Electrical Power Systems

Electrical Power Systems CONCEPT, THEORY AND PRACTICE SECOND EDITION SUBIR RAY Professor MVJ College of Engineering Bangalore PHI Learning Pfcte tofm Delhi-110092 2014

Preface xv Preface to the First Edition xvii Chapter 1 Introduction 1-11 1.1 Historical Development of Power Systems 1 1.2 Functional Requirements of a Power System 2 1.3 Sources of Energy for Generation of Electricity 3 1.4 Electric Energy Consumption 4 1.5 Power System Structure 4 1.6 Electrical Load 8 1.7 Interconnection 8 1.8 Operational Challenges of Interconnected System 10 1.9 Abnormal Situations 10 1.10 About this Book 11 Chapter 2 Fundamental Concepts of AC Circuits 12-28 2.1 Sinusoidal AC Quantities 13 2.1.1 Phasor Representation 14 2.1.2 Reactance 16 2.2 Power in AC Circuits 17 2.3 Three-phase Circuits 19 2.4 Transients in Electrical Circuits 20 2.5 Per Unit Representations of Electrical Quantities 24 2.5.1 Base Values 25 Review Questions 27 PART I ELECTRIC POWER TRANSMISSION AND DISTRIBUTION Chapter 3 General Considerations of Transmission and Distribution 31-43 3.1 Some Preliminary Issues 31 3.1.1 Choice of Frequency 33 3.1.2 Choice of Voltage 33 3.1.3 Mode of Transmission and Distribution 35 3.2 More Complicated Issues 39 3.2.1 Overhead Lines 40 v

3.2.2 Underground Cables 40 3.2.3 Substations and Distribution Systems 41 3.2.4 High Voltage DC Transmission 41 3.3 Expectation 41 Review Questions 43 Chapter 4 Electrical Characteristics, Modelling and Performance of Aerial Transmission Lines 44-120 4.1 Inductance of Aerial Lines 46 4.1.1 Fundamentals of Steady Magnetic Field 46 4.1.2 Magnetic Field of a Long Straight Conductor 48 4.1.3 Magnetic Field in a Group of Parallel Cylindrical Conductors 51 4.1.4 Inductance of Single-phase and Three-phase Lines 52 4.1.5 Concepts of Geometric Mean Distances 59 4.1.6 Bundled Conductors and Computation of Inductance 61 4.1.7 Computation of Inductance of Double-circuit Three-phase Lines 64 4.2 Capacitance of Aerial Lines 67 4.2.1 Fundamentals of Electric Field 67 4.2.2 Potential Difference between Two Points External to a Long Straight Isolated Conductor with Uniformly Distributed Charge 69 4.2.3 Potential Difference between Two Points due to Multiple Conductors 70 4.2.4 Capacitance of Single-phase and Three-phase Systems 71 4.2.5 Computation of Capacitance Using Geometric Mean Distances 74 4.2.6 Influence of Earth on Conductor Capacitance 77 4.3 Resistance 81 4.3.1 Shunt Conductance 82 4.4 An Exact Mathematical Model 83 4.4.1 Equivalent Circuit Model 88 4.4.2 Some Important Concepts 92 4.4.3 ABCD Constants of 'Electrically Short Lines' 96 4.4.4 Interpretation of the General Circuit Constants ABCD 97 4.4.5 Two Four-Terminal Networks in Cascade 97 4.5 Efficiency 99 4.6 Regulation 100 4.7 Some Important Observations 104 4.8 Power Equations and Line Compensation 107 Review Questions 117 Chapter 5 Overhead Line Construction 121-177 5.1 Route Selection 121 5.2 Line Supports 122 5.3 Sag and Clearance 127

5.4 Sag-Tension Relation 129 5.4.1 Effect of Wind and Ice Covering on Sag Calculation 135 5.5 Stringing of Transmission Lines 139 5.6 Location of Tower Structures 144 5.6.1 Span 144 5.6.2 Tower Spotting 144 5.7 Vibration of Conductors 145 5.8 Ground Wires 146 5.9 Insulators for Overhead Lines 146 5.9.1 Fundamentals of Insulation Breakdown 147 5.9.2 Materials 148 5.9.3 Types 149 5.10 Voltage Distribution Across a Suspension Insulator String 155 5.10.1 String Efficiency 158 5.10.2 Arcing Shield and Rings 158 5.10.3 Number of Disc Units in a String 159 5.10.4 Methods of Improving Voltage Distribution Across Insulator Strings 164 5.11 Electrical Tests on Line Insulations 166 5.11.1 Terms Used in Standards 166 5.11.2 High Voltage Tests on Line Insulators 167 5.12 Corona 169 5.12.1 Mechanism of Corona Power Loss in Air 171 Review Questions 175 Chapter 6 Underground Cables 178-207 6.1 Cable Components 178 6.1.1 Conductor 180 6.1.2 Insulating Material 181 6.1.3 Shields 183 6.1.4 Sheath, Jacket and Armour 183 6.2 Types of Power Cables and Constructional Features 184 6.3 Electrical Characteristics of Cables 186 6.3.1 Insulation Resistance of a Single-core Cable 186 6.3.2 Conductor Inductance 187 6.3.3 Cable Capacitance 188 6.3.4 Electric Stresses in Single-core Cables 192 6.3.5 Dielectric Losses and Loss Tangent of a Cable 197 6.3.6 Sheath and Armour Losses 199 6.4 Computation of Ampacity of Cables 199 6.5 Laying of Cables 201 6.6 Electrical Breakdown of Cables 202 6.7 DC Cables 204 Review Questions 205

Chapter 7 Substation and Distribution System 208-251 7.1 Substation 209 7.1.1 Types of Substations 210 7.1.2 Location of a Substation 211 7.1.3 Substation Equipments and Accessories 211 7.2 Layout of Substation 216 7.2.1 Bus Arrangements 216 7.2.2 Earthing 221 7.3 Distribution Systems 224 7.3.1 Primary Distribution System Arrangements 225 7.3.2 Primary Feeder Conductor Size 225 7.3.3 Secondary Distribution System Arrangements 230 7.3.4 Distributor Design 231 7.4 Transmission and Distribution Losses 241 7.4.1 Reasons for High Technical Losses 242 7.4.2 Application of Capacitors to Distribution System 242 Review Questions 250 PART II POWER SYSTEM OPERATION Chapter 8 Elements of Electric Power Generation 255-299 8.1 Basic Methods of Production of Electrical Energy 256 8.2 Conventional Methods of Electric Power Generation 256 8.3 Steam Power Stations 256 8.3.1 Main Components of a Steam Power Station 257 8.4 Hydro-electric Stations 261 8.4.1 Water Storage 261 8.4.2 Schematic Layout of a Hydro-electric Station 263 8.4.3 Pumped-Storage Plants 265 8.5 Nuclear Power Station 267 8.5.1 Principles of Atomic Physics Revisited 268 8.5.2 Components of a Nuclear Reactor 270 8.5.3 Some Common Reactor Types 272 8.5.4 Disposal of Nuclear Waste 272 8.5.5 Indian Nuclear Power Plants 273 8.6 Gas Turbine Plants 273 8.7 Salient Characteristics of Various Types of Power Plants 276 8.7.1 Cogeneration 276 8.7.2 Distribution Power Generation 279 8.8 Synchronous Generator Revisited 280 8.8.1 Basic Principles 281 8.8.2 Circuit Model for a Cylindrical Rotor Synchronous Generator 282 8.8.3 Concept of an Infinite Bus 286 8.8.4 Power Control of a Finite Machine Connected to an Infinite Bus 287

8.8.5 Salient Pole Synchronous Generator 295 8.8.6 Operational Constraints of a Synchronous Generator Connected to a Large Network 296 Review Questions 298 Chapter 9 Load Flow Studies 300-334 9.1 An Illustrative Two-bus System 300 9.2 Load Flow Problem 307 9.3 Power Flow Equations 307 9.3.1 System Variables 311 9.3.2 Classification of Buses 311 9.4 Gauss-Seidel Iterative Technique Applied to Solution of Power Flow Equations 313... 9.4.1 Computational Strategy 314 9.5 Newton-Raphson Algorithm for Solution of PFE 321 9.5.1 Elements of the Jacobian Matrix 324 9.5.2 Computational Steps for Solving PFEs by N-R Method 326 9.5.3 Sparsity Features 329 9.6 Fast Decoupled Technique 329 9.7 Representation of Tap Changing Transformer 331 Review Questions 333 Chapter 10 Power System Economics 335-372 10.1 Characteristics and Classification of Consumers 336 10.1.1 Diversity and Its Impact 338 10.2 Tariff Structure 340 10.2.1 Cost of Electrical Energy 341 10.2.2 Two-part Tariff 341 10.3 Operational Strategy to Meet Load Demand 344 10.4 Optimum Scheduling of Generators 347 10.4.1 Economics of Steam Plants 348 10.4.2 Optimum Scheduling for a Lossless System 349 10.4.3 Optimal Scheduling Considering Transmission Losses 353 10.4.4 Unit Commitment 361 10.5 Hydro-thermal Co-ordination 366 10.6 Short-term Load Forecasting (STLF) 369 Review Questions 370 PART III POWER SYSTEM TRANSIENTS AND PROTECTION Chapter 11 Introduction to Power System Transients 375-378 11.1 Basic Concepts of Transients 375 11.2 Classification of Power System Transients 376 11.3 Concepts of Protection 378

D Chapter 12 Over-Voltage Transients in Power Systems and Protection 379-428 12.1 What is Lightning? 379 12.1.1 Charge Formation in Cloud 380 12.1.2 Mechanism of a Lightning Stroke 382 12.1.3 Return Stroke Current 384 12.2 Lightning Over-Voltage 386 12.2.1 Interaction between Lightning and the Power System 386 12.3 Propagation of Lightning Current and Voltage along Transmission Lines 387 12.4 Shape of Lightning Voltage Waves 391 12.5 Reflection and Refraction of Rectangular Traveling Waves 393 12.5.1 Successive Reflections 397 12.6 Ground Wires 398 12.7 Switching Over-Voltages 400 12.7.1 Transient Initiated when a Fault is Cleared 401 12.7.2 Switching Over-Voltages due to Disconnection of an Unloaded Transformer 403 12.7.3 Over-Voltage due to Capacitance Switching 406 12.7.4 Over-Voltages due to Ferro-Resonance 408 12.7.5 Power Frequency Over-Voltages 412 12.7.6 Control of Over-Voltages Due to Switching 412 12.8 Protection of System Insulation against Transient Over-Voltages 412 12.9 Insulation Co-ordination 420 Review Questions 427 Chapter 13 Short-Circuit Phenomena 429-499 13.1 Symmetrical Faults 430 13.1.1 Sudden Three-Phase Short-Circuit of an Unloaded Generator 431 13.1.2 Explanation of Short-Circuit Currents 432 13.1.3 Mathematical Model Its Complexities 435 13.1.4 Simplified Models of Synchronous Machines for Fault Studies 435 13.1.5 Representation of Transmission Lines, Transformers and Loads 438 13.1.6 Short-Circuit Current Computation 439 13.2 Asymmetrical Faults 456 13.2.1 Symmetrical Components 456 13.2.2 Resolution of Three-Phasors into Their Symmetrical Components 457 13.2.3 Some Important Interpretations 459 13.2.4 Sequence Impedances in Symmetrical Systems 459 13.2.5 Power in Terms of Symmetrical Components 462 13.2.6 Sequence Impedances of Components 463 13.2.7 Phase Shift in Star-Delta Transformations 464 13.2.8 Assembling of System Sequence Networks 467 13.2.9 Computation of Asymmetrical Fault Current 469 13.2.10 Series Faults 487 13.2.11 A Systematic Approach to Fault Calculation 489

13.3 Neutral Grounding 491 13.3.1 Arcing Ground 492 13.3.2 Other Disadvantages of Ungrounded Systems 494 13.3.3 Grounded Systems 494 13.3.4 Types of Neutral Grounding 495 13.3.5 Present Grounding Practice 497 Review Questions 497 Chapter 14 Elements of Circuit-Breakers and Relays 500-563 14.1 Introduction 500 14.2 Zones of Protection 501 14.2.1 Overlapping of Zones 502 14.2.2 Back-up Protection Scheme 503 14.3 Function of Circuit-Breaker 503 14.4 Arc 504 14.5 Restriking or Recovery Voltage 505, 14.6 Arc Quenching Methods and Theories 507 14.7 Circuit-Breaker Rating 507 14.8 Fault Clearing Process 510 14.9 Types of Circuit-Breakers 511 14.9.1 Air-Break Circuit-Breaker 512 14.9.2 Oil Circuit-Breaker 513 14.9.3 Air-Blast Circuit-Breaker (ABCB) 516 14.9.4 Sulphur Hexaffuoride Circuit-Breakers 518 14.9.5 Vacuum Circuit-Breaker.>: 520 14.9.6 Selection of Circuit-Breakers 522 14.9.7 Auto-Reclosing 523 14.9.8 Trip-free Mechanism 524 14.10 Relays 524 14.10.1 Attributes of Protective Relaying 525 14.10.2 How Do Protective Relays Operate?... 526 14.10.3 Electromechanical Relays 526 14.10.4 Attracted-Armature Relays 526 14.10.5 Induction Type of Relay 527 14.10.6 Actuating Structures for Induction Rejays 529 14.10.7 Torque Equations in Induction Relay 529 14.10.8 General Torque Equation 531 14.10.9 Over-Current Relay and Its Characteristic 534 14.10.10 Time-Current Characteristics 536 14.11 Earth-Fault and Phase-Fault Relays 538 14.12 Differential Relays 538 14.13 Protection of Transmission and Distribution Lines 541 14.13.1 Protection of Distribution Feeders 541 14.13.2 Time Graded Scheme 541

14.13.3 Current Graded Scheme 542 14.13.4 Current and Time Graded System 542 14.13.5 Directional Time and Current Grading 544 14.13.6 Distance Protection '. 545 14.14 Protection of Transformers 550 14.14.1 Percentage Differential Protection 550 14.14.2 Earth Fault Protection 552 14.14.3 Overcurrent Protection 553 14.14.4 Gas Actuated Relay 554 14.15 Protection of Generators 555 14.15.1 Percentage Differential Protection 556 14.15.2 Negative Sequence Relay 558 14.16 Static Relays 559 14.17 Microprocessor-Based Relays 560 Review Questions 562 Chapter 15 Power System Stability 564-618 15.1 General Concept of Stability 565 15.2 Concept of Stability in Power System 566 15.2.1 Steady State Stability and Transient Stability 566 15.2.2 Stability Indicator 567 15.3 Power-angle Curve of a Synchronous Machine Connected to an Infinite Bus 567 15.4 The Elementary Mathematical Model 571 15.4.1 Swing Equation 571 15.5 Difficulties in Solving Swing Equation 576 15.5.1 Regulated Machines 577 15.5.2 Output Power 577 15.5.3 Synchronous Machine 578 15.5.4 Assumptions 578 15.6 Analysis of Steady State Stability of an Uncontrolled System 578 15.7 Equal Area Criterion 580 15.7.1 Finite Machine Connected to an Infinite Bus 580 15.7.2 Equal-Area Criterion Applied to a Simple Case 583 15.7.3 Application to Practical Cases 586 15.7.4 A Two-Area System 596 15.8 Step-by-Step Solution of Swing Equation 598 15.8.1 Discontinuity 600 15.9 Digital Computation Using Runge-Kutta Method 603 15.10 Methods for Enhancement of Stability 605 15.11 Voltage Stability 609 15.11.1 Definitions 609 15.11.2 Types of Voltage Stability 610 15.11.3 A Practical Example of Voltage Collapse 610

15.12 Prediction of Voltage Collapse 611 15.12.1 P-V and Q-V Curves 611 15.12.2 Index and Sensitivity Methods 616 15.13 Remedy 616 Review Questions 617 Chapter 16 FACTS and High Voltage DC Transmission 619-637 16.1 Constraints in a Transmission System 619 16.1.1 What are the Remedies? 620 16.2 Flexible AC Transmission Systems (FACTS) 620 16.2.1 Key Features of FACTS Technology 621 16.2.2 Power Converters 621 16.2.3 Development of FACTS Devices 622 16.2.4 Technology Underlying FACTS 623 16.3 High Voltage DC Transmission (HVDC Transmission) 626 16.3.1 Advantages of HVDC Transmission 627 16.3.2 Applications of DC Transmission 628 16.3.3 Economic Distance for HVDC Transmission 628 16.4 Configuration of DC Transmission Links 629 16.5 Rectifying and Inverting 632 16.5.1 Components 632 16.5.2 Rectifying and Inverting Systems 1 632 16.5.3 Circuit Elements 634 16.5.4 Configurations for DC Links 634 16.6 Disadvantages 636 16.7 Parallel Operation of AC and DC Systems 636 16.8 Indian Scenario 637 Chapter 17 Control of Active and Reactive Power 638-660 17.1 Active Power and Frequency Control 639 of Control Area 640 17.1.1 Concept 17.1.2 Isolated System 640 17.1.3 Transfer Function (Block Diagram of the Isolated System) 640 17.1.4 Automatic Load Frequency Control Loop and Steady State Response 646 17.1.5 Dynamic Response 647 17.1.6 Proportional Plus Integral Control 647 17.2 Automatic Load Frequency Control of Multiarea System 650 17.2.1 Tie Line Modelling 650 17.2.2 Block Diagram of Two Area System 651 17.2.3 Static Response of Two Area System 652 17.2.4 Dynamic Response of Two Area System 654 17.3 Reactive Power Control 655 17.3.1 Injection and Absorption of Reactive Power 655 17.3.2 Automatic Voltage Regulator (AVR) 656

W77M 17.3.3 Shunt Reactors 657 17.3.4 Shunt Capacitors 658 17.3.5 Series Capacitor 659 17.3.6 Synchronous Condensers or Compensators 660 17.3.7 Static Var System 660 Review Questions 660 Appendix 1 Laplace Transforms 661 Appendix 2 Iterative Methods for Solving Algebraic Equations 662-667 Appendix 3 Formation of Bus Admittance Matrix Using Singular Transformation 668-671 Appendix 4 Optimisation Technique 672-673 Bibliography 675-677 Index... 679-682