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wire MN, in Fig. 115, is superfluous; but for electric lighting this extra conductor is required, unless the lamps on the three circuits are balanced. If the currents in the three branches are not equal,

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100.

100 V3 =173.

then the wire MN carries the difference between them, so that its function corresponds closely with that of the neutral conductor in the ordinary three-wire system described on page 70.

Another method of connecting three-phase circuits is shown in Fig. 117, and is called the A (delta) connection, the arrangement in Fig. 115 being designated as the Y connection. In either of these cases any lamp L is fed simply by the E.M.F. due to a single armature winding, MA in Fig. 115, or QP in Fig. 117. If, however, a lamp is connected across the outer terminals of the Y circuits, it receives a voltage which is the resultant of two E.M.F.s, that are in series, but differ by 120° in phase. This is shown in Fig. 118, DA, B12..... DB, and DC representing respec

Fig. 118. Relative Voltage of A and y

Connections. tively the E.M.F.s of a three-phase armature winding with Y connection. Assuming the E.M.F. of each phase DC to be 100 volts, then the E.M.F. between A and C will be V3 = 1.73 times as great, or 173 volts.

Production of Rotary Field by Two-Phase Current. — An iron ring, wound with insulated wire, as represented in Fig. 119, is supplied with two-phase currents at the four equidistant points A, B, C, and D, the two conductors of one phase being connected at A and B, and those of the other phase at C and D. Considering only one current, and assuming it to enter at A, the direction of winding is such that it will produce a south pole at A, and a north pole

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at B, so that a compass needle placed inside the ring would tend to point vertically upward as indicated by the dotted arrow. This

condition is represented at 1, in Fig. 120, the current L M N having its maximum positive value, and the other current, P Q R, being zero at that instant. A moment later, the first current has decreased somewhat, and the other has increased, so that they are equal. In this case, each will tend to produce a south pole where it enters the

ring, at A and D respectively, Fig. 119. Ring Supplied with

so that a resultant polarity is

produced midway between, as shown at 2 by the arrow inclined at 45°. The next instant, at 90°, the current L M has fallen to zero, and the current P Q has reached its maximum, so that the arrow takes a horizontal position, as represented at 3. Again at 135°, the current L M has reversed, tending to make a south pole at the bottom of the ring, and the needle will incline downward at an angle of 45°, as shown at 4.

Two-Phase Current.

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By following the successive conditions, the needle will be found to take the various positions represented at 5, 6, 7, 8, and finally at 9, it returns to its original vertical direction, the current having completed one period. Thus the needle tends to be carried around continuously by the shifting resultant field, so long as the ring is supplied with two-phase currents.

Principle of Polyphase Motors. — It is this capability of producing continuous rotation that gives the polyphase currents their interest and value, since it enables motors to be operated very successfully. The ring with the magnetic needle, in Fig. 119, illustrates the principle of the synchronous polyphase motor, since the armature revolves in exact synchronism with the phases of the currents. If the needle is replaced by a cylinder of laminated iron wound with conductors, like an ordinary armature, except that they are short-circuited, it is found that it will revolve also; but in this case the speed is a little less than that of a synchronous armature, the difference being called the slip, usually amounting to from 1 to 5 per cent. This slip represents a relative motion of the rotating field, with respect to the armature conductors; consequently the latter are cut by the lines of force, thereby inducing currents in them. It is the action of the field upon these induced currents which causes the armature to revolve, this type being called the induction motor. It is a remarkable fact that no current is supplied to the moving part, so that it need have no electrical connections made to it except for purposes of starting and regulation.

In some cases the construction is modified so that the part in which the

+ H currents are induced revolves, and the other part is stationary. For this reason, and because no energy is supplied directly to the so-called armature, it is considered more correct to distinguish the two elements of an induction motor as rotor and stator, or primary and secondary. The Action of Three-Phase Currents

Fig. 121. Ring Supplied with in producing a rotary field is quite

Three-Phase Current. similar to that described for twophase currents. The ring in Fig. 121 is wound as before, but the current is led in at three equidistant points, H, Y, and 2, instead of at four points. Taking the instant when the current flowing in at H is a maximum, two currents flow out at Y and Z, each having one-half the value of the current entering at H. This tends to produce a south pole at H, and two north poles at Y and Z respectively. The resultant due to the latter is a south pole at T, midway between Y and Z, consequently a magnetic needle would take the position shown by the dotted arrow. (This condition is represented at 0° in Fig. 114.) A moment later (at 60° in Fig. 114) currents enter at both H and 2, and a maximum current flows out at Y, hence the needle would point toward V. At the end of another one-sixth of a period (at 120° in Fig. 114), the maximum current will enter at 2, and the needle would turn to that point, and so on until it had made a complete revolution in one period of the alternating current.

Actual Forms of Polyphase Motors. — The synchronous type of polyphase motor is similar in principle and construction to the corresponding generator, in fact, two identical machines may be used, one as generator and the other as motor, the same being true of single-phase alternating, as well as direct-current machines. In all these cases the field magnets must be supplied with direct current either from a separate exciter or from the machine itself, which, if it is an alternator, must be provided with a commutating device for that purpose.

The advantage of the polyphase over the single-phase synchronous motor is the fact that the former is self-starting, owing to the fact that it exerts some rotary effort even when standing still. In this case it acts as an induction motor, the armature being supplied with polyphase current, but the field circuit is left open until synchronous speed is reached. On the other hand, the single-phase motor has no starting torque, and has to be provided with some special device in order to bring it up to synchronism.

The practical forms of induction motor are self-starting with considerable torque, but they are generally arranged with some means for introducing resistance into the secondary circuit, in order to give them full torque when starting, and to prevent a great rush of current at that time.

CHAPTER IX.

TRANSFORMERS.

A TRANSFORMER consists essentially of two separate coils of insulated wire wound or placed upon an iron core. One of these coils, called the primary, receives alternating current from some source; and the other coil, called the secondary, delivers alternating current to any circuit that may be connected to its terminals. The action depends upon the physical principle that an alternating current sets up an alternating magnetic flux which tends to induce an alternating E.M.F. in a conductor that encloses the flux. The function of a transformer is to convert electrical energy at one voltage into electrical energy at another voltage.

For example, a transformer is supplied with an alternating cur- . rent of 1000 volts and 10 amperes, and it delivers a current of 100 volts and about 97 amperes. The input is 10 k. w., and the output is about 9.7 k.w., since there are losses amounting to about 3 per cent; that is, the efficiency is 97 per cent. In most cases transformers are used to reduce a high-voltage supply of energy into low-voltage energy that is safe and convenient for operating lamps, motors, and other devices. Sometimes they are employed to raise the pressure in order to transmit energy economically over long

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H

Fig. 122. Simple Transformer Circuit.

lines. The former are called step-down and the latter step-up transformers. For the sake of simplicity, a transformer is often represented as consisting of a ring of iron, CH, in Fig. 122, with a primary coil, P, and a secondary coil, S, wound upon it. In the

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