A. THREE-WIRE DIRECT-CURRENT GENERATOR 108. In such machines, either only one compensator or auto- transformer is used for deriving the neutral, as shown diagram- matically in Fig. 146, or two autotransformers in quadrature, as shown in Fig. 148, but rarely more. FIG. 148. — Three-wire machine with two compensators. As the efficiency of conversion of a direct-current converter with two autotransformers in quadrature (Fig. 148) is higher than that of a direct-current converter with single autotransformer (Fig. 146), it is preferable to use two (or even more) autotrans- formers where a large amount of power is to be converted, that is, where a very great unbalancing between the two sides of the three-wire system may occur, or one side may be practically unloaded while the other is overloaded. Where, however, the load is fairly distributed between the two sides of the system, that is, the neutral current (which is the difference between the currents on the two sides of the system) is small and so only a small part of the generator power is converted from one side to the other, and the efficiency of this conversion thus of negligible SYNCHRONOUS CONVERTERS 273 influence on the heating and the output of the machine, a single autotransformer is preferable because of its simplicity. In three- wire distribution systems the latter is practically always the case, that is, the load fairly balanced and the neutral current small. The size of the autotransformers depends upon the amount of unbalanced power, that is, the maximum difference between the load on the two sides of the three- wire system, and thus equals the product of neutral current iQ and voltage e between neutral and outside conductor; that is, in the three- wire system of vol- tage e per circuit, voltage 2e between the outside conductors, and maximum current i in the outside conductors, the generator power rating is p = 2 ei. Let now io = maximum unbalanced current in the neutral — usually not exceeding 10 to 20 per cent, of i — and using a single autotransformer, connected diametrically across the armature, Fig. 146, the maximum of the alternating voltage which it re- ceives is 2 e, and its effective voltage therefore e \/2. As the neutral current iQ divides when entering the autotransformer, the current in the compensating winding is -^ (neglecting the small z exciting current), and the volt-ampere capacity of the autotrans- former thus is and PQ _ 1 io P ~ 2 V2 i = 0.354 *°- x Even with the neutral current equal to the current in the out- side conductor, or the one side of the system fully loaded, the other not loaded, the autotransformer thus would have only 35.4 per cent, of the volt-ampere capacity of the generator, and as an autotransformer of ratio 1 -r- 1 is half the size of a trans- former of the same volt-ampere capacity, in this case the auto- transformer has, approximately, the size of a transformer of 17.7 per cent, of the size of the generator. With the maximum unbalancing of 20 per cent., or -r- = 0.2, 274 ELEMENTS OF ELECTRICAL ENGINEERING the autotransformer thus has 7 per cent, of the volt-ampere capacity of the generator, or the size of a transformer of only 3.5 per cent, of the generator capacity, that is, is very small, and this method is therefore the most convenient for deriving the neutral of a three- wire distribution system. When using n autotransformers, obviously each has - of the size which a single autotransformer would have. The disadvantage of the three-wire generator over two sepa- rate generators is that a three-wire generator can only divide the voltage in two equal parts, that is, the two sides of the system have the same voltage at the generator. The use of two separate generators, however, permits the production of a higher voltage on one side of the system than on the other, and thus takes care of the greater line drop on the more evenly loaded side. Even in the case, however, where a voltage difference between the two sides of the system is desired for controlling feeder drops, it can more economically be given by a separate booster in the neu- tral, as such a booster woul'd require only a capacity equal to the neutral current times half the desired voltage difference between the two sides, and with 20 per cent, neutral current and 10 per cent, voltage difference between the two sides, thus would have only 1 per cent, of the size of the generator.