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Matrix Analysis of Electrical Machinery
- 2nd Edition - January 1, 1974
- Author: N. N. Hancock
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 3 7 2 9 - 2
Matrix Analysis of Electrical Machinery, Second Edition is a 14-chapter edition that covers the systematic analysis of electrical machinery performance. This edition discusses the… Read more
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Request a sales quoteMatrix Analysis of Electrical Machinery, Second Edition is a 14-chapter edition that covers the systematic analysis of electrical machinery performance. This edition discusses the principles of various mathematical operations and their application to electrical machinery performance calculations. The introductory chapters deal with the matrix representation of algebraic equations and their application to static electrical networks. The following chapters describe the fundamentals of different transformers and rotating machines and present torque analysis in terms of the currents based on the principle of the conservation of energy. A chapter focuses on a number of linear transformations commonly used in machine analysis. This edition also describes the performance of other electrical machineries, such as direct current, single-phase and polyphase commutator, and alternating current machines. The concluding chapters cover the analysis of small oscillations and other machine problems. This edition is intended for readers who have some knowledge of or are concurrently studying the physical nature of electrical machines.
Preface to the Second Edition
Preface to the First Edition
1 Introduction
Conventions
Units
Parameters
2 Elements of Matrix Algebra
Matrix Representation of Simultaneous Equations
Multiplication of Matrices
Application of Matrices to the Solution of Simultaneous Linear Equations—Inversion
Singular Matrices
The Transpose and Inverse of a Product
Alternative Methods of Inversion
Compound Matrices
Linear Transformation
Reduction to Diagonal Form
The Advantages of Matrices
Types of Matrix
Differentiation and Integration of a Matrix
3 Application of Matrix Algebra to Static Electrical Networks
Laplace Transform Equations
Notation
Linear Transformation in Electrical Circuit Analysis
Choice of Transformations—Invariance of Power
Transformation of Voltage and Impedance for Invariant Power with a Given Current Transformation
4 Transformers
The Two-Winding Transformer
Parameters
The Three-Winding Transformer
Parameters
More Complicated Magnetic Circuits
5 The matrix Equations of the Basic Rotating Machines
The Matrix Equation of the Basic Commutator Machine
Matrix Equations of Slip-Ring and Squirrel-Cage Machines
The Matrix Equation of the Balanced Two-phase Machine with a Uniform Air-Gap (Induction Machine)
The Matrix Equation of the Balanced Two-phase Revolving-Arniature Salient-Pole Machine (Synchronous Machine)
The Form of the Transformed Impedance Matrix
Limitations of the Method
6 The Torque Expressions
The Energy Stored in the Magnetic Fields
Torque Expressions
Derivation of the Torque Expression from the Equation v = Ri+p(Li)
The Transformation of ∂L/∂θ
Derivation of the Torque Expression from the Equation v = Ri+Lpi+Gθi
The Mean Steady-State Torque in A.C. Machines
Direction of Torque
7 Linear Transformations in Circuits and Machines
Resolution of Rotor M.M.F.
Transformation between Two Sets of Stationary Axes (Brush-Shifting Transformation)
The Equivalence of Three-phase and Two-phase Systems
The Transformation from Three-phase to Two-phase Axes (a, b, c to α, β, o)
The Transformation from Three-phase Axes to Symmetrical Component Axes (a, b, o to p, n, o)
The Transformation from Two-phase Axes to Symmetrical Component Axes (α, β, o to p, n, o)
Steady-State and Instantaneous Symmetrical Components
Transformation from Two-phase Rotating Axes to Stationary Axes (α, β o to d, q, o)
Transformation from Three-phase Rotating Axes to Stationary Axes (a, b, c to d, q, o)
The Transformation from Stationary Axes to Forward and Backward Axes (d, q, o to f, b, o)
The Transformation of Stator Winding Axes
Physical Interpretation of Various Sets of Axes
Rotor
Stator
8 The Application of Matrix Techniques to Routine Performance Calculations
The Establishment of the Transient Impedance Matrix
Phasor Diagrams and Equivalent Circuits
Phasor Diagrams
Equivalent Circuits
Interconnections between Machines or between Machines and other Circuit Elements
Closed Circuits
Specific Types of Problem
(a) Given the Terminal Voltages of all Windings carrying Current, to Find the Currents
(b) Given the Terminal Voltages of all Windings carrying Current, to Find the Terminal Voltages of the Open-Circuited Windings
(c) Given the Terminal Voltages of Some Windings and the Currents in the Others, to Find the Remaining Currents and Voltages
(d) Given the Terminal Voltages to Find the Torque in Terms of the Speed or Phase Angle
(e) Given the Terminal Voltages, to Find the Speed and/or Currents at a Given Torque
The Analysis of Three-phase Machines
The Effects of Zero-Sequence Currents
9 D.C. and Single-phase Commutator Machines
The Series Commutator Machine
The Shunt Commutator Machine
The D.C. Shunt Motor
The D.C. Shunt Generator on Open Circuit
The D.C. Shunt Generator on Resistance Load
Parameters of D.C. Machines
Shunt and Separately Excited D.C. Machines
D.C. Series Machine
The Repulsion Motor
Steady-State Performance in Complex Terms
Steady-State Instantaneous Currents and Torque
10 The Steady-State Performance of Polyphase Machines
The Balanced Polyphase Induction Machine
Currents
Equivalent Circuit
Torque
Balanced Terminal Voltage
Unbalanced Terminal Voltage
Parameters
The Unbalanced Two-phase Induction Machine
Equivalent Circuit
Currents
Torque
Single-phase Operation of Induction Machine
Three-phase Machine
Two-phase Machine
Single-phase Machine
Parameters
The Polyphase Synchronous Machine with a Uniform Air-Gap and no Damper Windings
Phasor Diagram
Field Current Required for Given Armature Terminal Conditions
Torque
Parameters
The Polyphase Synchronous Machine with Salient Poles and no Damper Windings
Open-Circuit Condition
Short-circuit Condition
On Balanced Load as a Generator
Phasor Diagram
Torque
Parameters
11 Transient and Negative-Sequence Conditions in A.C. Machines
Balanced Induction Machine Transients
Sudden Application of Terminal Voltage
The Synchronous Machine with Salient Poles and No Damper Windings
Sudden Three-phase Short Circuit from Open Circuit
Field Current
Armature Currents
Impedance to Negative Sequence
Impedance to Negative Sequence Current
Impedance to Negative Sequence Voltage
The Synchronous Machine with Salient Poles and Damper Windings
Balanced Steady-State Conditions
Transient Conditions
Sudden Three-phase Short Circuit from Open Circuit
Impedance to Negative Sequence
Parameters
12 Small Oscillations
Separately Excited D.C. Machine
Balanced Induction Machine
Synchronous Machine
13 Miscellaneous Machine Problems
The Metadyne Generator with Its Quadrature Brushes Displaced
The Ferraris-Arno Phase Converter
The Polyphase Induction Machine with a Single-phase Secondary Circuit
Torque
Power Selsyns
The Single-phase Performance of the Synchronous Generator with a Uniform Air-Gap and No Damping Circuits
14 Conclusion
Appendices
A. Restriction on Rotor Windings
B. Torque under Saturated Conditions
Torque in Multi-circuit Device
Calculation of Torque
C. Definitions of Systems of Axes
D. Trigonometric Formula
Laplace Transforms
Exercises
Hints and Answers to Exercises
References
Index
- No. of pages: 368
- Language: English
- Edition: 2
- Published: January 1, 1974
- Imprint: Pergamon
- eBook ISBN: 9781483137292
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