book

Power System Analysis

by K. N. Shubhanga

May 2018

Intermediate to advanced

808 pages

19h 52m

English

Pearson Education India

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1.1 Performance of Large Power Systems and their Analysis1.2 Classification of Power System Stability Problems1.3 Power System Stability Analysis—Computational Issues1.4 Power System Stability—Modelling Issues1.4.1 Modelling of Dynamical Systems1.5 Electromechanical Energy Conversion1.5.1 Behaviour of an Inductor with Fixed Armature Core1.5.2 Behaviour of an Inductor with Movable Armature Core1.5.3 Primitive Machine with Rotating Armature without Rotor Coil1.5.4 Primitive Machine with Rotating Armature with a Rotor CoilReferencesReview Questions
2.1 Sinor Waveform for Conventional Power Generation2.2 Choice of Frequency for Power Generation2.3 Concept of Phasor Analysis in AC Sinusiodal Systems2.3.1 Phasor Representation 2.4 Power in Single-phase Circuits2.4.1 Instantaneous Power in a Pure Resistor Circuit2.4.2 Nature of Powers in an RL-series Circuit2.4.3 Nature of Powers in an RC-series Circuit2.4.4 Real Power Supply–Importance of Reactive Powers2.4.5 Complex Number Representation of Real and Reactive Powers2.4.6 Power Balance in Single-phase Circuits2.5 Power in Three-phase Systems2.5.1 Interconnection of Two Sources–Three-phase Systems2.5.2 Analysis of Real and Reactive Powers in Three-phase Systems2.5.3 Interpretation of Synchronous Operation in Terms of Power Angle2.5.4 Complex Power Calculations in Three-phase Balanced Systems2.5.5 Single-Line Diagrams of Three-phase Systems2.6 Per-unit Representation2.6.1 Procedure Employed for Per-unit Representation2.6.2 Per-unit Model of Transformers2.6.3 Example: A Sample Power System to Demonstrate Per-unit Calculations2.6.4 Per-unit Model of Transformers with Off-nominal Voltage Ratings2.7 Characteristics of a Typical Power System2.7.1 Characteristics of Generator and Primemover Systems2.7.2 Characteristics of Transmission and Distribution Systems2.7.3 Interconnected Operation of Power Systems2.7.4 Characteristics of LoadsReferencesReview Questions

3.1 Time-varying Parameters of a Synchronous Machine3.1.1 Derivation of a Time-varying Transformation3.1.2 Transformation Matrices in Different Reference-frames3.1.3 Some Properties of the Transformation Matrices3.1.4 A Change of Reference for Angle Measurement3.1.5 An Alternate Form of Park Transformation3.1.6 An Example with Park Transformation3.1.7 Power-variant Park Transformation3.2 Three-Phase-Based Phase-Locked Loop3.2.1 Transformation from abc-frame to Synchronous-frame3.2.2 Harmonic Oscillator3.2.3 Some Results3.3 Representation of a Transmission Line in Machine-Frame3.3.1 Derivation of Capacitor Voltages in 0dq-frame3.3.2 Summary of Equations in dq-frame3.3.3 Summary of Equations in DQ-frameReferencesReview Questions
4.1 Modelling of a Non-salient Pole Synchronous Machine4.1.1 Inductance Matrix for a Non-salient Pole Synchronous Machine4.2 Modelling of a Salient Pole Synchronous Machine4.2.1 Determination of Inductances of Stator Coils4.2.2 Determination of Mutual-inductances Between Stator and Rotor Coils4.2.3 Determination of Self- and Mutual-inductances of Rotor Coils4.2.4 Voltage Equation Using the Generator Convention4.2.5 Elements of Resistance Matrix4.3 Flux Linkage-current Equations in Rotor-reference Frame4.3.1 Determination of [LB] Matrix4.4 Voltage Equations in Rotor-reference Frame4.5 Expression for Torque in Rotor-reference Frame4.6 Case Studies4.6.1 Voltage Build-up on Open-circuit4.6.2 Steady-state Short-circuit4.6.3 Natural Response Under Short-circuit4.7 Rotor Mechanical Equation4.8 Analysis of Linear Systems4.8.1 Eigenvalue Analysis4.8.2 Modal Analysis of Linear Systems4.8.3 Solution of an LTI SystemReferencesReview Questions
5.1 Requirement of Generator Modelling Neglecting Stator Transients5.1.1 Short-circuit Analysis with Stator Transients Neglected5.1.2 Type of Standardised Synchronous Machine Models5.2 Operational Inductance Approach5.2.1 Natural Response Under Short-circuit Condition Using OI Model5.3 Per-unit Representation of Generator Quantities5.3.1 Base Quantities5.3.2 Per-unit Stator Voltage Equations5.3.3 Flux-linkage Expressions in per-unit for 1.1 Model5.3.4 Derivation of a State-space Model for d-axis Rotor Circuits without Damper Winding5.3.5 Derivation of State-space Model for q-axis Rotor Circuit5.4 Summary of Equations Pertaining to 1.1 Model5.5 A Case Study: Voltage Build-up on No-load5.6 Operational Impedance for 2.2 Model5.6.1 Operational Impedance for d-axis5.6.2 Operational Impedance for q-axis5.7 Summary of Equations Pertaining to 2.2 Model5.8 Swing Equation5.8.1 Swing Equation in Form-15.8.2 Swing Equation in Form-25.8.3 Swing Equation in Form-35.8.4 Summary of Different Forms of Swing Equations5.9 Steady-state Operation of Synchronous Generator5.9.1 Graphical Approach to Determine the Rotor-angle in Salient-pole Machines5.9.2 Example: Computation of Field Voltage Efd0 in a Salient-pole Machine5.9.3 Expression for Developed Torque Under Steady-state5.10 Steady-state Analysis: Space-phasor Approach 5.10.1 Space-phasor Due to Armature Currents-Revolving Field5.10.2 Space-phasor Diagram for Round Rotor Synchronous Machine5.10.3 Space-phasor Diagram for Salient-pole Synchronous Machine5.11 Modification of 2.2 Model and Equivalent Circuits5.11.1 Observations with Reduced-order Models5.11.2 Dynamic Equivalent Circuits for Generators5.12 Initial Condition Calculations5.12.1 Example: Initial Condition Evaluation in an SMIB System5.13 Example: Eigenvalue Analysis of a Generator Under Short-circuit Condition5.13.1 Short-circuit Analysis Considering Stator Transients5.13.2 Short-circuit Analysis Neglecting Stator Transients5.14 Example: Synchronisation of a Standalone Generator to Mains5.15 Example: Transient Stability Simulation of an Smib System5.15.1 SMIB System without AVR5.15.2 SMIB System with AVRReferencesReview Questions
6.1 System of Differential Equations: Some Observations6.2 Classification of Numerical Integration Algorithms6.2.1 Taylor Series-based Methods 6.2.2 Single-step and Multi-step Methods6.2.3 Self Starting and Non-self Starting Methods6.3 Accuracy and Stability of Numerical Integration Methods6.3.1 Accuracy of Numerical Integration Methods6.3.2 Stability of Numerical Integration Methods Through Eigenvalue Analysis6.4 Demonstration of Some Numerical Integration Methods6.4.1 Forward Euler Method6.4.2 Backward Euler Method6.4.3 Trapezoidal Method6.4.4 Runge-Kutta (RK) Fourth Order Method6.4.5 Variable-step Methods6.5 Example: Solution of Swing Equation6.5.1 Initial Condition Calculation for the Machine Variables and System Equations6.5.2 Solution of Swing Equations by Using Forward Euler Technique6.5.3 Solution of Swing Equations by Backward Euler and RK-4 Techniques6.5.4 Evaluation of Critical Clearing-angle Using Equal-area Criteria6.5.5 Large-signal Stability Evaluation Using Energy Function MethodReferencesReview Questions
7.1 Features of Non-linear Algebraic System of Equations7.2 Fixed-Point Iteration Method7.2.1 Example: A Scalar Function7.2.2 Example: Power Flow in a Simple Power System-17.2.3 Example: Power Flow in a Simple Power System-27.2.4 Example: Simultaneous Non-linear Equation7.3 Gauss Seidel Iteration Method7.4 Newton-Raphson Iteration Method7.4.1 Iterative Function for a Scalar System7.4.2 Iterative Function for a System with n Variables7.4.3 Example: Simultaneous Non-linear Equation with Newton-Raphson Method7.4.4 Example: Power Flow in a Simple Power System-1 (Newton-Raphson Method)7.4.5 Example: Power Flow in a Simple Power System-2 (Newton-Raphson Method)ReferencesReview Questions
8.1 Introduction to Fault Analysis8.2 Symmetrical Three-phase Short-Circuit Analysis8.2.1 Two-machine, Five-bus Power System8.2.2 Analysis of Fault Current Using Thevenin’s Theorem8.2.3 Calculation of Bus Voltages in a Faulted System8.2.4 Bus Voltage Calculation without the Knowledge of the Fault Current8.2.5 Calculation of System Quantities During a Fault8.2.6 Effect of Synchronous Machine Models on the Fault Current8.2.7 Symmetrical Fault Calculations Accounting Pre-fault Load Currents8.2.8 Short Circuit Capacity at a Bus8.3 Analysis of Unsymmetrical Faults8.3.1 Calculation of Sequence Voltages and Currents8.3.2 Sequence Impedances of Y- and ?-connected Passive Elements8.3.3 Sequence Impedances of Synchronous Machines8.3.4 Sequence Impedance of Transmission Lines8.3.5 Sequence Impedance of Transformers8.3.6 Example: Sequence Networks for a 2-machine 5-bus Power Systems8.3.7 Analysis of Unsymmetrical Short-circuit Faults8.3.8 Transient Stability Analysis for Unsymmetrical Shunt FaultsReferencesReview Questions
9.1 Sub-synchronous Resonance9.2 SsrStudy of a Simplified System9.2.1 Turbine-generator Mechanical Systems9.2.2 Electrical Systems9.2.3 System Parameters and Operating Conditions9.2.4 Analysis of Only Electrical Systems9.2.5 Analysis of Partial Systems9.2.6 Analysis of the Complete Systems9.2.7 Eigenvalue Analysis of the Complete SystemReferencesReview Questions
10.1 Turbine-Generator Mechanical System Equations10.1.1 The IEEE First Benchmark System and Modal Frequencies10.1.2 Linearisation of Mechanical System of Equations10.2 Generator Modelling10.2.1 Stator and Rotor Equations10.2.2 Linearisation of Te10.2.3 Linearisation of Electrical Equations10.3 Exciter Modelling10.3.1 Single-time Constant Static Exciter10.3.2 Derivation of ?Vg in terms of vQg and vDg Components10.4 Transmission Network Modelling10.4.1 Derivation of Capacitor Voltage Equations10.4.2 Derivation of Line Voltage Equations10.5 Listing of Linearised State Equations10.5.1 Interfacing of the Network to the Generator10.6 Machine-frame-based Time-domain Simulation of Ssr10.6.1 Computation of vgd and vgq in Simulation10.6.2 Initial Condition Calculations10.6.3 Case Studies and Modal-speed CalculationsReferencesReview Questions
11.1 Real and Reactive Power Controllers for a Synchronous Generator11.2 Functions and Types of Excitation Systems11.2.1 DC Excitation Systems11.2.2 AC Excitation Systems11.2.3 Static Excitation Systems11.2.4 State-space Model of Some System Functions11.2.5 Initial Condition Calculations for Exciters11.3 Prime Mover Controllers11.3.1 Influence of Prime Mover Controllers on Load Sharing11.3.2 Model of Hydraulic Turbines11.3.3 Model of Steam Turbines11.3.4 Modelling of Speed-Governing Systems11.4 Windup and Non-windup Type Limiters on Integrator Blocks11.4.1 Windup Type Limiter on Integrator Blocks11.4.2 Non-windup Type Limiter on Integrator BlocksReferencesReview Questions
12.1 Relative-Angular Stability Analysis12.1.1 Small-signal Stability Analysis of SMIB System12.1.2 A Mechanical Analogy12.2 Synchronising and Damping Torque Analysis12.3 Effect of a Fast-acting High-gain Static Exciter on smib System12.3.1 PSS Location and its Design12.4 Small-signal Stability Analysis of an Smib System12.4.1 Example: Small-signal Stability of SMIB System with 0.0 Model for Generator12.4.2 Example: Small-signal Stability of SMIB System with 1.0 Model for Generator12.4.3 Example: Small-signal Stability of SMIB System with 2.2 Model for Generator12.4.4 Modal Performance with AVR and PSSReferencesReview Questions
13.1 Importance of Modal Analysis of Power Systems13.2 Power System Oscillations13.2.1 Classification of Power System Oscillation13.2.2 Analysis of Small-signal Stability13.3 Spring-mass System Example13.3.1 Removal of Redundancy of a State13.3.2 Case-1: With External F1 Without Any Damping13.3.3 Case-2: With External F3 Without Any Damping13.3.4 Case-3: With External F3 With Damping B113.3.5 Case-4: With External F3 as a Step-signal Without Any Damping13.3.6 Case-5: With External F3 as a Step-signal With Damping B113.3.7 Performance Analysis in the COI-reference-frame13.4 Linearisation of Power System Modelling Equations13.4.1 Current-Injection Approach 13.5 Participation Matrix13.5.1 Determination of Nature of Oscillatory Modes13.6 Modal Analysis of a Two-machine Power System13.6.1 Base Case-Without Turbine13.6.2 A Reheat Turbine Enabled on Machine-113.7 Modal Analysis of Four-machine Modified Power System13.7.1 Base Case Loading Condition13.7.2 Base Case without Excitation Controllers13.7.3 Base Case with Reduced Loading Condition13.7.4 Base Case with Power System StabiliserReferencesReview Questions
14.1 Interfacing Generator to Network14.1.1 Influence of Dynamic Saliency of Generator14.1.2 Dummy-coil Approach14.1.3 Generator Source Current Calculations14.1.4 Modelling of Network Elements14.2 Centre of Inertia Reference14.2.1 Common-mode Frequency Calculation (Frequency Stability Analysis)14.2.2 Speed and Rotor-angle Calculations with respect to COI14.2.3 Swing Equations in COI-reference14.3 Structure of Power System Equations and its Solution14.3.1 Simultaneous Implicit Solution14.3.2 Partitioned Solution14.4 Load Modelling14.4.1 Load Model Classification14.4.2 Polynomial Load Representation14.4.3 Frequency-dependent Load Models14.5 Load Equivalent Circuit14.5.1 Modification of Constant Power-type Load Characteristics14.5.2 An Approach to Avoid Iterative Solution of Algebraic Equations14.6 A Summary of the Implementation Procedure14.7 Demonstration of System Frequency with Two-machine Power System14.7.1 Three-phase Fault without Frequency-dependent Loads14.7.2 Three-phase Fault with Frequency-dependent Loads14.7.3 Line Trip without Frequency-dependent Loads14.7.4 Line Trip with Frequency-dependent Loads14.7.5 Line Trip, Speed-governor on M-1 Enabled without Frequency-dependent Loads14.7.6 Line Trip, Speed-governor on M-1 Enabled with Frequency-dependent Loads14.7.7 Line Trip, Speed-governors on M-1 and M-2 Enabled with Frequency-dependent Loads14.8 Large Disturbance Performance14.8.1 Two-machine Power System14.8.2 Four-machine, 10-bus Power Systems14.8.3 50-machine, 145-bus the IEEE Power SystemsReferencesReview Questions
15.1 Induction Motor Model15.1.1 Fifth Order Induction Motor Model15.1.2 Per-unit Representation of the Induction Motor Model15.1.3 Reduced Order Model for the Induction Machine15.2 Modelling of dc Motor-driven Synchronous Generator15.2.1 DC Motor Modelling15.2.2 DC Motor Driving a Synchronous Generator15.2.3 Synchronisation of Two DC Motor-driven Synchronous Generators15.2.4 Synchronisation of a DC Motor-driven Generator to Mains SupplyReferencesReview Questions

Overview

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.