Birmingham Local Section

264 MORRIS AND LISTER: THE TESTING OF [Birmingham, BIRMINGHAM LOCAL SECTION. THE TESTING OF TRANSFORMERS AND TRANSFORMER IRON. By D. K. MORRIS, Ph.D., and G. A. LISTER, Associate Members. (Paper read on April 25, 1906.) SYNOPSIS.—1. Introduction. 2. Regulation diagram. 3. Diagram of voltage characteristic. 4. The short-circuit test. 5. Proposed standard transformer test. 6. The 3-point wattmeter method. 7. Standard tests for—(a) core losses: separation by constant-frequency test ; (6) copper losses; (c) efficiency; (d) heating ; (e) regulation. 8. The auxiliary transformer. 9. Special tests— (a) by means of extra turns ; (b) at half power factor; (c) out-of-phase test; (<i) 3-phase transformers. 10. Hysteresis by slow cyclic change—(a) method of constant induced voltage ; (b) theory; (c) application to testing of small samples. 11. Conclusion. APPENDIX.—The 3-point method. Temperature by the wattmeter. Improvements in the constant induced voltage method. Separation of hysteresis from eddy- current loss. 1. INTRODUCTION. In the testing of transformers the principal- qualities which may have to be investigated are :— (a)' Core losses. (b) Copper losses at all loads. (c) Efficiency at light loads as well as full load. (d) Heating at full load. (e) Regulation on all loads and power factors. (/) Insulation (not dealt with in the paper). The designer and manufacturer of the transformers may also require to know the extent to which the core loss is caused by hysteresis or eddy currents. In addition, it would be useful to deter- mine the excellence of the built-up magnetic circuit, having reference to the permeability of the iron and the low magnetic resistance of the joints. Excellent methods have been proposed for determining most of the above qualities, but it will be found that they involve the use of different and unusual sources of supply, and also of a considerable number and variety of electrical connections and instruments. Thus to separate the core losses a supply is required whose frequency can be varied, while direct current at low voltage is usually employed when 1906.] TRANSFORMERS AND TRANSFORMER IRON. 265 finding the copper drop or deriving the temperature rise from the increased resistance of the.windings. In order more quickly and conveniently to carry out these measure- ments, the authors propose a standard test involving but one set of connections, three instruments, and the normal supply. This method necessitates the use of two similar transformers, and is a modification of that first described in 1892 by Ayrton and Sumpner.* It is an application of the Kapp-Hopkinson or differential method of testing direct-current machines. Beforedealing with the standard test in detail, it will be convenient to describe a diagram which we have found very useful and indeed almost indispensable when dealing with any but the simplest transformer problems. This may readily be constructed for any transformer, and shows at a glance its behaviour as regards regulation on loads of any magnitude and power factor. The Characteristic Triangle.—When the primary winding of a transformer is excited from a constant-pressure supply the secondary voltage varies with the load by an amount depending upon the copper drop in the two windings and upon the leakage flux. The phases of the copper voltages are, of course, those of the currents in the respective windings, but these currents are not quite identical in phase, for they must be just so far out of phase with each other as will enable them together to provide that small out-of-phase magnetising force which will excite the core. This phase difference is very little indeed in all but the smallest transformers. The leakage flux is dependent upon the extent to which the ampere turns of the primary oppose those of the secondary ; and as the reluctance of the leakage paths occurs almost solely when they lie in air, the actual leakage flux is proportional to and in phase with the resultant opposition of magnetising forces, while the leakage voltage is in quadrature with it, and therefore, also, with the equivalent total copper drop. The resultant of these two voltages (the combined copper drop and the leakage voltage) is that which must be impressed on one of the windings in order that a current may flow when there is no external resistance in the secondary circuit. It is the "short-circuit" voltage, each component of which, and consequently the whole, is proportional to the current. By determining any two of these voltages, and calculating the third, a right- angled triangle can be constructed, whose sides represent the magnitude and phase of the respective voltages. We have called this triangle the characteristic triangle of the transformer. 2. TRANSFORMER REGULATION DIAGRAM. In Fig. 1, AC represents the combined resultant copper drop, BC the voltage due to the leakage flux, and AB the resultant voltage. In the case of a unity power-factor load—one in which the secondary current is in phase with the secondary terminal volts—the drop is that due to copper resistance only, the effect of the leakage being to cause a phase difference between the primary and secondary volts without * Electrician, vol. 29, 1892, p. 615. 266 MORRIS AND LISTER :• THE TESTING OF [Birmingham, actual reduction of the secondary terminal volts. If the secondary current lag, so that the power factor is equal, say, to 0-9, then the triangle will take up the position A B' C, in which A C is again the copper drop, but lagging in phase with respect to the secondary volts, and B' C the leakage volts. It will be seen that the latter now has a component in phase with the secondary voltage and tending to reduce it, the actual drop at the secondary terminals being given 1906.] TRANSFORMERS AND TRANSFORMER IRON. 267 by A D'. Similarly in the case of a leading current of, say, o"9 p.f., the drop is given by A D". This drop is considerably less than in the case of a lagging current, since the component of leakage in phase with the secondary voltage is a magnetising component, and tends to boost up the secondary volts. It is convenient to draw the triangle so that the scale of AC represents the copper drop for full-load current. A scale of current is then marked on A B. Current circles and load lines are now drawn ; and also lines radiating from A to represent the various positions of the line A B for different power factors. The drop in secondary voltage which will be caused by any current or load having any power factor, lag or lead, is then immediately obtained from the figure by inspection. Theoretically it is not correct to project the point B on to the base line, for the primary and secondary volts are not quite in phase. But in com- mercial transformers with moderate leakage the error is quite negligible. The correction, if it should be required, may be taken as equal to (B' D'Y2 — '—r—, which is to be added to the drop of secondary volts, 2 x py. volts r J unless the secondary current be leading sufficiently to cause a rise of voltage, in which case it is to be subtracted from the secondary rise. It has been assumed in the above description that the ratio of transformation is i : i. The diagram is constructed for transformers of any ratio, by expressing the primary voltages and current in terms of the secondary. The drop due to the no-load or magnetising current is so small in modern transformers that it has been omitted in the transformer diagram. The characteristic triangle should be drawn to correspond to full- load conditions, and the temperature to which its copper voltage corresponds should be specified. The angle a becomes less as the temperature rises, and the diagram can readily be corrected for any such rise. Variation in frequency affects the leakage voltage proportionally, without affecting the copper drop. Apart from temperature and frequency, however, the characteristic triangle does not alter in shape, but is simply proportional in magnitude to the current. 3. DIAGRAM OF VOLTAGE CHARACTERISTIC. A useful modification of this diagram is one in which the voltage characteristic is constructed, and from which, as in the first diagram, the regulation on all loads and power factor may be read direct (see Fig. 2). Construct the full-load characteristic triangle as shown. With centre A and radius A B describe a semicircle. Draw a line from A parallel to C B, and scale so that A G is equal to the full-load current. Mark on A B a scale of cos <p, so that A B is equal to unity. Draw a line at right angles to A B, from the point corresponding to the required power factor cutting the 268 MORRIS AND LISTER: THE TESTING OF [Birmingham, circle in E. Draw E F parallel to A G. Then the line A F is the regulation curve or voltage characteristic for that power factor, the secondary drop being read on the vertical scale. This diagram indicates a simple expression for the copper drop at any load or power factor. Let V,, V2, and V3 represent the short-circuit, leakage, and copper voltages respectively for a given current. Then the secondary drop is given by— V, sin (<p + 0) These two diagrams, which are modifications of the Kapp circle I ._X_ M.AXlMUf |_ POSJJI JLE_RIS I o 5- WITH FU X LOAD \ (5 SCALE — u- LEAKAC E 3 O AXIMU1 POSSIBLE DRCP WITH FUIX L< AD CURI EHT FIG.

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