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).