Engineering with Power

Transcription

1 Handbook of Power Systems Engineering with Power Electronics Applications Second Edition Yoshihide Hase Power System Engineering Consultant, Tokyo, Japan WILEY A John Wiley & Sons, Ltd., Publication

2 w""'/n Contents PREFACE ACKNOWLEDGEMENTS ABOUT THE AUTHOR xxi xxiii xxv INTRODUCTION xxvii 1 OVERHEAD TRANSMISSION LINES AND THEIR CIRCUIT CONSTANTS Overhead Transmission Lines with LR Constants Three-phase single circuit line without overhead grounding wire Three-phase single circuit line with OGW, OPGW Three-phase double circuit line with LR constants Stray Capacitance of Overhead Transmission Lines Stray capacitance of three-phase single circuit line Three-phase single circuit line with OGW Three-phase double circuit line Working Inductance and Working Capacitance Introduction of working inductance Introduction of working capacitance Special properties of working inductance and working capacitance MKS rational unit system and the various MKS practical units in electrical engineering field Supplement: Proof of Equivalent Radius r^, = r'/" for a Multi-bundled Conductor Equivalent radius for inductance calculation Equivalent radius of capacitance calculation 26 Coffee break 1: Electricity, its substance and methodology 27 2 SYMMETRICAL COORDINATE METHOD (SYMMETRICAL COMPONENTS) Fundamental Concept of Symmetrical Components Definition of Symmetrical Components Definition Implication of symmetrical components Conversion of Three-phase Circuit into Symmetrical Coordinated Circuit 34

3 viii 2.4 Transmission Lines by Symmetrical Components Single circuit line with LR constants Double circuit line with LR constants Single circuit line with stray capacitance C Double circuit line with C constants Typical Transmission Line Constants Typical line constants L, C constant values derived from typical travelling-wave velocity and surge impedance Generator by Symmetrical Components (Easy Description) Simplified symmetrical equations Reactance of generator Description of Three-phase Load Circuit by Symmetrical Components 52 3 FAULT ANALYSIS BY SYMMETRICAL COMPONENTS Fundamental Concept of Symmetrical Coordinate Method Line-to-ground Fault (Phase a to Ground Fault: 10G) Condition before the fault Condition of phase a to ground fault Voltages and currents at virtual terminal point f in the domain Voltages and currents at an arbitrary point under fault conditions Fault under no-load conditions Fault Analysis at Various Fault Modes Conductor Opening Single-phase (phase a) conductor opening Two-phases (phase b, c) conductor opening 65 Coffee break 2: Dawn of the world of electricity, from Coulomb to Ampere and Ohm 66 4 FAULT ANALYSIS OF PARALLEL CIRCUIT LINES (INCLUDING SIMULTANEOUS DOUBLE CIRCUIT FAULT) Two-phase Circuit and its Symmetrical Coordinate Method Definition and meaning Transformation process of double circuit line Double Circuit Line by Two-phase Symmetrical Transformation Transformation of typical two-phase circuits Transformation of double circuit line Fault Analysis of Double Circuit Line (General Process) Single Circuit Fault on the Double Circuit Line Line-to-ground fault (1#G) on one-side circuit Various one-side circuit faults Double Circuit Fault at Single Point f Circuit 1 phase a line-to-ground fault and circuit 2 phases b and c line-to-line faults at point f Circuit 1 phase a line-to-ground fault and circuit 2 phase b line-to-ground fault at point f (method 1) 82

4 A-connected ix Circuit 1 phase a line-to-ground fault and circuit 2 phase b line-to-ground fault at point f (method 2) Various double circuit faults at single point f Simultaneous Double Circuit Faults at Different Points f, F on the Same Line Circuit condition before fault Circuit 1 phase line-to-ground fault and a circuit 2 phase b line-to-ground fault at different points f, F Various double circuit faults at different points 89 5 PER UNIT METHOD AND INTRODUCTION OF TRANSFORMER CIRCUIT Fundamental Concept of the PU Method PU method of single-phase circuit Unitization of a single-phase three-winding transformer and its equivalent circuit PU Method for Three-phase Circuits Base quantities by PU method for three-phase circuits Unitization of three-phase circuit equations Three-phase Three-winding Transformer, its Symmetrical Components Equations, and the Equivalent Circuit X. X three-phase transformer Three-phase transformers with various winding connections Core structure and the zero-sequence excitation impedance Various winding methods and the effect of delta windings Harmonic frequency voltages/currents in the domain Base Quantity Modification of Unitized Impedance Note on % IZ of three-winding transformer Autotransformer Numerical Example to Find the Unitized Symmetrical Equivalent Circuit Supplement: Transformation from Equation 5.18 to Equation Coffee break 3: Faraday and Henry, the discoverers of the principle of electric energy application THE a-0-0 COORDINATE METHOD (CLARKE COMPONENTS) AND ITS APPLICATION Definition of Coordinate Method (a-p-0 Components) Interrelation Between a-p-q Components and Symmetrical Components The transformation of arbitrary waveform quantities Interrelation between a /8 0 and symmetrical components Circuit Equation and Impedance by the a f} 0 Coordinate Method Three-phase Circuit in a /6 0 Components Single circuit transmission line Double circuit transmission line Generator Transformer impedances and load impedances in the a-fi-o domain Fault Analysis by a-/8-0 Components Line-to-ground fault (phase a to ground fault: 1 <p G) The b-c phase line to ground fault Other mode short-circuit faults 141

5 X Open-conductor mode faults Advantages of a-fi-0 method SYMMETRICAL AND a-p- 0 COMPONENTS AS ANALYTICAL TOOLS FOR TRANSIENT PHENOMENA The Symbolic Method and its Application to Transient Phenomena Transient Analysis by Symmetrical and a ft 0 Components Comparison of Transient Analysis by Symmetrical and a f) 0 Components 150 Coffee break 4: Weber and other pioneers NEUTRAL GROUNDING METHODS Comparison of Neutral Grounding Methods Overvoltages the Unfaulted Phases Caused by on a Line-to-ground fault Arc-suppression Coil (Petersen Coil) Neutral Grounded Method Possibility of Voltage Resonance 160 Coffee break 5: Maxwell, the greatest scientist of the nineteenth century VISUAL VECTOR DIAGRAMS OF VOLTAGES AND CURRENTS UNDER FAULT CONDITIONS Three-phase Fault: 30S, 3$G (Solidly Neutral Grounding System, High-resistive Neutral Grounding System) Phase b-c Fault: 2$S (for Solidly Neutral Grounding System, High-resistive Neutral Grounding System) Phase a to Ground Fault: 10G (Solidly Neutral Grounding System) Double Line-to-ground (Phases b and c) Fault: 2#G (Solidly Neutral Grounding System) Phase a Line-to-ground Fault: 10G (High-resistive Neutral Grounding System) Double Line-to-ground (Phases b and c) Fault: 2<pG (High-resistive Neutral Grounding System) THEORY OF GENERATORS Mathematical Description of a Synchronous Generator The fundamental model Fundamental three-phase circuit equations Characteristics of inductances in the equations Introduction of d-q-0 Method (d-q-0 Components) Definition of d-q-0 method Mutual relation of d-q-0, a-b-c, and domains Characteristics of d-q-0 domain quantities Transformation of Generator Equations from a-b-c to d-q-0 Domain Transformation of generator equations to d-q-0 domain Physical meanings of generator's fundamental equations on the d-q-0 domain Unitization of generator d-q-0 domain equations Introduction of d-q-0 domain equivalent circuits 206

6 xi 10.4 Generator Operating Characteristics and its Vector Diagrams on d- and q-axes Plane Transient Phenomena and the Generator's Transient Reactances Initial condition just before sudden change Assorted d-axis and q-axis reactances for transient phenomena Symmetrical Equivalent Circuits of Generators Positive-sequence circuit Negative-sequence circuit Zero-sequence circuit Laplace-transformed Generator Equations and the Time Constants Laplace-transformed equations Measuring of Generator Reactances Measuring method of d-axis reactance xj and short-circuit ratio SCR Measuring method of d-axis reactance X2 and xq Relations Between the d-q-0 and a-j6-0 Domains Detailed Calculation of Generator Short-circuit Transient Current under Load Operation Transient short circuit calculation by Laplace transform Transient fault current by sudden three-phase terminal fault under no-load condition Supplement Supplement 1: Physical concept of linking flux and flux linkage Supplement 2: Proof of time constants T'd, Tj, V equation (10.108b) Supplement 3: The equations of the rational function and their transformation into expanded sub-sequential fractional equations Supplement 4: Calculation of the coefficients of equation Supplement 5: The formulae of the laplace transform (see also Appendix A) APPARENT POWER AND ITS EXPRESSION IN THE AND d-q-0 DOMAINS Apparent Power and its Symbolic Expression for Arbitrary Waveform Voltages and Currents Definition of apparent power Expansion of apparent power for arbitrary waveform voltages and currents Apparent Power of a Three-phase Circuit in the Domain Apparent Power in the d-q-0 Domain 246 Coffee break 6: Hertz, the discoverer and inventor of radio waves GENERATING POWER AND STEADY-STATE STABILITY Generating Power and the P-S and Q-S Curves Power Transfer Limit between a Generator and a Power System Network Equivalency between one-machine to infinite-bus system and two-machine system Apparent power of a generator 255

7 xii Power transfer limit of a generator (steady-state stability) Visual description of a generator's apparent power transfer limit Mechanical analogy of steady-state stability Supplement: Derivation of Equation from Equations (2) CD and THE GENERATOR AS ROTATING MACHINERY Mechanical (Kinetic) Power and Generating (Electrical) Power Mutual relation between mechanical input power and electrical output power Kinetic Equation of the Generator Dynamic characteristics of the generator (kinetic motion equation) Dynamic equation of generator as an electrical expression Mechanism of Power Conversion from Rotor Mechanical Power to Stator Electrical Power Speed Governors, the Rotating Speed Control Equipment for Generators 274 Coffee break 7: Brilliant dawn of the modern electrical age and the new twentieth century: TRANSIENT/DYNAMIC STABILITY, P-Q-V CHARACTERISTICS AND VOLTAGE STABILITY OF A POWER SYSTEM Steady-state Stability, Transient Stability, Dynamic Stability Steady-state stability Transient stability Dynamic stability Mechanical Acceleration Equation for the Two-generator System and Disturbance Response Transient Stability and Dynamic Stability (Case Study) Transient stability Dynamic stability Four-terminal Circuit and the P S Curve under Fault Conditions and Operational Reactance Circuit Circuit Trial calculation of P-S curve P-Q-V Characteristics and Voltage Stability (Voltage Instability Phenomena) Apparent power at sending terminal and receiving terminal Voltage sensitivity by small disturbance AP, AQ Circle diagram of apparent power P-Q-V characteristics, and P-V and Q-V curves P-Q-V characteristics and voltage instability phenomena V-Q control (voltage and reactive power control) of power systems Supplement 1: Derivation of AV/AP, AV/AQ Sensitivity Equation (Equation from Equation 14.19) Supplement 2: Derivation of Power Circle Diagram Equation (Equation from Equation CD) 299

8 15 GENERATOR CHARACTERISTICS WITH AVR AND STABLE OPERATION LIMIT Theory of AVR, and Transfer Function of Generator System with AVR Inherent transfer function of generator Transfer function ofgenerator+load Duties of AVR and Transfer Function of Generator+AVR 305 and Generator 15.3 Response Characteristics of Total System Operational Limit Introduction of s functions for AVR + exciter+generator + load Generator operational limit and its p - q coordinate expression Transmission Line Charging by Generator with AVR Line charging by generator without AVR Line charging by generator with AVR Supplement 1: Derivation of ej(s), eq(s) as Function of ef(s) (Equation 15.9 from Equations 15.7 and 15.8) Supplement 2: Derivation of eo(s) as Function of ef(s) (Equation from Equations 15.8 and 15.9) 314 Coffee break 8: Heaviside, the great benefactor of electrical engineering OPERATING CHARACTERISTICS AND THE CAPABILITY LIMITS OF GENERATORS General Equations of Generators in Terms of p-q Coordinates Rating Items and the Capability Curve of the Generator Rating items and capability curve Generator's locus in the p-q coordinate plane under various operating conditions Leading Power-factor (Under-excitation Domain) Operation, and UEL Function by AVR Generator as reactive power generator Overheating of stator core end by leading power-factor operation (low excitation) UEL (under-excitation limit) protection by AVR Operation in the over-excitation domain V-Q (Voltage and Reactive Power) Control by AVR Reactive power distribution for multiple generators and cross-current control P-f control and V-Q control Thermal Generators' Weak Points (Negative-sequence Current, Higher Harmonic Current, Shaft-torsional Distortion) Features of large generators today The thermal generator: smaller /2-withstanding capability Rotor overheating caused by d.c. and higher harmonic currents Transient torsional twisting torque of TG coupled shaft General Description of Modern Thermal/Nuclear TG Unit Steam turbine (ST) unit for thermal generation 347 turbines Combined Cycle (CC) system with gas/steam ST unit for nuclear generation Supplement: Derivation of Equation from Equation

9 xiv 17 R-X COORDINATES AND THE THEORY OF DIRECTIONAL DISTANCE RELAYS Protective Relays, Their Mission and Classification Duties of protective relays Classification of major relays Principle of Directional Distance Relays and R-X Coordinates Plane Fundamental function of directional distance relays R-X coordinates and their relation to P-Q coordinates and p-q coordinates Characteristics of DZ-Relays Impedance Locus in R-X Coordinates in Case of a Fault (under No-load Condition) Operation of DZ{S)-Relay for phase b-c line-to-line fault \2<j>S) Response of DZ(G)-Relay to phase a line-to-ground fault (1#G) Response of DZ(G)-Relay against phase b to c (line-to-line) short circuit fault (2$S) DZ-Ry for high-impedance neutral grounded system Impedance Locus under Normal States and Step-out Condition R-X locus under stable and unstable conditions Step-out detection and trip-lock of DZ-Relays Impedance Locus under Faults with Load Flow Conditions Loss of Excitation Detection by DZ-Relays Loss of excitation detection Supplement 1: The Drawing Method for the Locus Z = - A/(l ke'{) of Equation The locus for the case 8: constant, k: 0 to oo The locus for the case k: constant, 8:0 to Supplement 2: The Drawing Method for Z = 1 /(I /A + 1 /B) of Equation Coffee break 9: The symbolic method by complex numbers and Arthur Kennelly, the prominent pioneer TRAVELLING-WAVE (SURGE) PHENOMENA Theory of Travelling-wave Phenomena along Transmission Lines (Distributed-constants Circuit) Waveform equation of a transmission line (overhead line and cable) and the image of a travelling wave The general solution for voltage and current by Laplace transforms Four-terminal network equation between two arbitrary points Examination of line constants Approximation of Distributed-constants Circuit and Accuracy of Concentrated-constants Circuit Behaviour of Travelling Wave at a Transition Point Incident wave, transmitted wave and reflected wave at a transition point Behaviour of voltage and current travelling waves at typical transition points Surge Overvoltages and their Three Different and Confusing Notations Behaviour of Travelling Waves at a Lightning-strike Point 396

10 xv 18.6 Travelling-wave Phenomena of Three-phase Transmission Line Surge impedance of three-phase line Surge analysis of lightning by symmetrical coordinates (lightning strike on phase a conductor) Line-to-ground and Line-to-line Travelling Waves The Reflection Lattice and Transient Behaviour Modes The reflection lattice Oscillatory and non-oscillatory convergence Supplement 1: General Solution Equation for Differential Equation Supplement 2: Derivation of Equation from Equation Coffee break 10: Steinmetz, prominent benefactor of circuit theory and high-voltage technology SWITCHING SURGE PHENOMENA BY CIRCUIT-BREAKERS AND LINE SWITCHES Transient Calculation of a Single-Phase Circuit by Breaker Opening Calculation of fault current tripping (single-phase circuit) Calculation of current tripping (double power source circuit) Calculation of Transient Recovery Voltages Across a Breaker's Three Poles by 30S Fault Tripping Recovery voltage appearing at the first phase (pole) tripping Transient recovery voltage across a breaker's three poles by 3$S fault tripping Fundamental Concepts of High-voltage Circuit-breakers Fundamental concept of breakers Terminology of switching phenomena and breaker tripping capability Current Tripping by Circuit-breakers: Actual Phenomena Short-circuit current (lagging power-factor current) tripping Leading power-factor small-current tripping Short-distance line fault tripping (SLF) Current chopping phenomena by tripping small current with lagging power factor Step-out tripping Current-zero missing Overvoltages Caused by Breaker Closing (Close-switching Surge) Principles of overvoltage caused by breaker closing Resistive Tripping and Resistive Closing by Circuit-breakers Resistive tripping and resistive closing Standardized switching surge level requested by EHV/UHV breakers Overvoltage phenomena caused by tripping of breaker mechanism 448 with resistive tripping Overvoltage phenomena caused by closing of breaker with resistive closing mechanism Switching Surge Caused by Line Switches (Disconnecting Switches) LS-switching surge: the phenomena and mechanism Caused Influence of LS-switching surge 454

11 xvi 19.8 Supplement 1: Calculation of the Coefficients k-\ /C4 of Equation Supplement 2: Calculation of the Coefficients k^-kf, of Equation Coffee break 11: Fortescue's symmetrical components OVERVOLTAGE PHENOMENA Classification of Overvoltage Phenomena Fundamental (Power) Frequency Overvoltages (Non-resonant Phenomena) Ferranti effect Self-excitation of a generator Sudden load tripping or load failure Overvoltages of unfaulted phases by one line-to-ground fault Lower Frequency Harmonic Resonant Overvoltages Broad-area resonant phenomena (lower order frequency resonance) Local area resonant phenomena Interrupted ground fault of cable line in a neutral ungrounded system Switching Surges Overvoltages caused by breaker closing (breaker closing surge) Overvoltages caused by breaker tripping (breaker tripping surge) Switching surge by line switches Overvoltage Phenomena by Lightning Strikes Direct strike on phase conductors (direct flashover) Direct strike on OGW or tower structure (inverse flashover) Induced strokes (electrostatic induced strokes, electromagnetic induced strokes) INSULATION COORDINATION Overvoltages as Insulation Stresses Conduction and insulation Classification ofovervoltages Fundamental Concept of Insulation Coordination Concept of insulation coordination Specific principles of insulation strength and breakdown Countermeasures on Transmission Lines to Reduce Overvoltages and Flashover Adoption of possible large number of overhead grounding a wires (OGWs, OPGWs) Adoption of reasonable allocation and air clearances for conductors/grounding wires Reduction of surge impedance of the towers Adoption of arcing horns (arcing rings) Tower mounted arrester devices Adoption of unequal circuit insulation (double circuit line) Adoption of high-speed reclosing Overvoltage Protection at Substations Surge protection by metal-oxide surge arresters Metal-oxide arresters Ratings, classification and selection of arrester? 494

12 xvii Separation effects of station arresters 495 resistance reduction Station protection by OGWs, and grounding 21.5 Insulation Coordination Details Definition and some principal matters of standards Insulation configuration Insulation withstanding level and BIL, Standard insulation levels and their principles 504 BSL Insulation levels for power systems under 245 kv (Table 21.2A) Insulation levels for power systems over 245 kv (Tables 21.2B and C) 507 of insulation coordination Evaluation of degree Insulation of power cable Transfer Surge Voltages Through the Transformer, and Generator Protection Electrostatic transfer surge voltage Generator protection against transfer surge voltages through transformer Electromagnetic transfer voltage Internal High-frequency Voltage Oscillation of Transformers Caused by Incident Surge Equivalent circuit of transformer in EHF domain Transient oscillatory voltages caused by incident surge Reduction of internal oscillatory voltages Oil-filled Transformers Versus Gas-filled Transformers Supplement: Proof that Equation is the Solution of Equation Coffee break 12: Edith Clarke, the prominent woman electrician WAVEFORM DISTORTION AND LOWER ORDER HARMONIC RESONANCE Causes and Influences of Waveform Distortion Classification ofwaveform distortion Causes ofwaveform distortion Fault Current Waveform Distortion Caused on Cable Lines Introduction of transient current equation Evaluation of the transient fault current Waveform distortion and protective relays POWER CABLES AND POWER CABLE CIRCUITS Power Cables and Their General Features Classification Distinguishing Features of Power Cable Insulation Production process Various environmental layout conditions and required withstanding stresses Metallic sheath circuit and outer-covering insulation Electrical specification and factory testing levels Circuit Constants of Power Cables Inductances of cables Capacitance and surge impedance of cables 554

13 xviii 23.4 Metallic Sheath and Outer Covering Role of metallic sheath and outer covering Metallic sheath earthing methods Cross-bonding Metallic-shielding Method Cross-bonding method Surge voltage analysis on the cable sheath circuit and jointing boxes Surge Voltages: Phenomena Travelling Through a Power Cable Surge voltages at the cable infeed terminal point m Surge voltages at the cable outfeed terminal point n 23.7 Surge Voltages Phenomena on Cable and Overhead Line Jointing 565 Terminal Overvoltage behaviour on cable line caused by lightning surge from overhead line Switching surges arising on cable line Surge Voltages at Cable End Terminal Connected to GIS 568 Coffee break 13: Park's equations, the birth of the d-q-0 method APPROACHES FOR SPECIAL CIRCUITS On-load Tap-changing Transformer (LTC Transformer) Phase-shifting Transformer Introduction of fundamental equations Application for loop circuit lines Woodbridge Transformer and Scott Transformer Woodbridge winding transformer Scott winding transformer Neutral Grounding Transformer Mis-connection of Three-phase Orders Case 1: phase a-b-c to a-c-b mis-connection Case 2: phase a-b-c to b-c-a mis-connection 587 Coffee break 14: Power system engineering and insulation coordination THEORY OF INDUCTION GENERATORS AND MOTORS Introduction of Induction Motors and Their Driving Control Theory of Three-phase Induction Machines IM) with Wye-connected Rotor Windings Equations of induction machine in obc domain dqo domain transformed equations Phasor expression of dqo domain transformed equations Driving power and torque of induction machines Steady-state operation Squirrel-cage Type Induction Motors Circuit equation Characteristics of squirrel-cage induction machine Torque, air-gap flux, speed and power as basis of power electronic control Start-up operation Rated speed operation Over speed operation and braking operation Supplement 1: Calculation of Equations (25.17), (25.18), and (25.19) 627

14 xix 26 POWER ELECTRONIC DEVICES AND THE FUNDAMENTAL CONCEPT OF SWITCHING Power Electronics and the Fundamental Concept Power Switching by Power Devices Snubber Circuit Voltage Conversion by Switching Power Electronic Devices Classification and features of various power semiconductor devices Diodes Thyristors GTO (Gate turn-off thyristors) Bipolar junction transistor (BJT) or power transistor Power MOSFET (metal oxide semiconductor field effect transistor) IGBT (insulated gate bipolar transistors) IPM (intelligent power module) Mathematical Backgrounds for Power Electronic Application Analysis POWER ELECTRONIC CONVERTERS AC to DC Conversion: Rectifier by a Diode Single-phase rectifier with pure resistive load R Inductive load and the role of series connected inductance L Roles of freewheeling diodes and current smoothing reactors Single-phase diode bridge full-wave rectifier Roles of voltage smoothing capacitors Three-phase half-bridge rectifier Current over-lapping Three-phase full-bridge rectifier AC to DC Controlled Conversion: Rectifier by Thyristors Single-phase half-bridge rectifier by a thyristor Single-phase full-bridge rectifier with thyristors Three-phase full-bridge rectifier by thyristors Higher harmonics and ripple ratio Commutating reactances: effects of source side reactances DC to DC Converters (DC to DC Choppers) Voltage step-down converter (Buck chopper) Step up (boost) converter (Boost chopper) Buck-boost converter (step-down/step-up converter) Two-/four-quadrant converter (Composite chopper) Pulse width modulation control (PWM) of a dc-dc converter Multi-phase converter DC to AC Inverters Overview of inverters Single-phase type inverter Three-phase type inverter PWM (Pulse Width Modulation) Control of Inverters Principles of PWM (Pulse width modulation) control (Triangle modulation) Another PWM control schemes (tolerance band control) AC to AC Converter (Cycloconverter) Supplement: Transformer Core Flux Saturation (Flux Bias Caused by DC Biased Current Component) 692

15 MATHEMATICAL MATRIX XX 28 POWER ELECTRONICS APPLICATIONS IN UTILITY POWER SYSTEMS AND SOME INDUSTRIES Introduction Motor Drive Application Concept of induction motor driving control Volts per hertz (V/f) control (or AVAF inverter control) Constant torque and constant speed control Space vector PWM control of induction motor (sinusoidal control method) Phasevector PWM control (rotor flux oriented control) d-q- Sequence current PWM control (sinusoidal control practice) Generator Excitation System (Double-fed) Adjustable Speed Pumped Storage Generator-motor Unit Wind Generation Small Hydro Generation Solar Generation (Photovoltaic Generation) Static Var Compensators (SVC: Thyristor Based External Commutated Scheme) SVC (Static var compensators) TCR (Thyristor controlled reactors) and TCC (Thyristor controlled capacitors) Asymmetrical control method with PWM control for SVC STATCOM or SVG (Static var generator) Active Filters Base concept of active filters Active filter by d-q method Vector PWM control based on d-q method Converter modelling as d-q-coordinates Laplace transfer function Active filter by p-q method or by a-js-method High-Voltage DC Transmission (HVDC Transmission) FACTS (Flexible AC Transmission Systems) Technology Overview of FACTS TCSC (Thyristor-controlled series capacitor) and TPSC (Thyristor-protected series capacitor) Railway Applications Railway substation systems Electric train engine motor driving systems UPSs (Uninterruptible Power Supplies) 745 APPENDIX A - APPENDIX B - FORMULAE 747 EQUATION FORMULAE 751 ANALYTICAL METHODS INDEX 757 COMPONENTS INDEX 759 SUBJECT INDEX 763