Ampacities of underground cables

8/16/2019 Ampacities of underground cables

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Advances in Electrical Engineering Systems (AEES) 163

Vol. 1, No. 3, 2012, ISSN 2167-633X Copyright © World Science Publisher, United States

www.worldsciencepublisher.org

Practical and Theoretical Investigation of Current Carrying

Capacity (Ampacity) of Underground Cables

1Adel El-Faraskoury,

2Sherif Ghoneim,

2Ali Kasem Alaboudy,

2Ragab Salem,

3Sayed A. Ward

1Extra High Voltage Research Center, Egyptian Electricity Holding Company, Egypt, [email protected] of Industrial Education, Suez University, Suez Campus, Suez,

Egypt, [email protected]; [email protected] of Engineering, Benha University, Shoubra, Cairo, Egypt, [email protected]

Abstract – In urban areas, underground cables are commonly used for bulk power transmission. The utilization of

electricity in factories, domestic premises and other locations is typically performed by cables as they present the most

practical means of conveying electrical power to equipment, tools and other different applications. Estimation of cable

current carrying capacity (ampacity) gains higher potential in recent times due to the continuous increase of energy

utilization in modern electric power systems. This paper presents a theoretical study based on relevant IEC standards to

calculate the ampacity of underground cables under steady state conditions. The ampacity formula stated in IEC standards

are coded using Matlab software. Further, an untraditional experimental ampacity test of a 38/66 kV- XLPE/CU- 1 X 630

mm2 cable sample is performed in the extra high voltage research center. This paper proposes a new approach that uses the

complementary laboratory measurements in cable ampacity data preparation. The modified approach gives more accurate

estimation of cable parameters. The level of improvement is assessed through comparisons with the traditional ampacity

calculation techniques. Main factors that affect cable ampacity, such as the insulation condition, soil thermal resistivity,

bonding type, and depth of laying are examined. Based on paper results, cable ampacity is greatly affected by the installation

conditions and material properties.

Keywords – Underground cable; Cable ampacity; Soil thermal resistivity; Bonding type; Depth of laying

1. Introduction

Compared with transient temperature rises caused by

sudden application of bulk loads, the calculation of the

temperature rise of cable systems under steady state

conditions, which includes the effect of operation under a

repetitive load cycle, is relatively simple. Steady state cable

ampacity involves only the application of the thermal

equivalents of Ohm’s and Kirchoff’s laws to a relatively

simple thermal circuit. This analogy circuit usually has a

number of parallel paths with heat flows entering at several

points. However, heat flows and thermal resistances

involved should be carefully addressed. Differing methods

are sometimes used by various engineers. In general, all

thermal resistances are developed according the conductor

heat flowing through them. The ampacity or current

carrying capacity of a cable is defined as the maximum

current which the cable can carry continuously without the

temperature at any point in the insulation exceeding the

limits specified for the respectively material. The ampacity

depends upon the rate of heat generation within the cable as

well as the rate of heat dissipation from the cable to the

surroundings. In the case of underground cable systems, it is

convenient to utilize an effective thermal resistance for the

earth portion of the thermal circuit which includes the effect

of the loading cycle and the mutual heating effect of the

other cable of the system. Ampacity of an underground

cable system is determined by the capacity of the

installation to extract heat from the cable and dissipate it in

the surrounding soil and atmosphere. The maximum

operating temperature of a cable is a function of the

insulation damage experienced as a consequence of high

operating temperatures. Based on the duration of the currentcirculating in the conductors, the cable insulation can

withstand different temperature values [1]. There are three

standardized ampacity ratings: steady state, transient (or

emergency) and short-circuit. This paper focuses only on

cable steady state ampacity ratings. Theoretical and

experimental investigation of cable ampacity is conducted.

2. Cable ampacity calculation

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Adel El-Faraskoury, et al., AEES, Vol. 1, No. 3, pp. 163-169, 2012 164

The maximum temperature that the cable insulation can

be endured for long term determines its ampacity. The long

term and short term allowable maximum temperatures

ensure that the cable can operate safely, reliably and

economically. If the operating temperature exceeds certain

limit, the insulation aging becomes faster and thus shortens

the cable’s life span. In addition, the electrical and

mechanical properties, and thermal behavior must be

considered in choosing cable to ensure that the heat is not

exceeding the limited value while the transmission

capability is satisfied. The thermal behaviour of the

cables in underground lines during regimes of normal

load or under emergency not only depends on the

previous knowledge of the constructive characteristics

of the cable and the load curve that submitted, but

also of the way conditions where it is installed. Thus

other factors will have to be known as: amount of

loaded conductors, geometric configuration between

the cable, type of grounding of the metallic shields of

the cable, thermal characteristics of the materials

around of the cable (soil, ducts, concrete, "backfill",

etc), effect of the typical variation of the environment

(humidity and temperature in the land) and other

interferences caused for external sources of heat. Themaximum temperature that XLPE insulation enduring is 90

ºC, so when the cable core come to this temperature, the

current in the cable core is considered cable ampacity. IEC60287 support a method for calculation the cable ampacity

of 100% load current, which is a common method used in

all over the world. To find the ampacity, we first note that

the potential of every node in the circuit analogizes the

temperature of the regions between the layers. Thus, the

potential difference between the terminals of the circuits

and the innermost current source represents the temperature

rise of the core of the cable with respect to the ambient

temperature. Therefore the temperature of the cable's core is

the ambient temperature plus Δ t ; Figure 1 shows thermal

electrical equivalent.

Figure 1. Electrical equivalent of thermal circuit

From Figure (1) we can compute Δ t as follows:

( )

( )( )422

121

T T W W W

T W W W T W W t

ad c

sd cd c

+++

+++

+=∆

(1)

To derive an expression from where the ampacity can

be computed directly, the heat sources (electrical losses)

W' s are expressed as proportion of the conductor losses

(W c). The conductor losses are computed using the ac

resistance and the current. Thus, by substituting thefollowing expressions:

2

11 ,, I RW W W W W

acccacs === λ λ (2)

In (1) and re-arranging we have:

( )[ ]( )[ ]

43211

43214

1

5.0

T T nR RT

T T T nT W t I

++++

+++−∆=

λ λ (3)

From expression (3) one can compute the ampacity of a

cable by calculating the thermal resistances T , the loss

factors λ and the ac resistance R of the core of the cable.

The loss factors λ take into account eddy losses induced and

circulating currents, while R considers the temperature

dependency of the resistance [2,3,4,5]. T 1, T 2 is related with

insulation material and the cable’s physical dimension.

Besides the cable’s construction, T 4 also has relationship

with the soil thermal resistance coefficient, namely the

earth’s property and moisture content. If the three cables

contact with each other, the interrelationship of these cables

also should be considered in. The loss factor λ1, λ 2, relate

to the resistance of sheath and armour. The resistance is thefunction of temperature. In IEC standard, the temperature of

sheath and armour are estimated by the maximum

temperature insulation endured, but in effect, they also have

some relationship with ambient temperature and the current

in the cable core. So the cable ampacity calculated by IEC

standard has some errors. An iterative method for

calculation ampacity is provided in this paper based on

precise calculation of circulating current in cable sheath.

Firstly, the cable core is given an initial current, and the


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initial temperatures of the core and sheath are also given.

Secondly, iterative calculate their temperatures under this

current. Thirdly, change the core current continually based

on the temperature difference between the core and its

allowable maximum temperature, until this difference is

smaller than the given error [6]. When the conductor is

energized, heat is generated within the cable. This heat is

generated due to the I2R losses of the conductor, the

dielectric losses in the insulation and losses in the metallic

component of the cable. The ampacity of the cable is

dependent on the way this heat is transmitted to the cable

surface and ultimately dissipated to the surrounding. The

thermal resistances control heat dissipation from the

conductor. Thus the efficiency of heat dissipation is

dependent upon the various thermal resistances of the cable

material and the external backfill and soil plus the ambient

temperature around the cable. If the cable is able to

dissipate more heat, the cable can carry more current.

In the Neher-McGrath method [1], the thermal resistances

are either computed from basic principles or from

heuristics. One can appreciate, from Figure 3, that some of

the internal layers of a cable can be considered as tubular

geometries. The following expression is used for the

computation of the thermal resistance of tubular geometries:

==

1

2ln

2

1

r

r

AT

π

ρ ρ (4)

Equation (4) is applicable for most internal to the cable

layers (T 1, T 2, T 3). For complicated geometries and for the

layers external to the cable, such as three-core cables, duct

banks, etc., heuristics are used. The external to the cable

thermal resistivity is commonly computed assuming that thesurface of the earth in the neighborhood of the cable

installation is an isothermal. Kennelly made this assumption

in 1893 and it is still being used. This assumption allows for

the application of the image method to compute the external

to the cable thermal resistance (T 4). The following

expression results from the image method:

==

e D

L

AT

4ln

2

1

π

ρ ρ (5)

The thermal resistance of the layers external to the cable

(T 4) must also include the duct when present, and the airinside. The duct itself is of tubular geometry and it very

easy to model, however, the treatment of the air inside of a

duct is a complex matter. The heat transfer is dominated by

convection and radiation and not by conduction. There exist

simple formulas, which have been obtained experimentally

and that work fine for the conditions tested [5]. A software

code by Matlab is provided to calculate the ampacity at

different cases and the flowchart that explained the program

is shown in Figure 2.

3. Factors affecting cable ampacity

3.1 Effect of soil resistivity

Dry soils have much higher thermal resistivity than

moist soils. With sufficiently high ampacity thermal, run-

away conditions can occur. If cable current is high enough,

it will generate sufficient heat and if it is maintained for a

long enough time, the soil will become unstable and the

circuit will have to be de-rated or overheated. Cable

ampacity varies with change of soil resistivity, for both

with-conduit and the conduit-less cable. Cable ampacity is

proportional to soil conductivity; rising soil conductivity

dissipates more heat, and increase cable ampacity.

3.2 Effect of cable depth

Depth affects the ampacity of cables that buried with

conduit and conduit-less, in both homogeneous and

heterogeneous soil. Soil conductivity is reduced by

increasing the cable depth in the soil as well as less heat

dissipation, less ampacity. The closer the cable to earth’s

surface, the rate of cable ampacity changes will increase

[7].

4. Test arrangement

4.1 Theoretical study for ampacity

A computer program has been proposed using

MATLAB to calculate the current carrying capacity

(ampcity) for different underground cables. The flowchart

is presented in Figure (1). The program takes into account

the steady state conditions which based on the formulas in IEC

standards. Equation (1) is used to calculate the cable

ampacity and the parameters of the equation (1) should be

separately calculated dependant on the various factors like

cable construction types, installation types, installation

environment. Steady state conditions is considered when the

current flow through the cable is at a constant value and the

temperature of the cable is also constant i.e. the heatgenerated is equal to the heat dissipated. The temperature

depends on the type of cable and XLPE construction is

chosen where the maximum temperature normally for

steady-state is 90°C.


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Start

Read input data

1. Cable data

2. Temp. data

3. Soil resistivity

Calculate

1. The outer diameter of the cable, sheath diameter and insulation

diameter and different thicknesses

2. DC Resistance and AC resistance

3. Dielectric losses

4. Sheath loss factor 5. Armor loss factor

6. Thermal resistivities

Trifoil FormationFlat Formation

Ampacity Calculation

Double

bond

Emergency Steady state

Single

bond

Double

bond

Double

bond

Emergency Steady state

Single

bond

Double

bond

Write the ampacity of the different cases

Ampacity Calculation for different cable depth

Trifoil FormationFlat Formation


Ampacity Calculation for different soil temperature

Trifoil Formation


Flat Formation

Ampacity Calculation for different soil resistivity

Trifoil Formation


Flat Formation

End Figure 2. Flowchart of the Matlab program used for ampacity

calculation

The MATLAB program is provided to calculate the cables

ampcity for single bonded, double bonded and double

bonded emergency with equal load. The ampacity is

calculated at different grounding mode and comparing it

with manufactures based on IEC and it is shown in Table I

and Figures from Figure 3 to Figure 6 for the followingconditions; flat and trefoil formation, soil resistivity is 1.2

°C.m/w, the ground temperature at 25°C for cable sample

38/66 kV [8]. The thermal resistivity of soft depends on the

type of soil encountered as well as the physical conditions

of the soft. The conditions which most influence the

resistivity of a specific soil are the moisture content and dry

density. As the moisture content or dry density or both of a

soil increases, the soil resistivity decreases. The structural

composition of the soil also affects the soil resistivity. The

shape of the soil particles determines the surface contact

area between particles which affects the ability of the soil to

conduct heat. Figure 3 and Figure 4 show the variation of

ampacity for cable with soil resistivity and soil temperature,

respectively. For underground cable system the main heat

transfer mechanism is by conduction. Since, the

longitudinal dimension of a cable is always much larger

than the depth of the installation, the problem is considered

a two-dimensional heat conduction problem. Figure 5

shows the effect of depth on cable ampacity and Figure 6

shows the variation of ampacity with cable temperature.

Table 1. Comparison of cable ampacity between single

circuit and double circuits with manufactures

Bonded number

Ampacity

240

mm2

(Amp.)

400

mm2

(Amp.)

630

mm2

(Amp.)

800

mm2

(Amp.)

Single

Bonded

Flat 502 648 839 939

Trefoil 478 616 796 909

Double

Bonded

Flat 435 584 702 780

Trefoil 460 558 672 754

Double

Bonded

Emergency

Flat 484 649 778 865

Trefoil 511 620 746 737

Manufacturers

Flat 497 640 829 935

Trefoil 445 550 774 863

0.5 1 1.5 2 2.5 3 3.5 4300

400

500

600

700

800

900

1000

Soil Resitivity (oC w/m)

C u r r e n t ( A )

SoilRes for trfoil

SoilRes for flat

Figure 3. Variation of cable ampacity with soil resistivity


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10 15 20 25 30 35 40 45550

600

650

700

750

800

Degrees (C)

C u r r e n t ( A )

SoilTemp for trfoil

SoilTemp for flat

Figure 4. Effect of soil temperature on the ampacity of cable

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2640

660

680

700

720

740

760

780

800

820

Depth (b)

C u r r e n t ( A )

Depth for trfoil

Depth for flat

Figure 5. Effect of depth on ampacity

20 30 40 50 60 70 80 90 100 1100

100

200

300

400

500

600

700

800

900

Cable Temp - Degrees (C)

C u r r e n t ( A )

Emerg flat

Emerg trfoil

Dbl Bond flat

Dbl Bond trfoil

Sng Bond flat

Sng Bond trfoil

Figure 6. Variation of cable ampacity with temperature

4.2 Experimental study (Calibration of the

temperature method)

The calibration should be carried out in a draught-free

situation at a temperature of 20 ± 5 ºC. Temperature

recorders should be used to measure the conductor, over-

sheath and ambient temperature simultaneously. The

calibration should be performed on a minimum cable length10 m, taken from the same cable under test. IEC adopts a

cable system test approach and requires a minimum of 10 m

of the cable. The length should be such that the longitudinal

heat transfer to the cable ends does not affect the

temperature in the center 2 m of the cable by more than 1º

C. During calibration and during the test of the main loop

should be calculated according with either IEC 60287 or

60853[9], based on the measured external temperature of

the oversheath (TCS). The measurement should be done

with a thermocouple at the hottest spot, attached to or under

the external surface. The hottest current should be adjusted

to obtain the required value of the calculated conductor

temperature, based on the measured external temperature ofthe over-sheath [9]. The cable that used for calibration

should be identical to that used for the test, and the way

(path) of heat should be identical. After stabilization has

been reached the following should be noted and drawing

the curve as in Figure 7.

-

Ambient temperature

-

Conductor temperature

- Over-sheath temperature

- Heating current

Figure 7. Calibration of temperature for XLPE cable sample

38/66 kV – 1x 630 mm2

The heating currents in both the reference loop and

the test loop were kept equal at all time, thus the conductor

temperature of the reference loop in representative for the

conductor temperature of the test loop. The tests elevated

temperature is carried out two hours after thermal


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equilibrium has been established. it must develop a

consistent heating cycle to maintain the conductor

temperature adjustment generally cannot be made in

sufficient time during testing due to the large thermal time

constants of high voltage cables. In this test, the cable

sample 38 /66 kV – CU/XLPE/LEAD/HDPE – 1x 630

mm2 with 15m length as shown in Table II and Figure 8.

Table2. Heating cycle for xlpe cablesxlpe – cu- 38/66kv- 1x 630 mm2

No. ofheating

cycle

Requiredsteady

conductor

temp.

Heatingcurrent at

stable

condition

ooling per

cycle

VoltagePer

cycle

Heating per cycle

20

ºC Amp.

Total

duration

hr

Stable

temp.

hr

hr hr 2U

0

95-100 1600 8 2 16 2

4

72

Figure 8. Heating cycle for cable sample 38/66 kV – 1x 630 mm 2

Ambient temperature (Lab. Temperature) affects the

heating current as shown in Figure 9. Figure 10 shows the

relation between heating current with conductor

temperature during heating per cycle. The heating current

varies with the ambient temperature during heating cycle. Steady

state conditions are considered when the current flow

through the cable is at a constant value and the temperature

of the cable is also constant i.e. the heat generated is equalto the heat dissipated. The temperature depends on the type

of cable but XLPE construction is searched where the

maximum temperature normally for steady-state is 90ºC.

The IEC requirement is simply that the conductor be “at

this temperature” for at least 2 hours of the current on

period.

Figure 9. Variation of current with ambient temperature during test

period

Figure 10. Variation of heating current conductor temperature


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5. Conclusions

The theoretical and practical study for cable ampacity

estimation under steady state conditions shows that the

underground cable ampacity depends on the cable geometry

installation, its depth as well as on the soil thermal

resistivity. Cable ampacity is proportional to soil

conductivity; when soil conductivity increases, cableampacity will be increased. The results show that the cable

ampacity decreases with the increase of cable depth

installation under soil surface. By using MATLAB with thesteady state conditions based on IEC standards and comparing

with manufacturers, it gives good results. In facts that stand

out the importance of interaction with the manufacturers,

designer and installers of the line for attainment of coherent

data with the reality. The maximum operating temperature

of a cable is typically limited by its insulation material but

can also be limited by the maximum temperature which the

surrounding environment can be withstood without

degradation.

Acknowledgment

The authors would like to express his great thanks to the

team work of the Extra High Voltage Research Centre for

providing their facilities during this work.

References

[1] J. H. Neher, McGRATH, ’The calculation of the

temperature rise and load capability of cable system",

AIEE Transaction, vol.76, part 3, Octoper 1957,

pp.752-772.

[2]

Niv Hai-qing, Shi Yin- Xia, Wang Xaao- Bing, and

Zhang Yao “Calculation of ampacity of single core

cables with sheath circulating current based on iterative

method,” Guangzhou, 510640, China.

[3]

IEC Standard: Electric Cables – Calculation of

Current Rating – Part 1: Current rating equations

(100% load factor) and calculation of losses, Section 1:

General. Publication IEC-60287-1-1, 1994+A2:2001.

[4]

IEC Standard: Electric Cables – Calculation of

Current Rating – Part 2: Thermal resistance – Section

1: Calculation of thermal resistance. Publication IEC-

60287-2-1, 1994+A2:2001.

[5] Francis Codeleon “Calculation of underground cable

ampacity,” CYME International T& D, 2005.

[6]

T. IVO, Domingues, Oliverira, et al. ’Development of

one specialist system to determine the dynamic current

capacity of underground transmission lines with XLPE

cables,’ B1-202- CIGRE 2006.

[7] Amin Mahmoud, Solmaz Kahourzade, R.K.Lalwani”

Computation of Cable Ampacity by Finite Element

Method Under Voluntary Conditions” Australian

Journal of Basic and Applied Sciences, 5(5): 135-146,

2011

[8]

IEC Publ. 60840, 3rd ed., “Power Cables with Extruded

Insulation an their Accessories for Rated Voltages above

30 kV (Um =36 kV) up to 150 kV (Um=170 kV) – Test

Methods and requirements”, 2004-4.

[9] IEC Standard: Electric Cables – Calculation of the

cyclic and emergency current rating of cables – Part 2:

Cyclic rating of cables greater than 18/30 (36) kV and

emergency ratings for cables of all. Publication IEC-

853-2, (1989-2007).

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Ampacities of underground cables