VIII. Autotransformer 126. If in a transformer a part of the secondary winding is used as primary, or inversely, the transformer is an autotrans- former, sometimes also called compensator. Thus let in a transformer Fig. 172 primary current, voltage and turns be respectively ii, e^ ni, and secondary current, voltage and turns be t'2, e2, n2, thus the ratio of transformation a = — • n2 Assuming HI > nz, then in any n2 of the HI primary turns, the same voltage is induced as in the n2 secondary turns, and we could thus 300 ELEMENTS OF ELECTRICAL ENGINEERING use any n2 primary turns as secondary turns, provided we make them of sufficient copper section to carry the secondary current. The n2 turns in Fig. 173 thus are in common to primary and secondary circuit. As primary and secondary current are (ap- proximately) opposite in phase, the current in the common turns of Fig. 173 is (approximately, that is, neglecting exciting current) the difference between secondary and primary current, i2 —ii, thus less than the secondary current i'2, and as the result, the com- mon turns in Fig. 173 may be made of less copper section than the secondary turns in Fig. 172, while the number of primary turns is reduced by n2. Thus an autotransformer requires less copper, that is, is smaller and cheaper than a transformer of the same output. 127. In the transformer Fig. 172, the size is determined by the number of turns and turn sections, that is, by e\ X ii + £2 X iz FIG. 172. — Diagram of trans- former. FIG. 173. — Diagram of auto- transformer. (the turns being proportional to the voltage, the turn section to the current, the same magnetic flux assumed). But since 61 = aez and i\ = — , e\i\ = e2i2, and the size of the transformer Fig. 172 thus is proportional to 2 e-#2, that is, to 2 P, or twice the output. In the autotransformer Fig. 173, the nz common turns are tra- versed by the difference of secondary and primary current, at secondary voltage, and the size of this common part of the wind- ing thus is: 62 (iz — ii). The remaining part of the winding, of n\ — n2 turns, that is, of voltage e\ — e2) is traversed by the primary current ii, hence of size i\ (e\ — e2), and the total size of the autotransformer thus is : 62 (*2 — ii) + i\ (e\ — e2) ALTERNATING-CURRENT TRANSFORMER 301 but, substituting again for ii and ei, gives as the size of the auto- transformer: (ae2 - es) = 2 -"•('-3 hence, the ratio of size of autotransformer and of transformer of the same output, is: _ autotransformer _ 1. transformer a If the ratio a = 2, as transforming between 115 and 230 volts, 7 = J£, that is, the autotransformer has half the size of the trans- former, or, more correctly stated, the autotransformer is as large as a transformer of half the output. If the ratio a = 1.1, as raising (or lowering) the voltage 10 per cent, by autotransformer, this autotransformer has the size 7 = 0.1 that is, is as small as a transformer of one-tenth the out- put. If the ratio a = 10, as transforming between 2300 and 230, 7 = 0.9, that is, the autotransformer is only 10 per cent, smaller than the transformer. The saving in size — and therewith in efficiency and cost — by the use of the autotransformer thus is the greater, the lower the transformation ratio a, but becomes negligible at high trans- formation ratios. Thus autotransf ormers are very economical for use in moderate voltage transformation, as a voltage change by 10 or 20 per cent., or even for doubling the voltage, or dividing it in two, but not for high voltage ratios. 128. The most serious disadvantage of the autotransformer obviously is that it electrically interconnects primary and sec- ondary circuit and thereby puts the voltage of the higher voltage circuit onto the lower voltage circuit. Thus, when using auto- transformers, the insulation of the low voltage circuit and the high potential tests of all the apparatus used in the low voltage circuit must be those of the high voltage circuit. Furthermore, a ground in one of the two circuits of an autotransformer also is a ground on the other circuit, while with a transformer, a ground on the secondary does not ground the primary, and in- versely. With low voltages, as 115 -5- 230 volt transformation, this is usually of no importance. It would be a serious objection 302 ELEMENTS OF ELECTRICAL ENGINEERING when attempting the use of autotransformers between 2300 and 230 volts. For instance, a ground at the off side of the high- voltage winding, at A in Fig. 173, would put the entire secondary winding 2300 to 2070 volts above ground, and thus the secondary circuit would kill anybody who touches it while standing on the ground. Any transformer of voltage e\ and 62 and currents i\,i% can be converted into an autotransformer, by connecting primary and secondary in series, of voltages e\ + ez and ez and currents i\ and iz + i\. And inversely, any autotransformer, by disconnect- ing the two sections of the coil, would give (provided that the insulation is sufficient) a transformer of (ei — e^) X i\ primary, and ez X (i* — ii) secondary circuit. The regulation of an autotransformer is better, and the effi- ciency higher, than that of the same structure as transformer, and the per cent, reactance lower, that is the short-circuit current higher in the autotransformer than in the same structure as transformer. Very often it is difficult to build autotransformers with sufficiently high internal reactance, to make them safe under momentary short circuit as autotransformers, while they may be . perfectly safe as transformers, where the reactance is higher. This is a serious objection to the use of autotransformers in high-power systems.