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ThreePhase CircuitsAuthor: E.E. Kimberly Fig. 91 (a) is a threedimensioned representation of a magnetic field in which there are three revolving conductors displaced 120 degrees from one another on their common circular path.^{1} The voltages generated in them will then be displaced in time by 120 degrees, as shown in Fig. 91 (b) by the sinusoids e_{01}, e_{02}, and e_{03} and their corresponding vectors. The conductors will be said to have a positive sense from the back, or zero, end toward the nearer end, as indicated by the sequence of the numbers in the subscripts identifying the vectors which represent the voltages generated in them. It is common practice to connect the conductors or phases inside the machine, as at 0, so that the terminals 1, 2, and 3 only are necessary to connect the machine to its load. The generator is then said to be Yconnected or wyeconnected. A voltmeter connected to the terminals 1 and 2 in Fig. 91 (a) would be affected by the voltages E_{01} and E_{02}. However, if the circuit be traced through the two conductors from terminal 1 to terminal 2, the course would be in a negative sense through conductor 1 and in a positive sense through conductor 2. Therefore, the voltage appearing between terminals 1 and 2 will be the vector difference of E_{01} and E_{02}, and not their vector sum. It is not important whether this vector difference be taken as E_{01}E_{02} or E_{02}E_{01}. If, however, the voltage between terminals 1 and 2 is to be called E_{12}, and the double subscript is to be consistent in denoting the vector direction, it is necessary that E_{12} = E_{02}  E_{01}. Likewise, E_{23} = E_{03}  E_{02} and E_{31} = E_{01}  E_{03}. The voltages E_{01}, E_{02}, and E_{03} are called the phase voltages; and E_{12}, E_{23}, and E_{31} are called the linetoline voltages or simply the line voltages. The voltage at which a generator is rated is always the line voltage, unless otherwise stated. By the trigonometry of Fig. 91 (b),
Since E_{01} = E_{02} (in magnitude), or (91) Therefore, in a Yconnected, threephase system of balanced voltages, the line voltage equals times the phase voltage or linetoneutral voltage.


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