Equivalent circuits have been found valuable in the solution of certain problems in that they simplify the analysis. Furthermore, equivalent circuits provide a means of replacing magnetic coupling with simple impedance links thereby permitting the use of the calculating board for solution. In Part I of this paper, the general equivalent mesh for the n-winding transformer is derived, and other less rigorous transformer circuits are discussed and compared. In Part II the mesh equivalent for the general network having (m + l) points of entry is derived and its application is explained. The generalizations of Parts I and II provide a background for the particular problem treated in Part III in which the study of system networks involving groups of parallel transmission lines is considered. The usually difficult problem of accurately determining ground fault currents in such a system is readily solved by applying the special equivalent circuits developed in Part III to a calculating board set-up of the system. These circuits are particularly valuable in the solution of any problem involving an analysis of the zero phase impedance diagram of a system. The methods and circuits developed in this paper are perfectly general and have many evident applications other than those treated.

Equivalent Circuits-I

We suggest that Whites’ declining share of the U.S. population threatens their status as the most prototypical ethnic group in America. This prototypicality threat should lead to growing resistance toward diversity, motivated by the desire to reassert Whites’ standing as prototypical Americans. In Study 1, how dramatically Whites perceived their share of the population to decline predicted support for cultural assimilation, mediated by prototypicality threat (controlling for realistic and symbolic threat). This relationship held only among Whites who felt that ethnic groups differ in their prototypicality, not among those who saw all groups representing America equally. Study 2 experimentally manipulated exposure to demographic projections such that Whites who saw their group shrinking showed weaker diversity endorsement relative to those who believed their share to be stable, again mediated by prototypicality threat. These findings reveal Whites’ threatened prototypicality as a novel, emerging source of ...

No Longer “All-American”? Whites’ Defensive Reactions to Their Numerical Decline

Tracing a route through the recent ‘ugly history’ of British citizenship, this article advances two central claims. Firstly, British citizenship has been designed to fail specific groups and populations. Failure, it argues, is a design principle of British citizenship, in the most active and violent sense of the verb to design: to mark out, to indicate, to designate. Secondly, British citizenship is a biopolitics – a field of techniques and practices (legal, social, moral) through which populations are controlled and fashioned. This article begins with the 1981 Nationality Act and the violent conflicts between the police and black communities in Brixton that accompanied the passage of the Act through the British parliament. Employing Michel Foucault's concept of state racism, it argues that the 1981 Nationality Act marked a pivotal moment in the design of British citizenship and has operated as the template for a glut of subsequent nationality legislation that has shaped who can achieve citizenship. The c...

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Designed to fail: A biopolitics of British citizenship

The objective of this two-part paper is to provide clarity to physical concepts used in the field of transformer modeling, to dispel common misconceptions regarding numerical instabilities, and to present unified modeling techniques for low-frequency transients. This paper focuses on proper modeling of nonlinearities (magnetizing branches) since these components are critical to determine the low-frequency behavior. A good low-frequency model should properly represent: normal operation, inrush currents, open and short circuit, out-of-phase synchronization transient of step-up transformers, geomagnetic-induced currents, ferroresonance, and harmonics. This paper discusses the derivation of electrical dual models from the equivalent (magnetic) reluctance networks and the direct application of the principle of duality. It is shown that different dual models need to be derived for different transformer geometries and the advantages and disadvantages of each method are discussed. This paper also compares double-sided versus single-sided dual models, and shows that the double-sided model is a more general approach. The mathematical equivalency of several leakage models (negative inductance, mutual coupling, and BCTRAN) is demonstrated for three-winding transformers. It is also shown that contrary to common belief, a negative inductance is not the source of numerical oscillations, but they occur due to the use of noncorrect topological models for representing the core.

Duality Derived Transformer Models for Low-Frequency Electromagnetic Transients—Part I: Topological Models

A modular transformer arrangement providing power to a multi-level power converter includes a plurality of three phase transformers having delta or extended delta connected primary windings and delta or extended delta or wye or zig zag wye connected secondary windings and the multi-level power converter has full bridge power modules inputs connected to isolated secondaries of the transformer modules and outputs connected in series and/or in parallel to provide increased voltage and/or current or multiple phases which can be phase shifted with respect to the input to the transformer.

Modular transformer arrangement for use with multi-level power converter

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 Three-Circuit Transformers

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 dis-tortion 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 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, (1) APPLICATION AS A FREQUENCY MULTIPLIER The second and third harmonics of magnetization have been utilized in radio to multiply the supply frequency. Using a suf-ficient number of stages, theoretically any desired radio frequency may be obtained from commercial frequencies. However, the efficiency and regulation of the scheme are very poor, and this application has therefore become almost obsolete by the advent of the vacuum tube oscillator and the high-frequency alternator. When used at all, the number of stages would be kept to a minimum. (2) APPLICATION AS A SERIES CURRENT-LIMITING REACTOR The ordinary iron-core reactor is saturated at increasing values of load, and thus having a much lower reactance at short circuit than at normal load, is undesirable as a current-limiting reactor.

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

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.

Resolution of Transformer Reactance Into Primary and Secondary Reactances

Experience has established the fact that the neutral of a three-phase system may become subject to certain strange phenomena of instability under apparently normal conditions. The disturbances are of two distinct classes: (1) persistent shift or inversion of the neutral, resulting in unequal leg voltages; and, (2) persistent oscillation of the neutral (with equal effective voltage in all three legs) at approximately one-half, double, or triple frequency. While in the ultimate analysis saturation is at the basis of the phenomena, a more definite explanation is given as follows: 1. Neutral shift or inversion is a fundamental frequency phenomenon, and is due to the fact that the volt-ampere curve of the combination of an iron core reactor (transformer magnetizing current) in shunt with a suitable capacitor has one zone which is lagging and one which is leading. In a Y-Y bank of transformers, with suitable balanced line capacitances to neutral following a switching disturbance, one leg may act leading, the others lagging, and thus invert the neutral. 2. Oscillations of the neutral'tend to take place at its natural frequency, but since, due to inevitable losses, not all oscillations can persist, in course of the starting transient the oscillation is resolved to the nearest lower frequency which is able to draw energy from the circuit by approximating harmonic relationship to it. The even harmonics are accounted for by the persistence of residual in the core, whether left from previous excitation or brought about by the direct current component of starting transient.

Physical Nature of Neutral Instability

I LOOK back over half a century to refresh my memory of what being an American has meant to me progressively through all these years. Born in Armenia, I derived my earliest conception of America from story tellers, and it was about as fantastic as Alice's Wonderland. At the age of 21, while teaching arithmetic in a school, the thought occurred to me one winter morning that I should go to this romantic country. Within a few hours I was on the way. What? Such haste? Doesn't one wait to the end of the school year? Of course not; that is, not if one has indulged in a little free speech the night before in a public lecture at which unexpectedly some Turks were present, and this morning one has been notified to go to the government palace and hand the manuscript of his talk to the pasha. To the Armenians, a phantom inscription on the palace door said: “Enter. No exit.” In the Turkish Empire, only the Turks took their time; others hustled.

A. Boyajian

Papers

Theory of Three-Circuit Transformers

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

Resolution of Transformer Reactance Into Primary and Secondary Reactances

Physical Nature of Neutral Instability

I am an American