Saturday, January 26, 2013

External Characteristics of a Transformer

External Characteristics of a Transformer

Consider the performance of a transformer for several values of the complex load impedance Z2 = z2 ∠ φ2 If the primary voltage is constant and equal to its rated value, V1 = V1.rtd,variations in the complex load impedance will bring about changes in the primary and secondary currents 1 and 2 and in the secondary voltage 2 of the transformer.

The difference between the no-load and full-load secondary volt­ages expressed in terms of the former, with the primary voltage held constant, is called the voltage regulation of a transformer. To find it, it is usual to refer (transfer) the secondary voltage to the primary side. Then, V'2 = (w1/ w2) V2 . The no-load secondary voltage is practically equal to V1,rtd Therefore, we may write V1,rtd - V'2 . Ordinarily, the voltage regulation of a transformer is expressed as a percentage of the rated primary voltage

External Characteristics of a Transformer

From the simplified equivalent circuit diagram of a transfor­mer (see Fig. 17 a) and from its phasor diagram (see Fig. 17 b) it follows that

V1,rtd - V'2 ≈ (rsc cos φ2 + sc sin φ2 ) I1

or, by Eq. (8.20),

ΔV% = ( I1 / V1,rtd) (rsc cos φ2 + sc sin φ2 ) X 100% (8.21).

A plot of voltage regulation as a function of the load power fac­tor, cos φ2 , for I1 = const, is drawn up in Fig.18 a . The voltage regulation is a maximum when cos φ2 = cos φsc , in which case the internal voltage drop phasor ZscI1 is in the same direction as the primary voltage phasor VI (see Fig.17 b). In consequence,

V'2 = V1 - ZscIl

By plotting variations in the secondary voltage V2 as a function of the load current I2 for a constant load power factor and the rated primary voltage, we obtain what is known as the external characteristic of a transformer. As often as not, the external characteristic

External Characteristics of a Transformerof a transformer is constructed on a per-unit basis, that is, in terms of the ratio of the secondary voltage to its rated value, V2.rtd = n21V1,rtd in the open-circuit condition, and its load current ratio

kload = I2/I2.rtd (8.22)

where I2.rtd = I1.rtd /n21 is the load current at the rated primary current I1 = I1.rtd In view of Eqs. (8.20) and (8.21), the external characteristic of a transformer on a per-unit basis is defined by the following equation

V2/n21Vl. rtd = (1- ΔV %/100) = 1-kload (I1. rtd/V1. rtd)

                           X (rsc cos φ2 + sc sin φ2)

For φ2 > 0, the external characteristic is shown in Fig. 18 b.