Direct and alternating current manual; by unknow

Author:unknow
Language: eng
Format: epub
Tags: Electric testing
Publisher: New York, D. Van Nostrand company; [etc., etc.]
Published: 1911-03-25T05:00:00+00:00

A

Magn«titing Compon«nt

^8

—O- -B

Fia 2. Open-circuit diagram for a transformer with core loss, showing the two components of exciting current and the angle a ofhysteretic advance.

Digitized by VjOOQIC

§ 9. With Core Loss. —A transformer with an iron core differs from the ideal transformer just discussed because there is a loss in the iron due to hysteresis and eddy currents. The open-circuit diagram now becomes as shown in Fig. 2. The flux <f> is still in quadrature with £? and £s, in accordance with Faraday's fundamental law of induced electromotive force, e= — S(d<f>-T-dt). The exciting current /o, however, can no longer be a wattless quadrature current, for it must have an in-phase power component to supply the core losses due to hysteresis and eddy currents. This core loss component is

/h = watts core loss-T-£p.

The exciting current /^ is, accordingly, advanced in phase by an angle a, called the hysteretic* angle of advance.

It is seen, therefore, that Iq consists of two components— the core loss component In and the true magnetizing component /m which is wattless and in phase with the flux. The total exciting currentf is the vector sum of these two components:

§ 10. A constant potential transformer (one in which £p is constant) is a constant flux transformer. It therefore follows

* (§9a). As here defined, this angle includes the effect of eddy currents.

t(§9h). The exciting current of a transformer is distorted, t. e., has a wave form different from that of the electromotive force, on account of harmonics introduced by hysteresis. (See Appendix II., Exp. 6-A.) These harmonics—currents of 3, 5, 7, etc., times the fundamental frequency—are necessarily wattless. They do not appear, therefore, in the power component /h, but are included in the wattless component lu. Strictly speaking, alternating currents in which harmonics are present can not be represented by vectors in one plane; for practical purposes, however, the plane vector diagram, as here given, is sufficiently accurate. (See § 47, Exp. 6-A; also " The Effect of Iron in Distorting Alternating Current Wave Form," by Bedell and Tuttle, A. I. E. E., Sept., 1906; and " Vector Representation of Non-Harmonic Alternating Currents," by B. Arakawa, Physical Review, IQOQ-) These harmonics have the same value at all loads; at full load they form such a small part of the total current that the distortion which they produce is very small.

Digitized by VjOOQIC

S-C]

CIRCLE DIAGRAM.

183

/Cir€l« Locut, / Primtfy

that /o, /h and /m are constant, and remain constant under all loads. This would not be quite true in a transformer in which the primary line voltage E^ (and not £p) is constant; the difference in the two cases is very small.

§ II. Transformer Under Load. —The complete diagram for a constant potential transformer under non-inductive load is shown in Fig. 3. This will be seen to be exactly the same as Fig. 2, the open-circuit diagram, with certain additions. As in Fig. 2, we have the electromotive forces £? and £s opposite to each other in phase and in quadrature with the constant flux 4>.

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