الخميس، 3 فبراير، 2011

Parallel Operation of Transformers

 Parallel Operation of Transformers

For supplying a load in excess of the rating of an existing transformer, two or more transformers may be connected in parallel with the existing transformer. It is usually economical to install another transformer in parallel instead of replacing the existing transformer by a single larger unit. The cost of a spare unit in the case of two parallel transformers (of equal rating) is also lower than that of a single large transformer. In addition, it is preferable to have a parallel transformer for the reason of reliability. With this, at least half the load can be supplied with one transformer out of service. For parallel connection of transformers, primary windings of the
transformers are connected to source bus-bars and secondary windings are connected to the load bus-bars. There are various conditions that must be fulfilled for the successful parallel operation of transformers. These are as follows:
1. The line voltage ratios of the transformers must be equal (on each tap): If the transformers connected in parallel have slightly different voltage ratios, then due to the inequality of induced emfs in the secondary windings, a circulating current will flow in the loop formed by the secondary windings under the no-load condition, which may be much greater than the normal no-load current. The current will be quite high as the leakage impedance is low. When the secondary windings are loaded, this circulating current will tend to produce unequal loading on the two transformers, and it may not be possible to take the full load from this group of two parallel transformers (one of the transformers may get overloaded).
2. The transformers should have equal per-unit leakage impedances and the same ratio of equivalent leakage reactance to the equivalent resistance (X/R): If the ratings of both the transformers are equal, their per-unit leakage impedances should be equal in order to have equal loading of both the transformers. If the ratings are unequal, their per-unit leakage impedances based on their own ratings should be equal so that the currents carried by them will be proportional to their ratings. In other words, for unequal ratings, the numerical (ohmic) values of their impedances should be in inverse proportion to their ratings to have current in them in line with their ratings. A difference in the ratio of the reactance value to resistance value of the perunit impedance results in a different phase angle of the currents carried by the two paralleled transformers; one transformer will be working with a higher power factor and the other with a lower power factor than that of the combined output. Hence, the real power will not be proportionally shared by the transformers. 
3. The transformers should have the same polarity: The transformers should be properly connected with regard to their polarity. If they are connected with incorrect polarities then the two emfs, induced in the secondary windings which are in parallel, will act together in the local secondary circuit and produce a short
circuit.

The previous three conditions are applicable to both single-phase as well as threephase transformers. In addition to these three conditions, two more conditions are essential for the parallel operation of three-phase transformers:
4. The transformers should have the same phase sequence: The phase sequence of line voltages of both the transformers must be identical for parallel operation of three-phase transformers. If the phase sequence is an incorrect, in every cycle each pair of phases will get short-circuited.
5. The transformers should have the zero relative phase displacement between the secondary line voltages: The transformer windings can be connected in a variety of ways which produce different magnitudes and phase displacements of the secondary voltage. All the transformer connections can be classified into distinct vector groups. Each vector group notation consists of first an uppercase letter denoting HV connection, a second lowercase letter denoting LV connection, followed by a clock number representing LV winding’s phase displacement with respect to HV winding (at 12 o’clock). There are four groups into which all possible three-phase connections can be classified:
Group 1: Zero phase displacement (Yy0, Dd0, Dz0)
Group 2:180° phase displacement (Yy6, Dd6, Dz6)
Group 3: -30° phase displacement (Yd1, Dy1, Yz1)
Group 4: +30° phase displacement (Yd11, Dy11, Yz11)

In above notations, letters y (or Y), d (or D) and z represent star, delta and zigzag connections respectively. In order to have zero relative phase displacement of secondary side line voltages, the transformers belonging to the same group can be paralleled. For example, two transformers with Yd1 and Dy1 connections can be paralleled. The transformers of groups 1 and 2 can only be paralleled with transformers of their own group. However, the transformers of groups 3 and 4 can be paralleled by reversing the phase sequence of one of them. For example, a transformer with Yd1 1 connection (group 4) can be paralleled with that having Dy1 connection (group 3) by reversing the phase sequence of both primary and secondary terminals of the Dy1 transformer.

References
1. Say, M.G. The performance and design of alternating current machines, 2nd edition, Sir Isaac Pitman and Sons, London, 1955.
2. Toro, V.D. Principles of electrical engineering, 2nd edition, Prentice Hall, New Delhi, 1977.
3. Stevenson, W.D. Elements of power system analysis, 4th edition, McGraw- Hill, Tokyo, 1982, pp. 138–162.
4. MIT Press, Magnetic circuits and transformers, 14th edition, John Wiley and Sons, New York, 1962, pp. 259–406.

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