A. Boyajian

Theory of Three-Circuit Transformers

The characteristics of three-circuit transformers, the literature of which is very meager, are discussed here in considerable detail. The features of the scheme of treatment are as follows: 1. The scope and general aspects of the problems of three-circuit transformers are reviewed. 2. Some peculiar phenomena of considerable theoretical interest are cited. 3. An electrical network equivalent to the magnetically interlinked circuits of a three-circuit transformer is developed, useful in visualizing the problem and in predicting by inspection a number of its characteristics. 4. Two physical interpretations of the equivalent network are given to assist the understanding of its principle and its applications. 5. The case of auto transformers interconnecting three circuits is interpreted so that the formulas developed for three-circuit transformers become universally applicable regardless of the presence or absence of metallic interconnection among the three circuits inside the case. 6. Formulas are developed for the calculation of regulation with various loads in the different windings. 7. Formulas are developed for the division of load between two primary circuits, or two secondary circuits in parallel. 8. Formulas are developed for the equivalent effective impedance for short circuits. 9 The behaviour of a three-circuit transformer operating in parallel with a two-circuit transformer is analyzed so as to determine the flow or distribution of load kv-a. in the network. 10.

Theory of D-C. Excited Iron-Core Reactors and Regulators

In the usual electrical machinery the magnetic saturation characteristic of iron is a handicap and in a-c. circuits gives rise to such undesirable characteristics as wave distortion and variable reactance, decreasing with increasing load. Furthermore, these characteristics are inherent in the material and can not be controlled by design to suit individual requirements or changing load conditions. Control of these characteristics can, however, be accomplished if the mean magnetic density in the core be controlled by means of a suitable d-c. excitation, in which event, the saturation characteristics of the iron can be put to some useful applications.

Resolution of Transformer Reactance Into Primary and Secondary Reactances

The stand is taken that the resolution of the leakage reactance of a pair of windings into the individual reactances of the two windings is indeterminate unless referred to a third winding and that therefore it varies with the object in view when making the resolution. If the object is the influence of exciting current on performance, the problem is converted into a three-winding transformer problem by conceiving of the exciting current as produced by a (fictitious) load in a (fictitious) third winding. It is pointed out that the resolution of leakage reactance into individual reactances is possible only in the case of three windings, and that therefore in a transformer with three real windings and a fictitious exciting-current-load winding, constituting the equivalent of a four-winding transformer, the simple resolution fails, each winding having a different individual leakage reactance when associated with one pair of the remaining windings than when associated with another pair. Furthermore, the resolution made from the standpoint of real load currents will be different from that made from the standpoint of exciting current. Formulas are given for such resolutions, and experimental methods are described. The problem is also considered from the standpoint of flux distribution and linkages, and the limitations of some common views are pointed out.

Inversion Currents and Voltages in Auto-Transformers

Line grounds on the secondary of an auto-transformer, fed from a grounded system, tend to invert the neutral of the auto-transformer. If the auto-transformer is isolated, this may lead to larger voltages, and if grounded, to larger currents than what would ordinarily be expected. The analysis of an important installation (75,000-kv-a., three-phase units at Detroit) is given below, for various possible connections and conditions of operation. Features of the analysis are: (A) A novel theory and method of auto-transformer circuit representation was developed to handle some aspects of this problem that otherwise appeared elusive. The method is applicable to all networks involving auto-transformers. (B) The rather startling fact is brought out and explained that fault currents to ground on the secondary lines of an auto-transformer may be larger when stepping-up than when stepping-down. The prediction has been verified by test.

Bushing-Type Current Transformers for Metering

This paper describes a new development in connection with bushing type current-transformer metering circuits. While this development utilizes the two-stage principle and has the same order of accuracy as that of two-stage current transformers, it is different from the conventional two-stage current transformers in that it does not require two-stage wattmeters and watthour meters, but may be used with any wattmeter or watthour meter. The principle and connections of the transformer are explained, and performance curves of a typical unit are given.

Oscillations of a High-Voltage Secondary Winding

THE PHYSICAL THEORY of the characteristic oscillations of a high-voltage winding as a primary, that is, when the voltage disturbances are impressed directly across its terminals, is now well known.

Symmetrical-Components Analysis of the Four-Phase System

A. N. Garin (General Electric Company, Pittsfield, Mass.): This paper is, in my opinion, a welcome and perhaps even an overdue addition to the still rapidly growing literature of the method of symmetrical components. Although the fundamental principles and even the formulas for expressing the current and voltage vectors of a four-phase system in terms of their symmetrical components, and vice versa, have been published quite some time ago, as indicated by the references given in the paper, this, so far as I know, is the first presentation of the formulas for the fault currents.

A New Two-Phase to Six-Phase Transformer Connection of One Hundred Per cent Apparatus Economy

A new transformer connection of 100 per cent apparatus economy is described for transformation from two-phase to six-phase and vice versa. Its merits from various standpoints are compared with those of the Scott and the Woodbridge connections.

Cultural Training of the Engineer

It is generally recognized that a professional man must have a certain amount of cultural training, in addition to the technical, so as to be better balanced, more useful to the society, and more successful; and engineering curricula generally make provision for it. However, it appears questionable whether the cultural program is as well suited to its objectives as the technical programs are to theirs. As a parent, the author had occasion to look into this matter during the past several years and was led to the conclusion that the quality of the conception and execution of the cultural training of the engineer is definitely inferior to that of his technical training.

Abridgment of inversion currents and voltages in auto-transformers

Line grounds on the secondary of an auto-transformer, fed from a grounded system, tend to invert the neutral of the auto-transformer. If the auto-transformer is isolated, this may lead to larger voltages, and if grounded, to larger currents than what would ordinarily be expected. The analysis of an important installation (75,000-kv-a., three-phase units at Detroit) is given below, for various possible connections and conditions of operation. Features of the analysis are: (A) A novel theory and method of auto-transformer circuit representation was developed to handle some aspects of this problem that otherwise appeared elusive.2 The method is applicable to all networks involving auto-transformers. (B) The rather startling fact is brought out and explained that fault currents to ground on the secondary lines of an auto-transformer may be larger when stepping-up than when stepping-down. The prediction has been verified by test.