Rasika: The "normal" moisture content is going to be a function of how the insulation (plain Kraft paper, thermally upgraded paper, oil-impregnated paper, etc.) and whether the transformer is air-cooled or oil-filled. It will also depend on the age of the transformer - generally, a "plain" paper insulation will release moisture as it ages and a "thermally upgraded paper" will absorb moisture. The difference to the total amount of moisture in the transformer is minimal - it's more a matter of where the moisture ends up (in the insulation or intermixed with the oil).
A new power transformer is expected to have a water content in paper insulation (WCP) of less than 0.5% by weight. It is filled with mineral oil processed to have less than 10 mg/kg of water in accordance with IEEE C57.106. To put this information in perspective, a new transformer with 5000 kg of paper insulation and 20 000 kg of oil would have less than 25 kg of water in the paper and would be filled with oil containing less than 200 g of water.
It is highly desirable to keep WCP below one percent, but since water is a by-product of aging-related deterioration of paper and oil, the insulation in a transformer gradually becomes more moist. Over two or three decades, normal aging can increase the water content of the paper insulation to notebook paper’s natural moisture level of about 4–5%. If there is a leaky gasket or seal or if there is a breather with depleted desiccant, the transformer can breathe in humid air, greatly accelerating the accumulation of water in the oil/paper system. Actually, since the bottom of the transformer is normally cooler than the top, the paper insulation at the bottom of the windings becomes wetter than at the top. At or before the 4% level of WCP, a well-cared-for transformer may be subjected to a dry-out.
Converting energy to motion for more than half a century