Слике страница
PDF
ePub

distance between the cutting bars of the first winding, suppose we trisect it. Also, instead of adding one new winding, suppose we add two windings. The leading edges of the coils are placed 120 electrical degrees apart in this case. The resulting

[merged small][ocr errors][merged small][ocr errors][ocr errors][subsumed][subsumed][merged small][merged small][merged small][ocr errors][graphic][subsumed][subsumed][ocr errors][ocr errors][ocr errors][subsumed][merged small][merged small][merged small]

FIG. 7.-Line Wires Carrying the Currents Shown Above.

currents can then be plotted as three sine curves 120 degrees apart. See Figs. 6 and 7.

At the instant shown in Fig. 6, which is the point A of Fig. 7, current in phase I is positive and maximum; current in phase 2

[ocr errors]

is negative and increasing; current in phase 3 is negative and decreasing. At this point, as all others, the sum of the positive currents is equal to the sum of the negative.

[ocr errors]

Direct currents are ordinarily handled on two wires, one positive and the other negative; sometimes there is a ground return, but the effect is that of two wires. The three-wire system, so called, does not extend beyond the switchboard. The object of the three-wire generator is to provide two different voltages. There is a greater efficiency in running motors at higher voltages than lamps will stand, so the motors are connected between outside wires and take about 240 volts; while the lamps are connected outside to middle and take 120 volts.

Alternating currents can use two wires for each phase, but it is also possible to effect a saving of wiring when using polyphase current. Two-phase current can be handled on three wires, if the load is balanced. The fact that the resultant of three alternating currents 120 electrical degrees apart is zero, makes it possible to use three wires for three-phase current.

Suppose that the three wires are connected together at the far end. The current in each wire will be alternating just as in a simple alternator. But an alternating current requires a complete circuit, so that while current is going out on one wire it is returning over one or both of the others. This can be easily understood by referring to Fig. 7, and considering different points along the axis.

At A, current is flowing out over phase I and returning over 2 and 3.

At B, current is zero in phase 1. It is flowing out over phase 3 and returning over phase 2.

At C, current is flowing out over both phases 2 and 3, and returning over phase 1.

Any other points can be taken if the action is not made clear by considering the three already taken.

In connection with alternating currents a term which is frequently used is "power factor." A machine may be spoken of as having a high-power factor or low-power factor. High-power factor, of course, is the more desirable; and engineers, when designing, devote considerable time to methods of obtaining it. It has been shown that an alternating current is not always in phase with the voltage. The amount that the current lags or

leads is expressed as an angle. The natural cosine of this angle, which is called the phase angle, is the power factor. The more nearly the current is in phase with the voltage, the higher is the power factor; the cosine of zero degrees being one, while that of 90 degrees is zero.

We can represent current and voltage vectorially; for example, a lagging current, thus:

→E

FIG. 8.

and from the figure we can see that I cos @ is that component of the current which is in phase with the voltage. The total power delivered to a circuit is the product of the voltage and the component of the current which is in phase with the voltage. Or the total power is the product of three quantities, namely, voltage, current and power factor, for which an equation may be written: PEI cos 0.

Watts = volts amperes × power factor.

In electrical work power is usually expressed in watts or kilowatts. If for any reason we want to change this unit to horsepower we can do so by observing the relation that one horsepower is equal to 746 watts. A kilowatt is 1000 watts.

When a machine is in operation the power factor can be determined from readings of an ammeter, voltmeter, and wattmeter. For the wattmeter reading is El cos 0, which divided by EI, the product of the other two readings, gives cos 0, the power factor.

While an alternator may be delivering current at a certain voltage, the power delivered depends upon the power factor of the load, which is a variable and depends entirely on the load and not upon any characteristics of the alternator. Therefore, alternators are rated in volt amperes, or kilovolt amperes and not in watts or kilowatts.

The constants which impede the flow of alternating currents are three in number. They are all in the nature of a resistance and all are expressed in ohms. They consist of resistance, inductive reactance, and condensive reactance. As stated earlier, resistance tends to keep the current in phase with the voltage; inductive reactance to make it lag; and condensive reactance to make it lead. To find the impedance, which is the resultant of the three, we first take the difference between the inductive and condensive reactances, then find the resultant of the resistance and the remaining reactance. We may do this graphically, as in Fig. 8; or, as it is evident that we are merely finding the hypotenuse of a right triangle, we can do it just as well by the old familiar sum of the squares methods: Z2=R2+X2, where X2= (XL-Xc)2.

The last quantity of this equation is always positive, for the difference between the two numbers is squared, and the square is positive where the difference is positive or negative.

Ohm's law, which applies to direct currents, may be expressed as

E

an equation: I= where I is the current in amperes, E the

voltage in volts, and R the resistance in ohms. With alternating currents this equation takes the form: I=

E
where I is the cur-
"

rent in amperes, E the voltage in volts, and Z the impedance in ohms. Knowing any two we can find the other one. This equation is the foundation of all A. C. calculations.

We can now turn our attention to the induction motor. It seems weird at first that a propeller shaft can be made to turn over at any desired speed when nothing is touching it, but anything that is weird is interesting.

We are familiar with generator action which is that relative motion of a conductor, and a magnetic field induces current in the conductor. Here we have mechanical power being supplied and producing electrical power. The motor is just the opposite, for electrical power is supplied and is converted by the motor into mechanical.

The action of a motor depends upon the fact that a conductor carrying current and in a magnetic field will tend to move. If the stator sets up the magnetic field, and the conductors carrying current are secured to the shaft, the shaft will revolve. The rotor

windings of most motors are supplied current by means of brush contact on a commutator or slip rings; but the rotor windings of an induction motor are not supplied current. The rotor currents are all induced currents. The stator is supplied current. It sets up a magnetic field. This field revolves, the conductors of the rotor cut the magnetic lines of force of the revolving field, inducing currents in the rotor windings. Then we have the conditions which must be fulfilled in a motor; namely, a conductor carrying current in a magnetic field, so the rotor revolves.

This requires explanation. It is best to take one thing at a time, so the first step will be the consideration of the revolving magnetic field. The stator does not revolve, merely the magnetic field set up by the stator. In order to understand it we must get back to first principles.

A conductor carrying current has surrounding it magnetic lines of force, or a magnetic flux. If the conductor is bent around in a circle or loop all the lines that were on one side of the wire will be sent through the loop. By increasing the number of turns of the loop, we increase the number of magnetic lines threading through it. Solenoids, or electromagnets, are made this way. The lines threading through the coil are the same as those of any magnet, so that one end of the coil is a North pole and the other end a South pole. If we reverse the current through the coil, we reverse the polarity of the magnet; what was North now becomes South, for the flux is now in the opposite direction.

The winding on the stator of an induction motor has the same effect as the coil, lines of force thread through it, so a magnetic field is set up. Consider the two-phase stator shown in Fig. 9 A. Phase I sets up a field with the North pole at one side when the current is flowing in one direction. When the current is reversed the side that was North becomes South. So phase I sets up an alternating magnetic field. The frequency of the field is the same as the frequency of the stator current, for every time the current is reversed the field is also reversed.

Phase 2 does the same as phase 1. Its windings are placed 90 degrees from phase 1, so its field is at right angles to the field of phase 1. The current in phase 2 is 90 degrees later than the current of phase 1.

That the result is a revolving magnetic field can be seen if we consider the action of the two-phase current in Fig. 9.

« ПретходнаНастави »