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54 Power systems engineering ± fundamental concepts

Fig. 2.23 Wye±delta transformation.

current in each phase tends to become distorted, and the triplen harmonics are
allowed to flow locally in a delta-connected winding without entering the external
circuit. In electric motors a delta winding permits the use of a larger number of turns
of smaller-gauge wire, because the phase voltage is increased while the phase current
is decreased, compared with the wye connection.

2.9.2 The wye±delta transformation

A wye-connected load can be represented by a virtual load connected in delta, and
vice-versa, Figure 2.23. To transform the delta connection into a wye connection,

Z AB Z CA Z BC Z AB Z CA Z BC
Z A ˆ ; Z B ˆ ; Z C ˆ (2:27)
Z Z Z
where Z ˆ Z AB ‡ Z BC ‡ Z CA . To transform the wye connection into a delta con-
nection,

Y A Y B Y B Y C Y C Y A
Y AB ˆ ; Y BC ˆ ; Y CA ˆ (2:28)
Y Y Y Y Y Y

where Y Y ˆ Y A ‡ Y B ‡ Y C

2.9.3 Balancing an unbalanced load

It can be shown by means of a series of diagrams, that an unbalanced linear
ungrounded three-phase load can be transformed into a balanced, real three-phase
load without changing the power exchange between source and load, by connecting
an ideal reactive compensating networkin parallel with it. Assume that the load is
delta-connected with admittances Y ab ˆ G ab ‡ jB ab , Y bc ˆ G bc ‡ jB bc , Y ca ˆ G ca ‡
jB ca , as shown in Figure 2.24.
The power factor of each phase can be corrected to unity by connecting compen-
sating admittances in parallel, as shown, where jB gab ˆ jB ab ,jB gbc ˆ jB bc , and
jB gca ˆ jB ca . The resulting networkis real, Figure 2.25.