(Solved): Four single-phase transformers are operating in parallel. KVA rating-wise, all of them are iden ...

Four single-phase transformers are operating in parallel. KVA rating-wise, all of
them are identical. However, their series impedances and turn ratios are not equal.
The detail of the transformers is given below. Find out the circulating current flow-
ing through each of the transformers during No load conditions. If a resistive load
of 1 pu is connected to the end, what changes would you observe in the circulating
current? Explain your observation.

1. Four single-phase transformers are operating in parallel. KVA rating-wise, all of them are identical. However, their series impedances and turn ratios are not equal. The detail of the transformers is given below. Find out the circulating current flowing through each of the transformers during No load conditions. If a resistive load of \\( 1 \\mathrm{pu} \\) is connected to the end, what changes would you observe in the circulating current? Explain your observation. 1 Hint: Use the generalized formula to find out the current expression for an arbitrary member (transformer \\( \\mathrm{m} \\) ) of the parallel operating transformers family, comprising \\( \\mathrm{n} \\) transformer. \\[ \\begin{array}{l} I_{m}=\\frac{I_{L}}{z_{m} \\sum_{k=1}^{n} Y_{k}}+\\frac{V_{s} \\sum_{k=1}^{n}\\left(\\frac{Y_{k}}{a_{m}}-\\frac{Y_{k}}{a_{k}}\\right)}{z_{m} \\sum_{k=1}^{n} Y_{k}}, V_{L}=\\frac{V_{s} \\sum_{k=1}^{n} Y_{K}}{Y_{L}+\\sum_{k=1}^{n} Y_{k}} \\text {, and } \\\\ I_{L}=V_{L} \\dot{Y}_{L} \\end{array} \\] In the above expression of \\( I_{m} \\), the first term of the right-hand side denotes the load component of the current flowing through transformer \\( \\mathrm{m} \\). The second term comprising \\( V_{s} \\) indicates the circulating current. For equal turns ratio, the circulating current will become zero. \\( V_{s} \\) : Source Voltage, \\( I_{L} \\) :Load Current, \\( Y_{L} \\) : Load impedance, \\( Z_{m}=\\left(Y_{m}\\right)^{-1} \\) :impedance of the \\( m^{\\text {th }} \\) transformer, \\( a_{k} \\) : turns ratio of the \\( k^{\\text {th }} \\) transformer.