The transformer winding reactance at no-load can be calculated using the following formula:
Reactance = (2 * π * f * L) / K
Where:
π (pi) is a constant approximately equal to 3.14159
f is the frequency of the power supply in Hertz (Hz)
L is the inductance of the winding in Henrys (H)
K is a constant typically used to adjust the reactance calculation depending on the transformer's construction. For a two-winding transformer, K is equal to 1. For a three-winding transformer, K is equal to √3 (approximately 1.732).
The inductance of the winding (L) depends on the transformer's physical dimensions, such as the number of turns, the cross-sectional area of the winding, and the magnetic properties of the core material. The inductance can be calculated using more complex formulas, finite element analysis (FEA), or measured experimentally.
For a simpler estimation of the winding reactance at no-load, you can use empirical formulas that take into account the transformer's physical parameters. One such formula for single-phase transformers is as follows:
Reactance ≈ (2 * π * f * N * N * A * 10^-8) / K
Where:
N is the number of turns in the winding
A is the cross-sectional area of the winding in square centimeters (cm²)
It's important to note that this estimation might not be as accurate as a detailed analysis, but it can provide a rough idea of the winding reactance at no-load. For more precise results, you should consider the actual physical parameters and possibly perform FEA or measurements on the transformer. Additionally, for three-phase transformers, the calculation becomes more complex due to the phase relationships and magnetic interactions between windings. In such cases, it's best to rely on detailed transformer design data or consult with transformer experts.