**9.10, Transformer Tests**. The performance of a transformer can be calculated on the basis of its equivalent circuit which contains the following four main parameters:

- i. Equivalent resistance R
_{01}, as referred to primary (or secondary R_{02}). *ii.*Equivalent leakage resistance X_{01}as referred to primary (or secondary X_{02}).*iii.*Core loss conductance G_{0}(or resistance*R*_{0}*).**iv.*Magnetising susceptance*B*(or reactance_{0}*X*_{0}).

Theses parameters or constants can be determined by the following two tests:

- Open-circuit or no-load test.
- Short-circuit or impedance test.

The above two tests are *convenient to perform and very economical because they furnish **the required information **without actually loading the transformer. *

**9.10.1**** Open-circuit or no-load test (O.C. Test).** An open-circuit or no-load testis conducted to find:

- i. No-load loss or core loss.
- ii. No-load current I
_{0}which is helpful in finding*R*_{0}_{0}.

The connections for this test are made as shown in Fig. 38. One winding of the transformer* (usually high voltage winding) *is *left open *and the other is connected to its supply of *normal **voltage **and frequency. *Ammeter *A *and wattmeter *Ware *connected to measure *no-load current *(I_{0})* and **no-load input power (P*_{0}*) *respectively.

Fig. 38. Circuit diagram for open-circuit test.

As the primary no-load current *I _{0} *(as measured by ammeter) is small (usually 3 to 10% of rated load current) copper loss is negligibly small in primary (L.T. winding) and nil in secondary winding (it being open). Hence the

*wattmeter reading represents practically the core-loss under*

*no-load conditions*(and

*this loss is same for all loads).*

From the data available from this test *R _{0}, *X

*. cos ɸ*

_{0}*(no-load power factor),*

_{0}*I*can bet calculated as follows:

_{w}and I_{m}Now, Iron loss = P_{i} = input power on no-load

No-load current = P_{0} watts (say)

No-load current = I_{0}

Applied primary voltage = V_{1}

Also P_{0} = V_{1}I_{0} cos ɸ_{0} (where cos ɸ_{0} = no load power factor)

**Separation of core losses**. The core loss is made up of the following two parts:

- i. Eddy current loss.
- ii. Hysteresis loss.

Eddy current loss, *P _{e} *=

*AB*max

^{2}*f*where

^{2},*A*is constant.

Hysteresis loss* P _{h} *=

*BB*where

^{1.6}_{max}f^{2}.*B*is constant.

Total loss *= P _{e} *+

*P*=

_{h}*AB*

^{2}_{max}

*f*+

^{2}*BB*

^{1.6 }_{max}f.The values of constants *A *and *B *can be found out by conducting two experiments using- two different frequencies but the same maximum flux density; thereafter eddy current and hysteresis loss can be found separately.

**9.10.2. Short-circuit or impedance test (S.C. Test).** This test is conducted to determine the following:

- i. Full-load copper loss.
*ii.*Equivalent resistance and reactance*referred to metering side.*

In this test (Fig. 39) the terminals of the secondary winding *(usually low voltage winding) are *short-circuited by a thick conductor or through an ammeter which may serve the additional purpose of indicating rated load current. A low voltage, usually 5 to 10% of normal primary voltage, at correct frequency is applied to the primary and *is continuously increased till **full-load **currents flow in the primary as well as secondary windings *(as indicated by the respective ammeters).

*Since applied voltage is very **low low so flux linking with the core is very small and therefore, iron losses are so small that these can be neglected, the reading of the wattmeter gives total copper losses at full-load.*

Fig. 39. Short-circuit test.

The equivalent circuit of the transformer under short-circuit condition is shown in Fig. 40

Fig. 40. Equivalent circuit of transformer under short-circuit condition.

*V _{SC} = *voltage required to circulate rated load currents

*I _{1} *= reading of the ammeter on the primary side

*Z _{01} *= total impedance as referred to primary side

*R _{01} *= total resistance as referred to primary side

*X _{01} *= total reactance as referred to primary side.

Then, equivalent impedance as referred to primary side,

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