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Table of contents About the Authors Preface Acknowledgements Symbols Part I INTRODUCTION TO POWER SYSTEMS 1 Introduction 1.1 Stability and control of a dynamic system 1.2 Classification of power system dynamics 1.3 Two pairs of important quantities: reactive power/voltage and real power/frequency 1.4 Stability of power system 1.5 Security of power system 1.6 Brief historical overview 2 Power system components 2.1 Structure of the electrical power system 2.2 Generating units 2.2.1 Synchronous generators 2.2.2 Exciters and Automatic Voltage Regulators 2.2.3 Turbines and their governing systems 2.3 Substations 2.4 Transmission and distribution network 2.4.1 Overhead lines and underground cables 2.4.2 Transformers 2.4.3 Shunt and series elements 2.4.4 FACTS devices 2.5 Protection 2.6 Wide Area Measurement Systems 3 The power system in the steady-state 3.1. Transmission lines 3.1.1. Line equations and the pi-equivalent circuit 3.1.2. Performance of the transmission line 3.1.3. Underground cables 3.2. Transformers 3.2.1. Equivalent circuit 3.2.2. Off-nominal transformation ratio 3.3. Synchronous generators 3.3.1. Round-rotor machines 3.3.2. Salient-pole machines 3.3.3. Synchronous generator as a power source 3.3.4. Reactive power capability curve of a round-rotor generator 3.3.5.Voltage-reactive power capability characteristic 3.3.6. Including the equivalent network impedance 3.4. Power system loads 3.4.1. Lighting and heating 3.4.2. Induction motors 3.4.3. Static characteristics of the load 3.4.4. Load models 3.5. Network equations 3.6. Power flows in transmission networks 3.6.1. Control of power flows 3.6.2. Calculation of power flows Part II INTRODUCTION TO POWER SYSTEM DYNAMICS AND CONTROL 4 Electromagnetic phenomena 4.1. Fundamentals 4.2. Three-phase short-circuit on a synchronous generator 4.2.1. Three-phase short-circuit with the generator on no-load and winding resistance neglected 4.2.2. Including the effect of winding resistance 4.2.3. Armature flux paths and the equivalent reactances 4.2.4. Generator electromotive forces and equivalent circuits. 4.2.5. Short-circuit currents with the generator initially on no-load 4.2.6. Short-circuit currents in the loaded generator 4.2.7. Subtransient torque 4.3. Phase-to-phase short-circuit 4.3.1. Short-circuit current and flux with winding resistance neglected 4.3.2. Influence of the subtransient saliency 4.3.3. Influence of winding resistance 4.3.4. Subtransient torque 4.4. Synchronisation 4.5. Short circuit in a network and its clearing 5 Electromechanical dynamics ? small disturbances 5.1. Swing equation 5.2. Damping power 5.3. Equilibrium points 5.4. Steady-state stability of unregulated system 5.4.1. Pull-out power 5.4.2. Transient power-angle characteristics 5.4.3. Rotor swings and equal area criterion 5.4.4. Effect of damper windings 5.4.5. Effect of rotor flux linkage variation 5.4.6. Analysis of rotor swings around the equilibrium point 5.4.7. Mechanical analogues of the generator-infinite busbar system 5.5. Steady-state stability of the regulated system 5.5.1. Steady-state power-angle characteristic of regulated generator 5.5.2. Transient power-angle characteristic of the regulated generator 5.5.3. Effect of rotor flux linkage variation 5.5.4. Effect of AVR action on the damper windings 5.5.5. Compensating the negative damping components 6 Electromechanical dynamics ? large disturbances 6.1. Transient stability 6.1.1. Fault cleared without a change in the equivalent network impedance. 6.1.2. Short-circuit cleared with/without auto-reclosing 6.1.3. Power swings 6.1.4. Effect of flux decrement 6.1.5. Effect of the AVR 6.2. Swings in multi-machine systems 6.3. Direct method for stability assessment 6.3.1. Mathematical background 6.3.2. Energy-type Lyapunov function 6.3.3. Transient stability area 6.3.4. Equal area criterion 6.3.5. Direct Lyapunov method for a multi-machine system 6.4. Synchronisation 6.5. Asynchronous operation and resynchronisation 6.5.1. Transition to asynchronous operation 6.5.2. Asynchronous operation 6.5.3. Possibility of resynchronisation 6.6 Out-of-step protection systems 6.6.1. Impedance loci during power swings 6.6.2. Power swings blocking 6.6.3. Pole-slip protection of synchronous generator 6.6.4. Out-of-step tripping in network 6.6.5. Example of a blackout 6.7. Torsional oscillations in the drive shaft 6.7.1. The torsional natural frequencies of the turbine-generator rotor 6.7.2. Effect of system faults 6.7.3 Subsynchronous resonance 7 Wind power 7.1 Wind turbines 7.2 Induction machine equivalent circuit 7.3 Induction generator coupled to the grid 7.4 Induction generators with slightly increased speed range via external rotor resistance 7.5 Induction generators with signicantly increased speed range: doubly fed induction generators (DFIG?S) 7.6 Fully rated converter systems: wide speed control 7.7 Peak power tracking of variable speed wind turbines 7.8 Connections of wind farms 7.9 Fault behaviour of induction generators 7.10 Influence of wind generators on power system stability 8 Voltage stability 8.1. Network feasibility 8.2. Stability criteria 8.2.1. d?Q/dV criterion 8.2.2. dE/dV criterion 8.2.3. dQG/dQL criterion 8.3. Critical load demand and voltage collapse 8.3.1. Effects of increasing demand 8.3.2. Effect of network outages 8.3.3. Influence of the shape of the load characteristics 8.3.4. Influence of the voltage control 8.4. Static analysis 8.4.1. Voltage stability and load flow 8.4.2. Voltage stability indices 8.5. Dynamic analysis 8.5.1. The dynamics of voltage collapse 8.5.2. Examples of power system blackouts 8.5.3. Computer simulation of voltage collapse 8.6. Prevention of voltage collapse 8.7. Self-excitation of a generator operating on a capacitive load 8.7.1. Parametric resonance in RLC circiut 8.7.2. Self-excitation of a generator with open-circuited field winding 8.7.3. Self-excitation of a generator with closed field winding 8.7.4. Practical possibility of self-excitation 9 Frequency stability and control 9.1. Automatic generation control 9.1.1. Generation characteristic 9.1.2. Primary control 9.1.3. Secondary control 9.1.4. Tertiary control 9.1.5. AGC as a multi-level control 9.1.6. Defence plan against frequency instability 9.1.7. Quality assessment of frequency control 9.2. Stage I - Rotor swings in the generators 9.3. Stage II - Frequency drop 9.4. Stage III - Primary control 9.4.1. The importance of the spinning reserve 9.4.2. Frequency collapse 9.4.3. Under frequency load shedding 9.5. STAGE IV - Secondary control 9.5.1. Islanded systems 9.5.2. Interconnected systems and tie-line oscillations 9.6. FACTS devices in tie-lines 8.6.1. Incremental model of a multimachine system 9.6.2. State-variable control based on Lyapunov method 9.6.3. Example of simulation results 9.6.4. Coordination between AGC and series FACTS devices in tie-lines Part III ADVANCED TOPICS IN POWER SYSTEM DYNAMICS AND CONTROL 10 Stability enhancement 10.1. Power system stabilisers 10.1.1. PSS applied to the excitation system 10.1.2. PSS applied to the turbine governor 10.2. Fast valving 10.3. Braking resistors 10.4. Generator tripping 10.5. Shunt FACTS devices 10.5.1. Power-angle characteristic 10.5.2. State-variable control 10.5.3. Control based on local measurements 10.5.4. Examples of controllable shunt elements 10.5.5. Generalisation to multi-machine systems 10.5.6. Example of simulation results 10.6. Series compensators 10.6.1. State-variable control 10.6.2. Interpretation using the equal area criterion 10.6.3. Control strategy based on the squared current 10.6.4. Control based on other local measurements 10.6.5. Simulation results 10.7. Unified power flow controller 10.7.1. Power-angle characteristic 10.7.2. State-variable control 10.7.3. Control based on local measurements 10.7.4. Examples of simulation results 11 Advanced power system modelling 11.1. Synchronous generator 11.1.1. The flux-linkage equations in the stator reference frame 11.1.2. The flux-linkage equations in the rotor reference frame 11.1.3. Voltage equations 11.1.4. Generator reactances in terms of circuit quantities 11.1.5. Synchronous generator equations 11.1.6. Synchronous generator models 11.1.7. Saturation effects 11.2. Excitation Systems 11.2.1. Transducer and comparator model 11.2.2. Exciters and regulators 11.2.3. Power system stabiliser (PSS) 11.3. Turbines and turbine governors 11.3.1. Steam turbines 11.3.2. Hydraulic turbines 11.3.3 Wind turbines 11.4. FACTS devices 11.4.2. Shunt FACTS devices 11.4.2. Series FACTS devices 12 Steady-state stability of multimachine system 12.1. Mathematical background 12.1.1. Eigenvalues and eigenvectors 12.1.2. Diagonalisation of a square real matrix 12.1.3. Solution of matrix differential equation 12.1.4. Modal and sensitivity analysis 12.1.5. Modal form of the state equation with inputs 12.1.6. Nonlinear system 12.2. Steady-state stability of unregulated system 12.2.1. State-space equation 12.2.2. Simplified steady ? state stability conditions 12.2.3. Including the voltage characteristics of the loads 12.2.4. Transfer capability of the network 12.3. Steady-state stability of the regulated system 12.3.1 Generator and network 12.3.2. Including excitation system model and voltage control 12.3.3. Linear state equation of the system 12.3.4. Examples 13 Power system dynamic simulation 13.1. Numerical integration methods 13.2. The partitioned-solution 13.2.1. Partial matrix inversion 13.2.2. Matrix factorisation 13.2.3. Newton's method 13.2.4. Ways of avoiding iterations and multiple network solutions 13.3. The simultaneous solution methods 13.4. Comparison between the methods 14 Power system dynamic reduction ? equivalents 14.1. Types of equivalents 14.2. Network transformation 14.2.1. Elimination of nodes 14.2.2. Aggregation of nodes using Dimo's method 14.2.3. Aggregation of nodes using Zhukov's method 14.2.4. Coherency 14.3. Aggreation of generating units 14.4. Equivalent model of external subsystem 14.5. Coherency recognition 14.6. Properties of coherency-based equivalents 14.6.1. Electrical interpretation of Zhukov's aggregation 14.6.2. Incremental equivalent model 14.6.3. Modal interpretation of exact coherency 14.6.4. Eigenvalues and eigenvectors of equivalent model Appendices Index

Library of Congress Subject Headings for this publication:

Electric power system stability.

Electric power systems -- Control.