Calculating the transformer winding capacitance at maximum load current involves considering the winding geometry, dielectric material properties, and the maximum load current magnitude. The capacitance of a transformer winding can be modeled as a lumped capacitance between the winding turns, taking into account the inter-turn insulation, the winding configuration, and the dielectric constant of the insulating material.
The capacitance of a transformer winding can be approximated using the following formula:
C = (ε * A) / d
Where:
C is the capacitance of the winding (in farads),
ε is the permittivity (dielectric constant) of the insulating material,
A is the cross-sectional area of the winding (in square meters),
d is the effective distance between the windings (in meters).
To calculate the cross-sectional area of the winding (A), you need to know the dimensions of the winding conductor. If the conductor is rectangular, A = width * height; if the conductor is round, A = π * (radius^2).
The effective distance between the windings (d) is the sum of the insulating material thickness between the winding turns and any additional layers that separate the windings.
When it comes to selecting the permittivity value (ε), it depends on the type of insulating material used between the winding turns. For example, common materials such as paper, oil-impregnated paper, or polyester film have known dielectric constants that can be used in the calculation.
Once you have the capacitance value (C), you can use it to analyze the capacitive reactance (Xc) at the frequency of the load current (usually 50Hz or 60Hz for power systems):
Xc = 1 / (2 * π * f * C)
Where:
Xc is the capacitive reactance (in ohms),
π is Pi (approximately 3.14159),
f is the frequency of the load current (in Hz).
The capacitive reactance represents the opposition to the flow of alternating current due to the capacitance. At maximum load current, the capacitive reactance will have the most impact.
Keep in mind that the above calculation assumes ideal conditions, and in practice, there might be additional factors and complexities to consider, such as non-uniform winding geometry, proximity to other conductive parts, and the presence of additional capacitances in the transformer. Therefore, it's always best to consult detailed transformer design documentation or work with a professional electrical engineer for precise and accurate calculations.