# How to Calculate the Steady-state Temperature Field and Ampacity of Underground Cable System

Abstract: According to the principle that convection of ground surface and temperature of deep soil do not change, the open domain temperature field of underground is equivalent to close domain temperature field. The finite element method (FEM) is used to calculate the temperature field of underground cable system with given the load current. Loss in cable sheath is attributed to cable conductor by busing the thermal circuit method. The thin layers of cable are handled by harmonic mean method, and the cable is equivalent to two layers: conductor and outer sheath. The number of FEM nodes is reduced; the accuracy and rate of calculation is improved. The results of test and calculation show that the FEM is effective to calculate the temperature field and ampacity of underground cable system.

Key words:  Cable system, temperature field, finite element method, thermal circuit method, harmonic mean method, secant method, ampacity

Introduction

The calculation of underground cable ampacity was first studied by A.E.Kennelly in 1893 followed by Neher and McGrath. The IEC-60287 is based on their research. Based on Kennelly’s assumption, the thermal field of direct-buried cables meets the following requirements: ① the ground is isothermal surface; ② the surface of cable is isothermal surface; ③ the superposition principle is applicable. However, the actual temperature distribution does not conform to the assumption and calculation results of IEC-60287 tend to be conservative. As the cable is widely used in the field of power transmission and distribution, the precise measurement of ampacity is significant for improving the economy of cable lines. It is necessary to determine the temperature of cable conductor and environment if adjusting the cable load flexibly and dynamically according to the seasonal variation. The numerical calculation is to analyze the whole temperature field under given cable laying, permutation and load conditions. The temperatures of ground surface and cable surface are unknown variables. Hence, calculation results via numerical method are closer to the actual situation and the ampacity of cable is more accurate than the one by IEC-60287.