TRANSFORMER DESIGN

The Performance Advantages of Circular Windings

Staying at the leading edge of technology in the transformer industry requires a complete understanding of the major advantages of circular windings over rectangular windings. To develop a proper evaluation of why circular windings are better than rectangular windings, Virginia Transformer Corpor-ation has examined the nature of forces generated in windings and how each of these two types of windings copes with these forces. Circular windings can be a major asset to transformer owners when they are developing specifications for transformers above 5000 KVA. The following simplistic explanation can help to educate transformer purchasers as to the advantages.

Under the short circuit, the rectangular coil design transformer will undergo substantial geometry changes in the coil shape leading to coil/insulation damage because it wants to become circular. The impedance change is up to 7.5 per cent. The circular coil on the other hand remains circular, the natural shape and suffers no change in geometry and impedance.

How Forces are Generated in Transformer Windings
When the windings of transformer carry current, a leakage flux field is produced between the concentric windings (i.e. high voltage and low voltage windings). The principal component of the leakage flux is axial.

The current carried by the winding conductors (circumferential direction) interact with the leakage flux and produces forces.

Radial Forces
The nature of the leakage flux is such that it is mostly in the axial direction (except in the ends of the windings) and hence the maximum radial force occurs around the mid-height of the coils. Radial forces act outward on the outer winding and inward on the inner winding (Fig 2).

Axial Forces
Near the ends of the windings, a large part of the leakage flux bends towards the core leg and thereby causes a radial component of the flux. The interaction of this radial component of flux with the winding current produces axial forces that tend to compress (or telescope) the winding conductors along the vertical axis.

In short, there are both radial forces and axial forces generated in a transformer winding.

Short-Circuit Conditions Result in Very Large Forces
During the short circuit condition, large amount of currents flow through the windings. The forces generated in a transformer subject to short circuit conditions are magnified many times more compared to those under normal operating conditions.

For example, a transformer with 6 percent of leakage impedance will carry 16 times the rated current during short circuit and this will result in forces more than 250 times those under normal operating conditions. Also, the peak forces are much higher than the RMS forces. As an example, the radial forces in a 10 MVA transformer can exceed 100,000 lbs.

Circular Windings remain Circular under Short-Circuit -- No Change in the Geometry
In circular coils any radial forces tend to be distributed uniformly along the circumference of the coil. In circular windings the radial forces are resisted by the strength of the winding conductors, and in some cases the low-voltage winding tubes. The axial forces are resisted by the stiffness of the radial spacers and the beam strength of the conductors.

In circular coils the forces are limited to that particular phase coil and are borne by the coil itself, which is suitably designed to withstand the forces on its own strength. There is no change in the performance of the coils. The impedance changes during short circuit test is typically 1 per cent or less.

Rectangular Windings Try to Become Circular
The forces generated in the rectangular coil transformers are very similar to those in circular coil transformers. The radial forces tend to separate the inner winding from the outer winding. The inner winding tries to crush inwards. The outer winding tries to arch or bow away from the flat surfaces of the inner winding and the high-low gap.

Under radial forces, the rectangular windings tend to become circular (see Fig 4). This results in substantial change in geometry and the impedance.

For rectangular coils, the radial forces tend to concentrate at the corners of the coil and cause greater stresses in those regions.

By restraining the outer winding (mechanically) from moving, the forces on the inner winding greatly increased. If the inner winding happens to be a sheet winding, it tries to get displaced towards the corners.

The phase-to-phase gaps between rectangular coils are sometimes packed to restrain movement of coils in that area. Unfortunately, under such arrangement, the forces generated by one coil are passed on to the adjacent phase coil and hence the forces are compounded. The insulation may be damaged (coil failure) due to the mechanical restraint on windings/coils.

Change in High-Low Gap in Rectangular Winding
The short circuit forces in the rectangular windings tend to separate the windings and consequently increase the high-low gap. This increase results in variation of impedance. The standards allow 7ohm per cent variation of impedance after the short circuit test. In other words, a transformer will be deemed 'passed' if the variation is within 7ohm per cent.

In this section we shall show that the actual change in the high-low gap is nearly 20 per cent when the overall change is 7ohm per cent.

The ends (front and back) of rectangular windings are somewhat oval in shape and can be expected to undergo lesser change than the flat sides. For this analysis we have assumed 3 percent change in the ends. Also, of the total length of the high-low gap about 60 per cent is on the flat side and 40 per cent is on the ends.

Let us assume that the high-low gap was 'G' before the short circuit test.

Overall change = change in the ends + change in the flat sides (say 'X').

G * 1.075 =(40% of 'G') * 1.03 + (60 % of 'G') * 'X'

Or, 1.075 G = 0.412 G + 0.6 G * X

Solving for 'X', we get:

X = 1.105 (i.e. 10.5% change in High-Low gap).

Further, Figure 5 shows the nature of the deformation of high-low gap which is like an arch, and the highest reflection occurs in the center. Using trigonometry, it can be seen that the deformation in the center of the arch is nearly twice as much as the average change.

In other words, the percentage change in the high-low gap would be as much as 20 per cent (even though the average change may be within 7 ohm per cent).

Summary
Rectangular designs may be fine for distribution applications typically less than 5000 KVA. Ratings above 5000 KVA should be circular.

Rectangular windings tend to become circular under radial forces. This results in conductor movement, risk of failure and change in performance.

If the outer coils of a rectangular winding are re-strained from moving, the forces on the inner winding are greatly increased, thereby increasing the risk of conductor movements.

References

1. J & P Transformer Book, 11th Edition.
2. IEEE Std C 57.12. 90- 1993, Part II, Guide for Short-Circuit Testing of Distribution and Power Transformers.
3. IEEE Guide C 57.12.125 -1991, Guide for Failure Investigation, documentation and Analysis for Power Transformers and Shunt Reactors. (presently out of circulation).