Thermal analysis of power cables in soils of temperature-responsive thermal resistivity

Abstract

SynopsisConventional procedures for calculating current ratings of buried cables involve the concept of an ideal soil of uniform thermal resistivity. Having regard to the fact that actual soils can, as a result of cable heat generation causing migration of ground moisture, display local increases in thermal resistivity, it is shown that rating calculations can readily be made in relation to alternative idealised coils having various thermalresistivity/temperature characteristics. List of symbolsSo far as is practicable, the symbols are those conventionally employed in the calculation of cable current ratings. 1 A, B = constants d, D = distances from a cable and the thermal image thereof E -as defined in eqn. 19 / = ratio g,Jg n f = ratio g h lg ns f" = ratio gjg, ;w F,(/) = W, for a given cable F 2 (/) = 6 C -6 S , for a given cable F(Q) = 8b for a given soil F(8 S ) = equivalent cable surface temperature for a given soil (eqns. 48 and 50) g = soil thermal resistivity First subscripts h = dried-out soil m -mixed soil n = undried soil Second subscripts s = summer value w = winter value g$ = soil thermal resistivity at temperature d G n -self-heating coefficient G ln = mutual-heating coefficient G = external thermal resistance (particular) with subscripts as for g, but capitals G e = external thermal resistance (general) G' = internal thermal resistance G sb = thermal resistance of over-sheath cable components ('serving' and 'bedding') / = conductor current l m = conductor current at maximum rating / = axial depth of a cable log = see eqn. 1 and footnote thereto n -number of conductors in a cable r = outer radius of a cable R = radius of a dried-out zone or a.c. resistance per unit length of a conductor at maximum operating temperature (depending on context) v/> ^o -hypothetical radii of dried-out zones around middle and outer cables of a flat 3-cable group 1 R S RE = equivalent resistance per unit length of sheath and reinforcement (conventionally expressed as A/?) 5 = cable centre spacing 5 = a constant T= temperature, degC 6 = relative temperature (7" -T G ) First subscripts to T and 9 B = at dry-zone boundary C = of conductor carrying /," G = of ground surface N = within ground of resistivity g n S = of cable surface Second subscripts S = summer value U = in undried ground W = winter value z = at the z isothermal (eqn. 40) W -heat emission from one cable, W/cm Subscripts S = summer value M =. in soil of mixed resistivity TV = in soil of uniform resistivity x, y = co-ordinates of a point in the ground z = isothermal-identifying variable

Natural and forced-cooling of HV underground cables: UK practice

“…Where moisture migration occurs in the region of the cables, assumption (b) is not true, but the resultant increase in thermal resistance can be accounted for by methods derived by Cox [25] or Schmill [102]. The use of stabilised backfill materials, having dried out TRs similar to those of the indigenous soils, has simplified winter rating calculations but still leaves the problem of summer ratings.…”