Effects of environment on transient thermal performance of underground cables

Abstract

Two forms of cable installation are considered, direct burial and integral cooling. Existing methods for the calculation of transient temperatures in directly buried underground cables with changes in load assume a homogeneous environment of soil. In the present work, the effects of trench backfills of different thermal resistivities from the existing soil are investigated using a numerical method and a computer. The relative effects of the backfill and the soil on the transient temperatures are discussed. For times of up to 100 h after the application of a step function of the load current, the effective thermal resistivity of the cable environment approximates to that of the backfill. Using this value, established analytical techniques to represent the soil may be applied with reasonable accuracy. For times greater than this, the soil becomes increasingly important, and the full 2-dimensional heatflow approach is necessary. Temperatures in integrally cooled cables are readily calculable, but if, owing to a fault in the cooling system, the water flow ceases, new thermal models must be developed to facilitate the calculation of the subsequent cable-temperature rises. By means of practical experimentation, an approximate but simple representation for this condition, using a thermal network, is obtained, and is used in conjunction with the cable thermal network to compute conductor temperatures. LIST OF SYMBOLSC = thermal capacity, J/deg C d = cable spacing, mm g s = thermal resistivity of soil, deg C m/W gjj = thermal resistivity of backfill, deg C cm/W 1 = depth of cables, m K = thermal conductivity, W m/deg C K' = thermal conductance, W/deg C q = heat flow, W t = time At = time interval 9 = temperature rise above ambient, deg C d' = temperature after time interval At, °C a = diffusivity, m 2 / s Cp = specific heat, J / k g deg C p = density, k g / m 3 Subscripts s soil/cable interface surface Subscripts n any node INTRODUCTIONExisting methods for the computation of the transient temp e r a t u r e s in underground cables resulting from controlled load changes have been summarised by Goldenberg. 1 In highcapacity cable circuits at the higher transmission voltages, the cable environment is no longer a homogeneous media consisting of soil, but comprises the partial filling of the trench with selected backfill or the u s e of water-cooling pipes of various types. The precise analysis of cable t e m p e r a t u r e s in such environments is much more complex, and recourse must be made to appropriate numerical methods and a computer for a solution.Important temperature changes occur in artificial-cooling schemes when the coolant flow ceases owing to a failure. F o r these schemes, and for the selected backfill installation, the accurate prediction of temperature changes in the cables is important, and, for this to be achieved, the effects of environmental changes must be known and adequately represented in calculation. A study of the steady-state effect of such changes has been previously reported. 2 I=N, r V 2 . 1