Operation of a synchronous generator at leading power factor has been severely limited in the past because of stability considerations. A regulator, acting on a normal direct-axis field winding, can only extend the range of stability when the generator is loaded, and has no effect under unloaded conditions. An additional winding on the quadrature axis, provided with a suitable control, can, however, ensure stable operation at any leading-power-factor load, within the heating limit of the generator. The most effective control uses a closed loop actuated by a signal derived from the load angle. The theoretical treatment in the paper consists of two parts. First, some general results are deduced from simplified equations, particularly relating to the limitations of a direct-axis regulator and the benefit of using an angle signal with the quadrature regulator. More complete computations are then made to obtain stability-limit curves for many alternative schemes. The work is concerned with the steady-state stability of a l-machine system, in which a generator is connected to an infinite bus through a reactance. Experiments to confirm the theoretical results were carried out on the micromachine equipment at Imperial College. The alternatives studied included simple proportionate regulators and more elaborate schemes using first- and second derivative elements, and the angle signal was taken alternatively from the infinite bus and the generator terminals. Good agreement was obtained with the corresponding computations.

Improvement of alternator stability by controlled quadrature excitation

This paper deals with the dynamic stability of long distance a.c. transmission systems operating at above 1 surge impedance loading and compensated entirely by automatically controlled shunt inductance device referred to as Static Compensators. Generalised system equations in the form X = AX, with a careful choice of state variables are developed via the subsystem concept and the eigenvalue technique used to establish the stability limits. The static compensator and the excitation system control parameters are chosen in a coordinated manner from the stability limit plots, the extension of stability limits with a Static Compensator are quantised, later a second compensator is included for improving the system performance and interaction studies.

Dynamic Stability of Long Transmission Systems with Static Compensators and Synchronous Machines

A powerful but simple matrix method for the digital computer manipulation of large sets of differential and algebraic equations is introduced to the field of power systems. The method is first illustrated with reference to the linearized equations representing a general-purpose turboalternator model. Subsequently, the form of the system equations obtained as a result of the matrix method is seen to provide a unified approach to the determination of system stability limits using Routh, Nyquist, or eigenvalue methods. The normal state space form of the system equations is also shown to facilitate control studies. A previously suggested performance criterion for an excitation system is generalized, and a systematic method for the simultaneous optimization of governor and exciter control loops is suggested. This method of optimization does not require the evaluation of system transient responses. The manner in which the normal state space form of the system equations leads naturally to the synthesis of controllers which are optimal with respect to a chosen scalar quadratic performance index is indicated. With this form of control, the structure is not defined a priori but emerges from the computational algorithm and it becomes unnecessary to specify the source or the magnitude of the stabilizing signals required to provide an improved dynamic performance. Finally, the matrix method is shown to be effective for the manipulation of the nonlinear machine equations and these are obtained in a new form which is directly amenable to digital or analog computer solution.

Matrix methods for the study of a regulated synchronous machine

Methods which have been proposed for increasing the margin of stability in large generators generally act by controlling the generator electrical power output. A more direct control of the stability can be achieved by regulating the power input to the turbine. Simultaneous control of the field excitation and the turbine

Optimisation of Turbo-Generator Transient Performance by Differential Dynamic Programming

The paper describes analogue- and digital-computer studies of a synchronous machine with various 2-axis-excitation control systems. The steady-state and transient performances of the same machine are analysed, assuming different control schemes, such as rotor-angle control and asynchronised operation, and are compared with a conventional machine. The effects of damper windings, regulator time constants and stabilising circuits on the steady-state performance are shown by regulation curves. It is confirmed that the voltage-regulator loop gain has virtually no effect on steady-state stability, provided the winding with a.v.r. control is aligned with the flux axis by an angle regulator. The improved transient-stability limits obtained with high gains are shown. The fundamentally different transient behaviour of unregulated doubly excited and conventional synchronous machines is explained, and confirmed using accurate mathematical models of the machines. The method of `small oscillations? is applied to determine the speed stability of an asynchronised synchronous machine, and the transient performances of three different control schemes are compared in terms of swing curves and switching-time curves.

Stability of synchronous machines with 2-axis excitation systems

The paper records a detailed study of the effect of a voltage regulator on the stability of an alternator connected through a reactance to an infinite bus. The stability is analysed by means of Nyquist loci calculated for the transfer functions of alternator and regulator. The accuracy and speed of response of the system are also considered. The first part of the paper considers a simple regulator with proportional feedback, and it is shown that such an ideal regulator can extend the region of steady-state stability to a point corresponding to the maximum of the transient power-angle curve. Practical regulators are classified according to the nature of their transfer functions. The analysis provides a means of predicting their behaviour and explains how they affect the stability, accuracy and response. The effect of delay elements, integrator elements and derivative elements in the regulator is considered particularly; e.g. a buck-boost exciter, which effectively introduces an integrator element, gives good accuracy but less satisfactory response, and has a limited effect on stability, and a derivative regulator which gives rapid response and a large extension of the stability region, but has limited accuracy. Experiments performed on a model machine with various simulated regulators agreed well with the computed results. The computations allowed fully for the system parameters, including alternator resistance and alternator damping.

B. Adkins

Papers

Effect of excitation regulation on synchronous-machine stability