Stevenson J. Power system analysis

50 CHAPTER 2 TRANSFORMERS

Multiplyi

ng Eq. (2.24) by the admittance matrix gives

(2 .26)

Of course, the y and z parameters with the same subscripts are not simple

reciprocals of each other. If the terminals of coil 2 are open, then setting 12

in Eq. (2.24) shows that the open-circuit input impedance to coil 1 is

(2.27)

If the terminals of coil 2 are closed, then V

0 and Eq. (2.26) shows that the

short-circuit input impedance to coil 1 is

(2.28)

By substituting the expressions dening the z if from Eqs. (2.22) and (2.23) into -

Eq. (2.28), the reader can show that the apparent reactance of coil 1 is reduced

by the presence of closed coil 2. In Chap. 3 a similar result is found for the

synchronous machine under short-circuit conditions.