The voltage ratings and voltage ratios of the transformers should be the same.
Transformers should be properly connected with regard to their polarities.
The per unit or percentage impedance of the transformers should be equal.
The reactance/resistance ratios of the transformers should be the same.
Same Voltage Rating and Voltage Ratio
The voltage ratios of two transformers must be same but why?
The reason is simple if voltage ratio of two transformers is different and they put in parallel with same primary supply voltage, there will be a difference in secondary voltages. As secondaries of transformers complete a closed loop there will be circulating currents.In this case, the considerable amount of current is drawn by the transformers even without load.As the internal impedance of the transformer is small, a small voltage difference may cause sufficiently high circulating current causing unnecessary extra I²R loss.
Circulating Currents=IC= (EA-EB)/ZA+ZB
Connections with regard to Polarity
The polarity of all connected transformers must be same in order to avoid short circuit.The polarity of a transformer taken w.r.t dot notation.Dots of all transformers connected together on primary and secondary separately. If the polarity is opposite to each other, huge circulating current flows.In the below diagram right and wrong parallel operation connections are shown take a look.
The phase sequence must be identical for all parallel transformers.
This condition is can be applied only to poly-phase transformers. If the phase sequences are not same, then transformers cannot be connected in parallel.During the cycle, each pair of phases will be short-circuited.
Equal Percentage Impedance
The per unit (PU) impedance of each transformer on its own base must be same.This condition is also desirable for proper parallel operation of single phase transformers. If this condition is not met, the transformers will not share the load according to their kVA ratings.
Sometimes this condition is not fulfilled by the design of the transformers. In that case, it can be corrected by inserting proper amount of resistance or reactance or both in series with either primary or secondary circuits of the transformers where the impedance is below the value required to fulfill this condition.That is why per unit impedance of the connected transformers must be same.