POWER SYSTEM STABILITY AND CONTROL

Transcription

1 POWER SYSTEM STABILITY AND CONTROL P. KUNDUR Vice-President, Power Engineering Powertech Labs Inc., Surrey, British Columbia Formerly Manager Analytical Methods and Specialized Studies Department Power System Planning Division, Ontario Hydro, Toronto, Ontario and Adjunct Professor Department of Electrical and Computer Engineering UIIIVtMbliy Ul IUIUIUU, IUIUMIU, WllldllU Edited by Neal J. Balu Mark G. Lauby Power System Planning and Operations Program Electrical Systems Division Electric Power Research Institute 3412 Hillview Avenue Palo Alto, California McGraw-Hill, Inc. New York San Francisco Washington, D.C. Auckland Bogota Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto -

2 Contents FOREWORD PREFACE xix xxi PART I GENERAL BACKGROUND 1 GENERAL CHARACTERISTICS OF MODERN POWER SYSTEMS Evolution of electric power systems Structure of the power system Power system control Design and operating criteria for stability INTRODUCTION TO THE POWER SYSTEM STABILITY PROBLEM Basic concepts and definitions Rotor angle stability Voltage stability and voltage collapse Mid-term and long-term stability Classification of stability Historical review of stability problems VII

3 viii Contents PART II EQUIPMENT CHARACTERISTICS AND MODELLING 3 SYNCHRONOUS MACHINE THEORY AND MODELLING Physical description Armature and field structure Machines with multiple pole pairs MMF waveforms Direct and quadrature axes Mathematical description of a synchronous machine Review of magnetic circuit equations Basic equations of a synchronous machine The dqo transformation Per unit representation Per unit system for the stator quantities Per unit stator voltage equations Per unit rotor voltage equations Stator flux linkage equations Rotor flux linkage equations Per unit system for the rotor Per unit power and torque Alternative per unit systems and transformations Summary of per unit equations Equivalent circuits for direct and quadrature axes Steady-state analysis Voltage, current, and flux linkage relationships Phasor representation Rotor angle Steady-state equivalent circuit Procedure for computing steady-state values Electrical transient performance characteristics Short-circuit current in a simple RL circuit Three-phase short-circuit at the terminals of a synchronous machine Elimination of dc offset in short-circuit current Magnetic saturation Open-circuit and short-circuit characteristics Representation of saturation instability studies Improved modelling of saturation Equations of motion 128

4 Contents Review of mechanics of motion Swing equation Mechanical starting time Calculation of inertia constant Representation in system studies ix SYNCHRONOUS MACHINE PARAMETERS Operational parameters Standard parameters Frequency-response characteristics Determination of synchronous machine parameters SYNCHRONOUS MACHINE REPRESENTATION IN STABILITY STUDIES Simplifications essential for large-scale studies Neglect of stator p\\i terms Neglecting the effect of speed variations on stator voltages Simplified model with amortisseurs neglected Constant flux linkage model Classical model Constant flux linkage model including the effects of subtransient circuits Summary of simple models for different time frames Reactive capability limits Reactive capability curves V curves and compounding curves AC TRANSMISSION Transmission lines Electrical characteristics Performance equations Natural or surge impedance loading Equivalent circuit of a transmission line Typical parameters 209

5 X Contents Performance requirements of power transmission lines Voltage and current profile under no-load Voltage-power characteristics Power transfer and stability considerations Effect of line loss on V-P and Q-P characteristics Thermal limits Loadability characteristics Transformers Representation of two-winding transformers Representation of three-winding transformers Phase-shifting transformers Transfer of power between active sources Power-flow analysis Network equations Gauss-Seidel method Newton-Raphson (N-R) method Fast decoupled load-flow (FDLF) methods Comparison of the power-flow solution methods Sparsity-oriented triangular factorization Network reduction 7 POWER SYSTEM LOADS 7.1 Basic load-modelling concepts Static load models Dynamic load models 7.2 Modelling of induction motors Equations of an induction machine Steady-state characteristics Alternative rotor constructions Representation of saturation Per unit representation Representation in stability studies 7.3 Synchronous motor model 7.4 Acquisition of load-model parameters Measurement-based approach Component-based approach Sample load characteristics

6 Contents xi 8 EXCITATION SYSTEMS Excitation system requirements 8.2 Elements of an excitation system 8.3 Types of excitation systems DC excitation systems AC excitation systems Static excitation systems Recent developments and future trends 8.4 Dynamic performance measures Large-signal performance measures Small-signal performance measures 8.5 Control and protective functions AC and DC regulators Excitation system stabilizing circuits Power system stabilizer (PSS) Load compensation Underexcitation limiter Overexcitation limiter Volts-per-hertz limiter and protection Field-shorting circuits 8.6 Modelling of excitation systems Per unit system Modelling of excitation system components Modelling of complete excitation systems Field testing for model development and verification PRIME MOVERS AND ENERGY SUPPLY SYSTEMS Hydraulic turbines and governing systems Hydraulic turbine transfer function Nonlinear turbine model assuming inelastic water column Governors for hydraulic turbines Detailed hydraulic system model Guidelines for modelling hydraulic turbines Steam turbines and governing systems Modelling of steam turbines Steam turbine controls Steam turbine off-frequency capability 444

7 XII 9.3 Thermal energy systems Fossil-fuelled energy systems Nuclear-based energy systems Modelling of thermal energy systems Contents HIGH-VOLTAGE DIRECT-CURRENT TRANSMISSION HVDC system configurations and components Classification of HVDC links Components of HVDC transmission system Converter theory and performance equations Valve characteristics Converter circuits Converter transformer rating Multiple-bridge converters Abnormal operation Arc-back (backfire) Commutation failure Control of HVDC systems Basic principles of control Control implementation Converter firing-control systems Valve blocking and bypassing Starting, stopping, and power-flow reversal Controls for enhancement of ac system performance Harmonics and filters AC side harmonics DC side harmonics Influence of ac system strength on ac/dc system interaction Short-circuit ratio Reactive power and ac system strength Problems with low ESCR systems Solutions to problems associated with weak systems Effective inertia constant Forced commutation Responses to dc and ac system faults DC line faults Converter faults AC system faults 535

8 Contents 10.8 Multiterminal HVDC systems MTDC network configurations Control of MTDC systems 10.9 Modelling of HVDC systems Representation for power-flow solution Per unit system for dc quantities Representation for stability studies ли i /"TT CONTROL OF ACTIVE POWER AND REACTIVE POWER Active power and frequency control Fundamentals of speed governing Control of generating unit power output Composite regulating characteristic of power systems Response rates of turbine-governing systems Fundamentals of automatic generation control Implementation of AGC Underfrequency load shedding Reactive power and voltage control Production and absorption of reactive power Methods of voltage control Shunt reactors Shunt capacitors Series capacitors Synchronous condensers Static var systems Principles of transmission system compensation Modelling of reactive compensating devices Application of tap-changing transformers to transmission systems Distribution system voltage regulation Modelling of transformer ULTC control systems Power-flow analysis procedures Prefault power flows Postfault power flows

9 XIV Contents PART III SYSTEM STABILITY: physical aspects, analysis, and improvement 12 SMALL-SIGNAL STABILITY Fundamental concepts of stability of dynamic systems State-space representation Stability of a dynamic system Linearization Analysis of stability Eigenproperties of the state matrix Eigenvalues Eigenvectors Modal matrices Free motion of a dynamic system Mode shape, sensitivity, and participation factor Controllability and observability The concept of complex frequency Computation of eigenvalues Relationship between eigenproperties and transfer functions 719 Small-signal stability of a single-machine infinite bus system Generator represented by the classical model Effects of synchronous machine field circuit dynamics Effects of excitation system Power system stabilizer System state matrix with amortisseurs Small-signal stability of multimachine systems Special techniques for analysis of very large systems Characteristics of small-signal stability problems 13 TRANSIENT STABILITY An elementary view of transient stability Numerical integration methods Euler method Modified Euler method Runge-Kutta (R-K) methods Numerical stability of explicit integration methods Implicit integration methods 842

10 Contents 13.3 Simulation of power system dynamic response Structure of the power system model Synchronous machine representation Excitation system representation Transmission network and load representation Overall system equations Solution of overall system equations Analysis of unbalanced faults Introduction to symmetrical components Sequence impedances of synchronous machines Sequence impedances of transmission lines Sequence impedances of transformers Simulation of different types of faults Representation of open-conductor conditions Performance of protective relaying Transmission line protection Fault-clearing times Relaying quantities during swings Evaluation of distance relay performance during swings Prevention of tripping during transient conditions Automatic line reclosing Generator out-of-step protection Loss-of-excitation protection Case study of transient stability of a large system Direct method of transient stability analysis Description of the transient energy function approach Analysis of practical power systems Limitations of the direct methods VOLTAGE STABILITY Basic concepts related to voltage stability Transmission system characteristics Generator characteristics Load characteristics Characteristics of reactive compensating devices Voltage collapse Typical scenario of voltage collapse General characterization based on actual incidents 975 xv

11 xvi Classification of voltage stability 14.3 Voltage stability analysis Modelling requirements Dynamic analysis Static analysis Determination of shortest distance to instability The continuation power-flow analysis 14.4 Prevention of voltage collapse System design measures System-operating measures 15 SUBSYNCHRONOUS OSCILLATIONS 15.1 Turbine-generator torsional characteristics Shaft system model Torsional natural frequencies and mode shapes 15.2 Torsional interaction with power system controls Interaction with generator excitation controls Interaction with speed governors Interaction with nearby dc converters 15.3 Subsynchronous resonance Characteristics of series capacitor-compensated transmission systems Self-excitation due to induction generator effect Torsional interaction resulting in SSR Analytical methods Countermeasures to SSR problems 15.4 Impact of network-switching disturbances 15.5 Torsional interaction between closely coupled units 15.6 Hydro generator torsional characteristics 16 MID-TERM AND LONG-TERM STABILITY 16.1 Nature of system response to severe upsets 16.2 Distinction between mid-term and long-term stability 16.3 Power plant response during severe upsets Thermal power plants Hydro power plants

12 Contents xvii 16.4 Simulation of long-term dynamic response Purpose of long-term dynamic simulations Modelling requirements Numerical integration techniques Case studies of severe system upsets Case study involving an overgenerated island Case study involving an undergenerated island METHODS OF IMPROVING STABILITY Transient stability enhancement High-speed fault clearing Reduction of transmission system reactance Regulated shunt compensation Dynamic braking Reactor switching Independent-pole operation of circuit breakers Single-pole switching Steam turbine fast-valving Generator tripping Controlled system separation and load shedding High-speed excitation systems Discontinuous excitation control Control of HVDC transmission links Small-signal stability enhancement Power system stabilizers Supplementary control of static var compensators Supplementary control of HVDC transmission links INDEX 1167