Iec 60853 3 2002

NORME INTERNATIONALE CEI IEC INTERNATIONAL STANDARD 60853 3 Première édition First edition 2002 02 Calcul des capacités de transport des câbles pour les régimes de charge cycliques et de surcharge de[.]

Description générale

This method extends the techniques outlined in IEC 60853-1 and IEC 60853-2 for calculating the cyclic transport capacity factors of a cable in homogeneous soil conditions.

La méthode repose sur la connaissance de la température critique du sol, à partir de laquelle l’assèchement du sol intervient rapidement.

NOTE En l’absence d’information plus précise, cette température peut être prise égale à 50 °C.

The size of the dry zone is significantly influenced by the critical temperature For a given core temperature, the size of the dry zone greatly affects the transport capacity under constant load conditions, while having minimal impact on the ratio of transport capacity between cyclic and steady-state conditions.

Assuming that the critical soil temperature is equal to the peak cyclic temperature at the cable surface, a dry zone is about to form, indicating that the soil surrounding the cable has uniform characteristics corresponding to its in-situ wet state The cyclic transport capacity factor under these conditions can be derived from the methods outlined in IEC 60853-1 or IEC 60853-2.

This factor is then adjusted to apply to the steady-state transport capacity corresponding to the same assumed value of the critical temperature when a dry area appears This adjustment is made using the formula that provides the external thermal resistance of the cable relevant for steady-state calculations.

A factor can be utilized to multiply the steady-state transport capacity for any given value of the soil's critical temperature, allowing for the determination of the permissible peak current.

Principes

In general, the size of the dried area when its boundary reaches a specific critical heating in cyclic conditions is smaller than the area that would form for the same critical heating value in steady-state conditions A particular case occurs when the cable surface heating is exactly equal to the critical heating, resulting in a dried area that only forms in steady-state conditions However, a cyclic transport capacity factor determined in this scenario is applicable to the transport capacity in steady-state conditions for any other critical heating value and dried area size.

An additional step is required to utilize a cyclic current-carrying capacity factor based on a critical temperature equal to the surface temperature of the cable The calculations outlined in IEC 60853-1 and IEC 60853-2 for determining cyclic current-carrying capacity factors assume that the external thermal resistance of the cable remains constant in both steady-state and cyclic conditions.

The correct value of the current at the peak of the charging cycle is achieved when the cyclic transport capacity factor multiplies the steady-state transport capacity relative to this resistance value.

The equality of external thermal resistance applies under the assumption of uniform non-migration conditions as outlined in IEC 60287-2-1, IEC 60853-1, and IEC 60853-2 However, this does not hold true when drying occurs The size of the dry zone, and consequently the thermal resistance of the cable, varies with the type of load In such cases, the factor must be adjusted to serve as a multiplicative factor for the transport capacity determined for the highest value of thermal resistance observed in steady-state conditions This adjustment can be achieved by using the ratio of the external thermal resistances to be considered.

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This method is an extension of the techniques used in IEC 60853-1 and IEC 60853-2 for calculating cyclic rating factors for a cable in uniform soil.

The method relies on a knowledge of the soil critical temperature; this is the temperature at which drying out of the soil takes place rapidly.

NOTE In the absence of more precise information, this temperature may be taken as 50 °C.

The dry zone's size varies significantly with critical temperature, impacting the steady-state rating of a conductor at a specific temperature However, the cyclic factor that adjusts this steady-state rating remains largely unchanged.

The initial assumption is that the soil's critical temperature matches the maximum cyclic temperature of the cable surface, indicating a potential dry zone Consequently, the soil surrounding the cable is considered to have uniform properties reflective of its wet, on-site condition The cyclic rating factor for these circumstances is determined using the methods outlined in IEC 60853-1.

The adjustment of this factor is made to align with the steady-state rating at the same critical temperature, which results in a dried-out zone This adjustment utilizes formulas for the cable's external thermal resistance that are suitable for the steady-state process.

Such a factor can then be used to multiply the steady-state rating for any other soil critical temperature in order to obtain the appropriate permissible peak current.

The dry zone created by cyclic loading is generally smaller than that formed under steady-state loading for the same critical temperature rise A specific scenario occurs when the cable surface temperature matches the soil's critical temperature, resulting in a dry zone that only develops with steady-state loading Notably, the rating factor established for this scenario can be applied to steady-state ratings involving any critical temperature rise and dry zone size.

To effectively utilize a cyclic factor, it is essential to establish a critical temperature that matches the cable surface temperature This step is crucial due to the specific computational methods employed in the analysis.

IEC 60853-1 and IEC 60853-2 are used to determine cyclic rating factors, which assume that the external thermal resistance of the cable remains constant for both cyclic and steady-state loading The accurate peak current value for the load cycle is achieved by multiplying the steady-state rating by the cyclic factor, considering this resistance.

The equality of external thermal resistance, as outlined in IEC 60287-2-1, IEC 60853-1, and IEC 60853-2, holds true under uniform non-migration conditions; however, this changes when drying occurs The size of the dry zone affects the cable's external thermal resistance, which varies with the type of loading Consequently, the rating factor must be adjusted to account for the increased external thermal resistance observed in steady-state conditions This adjustment can be achieved by applying the ratio of the relevant external thermal resistances.

Le calcul du facteur de capacité de transport cyclique pour toute valeur de la température critique est effectué comme suit:

– la réponse thermique du câble, prenant en compte l’effet de sa capacité thermique interne, est obtenue en utilisant les formules appropriées de 4.2.1, 4.2.2 et 4.2.3 de la CEI 60853-2;

– la réponse thermique du sol et l’effet des câbles adjacents dans un circuit (le cas échéant) sont obtenus à partir des formules des articles 5 à 7 de la CEI 60853-2;

– l’effet de l’assèchement est obtenu selon 4.3.2.

General description

This method is an extension of the techniques used in IEC 60853-1 and IEC 60853-2 for calculating cyclic rating factors for a cable in uniform soil.

The method relies on a knowledge of the soil critical temperature; this is the temperature at which drying out of the soil takes place rapidly.

NOTE In the absence of more precise information, this temperature may be taken as 50 °C.

The dry zone's size varies significantly with critical temperature, impacting the steady-state rating of a conductor at a specific temperature However, the cyclic factor that adjusts this steady-state rating remains largely unchanged.

The initial assumption is that the soil's critical temperature matches the maximum cyclic temperature of the cable surface, indicating a potential dry zone Consequently, the soil surrounding the cable is considered to have uniform properties reflective of its wet, on-site condition The cyclic rating factor for these circumstances is determined using the methods outlined in IEC 60853-1.

The factor is modified to align with the steady-state rating at the same critical temperature, which results in a dried-out zone This adjustment utilizes formulas for the cable's external thermal resistance relevant to the steady-state process.

Such a factor can then be used to multiply the steady-state rating for any other soil critical temperature in order to obtain the appropriate permissible peak current.

Principles

The dry zone created by cyclic loading is typically smaller than that formed under steady-state loading for the same critical temperature rise A specific scenario occurs when the cable surface temperature matches the soil's critical temperature, resulting in a dry zone that only develops with steady-state loading Notably, the rating factor established for this scenario can be applied to steady-state ratings involving any critical temperature rise and dry zone size.

To effectively utilize a cyclic factor that corresponds to a critical temperature matching the cable surface temperature, an additional step is required due to the computational methods employed.

IEC 60853-1 and IEC 60853-2 are used to determine cyclic rating factors, which assume that the external thermal resistance of the cable remains constant for both cyclic and steady-state loading The accurate peak current value for the load cycle is achieved by multiplying the steady-state rating by the cyclic factor, considering this resistance.

The equality of external thermal resistance, as outlined in IEC 60287-2-1, IEC 60853-1, and IEC 60853-2, holds true under uniform non-migration conditions; however, this changes when drying occurs The size of the dry zone affects the cable's external thermal resistance, which varies with the type of loading Consequently, the rating factor must be adjusted to account for the increased external thermal resistance observed in steady-state conditions This adjustment can be achieved by applying the ratio of the relevant external thermal resistances.

Le calcul du facteur de capacité de transport cyclique pour toute valeur de la température critique est effectué comme suit:

– la réponse thermique du câble, prenant en compte l’effet de sa capacité thermique interne, est obtenue en utilisant les formules appropriées de 4.2.1, 4.2.2 et 4.2.3 de la CEI 60853-2;

– la réponse thermique du sol et l’effet des câbles adjacents dans un circuit (le cas échéant) sont obtenus à partir des formules des articles 5 à 7 de la CEI 60853-2;

– l’effet de l’assèchement est obtenu selon 4.3.2.

L'article 5 de la CEI 60853-2 donne plusieurs expressions possibles pour le facteur de capacité de transport cyclique, mais la formule générale est celle-ci:

The warm-ups discussed here primarily refer to those caused solely by Joule losses, and the equations provided account for this A symbol followed by a value or a symbol in parentheses indicates a quantity that varies over time, while a prime (′) on a symbol denotes a quantity related only to Joule losses.

NOTE 2 Le terme représentant l’effet de l’image du câble est omis dans l’équation (5) parce que l’on ne considère que des durées inférieures à 6 h.

= + (7) ó λ est le coefficient de pertes dans les écrans métalliques et les armures; à est le facteur de charge des pertes du cycle considộrộ.

The computation of a cyclic rating factor, for any critical temperature, is effected as follows:

– the thermal response of the cable, including the effect of its internal thermal capacitance, is obtained by the use of appropriate formulae from 4.2.1, 4.2.2 and 4.2.3 of IEC 60853-2;

– the thermal response of the soil, and the effect of adjacent cables in a group (if any), are obtained by the use of formulae from clauses 5 to 7 of IEC 60853-2;

– the effect of drying out is obtained by the use of 4.3.2.

Formulae

There are optional formulae for a cyclic rating factor in clause 5 of IEC 60853-2 but the general one is as follows:

The temperature increases mentioned primarily result from joule losses, and the relevant equations incorporate this factor at the necessary stages A symbol accompanied by a value or in parentheses denotes a time-varying quantity, while a prime (′) over a symbol signifies a quantity specifically associated with joule losses.

NOTE 2 The term representing the effect of the cable image is omitted from equation (5) because periods up to

= + (7) where λ is the sheath/armour loss factor; à is the loss load factor for the particular load cycle.

For cables with low internal thermal capacity, typically those rated up to 18/30(36) kV, the equations for calculating M are significantly simpler and can be found in IEC 60853-1.

The calculation considering the possibility of drying is conducted by adjusting factor M to account for the presence of a dry zone in steady state This adjustment is achieved by calculating the ratio of the surface heating of the cable to the core heating in cyclic conditions, using equation (8).

′ M k A (8) ó θ′c est l'échauffement admissible de l’âme en régime permanent, dû aux pertes joule, en kelvins (K); θ ′SPK est l'échauffement cyclique de crête de la surface du câble, en kelvins (K);

M est le facteur de capacité de transport cyclique déduit de l’équation (1).

′ = c d A 3 4 c T2 T T θ W θ (10) ó θ c est l'échauffement maximal admissible de l’âme, en kelvins (K), dû aux pertes totales du câble;

W d sont les pertes diélectriques du câble considéré, en W/m;

T A est la résistance thermique de l’isolation du câble, ou du câble équivalent, en K⋅m/W;

T 3 est la résistance thermique du revêtement du câble, en K⋅m/W;

T 4 est la résistance thermique externe du câble pour un sol présumé humide, en K⋅m/W.

The procedure for representing a three-core cable as an equivalent single-core cable is outlined in IEC 60853-2 Additionally, the peak heating of the cable's surface must be compared to the critical soil temperature, θ x, before proceeding, in order to assess the potential for drying out.

– si (θSPK′ +W d T 4 ) n’est pas supérieur à l’échauffement critique du sol, alors il n’y a pas d’assèchement et le facteur de capacité de transport cyclique est donné par M sans aucune correction;

If the peak surface temperature rise of the cable (\$θ_{SPK}' + W d T^4\$) exceeds the critical value, the corrected value \$M_1\$ must be calculated The corrected value is determined as follows:

For cables with negligible internal thermal capacitance, specifically those rated for voltages up to 18/30(36) kV, the equations for M are significantly simplified and are detailed in IEC 60853-1.

To address the potential issue of drying out, the factor M is modified to account for a dry zone under steady-state loading conditions This adjustment involves calculating the ratio of the cable surface temperature increase to the conductor temperature increase under cyclic loading, as outlined in equation (8).

The permissible steady-state temperature rise of the conductor due to joule losses is denoted as \$\theta'_{c}\$ in kelvins (K), while the peak cyclic temperature rise of the cable surface is represented as \$\theta'_{SPK}\$ in kelvins (K).

M is the cyclic rating factor derived from equation (1).

′ = c d A 3 4 c T2 T T θ W θ (10) where θ c is the permissible maximum conductor temperature rise due to total cable losses, in kelvins (K);

W d is the dielectric loss for the cable under consideration, in W/m;

T A is the thermal resistance of the cable, or equivalent cable, dielectric, in K⋅m/W;

T 3 is the thermal resistance of the cable covering, in K⋅m/W;

T 4 is the external thermal resistance of the cable assuming wet soil, in K⋅m/W.

NOTE The procedure for representing a three-core cable as an equivalent single core cable is set out in

According to IEC 60853-2, it is essential to verify the cable surface peak temperature rise against the critical temperature rise of the soil, denoted as θ x, to evaluate the potential for drying out before proceeding further.

If the sum of \$\theta_{SPK}' + W d T^4\$ does not exceed the critical temperature rise of the soil, drying will not occur, and the cyclic rating factor remains as \$M\$ without any adjustments.

If the peak temperature rise of the cable surface, represented by the expression $\theta_{SPK}' + W d T^4$, exceeds the critical threshold, it is necessary to compute the corrected value, denoted as $M_1$ The calculation of this corrected value follows a specific formula.

M k M θ θ (11) ó v est égal à ρ d /ρ w; ρ w est la résistivité thermique du sol humide, en K⋅m/W; ρ d est la résistivité thermique du sol sec, en K⋅m/W.

For cables with low internal thermal capacity, typically those rated up to 18/30(36) kV, the equation for adjusting the value of M remains unchanged However, the second part of the equation simplifies to $1 - M^2(1 - k)Y_0$.

Pour ces câbles, les pertes diélectriques peuvent généralement être négligées, et alors l’équation (10) devient θ c ′=θ c

M k M θ θ (11) where v is equal to ρ d /ρ w ; ρ w is the thermal resistivity of moist soil, in K⋅m/W; ρ d is the thermal resistivity of dry soil, in K⋅m/W.

For cables with negligible internal thermal capacitance, specifically those rated for voltages up to 18/30(36) kV, the modification of the value of M in equation (11) remains consistent, while the right-hand side of equation (8) simplifies to $1 - M^2(1 - k)Y_0$.

For these cables, the dielectric losses can usually be ignored and hence equation (10) becomes θ = c ′ θ c

L’exemple choisi porte sur un câble tripolaire de 400 mm 2 en cuivre à huile fluide 132 kV, à gaine de plomb et revêtement PVC.

Ce câble est utilisé pour illustrer la méthode de prise en compte de l’assèchement du sol; il est décrit en détail à l’annexe B.

Les principales caractéristiques requises pour le calcul du facteur de capacité de transport cyclique sont les suivantes: θ c = 65 K (au-dessus de la température ambiante à 20 °C) D e = 0,109 m

Les paramètres caractérisant le câble unipolaire équivalent − voir 4.2.1.2 et 4.2.2.2 de la

Le calcul du transitoire thermique partiel selon 4.2.3 de la CEI 60853-2 conduit aux valeurs suivantes: a = 0,002 09 b = 0,000 221

Données relatives au sol: ρ w = 1 K⋅m/W ρ d = 2,5 K⋅m/W θ x = 30 K δ = 0,000 0005 m 2 /s Profondeur de pose, L = 1 m

Les caractéristiques de la charge sont données à l’annexe B; le facteur de charges des pertes

La réponse α(t) du câble est donnée par l’équation (6), soit

The example chosen is that of a three-core 400 mm 2 copper, paper-insulated, 132 kV oil- filled, lead sheathed and PVC covered cable.

This cable is used to illustrate the method for dealing with dried-out soil; it is described in detail in annex B.

The principal details required for the calculation of the cyclic rating factor are as follows: θ c = 65 K (above an ambient of 20 °C) D e = 0,109 m

The equivalent single-core cable − see 4.2.1.2 and 4.2.2.2 of IEC 60853-2 − has the following parameters:

The calculation of cable partial transients according to 4.2.3 of IEC 60853-2 results in the following figures: a = 0,00 209 b = 0,000 221

Soil data: ρ w = 1 K⋅m/W ρ d = 2,5 K⋅m/W θ x = 30 K δ = 0,000 0005 m 2 /s Depth of laying, L = 1 m

Load characteristics are given in annex B; the loss load factor (à) is 0,504.

The cable response α(t) is given by equation (6) and is as follows:

La réponse thermique du sol s’obtient à partir des équations (5) et (7): ó m/W K 5734 ,

Le facteur de capacité de transport cyclique est donné par les équations (1), (2) et (3).

Les valeurs suivantes sont obtenues pour les paramètres dépendant du temps.

La valeur de M est 1,218, selon 5.2.1 de la CEI 60853-2.

Jusqu'à ce point, les calculs sont effectués selon la CEI 60853-2 qui traite le cas du facteur de capacité de transport cyclique avec un sol uniforme.

Ce qui suit constitue des calculs supplémentaires à effectuer pour prendre en compte un éventuel assèchement du sol.

Le rapport de l’échauffement de la surface du câble à la pointe à l’échauffement de l’âme selon l’équation (8) est le suivant:

The thermal response of the soil is obtained from equations (5) and (7): where

The cyclic rating factor is given by equations (1), (2) and (3).

The following values are obtained for the time dependent items:

The value of M is 1,218, from 5.2.1 of IEC 60853-2.

Up to this point, the calculations are those already given in IEC 60853-2 for the cyclic rating factor with uniform soil.

What follows is the additional computation required to deal with possible drying out.

The ratio of peak cable surface temperature rise to conductor temperature rise, from equation (8) is

L’échauffement de l’âme dû aux pertes joule, selon l’équation (10), est

′ θ K et l’échauffement de la surface du câble à la pointe dû à la fois aux pertes joule et aux pertes diélectriques est

Cette valeur est supérieure à la valeur critique de 30 K, de sorte qu’un assèchement est prévisible Lorsqu’un assèchement est prévu, le facteur corrigé est, selon l’équation (11),

La capacité de transport pour une charge constante avec assèchement lorsque l’échauffement critique est de 30 K est 520 A, de sorte que le courant à la pointe est 1,27 × 520d0A.

The conductor temperature rise due to joule losses, from equation (10), is

′ θ K and the peak cable surface temperature rise due to both joule losses and dielectric losses is

This is greater than the critical value of 30 K, so that drying can be expected The corrected rating factor when drying is expected is, from equation (11),

The steady-state rating with drying out when the critical temperature rise is 30 K is 520 A, so that the peak current is 1,27 × 520d0A.

Caractéristiques des câbles et de la courbe de charge utilisés pour exemple

B.1 Données relatives au câble et à ses conditions d’installation

C’est un câble tripolaire de 400 mm 2 en cuivre à huile fluide 132 kV, à gaine de plomb frettée et revêtement PVC.

Epaisseur de l’écran semi-conducteur sur âme 0,14 mm

Epaisseur de l’enveloppe isolante 9,5 mm

Epaisseur de l’écran semi-conducteur sur l’isolation 0,14 mm

Diamètre sur l’assemblage des conducteurs 91,60 mm

Diamètre sur le ruban de maintien 92,40 mm

Diamètre extérieur de la gaine de plomb 97,60 mm

Diamètre extérieur du revêtement PVC 109,00 mm

Résistance en alternatif de l’âme à la température de fonctionnement 61,5 × 10 –6 Ω/m

Facteur de pertes de la gaine 0,135

2 Les caractéristiques volumiques indiquent les volumes de chaque matériau pour un mètre de câble Ces carac- téristiques sont utilisées pour calculer la capacité thermique de chaque composant du câble.

Details of cables and load used for example

This is a three-core, 400 mm 2 copper conductor, 132 kV oil-filled, lead sheathed, reinforced and PVC covered cable.

Diameter over laid up cores 91,60 mm

Diameter over binder tape 92,40 mm

Diameter over lead sheath 97,60 mm

Diameter over PVC oversheath 109,00 mm

Conductor a.c resistance at working temperature 61,5 × 10 –6 Ω/m

2 The volumetric dimensions refer to the volume of each material in a one metre length of cable These dimensions are used to calculate the thermal capacitance of each cable component.

Résistance thermique de l’isolation, par conducteur 0,835 K⋅m/W

Données relatives au sol et aux conditions d’installation

Lorsque les caractéristiques du cycle de charge sont prises en compte dans l’exemple, seules sont utilisées les six dernières ordonnées réduites du cycle des pertes Ce sont les suivantes:

Période avant l’instant ó l’âme atteint sa valeur maximale h

Ordonnée du cycle de pertes

The recommended method in IEC 60853-1 and IEC 60853-2 utilizes load characteristics only over the last six hours, as the thermal effects of previous load variations can generally be represented by the average loss, specifically through the load loss factor.

Facteur de pertes pour un cycle de 24 h: 0,504.

Thermal resistance of insulation, per core 0,835 K⋅m/W

Where details of the load cycle are used in the example the last six hourly ordinates of the loss-load cycle are the only ones used These are

Period before time of maximum conductor temperature h

Ordinate of loss-load cycle

The IEC 60853-1 and IEC 60853-2 standards recommend using the load pattern from the last six hours, as the thermal effects of load changes before this period can typically be represented by the average loss, known as the loss-load factor.

Loss-load factor for 24 h cycle: 0,504.

Tiêu đề	Partie 3: Factor of Capacity of Transport Cyclic for Cables of All Voltages, with Partial Soil Drying
Chuyên ngành	Electrical Engineering
Thể loại	Standards Document
Năm xuất bản	2002

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