Richard Huber, P. Eng.
Richard Huber Engineering, Ltd.
North Vancouver, British Columbia
Canada
Technical Services Committee Member

Introduction
There are many transformers in use rated up to 10 MVA (10,000 kVA) that were originally wound using aluminum conductors. When dam­aged or when selected for rewind, the aluminum conductor is often replaced with copper conductor. This is usu­ally fairly routine when the conductor changes are undertaken within the bounds of the original transformer design. It is this type of change that will be reviewed in this article. It is not the intent to provide information here for the complete redesign of the transformer. It is important that all coil dimensions remain as close to the originals as possible.

In carrying out the type of change outlined above, there are some design issues and differences in material prop­erties that must be considered before proceeding with the work. Some of these issues are:

• The effect that the difference in thermal characteristics of the materials will have on short term overload capability.  
• The effect that the different mate­rial properties will have on the original blocking and bracing system.
• The effect that the difference in conductivity will have on con­ductor size.
• The effect that the difference in conductor size may have on coil resistance and reactance.
• The effect that the different conductor size may have on coil size (axial length) and hence its ability to withstand short circuits

Material characteristics
An aluminum alloy frequently used for magnet wire applications is 1350-O (E-Al 99.5–O). A common copper alloy used for magnet wire is C11000–O (CW004A–O), where the letter “O” indicates for both aluminum and copper that the material is fully annealed. Selected electrical, physical and mechanical characteristics of both aluminum and copper are shown in Table 1.

Thermal characteristics
An examination of the differences in the thermal characteristics of aluminum and copper shows that a coil made from copper can absorb more energy for a given temperature rise than a coil made from aluminum. This means that a copper coil can withstand higher short circuit currents or the same short circuit current for a longer period of time than an equivalent aluminum coil.

Physical characteristics
The thermal coefficient of linear expansion is lower for copper than for aluminum. So on large coils, provisions for expansion need not be as great for copper. Alternatively, any expansion provisions incorporated in the origi­nal design for aluminum will be more than adequate for copper. The density of copper is 3.3 times greater than alu­minum. Coils made from copper will consequently be heavier than similar coils made from aluminum. Even with about 61% of the conductor area of aluminum, a copper equivalent con­ductor will be about twice the weight of the original aluminum. Additional or stronger supports or blocking may be required for the copper coil.

Mechanical characteristics
Since the mechanical characteristics for copper all exceed those of alumi­num, a copper coil is able to better withstand all mechanical operating stresses. This assumes that the ratio of conductor width to depth is the same or similar and that the coils are blocked and supported in manner similar to the original.

The last point is important. When copper replaces aluminum, the wind­ing on the new coils may be shorter than the originals. If there is a signifi­cant difference between heights of the old and the new coils, the short circuit forces increase. The style of blocking may have to be changed to ensure that the coils are able to withstand the expected increase in short circuit forces. The leakage reactance will also increase as the coils become shorter. However, as part of any conductor material change every effort should be made to ensure that the coil is the same height as the original.

Material conductivity
As shown in Table 1, the differences in electrical con­ductivity or resistivity allow an aluminum conductor to be replaced by a copper conductor where the cross section is 61% of the aluminum conductor. Obvi­ously, the copper conductor will then require less space for the same number of turns. The effect this change in conductor size has on coil diameter (and mean length per turn) and coil height has to be considered. These two factors can impact the resistance and reactance of the coils.

Transformer impedance
Before doing a detailed re­view of the impact of conductor size on resistance and reactance, one should first consider the overall relationship between imped­ance, resistance and reactance. 

The impedance (Z) is usually shown on the nameplate as a percent­age value. It has two components, resistance (R) and reactance (X) which define the impedance according to the complex relationship Z = R + jX (where j = √-1). The X/R ratio can be used to establish the relative magnitudes of the two components.

In the transformer size range out­lined above, the X/R ratio can vary from approximately 5 to 25 with the smaller transformers having a ratio closer to 5 and the larger ones a ratio nearer to 25.

The resistance and re­actance can both be affected by coil geometry and the impact the resistance or reactance changes have on the trans­former impedance will be determined by the X/R ratio. One must therefore carefully consider any changes that will affect the coil geometry.

One should also be aware that the relevant standards specify a manu­facturing tolerance on the impedance of +/- 7.5% of the specified value. Some transformers exceed this value and one should consult the relevant standards listed at the end of this article to confirm the appropriate tolerance for the transformer under consideration.

Coil diameter versus resistance
Now consider how coil diameter and resistance may be affected by a change from aluminum to copper. The resistance of a transformer coil is de­termined by the conductor resistivity, the cross sectional dimensions of the conductor and the conductor length. As mentioned in the Material Conduc­tivity section of Part 1, the resistivity (or conductivity) of copper will allow the cross section to be reduced if the total length of the conductor remains the same as the original.  

For a simple layer wound cylindri­cal coil, the conductor length is deter­mined by the mean length per turn (MLT) multiplied by the number of turns. When changing from aluminum to a copper conductor, the MLT and  the conductor length may be affected by the choice of conductor dimensions.  

There are two extreme situations that can occur when selecting the dimensions of the copper conductor. For a copper conductor wound on a coil, if the di­mension of the conductor in the radial direction is the same as the aluminum one, the dimension in the axial direc­tion will be smaller than the aluminum one. Alternatively, if the dimension of the copper conductor in the axial direction is the same as the alu­minum conductor, the dimension in the radial direction will be smaller.

If the dimension of the copper con­ductor in the radial direction is selected to be the same as the original aluminum conductor, then the MLT will be un­changed. However, this selection will require a reduction in the dimension of the conductor in the axial direction to achieve the desired cross section. In this extreme case, the reduction of the dimen­sion in the axial direction may require additional space between turns or coils to ensure the height of the coil or wind­ing is exactly the same as the original. In a layer winding, this additional space can be provided by winding a suitable insulating cord adjacent to the conductor.

Now consider the case where the dimension of the copper conductor in the axial direction is the same as the original aluminum conductor. This means that the dimension in the ra­dial direction will have to be reduced to provide the correct cross section. Reducing the dimension in the radial direction will effectively reduce the MLT of the coil.

Let’s consider an example to il­lustrate the above case. Assume a three phase transformer, 13.8 kV – 600 volts, Y- ∆, 2 MVA, X/R = 5.75 (see Part 1), with layer wound cylindrical coils for the HV (high voltage) and LV (low voltage) windings. The original aluminum conductor on the HV coil was 4 mm x 7 mm, where 4 mm is the dimension in the radial direction. 

Referring to Figure 1, assume the inner diameter of the HV coil (D₁) is 350 mm and the outer diameter (D₂=D₁+2 x b2) is 390 mm. There are 4 layers on the HV coil and each is sepa­rated by a 10 mm duct spacer. The re­placement copper conductor has these dimensions: 2.4 mm x 7 mm. Note that the 2.4 mm dimension is approximate­ly 61% of 4 mm, resulting in a copper conductor with the same conductivity as the original aluminum conductor. As stated above, the dimension in the axial direction is 7mm, the same as the original aluminum conductor. If the inner diameter of the coil remains the same, the MLT₂ will be:

MLT₂ = π (D₁ + b2) where b2 = the radial dimension of the new coil
b2 = 4 x 2.4 mm + 3 x 10 mm = 39.6 mm
MLT₂ = π (350 + 39.6) =  1224 mm

The original MLT₁ was:
MLT₁ = π (350 + (4 x 4 + 3 x 10)) = 1244 mm

To ensure that the conductor length and the MLT remains the same, the in­ner diameter of the coil would have to be increased to the value D3 as shown in the rearranged formulas below:

1244 = π (D₃ + 39.6)
D₃ = (1244 – π 39.6)/π  = 356 mm

This means that the inner diam­eter of the HV coil would be increased by 6 mm (356 – 350) which would increase the spacing between the HV and LV coils. A cor­responding increase in the reactance of the transformer would occur. In order to determine whether the proposed increase is acceptable, one should look at how the reactance is determined from the coil geometry.

Transformer reactance
Transformer leakage reactance (X) is determined to a large extent by the coil dimensions and the spacing between the HV and LV windings. For layer wound cylindrical coils, this relationship can be described by the equation:

The w/3 term refers to the dimen­sion shown in Figure 1 in mm.
N = turns
I = current 
V = voltage

As part of the example cited in the Coil Diameter Versus Resistance sec­tion above, assume a layered LV wind­ing that has two layers separated by cooling ducts results in a “b1” dimen­sion of 12 mm. Assume that the original dimension “a” was 20 mm. From the Coil Diameter Versus Resistance sec­tion, the original aluminum conductor produced a “b2” dimension of 46 mm. Using the above equation for %X, the value of the bracketed term based on the original aluminum conductor is:

If the dimension “a” is increased by 3 mm to 23 mm as suggested in the Coil Diameter Versus Resistance section above, the reactance will also increase. The value of the bracketed term with the proposed increase in HV diameter and the 2.4 mm x 7 mm copper is:

The reactance will increase propor­tionally by approximately 2.3% of the original value.
If the inner diameter of the HV coil remains the same when the copper is used in place of the aluminum, the value of the bracketed term is:

This results in a decrease in reac­tance of approximately 5.3%.  

To summarize, the original alumi­num conductor resulted in a value of 39.6 for the bracketed term. Increasing the inside diameter of the HV coil as suggested in the Coil Diameter Versus Resistance section to keep the MLT of the copper conductor the same as the original resulted in a value of 40.2 for the bracketed term.  

Finally, if the inside diameter of the HV coil remains unchanged, the value of the bracketed term is 37.2. In both cases, the impedance change resulting from the change to a copper conductor was less than the allowed +/- 7.5%. In this example no change in coil diameter is required to meet this requirement. This is often the case but the result of course should be verified by calculation to ensure the replacement of the alumi­num conductor is carried out correctly.

One often has to take an iterative approach to arrive at a suitable solution to ensure the MLT and the conductor length remains the same as the original. In addition, impedance changes must be minimized. The “windability” of the chosen conductor size must also be considered. That is, the conductor dimensions must afford sufficient strength to allow the coils to be wound with adequate tension. Alternatively, the dimensions should not be so large as to require unusually high tension to wind the coil.

There are advantages and disad­vantages to the changes in impedance. Decreasing the impedance increases the inrush current and increases the short circuit current. Thus, the risk of mechanical damage to the transformer increases. However, decreasing the impedance causes the regulation of the transformer to increase.

The preceding analysis has been greatly simplified for illustrative purposes. Much more sophisticated algorithms can be used to arrive at an optimum solution. In addition, the impedance calculation for transform­ers with other coil configurations other  than that used for this example will require different geometric factors in the impedance formula. These factors can be calculated from first principles or some examples can be found in the literature.

Categories: Transformers, Wire

Tags: Wire Transformers

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