Livro Power System Stability And Control by Prabha Kundur

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Cover
	Contents
	Foreword
	Preface
	PART I GENERAL BACKGROUND
	1. GENERAL CHARACTERSTCS OF MODERN POWER SYSTEMS 3 
	1.1. Evolution of electric power systems
	1.2. Structure of the power system
	1.3. Power system control
	1.4. Design and operating criteria for stability
	References
	2. INTRODUCTION TO THE POWER SYSTEM STABILITY PROBLEM 17 
	2.1. Basic concepts and definitions
	2.1.1. Rotor angle stability
	2.1.1. Voltage stability and voltage collapse
	2.1.3. Mid-term and long-term stability
	2.2. Classification of stability
	2.3. Historical review of stability problems
	References
	PART II EQUIPMENT CHARACTERISTICS AND MODELLING
	3 SYNCHRONOUS MACHINE THEORY AND MODELLING 45
	3.1. Physical description
	3.1.1. Armature and field structure
	3.1.2. Machines with multiple pole pairs
	3.1.3. MMF waveforms
	3.1.4. Direct and quadrature axes
	3.2. Mathematical description of a synchronous machine
	3.2.1. Review of magnetic circuit equations
	3.2.2. Basic equations of a synchronous machine
	3.3. The dq0 transformation
	3.4. Per unit representation
	3.4.1. Per unit system for the stator quantities
	3.4.2. Per unit stator voltage equations 
	3.4.3. Per unit rotor voltage equations
	3.4.4. Stator flux Linkage equations
	3.4.5. Rotor flux linkage equations
	3.4.6. Per unit system for the rotor 
	3.4.7. Per unit power and torque
	3.4.8. Alternative per unIt systems and transformations
	3.4.9. Summary of per unit equations
	3.5. Equivalent circuits for direct and quadrature axes
	3.6. Steady-state analysis
	3.6.1 Voltage, current, and flux linkage relationships
	3.6.2 Phasor representation
	3.6.3 Rotor angle
	3.6.4 Steady-state equivalent circuit
	3.6.5 Procedure for computing steady-state values
	3.7 Electrical transient performance characteristics
	3.7.1 Short-circuit current ia a simple RL circuit
	3.7.2 Three-phase short-circuit at the terminals of a synchronous machine
	3.7.3 Elimination of dc offset in short-circuit current
	3.8 Magnetic saturation
	3.8.1 Open-circuit and short-circuit characteristics
	3.8.2 Representation of saturation in stability studies
	3.8.3 Improved modelling of saturation
	3.9 Equations of motion
	3.9.1 Review of mechanics of motion
	3.9.2 Swing equation
	3.9.3 Mechanical starting time
	3.9.4 Calculation of inertia constant
	3.9.5 Representation in system studies
	References
	4 SYNCHRONOUS MACHINE PARAMETERS 139
	4.1 Operational parameters 139
	4.2 Standard parameters 144
	4.3 Frequency-response characteristics 159
	4.4 Determination of synchronous machine parameters 161
	References 166
	5 SYNCHRONOUS MACHINE REPRESENTATION IN STABILITY STUDIES 169
	5.1 Simplifications essential for large-scale studies 169 
	5.1.1 Neglect of stator pψ terms 170 
	5.1.2 Neglecting the effect of speed variations on stator voltages 174 
	5.2 Simplified model with amortisseurs neglected 179 
	5.3 Constant flux linkage model 184 
	5.3.1 Classical model 184 
	5.3.2 Constant flux linkage model including the effcts of subtransient circuits 188 
	5.3.3 Summary of simple models for different time frames 190
	5.4 Reactive capability limits 191 
	5.4.1 Reactive capability curves 191 
	5.4.2 V curves and compounding curves 196 
	References 198 
	6 AC TRANSMISSION 199 
	6.1 Transmission lines 200 
	6.1.1 Electrical characteristics 200 
	6.1.2 Performance equations 201 
	6.1.3 Natural or surge impedance loading 205 
	6.1.4 Equivalent circuit of a transmission line 206 
	6.1.5 Typical parameters 209 
	6.1.6 Performance requirements of power transmission lines 211
	6.1.7 Voltage and current profile under no-load 211 
	6.1.8 Voltage-power characteristics 216
	6.1.9 Power transfer and stability considerations 221 
	6.1.10 Effect of line loss on V-P and Q-P characteristics 225 
	6.1.11 Thermal limits 226 
	6.1.12 Loadability characteristics 228 
	6.2 Transformers 231
	6.2.1 Representation of two-winding transformers 232 
	6.2.2 Representation of three-winding transformers 240 
	6.2.3 Phase-shifting transformers 245 
	6.3 Transfer of power between active sources 250 
	6.4 Power-flow analysis 255
	6.4.1 Network equations 257 
	6.4.2 Gauss-Seidel method 259 
	6.4.3 Newton-Raphson (N-R) method 260 
	6.4.4 Fast decoupled load-flow (FDLF) methods 264 
	6.4.5 Comparison of the power-flow solution methods 267 
	6.4.6 Sparsity-oriented trianguLar factorization 268 
	6.4.7 Network reduction 268 
	References 269 
	7 POWER SYSTEM LOADS 271
	7.1 Basic load-modelling concepts 271 
	7.1.1 Static load models 272 
	7.1.2 Dynamic load models 274
	7.2 Modelling of induction motors 279
	7.2.1 Equations of an induction machine 279 
	7.2.2 Steady-state characteristics 287
	7.2.3 Alternative rotor constructions 293
	7.2.4 Representation of saturation 296
	7.2.5 Per unit representation 297
	7.2.6 Representation in stability studies 300 
	7.3 Synchronous motor model 306 
	7.4 Acquisition of load-model parameters 306
	7.4.1 Measurement-based approach 306 
	7.4.2 Component-based approach 308
	7.4.3 Sample load characteristics 310 
	References 312
	8 EXCITATION SYSTEMS 315 
	8.1 Excitation system requirements 315 
	8.2 Elements of an excitation system 317
	8.3 Types of excitation systems 318 
	8.3.1 DC excitation systems 319
	8.3.2 AC excitation systems 320 
	8.3.3 Static excitation systems 323
	8.3.4 Recent developments and future trends 326 
	8.4 Dynamic performance measures 327 
	8.4.1 Large-signal performance measures 327 
	8.4.2 Small-signal performance measures 330 
	8.5 Control and protective functions 333 
	8.5.1 AC and DC regulators 333 
	8.5.2 Excitation system stabilizing circuits 334 
	8.5.3 Power system stabilizer (PSS) 335 
	8.5.4 Load compensation 335 
	8.5.5 Underexcitation limiter 337 
	8.5.6 Overexcitation limiter 337 
	8.5.7 Volts-per-hertz limiter and protection 339 
	8.5.8 Field-shorting circuits 340 
	8.6 Modelling of excitation systems 341 
	8.6.1 Per unit system 342 
	8.6.2 Modelling of excitation system components 347 
	8.6.3 Modelling of complete excitation systems 362 
	8.6.4 Field testing for model development and verification 372 
	References 373 
	9 PRIME MOVERS AND ENERGY SUPPLY SYSTEMS 377 
	9.1 Hydraulic turbines and governing systems 377 
	9.1.1 Hydraulic turbine transfer function 379 
	9.1.2 Nonlinear turbine model assuming inelastic water column 387 
	9.1.3 Governors for hydraulic turbines 394 
	9.1.4 Detailed hydraulic system model 404 
	9.1.5 Guidelines for modelling hydraulic turbines 417 
	9.2 Steam turbines and governing systems 418 
	9.2.1 Modelling of steam turbines 422 
	9.2.2 Steam turbine controls 432 
	9.2.3 Steam turbine off-frequency capability 444 
	9.3 Thermal energy systems 449 
	9.3.1 Fossil-fuelled energy systems 449 
	9.3.2 Nuclear-based energy systems 455
	9.3.3 Modelling of thermal energy systems 459 
	References 460 
	10 HIGH-VOLTAGE DIRECT-CURRENT TRANSMISSION 463
	10.1 HVDC system configurations and components 464 
	10.1.1 Classification of HVDC links 464 
	10.1.2 Components of HVDC transmission system 467 
	10.2 Converter theory and performance equations 468 
	10.2.1 Valve characteristics 49 
	10.2.2 Converter circuits 470 
	10.2.3 Converter transformer rating 492 
	10.2.4 Multiple-bridge converters 493 
	10.3 Abnormal operation 498 
	10.3.1 Arc-back (backfire) 498 
	10.3.2 Commutation failure 499 
	10.4 Control of HVDC systems 500 
	10.4.1 Basic principles of control 500 
	10.4.2 Control implementation 514 
	10.4.3 Converter firing-control systems 516 
	10.4.4 Valve blocking and bypassing 520 
	10.4.5 Starting, stopping, and power-flow reversal 521 
	10.4.6 Controls for enhancement of ac system performance 523 
	10.5 Harmonics and filters 524 
	10.5.1 AC side harmonics 524 
	10.5.2 DC side harmonics 527 
	10.6 Influence of ac system strength on ac/dc system interaction 528 
	10.6.1 Short-circuit ratio 528 
	10.6.2 Reactivepower and ac system strength 529 
	10.6.3 Problems with low ESCR systems 530 
	10.6.4 Solutions to problems associated with weak systems 531 
	10.6.5 Effective inertia constant 532 
	10.6.6 Forced commutation 532 
	10.7 Responses to dc and ac system faults 533 
	10.7.1 DC line faults 534 
	10.7.2 Converter faults 535 
	10.7.3 AC system faults 535 
	10.8 Multiterminal HVDC systems 538 
	10.8.1 MTDC network configurations 539 
	10.8.2 Control of MTDC systems 540 
	10.9 Modelling of HVDC systems 544 
	10.9.1 Representation for power-flow solution 544 
	10.9.2 Per unit system for dc quantities 564 
	10.9.3 Representation for stability studies 566 
	References 577 
	11 CONTROL OF ACTIVE POWER AND REACTIVE POWER 581 
	11.1 Active power and frequency control 581 
	11.1.1 Fundamentals of speed governing 582 
	11.1.2 Control of generating unit power output 592 
	11.1.3 Composite regulating characteristic of power systems 595 
	11.1.4 Response rates of turbine-governing systems 598 
	11.1.5 Fundamentals of automatic generation control 601 
	11.1.6 Implementation of AGC 617 
	11.1.7 Underfrequency load shedding 623 
	11.2 Reactive power and voltage control 627 
	11.2.1 Production and absorption of reactive power 627 
	11.2.2 Methods of voltage control 628 
	11.2.3 Shunt reactors 629 
	11.2.4 Shunt capacitors 631 
	11.2.5 Series capacitors 633 
	11.2.6 Synchronous condensers 638 
	11.2.7 Static var systems 639 
	11.2.8 Principles of transmission system compensation 654 
	11.2.9 Modelling of reactive compensating devices 672 
	11.2.10 Application of tap-changing transformers to transmission systems 678 
	11.2.11 Distribution system voltage regulation 679 
	11.2.12 Modelling of transformer ULTC control systems 684 
	11.3 Power-flow analysis procedures 687 
	11.3.1 Prefault power flows 687 
	11.3.2 Postfault power flows 688 
	References 691 
	PART III SYSTEM STABILITY: physical aspects, analysis, and improvement 
	12 SMALL-SIGNAL STABILITY 699 
	12.1 Fundamental concepts of stability of dynamic systems 700 
	12.1.1 State-space representation 700 
	12.1.2 Stability of a dynamic system 702 
	12.1.3 Linearization 703 
	12.1.4 Analysis of stability 706 
	12.2 Eigenproperties of the state matrix 707 
	12.2.1 Eigenvalues 707 
	12.2.2 Eigenvectors 707 
	12.2.3 Modal matrices 708 
	12.2.4 Free motion of a dynamic system 709 
	12.2.5 Mode shape, sensitivity, and participation factor 714 
	12.2.6 Controllability and observability 716 
	12.2.7 The concept of complex Frequency 717 
	12.2.8 Relationship between eigenproperties and transfer functions 719 
	12.2.9 Computation of eigenvalues 726 
	12.3 Small-signal stability of a single-machine infinite bus system 727 
	12.3.1 Generator represented by the classical model 728 
	12.3.2 Effects of synchronous machine field circuit dynamics 737 
	12.4 Effects of excitation system 758 
	12.5 Power system stabilizer 766 
	12.6 System state matrix with amortisseurs 782 
	12.7 Small-signal stability of multimachine systems 792 
	12.8 Special techniques for analysis of very large systems 799 
	12.9 Characteristics of small-signal stability problems 817 
	References 822 
	13 TRANSIENT STABILITY 827 
	13.1 An elementary view of transient stability 827 
	13.2 Numerical integration methods 836 
	13.2.1 Euler method 836 
	13.2.2 Modified Euler method 838 
	13.2.3 Runge-Kutta (R-K) methods 838 
	13.2.4 Numerical stability of explicit integration methods 841 
	13.2.5 Implicit integration methods 842 
	13.3 Simulation of power system dynamic response 848 
	13.3.1 Structure of the power system model 848 
	13.3.2 Synchronous machine representation 849 
	13.3.3 Excitation system representation 855 
	13.3.4 Transmission network and load representation 858 
	13.3.5 Overall system equations 859 
	13.3.6 Solution of overall system equations 861 
	13.4 Analysis of unbalanced faults 872 
	13.4.1 Introduction to symmetrical components 872 
	13.4.2 Sequence impedances of synchronous machines 877 
	13.4.3 Sequence impedances of transmission lines 884 
	13.4.4 Sequence impedances of transformers 884 
	13.4.5 Simulation of different types of faults 885 
	13.4.6 Representation of open-conductor conditions 898 
	13.5 Performance of protective relaying 903 
	13.5.1 Transmission line protection 903 
	13.5.2 Fault-clearing times 911 
	13.5.3 Relaying quantities during swings 914 
	13.5.4 Evaluation of distance relay performance during swings 919 
	13.5.5 Prevention of tripping during transient conditions 920 
	13.5.6 Automatic line reclosing 922 
	13.5.7 Generator out-of-step protection 923 
	13.5.8 Loss-of-excitation protection 927 
	13.6 Case study of transient stability of a large system 934 
	13.7 Direct method of transient stability analysis 941 
	13.7.1 Description of the transient energy function approach 941 
	13.7.2 Analysis of practical power systems 945 
	13.7.3 Limitations of the direct methods 954 
	References 954 
	14 VOLTAGE STABILITY 959 
	14.1 Basic concepts related to voltage stability 960 
	14.1.1 Transmission system characteristics 960 
	14.1.2 Generator characteristics 967 
	14.1.3 Load characteristics 968 
	14.1.4 Characteristics of reactive compensating devices 969 
	14.2 Voltage collapse 973 
	14.2.1 Typical scenario of voltage collapse 974 
	14.2.2 General characterization based on actual incidents 975 
	14.2.3 Classification of voltage stability 976 
	14.3 Voltage stability analysis 977 
	14.3.1 Modelling requirements 978 
	14.3.2 Dynamic analysis 978 
	14.3.3 Static analysis 990 
	14.3.4 Determination of shortest distance to instability 1007 
	14.3.5 The continuation power-flow analysis 1012 
	14.4 Prevention of voltage collapse 1019 
	14.4.1 System design measures 1019 
	14.4.2 System-operating measures 1021 
	References 1022 
	15 SUBSYNCHRONOUS OSCILLATIONS 1025 
	15.1 Turbine-generator torsional characteristics 1026 
	15.1.1 Shaft system model 1026 
	15.1.2 Torsional natural frequencies and mode shapes 1034 
	15.2 Torsional interaction with power system controls 1041 
	15.2.1 Interaction with generator excitation controls 1041 
	15.2.2 Interaction with speed governors 1047 
	15.2.3 Interaction with nearby dc converters 1047 
	15.3 Subsynchronous resonance 1050 
	15.3.1 Characteristics of series capacitor-compensated transmission systems 1050 
	15.3.2 Self-excitation due to induction generator effect 1052 
	15.3.3 Torsional interaction resulting in SSR 1053 
	15.3.4 Analytical methods 1053 
	15.3.5 Countermeasures to SSR problems 1060 
	15.4 Impact of network-switching disturbances 1061 
	15.5 Torsional interaction between closely coupled units 1065 
	15.6 Hydro generator torsional characteristics 1067 
	References 1068 
	16 MID-TERM AND LONG-TERM STABILITY 1073 
	16.1 Nature of system response to severe upsets 1073 
	16.2 Distinction between mid-term and long-term stability 1078 
	16.3 Power plant response during severe upsets 1079 
	16.3.1 Thermal power plants 1079 
	16.3.2 Hydro power plants 1081 
	16.4 Simulation of long-term dynamic response 1085 
	16.4.1 Purpose of long-term dynamic simulations 1085 
	16.4.2 Modelling requirements 1085 
	16.4.3 Numerical integration techniques 1087 
	16.5 Case studies of severe system upsets 1088 
	16.5.1 Case study involving an overgenerated island 1088 
	16.5.2 Case study involving an undergenerated island 1092 
	References 1099 
	17 METHODS OF IMPROVING STABILITY 1103 
	17.1 Transient stability enhancement 1104 
	17.1.1 High-speed fault clearing 1104 
	17.1.2 Reduction of transmission system reactance 1104 
	17.1.3 Regulated shunt compensation 1105 
	17.1.4 Dynamic braking 1106 
	17.1.5 Reactor switching 1106 
	17.1.6 Independent-pole operation of circuit breakers 1107 
	17.1.7 Single-pole switching 1107 
	17.1.8 Steam turbine fast-valving 1110 
	17.1.9 Generator tripping 1118 
	17.1.10 Controlled system separationand load shedding 1120 
	17.1.11 High-speed excitation systems 1121 
	17.1.12 Discontinuous excitation control 1124 
	17.1.13 Control of HVDC transmission links 1125 
	17.2 Small-signal stability enhancement 1127 
	17.2.1 Power system stabilizers 1128 
	17.2.2 Supplementary control of static var compensators 1142 
	17.2.3 Supplementary control of HVDC transmission links 1151 
	References 1161 
	Index