To take a specific case, let us assume V = 110 volts, I = 8 amperes, and R 1 ohm. Then we find from (29), (30), and R R(x-1)= R(1-x)=3 Figs. 28 and 29. Irregular Distribution of Lamps on Ring Circuit. x (31) that V,105 volts, V2 = 104 volts, r = 5 amperes, the current that flows upward from the+feeding-point is 8 - 5 = 3 amperes, the current in each lamp being 4 amperes. Fig. 29 represents the distribution of potential in this case, including the drop in each portion of the mains. The addition of more lamps to this circuit, whether symmetrically or unsymmetrically placed, would increase the total and average drop, also the maximum difference in voltage between lamps. The general conclusion is, that the three statements made on page 47 apply not only to the simple arrangement shown in Fig. 13, but also to almost any parallel system of mains, with the exception of peculiar conditions on an anti-parallel circuit, as explained in connection with Fig. 27. Hence it is ordinarily sufficient in practice to calculate the distribution of potential on a parallel system for full load, since the total or average drop, and the greatest difference in voltage between lamps, will almost always be smaller for any number or arrangement of lamps less than the maximum load. Heretofore the principal point that has been considered in discussing parallel systems has been the difference between the pressures supplied to the various lamps which are burning at the same time. But it has already been explained on page 35 that in cases where the total drop is considerable, — 10 per cent, for example, the voltage at the lamps will rise nearly that same percentage when the full load is thrown off, leaving only a few lamps. It will now be well to study the means employed to prevent variations in the voltage of a given lamp when others are thrown on or off the same circuit. Regulation of Voltage Supplied to Parallel Systems. The feeding-points in the various diagrams (Figs. 13 to 29) might in some cases be supplied with current directly from the generator, or the feeders may be so short that their resistance is insignificant. Under those circumstances it would only be necessary for the dynamo or other source to generate a constant pressure in order to supply the mains represented in Figs. 13, 15, and 16. If this were kept at 111 volts, the last group of lamps would receive 109 volts at full load, and no lamp could receive more than 111 volts, even if all but one were turned out, so that the extreme variation would be but one volt from the normal pressure of 110 volts. The large amount of copper used in these cases saves the trouble of regulation, and often might be worth the extra first cost. This is practically the way that the majority of isolated plants are operated, the size of the wires being made sufficient to limit the drop to a small amount so that the dynamos may be run at a fixed voltage. With wiring designed for a total drop of 4 per cent, the greatest variation from the average pressure would only be about 2 volts, and usually the maximum drop is between 2 and 4 per cent for isolated plants where the distances are moderate. In most cases, even the simplest, feeders are employed to connect the mains with the generators, so that the pressure lost in them must be included in determining the total drop. When the distances are greater, or it is attempted to save copper by using smaller conductors or by adopting such arrangements of mains as those represented in Figs. 17 to 22, the drop becomes too large to warrant the maintaining of a constant potential at the dynamo. Nevertheless, many small central stations and isolated generating plants are operated at an approximately fixed voltage, in spite of the fact that the drop may be 5 per cent or more. The usual practice in such cases is to run the dynamos about 2 per cent above the normal voltage of the lamps, the consequence being that at full load the latter receive about 3 per cent less pressure than that for which they are intended, assuming the drop to be 5 per cent. This custom arises from the fear of shortening the life of incandescent lamps by feeding them with too high a voltage. It appears to be a generally accepted idea that the rated pressure of a lamp is a limit above which it should never be allowed to rise. As a matter of fact, the voltage marked on the lamp should be considered as an average value, to be approximated as closely as possible at all times. It is a rare thing to see incandescent lamps burning even one or two per cent above their rated pressure, while they are very often operated considerably below this point. The author has observed in thousands of cases in America and Europe that incandescent lamps are usually run perceptibly below their proper voltage, and at least half of them are so low that they are positively dim. This is partly due to the usual falling off in the candle-power of lamps which occurs after they have burned for some time, amounting to a considerable loss after a run of 500 hours. This matter will be treated fully under the head of incandescent lamps. In isolated plants, and in many central stations. where lamp renewals are paid for by the user, this diminution in candle-power is great because of the tendency to unduly prolong the life of the lamps. But in stations or plants where it is desired to render good service, the lamps are renewed more frequently. The reason for generating a constant potential is the simplicity and convenience secured by so doing. The attendant merely has to keep the index of the volt meter at a certain point, by means of the ordinary rheostat in the shunt field circuit, being either instructed to do so, or naturally falling into that habit. It would greatly improve the service, however, if the pressure were kept at a given value for any number of amperes up to half load, and raised a certain percentage when the current exceeds that amount. For example, below half load the dynamo could be regulated to generate 2 volts higher potential than the normal voltage of lamps, which would again be increased 2 volts when the current is greater than half load, the total drop being 5 volts. In this way the pressure at the lamps would not be more than one or two volts high or low at any time, and the extra trouble or intelligence required would certainly be insignificant. Indeed, it would seem to be perfectly practicable to carry this plan further, and subdivide the load into three or even four parts instead of two. The instructions could be just as definite and almost as easily carried out as for one fixed potential. If this regulation were effected by hand, using the ordinary rheostat in the field circuit, it would be a rough approximation to the rise in voltage with increasing load which occurs automatically in an "over-compound" dynamo. Regulation by Means of Compound or Over-Compound Dynamos. - It would seem that an excellent way to operate systems in which a constant potential is required at the lamps or other receivers, is to employ generators which are over-compound wound to give a rise in voltage from no load to full load the same in amount as the total drop, thus automatically securing the desired result. An objection to this plan is the tendency for the E.M.F. of the dynamo to rise, and a very excessive current to flow in case of a short-circuit. The E.M.F. of a plain shunt machine, on the other hand, tends to fall with a short-circuit. But when properly protected by fuses or circuit-breakers this difficulty is not likely to be serious. Another difficulty that may arise in such a case is the fact that when there are two or more over-compound generators the pressure may be too high when only one is in use. For example, when one machine out of two is running with one-half of the total load, it will raise the voltage just as much as if both were working at full load, whereas it should only increase the pressure one-half of the maximum percentage of drop. This trouble may be avoided by always leaving in circuit the series coils of all the dynamos, or preferably by substituting an equivalent resistance for them when they are disconnected.* The manner of connecting two or more compound dynamos to operate in parallel is represented in Fig. 30. A is the armature, B the series, and C the shunt field coils, R the field rheostat, D, F, are switches connecting the main terminals of the dynamo with the 'bus bars G and I respectively, and E is a switch to connect the equalizer † H with the brush from which the series coil B leads. It is a common practice to mechanically join D, E, and F by a cross-bar so that they move together and form a three-pole switch. In such cases, when a dynamo is about to be connected to the circuit, the switches D, E, and F are left open, and the field magnet is excited by the shunt coil C, being regulated by the rheostat R until the pressure generated is a little greater (about one per cent) than the difference of potential between the 'bus bars G and I. This fact may be ascertained by comparing two volt meters This matter is explained in vol. i., p. 349. * † Vol. i., p. 348. |