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RADIAL TEMPERATURE DISTRIBUTION OF AAAC OVERHEAD LINEIN STATIONARY AND TRANSIENT CONDITIONS

M. Kang*, M. Strobach and C. M. Franck

Power Systems and High Voltage Laboratories, ETH Zurich,Physikstrasse 3, 8092 Zurich, Switzerland

*Email: kang@eeh.ee.ethz.ch

Abstract: Commonly, dynamic line rating (DLR) calculates conductor temperature with abasic energy balance equation, which assumes homogeneous conductor temperature.With this 0D temperature assumption, however, there is a risk that inner layers of theconductor might exceed the limit temperature, if the rating current approaches itsampacity. Since conductor overheating should be avoided for operational safety, it isvaluable to investigate radial temperature distributions of conductors. Throughout thisstudy, therefore, homogeneous 1D conductor model with a radial temperature distributionis simulated in steady and transient states. For steady state simulations, radialtemperature distributions under various ambient conditions are studied. Higher windvelocity, lower solar radiation, and lower ambient temperature make the temperaturegradients more pronounced. Also, transient temperature distribution is modeled with a

various stepwise current changes. When the core temperature reaches 80C,momentous radial temperature distributions are analyzed. Compared to the steady state,transient phases show smaller temperature differences between core and surface. Bothlower initial and higher final currents result in a flatter radial temperature distribution,whereas higher final currents cause faster transient heating. Compared to 0D calculations,the 1D model with a radial temperature distribution reduces the ampacity and preventsconductor core overheating.

1 INTRODUCTION

Aluminum is the most frequently used material [1,pp. 200] for overhead lines (OHLs) because of its

advantages. By mixing magnesium and silicon intoaluminum, all aluminum alloy conductor (AAAC)achieves more than 1.5 times higher strength,while sacrificing only 5% of ampacity (currentcarrying capacity, Iccc) [1, pp. 206].

Despite its advantages, the usability of AAAC islimited by its low operation temperature. AAACsstart recrystallization when they are heated up toover 100C, and lose the mechanical strength [1,pp. 202]. Also, its high thermal expansioncoefficient and low specific weight make AAACsmore vulnerable to sagging and vibration [1, pp.206]. For these reasons, the maximum allowabletemperature Tlimof AAAC is limited to 80C [3]. Tlimdetermines the ampacity under the given ambientconditions [4], since higher temperatures result inlarger sags and worse mechanical integrity ofconductors.

Therefore, Cigre [5], IEC [6], and IEEE [4]developed standard OHL models analyzing theconductor temperature. To simplify the calculation,the models commonly disregard the radialtemperature distribution, T(r)of the conductor.

These non-dimensional (0D) models are beneficialfor the static line rating (SLR). In SLR, the ratingcurrents are kept low for security reasons [10] and

enough margins exist between allowable andactual line temperatures. Therefore, the coretemperatures remain lower than the allowabletemperature in general.

The 0D models might not be suitable for dynamicline rating (DLR). DLR offers an improvedtemperature management of OHL conductors. It isenabled by accessing and real-time processing ofon-site conductor temperature and weatherinformation. DLR then not only optimizes currentloading of OHLs but also, minimizes operationalrisk by improving security and safety. Therefore,the conductors can be operated near Tlim. For thiscase, the 0D models may result in conductor coreoverheating, because they ignore the T(r)distribution.

To analyze the limits of 0D models on DLR, ahomogeneous cylindrical conductor is modeledand its radial temperature distribution is studied.The radial temperature distribution was researchedextensively by Morgan [7], and its significance onDLR was already suggested by Douglass [8].Nonetheless, parametric researches on stationaryand transient behavior of AAACs are still required.Throughout this paper, therefore, the conductortemperature T(r) is simulated with a 1D model forvarious stationary and transient states. Severalgroups of relevant weather conditions are variedfor steady state simulation, and several currentsteps are applied to transient phase simulation.

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2 1D CONDUCTOR MODELING

2.1 System and environment

Conductor: For the modeling, the conductor issimplified as a homogeneous cylinder with infinitelength. To study T(r) only, a uniform surfacetemperature Ts without angular and axial

temperature distribution is applied. An AAAC with aconductor cross section A=550mm

2 is used as a

reference material. It consists of 61 strands withd=3.4mm, and has total conductor diameterD=30.6mm. As the conductor geometry iscomparable to 61/3.5mm AAC in [7], the sameeffective radial thermal conductivity kr= 1.23W/mKis assumed. The other typical material properties of

AAAC are adopted from [5], and presented inTable 1.

Table 1:Reference AAAC properties at 20C

Properties Value

Diameter, D 30.51 [mm]

DC Resistivity, 32.7 nm]

Density, 2703 kg/m3

Heat capacity, c 909 J/kgK

Absorptivity, 0.5

Emissivity, 0.5

Effective radial thermal conductivity, kr 1.23 [W/mK]

Environment: Ambient temperature Ta,perpendicular wind velocity Vwand solar radiation

S are applied around the whole conductorcircumference. Utilities in Switzerland assumeconservative weather condition for the line rating[9]. For the operational safety, Vwand Sare fixedto a worst-case value while Ta varies to applyseasonal weather differences [10]. The conditionsare shown in Table 2.

Table 2:Seasonal weather conditions

Parameters

Ta[C] Vw[m/s] S[W/m ]

Winter 100.5 900Intermediate 20

Summer 40

2.2 Heat equations

The conductor system and environment satisfy thethermal equilibrium at the steady state [5]. Thepower gain of the system is the sum of Joule,ferromagnetic, solar, and corona heating per unittime (PJ, PM, PS,and Pi, respectively). It balancesthe power loss, which is the sum of convective,

radiative and evaporative cooling per unit time (Pc,Pr, and Pw, respectively). According to [7], thereduced equation for AAAC conductors is:

The T(r) distribution is described by the heatequation in the form of [7]:

[

]

where r is theconductor radius (0

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different values of Vw(0.5, 2.5, and 4.5m/s) and S(500, 900, and 1200W/m

2) are used in the

simulation. For each condition, Iccc is calculated.

These values are then used as references fortransient phase simulation.

Assuming similar weather conditions, steady state

ampacity from 1D and 0D models are calculatedand compared. All of them use the same maximumallowable temperature, 1D conductormodel has the maximum temperature at theconductor core, and the ampacity is the current at .Both IEEE and IEC models ignore the T(r)distribution and the ampacity is the current at

. Among the 0D models, only Cigre modeluses simplified assumptions for the radialtemperature distribution, and its ampacity isdefined as the current at Although Cigremodel denotes temperature differences between and [5], the radial temperature distribution is notconsidered for its ampacity analysis.

Transient phase: Transient simulations are donewith the winter weather condition of Table 2.Therefore, the steady state ampacity of thiscondition is used as a reference. For the transientphase, the allowable time interval tli mis defined asthe elapsed time to raise the conductortemperature to Tlim. By raising the current stepwise,transient T(r) distributions at t = tlim areinvestigated.

The stepwise change is done from initial current Ii(30% and 60% Iccc) to final current If(120%, 150%,and 200% Iccc). These situations should beinvestigated extreme situations for a line operatingfirst in (N)- and then in (N-1)-condition. The plansfor the transient current change are presented inTable 3.

Table 3:Transient current change plans

(% Iccc)

120% 150% 200%

(%I

ccc

) 30%Plan A

(30120)Plan B

(30150)Plan C

(30200)

60%Plan D

(60120)Plan E

(60150)Plan F

(60200)

3 RESULTS AND DISCUSSION

3.1 Influences of weather parameters onsteady state temperature distribution

By limiting Tc=Tlim=80C, the steady state T(r)

distributions for different weather conditions areobtained (See Figure 1). Since each weatherparameter influences the elements of heat balanceequation (1), T(r) and ampacity are varied with

parameter change. In addition to seasonal weatherconditions in Table 2, each weather parameter ismanipulated to investigate steady state T(r)

distribution.

Figure 1: T(r), comparison with different Ta (left),

Vw(center) and S(right), when .Among the weather parameters, Vwhas the largest

influence on T(r), and S has the smallest. Theequilibrium ampacity increases significantly with Vw,as the heat loss Pcincreases with the wind velocity.

Analysis for each parameter is done below.

Ambient temperature:To control the influence ofother parameters, fixed value of Vw=0.5m/s andS=900W/m

2 are used for Ta simulation. Lower Ta

results in larger T(r)gradients. Both Pcand Prof (1)increase with decreasing Ta [5]. Therefore, highercurrents are needed to increase PJfor equilibrium.Since Ta is the only variable of the static weatherconditions, this part of simulation result can be

used for SLR as well. To reach a core temperatureof 80C under the three different values of Ta=10,20, and 40C, current values of I=962.3A, 886.0A,and 703.8A are needed, respectively.

Wind velocity:To study the influence of Vwonly,fixed values of Ta=10C and S=900W/m

2are used

for this set of simulation. High wind velocitiesdecrease Ts significantly and cause larger T(r)gradients at the ampacity limit. Pcstrongly dependson Vw [5]. For the equilibrium of (1), ampacityincrease with Vw. To reach a core temperature of80C under the three different values of Vw =0.5,

2.5 and 4.5 m/s, the current values of I=962.3A,1395.7A, and 1670.8A are needed, respectively.

As mentioned above, the wind velocity is the mostinfluential parameter.

Solar radiation: Similarly, to cancel out theinfluence of the other parameters, Ta=10C andVw=0.5m/s are used. Decreasing the solarradiation causes a reduction of the total heat gainPS. When the other conditions are kept fixed, PJ

has to be increased to satisfy (1) with a highercurrent [5]. To reach a core temperature of 80Cunder the three different values of S = 500, 900,

and 1200 W/m2, current values of I=990.3A,962.3A, and 940.7A are needed, respectively.Compared to the other parameters, solar radiationhas relatively small influence on T(r)distribution.

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3.2 Steady state ampacity comparison

The ampacity values for the standard weatherconditions are presented in Table 4 for the 0Dmodels according to IEEE and Cigre, as well as forthe 1D model. Respecting the Tlim=80C value for

the core temperature results in a reduction of lineampacity as well.

Table 4: Seasonal ampacity comparison ofdifferent models

0D Iccc(A) 1D Iccc (A)

IEEE(Ts=80C)

Cigre(Tav=80C)

COMSOL(Tc=80C)

Winter 1069.9 1024.4 962.3

Intermediate 996.9 953.0 886.0

Summer 825.3 786.5 703.8

As shown in Figure 2, if the ampacity value

calculated from the IEEE (or IEC) 0D model wouldbe used in the 1D model, the whole conductortemperature (except its surface) exceeds Tlim andreaches a core temperature of 86.7C. When theCigre 0D model is used, half of the conductor areaexceeds Tlim, and Tc=83.2C Therefore, the T(r)distribution should be properly considered torespect the line security.

Figure 2: T(r) comparison of COMSOL 1D (solid,Iccc=1069.9A), Cigre 0D (dashed, Iccc =1024.4A),and IEEE 0D (dot, Iccc=962.3A) models at Winterambient condition.

The core temperature increase becomes worsewhen the weather conditions allow a higher

ampacity, since then PJ and T increase in

equations (4) and (6).

To analyze the influence of overrated ampacity, T(r)distributions with IEEE 0D model ampacity arepresented (see Figure 3). Among the simulation

results, the maximumTc=105C is obtained underthe weather condition of Ta=10C, Vw=4.5m/s, andS=900W/m

2. [9] shows that this weather condition

occurs frequently in Switzerland, and it may even

remain for a long time. According to [1, pp. 203],the mechanical strength of aluminum decreasesafter long-term exposures to high temperature.

After 100 hours, the residual strength is around 80%of the initial strength, and after 1000 hours, itdecreases to 60%.

Figure 3: T(r) comparison with different Ta (left),

Vw(center) and S(right), when

.

3.3 Transient phase analysis

The influence of initial and final current is analyzed.The ampacity of the 1D model at Winter condition(Iccc=962.3A, see Table 4) is used as a referenceampacity of the transient phase simulations. Fromthe initial currents 30% and 60% Iccc, Initial steadystate Tc=23.4C and 38.4C are obtained,respectively (see Figure 4). Currents for the initialand final states are presented in Table 5.

Table 5:Initial and final states for transient phase

Initial currents Final currents

% Iccc 30% 60% 120% 150% 200%

I (A) 289 577 1155 1443 1925

The temporal evolutions of under the 6 differentcurrent steps are depicted in Figure 4. Qualitatively,higher initial current decreases the heatingduration, and results in smaller Also, thetemperature rises faster when final currentbecomes higher.

Tlim=80C

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Figure 4: t vsTc with various current plans

Influence of Iion T(r):With a lower initial current,it is obvious that

increases. Also, the

temperature distribution becomes slightly flatterbecause the initial steady state T(r) distribution isflatter with a smaller initial current. However, theinfluence of Ii has only minor effect on conductortemperature distribution (cf. Fig. 5). This isbecause the Joule heating power caused by theovercurrent is not large enough compared to theradial heat flux to justify complete adiabatic heating.

Figure 5: T(r) comparison of transient case C andF

Influence of Ifon T(r): As higher If increases the

temperature rise rate, decreases. In otherwords, the time to lose heat to environment isreduced and the process becomes more adiabatic.Therefore, the momentous temperature distributionis not changed much from the shape of its initialsteady state T(r) distribution, if the applied finaltemperature is higher. However, Ifof 120% to 200%ampacity is not enough to observe a dramaticdifference in T(r) distribution. For those final

current values, the momentous T(r) distribution atTc=80C is not very different form the steady stateT(r) curve (see Figure 6). With higher If, the

surface temperature increases, and differencebetween each transient case is around 0.1C.

Figure 6: T(r) comparison of transient case D, E,and F

3.4 Time variables of transient phases

Table 6: allowable time interval for different

models

Plans(change in % Iccc)

0D (s),Ts= Tlim

1D (s),Tc= Tlim

(s)

A (30120) 1779 1479 300

B (30150) 784 684 100

C (30200) 366 328 38

D (60120) 1606 1263 343

E (60150) 647 548 99

F (60200) 288 248 40

with and without T(r) distribution is comparedand their differences are presented in Table 6. tlim

decreases by increasing If. For all plans, tlim issmaller for the 1D model. If a 0D model would beused for transient phase analysis, there is a risk ofoverheating the wire for tlim, as Tcexceeds Tlimforthe duration.

4 CONCLUSION

The possible benefits of considering the radialtemperature distribution for DLR are elucidated bya simple 1D conductor model. If 0D models areused for steady state ampacity calculation, Tcmight exceed Tlim by up to 25C even inreasonable weather conditions. Wind speed is themost influential parameter for the radialtemperature gradient, as it has the largest effect for

Tlim=80C

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increasing the ampacity. On the other hand,changes in solar radiation do not affect the T(r)distribution significantly.

0D models neglect the T(r)distribution and assumeTs or Tc as conductor temperature. This could bedangerous, since the long-term exposure to high

temperatures permanently deteriorates themechanical integrity of the conductor. This can beavoided by considering a radial temperaturedistribution. Even with the simple 1D model, theoverheating of conductor core can be prevented.By applying the model to calculation, ampacity atdifferent weather conditions is reduced by 10 to18%. This modified steady state ampacity witheach weather condition might offer accurateinformation for the overhead line operators.

Also, with a stepwise current change, transientphases are simulated. Intensity of initial current

and final current is the governing factors for thetransient characteristics. With a lower initial current,the transient temperature profile is flatter. Higherfinal current results in faster temperature increase.

Also, the T(r) becomes flatter with higher If, bykeeping the conductor away from the heat transfer.

can be adjusted with the 1D model. Byregulating current with Tc, the 1D model is able tocontrol the overhead line temperature. Comparedto 0D models, it prohibits the extra time for heatingthe inner layers of a conductor. This is importantfor real time controlling of current with DLR.

5 ACKNOWLEDGMENTS

This study is financially supported by Swiss electricresearch, Pfisterer, and Swissgrid.

6 REFERENCES

[1] F. Kiessling et al., Overhead Power Lines,Springer, 2003.

[2] M. Farzaneh et al., Electrical Design ofOverhead Power Transmission Lines,McGraw-Hill, 2013.

[3] EN 50331-3-4: Overhead electrical linesexceeding AC 45 kV. Part 3-4: NationalNormative Aspects for Germany. Brussels,CENELEC, 2001.

[4] Standard for Calculating the Current-Temperature of Bare Overhead Conductors,IEEE Std 738, 2006.

[5] Thermal Behavior of Overhead Conductors,Cigre Working Group 22.12, August 2002.

[6] Overhead electrical conductors-Calculationmethods for stranded bare conductors, IEC TR

61597, 1995.

[7] V. T. Morgan, The radial TemperatureDistribution and Effective Radial ThermalConductivity in Bare Solid and StrandedConductors, IEEE Transactions on PowerDelivery, pp. 1443-1452, 1990.

[8] D. A. Douglass, Radial and Axial TemperatureGradients in Bare Stranded Conductors, IEEETransactions on Power Delivery, Vol. PWRD-1,No. 2, April 1986.

[9] Leitungsverordnung LeV, SR 734.31, 30.

March 1994.

[10] Guide for Selection of Weather Parameters forBare Overhdad Conductor Ratings, CigreWorking Group B2.12, 2006.

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