qr code vb.net library * See note 27 in Appendix. in .NET

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* See note 27 in Appendix.
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426
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CHAPTER 10 Magnetic Coupling. Transformers
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Fig. 249
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Fig. 250
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or " 427 VAB 1:732Vp =308 p in which let us note that 1:732 3:* Next, let s consider the loop formed by lines B and C, as shown in Fig. 250. " Note that VBC is the voltage drop from line B to line C, as shown. If, now, we start at B and trace around the loop in the ccw sense, we have that " " " VBC Vnc Vnb and thus, upon making use of eqs. (425) and (424), we nd that " VBC j1:732Vp or " VBC 1:732Vp =2708 Lastly, let s consider the loop formed by lines C and A, as shown in Fig. 251. 429 428
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Fig. 251
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" Note that VCA is the voltage drop from line C to line A; if, now, we start at C and trace around the loop in the cw sense, we have that " " " VCA Vna Vnc and hence, upon making use of eqs. (423) and (425), we have that " VCA 1:5 j0:8660 Vp
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* See note 28 in Appendix.
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CHAPTER 10 Magnetic Coupling. Transformers
or (VCA being in the 2nd quadrant) " VCA 1:732Vp =1508 431
Now let us summarize what our algebraic work has revealed about the Yconnected generator of Fig. 248. To begin, let s bring together the equations for the three LINE VOLTAGES; thus " by eq: 427 : VAB 1:732Vp =308 by eq: 429 : " VBC 1:732Vp =2708 " by eq: 431 : VCA 1:732Vp =1508 432 433 434
The rst point we wish to note is that inspection of the above three equations shows that the magnitude of LINE VOLTAGE produced by a balanced Y-connected generator is equal to 1.732 times the magnitude of the PHASE VOLTAGE; that is VL 1:732Vp where VL is the magnitude of the line voltage; thus " " " jVAB j jVBC j jVCA j VL 436 435
The second thing we wish to nd is the complete VECTOR DIAGRAM showing the relationships among the various voltages in Fig. 248. In doing this, let us remember that " the phase voltage Vna is the reference vector in Fig. 248. Let us therefore begin with the vector diagram for the PHASE VOLTAGES, which is the vector diagram representation of eq. (421), as shown in Fig. 252. Now, to complete our diagram, all we need do is add the LINE VOLTAGE vectors to Fig. 252. This can be done by noting the following facts. " " First, by eq. (432), VAB leads the reference vector Vna by 308. " " Next, noting that =2708 = 908, eq. (433) shows that VBC lags Vna by 908. " " Lastly, noting that =1508 = 2108, eq. (434) shows that VCA lags Vna by 2108. Combining these facts with Fig. 252 gives the COMPLETE voltage vector diagram for Fig. 248, as shown in Fig. 253.
Fig. 252
Fig. 253
Thus, as Fig. 253 shows, in a balanced Y-connected generator the line-voltage vectors lead the phase-voltage vectors by 30 degrees.
CHAPTER 10 Magnetic Coupling. Transformers
Let us note that the transmission of large blocks of power requires that transmission-line voltage be as high as possible. This is necessary to prevent excessive power loss in the line. Thus, commercial power-line voltages in the order of 120,000 volts rms are commonly used. For several reasons, however, it s not practical to build power generators having such high output voltages. Thus, in the generation of large amounts of power, the generator will not usually be connected directly to the outgoing transmission line (as shown in Fig. 248). Instead, a relatively low value of generator voltage is used, which is then stepped up by a three-phase transformer to the desired high voltage for the transmission line. This is illustrated in Fig. 254, in which a balanced Y-connected generator is coupled to a transmission line through a delta-to-Y ( Y) step-up transformer.
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