A Method for the Sag-tension Calculation in Electrical Overhead Lines

7/31/2019 A Method for the Sag-tension Calculation in Electrical Overhead Lines

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Copyright 2011, Praise Worthy Prize S.r.l..Reprinted, with permission of Praise Worthy Prize S.r.l.. from the International Review of Electrical Engineering, IREE, Vol. 6. n. 3

A method for the sag-tension calculation in electrical overhead lines

I. Albizu1, A.J. Mazon1, E. Fernandez1

Abstract The sag and tension values of overhead conductors are influenced by the creepdeveloped during the line lifetime. This paper presents a method for the sag-tension calculation of

overhead conductors that is characterised by the creep sequential calculation. Thus, the creep

developed in previous stages influences the creep developed in subsequent stages. Two periods

are differenced in the creep development: the installation period and the operation period. The

relation between the creep development and the factors that influence it such as the installation

process and the operation conditions during the line lifetime is described step by step. Copyright

2011 Praise Worthy Prize S.r.l. - All rights reserved.

Keywords:Sag-tension, Overhead conductor, Creep

I. NomenclatureT tensionL lengthA areaE elastic modulus coefficient of thermal expansion weight temperatures span length stress total strain strain related to temperatureT strain related to tensionmc strain related to metallurgical creep

gs strain related to geometrical settlementt timeg related to span geometryc related to conductorcore related to corea related to aluminiumo related to reference condition

II. IntroductionThe aim of the sag-tension calculation is the

calculation of the installation tension as a function of thesag and tension limits. Sag-tension calculation methodsallow the calculation of the conductor sag and tension fordifferent conductor temperatures, and wind and ice loadconditions, taking into account the evolution of theconductor creep during the line lifetime [1]. The tensionis limited by the tension limit of the conductor and thetowers. The sag limit is related to the security distance toground and line crossings. If the crossing distance is

below the security distance, line faults could occur [2-5].

The most complete methods are those that consider anindependent core and aluminium behaviour and obtainthe creep value from experimental tests [6-8]. Thesemethods calculate the aluminium tension and for thisreason they calculate the knee-point temperature wherethe aluminium gets slack.

The most widely used method is the graphical method[6] that is implemented in commercial software programssuch as SAG10 or PLS-CADD. This method is based onstress-strain and creep experimental curves. The core andthe aluminium curves are obtained separately.

The strain summation method [7] was proposed as an

alternative to the graphical method. The method ischaracterized for having the conductor strain as thedependent variable. The strain can be caused by tension,temperature and creep. The creep is the result of theaddition of metallurgic creep and geometrical settlement.Each of these strains is evaluated individually and theyare added to obtain the total strain.

In [8], the authors developed a method for the specialrequirements of the gap-type conductors. The methodwas based on the strain summation method but somechanges and improvements were carried out. Forexample, independent core and aluminium referencelengths were considered and the calculation of the creep

developed during the installation was defined in detail.The authors have carried out the generalization of the

method. As a result, the method is valid not only for gap-type conductors but for any type of conductor, includingthe high temperature low sag (HTLS) conductors [9-12]and the conventional conductors such as the ACSR. Themain advantage of the method is the flexibility for theconsideration of several creep stages and the ability totake into account the influence of previous creep stages.

This paper gives a detailed description of the methodand it includes diagrams that relate all the parts of thecalculation algorithm. The relation between the outputsand the inputs of the algorithm parts are clearly definedfrom the installation of the conductor to the end of the


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line lifetime. The creep calculation during the installationis fully described as a function of the type of conductor(gap-type or non gap-type) and taking into account thetime the conductor is at rest and whether there ispretensioning or not. The calculation of creep developedduring the operation is also described.

III. Sag-Tension Calculation AlgorithmThe creep developed in previous stages influences the

creep developed in subsequent stages [13,14]. For thisreason, the algorithm makes a sequential calculation ofthe creep. Two periods are differenced in the creepdevelopment: the installation period and the operationperiod (Fig. 1). The creep developed during the operationdepends on the creep previously developed during theinstallation. The creep developed during each operationstage is calculated taking into account the creepdeveloped so far.

In each stage, the metallurgical creep mc and the creepdue to geometrical settlement gs are calculatedseparately. The metallurgical creep is calculated as afunction of the conductor tension T, the conductortemperature and the duration tof the stage. The straindue to geometrical settlement is assumed to beindependent of time. It is only dependent on theconductor construction and the historical maximumtension Tmax experienced. This calculation process iscarried out for the aluminium and the core separately.

gs

instcore ,

Installation

gs

insta,

mc

instcore ,

mc

insta,

max,instaT

max,instcoreT

gs

core 1,

Operation

stage 1

gs

a 1,

mc

core 1,

mc

a 1,

max1,aT

max1,coreT

gs

ncore ,

Operation

stage n

gs

na,

mc

ncore ,

mc

na,

max,naT

max,ncoreT

INSTALLATION OPERATION

Fig. 1. Creep and maximum tension evolution in time

When the method characterises the conductorinstallation it differentiates between the gap-typeconductors and the rest of conductors.

The conductor temperature and the wind and ice loadsare assumed to be constant during each operation stage.Thus, the parameters that characterise each stage i are thefollowing:

Conductor temperature i Load conditions (ice and wind) Duration ti

From the creep strain values calculated for theoperation stages, the tension values related to themaximum tension conditions are calculated by the statecalculation algorithm described in section IV. The

maximum tension conditions are characterised by theconductor temperature and the ice and wind load values.The tension limit values are defined for these conditions.The conditions are related to specific stages (after theinstallation, 10 year operation, etc.). Thus, from theinstallation tension Tinst, the algorithm calculates the

conductor tension in the defined maximum tensionconditions. The installation tension value Tinst is iterateduntil one of the maximum tension conditions does notallow increasing its value. The state calculationalgorithm determines the conductor tension valuecalculating separately the core tension Tcore and thealuminium tension Ta from the conductor temperature i,the wind and ice load and the creep mc

icore, ,mc

ia, ,gs

icore,

and gsia, of the corresponding stage (installation, stage 1,

stage 2, etc.).

IV. State Calculation AlgorithmThe state calculation algorithm is shown in Fig. 2. The

core tension Tcore is iterated until the difference betweenthe span geometry lengthLgand the conductor lengthLcis below a threshold value. The aluminium tension Tacannot go below its minimum value. This minimumvalue is zero or a negative value if aluminiumcompression is considered [15]. This is taken intoaccount in the algorithm when aluminium tension Ta isevaluated.

State calculation

gs

core

gs

a

mc

core

mc

a

Load

Core

(2,4)

Tcore

Aluminium

(1,3)

Span

geometry

Iterate on Tcore

untilLc =Lg

Lcore

La

Lg

Ta

Lc

+

+

Tc

Fig. 2. State calculation algorithm

The state calculation algorithm is based in thedependence of the core and aluminium lengths Lcore andLa on the strain values due to tension

T

core ,T

a ,

temperaturecore

,a

, and creep mccore

, mca

, score

, sa

,


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inst

Tinst

mc

insta ,

gs

insta ,Modified aluminium

stress-strain curve

(Fig. 5)insta ,

T

insta,

Thermal

expansion (7)

insta ,

Ta,inst

Elastic

deformation (8)

Ta,inst(%)

Aluminium

pre-sagging

tension

Geometrical

settlement (9)

Metallurgical

creep (6)tpre-sagging

max,instaT

Fig. 3. Creep developed in the aluminium of a gap-type conductor during the installation

modified

original

Fig. 4. Modified (1 h metallurgical creep removed) stress-strain curve

a,inst

a,inst

a,inst

Fig. 5. Modified (1 h metallurgical creep removed) aluminiumstress-strain curve

ssinstainsta

, (7)

ainsta

T

insta E,, (8)

insta

T

instainsta

gs

insta ,,,, (9)

Fig. 6 shows a diagram of the algorithm that

calculates the creep developed by the core during theinstallation of the gap-type conductors. The input valuesof the algorithm are the installation temperature inst, theinstallation sagging tension Tinst and the time the core isat rest under installation sagging tension trest. The outputsof the algorithm are the maximum tension max

,core instT

experienced and the deformation due to metallurgicalcreep

,mc

core inst and geometrical settlement ,gs

core inst .

The metallurgical creep ,mc

core inst is calculated as afunction of the core tension Tinst, the installationtemperature inst and the time the core is at rest trest. Themetallurgical creep in the core follows the law given in(6), where K, , and are constant coefficients thatrepresent the behaviour of the core steel. Thesecoefficients are different from those previously given forthe aluminium.

The deformation due to geometrical settlement

,gs

core inst is obtained from the stress-strain curves in a

similar way to the aluminium (10-12). This process hasbeen described above.

ssinstcoreinstcore

, (10)

coreinstcore

T

instcore E,, (11)

instcore

T

instcorecore

gs

instcore ,,, (12)


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inst

Tinst

mc

instcore ,

gs

instcore,Modified core

stress-strain curvecore

T

instcore ,

Thermal

expansion (10)

instcore ,

Elastic

deformation (11)

trest

Geometrical

settlement (12)

Metallurgical

creep (6)

max,instcoreT

Fig. 6. Creep developed in the core of a gap-type conductor during the installation

V.2. Non gap-typeConductorsIn the case of non gap-type conductors there is no

relative displacement between the core and thealuminium during the installation of the conductor.Hence, the total strains of the conductor c, thealuminium a and the core core have the same values. Forthis reason, the reference lengths of the core core

oL and the

aluminiuma

oL have the same values.It is recommended to maintain the conductors at rest

under the sagging tension Tinst for some hours in order toreduce the metallurgical creep during line operation. 12hours is recommended and 48 hours is desirable.

The deformation due to geometrical settlement isindependent from the duration of the period at rest. Itdepends on the sagging tension Tinst and the installationtemperature inst. Fig. 7 shows a diagram of the algorithmthat calculates the geometrical settlement creepdeveloped in the core

,gs

core inst and the aluminium ,s

a inst

during the installation. The deformation due to

geometrical settlement is obtained from the stress-straincurves of the conductor. In this case, the total strains ofthe aluminium a and the core core have the same values.Fig. 8 shows the way these strains are obtained. Firstly,the core and aluminium curves are displaced in the strainaxis to take into account the strain due to temperature

,core inst and ,a inst

. Then, from the tension Tinst and the

area of the conductorA, the conductor stress inst iscalculated and the total strain c is obtained from theconductor stress-strain curve. This strain value is thesame as the aluminium a and the core core strains.Besides, the stress values of the aluminium a and the

core core are calculated (13,14) from the virtual stress

values virtuala and

virtual

core obtained from the virtual

stress-strain curves of the aluminium and the core as it isshown in Fig. 8. From the stress values, the tensionvalues are obtained (15,16).

a

virtual

instainstaA

A ,, (13)

core

virtual

instcoreinstcoreA

A ,, (14)

ainstainsta AT ,max, (15)

coreinstcoreinstcore AT ,max

, (16)

While the conductor is at rest during the period trest,the deformation due to creep develops, the conductorstress value decreases and as a consequence the creepdeformation developed afterwards decreases too. In otherwords, the creep that results from a constant stress valueequal to the initial stress of the period is higher than thecreep that actually develops. To take into account thisfact, the calculation method follows the following steps.

Firstly, the initial reference length Lo,ini is calculated

taking into account the catenary conductor length Lgrelated to the installation tension Tinst, the creep straindue to geometrical settlement

,s

a inst calculated

previously, the strain due to tension Tinsta, and the strain

due to temperature insta, (17). The metallurgical creep is

not taken into account because it has not starteddeveloping yet.

gsinstainstaTinstaga

inio

core

inioinio

LLLL

,,,,,,

1 (17)


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inst

Tinst

Modified conductor

stress-strain curves

(Fig. 8)

gs

instcore,core

T

instcore,

Thermal

expansion

(7,10)

instcore,

Elastic

deformation

(8,11)

Geometrical

settlement (9,12)

a

gsinsta ,

insta ,

insta ,

instcore ,

Tension

(15,16)

max,instaT

max,instcoreT

T

insta ,

Fig. 7. Geometrical settlement creep developed in the core and the aluminium during the installation

core

aluminium

conductor

virtual

insta,

virtual

instcore,

inst

insta,

instcore,acore

c

Fig. 8. Modified conductor stress-strain curve

Then, to calculate the metallurgical creep developedduring the rest period trest, the method proposed byCIGRE [14] is used. This method divides the period oftime trest in short sub-periods in which the change instress and creep strain is small enough. Sub-periods inwhich the change in strain is around 20 m/m areconsidered. The initial tension of the first sub-period isthe installation tension Tinst. At the end of each sub-period, with the new creep values, the core andaluminium tension values are updated by the statecalculation algorithm and these are used to evaluate thecreep in the following sub-period. This process is carriedout until the period is completed. As a result, themetallurgical creep developed by the core mc

instcore, and

the aluminium mcinsta, , and the tension value Tat the endof the period are obtained.

At the end of the period, the conductor catenary lengthLgrelated to the final tension Tis higher than the initialconductor catenary length Lg related to Tinst, and for thisreason the conductor is retensioned to the initial value.Hence, a portion of the conductor is removed. Thus, thenew reference valueLo is lower than the initial referencevalueLo,ini and it is given by (18) taking into account themetallurgical creep mc

insta , developed during this period.

mc

insta

gs

instainsta

T

insta

ga

o

core

oo

LLLL

,,,,1

(18)

The conductor can be pretensioned during theinstallation process causing the geometrical settlement ofthe conductor and decreasing the deformation developedduring the operation. During the pretensioning period,the conductor is under a tension Tpret that is higher thanthe installation tension Tinst.

The calculation of the deformation due to geometricalsettlement is carried out in a similar way to thecalculation when there is no pretensioning. The onlydifference is the value of the tension. Thus, thecalculation algorithm is that given in Fig. 7 but with Tpretinstead ofTinst.

The calculation of the metallurgical creep is alsocarried out in a similar way to the calculation when thereis no pretensioning. The only difference is that when theinitial reference length Lo,ini corresponding to thebeginning of the period at rest is calculated, the creepdeveloped during the pretensioning period is taken intoaccount (19).

mcpretagspretainstaTinstag

inio

LL

,,,,,

1 (19)

VI. Creep Developed during the OperationTo calculate the creep developed during the operation,

the line lifetime is divided in operation stages where theconductor temperature and the wind and ice loads areassumed to be constant. The method calculatessequentially each of the operation stages.

Fig. 9 shows the calculation of the creep in theoperation stage i. The input values are the creep strainvalues mc

icore 1, ,mc

ia 1, ,gs

icore 1, andgs

ia 1, and the historical

maximum tension values max1, icoreT and

max1, iaT at the end of

the stage (i-1). The output values are the same but at the


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end of the stage i.

gs

icore 1,

gs

ia 1,

mc

icore 1,

mc

ia 1,

max1, iaT

max1, icoreT

Operation stage i

gs

icore,

gs

ia,

mc

icore,

mc

ia,

max,iaT

max,icoreT

i

Loadi

State

Calculation

(Fig. 2)

Tocore,i

Toa,i

Metallurgical

creep

calculation

Geometrical

settlement

calculation

ti

Fig. 9. Creep calculation in the operation stage i

In a first step, the initial tension values,o

a iT and ,o

core iT

corresponding to the creep at the end of the stage ( i-1)and the temperature and the load of the stage i are

calculated by the state calculation algorithm. From thesetension values the geometrical settlement is calculatedfirst and the metallurgical creep is calculated afterwards.

The initial tension values,o

a iT and ,o

core iT of the stage i

are compared with the historical maximum tension

values max 1, icoreT andmax

1, iaT . If they are lower, the creep

strain due to geometrical settlement and the maximumhistorical tension values do not change. If the initialtension value is higher, the creep strain due togeometrical settlement and the maximum historicaltension values are recalculated. Fig. 10 shows thecalculation of the geometrical settlement of the

aluminium gsia, . The total strain ia, is given by (20) and

the geometrical settlement of the aluminium gsia, is

calculated by the equation (21). The calculation for thecore is carried out in a similar way.

a

o

a

iaL

L, (20)

mc

iaia

T

iaia

gs

ia 1,,,,, (21)

The load due to wind or ice affects the span geometry

whereas the conductor behaviour is affected by theconductor temperature i. The algorithm iterates thetension value Tc until the difference between the spangeometry lengthLg and the conductor lengthLc is below

a threshold value. The conductor is characterised fromthe stress-strain curves of the core and the aluminium.These curves have been modified as it has beendescribed above (Fig. 4). Besides, below the maximumhistorical tension value, the behaviour of the aluminiumand the core is linear and is a function of the elasticmodulus (Fig. 11).

To make the calculation of the metallurgical creepdeveloped during the stage i, the period ti is divided inseveral sub-periods where stress and temperature valuesare considered to be constant. As it has been mentionedbefore, sub-periods in which the change in strain isaround 20 m/m are considered. To evaluate the creepduring the first sup-period, the core and aluminium stressvalues are calculated by the state calculation algorithmfrom the geometrical settlement calculated for the stage i,the metallurgical creep at the end of the stage (i-1) andthe temperature

i . At the end of each sub-period, the

core and aluminium tension values are updated. As aresult, the metallurgical creep developed by the core

mc

icore, and the aluminiummc

ia, are obtained.


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Aluminium geometrical settlement

Lc

gs

ia ,

Span

geometry

(catenaryequation)

i

Loadi

L Iterate on Tc

untilLg=Lc

Conductor

stress-strain

curve at stage

(i-1)

Tc

Tamax,iaT

Deformation

calculation

(20)

Elastic

deformation

La

Thermal

expansin

Geometrical

settlement (21)ia ,

T

ia ,

ia ,

mc

ia 1,

Fig. 10. Aluminium geometrical settlement calculation in the operation stage i

aluminiummax,ia

max1, ia

ia ,mc

ia 1, gs

ia 1,

T

ia ,

ia ,

gs

ia ,

stage (i-1)

stage i

Fig. 11. Stress-strain curve of the aluminium at the end of the stages

(i-1) and i

VII. Application ExampleThe described method is applied in an application

example. The span length is 350 m and the conductor isthe ZTACIR Hen. The installation tension is 1681 kg (15% RTS) and it has been carried out at 15 C.

The maximum tension conditions evaluated are thoseestablished in the Spanish regulation. The maximumtension condition in Spanish lines considers ice load at-20 C. Besides, a high temperature operation of the line

is expected. In order to model the effect of differentoperation temperatures, the conductor temperature is

assumed to be 15 C for 6 months, 30 C for 3 months,

60 C for 2 months and 120 C for one month every year.

VII.1. Creep Developed during the InstallationThe ZTACIR conductor is a non gap-type conductor

and for this reason the algorithm described in sub-sectionV.2 is applied. Thus, the geometrical settlement iscalculated with the algorithm given in Fig. 7 The inputsare the installation temperature inst (15 C) and tensionTinst (1681 kg). The obtained results are the geometricalsettlement of the core

,gs

core inst (6.5410-6) and the

aluminium,s

a inst (1.710-4), and the historical maximum

tension of the core max,instcoreT (812 kg) and the aluminiummax,a inst T (869 kg). For the metallurgical creep calculation,

the period the conductor is at rest trest is assumed to beone hour. The obtained results are the metallurgical creepdeveloped by the core mc

instcore, (3.5510-6) and the

aluminium mcinsta, (8.510

-6). As the ZTACIR is a non

gap-type conductor, the reference lengths coreoL and

a

oL

given by the equation (18) have the same value (350.65m). They are obtained from the catenary length of theinstalled conductorLg(350.89 m).


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VII.2. Creep Developed during the OperationThe creep developed for 10 years is calculated. The

first step is the definition of the operation stages. For thispurpose, in addition to the duration of the stage, theconductor temperature and the wind and ice loads havebeen defined. Each year is divided in 4 stages of

different length (6, 3, 2 and 1 month) where differentconductor temperatures are assumed (15 C, 30 C, 60C, 120 C). Besides, after 5 years in operation an iceload condition is assumed at -20 C. Hence, 41 stages arecalculated. The algorithm described in Fig. 9 is appliedto each of the stages.

Fig. 12 shows the evolution of the creep during the 10year period. The first 5 years there is an increase of themetallurgical creep that decreases the tension value. As aconsequence, the tension values are below the historicaltension values and no geometrical settlement isdeveloped. When the ice load occurs new historical

tension values are obtained for the core

max

coreT (1494 kg)and the aluminium max,a instT (2109 kg). Hence, geometrical

settlement is developed and it mainly affects thealuminium. During the last 5 years the metallurgicalcreep develops but much slower than at the beginning.

0,E+00

5,E05

1,E04

2,E04

2,E04

3,E04

0 1 2 3 4 5 6 7 8 9 10

M

etallurgicalcreepstrain

Time,yearCore Aluminium

0,E+00

1,E04

2,E04

3,E04

4,E04

5,E04

0 1 2 3 4 5 6 7 8 9 10

Geometricalsettlementstrain

Time,yearCore Aluminium

Fig. 12. Creep developed during the operation

VIII.ConclusionA complete description of a sag-tension calculation

algorithm developed by the authors has been presentedincluding a calculation example. The relation betweenthe creep development and the factors that influence it

such as the installation process and the operation

conditions during the line lifetime is described step bystep. The algorithm is characterised by the creepsequential calculation. Thus, the creep developed inprevious stages influences the creep developed insubsequent stages. Two periods are differenced in thecreep development: the installation period and the

operation period.The method is suitable for modelling the conductorbehaviour including the multiple stages during the linelifetime. Besides, it allows a detailed modelling of theinstallation process. The described algorithm takes intoaccount the interaction between the metallurgical creepand the geometrical settlement. Thus, the methodcalculates the installation tension for new lines takinginto account the expected conditions during the linelifetime. Furthermore, the method is also useful for thecalculation of the current state of lines in operationwhose historical operation conditions are known.

The method has several advantages over other

methods proposed in literature. Some advantages of thedeveloped method over the graphical method are relatedto the creep stages (several stages are calculatedsequentially and there is interaction betweenmetallurgical creep and creep due to wind or ice loads),the gap-type conductor installation (the aluminium creepis modelled and the steel is assumed to be at rest during aconfigurable duration), the high temperaturemetallurgical creep (independent core and aluminiumcreep calculation and coefficients as a function of theconductor type) and the pretensioning during theinstallation (it is included in the calculation method).Some advantages over the strain summation method arethe independent core and aluminium reference lengthsfor gap-type conductors and the detailed calculation ofthe creep developed during the installation.

Acknowledgements

This work is financially supported by the Universityof the Basque Country UPV/EHU under projectEHU09/18, the Ministerio of Ciencia e Innovacin underproject DPI2009-08454 and the Eusko JaurlaritzakoHezkuntza, Unibertsitate eta Ikerketa Saila (Euskalunibertsitate-sistemako ikerketa-taldeak Ref. IT532-10).

References

[1] CIGR B2-12 Brochure (Ref. No. 324), Sag-tension calculationmethods for overhead lines, 2007.

[2] H. Mokhlis, H.Y. Li, A.R. Khalid, The application of voltage sagspattern to locate a faulted section in distribution network,International Review of Electrical Engineering, vol. 5, n. 1, 2010,pp. 173-179.

[3] H. Mokhlis, A.H.A. Bakar, D.N.A. Talib, H. Mohamad, Theimprovement of voltage sags pattern approach to locate a fault indistribution network, International Review of ElectricalEngineering, vol. 5, n. 3, 2010, pp. 1159-1164.

[4] H. Mokhlis, H.Y. Li, H. Mohamad, A.H.A. Bakar, Acomprehensive fault location estimation using voltage sag profile

for non-homogenous distribution networks, International Reviewof Electrical Engineering, vol. 5, n. 5, 2010, pp. 2310-2316.


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[5] N. Kang, Y. Liao, New fault location technique for seriescompensated transmission lines, International Review ofElectrical Engineering, vol. 4, n. 6, 2009, pp. 1385-1390.

[6] T. Varney, Graphic method for sag-tension calculations for ACSRand other conductors, Alcoa, 1926.

[7] J.S. Barrett, S. Dutta, O. Nigol, A new computer model of ACSRconductors, IEEE Trans. Power App. Syst., vol. PAS-102 n. 3,1983, pp. 614-621.

[8] I. Albizu, A.J. Mazon, I. Zamora, Flexible strain-tensioncalculation method for gap-type overhead conductors, IEEETrans. on Power Del., vol. 24 n. 3, 2009, pp. 1529-1537.

[9] CIGR B2-12 Brochure (Ref. No. 244), Conductors for theuprating of overhead lines, 2004.

[10] I. Albizu, A.J. Mazon, V. Valverde, G. Buigues, Aspects to takeinto account in the application of mechanical calculation to hightemperature low sag conductors, IET Gener. Transm. Dis., vol. 4n. 5, 2010, pp. 631-640.

[11] Technical Specifications for the Installation of Gap TypeConductors. SAPREM Method, SAPREM, 2006.

[12] M. Landeira, P. Morentin, A.J. Mazon, I. Albizu, The hightemperature cable solution for electrical overhead distributionlines,DYNA, vol. 82 n. 5, 2007, pp. 226-230.

[13] CIGR 22-05, A practical method of conductor creepdetermination,ELECTRA, vol. 24, 1972, pp. 105-137.

[14] CIGR 22-05, Permanent elongation of conductors. Predictorequations and evaluation methods, ELECTRA, vol. 75, 1981, pp.63-98.

[15] O. Nigol, J.S. Barrett, Characteristics of ACSR conductors at hightemperatures and stresses, IEEE Trans. Power App. Syst., vol.PAS-100 n. 2, 1981, pp. 485-493.

[16] A method of stress-strain testing of aluminum conductor and a testfor determining the long time tensile creep of aluminumconductors in overhead lines, Electrical Technical Committee ofThe Aluminum Association, 1999

Authors information1Electrical Engineering Department

Faculty of Engineering of BilbaoUPV/EHU University of the Basque CountryAlda. Urquijo s/n48013-BilbaoSpaine-mails [email protected]

[email protected]@ehu.es

I. Albizu was born in Zumaia, Spain, in 1975.He received the M.Sc. degree in electronicinstrumentations systems from the Universityof Manchester Institute of Science andTechnology, Manchester, U.K., in 1999, andthe Ph.D. degree from the University of theBasque Country, Bilbao, Spain, in 2008.

Currently, he is a Lecturer with the ElectricalEngineering Department, Faculty of Engineering of Bilbao, Universityof the Basque Country. His research activities are concentrated in thearea of transmission-line thermal rating..

A.J. Mazon was born in Bilbao, Spain, in1965. He received the Ph.D. degree from theUniversity of the Basque Country, Bilbao,Spain, in 1994. In 1992, he was with LabeinResearch Laboratories.Currently, he is a Full-Time Professor in theElectrical Engineering Department, Faculty ofEngineering of Bilbao. His research activities

are concentrated in the area of electric power systems, transientssimulation, fault analysis, and transmission-line thermal rating.

E. Fernandez was born in Bilbao, Spain, in1973. She received her Ph.D. degree from theUniversity of the Basque Country, Bilbao,Spain, in 2008.Currently, she is a Lecturer with the ElectricalEngineering Department, Faculty ofEngineering of Bilbao, University of theBasque Country. Her research activities are

concentrated in the area of transmission-line thermal rating and low-voltage arc chutes studies.

A Method for the Sag-tension Calculation in Electrical Overhead Lines

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