The probabilistic rating of separate-pipe cooled underground cables

To protect cable insulation, a temperature limit needs to be imposed on cables during operation. Since heat generation is mainly current dependent, this limit translates into a current limit which represents the current rating of the system. Due to the uncertainty regarding the values of thermal parameters during operation, design values used to calculate ratings are chosen on a `worst condition' basis. However, while thermal parameters may reach design values during operation, they are very unlikely to all attain these values at the same time. Cables are therefore unlikely to reach temperature limits during normal operation and so can carry higher than rated currents. Thus, if cables are to be utilized effectively, parameter variations have to be taken into account when calculating current ratings. This can be achieved with the probabilistic method. A 400kV separate-pipe cooled cable system has been considered in this study. To obtain the probabilistic rating of the system, the Monte Carlo simulation method with random parameter values drawn from parameter distribution curves is used to obtain the probability density function of conductor temperature during operation. The probabilistic rating of the cable is then obtained from these curves. If cables are under-utilized the simulation is repeated for increased currents until a current is obtained which ensures proper utilization subject to temperature limits. The effect on the probabilistic rating of variations in water flow rates and inlet water temperatures are also studied. Various methods can be used for the thermal analysis of the cable system. Of these, the finite element method most accurately represents the complex geometry and varying material properties associated with underground cable systems and so has been used in the study. However, to reduce the substantial computer resources required by this method, coefficients (obtained from finite element analyses and representing the sensitivity of conductor temperature to parameter variations) are used to calculate conductor temperatures for small parameter variations. Parameter ranges for which sensitivity coefficients can be used accurately depend on the cable system and the particular parameter considered and have been obtained for the various parameters for the system under study. The system considered is conventionally rated at 2038A in Winter and 1792A in Summer. A probabilistic analysis (for the months of December and July) confirms that temperature limits are not reached during operation and that current increases of up to 20% (representing increases in power of up to 280MVA in December and 248MVA in July) are possible without exceeding temperature limits. With increases between 20% and 30%, limits are exceeded but can be controlled by adjusting water flow rates and inlet temperatures. For increases above 30%, adjustments to water flow rates and inlet temperatures might not be economically justified.