Parallel Operation of Single Phase Transformers


     In the last article, we have seen the reasons and conditions for the parallel operation of two or more transformers. Now let us see the parallel operation of single-phase transformers and how the load is shared among them.


Load Sharing by Two Transformers :


     Let us consider two transformers A and B are connected in parallel to the supply bus ( primary ) and load bus ( secondary ) as shown below. Similarly, two or more transformers can be connected in parallel depending upon the increase in load demand.

Parallel Operation of Single Phase Transformers

Let us summarize the conditions for satisfactory parallel operation of single-phase transformers,
  • The transformers should be suitable for the supply system voltage and frequency.
  • The polarity of the transformer should be ensured that properly connected.
  • Transformation or turn ratios of the transformers should be same.
  • The percentage ( per-unit ) impedance of the transformers should be same.
  • The transformer's ratios of resistance to reactance should be same.



     For satisfactory parallel operation, the transformers must meet the above conditions. Otherwise, under the no-load condition, the localized circulating current will be produced due to unequal induced EMFs in the secondaries to equalize the voltage in each transformer. Thus when the two transformers have loaded this results in an unequal share of the load with respect to their full kVA output and cause another transformer to overload. The equivalent circuit of the two transformers with unequal induced EMFs is shown below.

Parallel Operation of Single Phase Transformers

     However, it is difficult in practice to build such identical transformers. In order to reduce the circulating current, the difference between the voltage ratios of the transformers should least as possible. This is possible when the difference between the magnetizing current of the transformers is very small.

The circulating current will cause undesirable effects like,
  • The full kVA output of the transformers cannot be utilized to a full extent.
  • It overloads one transformer from the parallel connected group.
  • The copper losses in the transformers windings increases.


With Equal Voltage Ratio :

     When two transformers operating in parallel having equal voltage ratios ( i.e., EA = EB = E ), the total load current will be divided between them inversely as their equivalent impedance. Since the voltage ratios are the same if we neglect magnetizing currents of two transformers the equivalent circuit referred to as secondary is represented as shown below.

Parallel Operation of Single Phase Transformers

Let,
  • ZA & ZB = Impedances of the transformers A and B respectively.
  • IA & IB = Currents supplied to the load from transformers A and B respectively.
  • V2 = Common terminal load voltage.
  • I = Combined load current
  • V1 = Common supply input voltage.



From the above circuit, the voltage equation may be written as,

Parallel Operation of Single Phase Transformers

Where ZAB = combined impedance of ZA and ZB. Since both are in parallel the equivalent impedance is given by,

Parallel Operation of Single Phase Transformers

From equation (1), IA is given by,

Parallel Operation of Single Phase Transformers

Substituting the value of ZAB from equation (2) in equation (3),

Parallel Operation of Single Phase Transformers

Similarly, IB is given by,

Parallel Operation of Single Phase Transformers

Multiplying on both sides by V2 × 10-3 we have,

Parallel Operation of Single Phase Transformers


Let,
  • Q = V2 I × 10-3 = The combined load kVA
  • Q = V2 IA × 10-3 = kVA carried by transformer A
  • Q = V2 IB × 10-3 = kVA carried by transformer B

Parallel Operation of Single Phase Transformers

     If the ratios of resistance to reactance are not equal the power factors of the transformers A and B will be different and the expression for kVA supplied will remain the same. Hence, there must be an inverse relationship between the kVA carried and the impedance of the transformer to share the load to its full kVA output without overloading.

Parallel Operation of Single Phase Transformers

The phasor diagram of the transformers operating in parallel with their quantities is shown below.

Parallel Operation of Single Phase Transformers

Also check out - Necessity and conditions for parallel operation of transformers


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