How can you determine the transformer constants referred to the low voltage side if only one set of high voltage measurement is taken?

The process to determine the transformer constants referred to the low voltage side if only one set of high voltage measurement is taken , is to short circuit the low voltage side. Then the watt meter W, a voltage V and an ammeter A are connected in the high voltage side i.e. primary winding. A low voltage usually 5% to 10% of the rated supply voltage is applied to the primary and is continuously increase till full load current will flow both in primary and secondary winding.

     As 5% of rated voltage is necessary to overcome the impedance which is the only limiting component  of current flow through each winding. The impedance is formed by the resistance and reactance of two windings.

     Now the total impedance of the transformer is given by Z_T=V₁/I₁. Where V1 is the applied voltage and I1 is the rated current. Since flux is directly proportional to voltage, the mutual flux in the transformer under the short circuit test is very small. So,the iron or core losses can be neglected and the would exist only copper losses that can be measured by the watt meter placed in primary winding. Hence equivalent resistance is given by R_T=W/I²_{1 .}

Now, equivalent reactance of the transformer is given by X_T² =  Z²_T-R²_T