# Handbook of Power System Engineering

# Handbook of Power System Engineering

ISBN: 978-0-470-03367-8

May 2007

574 pages

## Description

Maintaining the reliable and efficient generation, transmission and distribution of electrical power is of the utmost importance in a world where electricity is the inevitable means of energy acquisition, transportation, and utilization, and the principle mode of communicating media. Our modern society is entirely dependent on electricity, so problems involving the continuous delivery of power can lead to the disruption and breakdown of vital economic and social infrastructures.This book brings together comprehensive technical information on power system engineering, covering the fundamental theory of power systems and their components, and the related analytical approaches.

**Key features:**

- Presents detailed theoretical explanations of simple power systems as an accessible basis for understanding the larger, more complex power systems.
- Examines widely the theory, practices and implementation of several power sub-systems such as generating plants, over-head transmission lines and power cable lines, sub-stations, including over-voltage protection, insulation coordination as well as power systems control and protection.
- Discusses steady-state and transient phenomena from basic power-frequency range to lightning- and switching-surge ranges, including system faults, wave-form distortion and lower-order harmonic resonance.
- Explains the dynamics of generators and power systems through essential mathematical equations, with many numerical examples.
- Analyses the historical progression of power system engineering, in particular the descriptive methods of electrical circuits for power systems.

Written by an author with a wealth of experience in the field, both in industry and academia, the *Handbook of Power System Engineering* provides a single reference work for practicing engineers, researchers and those working in industry that want to gain knowledge of all aspects of power systems. It is also valuable for advanced students taking courses or modules in power system engineering.

ACKNOWLEDGEMENTS.

ABOUT THE AUTHOR.

INTRODUCTION.

1 OVERHEAD TRANSMISSION LINES AND THEIR CIRCUIT CONSTANTS.

1.1 Overhead Transmission Lines with LR Constants.

1.2 Stray Capacitance of Overhead Transmission Lines.

1.3 Supplement: Additional Explanation for Equation 1.27.

2 SYMMETRICAL COORDINATE METHOD (SYMMETRICAL COMPONENTS).

2.1 Fundamental Concept of Symmetrical Components.

2.2 Definition of Symmetrical Components.

2.3 Conversion of Three-phase Circuit into Symmetrical Coordinated Circuit.

2.4 Transmission Lines by Symmetrical Components.

2.5 Typical Transmission Line Constants.

2.6 Generator by Symmetrical Components (Easy Description).

2.7 Description of Three-phase Load Circuit by Symmetrical Components.

3 FAULT ANALYSIS BY SYMMETRICAL COMPONENTS.

3.1 Fundamental Concept of Symmetrical Coordinate Method.

3.2 Line-to-ground Fault (Phase a to Ground Fault: 1øG).

3.3 Fault Analysis at Various Fault Modes.

3.4 Conductor Opening.

4 FAULT ANALYSIS OF PARALLEL CIRCUIT LINES (INCLUDING SIMULTANEOUS DOUBLE CIRCUIT FAULT).

4.1 Two-phase Circuit and its Symmetrical Coordinate Method.

4.2 Double Circuit Line by Two-phase Symmetrical Transformation.

4.3 Fault Analysis of Double Circuit Line (General Process).

4.4 Single Circuit Fault on the Double Circuit Line.

4.5 Double Circuit Fault at Single Point f.

4.6 Simultaneous Double Circuit Faults at Different Points f, F on the Same Line.

5 PER UNIT METHOD AND INTRODUCTION OF TRANSFORMER CIRCUIT.

5.1 Fundamental Concept of the PU Method.

5.2 PU Method for Three-phase Circuits.

5.3 Three-phase Three-winding Transformer, its Symmetrical Components Equations and the Equivalent Circuit.

5.4 Base Quantity Modification of Unitized Impedance.

5.5 Autotransformer.

5.6 Numerical Example to Find the Unitized Symmetrical Equivalent Circuit.

5.7 Supplement: Transformation from Equation 5.18 to Equation 5.19.

6 The α–β–0 COORDINATE METHOD (CLARKE COMPONENTS) AND ITS APPLICATION.

6.1 Definition of α–β–0 Coordinate Method (α–β–0 Components).

6.2 Interrelation Between α–β–0 Components and Symmetrical Components.

6.3 Circuit Equation and Impedance by the α–β–0 Coordinate Method.

6.4 Three-phase Circuit in α–β–0 Components.

6.5 Fault Analysis by α–β–0 Components.

7 SYMMETRICAL AND α–β–0 COMPONENTS AS ANALYTICAL TOOLS FOR TRANSIENT PHENOMENA.

7.1 The Symbolic Method and its Application to Transient Phenomena.

7.2 Transient Analysis by Symmetrical and α–β–0 Components.

7.3 Comparison of Transient Analysis by Symmetrical and α–β–0 Components.

8 NEUTRAL GROUNDING METHODS.

8.1 Comparison of Neutral Grounding Methods.

8.2 Overvoltages on the Unfaulted Phases Caused by a Line-to-ground Fault.

8.3 Possibility of Voltage Resonance.

8.4 Supplement: Arc-suppression Coil (Petersen Coil) Neutral Grounded Method.

9 VISUAL VECTOR DIAGRAMS OF VOLTAGES AND CURRENTS UNDER FAULT CONDITIONS.

9.1 Three-phase Fault: 3øS, 3øG (Solidly Neutral Grounding System, High-resistive Neutral Grounding System).

9.2 Phase b–c Fault: 2øS (for Solidly Neutral Grounding System, High-resistive Neutral Grounding System).

9.3 Phase a to Ground Fault: 1øG (Solidly Neutral Grounding System).

9.4 Double Line-to-ground (Phases b and c) Fault: 2øG (Solidly Neutral Grounding System).

9.5 Phase a Line-to-ground Fault: 1øG (High-resistive Neutral Grounding System).

9.6 Double Line-to-ground (Phases b and c) Fault: 2øG (High-resistive Neutral Grounding System).

10 THEORY OF GENERATORS.

10.1 Mathematical Description of a Synchronous Generator.

10.2 Introduction of d–q–0 Method (d–q–0 Components).

10.3 Transformation of Generator Equations from a–b–c to d–q–0 Domain.

10.4 Generator Operating Characteristics and it’s Vector Diagrams on d-and q-axes plain.

10.5 Transient Phenomena and the Generator’s Transient Reactances.

10.6 Symmetrical Equivalent Circuits of Generators.

10.7 Laplace-transformed Generator Equations and the Time Constants.

10.7.1 Laplace-transformed equations.

10.8 Relations Between the d–q–0 and a–b–0 Domains.

10.9 Detailed Calculation of Generator Short-circuit Transient Current under Load Operation.

10.10 Supplement 1: The Equations of the Rational Function and Their Transformation into Expanded Sub-sequential Fractional Equations.

10.11 Supplement 2: Calculation of the Coefficients of Equation 10.120.

10.12 Supplement 3: The Formulae of the Laplace Transform.

11 APPARENT POWER AND ITS EXPRESSION IN THE 0–1–2 AND d–q–0 DOMAINS.

11.1 Apparent Power and its Symbolic Expression for Arbitrary Waveform Voltages and Currents.

11.2 Apparent Power of a Three-phase Circuit in the 0–1–2 Domain.

11.3 Apparent Power in the d–q–0 Domain.

12 GENERATING POWER AND STEADY-STATE STABILITY.

12.1 Generating Power and the P–δ and Q–δ Curves.

12.2 Power Transfer Limit between a Generator and Power System Network.

12.3 Supplement: Derivation of Equation 12.17.

13 THE GENERATOR AS ROTATING MACHINERY.

13.1 Mechanical (Kinetic) Power and Generating (Electrical) Power.

13.2 Kinetic Equation of the Generator.

14 TRANSIENT/DYNAMIC STABILITY, P–Q–V CHARACTERISTICS AND VOLTAGE STABILITY OF A POWER SYSTEM.

14.1 Steady-state Stability, Transient Stability, Dynamic Stability.

14.2 Mechanical Acceleration Equation for the Two-generator System, and Disturbance Response.

14.3 Transient Stability and Dynamic Stability (Case Study).

14.4 Four-terminal Circuit and the P–d Curve under Fault Conditions.

14.5 P–Q–V Characteristics and Voltage Stability (Voltage Instability Phenomena).

14.6 Supplement 1: Derivation of Equation 14.20 from Equation 14.19.

14.7 Supplement 2: Derivation of Equation 14.30 from Equation 14.18 2.

15 GENERATOR CHARACTERISTICS WITH AVR AND STABLE OPERATION LIMIT.

15.1 Theory of AVR, and Transfer Function of Generator System with AVR.

15.2 Duties of AVR and Transfer Function of Generator + AVR.

15.3 Response Characteristics of Total System and Generator Operational Limit.

15.4 Transmission Line Charging by Generator with AVR.

15.5 Supplement 1: Derivation of Equation 15.9 from Equations 15.7 and 15.8.

15.6 Supplement 2: Derivation of Equation 15.10 from Equations 15.8 and 15.9.

16 OPERATING CHARACTERISTICS AND THE CAPABILITY LIMITS OF GENERATORS.

16.1 General Equations of Generators in Terms of p–q Coordinates.

16.2 Rating Items and the Capability Curve of the Generator.

16.3 Leading Power-factor (Under-excitation Domain) Operation, and UEL Function by AVR.

16.4 V–Q (Voltage and Reactive Power) Control by AVR.

16.5 Thermal Generators’ Weak Points (Negative-sequence Current, Higher Harmonic Current, Shaft-torsional Distortion).

16.6 General Description of Modern Thermal/Nuclear TG Unit.

16.7 Supplement: Derivation of Equation 16.14.

17 R–X COORDINATES AND THE THEORY OF DIRECTIONAL DISTANCE RELAYS.

17.1 Protective Relays, Their Mission and Classification.

17.2 Principle of Directional Distance Relays and R–X Coordinates Plane.

17.3 Impedance Locus in R–X Coordinates in Case of a Fault (under No-load Condition).

17.4 Impedance Locus under Normal States and Step-out Condition.

17.5 Impedance Locus under Faults with Load Flow Conditions.

17.6 Loss of Excitation Detection by DZ-Rys.

17.7 Supplement 1: The Drawing Method for the Locus Z = A/(1-ke^{iδ}) of Equation 17.22.

17.8 Supplement 2: The Drawing Method for Z = 1/(1/A + 1/B) of Equation 17.24.

18 TRAVELLING-WAVE (SURGE) PHENOMENA.

18.1 Theory of Travelling-wave Phenomena along Transmission Lines (Distributed-constants Circuit).

18.2 Approximation of Distributed-constants Circuit and Accuracy of Concentrated-constants Circuit.

18.3 Behaviour of Travelling Wave at a Transition Point.

18.4 Behaviour of Travelling Waves at a Lightning-strike Point.

18.5 Travelling-wave Phenomena of Three-phase Transmission Line.

18.6 Line-to-ground and Line-to-line Travelling Waves.

18.7 The Reflection Lattice and Transient Behaviour Modes.

18.8 Supplement 1: General Solution Equation 18.10 for Differential Equation 18.9.

18.9 Supplement 2: Derivation of Equation 18.19 from Equation 18.18.

19 SWITCHING SURGE PHENOMENA BY CIRCUIT-BREAKERS AND LINE SWITCHES.

19.1 Transient Calculation of a Single Phase Circuit by Breaker Opening.

19.2 Calculation of Transient Recovery Voltages Across a Breaker’s Three Poles by 3fS Fault Tripping.

19.3 Fundamental Concepts of High-voltage Circuit-breakers.

19.4 Actual Current Tripping Phenomena by Circuit-breakers.

19.5 Overvoltages Caused by Breaker Closing (Close-switching Surge).

19.6 Resistive Tripping and Resistive Closing by Circuit-breakers.

19.7 Switching Surge Caused by Line Switches (Disconnecting Switches).

19.8 Supplement 1: Calculation of the Coefficients k1k4 of Equation 19.6.

19.9 Supplement 2: Calculation of the Coefficients k1k6 of Equation 19.17.

20 OVERVOLTAGE PHENOMENA.

20.1 Classification of Overvoltage Phenomena.

20.2 Fundamental (Power) Frequency Overvoltages (Non-resonant Phenomena).

20.3 Lower Frequency Harmonic Resonant Overvoltages.

20.4 Switching Surges.

20.5 Overvoltage Phenomena by Lightning Strikes.

21 INSULATION COORDINATION.

21.1 Overvoltages as Insulation Stresses.

21.2 Fundamental Concept of Insulation Coordination.

21.3 Countermeasures on Transmission Lines to Reduce Overvoltages and Flashover.

21.4 Overvoltage Protection at Substations.

21.5 Insulation Coordination Details.

21.6 Transfer Surge Voltages Through the Transformer, and Generator Protection.

21.7 Internal High-frequency Voltage Oscillation of Transformers Caused by Incident Surge.

21.8 Oil-filled Transformers Versus Gas-filled Transformers.

21.9 Supplement: Proof that Equation 21.21 is the solution of Equation 21.20.

22 WAVEFORM DISTORTION AND LOWER ORDER HARMONIC RESONANCE.

22.1 Causes and Influences of Waveform Distortion.

22.2 Fault Current Waveform Distortion Caused on Cable Lines.

23 POWER CABLES.

23.1 Power Cables and Their General Features.

23.2 Circuit Constants of Power Cables.

23.3 Metallic Sheath and Outer Covering.

23.4 Cross-bonding Metallic-shielding Method.

23.5 Surge Voltages Arising on Phase Conductors and Sheath Circuits.

23.6 Surge Voltages on Overhead Line and Cable Combined Networks.

23.7 Surge Voltages at Cable End Terminal Connected to GIS.

24 APPROACHES FOR SPECIAL CIRCUITS.

24.1 On-load Tap-changing Transformer (LTC Transformer).

24.2 Phase-shifting Transformer.

24.3 Woodbridge Transformer and Scott Transformer.

24.4 Neutral Grounding Transformer.

24.5 Mis-connection of Three-phase Orders.

APPENDIX A – MATHEMATICAL FORMULAE.

APPENDIX B – MATRIX EQUATION FORMULAE.

ANALYTICAL METHODS INDEX.

COMPONENTS INDEX.

SUBJECT INDEX.

*IEEE Electrical Insulation Magazine*, May/June 2009)