Calculating the transformer winding inductance at minimum temperature involves considering the temperature coefficient of the winding material and using it to adjust the inductance value at a known reference temperature. Here are the steps to calculate the transformer winding inductance at minimum temperature:
Determine the inductance at a reference temperature: The first step is to determine the inductance of the winding at a known reference temperature. This could be the room temperature (usually around 25°C or 77°F) or any other temperature at which you have the inductance value available.
Obtain the temperature coefficient: The temperature coefficient is a measure of how much the inductance changes per degree Celsius (or per degree Fahrenheit) change in temperature. It is usually denoted by the symbol "α" and is given in units of percent per degree Celsius (%/°C) or percent per degree Fahrenheit (%/°F).
Determine the change in temperature: Calculate the temperature difference between the reference temperature and the minimum temperature. This will give you the change in temperature (ΔT) that you need to consider for the inductance adjustment.
Adjust the inductance using the temperature coefficient: Use the temperature coefficient (α) to adjust the inductance value from the reference temperature to the minimum temperature. The formula for adjusting the inductance is as follows:
Inductance at Minimum Temperature = Inductance at Reference Temperature × (1 + α × ΔT)
Where:
Inductance at Minimum Temperature is the desired inductance value at the minimum temperature.
Inductance at Reference Temperature is the known inductance value at the reference temperature.
α is the temperature coefficient (in %/°C or %/°F).
ΔT is the change in temperature (in °C or °F) between the minimum temperature and the reference temperature.
Calculate the final winding inductance: Use the adjusted inductance value to get the final winding inductance at the minimum temperature.
It's important to note that the temperature coefficient may not be linear across the entire temperature range, so this calculation provides an approximate value for the inductance at the minimum temperature based on the assumption of a linear relationship. Additionally, the accuracy of this calculation depends on the accuracy of the temperature coefficient and the assumption of a linear relationship between inductance and temperature.