# Validation of calculation method for deeply buried objects

Based on the example of a deeply buried tunnel, the effect of the deep burial thermal inertia advanced option on the cable ampacity is illustrated and validated.

Posted 2021-05-03
Categories: Validation

The calculation of temperatures of deep tunnels as well as deeply buried cables/ducts/pipes involves special considerations regarding their thermal inertia. In Cableizer, by default, deep burial thermal inertia is not considered. But in our buried and tunnel modules, the deep burial thermal inertia method can be activated in order to use an equivalent depth based on the IEEE transactions on power delivery paper 'Ampacity Calculation for Deeply Installed Cables' by E. Dorison, G.J. Anders, and F. Lesur, dated 2010.

After selecting the deep burial thermal inertia method, you can also adjust the expected life time $\tau_L$ of your cable system. As shown above, $\tau_L$ = 40 years was selected as in the publication by Dorison et.al, which is a typical value for the expected life time of XLPE cables.

### Validation

The following figure shows the installation of six cable systems of three 15 kV XLPE cables each in trefoil in a tunnel buried at a depth of 18 m (left: Cableizer, right: Reference). More details about the cables, the ambient conditions, and the tunnel installation can be found in section VII. Effect on Cable Ampacity in the publication by Dorison et.al.

Calculation results using the 'Heinhold' method in Cableizer show a good agreement with the published results of the external thermal resistance of the tunnel $T_e$, while the calculated ampacity $I_c$ generally was lower than in the publication by Dorison et.al. The resulting increase in rating is almost the same. Unfortunately, the publication does not in detail describe how the ampacities were calculated but all given parameters in the paper - including the cable thermal resistances $T_1$ and $T_3$ - were identical to the ones resulting from our calculation. The equivalent depth $L_{deep}$ is 15 m in both cases.

Calculation method$T_e$ Cableizer / Reference$I_c$ Cableizer / Reference
Without deep burial thermal inertia0.655 K.m/W0.655 K.m/W231.9 A258.0 A
With deep burial thermal inertia0.608 K.m/W0.607 K.m/W240.3 A267.0 A
Rating increase+3.62%+3.49%

The above simulations have been added to our comprehensive test suit in order to assure that future developments will not change our simulation results in an unexpectant and unnoticed way.

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