The General Theory of Alternating Current Machines: Application to Practical Problems

The book on The General Theory of Electrical Machines, by B. Adkins, which was published in 1957, has been well received, as a manual containing the theories on which practical methods of calculating machine performance can be based, and as a text-book for advanced students. Since 1957, many important developments have taken place in the practical application of electrical machine theory. The most important single factor in the development has been the increasing availability of the digital computer, which was only beginning to be used in the solution of machine and power system problems in 1957. Since most of the recent development, particularly that with which the authors have been concerned, has related to a. c. machines, the present book, which is in other respects an up-to-date version of the earlier book, deals primarily with a. c. machines. The second chapter on the primitive machine does deal to some extent with the d. c. machine, because the cross-field d. c. generator serves as an introduction to the two-axis theory and can be used to provide a simple explanation of some of the mathematical methods. The equations also apply directly to a. c. commutator machines. The use of the word 'general' in the title has been criticized. It was never intended to imply that the treatment was comprehen­ sive in the sense that every possible type of machine and problem The word is used in the sense that the theory can was dealt with.

1 The Basis of the General Theory.- 1.1 The idealized machine.- 1.2 The two-winding transformer. Explanation of sign conventions and the per-unit system for electrical quantities.- 1.3 Magneto-motive force and flux in the rotating machine.- 1.4 Voltage and torque equations of the machine. The per-unit system for mechanical quantities.- 1.5 The fundamental assumptions. Saturation, harmonics, leakage.- 1.6 Calculation and measurement of parameters.- 2 The Primitive Machine.- 2.1 The equations of the cross-field commutator machine.- 2.2 Application to a simple d.c. machine.- 2.3 Equations for small changes and small oscillations.- 2.4 Sudden short-circuit of a d.c. generator.- 3 The Steady-State Phasor Diagrams of A.C. Machines.- 3.1 Representation of sinusoidal m.m.f. and flux waves by space phasors.- 3.2 The induction motor.- 3.3 The uniform air-gap synchronous machine.- 3.4 The salient-pole synchronous machine.- 3.5 Characteristic of a synchronous machine connected to an external supply.- 4 The General Equations of A.C. Machines.- 4.1 Equations in terms of phase variables.- 4.2 Transformation between various reference frames.- 4.3 Direct derivation of two-axis equations.- 4.4 Simplified equations of a synchronous machine with two damper coils.- 4.5 Equivalent circuits, operational impedances and frequency response loci.- 4.6 Summary of the equations for the synchronous machine with two damper coils.- 4.7 Modified equations with more accurate coupling between field and damper windings.- 4.8 General equations of the induction motor.- 5 Types of Problem and Methods of Solution and Computation.- 5.1 Classification of problems and methods of solution.- 5.2 Modified machine equations in terms of rotor angle ?.- 5.3 The state variable method and the state-space concept.- 5.4 Calculation of system response and stability.- 5.5 Optimization. Performance indices.- 5.6 Computational techniques for transient studies.- 6 Automatic Control of Synchronous Machines.- 6.1 General.- 6.2 Excitation control of a.c. generators.- 6.3 Quadrature field winding. The divided-winding-rotor generator.- 6.4 Speed governors.- 7 A.C. Operation of Synchronous Machines.- 7.1 Steady operation of the synchronous machine at synchronous speed.- 7.2 Starting of a synchronous motor.- 7.3 Negative-sequence reactance of a synchronous machine.- 7.4 Small changes relative to a steady state.- 7.5 Approximate methods for forced oscillations.- 7.6 Free oscillations. Steady-state stability.- 8 Synchronous Generator Short-Circuit and System Faults.- 8.1 Symmetrical short-circuit of an unloaded synchronous generator.- 8.2 The analysis of short-circuit oscillograms.- 8.3 Short-circuit of a loaded synchronous generator.- 8.4 Unsymmetrical short-circuit of a synchronous generator.- 8.5 System fault calculations.- 8.6 Sudden load changes.- 9 Synchronous Machine Problems Requiring Step-by-Step Computations.- 9.1 Transient stability.- 9.2 Swing curves of a synchronous generator connected to an infinite bus.- 9.3 Loss of synchronism of a synchronous generator. Effect on rectifier excitation systems.- 9.4 Optimization of control inputs.- 9.5 Techniques for a multi-machine system.- 10 Effects of Saturation and Eddy Currents on Machine Performance.- 10.1 General.- 10.2 Methods of allowing for saturation.- 10.3 Effect of eddy currents in the magnetic material.- 10.4 Effect of eddy currents in the rotor conductors.- 11 Induction Motor Problems.- 11.1 Application of equations in primary reference frame.- 11.2 Equations in secondary reference frame. Complex form of the equations.- 11.3 Short-circuit and fault currents due to induction motors.- 11.4 Transient stability calculations.- 12 Application to Less Common Types of Machine.- 12.1 Classification in relation to the theory.- 12.2 Application of two-axis theory.- 12.3 Application of the phase equations.- 13 Appendices.- 13.1 Representation of a.c. and transient quantities by complex numbers. The generalized phasor.- 13.2 Current and voltage transformations when power is invariant.- 13.3 Operational methods.- 13.4 The per-unit system.- References.