Many transformers used in power systems have three windings per phase, the third winding being known as the tertiary. This winding is provided to enable compensation equipment to be connected at an economic voltage (e.g. 13 kV) and to provide a
Figure 3.33 Typical phase shifts in a power system-British
circulating current path for third harmonics so that these currents do not appear outside the transformer.
The three-winding transformer can be represented under balanced three phase conditions by a single-phase equivalent circuit of three impedances star-connected as shown in Figure 3.34. The values of the equivalent impedances Zp, Zs and Zt may be obtained by test. It is assumed that the no-load currents are negligible.
Zps = impedance of the primary when the secondary is short-circuited and the tertiary open
Zpt = impedance of the primary when the tertiary is short-circuited and the secondary open
Figure 3.34 (a) Three-winding transformer (b) and (c) equivalent circuits
Zst = impedance of the secondary when the tertiary is short-circuited and the primary open
The above impedances are in ohms referred to the same voltage base. Hence,
It should be noted that the star point st in Figure 3.34b is purely fictitious and that the diagram is a single-phase equivalent circuit. In most large transformers the value of Zs is very small and can be negative. All impedances must be referred to common volt-ampere and voltage bases. The complete equivalent circuit is shown in Figure 3.34(c) where T12 and T13 provide any off nominal turns ratio.