Search

This is not a physical or mathematical explanation or definition of voltage stability. Rather, it shows for a very simple case (to which, however, practically all cases of voltage stability or instability can be reduced) the very simple equations that apply. These very simple relations allow one to check the observations, measurements, or calculations for an actual system in order to put them in perspective and to evaluate their reasonableness.

THE use of the concept of time constants in the analysis of a-c rotating electric machine transients is well known.1 It is also well known that the short-circuit time constants of machines running at normal speed are not at all like those of the same machines at rest. The purposes of this paper are to show the continuous nature of the variation of the machine characteristics in the range of speed from zero to rated speed, and to determine the limits of applicability of the full-speed and standstill values and the behavior at low speed.

IN CASE of unbalanced faults on power systems, the voltage on the unfaulted phase or phases may often reach very high values. There may be an overvoltage caused by the short circuit itself and a further overvoltage caused by the clearing of the fault. In the present paper only the first type will be discussed. These unfaulted phase overvoltages may vary widely with the type of fault, the system constants and arrangement, and the kinds of synchronous machines affected. However, in faults not involving ground the presence of overvoltages depends on the fact that the synchronous machines supplying the fault current are not electrically symmetric-rotor machines. Thus, these overvoltages may be largely eliminated or reduced by a properly designed amortisseur winding. Even in case of overvoltages caused by faults involving ground there is a considerable reduction with such an amortisseur winding.

The application of series capacitors to compensate long-distance high-voltage transmission lines introduces potential modes of dynamic instability caused by interactions with synchronous machines and turbine-generator shaft torsional resonance. This paper describes the modes of ihstability and analytical methods used to predict the combinations of parameters which may lead to instability. Insight into the phenomena of modal interaction, a factor causing one of the unstable modes, is provided.

This paper shows the effect on the frequency stability and response of an electric power system of the use of steam-turbine reheat. It is shown that in general reheat tends to decrease the damping of the frequency variations of the system as a whole, to increase the damping of tie-line power oscillations, and to increase the maximum frequency deviation occasioned by an abrupt load change. The system responses were determined by means of an analog computer.

THE transmission of electric power over long distances has been the subject of considerable study,1 and it has been concluded that an effective way of increasing the permissible straightaway transmission distance is by means of series-capacitor compensation of part of the transmission-line inductive reactance. The introduction of longer lines together with capacitor compensation brings up several technical problems which must be considered if proper operation is to be assured. Studies of transient stability and switching times following faults and of abnormal overvoltages which may result from interaction of line capacitance and transformer exciting impedance at no load are presented in references 2 and 3 respectively. This paper presents the results of a study of hunting and self-excitation during normal operation as affected by line and machine characteristics.

THE object of this paper is to present the results of an analytical study of tie-line power control. This study was made as a logical development of the general subject of power system control. Previous work1,2 has indicated the general requirements of the prime-mover speed governors and the desirability of supplementary control to insure proper load division, frequency, and time. The general requirements of supplementary controls are given in the companion paper3 by Crary and McClure. In most cases these controls are satisfactorily obtained as rather slow corrective adjustments to the speed-governor mechanisms, but for certain types of load a more active tie-line load controller, which will tend to suppress transient load swings also, may be required. An example of this is a rapidly varying load, such as a strip mill supplied from local generation as well as from a tie to a larger power system, in which it may be desirable to keep the load variations off the tie line as much as possible.

Prime-mover response characteristics are influenced by the dynamics of turbines, boilers, and hydraulic systems, as well as by such control devices as speed governors and boiler-turbine controls. Some of the common types of prime-mover systems considered are the conventional single and double reheat systems, once-through units, and hydraulic turbine units. The pertinent phenomena are discussed, as are the implications of prime-mover response in the light of normal and emergency load-change duty.

During normal operation the prime-mover speed governors function principally as stabilizers, automatic power-frequency control taking over the job of maintaining tie-line power schedules, frequency, and time. The prime importance of dead band is reemphasized. During disturbances governors affect both frequency drop and relatively long-term power swings, but generation schedules are of equal importance in certain cases.

IT IS well known that when any portion of an electrical circuit is either opened or closed a transient condition will usually exist for some period, depending on the damping, before the circuit assumes its new steady state. In power circuits, such switching operations are the application and removal of faults or loads and the connecting or separating of various parts of a system. The transient conditions resulting from these switching operations give rise in some cases to overvoltages, which can be calculated by straightforward and more or less well-known methods, if the transient circuit parameters are known. However, in some instances voltages much higher than those predicted by such calculations have been obtained, and various explanations1–9 have been offered for these occurrences.

In a previous paper [ibid., vol. 72, pt. III, June 1953, pp. 562-71], the authors presented the results of a study of the performance of two interconnected steam-electric power-generating areas as affected by frequency and tie-line power controllers. The present paper extends this study to include hydroelectric power generating areas as well. As before, the object is to determine theoretically the best values of controller gains, that is, to find those controller settings that will result in best over-all system performance. The principal criterion of good performance is, also as before, the minimizing of any oscillations in tie-line power or system frequency resulting from load disturbances to either area. Thus, stability, rather than rapidity of response, is preferred, since the system actually is continually being disturbed by small and more or less random changes of load, rather than by the step load change used as a test disturbance in the study.

STEADY-STATE stability of synchronous machines is an old subject, and the fact that voltage regulators may on occasion increase the stability limit is more or less well known.1 The present paper, however, aims to contribute to the knowledge of the subject by

THIS paper∗ reviews and analyzes the steady-state stability characteristics of turbine generators taking the effects of saturation into account. The need for such an analysis has become particularly important with the recent trend toward 3,600-rpm units of large capacity. With the development of such units, the designer is forced in the direction of reducing the weight of the rotor per kilovolt-ampere in order to keep the length and diameter within reasonable limits. However, the reduction in weight of the rotor tends to reduce the short-circuit ratio, which has long been used as a measure of the stability characteristics. The determination of the stability characteristics which may reasonably be expected from a machine, and the validity of short-circuit ratio as a criterion for steady-state stability were considered important enough to justify an analysis. Although the paper deals primarily with the cylindrical-rotor type of generator, the results also apply in general to the salient-pole type.

AS PROGRESS in the design and in the calculation of performance of synchronous machines has been made it has become necessary to specify their characteristics with continually greater accuracy. The predetermination of short-circuit currents, voltage dip on sudden application of load, stability characteristics during system disturbances, excitation requirements, and many other characteristics has been made possible by the development of an adequate theory, confirmed and refined by operating and test experience. The machine characteristics commonly used to predict performance usually are specified in terms of various reactances and time constants. As the number of these quantities and the accuracy to which they must be known has increased, certain inconsistencies among methods of definition, calculation, and test have become apparent. These should ideally all result in the same value. If they differ, one naturally would be inclined to consider the test value as the true reactance. In any case in which a reactance of a particular machine is specified, a method of testing for that reactance also must be specified, and any other definition of the reactance has little practical significance. In this sense the criterion of a good method of calculating the reactance is that it predict as nearly as possible the value which will be found by the specified test method. It, of course, can be asked legitimately whether the specified reactance is the proper one in view of the use to which it is to be put, and the definition is intended to describe the reactance so as to answer this question.

This paper presents (1) a more nearly complete and exact criterion of instability or hunting of a synchronous machine as influenced by its armature or tie line resistance, (2) a general stability criterion which includes in one formula three previously separately treated cases: the usual steady state power limit, rotor hunting produced by armature resistance, and self-excitation produced by series capacitance in the armature circuit, and (3) an indication, by means of a numerical example, of the limitations of the previously used approximate criterion for hunting due to armature resistance. In previous treatments, hunting, self-excitation, and loss of synchronism have been considered only separately, neglecting their mutual interactions. The present paper, on the other hand, considers their mutual effects and thus provides a general analysis by reference to which the limitations and proper fields of application of the approximate formulas may be found. Application of the complete criterion given is however rather laborious, and it is not suggested for general use in place of the approximate forms.

One of the most important problems in the theory of rotating electric machinery is that of accounting for saturation effects. This paper adapts the results of the analysis of eddy current effects in semi-infinite solid saturated iron to develop the high-frequency operational and equivalent circuit impedances of a solid rotor machine. Parts I, II, and III of this series have presented a development of the basic theory, an investigation of the effects of curvature and a consideration of end effects, respectively. 1-3 Another paper has investigated the effects of field leakage. 4 This paper utilizes the electromagnetic model of Part I, neglecting the minor effects of curvature and finite length, except that the rotor iron is assumed to have a rectangular saturation curve.1 With the aid of this model, operational-and equivalent-circuit impedance equations are developed for conditions with relatively high-frequency eddy currents wherein the air gap fields are essentially one dimensional. Per-unit numerical data are given which illustrate the theoretical effect of saturation in increasing the resistive rotor impedance components over those obtained from a linear analysis.

IT has for many years been recognized that voltage surges of considerable magnitude could be produced under certain system conditions by switching operations or by arcing faults. Such voltage surges have been studied in some detail in the past, and various theories have been developed to explain their occurrence and to predict their magnitude. The theories were in most cases sound, but the prediction of surge magnitude was on a rather insecure basis.

SELSYN systems are used very widely as power drives and as indicators when it is necessary to have the position of an element correspond synchronously with that of a controlling element which is remotely located. The receiver Selsyn is used either directly as the output driving motor or as an input to a following power-amplifying stage of a control system.∗ In the study of such Selsyn systems and of the control systems of which Selsyn systems form one of the links, it becomes necessary to determine the hunting-torque characteristics of these machines (that is, the damping and synchronizing torques for small oscillations) as affected by speed, load, oscillation frequency, and, of course, the various design factors. The direct calculation of these hunting-torque characteristics is difficult, but within the past few years methods have been developed whereby the machine performance may be represented by equivalent static electric circuits. The purposes of this paper are: 1. To show how these hunting-torque characteristics can be simply determined by measurements on equivalent electric circuits set up on an a-c network analyzer. 2. To present some of the results of studies made of specific Selsyn systems.

THE renewed attention now being given to transmission of power from hydroelectric sites located at moderate and long distances from their load areas requires a re-evaluation of some of the factors affecting power system stability. This paper shows that the electrical loadings of long distance transmission systems may be increased a significant amount by the use of automatically controlled excitation and proper co-ordination of the apparatus characteristics.

THE factors involving current-transformer performance that affect the operation of protective equipment have recently received considerable attention.1–3 The fact that the transient performance may be greatly different from the steady-state performance has been recognized, but little quantitative data on transient performance have been published. Data from oscillograph records of tests and from approximate analytical methods have definitely indicated the magnitudes of the expected steady-state errors and at the same time conveyed the thought that the transient errors would be very much larger. This paper presents some of the results of a study of current-transformer transient performance that has been made on the differential analyzer with the effects of transformer saturation more accurately considered.

Self-excitation can result from using series capacitors in EHV transmission circuits if the series compensation is large and the circuit resistance small. Such a condition can be realized in a highly compensated transmission line using bundle conductors. An analytical approach to solve for the borderline conditions between stability and instability is presented. The analysis presented is suitable for the simultaneous consideration of both electromechanical (hunting) and primarily electrical (self-excitation) oscillations using lumped circuit constants, or for cases of distributed circuit parameters (long lines and/or solid-rotor generators). Numerical examples are included.

The range of application of current transformers in bus differential protective systems is limited by saturation in the transformer cores under fault conditions, which may sometimes result in improper relay operations. It is shown that the addition of impedance in the relay circuit will reduce the relay current under fault conditions so as to increase the range of applications for which standard current transformers may be used.

The phenomena of stability of synchronous machines under small perturbations is explored by examining the case of a single machine connected to an infinite bus through external reactance.

To assure reliability of electric power, it is essential to have effective transmission and adequate interconnections, adherence to operating limitations, and recognition that, in spite of all that can be done, there is always the chance that an unforeseen contingency will cause system separation and possibly generator deficiency. The first consideration requires system studies to demonstrate that no single disturbance will cause cascading tripouts of lines or generators; the second may be facilitated by automatic monitoring of the system condition; the third requires automatic load shedding on low frequency.

In the normal steady-state operation of a power system, proper load division, frequency, and time are maintained by manual or automatic system control, while the transient swings occasioned by load changes are absorbed by the inertias and speed governors of the individual generating units. With improvements in reliability and performance of systems and their interconnections, it is a natural development that further careful attention and study be given to the basic speed governors and their effects on system operation.1,5,6 It is desirable to determine the requirements which a good governing mechanism should fulfill, and the effects of specific governor and system characteristics on over-all system performance. Moreover, under certain conditions some governors may accentuate rather than reduce the magnitudes of the frequency swings, and it is desirable to know the conditions for which this may occur.

The first two parts of this series have developed the analysis of solid rotor machines for both flat and cylindrical models of infinite length. 1,2 The objective of this part is to present a representation of a finite length, flat model so that a correction for end effects may be incorporated in the operational impedance expressions. The correction presented gives a first-order approximation for this effect. The field analysis considering finite length is also of value in calculating air gap and rotor body spatial distributions of field quantities.

SYNCHRONOUS machines, operating with a-c excitation on both stator and rotor are used in many applications, for example, as induction frequency converters, as power and instrument Selsyn drives, and as variable speed power drives. Reference 1 has mentioned particularly the variable speed fan drive, and presented equations for the small oscillations of one such doubly fed machine. Reference 2 has also previously given the equations of hunting of the doubly fed machine (part XIV, section IV) in connection with the general study of oscillations of rotating machines. However, since the present authors have been using in their own work equations which seem to them to be more convenient and simpler in form for calculations, and since it now seems desirable to present not only general equations but also some of the more fundamental and significant performance characteristics of these machines, it is thought that this paper may now be appropriate. The form of the equations developed possesses the additional novelty of facilitating the setting up of equivalent circuits for hunting on the a-c network analyzer, and allowing the quick determination of the damping and synchronizing torques directly by wattmeter readings.

This paper presents the results of calculations made to determine the magnitude of the error in measurements of changes in bus voltages resulting from the assumption of a symmetric-rotor synchronous machine as usually made in transient stability studies on the a-c network analyzer. It is found that in some cases the effect of transient rotor saliency is important. (See the Appendix for explanation of terms.) In such cases the curves of this paper may be used to help estimate the magnitude of the error involved.

I am highly honored to accept this medal in memory of so eminent an engineer as Mr. Lamme. May I also say that I was not only surprised but also, to a degree, shocked when I was first informed of this honor. I had always thought of medals as being given either to bright young men, to encourage them to further efforts, or to distinguished old men, in order to provide an occasion to learn their philosophy of life and work. However, the middle-aged man, in which group I had up to now classified myself, actively engaged in the practice of his profession, is normally under such competitive, family, and financial pressure that he does not need any additional encouragement, while at the same time he has been so busy that he has not yet developed a philosophy worth listening to. So it is truly a special pleasure to be included among the group of distinguished recipients of the Lamme Medal, whose contributions to the development of electrical equipment have been so great. I am especially pleased to recall that I have had the privilege of being personally acquainted with 15 out of the 34 recipients. I recall also that A. B. Field, the first Lamme Medalist, wrote a very stimulating article on liquid cooling of rotating machinery — which today still has a very modern theme — that influenced my own studies of liquid cooling made during the early 1930's under the direction of H. M. Hobart.

In this paper a rigorous mathematical analysis of a synchronous machine with solid cylindrical rotor is presented. The analysis embodies a departure from the usual method of considering machine performance by means of circuit theory, and presents an attack from the point of view of field-distribution theory. Such an analysis is desirable, for it provides a definite means of considering the effect of eddy currents in the solid iron rotor.

A STUDY WAS MADE recently to determine the magnitude of the angular swing produced in a synchronous condenser by sudden application of an arc-furnace load, and the effect of this swing on the magnitude of the voltage dip.

THE ANALYSIS of solid-rotor synchronous machines presented previously1 is extended in three ways: (1) by expressing the results of the analysis in a more convenient form; (2) by presenting additional numerical results; and (3) by outlining a new analytical attack.

THIS ARTICLE extends a previous study1 to include hydroelectric power generating areas. As before, the object is to determine theoretically the best values of controller gains; that is, to find those controller settings that will result in best over-all system performance.

RECENTLY there has been considerable discussion of the benefits with respect to electric power system stability to be obtained by the use of a properly designed angle regulator. An angle regulator applied to a synchronous machine is defined here as a regulator that varies the machine excitation voltage in response to changes in the angle between the rotor interpole axis and the effective system voltage so as to tend to restore the initially set angle. The purpose of this article is to present the results of an analytical exploration of the possibilities of the angle regulator as regards stability. In particular, since voltage regulators already are used extensively, and since their use as aids in power-system stability already has been studied, it has seemed appropriate to compare the action of an angle regulator with that of a voltage regulator.