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B2-108 21, rue d’Artois, F-75008 PARIS CIGRE 2012 http : //www.cigre.org Radial and Longitudinal Temperature Gradients in Bare Stranded Conductors with High Current Densities B. CLAIRMONT D.A. DOUGLASS J. INGLESIAS Z. PETER EPRI PDC, Inc. RedElectrica Kinectrics, Inc. USA USA Spain Canada SUMMARY At low current densities (< 2 amp/mm2), the radial and longitudinal temperature variation in bare stranded transmission line conductors can be ignored. At higher current densities, and therefore higher operating temperatures, however, the radial and axial variation in temperature must be considered. When the conductor core is hotter than the surface, the sag and possible loss of tensile strength due to annealing can be underestimated. When the conductor temperature varies along the line from span to span, locally high temperatures can be overlooked and the average line section temperature wrongly estimated for line survey measurements. Conventional and High-Temperature Low-Sag (HTLS) bare stranded conductors are constructed similarly. One or more layers of round or trapezoidal aluminium strands are wound helically around a steel or composite core. The core exists primarily for mechanical strength and to limit conductor expansion at high operating temperatures while the aluminium strands carry almost all the electrical current (e.g. 98% to 99%). Given the 20 to 45 mm overall diameter of transmission line conductors, the variation in current density between aluminium layers due to “skin effect” is typically less than 10% and 40% to 60% the Joule heat is generated in the inner aluminium layers. The flow of this heat to the conductor surface produces a radial temperature drop. Experiments were undertaken to test an improved calculation model for radial temperature drop. These included a simulation of aluminium strand layer contact with machined aluminium plates and thermocouple measurements on ACSR conductors with 3 and 4 layers of aluminium. The results indicate that radial temperature drop is significant (10oC to 30oC) especially when the aluminium layers are carrying little or no tension due to plastic or thermal elongation. The axial conductor temperature variation along an overhead line was modelled mathematically. It is concluded that there is almost no temperature equalization along overhead lines with bare stranded overhead conductors. The temperature measured at a single location within a line section may be quite different from the average conductor temperature in any line section. In certain spans, shielded by terrain or foliage, short sections of conductor can be damaged by higher than expected temperatures. KEYWORDS Thermal Ratings, High Temperature Sag, Radial Temperature Drop, Longitudinal Temperature Variation, Aluminum strand layers, Effective radial thermal conductivity. [email protected] INTRODUCTION & BACKGROUND The design and rating of overhead transmission lines has changed dramatically in recent years. Bare stranded transmission conductors are being operated at much higher current densities and temperatures and new types of high temperature conductor have been introduced. Where in the past, it was not unusual to design overhead lines for a maximum operating conductor temperature of 50oC, in recent years, lines are being designed or re-designed to allow conventional steel-cored ACSR conductors to operate at 100oC or more and commercially available HTLS conductors at 200oC or more. Since bare overhead stranded conductors used in transmission lines normally have at least two layers of aluminum strands, the flow of heat generated in these inner layers of aluminum cause a temperature drop from the inside of the conductor to the outside. This temperature difference is referred to in this paper as the conductor’s radial temperature drop. At high current densities, the higher temperature of the core can increase sags or accelerate aging. Weather conditions do not directly affect the radial drop but can change the aluminum electrical resistance by changing its average temperature. Unless tapped, overhead transmission line conductors carry the same current between substation terminations. Thus the heat generated per unit length is the same all along the line. Similarly, air temperature and solar heating are usually similar along an overhead line unless it is very long or changes elevation sharply. Thus the heat input from Ohmic losses and solar heating are essentially constant along the line. The wind speed and direction relative to the conductor can, however, vary sharply from span to span, especially with low speed turbulent winds. Although aluminum is an excellent thermal conductor, the small crossection area of a typical bare overhead conductor makes the axial thermal resistance high and allows little or no axial heat transfer. As a result, sheltered spans can be significantly hotter than open sections of the line when the line current density is high. As with radial heat conduction, the difference in temperature between spans at low current density is usually negligible. The current density required to produce the line’s maximum allowable temperature depends upon the outside diameter of the conductor and the assumed weather conditions. For a small, 200 mm2, twolayer conductor, the current density at surface temperature of 100C may be in the range of 1 amps/mm2 while the current density of an 800 mm2 three-layer conductor may only be the The range of current densities found in bare overhead conductors is usually HEAT BALANCE FOR BARE OVERHEAD CONDUCTORS Even if a bare overhead conductor carries no current, during the day absorption of solar heat is sufficient to raise the conductor temperature 5oC to 10oC above the temperature of the surrounding air. This conductor temperature is normally referred to as the solar temperature of the conductor. At night the solar temperature is essentially equal to the air temperature. Air temperature and solar heat intensity vary little from span to span, so the conductor temperature along the line varies no more than a few degrees if there is no current. When there is current, heat is generated through Ohmic losses. The heat generated is equal to the resistance of the conductor times the square of the current through it. At low current levels, the bare conductor temperature may be only slightly above the solar temperature but at high current levels the bare conductor can be quite high. For example, for a 405 mm2 bare stranded aluminum conductor, a current of 1500 amps produces a temperature rise above solar temperature of between 35oC and 115oC. These calculations which involve the heat balance at the surface of the conductor are normally performed using one of the standard methods such as CIGRE Technical Brochure 207 and all assume a unit length of conductor exposed to the same weather conditions. Weather conditions, particularly wind speed and direction, vary along transmission lines. At high current loads, one would expect the conductor temperature to vary along the line as well. Similarly, with bare stranded conductors having 2 or more layers of aluminum strands, a significant portion of the Ohmic heat is produced in the inner layers of the conductor and must be conducted to the surface layer in order to be part of the heat balance there. At high current levels, especially for 2 three and four layers of aluminum strands, one would expect that the temperature of the inner layers in higher than the surface. This paper concerns both mathematical calculations and experimental measurements of the variation in conductor temperature both axially along the line and radially within the conductor. RADIAL HEAT FLOW IN BARE CONDUCTORS 1 Do Di 2 RI TC TS 2 ln 2 kr 2 Do Di 2 Di 2 CIGRE Technical Brochure 207 suggests a rather simple algebraic equation for the calculation of radial temperature drop as shown in the adjacent equation. In ACSR conductors, 98 to 99% of the heat is generated in the aluminum strands so the conductor is modeled as a solid hollow cylinder with uniform heat generation in the aluminum layers and an effective radial thermal conductivity (kr). The reference brochure recommends using a value of 2 watts/m-oC but that is too high for stranded ACSR and other high temperature conductors operating at high current and temperature levels. Where: TC= Core temperature [oC] TS = Outer layer temperature [oC] R = Resistance [Ohms/m] I = Current in conductor [amps] Di=core diameter [mm] Do=outside diameter [mm] kr=eff. radial therm. cond [watts/m- oC] EFFECTIVE RADIAL THERMAL CONDUCTIVITY The thermal conductivity of aluminum is 237 W/m- oC [2]. The conventional (e.g. ACSR, AAC, ACAR etc) and HTLS conductors (ACCR, ACSS etc.) contain both aluminum strands and core strands (steel, aluminum oxide, carbon fibre etc) with air gaps between the circular or trapezoidal aluminum strands. Due to its heterogeneous structure, heat conduction analysis for bare overhead conductors is more complex than if it were simply homogenous (e.g. solid aluminum bar). Air gaps hinder heat conduction, while contact surfaces between strands increase thermal resistance. The heat is conducted through contact surfaces between strands and through triangular air voids between layers. As shown in the preceding equation, this problem is dealt with by introducing a new transport coefficient, the effective radial thermal conductivity (also known as “apparent”, “resultant” or effective conductivity in the literature [3]. The effective radial thermal conductivity must be determined by modeling or by measurements. The relevant literature [3] offers certain theoretical models for estimating the equivalent thermal conductivity. Some of these models needs input from measurements and mostly offer a rough estimation for the equivalent thermal conductivity. Flat plate experiment Figure 1 Effective radial thermal conductivity increases with pressure between the machined aluminum plates. Effective Thermal Conductivity from Machined Plate Experiment Effective rectangular thermal conductivity [watts/m-C] 2.5 Measurements of radial temperature gradients are difficult in multi-layer stranded conductors. The strands are small and thermocouple placement is difficult. Control of inter-layer pressure is difficult since tension distributions between strand layers and between aluminum and steel core strands is difficult to control. 2 1.5 1 0.5 0 0 0.5 1 1.5 2 2.5 3 3.5 Pressure Between Plates [kiloPascals] 4 4.5 5 In order to simplify such measurements and gain insight into 3 the heat flow phenomena between aluminum layers, flat aluminum plates were machined to simulate strand layers. The effect of tension in the conductor aluminum strand layers was simulated by placing weights on the stacked plates. The Impact of Pressure on Conductivity As the pressure between the plates is increased, the conductivity increased as shown in Figure 1 where the thermal conductivity increases by a factor of about 2 as the weights are increased. One would therefore expect that the radial temperature drop decreases with the radial pressure between the strand layers and that the trapezoidal strands would yield lower radial temperature drops than round strands when under pressure. EXPERIMENTS WITH TENSIONED, STRANDED CONDUCTOR Measurements of radial temperature differences with thermocouples placed within bare stranded conductors are difficult because the dimensions are small and if it difficult to secure the location of the TCs given the high currents and temperatures generated. Prior Experiments There have been quite a few laboratory experiments undertaken to determine the radial temperature variation in bare stranded overhead conductors. Reference [8] reports temperature gradients measured on tensioned new and aged ACSR conductors. The measurements were obtained from indoor and outdoor laboratory test at various temperatures exceeding 300°C. The measurements in this study were taken at stead-state conditions under steady wind (0, 0.6 and 2.4 m/sec) and tension (22 kN) conditions. It was found that the temperature difference between core and surface of ACSR conductor is in order of 10% for new conductor and 20% for aged conductors, depending on conductor construction and age [8]. The measured temperature gradient in conductors was in the range of 20 to 50 °C, in general. The derived equivalent thermal conductivity is shown in Table 1. It was concluded by Reference [4] that the radial equivalent thermal conductivity in conductors is independent of generated heat and increases with increasing conductor tension and increasing air pressure. Thermocouple Placement, Tension Control and Forced Cooling As shown in Figure 2, Thermocouples were placed between strands in the same layer. Small shifts in the position of the thermocouples can cause significant measurement errors. The steel core of the conductor was gripped separately from the surrounding aluminum layers so that the tension in the aluminum layers can be adjusted independently of the steel core. The external convection rate of the experimental conductor can be changed by turning fans on and off. Changes in wind speed sharply affected the surface temperature but not the temperature drop from core to surface. Radial Temperature Measurements Using the preceding experimental set-up, measurements were made on three large conductors: Lapwing 45/7 805 mm2 ACSR Cumberland 42/19 975 mm2 (3-layer) ACSR/TW Santee 64/19 1330 mm2 (4-layer) ACSR/TW These laboratory tests are limited to large conductors but consider both round strand and trapezoidal strand aluminum. 4 Table 1 Summary of Previous Radial Temperature Measurements Source/ Reference Alcan* [5] Alcan* [5] Kaiser* [5] Dale/PTI [5] Dale/PTI [5] Dale/PTI [5] OHRD* [8] OHRD* [8] OHRD* [8] OHRD* [8] OHRD* [8] Z.Peter [10] V.T. Morgan [6] V.T. Morgan [6] V.T. Morgan [6] V.T. Morgan [6] V.T. Morgan [6] V.T. Morgan [6] Conductor Condition ACSR, round ACSR, round ACSR, round ACSR, round ACSR, round SDC ACSR, round ACSR, round ACSR, round ACSR, round ACSR, round ACSR, round ACSR, round ACSR, round ACSR, round ACSR, round ACSR, compact ACSR, round new old new old old new new new new Area (mm2) 402.84, Condor 689.14, Bersimis 523.68, Curlew 402.84, Drake Dove Stranding Tension (kN) Span (m) Radial Thermal Conductivity (W/mK) 54/7 - 15 3.7 42/7 - 15 2.5 54/7 Low 1.2 1.2-2.1 26/7 2.22 6 2.4-2.6 1985 26/7 2.22 145, outdoor 2.6 1985 2.22 6 2.1 1985 54/7 22.24 indoor 1.4 1977 26/7 22.24 indoor 2.3 1977 26/7 22.24 indoor 2.3 1977 26/7 22.24 365, outdoor 3.0 1977 26/7 22.24 122, outdoor 3.6 1977 45/7 Low indoor 644.54 402.84, Condor 402.84, Drake 402.84, Drake 402.84, Drake 402.84, Drake 689.14, Bersimis new 596.41 54/7 28.78 outdoor new 519.39 54/7 5 indoor new 519.39 54/7 20 indoor new 179.38 30/7 Low new 170.26 18/7 Low new 417.03 54/7 Low - 3.5-5.7 AVG=4.6 0.74-5.2 AVG=2.22 0.64-1.6 AVG=1.06 1.05-1.12 AVG=1.1 1.16-4.68 AVG=3.39 4.18-5.89 AVG=4.70 1.15-6.94 AVG=2.46 Year 2006 1985 1985 1985 1985 1985 1985 The conductors were placed in the laboratory test span shown in Figure 2. A special collet was manufactured and welded to the aluminum strands at one end of the span. This allowed the aluminum strand layer tension to be controlled separately from the steel core. To offer a degree of control over the tension in the aluminum strand layers, (0 to 2000 lbs) all of the aluminum strands were welded into a drilled aluminum thick-walled tube end-fitting which fits over the steel core at one end of the test span. Figure 2 Experimental Set-up to control aluminum layer tension separately. 5 Radial Temperature Difference as a Function of Current Density with Tension in Aluminum Strand Layers Radial Temperature Drop Core to Surface - deg C 30 Dashed lines indicate the calculated radial temperature drop for a radial thermal conductivity of 1.5 25 20 Lapwing DT-C 15 Cumberland DT-C Santee DT-C 10 5 0 1.00 1.50 2.00 2.50 3.00 3.50 Current Density - Amps/mm2 Figure 3 - Radial temperature drop versus current density for Lapwing, Cumberland, and Santee ACSR with 2 kN tension in the aluminum layers. Radial Temperature Difference as a Function of Current Density with Slack Aluminum Strand Layers Radial Temperature Drop Core to Surface - deg C 30 25 Lapwing DT-C 20 Cumberland DT-C Santee DT-C 15 10 Dashed lines indicate the calculated radial temperature drop for a radial thermal conductivity of 0.7 w/m-C 5 0 1.00 1.50 2.00 2.50 3.00 Current Density - Amps/mm2 3.50 Large conductors such as these are less efficient in convecting and radiating heat to the surrounding air than small conductors. Therefore the current densities required to produce a given surface temperature are lower. For example, at a current density of 3 amps/mm2, 400 mm2 and 800 mm2 conductors produce surface temperatures of 120°C and 180 °C, respectively. As shown in Figure 3 and Figure 4, the radial temperature drop for each of the tested conductors increased with current density and that the tests where there was little or no aluminum tension yielded radial temperature drops which were about twice as high as occurred with tension in the aluminum layers. The dashed lines indicated reasonable agreement between calculations using the simplified equation with thermal conductivities of 0.7 and 1.5 watts/m-°C, for untensioned and tension aluminum strands, respectively. Figure 4 - Radial temperature drop versus current density for Lapwing, Cumberland, and Santee ACSR with no tension in the aluminum layers. Axial Temperature Variation We can investigate the longitudinal variation of conductor temperature by ignoring any radial variation and deriving the following differential equation for axial heat transfer within the bare stranded conductor. If there is no axial variation along the conductor, d 2T k x A 2 qconv qrad R (T ) I 2 then the heat balance between heat input from solar heating dx and Ohmic losses equals the heat lost by convection and radiation. The convection and radiation terms in the equation can be represented by linear functions of T-Ts. 6 Figure 5 - Numerical model of axial temperature variation along a current-carrying bare stranded conductor. Examples of Temperature Equalization 160 160 150 150 Conductor Temperature - deg C Conductor Temperature - deg C Bare overhead conductors carrying ordinary rated current levels of about 1 amp/mm2, produce about 50 watts/meter due to Ohmic heating. Very little of the heat generated within the conductor is transmitted axially, even when the temperature varies due to varying wind cooling as shown in Figure 6 (for a 10 meter and 1 meter shielded section). The conductor temperature is determined by the local weather conditions with very little axial heat flow between conductor sections at different temperature. 140 130 120 110 140 130 120 110 100 100 15 17 19 21 23 25 27 29 31 33 Distance Along Conductor - meters TCss TC10 35 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 23 Distance Along Conductor - meters TC-ZeroAxialConductivity TC-NormalThermalConductivity Figure 6 - Calculated temperature distribution for 10 & 1 meter long sheltered sections of conductor. Wind speed is 1.6 mps at all points outside the 1 meter section where it is only 0.6 mps. The Impact of Current Density Even with the line subject to full summer solar heating, the conductor temperature varies little along the line with varying wind speed and direction. At high current densities, however, the conductor temperature can vary greatly along the line. The tension in each line section varies with the average temperature of the line section. The lower tension produced in hot spans is equalized by adjacent cooler spans but the temperature of each is not affected by the hotter or cooler temperature of adjacent spans. Effective Average Perpendicular Wind Speed The average effective perpendicular wind speed of a line section is defined as that wind speed perpendicular to the conductor which yields the same tension and average temperature as the actual wind along the line section. 7 Conclusions At current densities above 1 to 2 amp/mm2, the conventional concept of specifying or measuring a single temperature for bare stranded overhead conductors should be reconsidered. The temperature of the conductor core wires can be significantly higher than the surface and the average temperature of the conductor crossection can vary from span to span along the line. The specific current density, above which such effects become important, is a function of the conductor diameter. A current density of 2 amps/mm2 is required in a 200 mm2 conductor to produce the same surface temperature as a current density 1 amp/mm2 in an 800 mm2 conductor. The simplified radial temperature drop calculation equation provided in Technical Brochure 207 is in reasonable agreement with laboratory measurements made with large ACSR conductors (800 to 1300 mm2). The effective radial thermal conductivity value for tested conductors with tension in the aluminum strand layers is found to be in the range of 1.5. When the same conductor samples were tested with slack aluminum strand layers, the conductivity was found to be in the range of 0.7 watts/m°C. The temperature drop in typical transmission conductors (e.g. 20 to 40 mm diameter) can be as high as 10 to 20oC even with light tension in the aluminum layers and 20 to 40 oC when the aluminum strands are slack (no tension). When there is no tension in the aluminum layers, it appears that the radial temperature drop occurs for both round and trapezoidally shaped aluminum strands. Ignoring the higher core temperature of bare stranded conductors can lead to underestimation of conductor sag and material degradation. Even at moderate current densities, the longitudinal variation of conductor temperature from span to span needs to be considered when performing field surveys with lines “in-service”. BIBLIOGRAPHY [1] CIGRE WG 22.12, “Thermal Behaviour of Overhead Conductors”, Technical Brochure 207, August 2002. [2] Frank P. Incropera, David P. DeWitt: Heat and Mass Transfer, 5th ed. John Wiley & Sons, 2002, pp.410-412, 905. [3] L. I. Kiss, “Thermo-physical properties in heat conduction”, Lecture notes, Université de Liège, LAS, 1996. [4] V.T. Morgan, “Effects of axial tension and reduced air pressure on the radial thermal conductivity of a stranded conductor”, IEEE Transaction on Power Delivery, Vol. 8, No.2, April 1993. [5] D. A. Douglass, “Radial and axial temperature gradients in bare stranded conductor”, IEEE Transaction on Power Delivery, Vol. PWRD-1, No.2, April 1986. [6] V.T. Morgan, D. K. Geddey, “Temperature distribution within ACSR conductors”, Cigre 22-101, 1992 Session, August 30- September 5. [7] W. Z. Black, S. S. Collins, J. F. Hall, “Theoretical model for temperature gradients within bare overhead conductors”, IEEE Transaction on Power Delivery, Vol. 3, No.2, April 1988. [8] G. J. Clarke, “Summary report on the effects of high operating temperatures on conductors and hardware behaviour”, Ontario Hydro Research Division Report No. 77-177-H, April 25, 1977. [9] D. A. Douglass, L.A. Kirkpatrick, “AC Resistance of ACSR – Magnetic and Temperature Effects”, IEEE Transaction on Power Apparatus and Systems, Vol. PAS-104, No. 6, June 1985. ACKNOWLEDGEMENT The authors acknowledge the many technical contributions of Dr. V.T. Morgan. 8