Amitava Bose*
Abstract
In the past, transmission of power was predominantly through overhead lines. It was only in the last leg that underground power cables were used for distribution of power to the load distribution centre’s and consumers in the urban area. High voltage XLPE cable technology has rapidly advanced, largely changing the landscape of extra high voltage underground power transmission system, which is seen to gradually “cannibalize” the overhead transmission lines, mainly in the metropolis. In present times, right-of-way problems & environmental restrictions on overhead transmission lines in metropolitan cities & populated towns have led to accelerated growth in the extra high voltage underground power transmission lines using XLPE cables. Also in many cities, outages of overhead lines, which are raising concerns on safety are necessarily being dismantled and are being substituted with underground lines. From the standpoint of land availability, cost of real estate, environmental & ecological issues, safety concerns, system maintenance and reduction of transmission losses, EHV underground transmission heavily outweighs overhead transmission system. It is now compelling evident that the only means to bring power into the urban area is through underground system. However, in India, cities are saddled with bottlenecks arising out of high-density buildings and structures, heavy congestion in roadways, crisscrossing of pipelines, telephone lines and distribution cables. These hindrances open immense challenges for constructing underground EHV power transmission corridors. This problem is not restricted to a few cities & town but is pan-India covering nearly all tier-I & tier-II cities. Such challenges during the installation work require unique technical solutions on case-to-case basis, both in-terms of selecting the appropriate design of EHV power cable and the installation methods. The topic of this paper focuses on key design factors for selection of EHV XLPE cables for improving the transmission performance of underground EHV power cable transmission system. The article has been divided into 2 sections; section-1: cable selection criteria & section-2: critical cable installation criteria.
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Section-1: Cable Selection Criteria
The selection of extra high voltage (EHV) XLPE cables is dependent on a number of criteria. The foremost criterion is the determination of ampacity or the current carrying capacity. Depending on the MVA rating of the cable feeder section, the conductor size is tentatively estimated. The size of the cable conductor and the conductor material (e.g. copper or aluminium) dictates the ampacity of the cable. However, there are a large number of factors, which influence the current carrying capacity of the cable. To understand these factors, the fundamental theory needs to be understood.
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Basic Theory on Current Carrying Capacity of Cable
The ampacity or the current carrying capacity of the cable depends on how efficiently the heat generated within the cable is dissipated into the environment. The maximum rated ampacity considers the steady-state condition with 100% daily load factor. Therefore, the significance of the maximum rated ampacity is conceptual rather than practical. The heat dissipation factor can be better understood from the thermal equations of conduction, convection and radiation.
The total heat flow from within the cable
WTotal = WConduction + WConvection + WRadiation
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Heat Transfer Equilibrium
As mentioned above, the heat dissipation in the form of conduction, convection and radiation depending on the installation conditions, occurs in the cable whereby an equilibrium state or steady state is reached.
Thus: WG + Wext = Wdissp + ΔWs
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WG – rate of heat generated internally by the cable (conductor, dielectric, sheath)
Wext – external source of heat transferred into the cable
Wdissp – heat dissipated by conductor, convection & radiation
ΔWs – rate of change of heat stored within the cable
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When, WG + Wext > Wdissp + ΔWs
Cumulative heat buildup or thermal runaway occurs resulting to failure of the cable. The current rating, which is responsible for the heat generation is dependant on the efficiency of the heat dissipation. The current rating is thus derived from the heat flow thermal equation.
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Selection of Cable
Selection of cables involves techno-economic consideration. The factors relating to economic considerations are:
a) Initial investment (cost of cable & installation cost)
b) Operating cost (cost of total losses per annum) – conductor loss I2R, dielectric loss and sheath loss.
Based on the above, the optimum size of cable can be selected. The ampacity is a key factor, other factors e.g. voltage drop, losses, short circuit current withstand capacity, cyclic load factor and installation methods are inextricably linked with the continuous current capacity.
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Derivation of Ampacity
The ampacity (I) of the cable is derived from the heat flow circuit, which is analogous to an electrical circuit diagram.
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Where;
R = the a.c. resistance per unit length of the conductor at maximum operating temperature (Ω/m)
Wd = the dielectric loss per unit length for the insulation surrounding the conductor (W/m)
T1 = the thermal resistance per unit length between one conductor and the sheath (K.m/W)
T2 = the thermal resistance per unit length of the bedding between sheath and armour (K.m/W)
T3 = the thermal resistance per unit length of the external serving of the cable (K.m/W):
T4 = the thermal resistance per unit length between the cable surface and the surrounding medium (K.m/W)
n = Number of load-carrying conductors in the cable (conductors of equal size and carrying the same load)
λ1 = the ratio of losses in the metal sheath to total losses in all conductors in that cable
λ2 = the ratio of losses in the armouring to total losses in all conductors in that cable
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Basic Criteria
a) The conductor temperature: The current rating is a function of the conductor cross section area and the temperature over the ambient temperature i.e. (Өconductor – Өambient)
b) The maximum conductor temperature: For XLPE, insulation is 90oC (i.e. Өc (max) = 90oC) for steady-state condition and is defined as the temperature corresponding to the maximum continuous current rating.
c) Cable construction: The heat dissipation from the conductor to the ambient depends on the thermal resistivity of the layers of material over the conductor i.e. insulation, tapes, sheath and also on the thickness of these material. Hence the cable construction plays a role in the current rating of the cable.
d) The thermal resistivity of the surrounding: The current rating depends on the thermal resistivity of the surrounding where the heat within the cable is finally dissipated.
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Factors Influencing the Current Rating
Cable manufacturers provide the maximum current rating based on maximum conductor temperature however the following factors needs to be considered to arrive at the final current rating:
a) Formation of laid cables – Trefoil or flat formation of laying.
b) Sheath bonding – Both end bonded or cross-bonded/ single end bonded. As in both end bonded-system results to a circulating sheath current, which in turn heats the cable and reduces the current rating.
c) Depth of laying – Rating factors for various depth of laying to be applied by the installer. The current rating reduces with the increase in depth due to poor heat dissipation.
d) Ambient temperature (ground/air) – Rating factors for changes in ambient temperature has to be applied by the installer.
e) Spacing between cables – When cables are spaced apart, there is less effect of mutual heating. The adjustment factors for various spacing are provided by the manufacturer, which needs to be applied by the user.
f) Group rating factors – Adjustments for groups of cables in the ground, the current rating needs to be adjusted using the group rating factor by the installer. In case the current loading is not more than 30% of the rated load, the adjustment can be ignored. The limiting factor in current rating is the temperature of the conductor adjacent to insulation, which does not cause thermal deterioration to the insulation. The proximity effect of a number of cables to one another has an appreciable effect on the current rating. The amount of heat to be dissipated is proportional to the number of cables, but the number of free paths by which heat can escape into the general body of the earth is reduced.
g) Correction factor for cable lay inside the duct/pipe – When cables are laid inside the ducts, the heat dissipation is affected. The de-rating factors for:
• Cable laid partially in ducts/pipes (fp=0.94)
• Cable laid in separate ducts/pipes (fp= 0.90)
• Cable laid in common pipes (fp= 0.90)
In case cables laid directly or drawn into ducts and maintained on load, the whole locality immediately surrounding the cable attains steady-state temperature above the general level. Consequently the current rating of cable is de-rated. However, when the cables laid in ducts/pipes constitute less than 10%, the de-rating factor can be ignored. (Cable should be laid in single pipe having approximately twice the diameter of cable).
h) Neighbouring cables – The effect of other cable circuits need to be taken into account, which cause mutual heating.
i) Correction for thermal resistivity of ground/ backfilling material by measurement at site: The characteristics of soil plays an important role in the current rating of the cable as the thermal resistivity varies widely depending on the soil characteristics and the moisture content. The thermal resistivity depends on a number of factors, e.g. the nature of the soil, its moisture content and degree of compaction. The soil compaction is depending on the ratio of total volume of voids, which might be filled with air, water or a combination of both. Loose soil tends to have high void count. The trapped air in the voids increases the soil thermal resistivity as air is a bad conductor of heat. However, only in a well-graded soil, good compaction is achievable. It is important to ensure that the backfill in the trench is well compacted. The thermal resistivity and the natural temperature of the soil needs to be taken into account. The content of moisture in the soil largely reduces the thermal resistivity. It is necessary to measure the actual ground thermal resistivity along the route. The measurement of thermal resistivity during hot & dry season need to be applied, for considering factor of safety. Thermal soil resistivity is usually subject to slow variation with the passage of time. Thermal resistivity (T4) factor need to be applied by the installer for adjustment in current rating:
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ρ T = soil thermal resistivity (Km/W)
L = depth of laying (mm)
Dc = overall diameter of cable
Finally, the adjusted current rating can be obtained by applying the above factors with the standard current rating.
j) Cyclic load factor: The load factor of power transmission of the underground cable transmission line varies with time i.e. annually, monthly, weekly or daily. The load factor (Lf) of the transmission line over the period of time is obtained by the area under the Load versus daily time curve as expressed below:
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Where: Imax – peak value of current over daily period T (24 hrs)
In case of substantial daily load variation, the value of (Lf) is lower, hence there is less loading of the cable system. Therefore, a lower size of cable can be selected for a particular peak load (Imax) which is not a constant load.
k) Correction for neighbouring utilities such as other power cables, hot water pipes etc. running in close proximity with EHV cables.
l) Forced cooling (air draft, cold water pipes) for improving heat dissipation.
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Short Circuit Rating:
On selecting the conductor size based on the above criteria and the techno-economic consideration i.e. loss capitalization cost, it is necessary to check whether the selected conductor size is capable to withstand the symmetric short circuit current. For calculating the short circuit current, the adiabatic principle is used, i.e. the heat generated by the conductor due to the short circuit current is absorbed by the conductor and no heat is lost by dissipation. The symmetric short circuit current can be calculated using the formula given below:
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Where; I= short-circuit current (r.m.s. over duration) (A)
T = duration of short circuit (second)
K = constant for the material of the conductor
S = area of conductor (mm2)
θ1= final temperature (oC)
θ0 = initial temperature (oC)
ß = reciprocal of the temperature coefficient of resistance (α) of the conductor (per degree celsius at 0oC)
In the above, ‘conductor’ refers to the current carrying component. The constants for the metals are given below:
K2 = Qc (ß + 20)
ρ20
Where; Qc = volumetric specific heat of the conductor at 20oC (J/oCmm3)
ρ20 = resistivity of conductor metal at 20oC (Ωmm)
Constants for metals:
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The selected conductor size based on the ampacity after adjusting with the rating factors and installation factors has to be compared with the size derived from the symmetrical short circuit fault level. The higher size between these two conditions is selected.
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Earth Fault Rating
The system earth fault rating has to be carried by metallic sheath of the cable. It is therefore, imperative to provide the requisite cross-sectional area of the metallic sheath by providing adequate thickness of the metallic sheath. The cross-sectional area of the metallic sheath can be derived from the above two equation considering the final temperature θ1 as the maximum permissible short circuit temperature of the metallic sheath and considering the value of (I) as the permissible earth fault rating. From the derived cross-sectional area the thickness of metallic sheath can be determined.
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Section-2: Critical Cable Installation Criteria
The installation techniques of EHV cables are governed by a number of factors depending on where and how the cable is to be installed. The installed cable is subjected to 2-major influencing factors.
– Ambient temperature – which has been discussed for selection of cables.
– Thermo mechanical effects on the cable
We shall now discuss on the thermo mechanical effects, which has a critical influence on the cable.
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Principle of Thermo Mechanical Effects:
a) During heavy short-circuit, mechanical stress are created due to:
• Rapid expansion & contraction of the conductors leading to axial force.
• Repulsive forces due to intense magnetic field between the cables
{Fm=(µ0/2л).(Ik2/s)kN/m}
Fm = short circuit magnetic force (kN/m)
Ik = peak short circuit current (A)
S = axial spacing between conductors (m)
µ0 = 4л x 10-7 H/m
The combinations of thermal and magnetic stress are imposed on the cable, joints & terminations. To restrain the expansion (i.e. assuming no expansion is allowed to take place) a massive force would be required to counter balance the expansionary force. The cleats have to be designed considering the magnetic and expansionary forces.
When cables are laid over-ground on RCC trenches without backfilling in trays/ ladders, ducts, tunnels, special laying technique has to be adopted to compensate thermal expansion and severe mechanical stress under short circuit condition.
b) Methods to compensate mechanical stresses due to thermal expansion for annual temperature variation:
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During thermal stress, the conductor expands. Theoretically, to restrain this expansion (i.e. no expansion is permitted) necessary force would be required to produce the same elongation. This is a tremendous force, which cannot be realized in practice. Therefore, with the rapid expansion, the cable tends to cause snaking, which releases the stress. Hence when cables are laid above ground i.e. in tunnels, in civil trenches, trays etc., pre-snaking i.e. cables are essentially laid either in vertical or horizontal snaking formation.
The annual temperature variation (Δty) is considered as 650C as design constant for expansion and shrinkage. This is mainly influenced by seasonal temperature charge. Factor (Δty) is considered for this axial force effect on the cable due to linear expansion & contraction. The daily temperature variation (Δtd) is due to daily load variation and design constant is considered as 250C. Factor Δtd has effect on the radial and axial expansion leading to fatigue of the metallic sheath.
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Direct Burial of Cables in Ground
When the cables are laid in direct burial, the earth provides the force restraining the expansion. Hence, for direct burial no off-set and strain release methods, as discussed below are necessary.
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Cables Installed in Tunnels
Cables in Tunnels are installed in snaking formation to relax the thermal expansion axial force. The snaking can be in horizontal formation or in vertical formation, the choice depends on the space availability and cost factor. Horizontal formation is more cost intensive than vertical formation as cable trays are required to support the cable throughout the cable route. The cable tray has to be supported by cable cleats every half pitch of snaking. The snake pitch is between 6 to 9m and the width of the snake is between 1.5 to 2 times the diameter of the cable.
Vertical snaking requires support structure with rope at every pitch of snaking. The cleats are required at every 5 pitch of snaking. The snake pitch is between 4.5 to 7.2m and the width of the snake is between 1.5 to 2 times the diameter of the cable.
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Snaking Design:
• To access the space available for snaking
• Method to restrain axial force of the cable at the end of snaking
• Intervals of fixing cleats in the tunnel
Depending on the tunnel’s space & slope, selection of vertical or horizontal snaking is decided.
The space parameters which are required for snaking are:
P Snake width (B)
P Half snake pitch (L)
P Displacement width (n)
To estimate the displacement width (n) during thermal expansion can be calculated from the following equations:
n= (B2+2.L.α.t.L.0.8)0.5-B
Where, snaking parameters are:
α = Coefficient of linear expansion (20 x 10-6 /oC)
t = Design factor for annual rise of temperature (65oC) – based on maximum cable conductor operating temperature of 90oC and ambient temperature of 25oC.
µ = Coefficient of friction between cable and support (in case of horizontal snaking)
EI = Flexural rigidity (kg mm2)
The snaking space (Ss) required for snaking is arrived by the following:
Ss = Cable diameter (D) + Initial Snake width (B) + Displacement (n)
Vertical Snaking space (Ss) = D + B + n
Horizontal Snaking space (Ss) for trefoil formation = 2D + B + n
Horizontal Snaking space (Ss) for flat formation with cable spacing (S)
Ss = 2D + S + B + n
Flexural Rigidity (EI) – example for copper cable with aluminium sheath can be calculated using the following formula:
EI = Ec.Ic + Ei.Ii + Em.Im
Ec = Young’s modulus of copper conductor (750 kg/mm2)
Ic = л (dc4)/64
Where;
dc= diameter of the conductor (mm)
Ei = young’s modulus of XLPE Insulation (40 kg/mm2)
Ii = л (di2 – dc4)/64
Where;
di = diameter over insulation (mm)
dc = diameter over conductor (mm)
Em = young’s modulus of aluminium sheath (1100 Kg/mm2)
Im = л (dm3.t)/8
Where;
dm= average mean diameter of the aluminium sheath
t = thickness of aluminium sheath.
Cable laying:
Cable Pulling – Basic Design Factors
The maximum permissible pulling tension depends on the cross-sectional area of the conductor. Prior to the actual pulling of the cable, the pulling tension is calculated to verify that the same is less than the maximum pulling tension and the side wall pressure (as formula given below):
Copper conductor: Maximum permissible pulling tension = (conductor area in mm2) x 7kg/mm2
Aluminium conductor: Maximum permissible pulling tension = (conductor area in mm2) x 4kg/mm2
Maximum Permissible Cable Sidewall Pressure
Pswp = T/R
Where: Pswp= sidewall pressure (kg/m)
T= pulling tension at exit from bend (kg)
R= bending radius (m)
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Pulling Tension (Three common equations)
a) Horizontal straight line T = µWL + T0
b) Bend Section T = Ti.Cosh(µӨ) +{T12+(WR)2}0.5 Sinh(µӨ)
c) Inclined plane
(i) Ti = W.L (µ.Cos Өi + Sin Өi) Upwards
(ii) Ti = W.L (µ. Cos Өi – Sin Өi) Downwards
Where;
T= pulling tension (kgf)
T0 = back tension (kgf)
Ti = inlet Pulling tension (kg) at the start of curvature point
µ = coefficient of friction
W= weight of cable per meter (kg/m)
L = cable length (m)
R = bending radius (m)
Ө = Bending angle (radians)
Өi = Tilt angle (radian)
Typical Coefficient of Friction (µ)
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Calculation of Pulling Tension; refer to figure (1)
The figure can be divided into 5 sections where the pulling force (kgf) are T1 (Horizontal straight line of L1 length), T2 (Bend Section), T3 (Horizontal straight line of L3 length), T4 (Bend Section) & T5 (Horizontal straight line of L5 length),
T1 = µWL1 + T0
T2 = T1.Cosh(µӨ) +{T12+(WR)2}0.5 Sinh(µӨ)
T3 = µWL3 + T2
T4 = T3.Cosh(µӨ) +{T32+(WR)2}0.5 Sinh(µӨ)
We need to check the side wall pressure (Pswp) at the last bend which would experience the highest tension.
Therefore, Pswp = T3/R > T4 ; condition should be satisfied
T5 = µWL5 + T4
Hence, the net pulling force (kgf) by the winch is T5 = µWL5 + T4
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Conclusion:
The maximum rated ampacity of the cable is conceptual rather than practical. While selecting the size of cable, it is imperative to consider the rating factors and the installation conditions for adjustment of the current rating. By improving heat dissipation of the cable, the current rating can be improved. The installation of cables above the ground is more complex than underground i.e. in tunnels and in ducts, which require special installation design, such as snaking and off-setting with special cleats. Attention needs to be given to the hauling force of the winch, while pulling the cable with a check on the side wall pleasure.
———————————————————————————-/—————-* Sr. VP – Marketing, Universal Cables Ltd.