2nd Edition

Analysis of Synchronous Machines

By T.A. Lipo Copyright 2012
    606 Pages 252 B/W Illustrations
    by CRC Press

    606 Pages 252 B/W Illustrations
    by CRC Press

    Analysis of Synchronous Machines, Second Edition is a thoroughly modern treatment of an old subject. Courses generally teach about synchronous machines by introducing the steady-state per phase equivalent circuit without a clear, thorough presentation of the source of this circuit representation, which is a crucial aspect. Taking a different approach, this book provides a deeper understanding of complex electromechanical drives.

    Focusing on the terminal rather than on the internal characteristics of machines, the book begins with the general concept of winding functions, describing the placement of any practical winding in the slots of the machine. This representation enables readers to clearly understand the calculation of all relevant self- and mutual inductances of the machine. It also helps them to more easily conceptualize the machine in a rotating system of coordinates, at which point they can clearly understand the origin of this important representation of the machine.

    • Provides numerical examples
    • Addresses Park’s equations starting from winding functions
    • Describes operation of a synchronous machine as an LCI motor drive
    • Presents synchronous machine transient simulation, as well as voltage regulation

    Applying his experience from more than 30 years of teaching the subject at the University of Wisconsin, author T.A. Lipo presents the solution of the circuit both in classical form using phasor representation and also by introducing an approach that applies MathCAD®, which greatly simplifies and expands the average student’s problem-solving capability. The remainder of the text describes how to deal with various types of transients—such as constant speed transients—as well as unbalanced operation and faults and small signal modeling for transient stability and dynamic stability.

    Finally, the author addresses large signal modeling using MATLAB®/Simulink®, for complete solution of the non-linear equations of the salient pole synchronous machine. A valuable tool for learning, this updated edition offers thoroughly revised content, adding new detail and better-quality figures.

    Winding Distribution in an Ideal Machine

    Introduction

    The Winding Function

    Calculation of the Winding Function

    Multipole Winding Configurations

    Inductances of an Ideal Doubly Cylindrical Machine

    Calculation of Winding Inductances

    Mutual Inductance Calculation—An Example

    Winding Functions for Multiple Circuits

    Analysis of a Shorted Coil—An Example

    General Case for C Circuits

    Winding Function Modifications for Salient-Pole Machines

    Leakage Inductances of Synchronous Machines

    Practical Winding Design


    Reference Frame Theory

    Introduction

    Rotating Reference Frames

    Transformation of Three-Phase Circuit Variables to a Rotating Reference Frame

    Stationary Three-Phase r–L Circuits Observed in a d–q–n Reference Frame

    Matrix Approach to the d–q–n Transformation

    The d–q–n Transformation Applied to a Simple Three-Phase Cylindrical Inductor

    Winding Functions in a d–q–n Reference Frame

    Direct Computation of d–q–n Inductances of a Cylindrical Three-Phase Inductor


    The d–q Equations of a Synchronous Machine

    Introduction

    Physical Description

    Synchronous Machine Equations in the Phase Variable or as-, bs-, cs- Reference Frame

    Transformation of the Stator Voltage Equations to a Rotating Reference Frame

    Transformation of Stator Flux Linkages to a Rotating Reference Frame

    Winding Functions of the Three-Phase Stator Windings in a d–q–n Reference Frame

    Winding Functions of the Rotor Windings

    Calculation of Stator Magnetizing Inductances

    Mutual Inductances between Stator and Rotor Circuits

    d–q Transformation of the Rotor Flux Linkage Equation

    Power Input

    Torque Equation

    Summary of Synchronous Machine Equations Expressed in Physical Units

    Turns Ratio Transformation of the Flux Linkage Equations

    System Equations in Physical Units Using Hybrid Flux Linkages

    Synchronous Machine Equations in Per Unit Form


    Steady-State Behavior of Synchronous Machines

    Introduction

    d–q Axes Orientation

    Steady-State Form of Park’s Equations

    Steady-State Torque Equation

    Steady-State Power Equation

    Steady-State Reactive Power

    Graphical Interpretation of the Steady-State Equations

    Steady-State Vector Diagram

    Vector Interpretation of Power and Torque

    Phasor Form of the Steady-State Equations

    Equivalent Circuits of a Synchronous Machine

    Solutions of the Phasor Equations

    Solution of the Steady-State Synchronous Machine Equations Using MathCAD

    Open-Circuit and Short-Circuit Characteristics

    Saturation Modeling of Synchronous Machines Under Load

    Construction of the Phasor Diagram for a Saturated Round-Rotor Machine

    Calculation of the Phasor Diagram for a Saturated Salient-Pole Synchronous Machine

    Zero Power Factor Characteristic and the Potier Triangle

    Other Reactance Measurements

    Steady-State Operating Characteristics

    Calculation of Pulsating and Average Torque during Starting of Synchronous Motors


    Transient Analysis of Synchronous Machines

    Introduction

    Theorem of Constant Flux Linkages

    Behavior of Stator Flux Linkages on Short-Circuit

    Three-Phase Short-Circuit, No Damper Circuits, Resistances Neglected

    Three-Phase Short-Circuit from Open Circuit, Resistances and Damper Windings Neglected

    Short-Circuit from Loaded Condition, Stator Resistance and Damper Winding Neglected

    Three-Phase Short-Circuit from Open Circuit, Effect of

    Resistances Included, No Dampers

    Extension of the Theory to Machines with Damper Windings

    Short-Circuit of a Loaded Generator, Dampers Included

    Vector Diagrams for Sudden Voltage Changes

    Effect of Exciter Response

    Transient Solutions Utilizing Modal Analysis

    Comparison of Modal Analysis Solution with Conventional Methods

    Unsymmetrical Short-Circuits


    Power System Transient Stability

    Introduction

    Assumptions

    Torque Angle Curves

    Mechanical Acceleration Equation in Per Unit

    Equal Area Criterion for Transient Stability

    Transient Stability Analysis

    Transient Stability of a Two Machine System

    Multi-Machine Transient Stability Analysis

    Types of Faults and Effect on Stability

    Step-by-Step Solution Methods Including Saturation

    Machine Model Including Saturation

    Summary-Step-by-Step Method for Calculating Synchronous Machine Transients


    Excitation Systems and Dynamic Stability

    Introduction

    Generator Response to System Disturbances

    Sources of System Damping

    Excitation System Hardware Implementations

    IEEE Type 1 Excitation System

    Excitation Design Principles

    Effect of the Excitation System on Dynamic Stability


    Naturally Commutated Synchronous Motor Drives

    Introduction

    Load Commutated Inverter (LCI) Synchronous Motor Drives

    Principle of Inverter Operation

    Fundamental Component Representation

    Control Considerations

    Starting Considerations

    Detailed Steady-State Analysis

    Time Step Solution

    Sample Calculations

    Torque Capability Curves

    Constant Speed Performance

    Comparison of State Space and Phasor Diagram Solutions


    Extension of d–q Theory to Unbalanced Operation

    Introduction

    Source Voltage Formulation

    System Equations to Be Solved

    System Formulation with Non-Sinusoidal Stator Voltages

    Solution for Currents

    Solution for Electromagnetic Torque

    Example Solutions


    Linearization of the Synchronous Machine Equations

    Introduction

    Park’s Equations in Physical Units

    Linearization Process

    Transfer Functions of a Synchronous Machine

    Solution of the State Space and Measurement Equations

    Design of a Terminal Voltage Controller

    Design of a Classical Regulator


    Computer Simulation of Synchronous Machines

    Introduction

    Simulation Equations

    MATLAB® Simulation of Park’s Equations

    Steady-State Check of Simulation

    Simulation of the Equations of Transformation

    Simulation Study

    Consideration of Saturation Effects

    Air Gap Saturation

    Field Saturation

    Approximate Models of Synchronous Machines

     

    Appendix 1: Identities Useful in AC Machine Analysis

    Appendix 2: Time Domain Solution of the State Equation

    Appendix 3: Three-Phase Fault

    Appendix 4: TrafunSM

    Appendix 5: SMHB Synchronous Machine Harmonic Balance

    Biography

    Thomas A. Lipo received his BEE and MS degrees at Marquette University and his Ph.D from the University of Wisconsin in 1968. After 10 years at the Corporate R&D Center of the General Electric Company in Schenectady. New York, he joined Purdue University as professor in 1978 and subsequently took the same position at the University of Wisconsin in 1980. He was granted the 2004 Hilldale Award, the university’s most prestigious award for scientific achievement. He has published more than 550 technical papers, secured 35 U.S. patents, and written five books in his discipline. He is a Fellow of IEEE and IET (London), and he is also a member of the National Academy of Engineering (USA) and the Royal Academy of Engineering (UK).