Influence of soil-moisture migration on power rating of cables in h.v. transmission systems

Arman, A.N.; Cherry, D.M.; Gosland, L.; Hollingsworth, Pierce

doi:10.1049/piee.1964.0159

Cited by 26 publications

(4 citation statements)

References 2 publications

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“…Of these factors, moisture content is particularly important, small decreases in moisture content leading to significant increases in thermal resistivity. 1 This has to be taken into account in designing cable systems to carry sustained loads during summer to minimise the dangers related to the drying out of the surrounding soil. The problem is usually solved by the use of 'stabilised backfills' having an acceptable thermal resistivity in the dried-out state; these are placed in the immediate vicinity of the cables.…”

Section: Statement Of the Problemmentioning

confidence: 99%

Calculation of the external thermal resistance of buried cables through conformal transformation

Luoni

Morello

Holdup³

1972

Proc. Inst. Electr. Eng. UK

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The calculation of the outside thermal resistance of a buried cable system related to uniform, nonuniform and temperature-dependent resistivity of soil can be made, if a suitable transformation of the thermal field is automatically drawn and the resistance is computed on the transformed field. A suitable conformal transformation is analysed-giving rise to maps of the transformed field. On the maps, the calculation of resistances involves simple operations even when the soil is nonuniform and of temperature-dependent resistivity, provided some approximations are introduced. The errors incurred by such approximations are slight and can be checked, when necessary, by direct computation of the thermal field. The calculation of resistances on the maps can also be carried out by means of automatic design programs. LIST OF SYMBOLSc = cable circumference D = cable diameter g = thermal resistivity hj = constant proportional to power loss of source i = general numerical suffix kj, l n j = lengths read on transformed maps m ' = number of source pairs p = vertical distance of cable centre from x axis q = horizontal distance of cable centre from y axis R = thermal resistance r = modulus of co-ordinate z Ru R 3 = thermal resistance for lateral cables R 2 = thermal resistance for centre cable 5 = position of cable centre (q -jp) T = temperature T c = isotherm at which soil resistivity changes (normally 50°C) T Q = ambient temperature Ti = cable surface temperature W = cable power loss Y o = earth surface in transformed plane Yj_ = cable surface in transformed plane z = complex co-ordinate (x + jy) in original plane Z = complex co-ordinate (X + jY) in transformed plane zj, zi = co-ordinates of point sources in original plane 6 = displacement of point source 6 = argument of co-ordinate z

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Section: Statement Of the Problemmentioning

confidence: 99%

Calculation of the external thermal resistance of buried cables through conformal transformation

Luoni

Morello

Holdup³

1972

Proc. Inst. Electr. Eng. UK

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“…The effect of these rating reductions on the capital investment required for transmission was clear, and so emphasised the importance of evolving practical installation methods aimed at achieving maximum current ratings [22]. Three alternatives were considered as possible solutions to the problem:…”

Section: Results Of Field Testsmentioning

confidence: 99%

“…Work conducted in the USA, and some of the earlier findings of the ERA field tests, indicated that an improvement to the cable environment could be achieved by the use of a 'thermal sand' with a distributed range of particle sizes [21,22]. Further work in the UK by the cable manufacturers resulted in the standardisation of the special backfill materials defined in Reference 29.…”

Section: Selected and Stabilised Backfill Materialsmentioning

confidence: 99%

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

Williams

1982

IEE Proc. A Phys. Sci. Meas. Instrum. Manage. Educ. Rev. UK

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The paper reviews the progress of the various forms of cable cooling systems that have been developed for the UK CEGB's major high-voltage transmission network. The generation and transmission system in the UK prior to the establishment of the 132kV grid is discussed, together with the reasons for building the higher-voltage network. The statutory duties of the CEGB and its transmission responsibilities are outlined, special reference being made to the undergrounding of part of the network for amenity reasons. The investigations of soil properties, their effect on cable ratings and the subsequent adoption of standardised thermal resistivity and temperature values are considered, together with the development of special backfill materials. The different types of forced cooling system are discussed: separate water-pipe, trough and weir, air, integrally and internally cooled methods being covered comprehensively. Rating limitations caused by cable joints, and the methods used to overcome them, are included. Cooling stations and the plant and control equipment installed therein are described, reference being made to the different sources of coolant, e.g. air, borehole water, river or lake water etc. A brief description of the computer methods of solving the complex equations derived for forced cooling installations, using thermal image, finite difference, finite element and analytical techniques, is given. The Appendix comprises three Tables, giving the essential design details of naturally cooled, separate-pipe water-cooled and tunnel systems installed on the CEGB's transmission system.

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“…* • For instance, for the centre cable of a group of three buried in open flat formation Using a relative scale of Celsius steps (degC R ) so that 0°C R corresponds to ground surface temperature T G°C , 6 SU can be subdivided into two components, namely OSU=(0SU-OB) + OB (2) the components representing, respectively, the temperature differences within and external to the 9 B isothermal, as in Fig. la.…”

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confidence: 99%

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

Cox¹,

Coates

1965

Proc. Inst. Electr. Eng. UK

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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

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Influence of soil-moisture migration on power rating of cables in h.v. transmission systems

Cited by 26 publications

References 2 publications

Calculation of the external thermal resistance of buried cables through conformal transformation

Calculation of the external thermal resistance of buried cables through conformal transformation

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

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

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