IX. Reactors (Reactive Coils, Reactances) 129. The reactor consists of one electric circuit interlinked with a magnetic circuit, and its purpose is, not to transform power, but to produce wattless or reactive power, that is, lagging current, or what amounts to the same, leading voltage. While therefore theoretically we cannot speak of an ''efficiency" of a reactor, since there is no power output, nevertheless in the in- dustry the expression " efficiency of a reactive coil" is gener- ally used, and generally understood, in the conventional definition : T^C • 1°SS Efficiency = 1 — -. — input and the input is given in total volt-amperes, the loss in energy volt-amperes, that is, watts. The efficiency then is 1 — power- factor. ALTERNATING-CURRENT TRANSFORMER 303 The transformer at open circuit is a reactor, but a very poor one, as its power-factor is high, that is, the efficiency low. In the transformer, the exciting ampere-turns are the (vector) difference between primary and secondary ampere-turns, are wasted, and therefore made as low as possible, by using a closed magnetic circuit. In the reactor, no secondary circuit exists, but the exciting ampere-turns are the purpose of the device, thus should be as large as possible. That is, to convert a trans- former into a reactor, the reluctance of the magnetic circuit must be increased so as to make the exciting ampere-turns equal to the total full-load ampere-turns of the structure as transformer. This is done by inserting an air gap into the magnetic circuit. Such a gap may be either a single gap, or a number of smaller air gaps, or one or a number of slots cutting almost through the magnetic circuit, but leaving narrow bridges, FIG. 174. — Bridged air-gap reactor. as shown in Fig. 174. This latter offers the advantage of a better mechanical structure, less liability to noise and to magnetic leakage, but when used in series in high voltage circuits, may lead to voltage peaks at the moment of current reversal, which may endanger the insulation. The use of a number of small air gaps instead of one large one distributes the magnetic leakage and thus gives less liability to eddy currents in the conductors. 130. A transformer of output P = e2iz has a size of winding space of ezi2 + #iii = 2 e2z*2, that is (with the air gap inserted into the magnetic circuit), gives a reactor of the capacity ei = 2 P. That is, a reactor has the size of a transformer of half its output. Reactors are frequently used in series to apparatus, and the vol- tage consumed by the reactance then varies with the current, and is, due to the air gap, proportional to the current up to the value where the iron part of the reactance begins to saturate, as shown by the characteristic curve of a reactance, Fig. 175, the "volt- 304 ELEMENTS OF ELECTRICAL ENGINEERING ampere characteristic." Then the voltage increases less than proportional to the current, or inversely, the current increases out of proportion to the voltage, that is, the reactance decreases and wave-shape distortion occurs. Reactances thus must be designed so that at the highest currents (or voltages), at which they may be called upon to develop their reactance, their magnetic circuit is still below saturation. Industrially, reactors are often denoted in per cent. Thus for Volt- REACTOR Ampere Characteristic Rec Vo ts e FIG. 175. — Volt-ampere characteristic of reactor. phase control in synchronous converter circuits, 15 per cent, re- actances are used. This means, at full-load current, the voltage consumed by these reactances is 15 per cent, of the circuit voltage. 131. With the increasing size and increasing voltage of modern central stations and the use of high-speed turbo-alternators ca- pable of momentarily giving very high short-circuit currents, the amount of power, which can be developed momentarily by a short circuit in the system near the generating station, has reached such ALTERNATING-CURRENT TRANSFORMER 305 destructive values, that a limitation of this power has become necessary, and as economy of operation forbids sectionalizing the system into a number of smaller units, this has led to the exten- sive use of power-limiting reactances, in the generator leads, in the bus bars, tie feeders and even the power feeders. Such re- actances are used of 2' to 8 per cent., and in bus bars even up to 25 per cent., and in case of a local short circuit, limit the current which can flow. Thus a 4 per cent, reactance would at a short circuit just beyond the reactance limit the current to -r - = 4 per cent. 25 times the normal, etc. But to do so, the reactance must still be there at twenty-five times its rated current, that is, when ab- sorbing full circuit voltage instead of its normal 4 per cent, thereof. If then iron is used in the magnetic circuit of such a reactance, the density must be so low, that at twenty-five times this density (or at 12.5 times with an 8 per cent, reactance, etc.), it does not yet saturate. When limited to such very low mag- netic densities in the iron, the mass of iron becomes so enormous, that it becomes more economical to use an air circuit throughout. Reactances, which must retain their reactance, that is, must not saturate at many times their normal current, such as power limiting reactances, thus are built without iron in the magnetic circuit. E. INDUCTION MACHINES