Stacking factor and window space factor

Stacking factor

The core is built of thin laminations insulated from each other by varnish or oxide. Some of the gross cross-section is therefore insulation, not iron.

$$\text{Stacking factor } K_i = \frac{\text{net iron area } A_i}{\text{gross core area } A_{gi}}$$

Typical value is about 0.9 (0.88–0.92), depending on lamination thickness and insulation coating. Thinner laminations give a lower stacking factor.

Window space factor

The window holds conductors plus their insulation, the insulation between layers and windings, ducts and clearances.

$$\text{Window space factor } K_w = \frac{\text{copper area in window}}{\text{total window area } A_w}$$

Selecting $K_w$ for different ratings

$K_w$ depends mainly on voltage rating and output. Empirical formulas (Sawhney) for the HV voltage in kV:

Example: an 11 kV, 100 kVA transformer has $K_w = 8/(30 + 11) = 0.195$. $K_w$ is roughly 0.1–0.4 for most transformers.

Larger units use bigger conductors (strips), so the insulation is a smaller fraction of the area and $K_w$ rises with kVA for the same voltage.

Why higher voltage transformers have lower $K_w$

• Insulation thickness on conductors, between layers, between LV and HV, and to the yoke must increase with voltage.
• Larger clearances and oil ducts are needed to withstand impulse and test voltages.
• HV windings carry small currents, so conductors are thin; the insulation covering forms a large fraction of each conductor's area.

So a larger part of the window is occupied by insulation and space, and the copper fraction ($K_w$) falls, as the formula $K_w \propto 1/(30 + kV)$ shows.