________________________2
1.1.3 Potential or Voltage _________________________________3
1.1.4 Ground _________________________________5
1.1.5 Conductivity _________________________________5
1.1.6 Current _________________________________6
1.2 Ohm’s law _________________________________8
1.2.1 Resistance _________________________________9
1.2.2 Conductance _________________________________10
1.2.3 Insulation _________________________________11
1.3 Circuit Fundamentals _________________________________11
1.3.1 Static Charge _________________________________11
1.3.2 Electric Circuits _________________________________12
1.3.3 Voltage Drop _________________________________13
1.3.4 Electric Shock _________________________________13
1.4 Resistive Heating _________________________________14
1.4.1 Calculating Resistive Heating _________________________________15
1.4.2 Transmission Voltage and Resistive Losses _________________________________17
1.5 Electric and Magnetic Fields _________________________________18
1.5.1 The Field as a Concept _________________________________18
1.5.2 Electric Fields _________________________________19
1.5.3 Magnetic Fields _________________________________21
1.5.4 Electromagnetic Induction _________________________________24
1.5.5 Electromagnetic Fields and Health Effects _________________________________25
1.5.6 Electromagnetic Radiation _________________________________26
2. Basic Circuit Analysis _________________________________30
2.1 Modeling Circuits _________________________________30
2.2 Series and Parallel Circuits _________________________________31
2.2.1 Resistance in Series _________________________________32
2.2.2 Resistance in Parallel _________________________________33
2.2.3 Network Reduction _________________________________35
2.2.4 Practical Aspects _________________________________36
2.3 Kirchhoff’s Laws _________________________________37
2.3.1 Kirchhoff’s Voltage Law _________________________________38
2.3.2 Kirchhoff’s Current Law _________________________________39
2.3.3 Application to Simple Circuits _________________________________40
2.3.4 The Superposition Principle _________________________________41
2.4 Magnetic Circuits _________________________________44
3. AC Power _________________________________49
3.1 Alternating Current and Voltage _________________________________49
3.1.1 Historical Notes _________________________________49
3.1.2 Mathematical Description _________________________________50
3.1.3 The rms Value _________________________________53
3.2 Reactance _________________________________55
3.2.1 Inductance _________________________________55
3.2.2 Capacitance _________________________________58
3.2.3 Impedance _________________________________64
3.2.4 Admittance _________________________________64
3.3 Power _________________________________66
3.3.1 Definition of Electric Power _________________________________66
3.3.2 Complex Power _________________________________68
3.3.3 The Significance of Reactive Power _________________________________73
3.4 Phasor Notation _________________________________75
3.4.1 Phasors as Graphics _________________________________75
3.4.2 Phasors as Exponentials _________________________________78
3.4.3 Operations with Phasors _________________________________80
4. Generators _________________________________85
4.1 The Simple Generator _________________________________86
4.2 The Synchronous Generator _________________________________92
4.2.1 Basic Components and Functioning _________________________________92
4.2.2 Other Design Aspects _________________________________97
4.3 Operational Control of Synchronous Generators _________________________________100
4.3.1 Single Generator: Real Power _________________________________100
4.3.2 Single Generator: Reactive Power _________________________________101
4.3.3 Multiple Generators: Real Power _________________________________107
4.3.4 Multiple Generators: Reactive Power _________________________________112
4.4 Operating Limits _________________________________115
4.5 The Induction Generator _________________________________118
4.5.1 General Characteristics _________________________________118
4.5.2 Electromagnetic Characteristics _________________________________120
4.6 Inverters _________________________________123
5. Loads _________________________________127
5.1 Resistive Loads _________________________________128
5.2 Motors _________________________________131
5.3 Electronic Devices _________________________________134
5.4 Load from the System Perspective _________________________________136
5.4.1 Coincident and Noncoincident Demand _________________________________137
5.4.2 Load Profiles and Load Duration Curve _________________________________138
5.5 Single- and Multiphase Connections _________________________________140
6. Transmission and Distribution _________________________________144
6.1 System Structure _________________________________144
6.1.1 Historical Notes _________________________________144
6.1.2 Structural Features _________________________________147
6.1.3 Sample Diagram _________________________________149
6.1.4 Topology _________________________________150
6.1.5 Loop Flow _________________________________153
6.1.6 Stations and Substations_________________________________ 156
6.1.7 Reconfiguring the System _________________________________158
6.2 Three-Phase Transmission _________________________________159
6.2.1 Rationale for Three Phases _________________________________160
6.2.2 Balancing Loads _________________________________163
6.2.3 Delta and Wye Connections _________________________________164
6.2.4 Per-Phase Analysis _________________________________166
6.2.5 Three-Phase Power _________________________________166
6.2.6 D.C. Transmission _________________________________167
6.3 Transformers _________________________________168
6.3.1 General Properties _________________________________168
6.3.2 Transformer Heating _________________________________170
6.3.3 Delta and Wye Transformers _________________________________172
6.4 Characteristics of Power Lines _________________________________175
6.4.1 Conductors _________________________________175
6.4.2 Towers, Insulators, and Other Components _________________________________179
6.5 Loading _________________________________182
6.5.1 Thermal Limits _________________________________182
6.5.2 Stability Limit _________________________________183
6.6 Voltage Control _________________________________184
6.7 Protection _________________________________188
6.7.1 Basics of Protection and Protective Devices _________________________________188
6.7.2 Protection Coordination _________________________________192
7. Power Flow Analysis_________________________________ 195
7.1 Introduction _________________________________195
7.2 The Power Flow Problem _________________________________197
7.2.1 Network Representation _________________________________197
7.2.2 Choice of Variables _________________________________198
7.2.3 Types of Buses _________________________________201
7.2.4 Variables for Balancing Real Power _________________________________201
7.2.5 Variables for Balancing Reactive Power _________________________________202
7.2.6 The Slack Bus _________________________________204
7.2.7 Summary of Variables _________________________________205
7.3 Example with Interpretation of Results _________________________________206
7.3.1 Six-Bus Example _________________________________206
7.3.2 Tweaking the Case _________________________________210
7.3.3 Conceptualizing Power Flow _________________________________211
7.4 Power Flow Equations and Solution Methods _________________________________214
7.4.1 Derivation of Power Flow Equations _________________________________214
7.4.2 Solution Methods _________________________________217
7.4.3 Decoupled Power Flow _________________________________224
7.5 Applications and Optimal Power Flow_________________________________ 226
8. System Performance _________________________________229
8.1 Reliability _________________________________229
8.1.1 Measures of Reliability _________________________________229
8.1.2 Valuation of Reliability _________________________________231
8.2 Security _________________________________233
8.3 Stability _________________________________234
8.3.1 The Concept of Stability _________________________________234
8.3.2 Steady-State Stability _________________________________236
8.3.3 Dynamic Stability _________________________________240
8.3.4 Voltage Stability _________________________________249
8.4 Power Quality _________________________________250
8.4.1 Voltage _________________________________251
8.4.2 Frequency _________________________________253
8.4.3 Waveform _________________________________255
9. System Operation, Management, and New Technology _________________________________259
9.1 Operation and Control on Different Time Scales _________________________________260
9.1.1 The Scale of a Cycle _________________________________261
9.1.2 The Scale of Real-Time Operation_________________________________ 262
9.1.3 The Scale of Scheduling _________________________________264
9.1.4 The Planning Scale _________________________________267
9.2 New Technology _________________________________268
9.2.1 Storage _________________________________268
9.2.2 Distributed Generation _________________________________271
9.2.3 Automation_________________________________ 278
9.2.4 FACTS _________________________________280
9.3 Human Factors _________________________________281
9.3.1 Operators and Engineers _________________________________281
9.3.2 Cognitive Representations of Power Systems _________________________________282
9.3.3 Operational Criteria _________________________________285
9.3.4 Implications for Technological Innovation _________________________________291
9.4 Implications for Restructuring _________________________________292
Appendix: Symbols, Units, Abbreviations, and Acronyms _________________________________298
Index_________________________________ 302
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