The conditions that must be followed for satisfactory parallel operation of transformers are as follows :

1) The supply system voltage and frequency must suit the primary windings of the transformers.

2) The transformers that are connected must have same polarity. In case of three phase transformers the transformers should have same angular displacement and phase same sequence.

3) The voltage ratios of primaries and secondaries of the transformers must be same.

4) The percentage impedances should be equal in magnitude and have same X/R ratio in order to avoid circulating currents and operating at different power factors.

5) If the transformers have the different KVA ratings, the equivalent impedances should be inversely proportional to individual KVA rating to avoid circulating currents.

__1.1 Explanation of conditions__

The condition (1) can be easily satisfied.

The condition (2) is an important condition for the faithful parallel operation of transformers. The secondary windings of the two transformers which are connected in parallel are either in phase with each other having zero degree phase displacement between the voltages or the voltages are in opposite time-phase relationship with a phase difference of between them. A closed series circuit is formed by this parallel connection.

If two voltages are having same phase relationship, the induced voltages from either common connection to the other are in the same direction. Thus there is no current flow in the series circuit. Thus the parallel operation works satisfactory with no load connected. The windings so connected will have same polarity.

If the two voltages are in phase opposition, the induced voltages from either common connection to the other are in opposite directions, hence adding to one another in the series circuit. Thus a large current will flow in the series circuit which is equivalent to a short circuit on both transformers. The two windings will have opposite polarity and parallel operation will not work properly.

This polarity designation should not be confused with the terms additive polarity and subtractive polarity as applied to individual units which are used only to give the relative directions of induced voltages and are helpful in proper paralleling of the transformers.

If the lead marking is not available while marking parallel connection then it is suggested that the two leads located in similar positions with respect to the bank is connected together and a fuse of low current rating is inserted between remaining leads. with windings having similar polarity the voltage across the fuse will be zero and no current will flow. If the windings arr of opposite polarity the voltage across the fuse will be twice the voltage of either winding. Thus short circuit current will flow and fuse will blow out. This in this case the connections are to be interchanged for reliable parallel operation.

For parallel operation of three phase transformers having same voltage ratio, polarity may be not required to be considered. For satisfactory operation, the angular displacement and phase rotation between the two units to be paralleled must be the same. Paralleling of three phase transformers is simplified by standardizing the lead markings and various three phase connections have been placed in three different groups depending upon their angular displacement. The advantage of this is that it is not required to test for polarity, angular displacement and phase rotation.

If condition (3) i.e. voltage ratios of primaries and secondaries of the transformers must be same is not satisfied the difference in voltage between the windings will cause a current to flow in the circuit at all time. This circulating current will be limited only by the sum of the impedances of the two transformers. Though this condition is not perfectly met still parallel operation is possible at the cost of the circulating current. When load is connected across the secondaries this circulating current in local circuit with produce unequal loading condition.

where % I

_{c }= Percentage circulating current in % of normal load current of one transformer. % e = Percentage of normal voltage indicating difference in voltage between the two windings.

% I Z

_{1 }= Percentage impedance of transformers 1. % I Z

_{2 }= Percentage impedance of transformer 2. In the above formula it is assumed that the capacity of both the units as the same.

**Key Point**: With different capacities, the percent impedances in the formula should be based upon the same KVA rating and the percent circulating current is then percent of normal load current at this same KVA rating.

If there is small difference between the ratios of transformers connected in parallel then it will produce relatively large circulating current.

**Key Point**: For satisfactory parallel operation, the circulating current should be not exceed 10 percent of normal load current.

By making use of balance coil in case of single phase and three phase transformers with different voltage ratios parallel operation will be reliable.

With violence of condition (4) i.e. if the percentage impedancea are not equal in magnitude then also parallel operation is possible. Under this case the impedance triangles are not identical in shape and size. Also the two transformers will operate at different power factors from the power factor of the combined load. One transformer will operate at higher power factors and the other will operate at a lower power factor that of combined load. The effect of this will be that the two transformers will not share the load in proportion to their KVA ratings.

The ratios of resistance to reactance must also be same for each the transformers. So that the currents in each of the transformers are in phase. If these ratios are not same, the currents in the transformers are not on phase and the sum of the winding current will be greater than the line current.

If the percentage impedance of all the units connected in parallel is same then the load will divide in the individual units in the ratio of their capacities even if the error is introduced due to unequal ratio of resistance and reactance. The total permissible load will be equal to the sum of capacities of the individual units connected in parallel.

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