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# Audel electrical course for apprentices and journeymen - Rosenberg P.

Rosenberg P. Audel electrical course for apprentices and journeymen - Wiley & sons , 2004. - 424 p.
ISBN: 0-764-54200-1
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Two-Phase Systems
Figure 23-1 illustrates two alternators, namely, No. 1 and No. 2. For this explanation, envision both alternators connected to the same shaft, so that their windings are 90 electrical degrees apart. A voltage of 100 volts has been selected for the output voltage of each alternator.
Figure 23-1 Two-phase system.
In Figure 23-2 the two alternator windings are illustrated 90° out of phase. There are two methods of two-phase transmission: One is four-wire and the other three-wire. For three-wire transmission, B1 and B2 are connected together, forming B for one conductor, and A and C as the other two conductors.
255
256 Chapter 23
Figure 23-2 Two-phase windings 90° apart.
This three-wire connection gives 100 volts between B and C, 100 volts between A and B, and 141 volts between A and C. This is shown by the vector diagram in Figure 23-3. Here E1 is 100 volts and E2 is 100 volts. These two voltages are 90° out of phase, so the diagonal line E will be 100 X V2 = 100 X 1.41 = 141 volts between A and C in Figure 23-2.
Figure 23-3 Vector diagram of two-phase voltages.
With four-wire two-phase, there would be two 100-volt circuits with no connection between them, as illustrated in Figure 23-4. Windings A and B are not connected together. Winding A supplies
Polyphase Circuits 257
Figure 23-4 Two-phase four-wire system.
conductors C and D. Winding B supplies conductors E and F. The two circuits are 90° out of phase.
Three-Phase Systems
Three-phase could be considered similar to two-phase, namely, three one-phase alternators connected to one shaft so that each alternator is in turn 120° out of phase with the preceding alternator. To be more practical, a single alternator has three windings on the stator or rotor, as the case may be. These windings are connected so that they are 120° apart. They may be connected either wye or delta. Figure 23-5A illustrates a wye connection. The three phases are A, B, and C, with all windings connected at a common point X. Figure 23-5B illustrates a delta connection. The three phases, A-B, B-C, and C-A, connect as shown in this illustration.
Single-phase alternators with distributed windings will have less output than with concentrated windings. The reason for this is that part of the voltage is obtained at a disadvantage due to the various phase angles between the sections of the windings. To correct this, if the sections could be made to deliver their voltages independently, a closer approximation to the arithmetic sums of their separate voltages could be more nearly obtained.
258 Chapter 23
A
C
C
A
(A) Wye connection.
(B) Delta connection.
Figure 23-5 Common three-phase connections.
Figure 23-6 shows a three-phase alternator winding connected in wye as shown in Figure 23-5A. The windings are 60° apart, but if they are connected in separate circuits as shown in Figure 23-6, a great gain is affected. Conductor E is in series with conductor F, which is 180° away from E. Conductor G, 60° away from E, is in series with H, which is 60° away from F. Conductor I is in series with conductor K and is 60° away from G.
Assuming that the six conductors were brought out to three separate circuits, a voltage output such as in Figure 23-7 would be the result. For the purpose of economy, it is desirable to combine these into one circuit, with three conductors instead of six conductors.
B'
Figure 23-6 Three-phase alternator winding-connected wye.
L
Polyphase Circuits 259
Figure 23-7 Three emfs 60° apart.
The most economical winding is the placing of conductors 60° apart, as shown in Figure 23-6.
It is then possible to connect these windings so as to deliver voltages 120° apart as shown in Figure 23-8. Points E, I, and H in Figure 23-6 are 120° apart in phase and are brought out to a common point, L. The other ends of E, I, and H, namely, G, F, and K, are likewise 120° apart and lead to the external circuit fed by A1, B1, and C1.
B
/ \ / a X "AA'A . A /'
' X ' _A\ J f \ * * \ ' tx
Figure 23-8 Three emfs 120° apart in phase.
This connection actually reverses winding G-H in relation to windings E-F and I-K. Thus the results are a wye connection as illustrated in Figure 23-5A, and sine waves as illustrated in
260 Chapter 23
Figure 23-8, in which it may be observed that there is an equal current in both directions at the same time.
If winding G-H had not been reversed, sine waves as illustrated in Figure 23-7 would have resulted. There is no balance and the economy wouldn’t be as good as that obtained in Figure 23-8. This results in a saving in copper.
Figure 23-9 graphically shows what happens when one phase of a three-phase alternator is reversed, to obtain sine waves as in Figure 23-8 instead of those shown in Figure 23-7.
Figure 23-9 Reversal of one phase to alter the 60° relation of the phases to 120°.
Phases A, B, and C are 60° apart. This would give sine waves as in Figure 23-7 and an unbalanced current and voltage relationship. By taking OB and reversing it to OD, this places all phases in a 120° relationship.
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