Figure 5 - Expected life for thermally upgraded paper and its dependence upon moisture, oxygen and temperature

NOTE 2 Figure 4 and Figure 5 indicate expected life values that are based on residual DP value of 200, and that are derived under the laboratory controlled condition as given in text above, (e.g. constant moisture content, constant and homogenous temperature, etc.). However, to evaluate the expected life of a transformer the real service conditions are considered (e.g. loading history and prediction, ambient temperature, insulation material and insulation moisture contamination). The moisture contamination estimate is usually based on the corresponding equilibrium curves for moisture partition between oil and paper, (e.g. WCO vs WCP or RH vs WCP).

### Relative ageing rate

Although ageing or deterioration of insulation is a time function of temperature, moisture content, oxygen content and acid content, the model presented in this document is based only on the insulation temperature as the controlling parameter.

An example of how all ageing parameters can be taken into account is given in Annex A.

Since the temperature distribution is not uniform, the part that is operating at the highest temperature will normally undergo the greatest deterioration. Therefore, the rate of ageing is referred to the winding hot-spot temperature. In this case, the relative ageing rate \(V\) is defined according to Equation (2) for non-thermally upgraded paper and to Equation (3) for thermally upgraded paper (see [27]).

\[V=2^{\left(\theta_{\mathrm{h}}-98\right)/6} \tag{2}\]

\[V=e^{\left(\frac{15~{}000}{110~{}273}-\frac{15~{}000}{\theta_{\mathrm{h}}+273} \right)} \tag{3}\]