A mathematical model to measure instantaneous moisture content in transformer insulation cellulose

Solid transformer insulation is mainly composed of cellulosic materials, in the form of pressboard, Kraft paper and wood. Oil is used to impregnate voids in the cellulose. The water content of cellulose usually increases over the life of the transformer, caused by both moisture ingress and the gradual degradation of cellulose, which produces moisture as an aging by-product. Equilibrium curves are used to estimate the moisture content of cellulosic insulation using the vapor pressure of water dissolved in the oil. However, a very long duration is required for water to attain this equilibrium partition, much longer than the usual daily cyclic temperature profile of a transformer, and thus it is very unlikely for the insulation to reach this state. In this paper a novel method to estimate the moisture in cellulose during non-equilibrium conditions is presented. The water adsorbed by the cellulose migrates in and out the oil, and the diffusivity depends on the temperature and the concentration of moisture in the cellulosic insulation. This diffusion is mainly governed by Fick's law. For a transformer, the change in moisture content of oil in a small duration is mainly due to the moisture content in the cellulosic insulation. This paper presents a method to estimate the moisture content of cellulosic insulation of the transformer at that instant from the change in the moisture content of the oil.