Page 107 - Electric Machinery Fundamentals

TRANSFORMERS 83

FIGURE 2- 12
The core-loss current in a tnlnsfonner.

( The other component of the no-load current in the transfonner is the current
required to supply power to make up the hysteresis and eddy current losses in the
core. This is the core-loss current. Assume that the flux in the core is sinusoidal.
Since the eddy currents in the core are proportional to dc/>Idt, the eddy currents are
largest when the flux in the core is passing through 0 Wb. Therefore, the core-loss
current is greatest as the flux passes through zero. The total current required to
make up for core losses is shown in Figure 2- 12.
Notice the following points about the core-loss current:

1. The core-loss current is nonlinear because of the nonlinear effects of hysteresis.
2. The fundamental component of the core-loss current is in phase with the volt-
age applied to the core.
The total no-load CUlTcn t in the core is called the excitation. current of the
transformer. It is just the sum of the magnetization current and the core-loss cur-
rent in the core:

(2-30)
The total excitation CLUTent in a typical transformer core is shown in Figure 2-13.
In a well-designed power transformer, the excitation current is much smaller than
the full-load current of the transformer.

The Cnrrent Ratio on a Transformer and the
Dot Convention
Now suppose that a load is connected to the secondary of the transformer. The re-
sulting circuit is shown in Figure 2-14. Notice the dots on the windings of the trans-
former. As in the ideal transformer previously described, the dots help determine the
polarity of the voltages and currents in the core without having to physically exam-
ine its windings. The physical significance of the dot convention is that a current
flowing into the dotted end of a winding produces a positive magnetomotiveforce?:F,