Evaluation of a buried power cable's thermal behavior using phase diagrams and calculation of the phase difference between temperature and power

• A dynamic thermal analysis of an underground power cable.
• Calculation of the increase in the cable's temperature over one year period.
• Presentation of the Temperature–Power phase diagrams for various time periods.
• Calculation of the phase difference between power and temperature.

As most of the studies about thermal behavior of cables perform the steady state thermal analysis, a dynamic analysis of these problems can be proved very interesting. In the current study, a dynamic thermal analysis of an underground cable which operates under a continuously changing load and thus continuously changing Joule losses is carried out. With the Joule losses as the input signal it is proved that the thermal time constants in the range up to several hours are possible. It is also observed that the dynamic analysis, presented in this work, indicates an increase on the peak value of the cable's temperature that can reach up to 81%. This increase proves the importance of a dynamic analysis. Furthermore, the comparison between the steady state and dynamic analysis resulted in the conclusion that it is practically impossible to achieve steady state condition for power losses other than the mean value, thus steady state analysis cannot determine the instantaneous temperature of the cable. The analysis is based on the Temperature–Power (T–P) phase diagrams which are proved to be a more suitable representation method of the results comparing to the Temperature–Time plots. Lastly, the phase difference between the power and the temperature vectors is calculated.