__External Characteristics of a Transformer __

Consider the performance of a transformer for several values of the complex load impedance * Z_{2}* =

*z*

_{2}∠ φ

_{2 }If the primary voltage is constant and equal to its rated value,

*V*

_{1}=

*V*

_{1.rtd},variations in the complex load impedance will bring about changes in the primary and secondary currents

*İ*and

_{1}*İ*

_{2}and in the secondary voltage

*V̇*

_{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}* = (

*w*

_{1}/

*w*

_{2})

*V*

_{2 }. The no-load secondary voltage is practically equal to

*V*

_{1},

_{rtd}Therefore, we may write

*V*

_{1},

_{rtd}-

*V*'

_{2}. Ordinarily, the voltage regulation of a transformer is expressed as a percentage of the rated primary voltage

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

*V*_{1},_{rtd }-_{ }*V' _{2 }*≈ (

*r*

_{sc}cos φ

_{2 }+

_{sc}sin φ

_{2 })

*I*

_{1}or, by Eq. (8.20),

Δ*V*%_{ }= ( *I*_{1} /_{ }*V _{1,rtd}*) (

*r*

_{sc}cos φ

_{2 }+

_{sc}sin φ

_{2 })

*X 100%*(8.21).

_{ }A plot of voltage regulation as a function of the load power factor, cos φ_{2} , for *I*_{1} = const, is drawn up in Fig.18 a . The voltage regulation is a maximum when cos φ_{2 }= cos φ_{sc }, in which case the internal voltage drop phasor __Z___{sc}*I*_{1}* *is in the same direction as the primary voltage phasor VI (see Fig.17 b). In consequence,

*V*'_{2} = *V*_{1} - *Z*_{sc}*I*_{l}

By plotting variations in the secondary voltage *V*_{2} as a function of the load current *I*_{2} 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

of a transformer is constructed on a per-unit basis, that is, in terms of the ratio of the secondary voltage to its rated value, *V*_{2}._{rtd} = *n*_{21}*V*_{1},_{rtd} in the open-circuit condition, and its load current ratio

*k _{load}*

_{ }=

*I*

_{2}/

*I*

_{2.rtd }(8.22)

where *I*_{2}._{rtd} = *I*_{1}._{rtd} /*n*_{21} is the load current at the rated primary current *I*_{1} = *I*_{1}._{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

*V*_{2}/*n*_{21}*V*_{l. rtd }= (1- Δ*V* %/100) = 1-*k*_{load} (*I*_{1. rtd}/V_{1. rtd})

X (*r*_{sc} cos φ_{2} + _{sc} sin φ_{2})

For φ_{2 }> 0, the external characteristic is shown in Fig. 18 b.