R.G. Harley

The general theory of alternating current machines : application to practical problems

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.

D,Q reference frames for the simulation of induction motors

Abstract This paper presents the equations of three preferable reference frames for use in the simulation of induction machines when using the d,q 2-axis theory. It uses case studies to demonstrate that the choice of the reference frame depends on the problem to be solved and the type of computer available (analog or digital).

Estimating Synchronous Machine Electrical Parameters from Frequency Response Tests

A method of obtaining synchronous machine d and q axis impedances by test as a function of frequency of d,q components has recently been proposed by de Mello and Hannett [1]. Their proposal ends by determination of the numerical values for the operational inductances Ld(j2w), Lq(j2w) or impedances Zd(j2w), Zq(j2w) at different values of W, the speed of the machine at which the tests are conducted; however, they do not show how the values of actual parameters such as inductances and time constants are to be obtained from the curves of operational inductance versus frequency.

Adaptive neural speed controller of a dc motor

An adaptive neural speed controller of a dc motor is proposed. The artificial neural network (ANN) is trained by the online backpropagation algorithm. The output of the ANN gives the control voltage applied to the dc motor. The difference between the reference and the actual rotor speed of the motor is backpropagated through the ANN at each step of the control process for updating the connection weights of the ANN. The control scheme requires neither a knowledge of any motor parameters, nor preferential training of the ANN. The performance of the controller is simulated depending on the rotor speed noise of the motor, the rapidity of its dynamics, the sampling period, and the sharp instantaneous change of the load, or in the reference speed trajectory.

Sensitivity of Subsynchronous Resonance Predictions to Turbo-Generator Modal Parameter Values and to Omitting Certain Active Subsynchronous Modes

In a subsynchronous resonance stability stuiy the predicted CRITICAL COMPENSATION LEVEL (CCL) depends on the mathematical model and parameter values, particularly on the mechanical damping or decrement factor. Measurements of the mechanical parameters yield values for modal inertia, modal damping etc. so that the mechanical system equations have to be transformed into modal form in order to use the measured data in simulation studies. This paper investigates the sensitivity of the predicted CCL values (for a particular case study) to uncertainties in the different modal parametes and finds that the modal damping or decrement factor is more critical than modal inertia or mode shape. It carries on to show how the modal model can be reduced from 12th to 4th order and still yield acceptable results; this would lead to considerable simplfication and saving of computer time in multi-machine SSR studies.

Effects of Reactive Compensation on Induction Motor Dynamic Performance

Induction motors are known to cause voltage dip, inrush current, and a low lagging power factor in the distribution network. To compensate for these effects shunt capacitor banks are generally used. Recently, however, an increasing number of utility operation departments are reporting increased occurrence of poor motor performance and excessive voltage dips during starting and running although they properly used shunt capacitor banks. The use of series capacitor banks appears to be helpful in some cases, while erratic and unexplained motor behaviour occurs in other cases.

Stabilizing SSR oscillations with a shunt reactor controller for uncertain levels of series compensation

The authors demonstrate how frequency-domain techniques based on I. Horowitz et al.s (1986) quantitative feedback theory can be applied to the design of fixed-parameter controllers in power systems where the plant parameters have large uncertainties. They present the design of a controller for a shunt reactor to eliminate torsional shaft oscillations in a turbogenerator susceptible to subsynchronous resonance (SSR). The considered parameter uncertainty is the series capacitor compensation level, which has been assumed to vary between 12% and 76%. Simulated transients results of the uncontrolled/controlled system are depicted. >

Optimal output feedback design of a shunt reactor controller for damping torsional oscillations

Abstract Suppression of the torsional oscillations of a turbogenerator by means of a shunt reactor placed at the turbogenerator terminals has been proposed by others and would appear to be the most promising of all the counter-measures suggested so far. This paper investigates the damping of subsynchronous resonance (SSR) oscillations by using such a shunt reactor stabilizer and placing it at the high voltage instead of the low voltage side of the generator step-up transformer. It shows how the shunt reactor controller (SRC) is designed by employing optimal output feedback techniques. A digitally computed step-by-step solution of the 31 non-linear differential equations yields the transient response of the non-linear system and illustrates the stabilizing effect of the shunt reactor controller, even for an initially unstable plant.

Transient Behavior of Induction Motor Flux and Torque During Run-Up

This paper analyses the various flux components that exist within symmetrical three phase cage induction motors, and how they manifest themselves as torque oscillations during run-up. A small, a medium and a large motor are evaluated to show that recent explanations of this phenomena by way of only the airgap flux may be misleading due to a lack of generally applying to motors of different sizes and parameter combinations.

Optimal and multivariable control of a turbogenerator

Abstract This paper describes an investigation into the use of modern control methods to design multivariable controllers which improve the performance of a turbogenerator. It presents the turbogenerator non-linear mathematical model from which a linearized model is deduced. The inverse Nyquist array method and the theory of optimal control are both applied to the linearized model to generate two alternative control schemes. The schemes are then implemented on the non-linear model for simulation by computer in order to assess their dynamic performance. Results from these modern multivariable control schemes are compared with those of the classical familiar automatic voltage regulator and speed governor systems.