Water activity is the amount of water in a substance relative to the total amount of water it can hold. It is the ratio of the vapor pressure of water in a substance divided by the vapor pressure above pure water.
Pv: Vapour/partial pressure of water in oil
P0: Vapour/partial pressure above pure water
WCO: Water content of Oil
S: Solubility of oil to water
T: Temperature. All of these parameters must be at the same temperature at equilibrium.
In these calculations, P0 refers to the saturation point of water in oil. If Pv = P0 then the oil can be considered fully saturated with water. Any additional moisture added to the oil will form free water which will sink to the bottom of the transformer.
Water activity is equal to equilibrium relative humidity divided by 100.
This results in a unitless value between 0 and 1, with 1 being fully saturated oil. For example, a water activity of 0.5 would equate to a relative humidity of water in oil at equilibrium of 50%.
[1] Saha, Tapan Kumar, and Purkait, Prithwiraj. Transformer Ageing: Monitoring and Estimation Techniques: Monitoring and Estimation Techniques. 1st ed., Wiley, 2017.
[2] Martin, D, et al. “Improving the Determination of Water Content of Power Transformer Insulation Paper near the End of Its Functional Life.” 2016 Australasian Universities Power Engineering Conference (AUPEC), 2016, pp. 1–6.
