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Power system analysis

Book Description

Power System Analysis: A Dynamic Perspective a text designed to serve as a bridge between the undergraduate course on power systems and the complex modelling and computational tools used in the dynamic analysis of practical power systems. With extensive teaching and research experience in the field, the author presents fundamental and advanced concepts using rigorous mathematical analysis and extensive time-domain simulation results. The text also includes numerous plots with clear explanation for easy understanding.

Table of Contents

  1. Cover
  2. About Pearson
  3. Title Page
  4. Brief Contents
  5. Contents
  6. Foreword
  7. Preface
  8. About the Author
  9. 1. Introduction to Power System Analysis
    1. 1.1 Performance of Large Power Systems and their Analysis
    2. 1.2 Classification of Power System Stability Problems
    3. 1.3 Power System Stability Analysis—Computational Issues
    4. 1.4 Power System Stability—Modelling Issues
      1. 1.4.1 Modelling of Dynamical Systems
    5. 1.5 Electromechanical Energy Conversion
      1. 1.5.1 Behaviour of an Inductor with Fixed Armature Core
      2. 1.5.2 Behaviour of an Inductor with Movable Armature Core
      3. 1.5.3 Primitive Machine with Rotating Armature without Rotor Coil
      4. 1.5.4 Primitive Machine with Rotating Armature with a Rotor Coil
    6. References
    7. Review Questions
  10. 2. Basics of Power Systems
    1. 2.1 Sinor Waveform for Conventional Power Generation
    2. 2.2 Choice of Frequency for Power Generation
    3. 2.3 Concept of Phasor Analysis in AC Sinusiodal Systems
      1. 2.3.1 Phasor Representation
    4. 2.4 Power in Single-phase Circuits
      1. 2.4.1 Instantaneous Power in a Pure Resistor Circuit
      2. 2.4.2 Nature of Powers in an RL-series Circuit
      3. 2.4.3 Nature of Powers in an RC-series Circuit
      4. 2.4.4 Real Power Supply–Importance of Reactive Powers
      5. 2.4.5 Complex Number Representation of Real and Reactive Powers
      6. 2.4.6 Power Balance in Single-phase Circuits
    5. 2.5 Power in Three-phase Systems
      1. 2.5.1 Interconnection of Two Sources–Three-phase Systems
      2. 2.5.2 Analysis of Real and Reactive Powers in Three-phase Systems
      3. 2.5.3 Interpretation of Synchronous Operation in Terms of Power Angle
      4. 2.5.4 Complex Power Calculations in Three-phase Balanced Systems
      5. 2.5.5 Single-Line Diagrams of Three-phase Systems
    6. 2.6 Per-unit Representation
      1. 2.6.1 Procedure Employed for Per-unit Representation
      2. 2.6.2 Per-unit Model of Transformers
      3. 2.6.3 Example: A Sample Power System to Demonstrate Per-unit Calculations
      4. 2.6.4 Per-unit Model of Transformers with Off-nominal Voltage Ratings
    7. 2.7 Characteristics of a Typical Power System
      1. 2.7.1 Characteristics of Generator and Primemover Systems
      2. 2.7.2 Characteristics of Transmission and Distribution Systems
      3. 2.7.3 Interconnected Operation of Power Systems
      4. 2.7.4 Characteristics of Loads
    8. References
    9. Review Questions
  11. 3. Park-Based Transformations
    1. 3.1 Time-varying Parameters of a Synchronous Machine
      1. 3.1.1 Derivation of a Time-varying Transformation
      2. 3.1.2 Transformation Matrices in Different Reference-frames
      3. 3.1.3 Some Properties of the Transformation Matrices
      4. 3.1.4 A Change of Reference for Angle Measurement
      5. 3.1.5 An Alternate Form of Park Transformation
      6. 3.1.6 An Example with Park Transformation
      7. 3.1.7 Power-variant Park Transformation
    2. 3.2 Three-Phase-Based Phase-Locked Loop
      1. 3.2.1 Transformation from abc-frame to Synchronous-frame
      2. 3.2.2 Harmonic Oscillator
      3. 3.2.3 Some Results
    3. 3.3 Representation of a Transmission Line in Machine-Frame
      1. 3.3.1 Derivation of Capacitor Voltages in 0dq-frame
      2. 3.3.2 Summary of Equations in dq-frame
      3. 3.3.3 Summary of Equations in DQ-frame
    4. References
    5. Review Questions
  12. 4. Synchronous Machine Modelling Using Primitive Parameters
    1. 4.1 Modelling of a Non-salient Pole Synchronous Machine
      1. 4.1.1 Inductance Matrix for a Non-salient Pole Synchronous Machine
    2. 4.2 Modelling of a Salient Pole Synchronous Machine
      1. 4.2.1 Determination of Inductances of Stator Coils
      2. 4.2.2 Determination of Mutual-inductances Between Stator and Rotor Coils
      3. 4.2.3 Determination of Self- and Mutual-inductances of Rotor Coils
      4. 4.2.4 Voltage Equation Using the Generator Convention
      5. 4.2.5 Elements of Resistance Matrix
    3. 4.3 Flux Linkage-current Equations in Rotor-reference Frame
      1. 4.3.1 Determination of [LB] Matrix
    4. 4.4 Voltage Equations in Rotor-reference Frame
    5. 4.5 Expression for Torque in Rotor-reference Frame
    6. 4.6 Case Studies
      1. 4.6.1 Voltage Build-up on Open-circuit
      2. 4.6.2 Steady-state Short-circuit
      3. 4.6.3 Natural Response Under Short-circuit
    7. 4.7 Rotor Mechanical Equation
    8. 4.8 Analysis of Linear Systems
      1. 4.8.1 Eigenvalue Analysis
      2. 4.8.2 Modal Analysis of Linear Systems
      3. 4.8.3 Solution of an LTI System
    9. References
    10. Review Questions
  13. 5. The Standard Parameters of Synchronous Machine
    1. 5.1 Requirement of Generator Modelling Neglecting Stator Transients
      1. 5.1.1 Short-circuit Analysis with Stator Transients Neglected
      2. 5.1.2 Type of Standardised Synchronous Machine Models
    2. 5.2 Operational Inductance Approach
      1. 5.2.1 Natural Response Under Short-circuit Condition Using OI Model
    3. 5.3 Per-unit Representation of Generator Quantities
      1. 5.3.1 Base Quantities
      2. 5.3.2 Per-unit Stator Voltage Equations
      3. 5.3.3 Flux-linkage Expressions in per-unit for 1.1 Model
      4. 5.3.4 Derivation of a State-space Model for d-axis Rotor Circuits without Damper Winding
      5. 5.3.5 Derivation of State-space Model for q-axis Rotor Circuit
    4. 5.4 Summary of Equations Pertaining to 1.1 Model
    5. 5.5 A Case Study: Voltage Build-up on No-load
    6. 5.6 Operational Impedance for 2.2 Model
      1. 5.6.1 Operational Impedance for d-axis
      2. 5.6.2 Operational Impedance for q-axis
    7. 5.7 Summary of Equations Pertaining to 2.2 Model
    8. 5.8 Swing Equation
      1. 5.8.1 Swing Equation in Form-1
      2. 5.8.2 Swing Equation in Form-2
      3. 5.8.3 Swing Equation in Form-3
      4. 5.8.4 Summary of Different Forms of Swing Equations
    9. 5.9 Steady-state Operation of Synchronous Generator
      1. 5.9.1 Graphical Approach to Determine the Rotor-angle in Salient-pole Machines
      2. 5.9.2 Example: Computation of Field Voltage Efd0 in a Salient-pole Machine
      3. 5.9.3 Expression for Developed Torque Under Steady-state
    10. 5.10 Steady-state Analysis: Space-phasor Approach
      1. 5.10.1 Space-phasor Due to Armature Currents-Revolving Field
      2. 5.10.2 Space-phasor Diagram for Round Rotor Synchronous Machine
      3. 5.10.3 Space-phasor Diagram for Salient-pole Synchronous Machine
    11. 5.11 Modification of 2.2 Model and Equivalent Circuits
      1. 5.11.1 Observations with Reduced-order Models
      2. 5.11.2 Dynamic Equivalent Circuits for Generators
    12. 5.12 Initial Condition Calculations
      1. 5.12.1 Example: Initial Condition Evaluation in an SMIB System
    13. 5.13 Example: Eigenvalue Analysis of a Generator Under Short-circuit Condition
      1. 5.13.1 Short-circuit Analysis Considering Stator Transients
      2. 5.13.2 Short-circuit Analysis Neglecting Stator Transients
    14. 5.14 Example: Synchronisation of a Standalone Generator to Mains
    15. 5.15 Example: Transient Stability Simulation of an Smib System
      1. 5.15.1 SMIB System without AVR
      2. 5.15.2 SMIB System with AVR
    16. References
    17. Review Questions
  14. 6. Numerical Integration of ODEs
    1. 6.1 System of Differential Equations: Some Observations
    2. 6.2 Classification of Numerical Integration Algorithms
      1. 6.2.1 Taylor Series-based Methods
      2. 6.2.2 Single-step and Multi-step Methods
      3. 6.2.3 Self Starting and Non-self Starting Methods
    3. 6.3 Accuracy and Stability of Numerical Integration Methods
      1. 6.3.1 Accuracy of Numerical Integration Methods
      2. 6.3.2 Stability of Numerical Integration Methods Through Eigenvalue Analysis
    4. 6.4 Demonstration of Some Numerical Integration Methods
      1. 6.4.1 Forward Euler Method
      2. 6.4.2 Backward Euler Method
      3. 6.4.3 Trapezoidal Method
      4. 6.4.4 Runge-Kutta (RK) Fourth Order Method
      5. 6.4.5 Variable-step Methods
    5. 6.5 Example: Solution of Swing Equation
      1. 6.5.1 Initial Condition Calculation for the Machine Variables and System Equations
      2. 6.5.2 Solution of Swing Equations by Using Forward Euler Technique
      3. 6.5.3 Solution of Swing Equations by Backward Euler and RK-4 Techniques
      4. 6.5.4 Evaluation of Critical Clearing-angle Using Equal-area Criteria
      5. 6.5.5 Large-signal Stability Evaluation Using Energy Function Method
    6. References
    7. Review Questions
  15. 7. Numerical Iterative Methods
    1. 7.1 Features of Non-linear Algebraic System of Equations
    2. 7.2 Fixed-Point Iteration Method
      1. 7.2.1 Example: A Scalar Function
      2. 7.2.2 Example: Power Flow in a Simple Power System-1
      3. 7.2.3 Example: Power Flow in a Simple Power System-2
      4. 7.2.4 Example: Simultaneous Non-linear Equation
    3. 7.3 Gauss Seidel Iteration Method
    4. 7.4 Newton-Raphson Iteration Method
      1. 7.4.1 Iterative Function for a Scalar System
      2. 7.4.2 Iterative Function for a System with n Variables
      3. 7.4.3 Example: Simultaneous Non-linear Equation with Newton-Raphson Method
      4. 7.4.4 Example: Power Flow in a Simple Power System-1 (Newton-Raphson Method)
      5. 7.4.5 Example: Power Flow in a Simple Power System-2 (Newton-Raphson Method)
    5. References
    6. Review Questions
  16. 8. Fault Analysis of Power Systems
    1. 8.1 Introduction to Fault Analysis
    2. 8.2 Symmetrical Three-phase Short-Circuit Analysis
      1. 8.2.1 Two-machine, Five-bus Power System
      2. 8.2.2 Analysis of Fault Current Using Thevenin’s Theorem
      3. 8.2.3 Calculation of Bus Voltages in a Faulted System
      4. 8.2.4 Bus Voltage Calculation without the Knowledge of the Fault Current
      5. 8.2.5 Calculation of System Quantities During a Fault
      6. 8.2.6 Effect of Synchronous Machine Models on the Fault Current
      7. 8.2.7 Symmetrical Fault Calculations Accounting Pre-fault Load Currents
      8. 8.2.8 Short Circuit Capacity at a Bus
    3. 8.3 Analysis of Unsymmetrical Faults
      1. 8.3.1 Calculation of Sequence Voltages and Currents
      2. 8.3.2 Sequence Impedances of Y- and ?-connected Passive Elements
      3. 8.3.3 Sequence Impedances of Synchronous Machines
      4. 8.3.4 Sequence Impedance of Transmission Lines
      5. 8.3.5 Sequence Impedance of Transformers
      6. 8.3.6 Example: Sequence Networks for a 2-machine 5-bus Power Systems
      7. 8.3.7 Analysis of Unsymmetrical Short-circuit Faults
      8. 8.3.8 Transient Stability Analysis for Unsymmetrical Shunt Faults
    4. References
    5. Review Questions
  17. 9. Introduction to Sub-synchronous Resonance
    1. 9.1 Sub-synchronous Resonance
    2. 9.2 SsrStudy of a Simplified System
      1. 9.2.1 Turbine-generator Mechanical Systems
      2. 9.2.2 Electrical Systems
      3. 9.2.3 System Parameters and Operating Conditions
      4. 9.2.4 Analysis of Only Electrical Systems
      5. 9.2.5 Analysis of Partial Systems
      6. 9.2.6 Analysis of the Complete Systems
      7. 9.2.7 Eigenvalue Analysis of the Complete System
    3. References
    4. Review Questions
  18. 10. Ssr Analysis of the Ieee First Benchmark Model
    1. 10.1 Turbine-Generator Mechanical System Equations
      1. 10.1.1 The IEEE First Benchmark System and Modal Frequencies
      2. 10.1.2 Linearisation of Mechanical System of Equations
    2. 10.2 Generator Modelling
      1. 10.2.1 Stator and Rotor Equations
      2. 10.2.2 Linearisation of Te
      3. 10.2.3 Linearisation of Electrical Equations
    3. 10.3 Exciter Modelling
      1. 10.3.1 Single-time Constant Static Exciter
      2. 10.3.2 Derivation of ?Vg in terms of vQg and vDg Components
    4. 10.4 Transmission Network Modelling
      1. 10.4.1 Derivation of Capacitor Voltage Equations
      2. 10.4.2 Derivation of Line Voltage Equations
    5. 10.5 Listing of Linearised State Equations
      1. 10.5.1 Interfacing of the Network to the Generator
    6. 10.6 Machine-frame-based Time-domain Simulation of Ssr
      1. 10.6.1 Computation of vgd and vgq in Simulation
      2. 10.6.2 Initial Condition Calculations
      3. 10.6.3 Case Studies and Modal-speed Calculations
    7. References
    8. Review Questions
  19. 11. Controllers for Synchronous Generator
    1. 11.1 Real and Reactive Power Controllers for a Synchronous Generator
    2. 11.2 Functions and Types of Excitation Systems
      1. 11.2.1 DC Excitation Systems
      2. 11.2.2 AC Excitation Systems
      3. 11.2.3 Static Excitation Systems
      4. 11.2.4 State-space Model of Some System Functions
      5. 11.2.5 Initial Condition Calculations for Exciters
    3. 11.3 Prime Mover Controllers
      1. 11.3.1 Influence of Prime Mover Controllers on Load Sharing
      2. 11.3.2 Model of Hydraulic Turbines
      3. 11.3.3 Model of Steam Turbines
      4. 11.3.4 Modelling of Speed-Governing Systems
    4. 11.4 Windup and Non-windup Type Limiters on Integrator Blocks
      1. 11.4.1 Windup Type Limiter on Integrator Blocks
      2. 11.4.2 Non-windup Type Limiter on Integrator Blocks
    5. References
    6. Review Questions
  20. 12. Power System Angle Stability
    1. 12.1 Relative-Angular Stability Analysis
      1. 12.1.1 Small-signal Stability Analysis of SMIB System
      2. 12.1.2 A Mechanical Analogy
    2. 12.2 Synchronising and Damping Torque Analysis
    3. 12.3 Effect of a Fast-acting High-gain Static Exciter on smib System
      1. 12.3.1 PSS Location and its Design
    4. 12.4 Small-signal Stability Analysis of an Smib System
      1. 12.4.1 Example: Small-signal Stability of SMIB System with 0.0 Model for Generator
      2. 12.4.2 Example: Small-signal Stability of SMIB System with 1.0 Model for Generator
      3. 12.4.3 Example: Small-signal Stability of SMIB System with 2.2 Model for Generator
      4. 12.4.4 Modal Performance with AVR and PSS
    5. References
    6. Review Questions
  21. 13. Modal Analysis of Power Systems with Interconnected Generators
    1. 13.1 Importance of Modal Analysis of Power Systems
    2. 13.2 Power System Oscillations
      1. 13.2.1 Classification of Power System Oscillation
      2. 13.2.2 Analysis of Small-signal Stability
    3. 13.3 Spring-mass System Example
      1. 13.3.1 Removal of Redundancy of a State
      2. 13.3.2 Case-1: With External F1 Without Any Damping
      3. 13.3.3 Case-2: With External F3 Without Any Damping
      4. 13.3.4 Case-3: With External F3 With Damping B1
      5. 13.3.5 Case-4: With External F3 as a Step-signal Without Any Damping
      6. 13.3.6 Case-5: With External F3 as a Step-signal With Damping B1
      7. 13.3.7 Performance Analysis in the COI-reference-frame
    4. 13.4 Linearisation of Power System Modelling Equations
      1. 13.4.1 Current-Injection Approach
    5. 13.5 Participation Matrix
      1. 13.5.1 Determination of Nature of Oscillatory Modes
    6. 13.6 Modal Analysis of a Two-machine Power System
      1. 13.6.1 Base Case-Without Turbine
      2. 13.6.2 A Reheat Turbine Enabled on Machine-1
    7. 13.7 Modal Analysis of Four-machine Modified Power System
      1. 13.7.1 Base Case Loading Condition
      2. 13.7.2 Base Case without Excitation Controllers
      3. 13.7.3 Base Case with Reduced Loading Condition
      4. 13.7.4 Base Case with Power System Stabiliser
    8. References
    9. Review Questions
  22. 14. Transient Stability Analysis of Power Systems with Interconnected Generators
    1. 14.1 Interfacing Generator to Network
      1. 14.1.1 Influence of Dynamic Saliency of Generator
      2. 14.1.2 Dummy-coil Approach
      3. 14.1.3 Generator Source Current Calculations
      4. 14.1.4 Modelling of Network Elements
    2. 14.2 Centre of Inertia Reference
      1. 14.2.1 Common-mode Frequency Calculation (Frequency Stability Analysis)
      2. 14.2.2 Speed and Rotor-angle Calculations with respect to COI
      3. 14.2.3 Swing Equations in COI-reference
    3. 14.3 Structure of Power System Equations and its Solution
      1. 14.3.1 Simultaneous Implicit Solution
      2. 14.3.2 Partitioned Solution
    4. 14.4 Load Modelling
      1. 14.4.1 Load Model Classification
      2. 14.4.2 Polynomial Load Representation
      3. 14.4.3 Frequency-dependent Load Models
    5. 14.5 Load Equivalent Circuit
      1. 14.5.1 Modification of Constant Power-type Load Characteristics
      2. 14.5.2 An Approach to Avoid Iterative Solution of Algebraic Equations
    6. 14.6 A Summary of the Implementation Procedure
    7. 14.7 Demonstration of System Frequency with Two-machine Power System
      1. 14.7.1 Three-phase Fault without Frequency-dependent Loads
      2. 14.7.2 Three-phase Fault with Frequency-dependent Loads
      3. 14.7.3 Line Trip without Frequency-dependent Loads
      4. 14.7.4 Line Trip with Frequency-dependent Loads
      5. 14.7.5 Line Trip, Speed-governor on M-1 Enabled without Frequency-dependent Loads
      6. 14.7.6 Line Trip, Speed-governor on M-1 Enabled with Frequency-dependent Loads
      7. 14.7.7 Line Trip, Speed-governors on M-1 and M-2 Enabled with Frequency-dependent Loads
    8. 14.8 Large Disturbance Performance
      1. 14.8.1 Two-machine Power System
      2. 14.8.2 Four-machine, 10-bus Power Systems
      3. 14.8.3 50-machine, 145-bus the IEEE Power Systems
    9. References
    10. Review Questions
  23. 15. Dynamic Modelling of Some Electrical Machines and their Power-flow Analysis
    1. 15.1 Induction Motor Model
      1. 15.1.1 Fifth Order Induction Motor Model
      2. 15.1.2 Per-unit Representation of the Induction Motor Model
      3. 15.1.3 Reduced Order Model for the Induction Machine
    2. 15.2 Modelling of dc Motor-driven Synchronous Generator
      1. 15.2.1 DC Motor Modelling
      2. 15.2.2 DC Motor Driving a Synchronous Generator
      3. 15.2.3 Synchronisation of Two DC Motor-driven Synchronous Generators
      4. 15.2.4 Synchronisation of a DC Motor-driven Generator to Mains Supply
    3. References
    4. Review Questions
  24. Index
  25. Copyright