Study of The Effect of Convective Heat Transfer on Cooling ...1249010/FULLTEXT01.pdf · Study of The E ect of Convective Heat Transfer on Cooling of Overhead Line Conductors Based

INOM EXAMENSARBETE ,AVANCERAD NIVÅ, 30 HP

, STOCKHOLM SVERIGE 2018

Study of The Effect of Convective Heat Transfer on Cooling of Overhead Line Conductors Based on Wind Tunnel Experimental Results

Studie av Effekten av Konvektiv Värmeöverföring vid Kylning av Ledningsledare Baserat på Experimentellt Resultat från Vindtunneln

WADIH NAIM

KTHSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Study of The Effect of Convective Heat Transfer on Cooling of Overhead LineConductors Based on Wind Tunnel Experimental Results

Studie av Effekten av Konvektiv Varmeoverforing vid Kylning avLedningsledare Baserat pa Experimentellt Resultat fran Vindtunneln

Master Thesis Project

Wadih Naim

Supervisor: Kateryna Morozovska

Examiner: Patrik Hilber

A thesis presented for the degree ofM.Sc. in Electric Power Engineering

School of Electrical Engineering and Computer ScienceKungliga Tekniska Hogskolan (KTH Royal Institute of Technology)

Stockholm, SwedenAugust 2018

Study of The Effect of Convective Heat Transfer on Cooling of Overhead Line ConductorsBased on Wind Tunnel Experimental Results

Wadih Naim KTH, Stockholm, 2018

Acknowledgement

This thesis is the final stage of the Master of Science program in electric power engi-neering at KTH. The project was initiated and supervised by MSc. Kateryna Morozovska,to whom I offer my utmost gratitude, and was performed within the RCAM group at theElectromagnetic Engineering (ETK) department of the school of Electrical Engineering andComputer Science. MSc. Morozovska provided me with strong support and encouragementto pursue several research aspects of this project, and with helpful advice in terms of plan-ning and learning resources. Additionally, I would like to thank Dr. Patrik Hilber who isthe examiner of this thesis. Dr. Hilber gave me the opportunity to attend lectures andhave access to the reading material of the course “Reliability Evaluation of Electrical PowerSystems,” from which I had the inspiration to work on a paper titled “Effects of DynamicLine Rating on the Durability and Mechanical Strength of Aluminum Cable Steel Reinforced(ACSR) Conductors” in cooperation with Dr. Hilber and MSc. Morozovska (see Appendix1). I would also like to offer my gratitude to Dr. Tor Laneryd (R&D Engineer, ABB Cor-porate Research) who provided crucial advice related to CFD modeling and simulation.

Throughout the last two years, my professors at KTH provided me with excellent men-torship, for which I am grateful. They taught me how to perform independent researchwhich enabled me to reach this point at my education. So, I would like to thank them all.

Last but not least, I would like to thank my loving mom, dad, and two brothers whokept my spirit up throughout all of the challenging times during my graduate studies.

1



Abstract

It is important to keep an overhead power line within rated operating conditions. Thus,an accurate prediction of the conductor’s thermal and electrical behavior leads to an in-crease in reliability and efficiency. Under DLR operation, the current rating is adjustedbased on ambient weather and solar conditions to allow for dynamic line loading. Therating adjustment takes into account the cooling mechanisms acting on the conductor. Inthis thesis, cooling by means of convective heat transfer is studied based on wind tunnelexperimental measurements of three different conductor samples. Convection contributesto most of the cooling; however, it is affected by wind speed and direction. Two angle ofattacks were studied (40 and 90), where perpendicular flow was found to result in bettercooling. The location of boundary layer separation highly affects the surface distribution ofcooling, which is non-uniform. Oblique wind flow results in reduction in overall cooling dueto earlier boundary layer separation. Finally, the surface average convective heat transfercoefficient correlates non-linearly with the Reynolds number, where higher wind speeds andlarger conductor diameters can lead to significant improvements in cooling while keepingrelatively low current densities. The existing standards of IEEE and CIGRE were found tooverestimate the effect of convective cooling for the specific experimental cases.

Keywords: heat balance, overhead conductor, convective cooling, dynamic line rating(DLR)

2



Sammanfattning

Det ar viktigt att halla en kraftoverforingsledning inom nominella driftsforhallanden.Saledes leder en korrekt forutsagelse av ledarens termiska och elektriska beteende till en okadtillforlitlighet och effektivitet. Under DLR-drift justeras nuvardet baserat pa omgivandevader och solforhallanden for att mojliggora dynamisk belastning. Klassificeringsjusterin-gen tar hansyn till de kylmekanismer som verkar pa ledaren. I denna avhandling studeraskylning med hjalp av konvektiv varmeoverforing baserat pa provning av vindtunnel av treolika ledartyper. Konvektion bidrar till det mesta av kylningen. Det paverkas dock av vind-hastighet och riktning. Tva angreppsvinkelar studerades (40 och 90), dar vinkelratt flodebefanns resultera i battre kylning. Placeringen av ytskiktseparationen har stor inverkanpa ytfordelningen av kylning, vilken ar ojamn. Skra vindflode resulterar i minskning avden totala kylningen pa grund av tidigare separering av gransskiktet. Slutligen korrelerarden ytvardesoverforingskoefficienten for ytvardet icke-linjart med Reynolds-talet, dar hogrevindhastigheter och storre ledardiametrar kan leda till signifikanta forbattringar i kylningsamtidigt som relativt laga stromtathet halls. De befintliga standarderna for IEEE ochCIGRE visade sig overskatta effekten av konvektiv kylning for de specifika experimentellafallen.

Nyckelord: varmebalans, luftledare, konvektiv kylning, dynamisk linjestorlek (DLR)

3



Contents

List of figures 6

List of tables 8

1 Introduction 101.1 Project Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Literature Review 112.1 Transmission Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Line Sagging and Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Dynamic Line Rating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Methodology 163.1 IEEE Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 CIGRE Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4 Assumptions and Approximations . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4.1 Surface-to-Surface Radiation: A Simplified Approach . . . . . . . . . . 233.4.2 Cylinder in External Cross Flow . . . . . . . . . . . . . . . . . . . . . 243.4.3 Other Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.5 Mathematical Implementation and Data Fitting . . . . . . . . . . . . . . . . . 253.6 Computational Fluid Dynamics (CFD) Simulations . . . . . . . . . . . . . . . 26

4 Comparison of Existing Methods 29

5 Preliminary Analysis of Measured Data 325.1 Aluminum Rod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.2 Aluminum Conductor (Al59) . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.1 40 Angle of Attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2.2 90 Angle of Attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.3 Steel Reinforced-Aluminum Conductor (ACSR) . . . . . . . . . . . . . . . . . 405.3.1 40 Angle of Attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.3.2 90 Angle of Attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.4 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6 Mathematical Thermal Model Results 466.1 Experimental Value of The Convective Heat Transfer Coefficient . . . . . . . 466.2 Curve Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7 CFD Model Results 537.1 Aluminum Rod in a 90 Laminar Cross Flow . . . . . . . . . . . . . . . . . . 537.2 Stranded Conductor in a 40 Laminar Flow . . . . . . . . . . . . . . . . . . . 557.3 Stranded Conductor in a 90 Laminar Cross Flow . . . . . . . . . . . . . . . 56

8 Final Comparison and Discussion 58

9 Conclusion and Future Work 629.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

References 64

4



Appendix 1: Effects of Dynamic Line Rating on the Durability and Mechan-ical Strength of Aluminum Cable Steel Reinforced (ACSR) Conductors 66

Appendix 2: Detailed Plots and CFD Figures 73

5



List of figures

1 An illustration of a power system [2]. . . . . . . . . . . . . . . . . . . . . . . . 112 A plot of two different catenary curves (hyperbolic cosine functions) [per-unit]. 133 Three-dimensional illustration of the test object inside the wind tunnel . . . 224 Cross Section: The four quadrants of the conductor sample . . . . . . . . . . 225 Step function used to simulate starting of wind flow . . . . . . . . . . . . . . 276 Model and mesh used for the case of an aluminum rod under cross flow (left

to right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Model and mesh used for the case of a stranded conductor under 40 flow

(left to right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 Model and mesh used for the case of a stranded conductor under cross flow

(left to right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Comparison of calculation methods of convective heat transfer coefficient for

the ACSR conductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3010 Comparison of calculation methods of convective heat transfer coefficient for

the Al59 conductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3011 Effect factor of the angle of attack on convection according to IEEE (equation

14) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3112 Average Input Current Density (Aluminum Rod) . . . . . . . . . . . . . . . . 3313 Aluminum Rod Surface temperature at 4 m/s . . . . . . . . . . . . . . . . . . 3314 Aluminum Rod Surface temperature at 12 m/s . . . . . . . . . . . . . . . . . 3415 Aluminum Rod Surface temperature at 20 m/s . . . . . . . . . . . . . . . . . 3416 Average Input Current Density (Stranded Aluminum Conductor (Al59) at

AoA = 40) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3517 Stranded Aluminum Conductor (Al59) Surface temperature at 4 m/s (AoA

= 40) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3618 Stranded Aluminum Conductor (Al59) Surface temperature at 12 m/s (AoA


= 40) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3720 Average Input Current Density (Stranded Aluminum Conductor (Al59) at

AoA = 90) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3821 Stranded Aluminum Conductor (Al59) Surface temperature at 4 m/s (AoA



= 90) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3924 Average Input Current Density (Stranded Steel-Reinforced Aluminum Con-

ductor (ACSR) at AoA = 40) . . . . . . . . . . . . . . . . . . . . . . . . . . 4025 Stranded Steel-Reinforced Aluminum Conductor (ACSR) Surface and Core

Temperatures at 2 m/s (AoA = 40) . . . . . . . . . . . . . . . . . . . . . . . 4126 Stranded Steel-Reinforced Aluminum Conductor (ACSR) Surface and Core

Temperatures at 4 m/s (AoA = 40) . . . . . . . . . . . . . . . . . . . . . . . 4127 Stranded Steel-Reinforced Aluminum Conductor (ACSR) Surface and Core

Temperatures at 6 m/s (AoA = 40) . . . . . . . . . . . . . . . . . . . . . . . 4228 Average Input Current Density (Stranded Steel-Reinforced Aluminum Con-

ductor (ACSR) at AoA = 90) . . . . . . . . . . . . . . . . . . . . . . . . . . 4329 Stranded Steel-Reinforced Aluminum Conductor (ACSR) Surface and Core

Temperatures at 2 m/s (AoA = 90) . . . . . . . . . . . . . . . . . . . . . . . 43

6



30 Stranded Steel-Reinforced Aluminum Conductor (ACSR) Surface and CoreTemperatures at 4 m/s (AoA = 90) . . . . . . . . . . . . . . . . . . . . . . . 44

31 Stranded Steel-Reinforced Aluminum Conductor (ACSR) Surface and CoreTemperatures at 6 m/s (AoA = 90) . . . . . . . . . . . . . . . . . . . . . . . 44

32 Local convective heat transfer coefficient on the surface of the four quadrantsof the aluminum rod under cross flow . . . . . . . . . . . . . . . . . . . . . . . 47

33 Local convective heat transfer coefficient on the surface of the four quadrantsof the Al59 conductor under wind flow of AoA = 40 . . . . . . . . . . . . . . 47

34 Local convective heat transfer coefficient on the surface of the four quadrantsof the Al59 conductor under cross flow . . . . . . . . . . . . . . . . . . . . . . 48

35 Local convective heat transfer coefficient on the surface of the four quadrantsof the ACSR conductor under wind flow of AoA = 40 . . . . . . . . . . . . . 49

36 Local convective heat transfer coefficient on the surface of the four quadrantsof the ACSR conductor under wind flow of AoA = 90 . . . . . . . . . . . . . 49

37 Total surface-average convective heat transfer coefficients of the aluminumrod and Al59 conductors at different AoA’s and wind speed up to 24 m/s . . 50

38 Total surface-average convective heat transfer coefficients of the aluminumrod, Al59, and ACSR conductors at different AoA’s and wind speed up to 6m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

39 Surface plot of wind speed around a cylindrical rod under cross flow of inletspeed = 5 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

40 Surface plot of wind speed around a cylindrical rod under cross flow of inletspeed = 12 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

41 Surface plot of wind speed around a stranded conductor under laminar flowof inlet speed = 5 m/s and AoA = 40 . . . . . . . . . . . . . . . . . . . . . . 55

42 Surface plot of wind speed around a stranded conductor under laminar flowof inlet speed = 12 m/s and AoA = 40 . . . . . . . . . . . . . . . . . . . . . 56

43 Surface plot of wind speed around a stranded conductor under cross flow ofinlet speed = 5 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

44 Surface plot of wind speed around a stranded conductor under cross flow ofinlet speed = 12 m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

45 Experimental and standardized surface-averaged heat transfer coefficients ofan Al59 stranded conductor under wind flow of AoA = 40 . . . . . . . . . . 58

46 Experimental and standardized surface-averaged heat transfer coefficients ofan Al59 stranded conductor under wind flow of AoA = 90 . . . . . . . . . . 59

47 Experimental and standardized surface-averaged heat transfer coefficients ofan ACSR stranded conductor under wind flow of AoA = 40 . . . . . . . . . 59

48 Experimental and standardized surface-averaged heat transfer coefficients ofan ACSR stranded conductor under wind flow of AoA = 90 . . . . . . . . . 60

7



List of tables

1 Available Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 Results of curve fitting of the experimental value of the convective heat trans-

fer coefficient versus the Reynolds number . . . . . . . . . . . . . . . . . . . . 523 Factor of deviation between the standardized estimation of the convective

heat transfer coefficient and the experimental results at different wind speeds 60

8



List of Symbols and Abbreviations

• DLR: Dynamic Line Rating

• SLR: Static Line Rating

• SAR: Seasonal Ambient Rating

• AAR: Ambient Adjusted Rating

• ACSR: Aluminum Conductor Steel-Reinforced

• IEEE: Institute of Electrical and Electronics Engineers

• CIGRE: Conseil International des Grands Reseaux Electriques

• AoA: Angle of Attack

• AC: Alternating Current

• DC: Direct Current

• CFD: Computational Fluid Dynamics

• FEM: Finite Element Method

9



1 Introduction

In general, the electric operation of power conductors is limited by thermal parameters.The only controllable input during operation is the electric current. Traditionally currentratings are fixed and limited by sagging for bare overhead lines, and thermal breakdown forinsulated cables under worst case scenarios. Yet in reality, ambient conditions can be favor-able for increased current ratings. Dynamic Line Rating (DLR) is based on that concept,where solar heating and overall cooling are calculated based on real-time data. Predomi-nantly, conductor cooling occurs by convective heat transfer, followed by infrared radiation.While radiation calculation methods are well established, calculation of convective coolingis estimative for stranded conductors, mainly due to irregular surface geometry.

In this report, the convective heat transfer coefficient is isolated analytically, followed bypractical implementation on existing wind tunnel experimental data. The methodology isoptimized for the controlled experimental environment, where local heat transfer coefficientscan be observed on several locations on the conductor sample. Through observations of sim-ulated fluid dynamic behavior around the sample, the experimental data are interpretedaccordingly. Finally, an improved calculation method is presented to fit the experimentaldata for the given ranges of wind speed and angle of attack.

From an ethical perspective, increased accuracy in DLR implementation leads to severalenhancements in the society. Starting with an improvement in reliability of transmissionnetworks, power producers and consumers alike would have better access to infrastructurewith reduced outages. In terms of resources, higher reliability leads to utilizing the powerlines for a longer lifetime while reducing unnecessary faults and replacements. Additionally,accurate current ratings result in optimized operation efficiency, allowing for integration ofmore renewable resources without the need of installing new power lines. Again, this is costeffective in terms of initial resources and running costs. All in all, the general impact is,therefore, in economic value and sustainability.

Note that the figures in this thesis have colored legends.

1.1 Project Goals

The primary objectives of the project are:

• Review of existing literature about DLR and convective heat transfer.

• Preliminary comparison of previous methods and models, namely IEEE and CIGREstandards.

• Analysis of previous wind tunnel experimental data.

• Study of the local and surface average convective heat transfer coefficient.

• Developing an improved convective cooling calculation that fits the measured data.

• Observing the thermal behavior of the conductor sample and providing physical ex-planations.

• Final comparison of existing standards with the results from measured data.

• Proposing possible implementations and future work in the subject area.

10



2 Literature Review

In this chapter, a basic overview of transmission grids and line faults is discussed toprovide a background on the traditional concepts behind the selection of rated operatingconditions of overhead lines. Then, the concept of dynamic line rating (DLR) is introducedas a solution for increasing the economic efficiency of overhead lines while maintaining safeoperation. Dynamic line rating is implemented based on heat transfer theory, which isdiscussed at the end of the chapter.

2.1 Transmission Grid

Simply described, a power system comprises four basic elements (see Figure 1): genera-tion, transmission, distribution, and consumption. At generation level, power is generatedin bulk and voltage is stepped up. Then, the electrical energy is transferred over two net-works; the transmission, and distribution grids. The distinction between transmission anddistribution networks is based on voltage levels. Typically, transmission grids are rated forvoltages higher than 69 kV [1], which is referred to as high voltage (HV) by convention. Onthe other hand, distribution grids are operated under medium (MV) and low (LV) voltageswhich are less than 69 kV. Finally, consumers are served by the power distribution system.

Figure 1: An illustration of a power system [2].

11



While at a distribution level energy is transferred over several branches in the network,at a transmission level, energy is transferred in bulk over longer distances. When dealingwith long distances, the operation under high voltages allows for the reduction of currentlevels, and thus, reducing resistive power losses, and the conductor’s cross sectional area.Consequently, transmission grids are used to transfer power from remote locations wheregeneration occurs (e.g. hydropower plants, or wind farms) at a feasible efficiency.

Several components are needed in a transmission grid. Starting from transformers usedto step up or step down the voltage between different stages in the network. Additionally,switchgear (e.g. circuit breakers, switches) and protection systems (e.g. protective relays)are used to operate the grid reliably. Conductors can be installed either as overhead lines, orpower cables. Also, insulators are used to prevent flash-overs and to support power lines ona transmission tower. Thus, electrical stress has to be taken in consideration when designinga transmission grid based on the desired voltage level. So, to keep the system economicallyfeasible, there is an upper limitation to how high the voltage can be.

Power cables are installed in cable tunnels or directly buried underground mainly insensitive locations, such as, urban and residential areas. While overhead lines are installed ontransmission towers relatively away from densely populated areas. However, the installationprocess of power cables is much more costly than that of overhead lines. Thus, overheadlines are usually predominant in transmission networks. In electrical systems, copper andaluminum are used as conductors. Despite its higher resistivity, aluminum is more favorablesince it is lighter and costs less than copper. There is a wide array of conductor types,including alloys, and steel-reinforced variants.

2.2 Line Sagging and Faults

In a power system, overhead lines are the most susceptible to faults with a probabilityof 50%, as compared to underground cables with a fault probability of 9% [3]. In general,faults can be described as series or shunt. A series fault is simply an interruption of currentflow in a conductor which may be caused by physical damage while there is no contact withanother conductor or ground. On the other hand, shunt faults can be classified as phase orground faults. Phase faults can be either between three phases (L-L-L), or two (L-L) andthey are the most severe, yet, combined, they are the least probable (8% for L-L, and 2%for L-L-L). As for ground faults, they involve at least one phase in contact with the ground,for example, one phase to ground (L-G), or two phases to ground (L-L-G). Although theyare the least severe, line to ground faults (L-G) have a probability of 85% followed by L-L-Gfaults with a 5% probability and higher severity [3]. In some systems where a neutral con-ductor is present, faults involving the neutral can occur, such as, a line to neutral fault (L-N).

Since ground faults are the most common type of faults by far, they have the greatestimpact on the reliability of the power system and on the protection devices. While groundfaults can happen due to extreme weather conditions, natural disasters, or accidents, severalother cases can be prevented by design. Depending on the terrain, the lower an overheadline sags, the higher the chance of touching a grounded object, such as a tree, and causing aground fault. Cases like this can avoided by setting an operational limit for the conductorin the form of a power rating, or current rating at a specific voltage. This limit can be setby studying the terrain and identifying a critical span in which the tolerance to sagging isat its lowest.

12



An overhead line would naturally sag due to its weight, forming a geometric shape knownas a catenary curve (see figure 2). A catenary curve is formed whenever a chord of uniformdensity (or in other words, uniform mass distribution) is connected to two points and isacted upon by a uniform force (gravity/weight in the case of an overhead line) [4]. Thisintroduces tensile forces at the two points of connection on the transmission towers. Thesetensile forces affect the structural design of the towers, what sets a mechanical limit to howtight an overhead line can be. Due to resistive power losses, the conductor is heated. Then,thermal expansion further contributes to line sagging, and high temperatures lead to theannealing of the metal, reducing its tensile strength [5]. As mentioned earlier, a maximumcurrent can be calculated based on the critical span. In conclusion, the overhead line hasto be installed and operated with respect to the maximum possible tensile force, and themaximum allowable sagging to reduce the number of ground faults.

Figure 2: A plot of two different catenary curves (hyperbolic cosine functions) [per-unit].

2.3 Dynamic Line Rating

Traditionally, rated operation of an overhead line is specified while taking worst casescenarios into consideration. The rating is kept unchanged, hence, this approach is referredto as static line rating (SLR). The considered worst case scenarios may include conditionssuch as extreme weather, or high solar heating. Although the SLR method maintains anoverhead line under a safe operating scheme, it does not employ the full possible capacityof the line.

Worst case conditions are not always present in the system. Moreover, power con-sumption is not static, and with the rise of renewable energy production, power generation

13



fluctuates based on the availability of the renewable resource, such as, wind, or wave power.If static line rating is used, the demand on larger transfer of power would result in a need toinstall new power lines. Those power lines would be serving a temporary demand, nonethe-less. Therefore, a more economical method can be employed when extreme conditions arenot present in order to accommodate temporary fluctuations in generation and consumptionof electricity. This method is referred to as dynamic line rating (DLR), in which maximumcurrent limits are calculated based on current existing conditions while thermal damage ofthe conductor is prevented. Some transmission system operators use similar methods, suchas seasonal (SAR) and ambient (AAR) adjusted ratings. SAR is implemented by havinga static rating for relatively long intervals of times. As for AAR, it only relies on ambienttemperature measurements to set the line rating in real-time; however, since it does notinclude other time-sensitive parameters (e.g. wind speed), it is not considered to be dy-namic. A DLR technology is mainly composed of a set of sensors, communication devices,and a software. The sensors measure weather data (wind speed, ambient temperature, solarradiation) and/or line parameters (tension, sag, line temperature). Then, the informationis fed to the DLR software in order to calculate the maximum possible rating based on themeasured environmental data, which in turn is fed to the grid’s control system. The appli-cation of real-time DLR can practically increase a line’s rating by 25%. Higher increase incapacity can be achieved; however, that is limited by the settings of the protection system[6].

All in all, implementation of dynamic line rating introduces several advantages to atransmission system. Starting from increased economic efficiency; that is the ratio betweenthe monetary value of the transferred power, and that of the initial investment and mainte-nance costs. Also, the operational flexibility of the transmission system is improved. DLRcan contribute in the reduction of greenhouse gas emissions by allowing for integration ofmore renewable energy generation. Finally, by allowing for higher power capacities, conges-tion costs inflicted on consumers can be reduced.

2.4 Heat Transfer

Dynamic line rating is based on the concept of heat balance. That is, for a stable linetemperature, all heat gain should be in equilibrium with all heat losses. A conductor gainsheat due to current flow (Joule’s law: P = RI2), induced heating (also known as electro-magnetic heating), and solar radiation. While heat loss, or cooling, occurs due to radiation,convection, and precipitation.

Heat transfer is defined as the exchange of thermal energy by a certain mechanism due toa spatial difference in temperature (temperature gradient) [7]. In this chapter, three typesof heat transfer mechanisms are covered, which are conduction, radiation, and convection.Conduction can occur in solids and stationary fluids (liquids and gases). At a microscopiclevel, conduction can be described as a transfer of kinetic energy from highly energetic par-ticles to less energetic ones within a medium, and by free electrons in the case of electricallyconductive materials. According to Fourier’s law (equation 1), the heat flux due to con-duction is directly proportional to the thermal conductivity “k” [W/m.K] of the materialand the rate of change of temperature “dT” [K] over a spatial dimension “dx” [m]. In thecase of an overhead line, heat is transferred over the line by conduction, leading to thermalexpansion which is expressed as line sagging. [7]

14



q[W/m2] = −kdTdx

(1)

Unlike conduction, heat transfer by radiation does not require a material medium, andcan occur in vacuum. That is due to the fact that energy from radiation is transported byelectromagnetic waves. Emission from a surface is limited by a maximum value describedby the Stefan-Boltzmann law for an ideal radiator, which relates the emissive power non-linearly with surface temperature. Yet, each type of a real material has a different valueof emissivity “ε” (unit-less) which is between zero and one. Finally, equation 2 shows heatflux per unit area due to radiation as a difference between emission and absorption, where“σB” [W/m2.K4] is the Stefan-Boltzmann’s constant, Ts [K] is the surface temperature ofthe material, and Ta [K] is the ambient temperature. [7]

E[W/m2] = εσB(T 4s − T 4

a ) (2)

σB = 5.67 ∗ 108W/m2.K4

Convection strictly occurs in liquids and gases, since by definition it involves the com-bined effect of macroscopic bulk movements of a fluid and conduction processes. Addition-ally, convection can be categorized as natural or forced. Natural convection occurs due tobuoyancy forces which are caused by changes in the densities of various regions within thefluid. Thus, a buoyancy flow is triggered in two opposite directions until a final stable tem-perature is reached. In the case of forced convection, when an external flow is sufficientlyclose to a material’s surface, a boundary layer is formed in which the speed of flow is dis-tributed over a gradient [8]. Equation 3 describes the heat flux per unit area regardless ofthe type of convection, where “h” [W/m2.K] is the convective heat transfer coefficient, Tsis the surface temperature of the material, and T∞ is the temperature at the edge of thefluid’s boundary layer. This equation is a generalized form of Newton’s law of cooling inorder to include the opposite case; i.e. heat transfer from the fluid to the material.

qc[W/m2] = h(Ts − T∞) (3)

15



3 Methodology

In this chapter, the used equations and models are presented. Since the scope of thisproject is mainly to study the convective heat transfer coefficient “h”, the first general ap-proach that was taken is to isolate the coefficient analytically from the heat balance equation,and then use the resulting analytical formula to calculate “h”[W/m.K] by implementationon the given experimental data. The heat balance equation can be studied either duringsteady state conditions of weather and current, or during transient conditions. As shownin equation 4, in a steady state, the heat gained by an object through one or more heatsources is equal to the overall lost heat due to heat transfer by the mechanisms described inthe literature review. On the other hand, a transient state can be described by a first orderordinary differential equation (eq. 5) in which the difference between the gained and lostheat is equal to the rate of change of temperature with respect to time. In this approach,the thermal behavior of the conductor was studied according to guidelines stated in existingstandards, namely from IEEE and CIGRE, where calculation methods are optimized foroverhead power lines.

Hgain = Hloss (4)

Hgain −Hloss =dT

dt(5)

As a second approach, the wind speed distribution around the conductor was simulatedusing CFD in order to observe any micro-turbulence events close to the outer strands surface,and the nature of convection on different locations of the conductor’s surface. By knowingwhether the convection process is natural or forced on a certain location, the behaviorsexpressed in the experimental data can be better explained. Plus, it would be possible tostudy the convective heat transfer coefficient locally instead of assuming a surface average.

Note that all quantities in this report are stated in SI units unless otherwise indicated.Temperatures are expressed in C and converted to kelvin (K) when needed.

3.1 IEEE Standard

In an attempt to have a practical and uniform method for studying the thermal behaviorof a power conductor, IEEE issued a standardized set of calculations in 1986. Specifically,IEEE Std738 TMis for Calculating the Current-Temperature Relationship of Bare OverheadConductors. In this project, IEEE Std738TM– 2012 is used [9] which is the most recentrevision approved in 2013. Based on weather and electric current conditions, the standardsets two cases of steady and transient states. In general, the proposed formulae follow thesame concepts as in equations 4 and 5. Both of the steady and transient states are discussedin the next chapter.

By definition, heat gain is the sum of all heat sources acting on the overhead conductor.IEEE limits the heat sources to two; Joule heating (qj) [W/m], and solar heating (qs) [W/m].The first is governed by Joule’s law which relates the generated heat power proportionallyto the square of the electric current “I” [A] flowing in a conductor (eq. 6), where “R” [Ω/m]

16



is the temperature-dependent electric resistance (eq. 7). Whereas the rate of solar heatingis the contribution of the total solar and sky radiated heat intensity “Qse” [W/m2] on theprojected surface area “A′” [m2/m] of a conductor of absorptivity αs. Solar heating also de-pends on the geographic elevation, time of day, and the azimuth (Z[]) and altitude (Hc[

])of the sun. Equations 8 and 9 show the calculation method advised by IEEE. Nonetheless,the standard goes more into details regarding the solar parameters [9].

qj = R(Tavg).I2 (6)

R(Tavg) =R(Thigh)–R(Tlow)

Thigh − Tlow(Tavg − Tlow) +R(Tlow) (7)

Where Thigh and Tlow can be obtained from the standard’s tables or manufacturer’s data.

qs = αsQsesin(θ)A′ (8)

θ = arccos(cos(Hc)cos(Zc–Z1)) (9)

The accuracy of heating calculations mainly depends on an accurate calculation of theconductor’s resistance. For alternating current (AC), the resistance increases due to skineffect. However, this effect is less accented with conductors of small to medium diameters.In addition to that, at current densities higher than 1.5 A/mm2, the effective resistance ofconductors containing ferrous strands increases due to magnetic hysteresis and eddy cur-rents. However, for three-layer ACSR the resistance increases slightly at high currents dueto partial cancellation of the magnetic field [7].

Regarding the heat loss, it is the total contribution of the heat transfer mechanismsacting on the conductor. IEEE provides guidelines for calculating radiative cooling (eq 10),and convective cooling (eq. 11, 12, and 15). Cooling by radiation has a non-linear relationwith the conductor’s surface temperature (Ts). Additionally, it depends on the conductor’seffective diameter (D0[m]), and its material’s emissivity (ε). As for convective cooling, itvaries linearly with the surface temperature Ts during forced convection. The nature ofconvection largely depends on the fluid properties (air in this case) and the flow parameters(speed and angle), which are characterized by the unit-less Reynolds Number (NRe) shownin equation 13, the coefficient of thermal conductivity of air kf [W/m.C], and the angle ofattack factor Kangle (eq. 14).

qr = 17.8D0ε((Ts + 273

100)4 − (

Ta + 273

100)4) (10)

Where Ta is the ambient temperature.

qc1 = Kangle(1.01 + 1.35N0.52Re )kf (Ts–Ta) (11)

qc2 = Kangle(0.754)N0.5Re kf (Ts–Ta) (12)

NRe =D0ρfVwµf

(13)

Where ρf [kg/m3] and µf [kg/m.s] are respectively the density and dynamic viscosity ofair at the boundary layer temperature Tfilm (eq. 16), while Vw [m/s] is the wind speed.

17



Kangle = 1.194–cos(φ) + 0.194cos(2φ) + 0.368sin(2φ) (14)

Where φ is the angle between the direction of wind flow and the axis of the conductor.

qcn = 3.645ρfD0.750 (Ts–Ta)1.25 (15)

Ideally, the nature of convection has to be identified prior to calculation of the rate ofconvective cooling for better accuracy. However, IEEE tackles this issue by recommendingthe calculation of forced (eq. 11 and 12) and natural (eq. 15) simultaneously when deal-ing with very low wind speed, and then selecting whichever has a higher value. Normally,natural convection occurs at zero, or close-to-zero wind speeds; thus, obviously indicatingthat it is much less effective than forced convection. Even for the case of forced convection,both of equations 11 and 12 are to be calculated and then the highest value should be chosen.

The standard considers air to be a uniform and isothermal fluid; i.e. it has invariantdensity, dynamic viscosity, and coefficient of thermal conductivity at an averaged boundarylayer temperature Tfilm. Tfilm is given by equation 16.

Tfilm =Ts + Ta

2(16)

3.2 CIGRE Standard

CIGRE Technical Brochure (TB) 207 [10] provides a set of methods to study the thermalrating of bare overhead conductors operating at low current densities (below 1.5 A/mm2)and at constant weather conditions. The basic concept of the standard is the same as the onepresented in equations 4 and 5. Due to the limitations of TB 207, a more recent standardwas issued by CIGRE in 2014 [11]. The new TB 601 provides more accurate calculationmethods for varying weather conditions, operation at very high current densities, and hightemperatures in order to allow for better estimations of sagging. However, by comparing thecalculations from TB 207 with those from TB 601, the accuracy of TB 207 is still acceptableat current densities up to 2 A/mm2, whereas TB 601 yields thermal ratings that are 1 to 5% lower than those yielded by using TB 207 [12]. With all that in mind, CIGRE does notrecommend operation under the maximum current ratings or under over-estimated weatherconditions found using the standard’s methods.

In this standard, heat gain is attributed to four different sources: Joule PJ [W/m], mag-netic PM [W/m], solar PS [W/m], and corona heating Pi[W/m]. Joule heating is the productof the temperature-dependent resistance with the square of the conductor’s current (eq.17). During AC operation, the effective resistance increases due to skin effect that causesnon-uniform current densities inside the conductor. TB 207 compensates for this effect byintroducing a factor kj that has an average value of 1.0123. Thus, for non-ferrous con-ductors, the AC resistance RAC [Ω/m] can be calculated by multiplying the DC resistanceRDC [Ω/m] by kj (eq. 19). In turn, the AC resistance can be included in equation 17 for

18



calculating Joule heating more accurately.

PJ = RDC(T )I2 (17)

RDC(T ) = R(Tref )(1 + α(Tavg − Tref )) (18)

Where Tref is the reference temperature (in this case Tref = Ta), Tavg is the averagetemperature of the conductor, and α is the temperature coefficient of resistance per degreekelvin (not to be confused with absorptivity).

For non-ferrous conductors:RAC = kjRDC (19)

Magnetic heating occurs when ferrous materials (e.g. Steel) are present in the conductordue to hysteresis and circulation of eddy currents. TB 207 provides a simplified approachfor magnetic heating calculation by including its effect in the Joule heating equation. Equa-tion 20 shows the relation between the AC resistance of a ferrous conductor with its DCresistance. Then, PM is no longer needed to be accounted for in the heat balance equation.[10]

For ferrous conductors:

RAC = (kj + 2.36 ∗ 10−5IAC)RDC (20)

Where IAC is the RMS value of the AC current.

As for solar heating, CIGRE takes into consideration the inclination of the solar beams,the diffusion of sky radiation, the reflectance of the ground below the conductor, and thealtitude of the sun. However, due to financial restraints caused by costs of measurements,a more practical approach is provided. It is expressed as the product of the conductor’ssurface absorptivity αs, global solar radiation S[W/m2], and the external diameter of theconductor D0[m] (eq. 21). [10]

PS = αsSD0 (21)

Coronas are luminous and audible discharges that occur due to the ionization of airmolecules around a conductor, and can happen much earlier before a total breakdown [13].However, the probability of inception of corona discharges is only considerable at high airhumidity [11], high voltages, and increases with temperature [14]. Therefore, the effect ofcorona heating Pi is negligible at rated operation and normal conditions.

The cooling mechanisms that contribute to heat loss are: evaporation, radiation, andconvection. Evaporative cooling Pw[W/m] is, in fact, a form of mass transfer since thehumidity on the conductor’s surface is turned into water vapor that dissipates into the at-mosphere. Yet, in order to have a significant effect, the conductor has to be fully wet whichmostly occurs in the presence of precipitation [15] or through artificial cooling [16]. Thus,in both of CIGRE TB 206 and TB 601, the effect of evaporative cooling is ignored.

19



Radiative cooling depends on the emissivity of the conductor’s surface which is largelyaffected by ageing and the accumulation of pollutants. Pr[W/m] is given by equation 22:

Pr = πD0εσB((Ts + 273)4 − (Ta + 273)4) (22)

Convection Pc[W/m] contributes to the majority of the cooling in the heat balance equa-tion. CIGRE uses the same general equation for calculating Pc for both of forced and naturalconvection (eq. 23), however, the calculation details of the Nusselt number (Nu) differ foreach case.

Pc = πλf (Ts–Ta)Nu (23)

For the case of forced convection, the Nusselt number (eq. 24) is dependent on theReynolds number and two constants, B1, and n. B1 and n can be obtained from tabulateddata in the standard based on the range of the Reynod’s number. In CIGRE, the Reynoldsnumber is calculated using equation 25.

Nu = B1(Re)n (24)

Re =ρrV D0

νf(25)

Natural convection, on the other hand, the Nusslet number (eq. 26) is dependent on theGrashof number Gr (eq. 27), the Prandtl number Pr (eq. 28), and two constants A2 andm2. A2 and m2 can be obtained from tabulated data in the standard based on the range ofthe product of Gr and Pr.

Nu = A2(Gr.Pr)m2 (26)

Gr =D3

0(Ts–Ta)g

(Tf + 273)ν2f(27)

Pr = 0.715–2.5 ∗ 10−4Tf (28)

At a gravity g = 9.807m/s2, and temperature of the boundary layer Tf (eq. 16), air’skinematic viscosity νf [m2/s] (not to be confused with dynamic viscosity µf ), thermal con-ductivity λf [W/m.K], and relative density ρr can be found using the following equations:

νf = 1.32 ∗ 10−5 + 9.5 ∗ 10−8Tf (29)

λf = 2.42 ∗ 10−2 + 7.2 ∗ 10−5Tf (30)

20



ρr =ρ

ρ0(31)

Where ρ is the density of air at a specified altitude, and ρ0 is the same but at sea level.Then, at sea level, ρr = 1. [10]

In CIGRE TB 601 [11], an approach to account for wind direction is presented. Theangle of attack is denoted by δ, and the resulting Nusselt number Nuδ is compared to theNusselt number during a perpendicular flow Nu90. Equation 32 is for smooth conductors,and equations 33 and 34 are for stranded conductors for different values of δ. However,these equations are only applicable for Reynolds numbers below 4000. This implies that fora conductor with a diameter of 21-24 mm, the equations are applicable only at wind speedsup to 3 m/s. Note that the equations predict that perpendicular flow results in optimalconvective cooling.

NuδNu90

= (sin2(δ) + 0.0169cos2(δ))0.225 (32)

For δ 6 24:NuδNu90

= 0.42 + 0.68(sin(δ))1.08 (33)

For δ > 24:NuδNu90

= 0.42 + 0.58(sin(δ))0.9 (34)

3.3 Experimental Setup

This thesis is based on previous experimental work that was performed in a wind tunnelfacility at KTH Royal Institute of Technology. The experiment was done under a priorhypothesis stating that forced convection may have higher effects on conductor cooling thanwhat is shown by IEEE and CIGRE thermal rating standards [17].

As shown in figure 3, the basic principle of the experiment is to place a sample of anoverhead power line inside a cuboid-shaped wind tunnel, and exposing it to wind flow froma single direction. Three types of conductor samples were tested, a stranded aluminumalloy conductor (Al59-241 [18]), an aluminum rod of the same diameter, and a strandedsteel-reinforced aluminum conductor (ACSR FeAl329). The conductor is fitted with ther-mocouples placed on different locations to measure the thermal behavior. If the conductor’scross section is divided into four quadrants (refer to figure 4, and Appendix 1 for detailedstrand illustration), then the thermocouple installed on the quadrant facing the wind flowmeasures the “front” surface temperature of the conductor. While the one installed oneither one of the two quadrants on the axis that is perpendicular to the direction of windflow measures the “top” or “bottom” surface temperatures. The top and bottom quadrantsare equivalent in terms of temperature measurement, then, hereinafter either quadrant isreferred to by the ”top” notation. The thermocouple installed on the quadrant in the op-posite direction of wind flow measures the “back” surface temperature. In addition to thesurface thermocouples, the ACSR is fitted with thermocouples on the steel core to measure“core front”, “core top”, and “core back” temperatures.

21



Figure 3: Three-dimensional illustration of the test object inside the wind tunnel

Figure 4: Cross Section: The four quadrants of the conductor sample

22



The testing procedure starts by electrically heating the conductor and then exposing itto wind flow. Thus, RMS current, wind speed, and angle of attack are the test quantitativeparameters. Also, the conductor type can be considered as a qualitative parameter. Inthe controlled experimental environment, the ambient conditions are kept constant (Ta =295K), while the test parameters are varied. The measured variables are the previouslymentioned surface and core temperatures. The conductor was heated to maximum allowabletemperature, then exposed to wind flow, and left to finally cool down to steady state (orthermal equilibrium).

3.4 Assumptions and Approximations

Due to the nature of the controlled experimental environment, several assumptions andapproximations can be made in order to simplify the problem and optimize the methodologyfor the given conditions. In this section, the reasoning behind these assumptions is presentedin detail.

3.4.1 Surface-to-Surface Radiation: A Simplified Approach

The heat balance equation of an overhead conductor accounts for heating from solarradiation, which in this case it is not applicable since the conductor is enclosed inside thewind tunnel. Thus, heat gain is only the sum of Joule and magnetic heating.

Yet, the radiation emitted by the conductor can get reflected by the walls of the windtunnel, and then get re-absorbed at the conductor’s surface. Considering the geometry of theexperimental setup, an incident angle of 90 , between the radiated electromagnetic wavesand the plane of the tunnel’s wall, is needed for re-absorption to occur. Moreover, sinceradiation waves propagate at the speed of light, the dimension of distance can be ignored.Thus, the conductor cylindrical surface can be approximated as a flat plane. This makesthe problem a classical example of surface-to-surface radiation [7].

Depending on the index of refraction of a material, a part of an incident electromagneticwave is refracted inside the material, and another part is reflected back with an angle equalto the incident angle [19]. However, the energy of the reflected wave is less than that of theincident wave. In the case of surface-to-surface radiation, for every iteration of reflection andrefraction, the energy level of the reflected waves decreases, especially that the wind tunnelwalls are made of black-painted plywood. Normally, wood absorbs 70 to 90% of infrared(IR) radiation within 0.3 mm of its thickness [20]. Also, the emissivity of plywood is 0.91[21]. Therefore, the wind tunnel walls can be approximated as a blackbody. By definition,a blackbody is an object that absorbs all incident radiation [22]. In conclusion, the effect ofthe surface-to-surface radiation can be neglected in the heat balance equation.

23



3.4.2 Cylinder in External Cross Flow

A classical problem is the case of a smooth circular cylinder under external fluid crossflow. What is meant by cross flow is that it is perpendicular to the longitudinal axis of thecylinder. Plus, it is unidirectional from an inlet source to an outlet. It is also characterizedby a favorable pressure gradient (i.e. negative) until a minimum pressure is reached, andthen followed by an adverse pressure gradient (i.e. positive) without any discontinuities.When the pressure gradient is favorable, a boundary layer is formed. However, at minimumpressure close to the cylinder’s surface, the flow goes through a transitional phase until theboundary layer separates from the surface and turbulent flow occurs to form what is knownas a “wake”. Under adverse pressure gradient, the boundary layer develops briefly beforeseparation and flow reversal [7]. Within the wake, a set of vortexes are shed under the effectof a phenomenon known as von Karman vortex streets [23]. Finally, the stream recoversback to laminar flow.

An overhead conductor is similar to a circular cylinder, albeit, with a rougher surface.Thus, the case of a cylinder in external cross flow can be used as a basis to study theflow around the used conductor samples. To put matters into perspective, a classificationinto two groups can be made: low Reynolds number (< 2 ∗ 105), and high Reynolds number(> 2∗105). For cases with a low Reynolds number, the separation and transition to turbulentflow occurs around an angle of 80, at the cylinder’s surface, clockwise and counter-clockwisefrom the axis of wind flow. Whereas for cases with a high Reynolds number, the same occursat an angle of 140 [7]. By applying equation 25 for a wind speed of 12 m/s and at roomtemperature, a cylinder having a diameter of 25 cm is needed to result into a high Reynoldsnumber. Obviously, that is not applicable for overhead power lines. Therefore, in thisproject only the category of low Reynolds number is considered. By referring to figure4, it is expected to observe the transitional phase near the top of the conductor in thesimulations.

3.4.3 Other Considerations

The input wind flow is assumed to be always laminar at the inlet of the wind tunnel.Consequently, it is uniform in direction and has a constant average speed. As for the fluiditself, air can be generally approximated as a two-species fluid (i.e. a binary mixture),namely composed of diatomic nitrogen (80%) and diatomic oxygen (20%). Additionally, airdensity, viscosity, and thermal conductivity are assumed to be constant and invariant withfilm temperature at sea level. As shown in sections 3.1 and 3.2, the effect of temperatureon those properties has a low magnitude on their values. As a result, the heat transfer influids and fluid dynamics problems can be decoupled. Then, it is only needed to simulatefluid dynamics to observe flow properties.

In reality, wind flow and air properties are averaged over specific periods of time. Also,when a power line sags, the wind speed is not equal at all points on the conductor. In thewind shear the speed varies with altitude [24], so a sag of 7 meters, for example, mightresult in a variation of around 1 m/s between the lowest point and near the transmissiontower. This is also applicable to lines placed on different heights between towers. In theexperiment, this effect is not applicable, and therefore, neglected in this thesis.

Since air properties are assumed to be temperature independent, the convective heat

24



transfer coefficient is invariant during transient heating or cooling as long as the wind speedis kept constant and regardless of the set electric current.

As for the conductor itself, its internal temperature is not uniform in reality, especially forACSR power lines [9] [10] [11]. In fact, it can be modeled as an electric circuit where thermalresistance is represented as an equivalent electric resistance, and heat storage or thermalcapacitance is represented as an equivalent electric capacitance [25]. However, since theproject’s scope is to study the convective cooling component, only surface temperatures arenecessary. As previously mentioned, surface temperature measurements from four quadrantsof the conductor samples were taken during the experiment. The electric current distributionwithin the conductor is assumed to be uniform concentrically, making the contribution ofthe conductor’s four quadrants to Joule heating equal. This assumption is valid due tothe fact that the skin effect is less prominent at low frequencies (50 Hz in this case) [26].Moreover, conductive heat transfer at the points where the sample is fixed on the tunnelwalls is ignored due to the poor thermal conductivity of wood [27].

3.5 Mathematical Implementation and Data Fitting

The experimental data was inputted to MATLAB as two-dimensional arrays to allow foriterative calculations. There was an inherent problem in that data where every vector hada different length; however, this was overcome by ignoring cells with “NaN” values. Also,data plots of the electric current parameter for each type of conductor were generated inorder to check whether quantitative comparability is possible. As well as, MATLAB wasused to generate data plots of measured temperatures at the previously mentioned locationsfor different wind speeds to visualize the rate of cooling.

Based on the assumptions and approximations presented in the previous section, thefinal form of the steady-state heat balance equation is given in eq. 35. The code was writtento make use of conditional if statements to input desired method of calculation, conductortype, and angle of attack (AoA). Then, parameters are set, and the convective heat transfercoefficient is isolated from the heat balance equation.

PJ = Pc + Pr (35)

During transient heating or cooling, the heat balance equation accounts for the derivativeof temperature with time, as shown in equation 36, where mCp is the total heat capacity([J/m.K] or [J/m.C]). It was shown earlier that the convective heat transfer coefficientremains invariant between transient and steady states. Thus, to simplify calculations, onlythe steady state is analyzed according to equation 38 where the experimental heat trans-fer coefficient (hexp[W/m.K]) is calculated based on the experimental value of convectivecooling (Pc(exp)[W/m]). The “ode45” built-in MATLAB function can be used to solve thetransient state’s ordinary differential equation (ODE) for a numerical value of the surfacetemperature. The ODE, of general form shown in eq. 37 is in first order with constantcoefficients (a, b, and c) and includes a fourth-degree component due to radiative cooling.Numerical solutions for this form of ODE are provided in both of IEEE [9] and CIGRE[10][11] standards. However, that would only be useful in the absence of experimental data.

1

mCp

dT

dt= PJ–Pc–Pr (36)

25



dT

dt= aT 4 + bT + c (37)

hexp =Pc(exp)

∆T=PJ–Pr

∆T(38)

Finally, the built-in curve fitting tool (cftool) is used to generate code for data fittingfunctions to correlate different values. Most importantly, the convective heat transfer coef-ficient is correlated with wind speed using that tool within a confidence level of 95%.

For this project, MATLAB was used under a student license.

3.6 Computational Fluid Dynamics (CFD) Simulations

As described earlier, the expression of the convective heat transfer coefficient shows de-pendencies on fluid properties, conductor’s effective diameter, angle of attack of wind, andwind speed. These dependencies were expressed in dimensionless numbers, namely, Reynoldsand Nusselt numbers. For the application of concern, hereby, the wind flow parameters arevariable. Then, an insight into the distribution of the velocity field of wind around theconductor aids in estimating its correlation with the heat transfer coefficient. Basically,by applying the laws of conservation of mass and momentum, computer simulations can beperformed on the test object to approximate the speed distribution in space [28]. Those sim-ulations are known as Computational Fluid Dynamics (CFD), and they are applied throughthe Finite Element Method (FEM).

First of all, the problem area Ω has to be defined. Three-dimensional simulation requireshigh computational power, so, it is better to avoid it. Due to symmetrical properties ofthe experimental setup and the laminar wind flow, Ω can be reduced to a two-dimensionalgeometry that includes the conductor’s cross section. Through trial and error, the bestconfiguration was to have a distance equivalent to two diameters (2D0) in front of the con-ductor, 1.5D0 above and below it, and 10D0 behind it. This configuration was made sincerotational symmetry could not be utilized due to the flow characteristics discussed in section3.4.2. After the geometry is built, the material properties have to be assigned. COMSOLMultiphysics software package was used. From COMSOL’s built-in library of materials, airwas selected in the area surrounding the conductor, where its density and dynamic viscositywere set to room-temperature (293.15K) values [19][29]. The conductor’s material is notneeded since the fluid dynamics problem is decoupled from heat transfer.

The next step was to set the physical equations. COMSOL already includes the equa-tions of conservation of mass and momentum needed for laminar flow computations. Themodel was configured for incompressible flow without including the effect of gravity for sim-plification. Normally for this case, if turbulent flow simulation is needed, the k − ω modelis suitable because it is optimized for low Reynolds numbers [30]. The initial values ofthe velocity field and pressure were set to zero, whereas the initial temperature was set to293.15K (room temperature).

As for the boundary conditions, the walls were set to be stationary with no slip or leak-age. As for the inlet, the inflow was set to a value of the input speed multiplied by a stepfunction (see figure 5) to simulate the start-up of the wind tunnel’s fan. The outlet wasset to have an initial zero pressure value with suppression of backflow as a pre-cautionarymeasure. Then, a physics-controlled triangular mesh is constructed. For the aluminum rodcase (figure 6), the mesh is set to be “fine” in terms of element size since the rod’s surface is

26



smooth, while for the stranded conductor case (figures 7 and 8), a “finer” mesh element sizeis needed due to the existence of singularities between strands at the conductor’s surface.

Figure 5: Step function used to simulate starting of wind flow

Figure 6: Model and mesh used for the case of an aluminum rod under cross flow (left to right)

In figure 7, the quasi-circular cross section of the stranded conductor is projected on theaxis of the wind flow of a 40 angle of attack. The resulting shape is a quasi-elliptical crosssection with a major axis 2a = D0

cos(40) , and a minor axis 2b = D0. Thus, the case becomes

similar to the two-dimensional fluid dynamic behavior of an elliptical cylinder. Based onprevious studies in the literature, the aspect ratio (or axis ratio = b

a ) has a significant im-pact on the heat transfer coefficient and the onset of vortex shedding for a smooth ellipticalcylinder, where the lower the aspect ratio is, the higher the Nusselt number becomes[31][32].This is contradictory with equations 33 and 34.

Finally, the computation is done as a time dependent study with time steps of 0.2seach. The CFD results are used to complement the observations and analysis done on theexperimental results.

27



Figure 7: Model and mesh used for the case of a stranded conductor under 40 flow (left to right)

Figure 8: Model and mesh used for the case of a stranded conductor under cross flow (left to right)

28



4 Comparison of Existing Methods

Based on equations 35 and 36, a general comparison of the existing thermal rating meth-ods can be made. Both methods follow the same general form for the heat balance equationduring steady and transient states. In terms of heat gain, CIGRE provides a more detailedcalculation method than IEEE in regards to the temperature-dependent resistance, the skineffect and magnetic heating. Yet, both standards take an average of the surface tempera-ture of the conductor. As for heat loss, the radiative cooling calculation is equivalent forboth methods. The only apparent difference is that IEEE expresses the radiative coefficientnumerically while CIGRE expresses it symbolically, yet both of them are constants onlydepending on conductor’s parameters.

The significant differences between the two standards are noticed in the convective cool-ing calculation method. The equation of natural convection in CIGRE is always linear withtemperature, while in IEEE the equation is non-linear with temperature. More importantly,the calculation of forced convective cooling is dealt with differently in both standards. First,IEEE provides general equations for calculation at any angle of attack. On the other hand,CIGRE TB 601 provides a limited approach which is not applicable at medium to highwind speeds for power conductors. CIGRE provides the same general equation for bothof forced and natural cooling; however, different correlations of the Nusselt number withthe Reynolds, Grashof, and Prandtl numbers are tabulated. IEEE standard does not relyon tabulated data, but it provides a more generic approach which makes it more practicalfor engineering applications. Although CIGRE uses kinematic viscosity instead of dynamicviscosity, it uses relative air density, thus, the Reynolds number calculation is equivalent inboth standards.

In figures 9 and 10, the convective heat transfer coefficient is plotted based on the defini-tion in equation 3; i.e. by grouping all of the values multiplied by the temperature differenceusing the same physical properties of air and for two conductors (ACSR and Al59 respec-tively). For IEEE, plots of the two experimental angle of attacks are shown based on theequations presented in section 3.1. As for CIGRE, only one plot is shown for forced con-vection based on the equations presented in section 3.2 and tables provided in CIGRE TB601 [9]. In brief, h90c1, h90c2, h40c1, and h40c2 are based on IEEE calculations for angles ofattack of 90 and 40 respectively. While h90CIGRE is based on CIGRE for a 90 angle of at-tack. At 40, the method presented in CIGRE TB 601 is not applicable for this specific case.

On average, when h90c2 and h90CIGRE are compared, CIGRE seems to overestimate theheat transfer coefficient by 32.7 %. As discussed earlier, IEEE recommends choosing thehighest of the two heat transfer coefficients. At very low wind speeds (less than 2 m/s), thecoefficients are approximately equal with less than 1% of difference. While for the rest of thespeed range, equation 12 (h90c2 and h40c2) yields a higher estimation than equation 11 (h90c1and h40c1). Therefore, equation 12 should be used for the estimation of forced convectivecooling when following the IEEE standard. The effect of wind direction is significant whenusing IEEE’s equations. At a direction of 40, the heat transfer coefficient h40c2 is 17.6 %lower on average than h90c2 at a 90 direction. This implies, that IEEE considers obliquewind flow to be less effective for convective cooling (refer to Figure 11). That observationis in accordance with the equations provided by CIGRE TB 601.

29



Figure 9: Comparison of calculation methods of convective heat transfer coefficient for the ACSR conductor

Figure 10: Comparison of calculation methods of convective heat transfer coefficient for the Al59 conductor

30



Figure 11: Effect factor of the angle of attack on convection according to IEEE (equation 14)

31



5 Preliminary Analysis of Measured Data

Table 1 summarizes the availability of the datasets that were obtained from the exper-imental setup. Surface temperature measurements were taken for all the conductors andall quadrants except for the case of the ACSR conductor under cross flow, where measure-ments at the front and top of the conductor are missing. Core temperature measurementswere taken only for the ACSR conductor; however, some data is missing as shown in thetable. The missing data pose a problem to the direct comparability of the data. Althoughthe experimental environment was controlled, a few anomalies and errors are present in themeasurements. Thus, there is a necessity to circumvent these anomalies in order to have anaccurate comparison. This is further discussed in chapter 6.

Table 1: Available Experimental Data

In this chapter, the analysis of the datasets is started with checking the input parametersfirst to ensure a good quality of comparison. In all of the cases, the input wind speeds werevirtually constant throughout the testing period except for a short period of time when thewind tunnel’s fan is started. However, the fan startup behavior is approximately identical toan ideal step function. In the following sections, plots of the input current density are shownin order to check for consistency and to conclude whether the effect of magnetic heating issignificant. As for the output data, temperature plots are presented to observe the thermalbehavior of the conductor in question under different wind speeds.

5.1 Aluminum Rod

The first tested case was that of an aluminum rod exposed to wind speeds ranging from 1to 24 m/s, at a 90 angle of attack. In figure 12, the average input current density variesbetween 0.6 and 0.8 A/mm2 while staying below the 1.5 A/mm2 limit set in both of IEEEand CIGRE standards. Magnetic heating due to hysteresis is non-existent since the con-ductor does not have any ferromagnetic material. Although the variation in input currentis present, it can be considered minor. Therefore, Joule heating is fairly consistent over thefull range of wind speeds.

32



Figure 12: Average Input Current Density (Aluminum Rod)

Figures 13, 14, and 15 show the thermal behavior of the aluminum rod at wind speedsof 4, 12, and 20 m/s respectively, where transient cooling is observed. At all wind speeds,it is evident that the top quadrants undergo most of the cooling since their temperaturewhen a steady state is reached is lower than that of both the front, and back quadrants. At12 and 20 m/s, the front and back quadrants reach approximately the same steady statetemperature; at different rates nonetheless, where the front quadrant cools down faster thanthe back quadrant. At 4 m/s, the front quadrant reaches a lower steady state temperaturethan that at the back. This indicates that at low speeds convective cooling is higher at thefront than that at the back.

Figure 13: Aluminum Rod Surface temperature at 4 m/s

33





34



5.2 Aluminum Conductor (Al59)

The conductor in this case is a sample of a stranded aluminum alloy (Al59) power line.The sample was exposed to wind flows of wind speeds ranging from 1 to 24 m/s and twoangle of attacks. The conductor is made of non-ferrous material, so heating due to magnetichysteresis is not applicable in this case.

5.2.1 40 Angle of Attack

As shown in figure 16, the average input current density is stable and below 1.5 A/mm2

over the full range of wind speeds. Figures 17, 18, and 19 show the thermal behavior at4, 12, and 20 m/s respectively, where the conductor undergoes transient cooling under anAoA of 40. At all of the three wind speeds, the front quadrant’s steady state temperatureis the lowest. At 12 and 20 m/s, steady state temperatures at the top and back quadrantsare approximately equal. While at 4 m/s, the temperatures at the front and back are equaland lower than the temperature at the top when steady state is reached. Therefore, thedistribution of forced convection is uneven across the conductor’s surface where the frontquadrant undergoes the highest cooling.

Figure 16: Average Input Current Density (Stranded Aluminum Conductor (Al59) at AoA = 40)

35



Figure 17: Stranded Aluminum Conductor (Al59) Surface temperature at 4 m/s (AoA = 40)


36





The average input current density is below 1.5 A/mm2 and slightly variable over the fullrange of wind speeds (see figure 20). Figures 21, 22, and 23 illustrate the transient thermalcooling behavior of the Al59 conductor under an AoA of 90 at 4, 12, and 20 m/s respec-tively. At all wind speeds, convective cooling is lowest at the back quadrant since the steadystate temperature is higher than that at the front and top quadrants. At 4 m/s, steadystate temperatures at the top and front quadrants are approximately equal. However, at12 and 20 m/s, the top quadrants undergo higher forced convective cooling as their steadystate temperature drops below that at the front.

37



Figure 20: Average Input Current Density (Stranded Aluminum Conductor (Al59) at AoA = 90)


38





39



5.3 Steel Reinforced-Aluminum Conductor (ACSR)

The conductor in this case is a stranded line composed of two layers of ferrous (steel)core, for increased mechanical strength and reduced sag, as well as three layers of aluminumstrands surrounding the core. The range of the wind speed was intended to be from 1 to6 m/s with two angles of attack (40 and 90). The conductor was first heated at no-windconditions, and then the wind speed was stepped up by 1 m/s to start cooling. After that,the conductor was heated again by increasing the input current to reach the initial hightemperature, and then, the wind speed was increased by another 1 m/s to cool down theconductor. This was repeated until a speed of 6 m/s was reached. The temperature wasmeasured both on the conductor surface and in the steel core in different locations. Byignoring the miniature air gaps between the conductor’s strands, the cooling of the steelcore is estimated to be purely conductive.


As shown in figure 24, the average input current density is not consistent over the rangeof wind speeds. It rises from 0.6 A/mm2 at 1 m/s, to 1.1 A/mm2 at 6 m/s. While thecurrent density is not constant, it is still below the 1.5 A/mm2 limit. Thus, the assumptionthat magnetic heating is negligible is still valid. Yet, Joule heating is not the same overdifferent wind speeds, rendering direct quantitative comparison to be inaccurate.

Figure 24: Average Input Current Density (Stranded Steel-Reinforced Aluminum Conductor (ACSR) atAoA = 40)

In figures 25, 26, and 27, the thermal behavior of the ACSR conductor under an AoA of40 is shown at wind speeds of 2, 4, and 6 m/s respectively. The conductor goes througha transient cooling phase, followed by transient heating in order to prepare for the nextcooling cycle as described earlier. The final stage of the experiment was at 6 m/s. At 2 m/s,

40



the heating phase is not smooth since the current was adjusted twice in order to reach theinitial high temperature. At the surface, the top quadrants undergo the highest cooling at2 m/s, whereas at 4 and 6 m/s the cooling is virtually equal at the front and top quadrants.At all wind speeds, the surface back quadrant undergoes the lowest cooling. The steel coreis cooled conductively and it follows the same trend of temperature variation of the surface,however, the core temperature is generally 6 to 7C higher for every corresponding quad-rant.

Figure 25: Stranded Steel-Reinforced Aluminum Conductor (ACSR) Surface and Core Temperatures at 2m/s (AoA = 40)


At 6 m/s, an average current density of 1.1 A/mm2 was used. Due to higher Joule heat-

41



ing, the resulting convective cooling at that wind speed appears to be insufficient for therespective time duration since the temperature variation is minimal, and so, the resultingcurves are smoother. Also, it is possible that there was an error in measurement since thesurface back and core top temperatures are exactly equal.



In figure 28, the average input current density was varied between 0.6 and 1.3 A/mm2

with an exception of the case of 2 m/s. At 2 m/s, an error in current and temperaturemeasurement occurred around the end of testing time due to a technical malfunction, causinga spike in average current density above 1.5 A/mm2. However, as shown in figure 29 thetemperature range is normal for most of the test duration. Then, the current spike did notoccur physically, and thus, it is safe to neglect it and consider the temperature measurementsbefore the error occurred (refer to Appendix 2 for more detailed figures of input current).

Figures 29, 30, and 31 show the thermal behavior of the conductor under transientcooling and transient heating under cross flow of speeds 2, 4, and 6 m/s. As mentioned intable 1, the surface front and top measurements are absent. Moreover, the data from surfaceback temperature measurements is exactly equal to that at the core front. This confirmsthe existence of a technical error in measurement. Normally, the core top temperature is 3to 4C lower than the that at the surface back.

42



Figure 28: Average Input Current Density (Stranded Steel-Reinforced Aluminum Conductor (ACSR) atAoA = 90)


43





44



5.4 Comparison

At an AoA of 90, the aluminum rod and the Al59 stranded conductor show comparablebehaviors. First, convective cooling is highest at the top for all speeds. A transition in ther-mal behavior is observed at the front and back quadrants when the wind speed increasesfrom low (4 m/s) to medium and high values (12 and 20 m/s). This indicates a non-linearrelation between the convective heat transfer coefficient and the Reynolds number, whichincludes wind speed.

At an AoA of 40, the Al59 conductor shows a different thermal behavior from thatunder perpendicular cross flow. The front quadrant is exposed to the highest convectivecooling, whereas the top and back quadrants are within the same range. This points to apossibility of earlier separation of the boundary layer, resulting in lower wind speed distri-butions of turbulent nature near the top and back. This is further investigated in chapter 7.

Finally, due to technical errors in measurement and inconsistent input currents for theACSR case, direct comparison based on temperature readings is not possible. Rather, theconvective heat transfer coefficient has to be isolated for an accurate comparison since it isconsidered to be independent of current and temperature (see section 3.4.3). This processis further detailed in chapter 6.

45



6 Mathematical Thermal Model Results

As discussed in chapter 3, the convective heat transfer coefficient is equivalent at bothof transient and steady thermal and electric current states. Consequently, equation 38 wasused to isolate the experimental value of the coefficient. For confirmation of steady statebehavior, the derivative of temperature was calculated from the experimental data. Then,time intervals in which the derivative of temperature is zero or approximately zero are se-lected to perform steady-state calculations.

First the local convective heat transfer coefficient was calculated for every quadrant. Forthat, Joule heating and radiative cooling methods from IEEE and CIGRE were used. Itwas previously shown that radiative cooling equations are interchangeable between the twostandards. Thus, in this chapter the subscripts IEEE and CIGRE are used to indicatethat the respective Joule heating calculation method was used. Additionally, since all theconductors were assumed to be internally axially symmetric, each quadrant contributes to aquarter of the total Joule heating and radiative cooling. Finally, the revised form of equation38 for local convective heat transfer coefficient becomes as shown in equation 39.

hlocal[W/m.K] =0.25PJ − 0.25Pr

Ts − Ta(39)

To calculate the overall surface average convective heat transfer coefficient (havg), equa-tion 40 is used. Every quadrant is weighted by a factor of one since Joule heating andradiative cooling were already divided in equation 40.

havg[W/m.K] = hfront + 2htop + hback (40)

Where hfront, htop and hback are the experimental values of the local convective heattransfer coefficients of the front, top, and back quadrants respectively calculated based onequation39 and the provided data.

6.1 Experimental Value of The Convective Heat Transfer Coeffi-cient

Figure 32 shows the local convective heat transfer coefficients at each quadrant of thealuminum rod under perpendicular cross flow. Due to measurement errors (see figure 15),the values at 20 and 22 m/s are not reliable. Nevertheless, based on the rest of the values, ageneral trend is observed. Convective cooling at the top part of the rod is the highest at allspeeds. At low speeds up to 4 m/s, the difference between the top and the other two quad-rants is less prominent than the difference at higher speeds. Therefore, at medium to highspeeds, most of the convective cooling occurs at the top. Convection at the back is lower thanthat at the front up to 11 m/s. At speeds higher than 11 m/s, a transition occurs in whichconvection at the back becomes higher which is probably due to turbulence (see section 7.1).

46



Figure 32: Local convective heat transfer coefficient on the surface of the four quadrants of the aluminumrod under cross flow

Figures 33 and 34 show the calculation of local results for the Al59 conductor underwind flow of 40 and 90 AoA respectively. The main and obvious difference is in the localconvective heat transfer coefficient at the top of the conductor. At an oblique wind flow, itdrops significantly compared to the perpendicular cross flow case at high wind speeds. Still,at low wind speeds up to 7 m/s, the local coefficients of the top and front quadrants arenearly equal. As predicted in section 5.2, in case of oblique wind flow, convective cooling atthe front is the highest, whereas cooling at the top and back are approximately equal. How-ever, convective cooling at the front and back have close values for both types of wind flows.

Figure 33: Local convective heat transfer coefficient on the surface of the four quadrants of the Al59conductor under wind flow of AoA = 40

47



Figure 34: Local convective heat transfer coefficient on the surface of the four quadrants of the Al59conductor under cross flow

As for the ACSR case, since surface front and top measurements are absent in the caseof perpendicular cross flow, the respective local convective heat transfer coefficients werededuced from the oblique flow case. It is important to note that this is an estimative ap-proach based on the observation made for the Al59 conductor, where at low wind speedsthe top and front coefficients behave similarly for both types of wind flow. This observationis applicable for the ACSR case especially that the tested wind speed range was from 1to 6 m/s. Similarly, at higher wind speeds, convective cooling at the top is expected tobe significantly higher during perpendicular cross flow in reality, yet the estimation here islimited to low wind speeds. The calculation method is shown in equations 41 and 42.

hfront(90) = (hfront(40)

hback(90))hback(90) (41)

htop(90) = (htop(40)

hback(90))hback(90) (42)

In figures 35 and 36, the calculation results of the local coefficient are shown for theACSR conductor and wind flows of 40 AoA, and 90 AoA respectively. In both cases, thelocal coefficients at the top and front are higher than that at the back.

48



Figure 35: Local convective heat transfer coefficient on the surface of the four quadrants of the ACSRconductor under wind flow of AoA = 40

Figure 36: Local convective heat transfer coefficient on the surface of the four quadrants of the ACSRconductor under wind flow of AoA = 90

49



Figure 37 shows a comparison of the surface average convective cooling coefficient ofthe aluminum rod, and the two cases of the Al59 stranded conductor for wind speeds upto 24 m/s. The convective behavior of the aluminum rod diverges from that of the Al59conductor at 8 m/s and becomes lower in value. As previously shown, perpendicular flow ismore optimal than oblique flow. Figure 38 shows a comparison of the latter cases with thesurface average coefficients of the ACSR conductor under oblique and perpendicular flowsfor wind speeds up to 6 m/s (low speed range). The ACSR conductor at 90 AoA has thehighest coefficient. The ACSR’s diameter is larger by 3.5 mm than those of the rod andAl59 conductor, then, this contributes to an increase of 17.4% in the Reynolds number.However, at 6 m/s the ACSR’s coefficient is higher by 60% which confirms the nonlinearityof convective cooling with the Reynolds number.

Figure 37: Total surface-average convective heat transfer coefficients of the aluminum rod and Al59 con-ductors at different AoA’s and wind speed up to 24 m/s

50



Figure 38: Total surface-average convective heat transfer coefficients of the aluminum rod, Al59, and ACSRconductors at different AoA’s and wind speed up to 6 m/s

6.2 Curve Fitting

Based on equation 13 or 25, a vector containing the Reynolds number Re for the neededwind speed range is initialized. From section 6.1, the relation of Re with convective coolingis non-linear. In MATLAB’s built-in curve fitting tool, different configurations of data fit-ting functions were tried on the results of section 6.1. The function that yielded the highestR-square value; i.e. best coverage of variations in data, was the power law with two termsshown in equation 43.

havg = a(Re)b + c (43)

In equation 43, a, b, and c are constants summarized in table 2. These data fits cover thecase of Al59 on a wind speed range of 1 to 24 m/s. Whereas, for the ACSR case the range isfrom 1 to 6 m/s. The Al59 fits could be generalized to the ACSR since both conductors havesimilar stranded surfaces; however, this needs to be confirmed by further experimentation.

51



Table 2: Results of curve fitting of the experimental value of the convective heat transfer coefficient versusthe Reynolds number

52



7 CFD Model Results

The results of the CFD simulations are illustrated and analyzed in this chapter. So far,the analysis was made based on the thermal behavior of the conductor and the variation ofthe local convective heat transfer coefficients on its surface. In this chapter, the behavior ofthe fluid movements around the conductor is analyzed in order to explain and validate theprevious observations. Surface plots of wind speed spatial distribution were generated in thesimulation software. The behavior of wind around the conductor is a dynamic phenomenon,thus, only single instants in time are described (refer to Appendix 2 for further detailed fig-ures). In general, the flow at the inlet is activated through a step function (see section 3.7).The inlet speed is averaged where its maximum value is at the inlet’s midpoint. In the wakeof the conductor sample, the phenomenon of vortex shedding is observed. Nonetheless, whatoccurs within the wake away from the sample is not directly relevant to the flow behaviornear the sample’s surface.

The test cases are classified in three; smooth cylindrical rod (section 7.1), and strandedconductor under 40 (section 7.2) and 90 (section 7.3). Both of the Al59 and ACSR con-ductors are stranded and have comparable surface shapes, and thus, the CFD models insections 7.2 and 7.3 are applicable to both of them.

7.1 Aluminum Rod in a 90 Laminar Cross Flow

In figures 39 and 40, simulations of laminar cross wind flow at 5 and 12 m/s around thecylindrical rod are shown. The flow behavior is consistent with the theoretical descriptionprovided in section 3.4.2. At the front quadrant, there is a small portion of surface where theboundary layer does not attach, resulting in a very low wind speed, and consequently, lowconvective coling at that point. As expected, the separation occurs at an angle of around80 from the axis of wind flow. Thus, boundary layer separation is within the top quadrantand so is the transition phase. Near transition, the wind speed rises by up to 100% above theinlet speed. This explains the dominant convective cooling at the top quadrant observed inchapter 7. At 5 m/s, wind speed near the back quadrant is approximately zero, indicating anatural convective behavior. At 12 m/s, a part of the back quadrant undergoes wind speedsslightly lower than the inlet speed, but higher than the wind speed near the front quadrant.This results in divergence between front and back local convective cooling coefficient shownin figure 32.

53



Figure 39: Surface plot of wind speed around a cylindrical rod under cross flow of inlet speed = 5 m/s

Figure 40: Surface plot of wind speed around a cylindrical rod under cross flow of inlet speed = 12 m/s

54



7.2 Stranded Conductor in a 40 Laminar Flow

At 40 AoA, the conductor is modeled as an elliptical cross section in the direction of windflow in order to benefit from a simplified two-dimensional simulation. It is important notto confuse the behavior shown in the simulations with the behavior of a three-dimensionalelliptical cylinder. In figures 41 and 42, laminar flows of 5 and 12 m/s are shown respectively.In both cases, boundary layer separation and transition to turbulent flow occur at the edgesof the front quadrant. Therefore the conductor’s surface area where the boundary layer isde-attached covers the back and most of the top quadrants. This explains how in figure 42the front convective cooling coefficient was the highest even though one of the front strandshas near zero wind speed. Finally, the speed rise near boundary layer separation is limitedto less than 70% above the inlet speed.

Figure 41: Surface plot of wind speed around a stranded conductor under laminar flow of inlet speed = 5m/s and AoA = 40

55



Figure 42: Surface plot of wind speed around a stranded conductor under laminar flow of inlet speed =12 m/s and AoA = 40

7.3 Stranded Conductor in a 90 Laminar Cross Flow

At first glance, a stranded conductor has a higher outer surface area than that of a cylindricalrod of the same diameter due to grooves between the strands of the outer layer. However,as shown in figures 43 and 44, before the boundary layer separates completely, it brieflyde-attaches from the surface of one strand and then re-attaches at the surface of the nextstrand leading to reduced convection at the grooves. Thus, the overall diameter remains asthe characteristic length for calculating the Reynolds number in both of the cases of strandedand smooth conductors. Yet at perpendicular flow, the complete boundary layer separationis delayed closer to an angle of 90 with the direction of flow. This location corresponds tothe middle of the top quadrant were a rise in wind speed by up to 100% above inlet speedis observed. At the back quadrant, near-zero wind speeds are observed indicating naturalconvective behavior. This is also the case for a portion of the front quadrant. Therefore,these observations in wind speed distribution further justify the calculation shown in chapter6.

56



Figure 43: Surface plot of wind speed around a stranded conductor under cross flow of inlet speed = 5m/s

Figure 44: Surface plot of wind speed around a stranded conductor under cross flow of inlet speed = 12m/s

57



8 Final Comparison and Discussion

In chapter 6, the results of using Joule heating and radiative cooling calculation meth-ods provided by both of IEEE and CIGRE standards are equivalent. That is mainly dueto maintaining the input current density below 1.5 A/mm2, which caused any magneticheating effect to be negligible. At high current densities, the heating effect would be higher;albeit, the convective heat transfer coefficient remains unchanged since it is dependent onthe conductor’s surface geometry and wind parameters. Additionally, since the test wasunder a low frequency, the skin effect was not very prominent. Thus, in this chapter theexperimental heat transfer coefficient is referred to by h40Exp and h90Exp for flows of40 and 90 AoA respectively. By comparing the experimental surface average convec-tive heat transfer coefficients in chapter 6 with the standardized calculations in chapter 4,both of the standards overestimate the effect of convective cooling (figures 45, 46, 47, and48). A single exception to the trend is for IEEE at wind speeds higher than 19 m/s andAoA of 90, where the standard underestimates the convective heat transfer coefficient (seefigure 46). Among all the methods, IEEE’s was the closest to the experimental behavior.This means if only the standards are followed to calculate dynamic line rating, this leadsto overestimated current ratings. Hence, considerations to real-life conditions are necessary.

Figure 45: Experimental and standardized surface-averaged heat transfer coefficients of an Al59 strandedconductor under wind flow of AoA = 40

As a general trend, a flow angle of attack of 40 resulted in poorer overall convectivecooling (figures 45 and 47) . This trend is supported by observing the higher steady statemeasured temperatures for oblique flow shown in chapter 5. The biggest impact of obliqueflow is on the convective cooling at the top, which is shown in chapter 6, and predicted byCFD simulations due to early separation of boundary layer at the conductor’s surface.

58



Figure 46: Experimental and standardized surface-averaged heat transfer coefficients of an Al59 strandedconductor under wind flow of AoA = 90

Figure 47: Experimental and standardized surface-averaged heat transfer coefficients of an ACSR strandedconductor under wind flow of AoA = 40

59



Figure 48: Experimental and standardized surface-averaged heat transfer coefficients of an ACSR strandedconductor under wind flow of AoA = 90

In table 3, the numerical deviations between the standardized estimation of IEEE andCIGRE and the experimental results are summarized at selected wind speeds. The factorof deviation from hexp at low speeds (3 and 6 m/s) is more dramatic than that at higherspeeds. In brief, the table shows that the higher the wind speed is, the closer IEEE’s and CI-GRE’s estimations of the convective heat transfer coefficient are to the experimental value.Nonetheless, the deviation is still considered significant.

Table 3: Factor of deviation between the standardized estimation of the convective heat transfer coefficientand the experimental results at different wind speeds

For perpendicular flow, most of the convective cooling occurs at the top quadrant of allthe conductor samples. This is observed in the CFD simulations as a significant increase inwind speed compared to the inlet speed near the top of the conductors. Also, as predictedin CIGRE TB 601 [11] and IEEE [9], perpendicular flow is optimal for convective cooling in

60



reality.

Finally, the surface average convective heat transfer coefficient is correlated with theReynolds number using the power law with two terms. This implies that the coefficient ismainly dependent on properties of air and its flow, as well as, the geometry of the conduc-tor’s surface. Due to the non-linear correlation, an increase in wind speed or in conductordiameter results in a much improved convective cooling, allowing for higher current ratings.

61



9 Conclusion and Future Work

9.1 Conclusion

In this thesis, the convective cooling behavior of three conductors under different windconditions is investigated based on previously measured data. The existing methods providedby IEEE and CIGRE standards are shown to mostly overestimate the effect of convectivecooling when applied on the three types of conductors. In comparison with the experimentalvalue of the convective heat transfer coefficient, the deviation is variant with different windspeeds and angles of attack. At high wind speeds and perpendicular flow, the standardsprovide better estimations than those at low speeds or oblique wind flow. IEEE yields closerestimations in general than CIGRE. Yet, in all cases, the deviations of both standards aresignificant (refer to table 3, Chapter 8).

Then a calculation methodology is provided based on data fittings to better estimate theoverall convective cooling coefficient. The measured data demonstrates different thermalbehaviors at low versus high wind speeds, where non-uniformity of surface convective cool-ing is observed to be more prominent at high speeds. CFD simulations are used to explainthis phenomenon based on investigating wind speed distributions at different locations on aconductor’s surface, and observing the stage of boundary layer separation.

It is observed that perpendicular flow is the optimal case for forced convection, wheremost of the cooling occurs at the top quadrants of the tested conductor. Oblique wind flowresults in a significant drop in convective cooling at high wind speeds, mainly due to reducedcooling at the conductor’s top quadrant. This behavior is directly related to the location ofthe boundary layer separation, where late separation in case of perpendicular flow resultsin higher cooling. Finally, the convective heat transfer coefficient was proven to be nonlin-early dependent on the Reynolds number, which implies that higher wind speeds and largerconductor diameters result in significant improvements in convective cooling while keepingacceptable current densities.

9.2 Future Work

For increased accuracy of thermal behavior calculations, several measures can be takenin the future. Heat transfer is decoupled from fluid dynamics in this thesis since the scopeis mainly related to convective cooling, however, coupled simulations can be performed toavoid physical experiments. Nonetheless, further experimentation would have a positiveimpact on improving the overall heat balance calculations. For instance, experimental mea-surements of emissivity by means of infrared laser thermometers can be taken to improvethe calculation of radiative cooling.

Specifically, steady state measurements for an ACSR conductor over a range of high windspeeds are needed to confirm the findings in section 6.2. Moreover, it would be optimal toinstall on-line thermocouples on an operating power line at a critical span to provide real timemeasurements of convective cooling, leading to better estimations of dynamic line ratings.

62



This would also be desirable since the wind velocity field is variant in three dimensions inreality as opposed to the unidirectional laminar flow of a wind tunnel. Finally, the effect ofthe variation between standardized thermal ratings and real measurements on line saggingneeds to be studied in order to guarantee safe operation under DLR.

63



References

[1] Ravi S. Gorur, High-Voltage Transmission, Department of Electrical Engineering, Ari-zona State University, Tempe, Arizona, USA, 2005.

[2] Wikimedia Creative Commons Attribution 3.0 license, Electricity Grid Schematic,retrieved from:https://en.wikipedia.org/wiki/Electric˙power˙distribution#/media/File:Electricity˙Grid˙Schematic˙English.svg

[3] Y.G. Paithankar, S.R. Bhide, Fundamentals of Power System Protection, 2nd edition,Delhi, 2014.

[4] T. Modric et al, 3D Computation of the Overhead Power Lines Electric Field, Universityof Split, Croatia, 2017.

[5] Marco Merante, Application of dynamic rating to improve transportation capability of thepower systems connected to wind power plants, KTH, School of Electrical Engineering,Stockholm, Sweden, 2018.

[6] United States Department of Energy, Dynamic Line Rating Systems for TransmissionLines: Topical Report, Smart Grid Demonstration Programs, April 2014.

[7] F. Incopera, T. L. Bergman, A. S. Lavine, Fundamentals of Heat and Mass Transfer,7th edition, John Wiley and Sons, 2011.

[8] Michel Rieutord, Fluid Dynamics: An Introduction. Springer International Publishing,Springer International Publishing, Cham, 2015.

[9] IEEE std 738-2012 (Revision of IEEE std 738-2006 - incorporates IEEE std 738-2012cor 1-2013), IEEE standard for calculating the current-temperature relationship of bareoverhead conductors, Dec 2013.

[10] R. Stephen, D. Douglas, M. Gaudry, H. Argasinska, K. Bakic, S. Hoffman, J. Iglesias,F. Jakl, J. Katoh, T. Kikuta, R. Kimata, T. Kumeda, S. Hodgkinson, G. Mirosevic, V.Morgan, Y. Motlis, D. Muftic, Y. Ojala, M. Olofsson, T.O. Seppa, R. Thrash, S. Ueda,L. Varga, Thermal behaviour of overhead conductors (Technical Brochure 207), CIGREworking group 22.12, August, 2002.

[11] J. Iglesias, G. Watt, D. Douglass, V. Morgan, R. Stephen, M. Bertinat, D. Muftic,R. Puffer, D. Guery, S. Ueda, K. Bakic, and S. Hoffmann, Guide for thermal ratingcalculation of overhead lines (Technical Brochure 601), CIGRE working group B2.43,2014.

[12] E. Petersson, Comparison of previous most recent CIGRE recommendation for thermalrating calculations of overhead lines, 12th International Conference on Live Maintenance(ICOLM), IEEE, 2017.

[13] E. Kuffel, W.S. Zaengl, J. Kuffel, High Voltage Engineering: Fundamentals, 2nd edition.Published by: Butterworth-Heinemann, 2000.

[14] H.J. Vermeulen, G.J. Reid, Effects of Conductor Temperature on Corona Inception,Dept. of Electrical and Electronic Engineering, Stellenbosch University, Private Bag X1,Matieland, 7602, South Africa

[15] M. Maksic, G. Kosek, V. Djurica, A. Souvent, R. Trobec, Dynamic Thermal Rating ofPower Lines in Raining Conditions – Model and Measurements, IEEE, 2016.

64



[16] B.M. Weedy, F.R.F de Lima, Evaporative Cooling of Power Cables – Prediction ofSteady State Operation, University of Southampton, UK, February 1982.

[17] K. Morozovska, Dynamic Rating of Power Lines and Transformers for Wind EnergyIntegration, KTH, School of Electrical Engineering and Computer Science (EECS), Elec-tromagnetic Engineering (RCAM), Stockholm, Sweden, 2018.

[18] APAR, Al59 241 mm2 datasheet, retrieved from: http://www.apar.com/pdf/technical-details/Cond˙10.pdf

[19] R. A. Serway, J. W. Jewett, Physics for Scientists and Engineers, 6th edition, ThomsonBrooks/Cole, 2004

[20] Anna Dupleix, Domingos De Sousa Meneses, Mark Hughes, Remy Marchal, Mid-infrared absorption properties of green wood, 2013

[21] Reflective Insulation Manufacturers Association International (RIMA), A Review ofInterior Radiation Control Coating Research, Technical Bulletin #112, 2014.

[22] Claes Johnson, Mathematical Physics of Blackbody Radiation, Icarus iDucation, Stock-holm, 2012.

[23] D. Canuto, K. Taira, Two-Dimensional Compressible Viscous Flow around a CircularCylinder, Department of Mechanical Engineering, Florida A&M / Florida State Univer-sity, Tallahassee, FL 32310, USA, 2017.

[24] J.F. Manwell, J.G. McGowan, A.L. Rogers, Wind Energy Explained: Theory, Design,and Application, 2nd Edition, John Wiley & Sons, 2009.

[25] S. Li, R. Challoo, R. A. McLauchlan, Heat Transfer Simulation Using PSPice, TexasA&M University, 2003 ASME Summer Heat Transfer Conference, ASME, Nevada, USA,July 2003.

[26] M. Greconici, G. Madescu, M. Mot, Skin Effect Analysis in a Free Space Conductor,NIS, August 2010.

[27] W.P. Goss, R.G. Miller, Thermal Properties of Wood and Wooden Products, ASHRAEHandbook-Fundamentals, ASHRAE, 1989.

[28] R. Bhaskaran, L. Collins, Introduction to CFD Basics, School of Mechanical andAerospace Engineering, Cornell University.

[29] The Engineering Tool Box (2005), Dry Air Properties at Temperatures Ranging from175 to 1900 K, retrieved from: https://www.engineeringtoolbox.com/dry-air-properties-d˙973.html

[30] Walter Frei, Choice of Turbulence Model for CFD Applications, COMSOL Blogs, July2017. Retrieved from: https://www.comsol.com/blogs/which-turbulence-model-should-choose-cfd-application

[31] S.A. Johnson, M.C. Thompson, K. Hourigan, Flow Past Elliptical Cylinders at LowReynolds Numbers, 14th Autralian Fluid Mechanics Conference, Adelaide University,Adelaide, Australia, December 2001.

[32] W.A. Khan, J.R. Culham, M.M. Yovanovich, Fluid Flow Around and Heat Transferfrom Elliptical Cylinders: Analytical Approach, Journal of Thermophysics and HeatTransfer, Vol. 19, No. 2, April-June 2005.

65



Appendix 1: Effects of Dynamic Line Rating on theDurability and Mechanical Strength of Aluminum CableSteel Reinforced (ACSR) Conductors

On the following page, enclosed is a paper that was submitted and accepted for publica-tion in the proceedings of the 10th International Conference on Applied Energy (ICAE2018),22-25 August 2018, Hong Kong, China.

The topic of the paper is based on the observation stated in the data analysis part ofthis thesis where the steel core of an ACSR had different temperatures than those of thealuminum surface. That implied a difference in the thermal expansion of the steel core andthe aluminum strands, and thus, allowing for fretting events to occur. In the paper, theeffect of those fretting events on the durability of the ACSR over-head line during operationunder dynamic line rating is investigated.

66

Available online at www.sciencedirect.com

ScienceDirect

Energy Procedia 00 (2018) 000–000

www.elsevier.com/locate/procedia

1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved.

Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018).

10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, China

Effects of Dynamic Line Rating on the Durability and Mechanical

Strength of Aluminum Cable Steel Reinforced (ACSR) Conductors

Wadih Naima, Kateryna Morozovskaa*, Patrik Hilbera

aKTH Royal Institute of Technology, School of Electrical Engineering and Computer Science, Department of Electromagnetic Engineering,

Stockholm 100-44, Sweden

Abstract

Dynamic Line Rating (DLR) is an emerging technology, which provides better utilization of power lines, by using real-time

information on the weather parameters to dynamically adjust line rating limits. The power line capacity is highly dependent on its

heat balance. The heat balance is influenced by external factors such as wind speed, ambient temperature, humidity, solar

radiation and load. DLR analyses have shown high economical and reliability benefits from power system perspective. However,

the mechanical stress on the conductor due to differences in thermal expansion characteristics of Aluminum and Steel materials

could lead to faster ageing and mechanical damages. The study aims to provide better understanding of the risks associated with

DLR application, which can affect conductor’s mechanical lifetime. The reliability analysis of transient expansion and shrinkage

of the material has identified the risks to the conductor mechanical strength that are associated with dynamic heating and cooling.

Copyright © 2018 Elsevier Ltd. All rights reserved.

Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied

Energy (ICAE2018).

Keywords: dynamic line rating, material ageing, heat and mass transfer

1. Introduction

There is an increasing trend toward the application of DLR in power networks in order to improve the integration

of renewables and to optimize the operation of existing power lines. Many studies associated with DLR often take

into account only steady-state conditions. Steady state conditions might be a good representation of the system

properties; however, they do not provide accurate information about the material conditions [1]. A transient

* Corresponding author. Tel.: +46-762-55-29-77.

E-mail address: [email protected]

2 Wadih Naim / Energy Procedia 00 (2018) 000–000

phenomenon affects the interaction between two materials and might create additional mechanical stress between

two types of metals, specifically steel and aluminum conductors, when the heating process is switched to cooling

process and vice versa.

Nomenclature

α thermal expansion coefficient

L conductor length

t time

T temperature

E Young’s modulus for elasticity

R(t) Reliability function

F(t) Failure rate reliability function

Fpu (t) Normalized risk factor due to friction forces

Ffriction(t) Friction force

λ Failure rate

τ time-scaling factor in case of no DLR

σ mechanical stress

ε mechanical strain

The ACSR (Aluminum Cable Steel-Reinforced) conductors are composed of a group of small metal strands, the

core part of the conductor consists of steel strands and the strands in the outer part are made of aluminum alloy as

can be seen in Figure 1. Steel and aluminum have different material properties when it comes to heating and cooling

operations. Steel material has lower rate of thermal expansion than aluminum. Therefore, during transient heating

the steel core expands slower than the aluminum coating, and during transient cooling operation the steel core

shrinks slower than the aluminum coating.

Figure 1 ACSR conductor cross-sectional area

An ACSR overhead line (Figure 1) is expected to remain in operation for an average lifetime of 54 years under

clean and moderate environmental condition, or 46 years under heavy pollution. However, the variance in lifetime is

14-15 years, which is relatively high. This is due to several factors among which mechanical fatigue and

contamination are two of the most prominent [2].

During thermal expansion due to the difference in the expansion rate, cavities are formed between the strands of

aluminum and steel. In the process, these cavities are filled by contaminants that were initially on the surface of the

conductor, such as humidity, dust and metal oxides, potentially leading to degradation and galvanic corrosion. When

the process is reversed the contaminants create additional mechanical stress on shrinkage of the conductor strands

and could potentially cause mechanical fatigue, and eventually the breaking of the outer aluminum strands [3]. Plus,

Wadih Naim / Energy Procedia 00 (2018) 000–000 3

friction forces are exterted on the metallic conductor which leads to a “fretting event”; i.e. wear and tear of the

conductor wires due to friction. The breaking of the strands causes the conductor to perform below design

specifications, with effects including, higher current densities in some parts of the conductor (loss of ampacity),

reduction in tolerance to mechanical stress, and the creation of potentially dangerous spots along a power line

leading to faults.

2. Method description

The steel core undergoes heat exchange mainly by conduction; therefore, its transient thermal response is slower

than that of the surrounding aluminum strands. For any temperature changes ΔT, the rate of thermal

expansion/shrinkage for Steel is lower than for aluminium (1) and (2). Consequently, at every transient thermal

event, displacements between steel and aluminum occur and lead to friction stress, resulting in fluctuations in tensile

forces on top of the initial physical load. Under room temperature, the Young’s modulus of elasticity for steel is E =

200 GPa [4], and for aluminium E = 70 GPa [5]. In Figure 1, the stress-strain characteristics of steel and aluminum

are shown according to Hooke’s Law (3). The difference in elasticity (almost by a factor of 3) indicates that the

limiting factor for mechanical strain is the aluminum as it is more vulnerable to deformation. Thus, reliability

analysis oriented towards the behaviour of the aluminum conductor is of higher significance.

St AldT dT

dt dt (1)

dL L dT (2)

E (3)

Initial conditions: at t=0, Lst(0)=LAl(0)=constant. If we differentiate (2) with respect to time we get (4). Applying

(1) to (2) results in the relation (5).

Figure 2 Stress-strain characteristics of steel and aluminium


dL dTL

dt dt (4)

St AldL dL

dt dt (5)

The corrosion behavior of Aluminum mostly worsens non-linearly with the value of the friction force [6]. To

quantify this relation, a normalized risk factor Fpu(t) is introduced in equation (6) as the ratio of a friction force over

the maximum friction force after long exposure to fretting events (>105 events) based on the data in [6]. This risk

factor is used to examine the impact of the implementation of DLR on the reliability function ‘R(t)’ of a

hypothetical ACSR transmission line. Exponential survival function [7] is presented by (7) and (8).

5

( )( )

( 10 )

frictionpu

friction

F tF t

F t

(6)

( ) tR t e (7)

( ) 1 ( )R t F t (8)

The model is dependent on the number of fretting events that the conductor experiences with DLR compared to

the standard rating. Conductor fretting events can be of two types: expansion of the material due to heating and

shrinkage of the material due to cooling; thus, a single event corresponds to a single thermal transient. The

assumptions regarding the number of fretting events that the conductor experiences with standard rating and with

DLR are provided by (9). In the no DLR case, the number of fretting events is limited to weather changes

(night/day), and peak hours of power consumption which also can coincide with night/day changes. As for the DLR

case, a worst case scenario is considered, where the line rating is adjusted on an hourly basis. The time-scaling

factor is defined as the ratio between number of fretting events per day between DLR and standard rating and is

shown by (9).

3 4[ / ]

24[ / ]

no DLR fretting events day

DLR fretting events day

248

3 (9)

Assuming constant failure rate λ, the reliability function for standardly rating (10) and DLR (11) are built.

1( )t

R t e

(10)

( )

2 ( ) pu

tF t

R t e

(11)

The ratio between reliabilities of the standardly rated conductor and DLR conductor is found using (12).

1( ) [ ( 1)]( )2

1

( )

( )

pu

pu

tF t t

F t

t

R t ee

R t e

(12)

Wadih Naim / Energy Procedia 00 (2018) 000–000 5

3. Results and discussion

In Figure 3, it is shown how over an increasing number of fretting events, the risk of failure increases due to the

underlying wear and tear of the aluminum strands. A risk factor of 1 indicates the maximum impact of friction

forces on the durability of the aluminum strands. Based on the data in [6], the presence of the NaCl solution as a

contaminant results in lower friction forces due to lubrication; however, it causes more severe wear and tear than

that in the case of no contaminants. Since it is initially hypothesized that the difference in thermal expansion rates

allows contaminants to reach the conductor’s core, the presence of NaCl as a contaminant is considered here as a

worst case scenario. After a large number of fretting events, the risk factor saturates which implies the occurrence of

critical damage to the Aluminum conductor. In the same figure, the ratio mentioned in (9) is plotted to show the

consequence of exposure to fretting caused by DLR, as opposed to the case of no DLR, on the reliability function.

Therefore, the implication of the excessive use of DLR is a trade-off with the durability of a conductor.

Based on the information obtained from Figure 3, generic reliability and failure rate functions are calculated and

plotted in Figure 4 and Figure 5 respectively based on (8), (10), and (11). From (9), the time-scaling factor is needed

in order to objectively compare the cases of DLR and standard rating. The impact of fretting caused by DLR is

reflected as a faster deterioration in reliability, increase in failure rate, and eventually, a reduction in the over-all per-

unit lifetime. It is important to note that the impact of DLR depends on the time-scaling factor, or in other words, the

fashion in which DLR is applied (e.g. hourly, day/night, daily, etc.).

Since an exponential distribution is used to model the reliability function (7), changes in failure rate ‘λ’ can lead

to significant implications on reliability. As an example, three different cases are shown in Figure 6, where three

constant failure rates that differ logarithmically (1 to the power of 10) are used. While it is obvious that a lower

failure rate indicates higher reliability, the significant impact of ‘λ’ suggests that it is worthwhile to consider the

effect of DLR.

Figure 6 Visualization of the magnitude of change on reliability with different failure rates

Figure 5 Generic Failure Rate Functions before and after Implementation of DLR using a time-scaling factor of τ=8

Figure 4 Generic reliability functions before and after implementation of DLR using time-scaling factor of τ=8

Figure 3 Risk of failure factor and ratio of change in reliability


4. Conclusions

The durability of an ACSR overhead line depends on several factors that contribute to its wear and tear. The

effect of fretting caused by the application of Dynamic Line Rating (DLR) was investigated by means of introducing

a normalized risk factor that represents the relation between friction forces and number of fretting events. The

reliability function was modeled based on the exponential distribution. By using a time-scaling factor and including

the previously mentioned risk factor in the reliability function under DLR, the consequences of DLR were observed

and compared with the standard line rating (SLR) case. It was shown that there are potential negative impacts on the

reliability and lifetime of an ACSR conductor. Therefore, the application of DLR has to be considered as a trade-off

with durability, and the frequency of rating changes has to limited so that the lines is kept within acceptable values

of reliability.

Acknowledgements

The authors would like to thank Energiforsk Wind Research program for financing the project. This work was

conducted within STandUP for Wind, part of the STandUP for Energy strategic research framework.

References

[1] K. Morozovska, "Dynamic Rating of Power Lines and Transformers for Wind Energy Integration," KTH Royal

Institute of Technology, Stockholm, 2018.

[2] International Electrotechnical Commission (IEC), "Strategic asset management of power networks," IEC,

Geneva, 2015.

[3] N. Murray, F. Besnard , D. McGuire and K. Scissum, "Conductor Corrosion Inspection of Aluminum Conductor

Steel Reinforced Transmission Lines," in 2016 IEEE/PES Transmission and Distribution Conference and

Exposition (T&D), Dallas, 2016.

[4] M. Mahendran, "The Modulus of Elasticity of Steel - Is it 200 GPa?," in Thirteenth International Specialty

Conference on Cold-Formed Steel Structures, St. Louis, 1996.

[5] A. da Silva Scari, B. Pockszevnicki, J. Landre Jn. and P. Almeida Magalhaes Jn., "Stress-Strain Compression of

AA6082-T6 Aluminum Alloy at Room Temperature," Journal of Structures, p. 7, 2014.

[6] X. Ma, L. Gao, J. Zhang and L.-C. Zhang, "Fretting Wear Behaviors of Aluminum Cable Steel Reinforced

(ACSR) Conductors in High-Voltage Transmission Line," Metals, vol. 7, p. 373, 2017.

[7] M. Rausand and A. Høyland, System Reliability Theory: Models, Statistical Methods, and Applications, 2nd

edition, Hoboken: John Wiley & Sons, 2004.



Appendix 2: Detailed Plots andCFD Figures

73



Aluminum Rod:

Figure: Inlet Wind Speeds

Figure: Input Currents

i



Figure: Average Input Current

Figure: Front Temperatures

ii



Figure: Top Temperatures

Figure: Back Temperatures

iii



Al59 Conductor (40 AoA):



iv





v





vi



Al59 Conductor (90 AoA):



vii





viii





ix



ACSR Conductor (40 AoA):



x





xi





xii



Figure: Core Top Temperatures

Figure: Core Back Temperatures

xiii



ACSR Conductor (90 AoA):



xiv





xv



Figure: Core Top Temperatures

Figure: Core Front Temperatures

xvi



Aluminum Rod CFD:

At 1 m/s:

Figure: Wind Velocity [m/s] Surface Plot at t = 60s


xvii





xviii



At 3 m/s:



xix





xx



At 5 m/s:



xxi





xxii



At 12 m/s:



xxiii





xxiv



Stranded Conductor (40 AoA) CFD:

At 1 m/s:



xxv





xxvi



At 3 m/s:



xxvii





xxviii



At 5 m/s:



xxix





xxx



At 12 m/s:



xxxi





xxxii



Stranded Conductor (90 AoA) CFD:

At 1 m/s:



xxxiii





xxxiv



At 3 m/s:



xxxv





xxxvi



At 5 m/s:



xxxvii





xxxviii



At 12 m/s:



xxxix





xl

TRITA EECS-EX-2018:495

ISSN 1653-5146

www.kth.se

Documents

Study of The Effect of Convective Heat Transfer on Cooling ...1249010/FULLTEXT01.pdf · Study of The E ect of Convective Heat Transfer on Cooling of Overhead Line Conductors Based