Calculation accuracy of high-temperature sag for ACSR in existing lines

Transcription

1 Calculation accuracy of high-temperature sag for ACSR in existing lines D. Loudon, EFLA, Norway D.A. Douglass*, DPC, LLC, USA R.G. Stephen, ESKOM, South Africa G.C. Sibilant, EPRI/UKZN, USA Abstract According to a CIGRE questionnaire completed in 2003, over 80% of existing lines were built with steel reinforced aluminium conductors (ACSR). Therefore, when attempting to increase the thermal rating of existing High Voltage (50 kv to 345 kv) transmission lines, lowcost line uprating methods often involve allowing the existing ACSR conductors to operate at an increased Maximum Allowable Conductor Temperature ( MACT ) temperature. Of course, minimum electrical clearances to ground, buildings and other lines must be maintained and the conductor system unharmed by operating at higher temperatures. If these criteria are not met, the line must be reconductored or rebuilt. For ACSR, all sag-tension calculation methods assume that the unstressed length of aluminium and steel layers is the same before and after installation. After initially sagging the conductor, high line currents cause the conductor temperature and sag to increase. CIGRE Technical Brochure 324 suggests two linear and one non-linear conductor model. The Experimental Plastic Elongation (EPE) model considers the aluminium layers and steel core separately. The paper explains and quantifies the various factors that influence the calculation of ACSR sag at high temperature. The thermal elongation rate of the aluminium layer(s) is twice that of the steel core, and, while the total tension decreases with increasing temperature, the tension in the aluminium layers decreases faster than the tension in the steel core. For strong ACSR conductors in short spans operated above 75oC, the aluminium layer tension may reach zero at a knee-point temperature (KPT) which is less than the line s actual or proposed templating temperature. Since, above the KPT, the rate of sag increase with temperature is reduced, the determination of KPT is a significant factor in evaluating line uprating methods using the existing conductors. If the aluminium layers of ACSR undergo plastic elongation due to metallurgical creep or high tension load events, then the knee-point temperature of the conductor is reduced, typically decreasing over the life of the line. In calculating the conductor sag at temperatures above the KPT, the possibility of compression forces, residual manufacturing stress, and greater than anticipated plastic elongation of the aluminium layers must be considered. 1. Introduction & Background In designing a new overhead transmission line, one of the most basic and necessary calculations is that of sagtension. CIGRE Technical Brochure 324 [1] explains the calculation of sag and tension for bare overhead conductors under various ice/wind conditions and at the high conductor temperatures produced by the line s highest power flow. Based on these calculations, span lengths and structure heights are chosen to meet the structure loads and electrical clearance requirements over the life of the line. In evaluating existing lines, power flow constraints on the AC Transmission System are often the result of inadequate thermal rating on older existing High Voltage (50 kv to 345 kv) transmission lines, built with one ACSR conductor per phase. Increasing the thermal rating of these existing lines can often be accomplished by increasing the maximum design temperature of the lines if this can be done while continuing to maintain minimum electrical clearances to ground, buildings and other lines. As described in [2], if the sag of these ACSR conductors * Da.douglass@ieee.org KEYWORDS High temperature sag, knee-point temperature (KPT), aluminium layer axial compression, ACSR, LiDAR, Linear Elastic, Simplified Plastic Elongation, Experimental Plastic Elongation. 39

2 at the higher temperature is not adequate, then the line s conductors may be re-tensioned, the support heights raised, the line reconductored with High-Temperature, Low-Sag (HTLS) conductor of the same diameter, or the line simply replaced by a new line with adequate thermal capacity. The initial step in determining the choice of thermal uprating method for an existing line, is to make a detailed measurement of conductor position and terrain survey for the entire line. Increasingly, this is done with airborne LiDAR ( Light Detection and Ranging ). In most cases, these older lines are lightly loaded (electrically) when the system is operating normally. Even with the line in service, the conductor temperature is typically within 5 o C to 15 o C of air temperature since the current in most lines is less than 0.5 amps/mm2. At higher current densities, the conductor temperature which corresponds to the measured sag must be calculated. 2. Errors in High Temperature Sag TB244 [2] includes a useful table estimating high temperature sag errors due to various factors. The table is reproduced here (see Table 1) with certain modifications. All three conductors are strung to an initial tension equal to about 25% of their breaking strength. Notice that the sag in Table 1, at 20 C, is approximately 5 m, and that the sag increases by about 3 meters when the conductor temperature increases to 120 C. The calculated high temperature sag can vary by as much as a meter due to imperfect tension equalization [3] at supports for all three ACSR conductors. Indeed, sag errors due to imperfect tension equalization, occur for all aluminium conductor as well as ACSR. As per Table 1, the second largest variation in calculated sag at 120 C is due to the choice of conductor stress-strain model. The models are discussed at length in [2] and also in this paper. Other factors, including additional heating of three-layer ACSR at high current due to the steel core [4], variation in the conductor temperature when manufactured, creep of aluminium at high temperature, and variation in thermal elongation rate due to high stress, produce relatively small errors, typically less than 0.15 m, but can be important in certain situations. Table 1: Sag Errors at High Temperature for three Different ACSR Strandings Typical Errors for High-temperature Sag Calculations ACSR Drake ACSR Condor ACSR Tern Aluminium area (strands) 403 mm2 (26) 403 mm2 (54) 403 mm2 (45) Steel area (strands) 66 mm2 (7) 53 mm2 (7) 28 mm2 (7) Final tension at 20oC N N N Equivalent span length 250 m 250 m 250 m Sag at 20 C 4.84 m 5.06 m 5.36 m Effect of Conductor Stress-strain model on final 120 ºC sag: Single conductor modulus & CTE (LE or SPE) 7.76 m 7.78 m 8.53 m Separate modulus & CTE (Graphical method) - no Residual stress (EPE) 7.00 m 7.53 m 8.53 m Graphical method with typical 20 MPa residual stress offset m 7.73 m 8.53 m Additional sag errors at 120 ºC : Temperature difference core/surface m m m Change of elastic modulus vs. temperature m m m High temperature creep m Multiple span effects +0.6 to to -0.9 m +0.5 to -0.8 m Effect of core magnetisation losses m m Effect of manufacturing temperature +/ /

3 3. Stress-strain models for sag-tension calculation The stress-strain mechanical models for ACSR, used in sag-tension calculations, assume that: (1) the manufactured lengths (i.e. unstressed lengths) of the steel core and the aluminium layers are the same; (2) the mechanical behaviour of the steel core is close to elastic and yields only a small amount of plastic elongation at high load events, and; (3) the thermal elongation of both the steel core and the outer aluminium layers are linear with temperature. In addition, the common conductor elongation models can consider the thermal and mechanical elongation of the steel core and the outer aluminium layers separately. The models for conductor elongation of ACSR, differ in how the plastic elongation and, to a lesser extent, the linear elongation of the aluminium layers are modelled. At high mechanical loading and high temperature, the choice of model affects the calculated conductor sag. CIGRE Technical Brochure 324 [1] suggests three alternative mechanical conductor models, each models the steel core similarly (e.g. a linear spring ) and the aluminium layers differently. The Linear Elastic (LE) model [5] assumes that there is no plastic elongation in the aluminium layers (the steel core and the aluminium layers are modelled as parallel springs). The Simplified Plastic Elongation (SPE) model allows for plastic conductor elongation but on the basis of field experience rather than calculation. As explained in the next section of this paper, for both the LE and SPE conductor models, the conductor is represented mechanically with a single composite conductor modulus (E AC ) and thermally with a single composite conductor Coefficient of Thermal Elongation (CTE AC ). Also, in reference [1], a third conductor model, the Experimental Plastic Elongation (EPE) model, is defined. The EPE model is very similar to the Varney graphical method [6]. It models the mechanical and thermal behaviour of the aluminium layers and the steel core, separately. The mechanical stress and strain behaviour of the aluminium layers and the steel core are measured experimentally as is the plastic elongation of the conductor. The thermal elongation of the aluminium and steel core are modelled separately but not typically measured. The generally non-linear mechanical stress-strain behaviour of the conductor components is represented by a polynomial equation. 4. Linear conductor thermal elongation model The initial sag and tension of bare overhead transmission conductors change with the conductor length and with conductor weight per unit length due to ice and/or wind loading. Conductor length changes as the result of plastic and elastic elongation and due to thermal elongation. Elastic elongation and thermal elongation are reversible (returning to the initial tension and temperature yields the initial length). Plastic elongation occurs due to permanent elongation during high tension events and, at normal everyday tension, metallurgical creep elongation of aluminium. Thermal elongation is the result of variations in air temperature, solar heating, and line current. For bare overhead conductors that are entirely stranded from aluminium wires (e.g. All Aluminium Conductor), the conductor s coefficient of thermal elongation (CTE) is taken equal to that of the aluminium wires (23E-6 per oc). For bare overhead conductors that are stranded with one or more layers of aluminium wires surrounding a steel (or composite) core, the conductor s CTE can be calculated on the basis of the CTE s and Elastic Modulii of aluminium and the core material accounting for the cross section areas of each component. Where the subscripts A refers to Aluminium, C refers to the Core, and AC refers to the complete conductor. Note that for most ACSR conductors, the composite CTE is closer to aluminium than to steel. For 26/7 ACSR, the composite CTE is 18.8 whereas the aluminium CTE is 23 and the steel core CTE is Non-linear coefficient of thermal elongation model The equation for CTE AC is derived by assuming that (1) both the aluminium layers and the core are under tension 41

4 Figure 1: Initial component tensions in aluminium layers and steel core for 54/7 ACSR in a 300 m span as a function of conductor temperature. and that (2) the length of the aluminium layers and the core must remain equal. For an aluminium conductor with a steel core (i.e. ACSR), suspended in a catenary, the aluminium strand layers of ACSR elongate at twice the rate of the steel core. If the conductor is modelled with the EPE method, the tension of the steel core and the surrounding aluminium layers are modelled separately. Therefore, as the ACSR conductor temperature increases, the total conductor length and sag increase and the total conductor tension decreases. However, for the lengths of the steel core and the surrounding aluminium layers to remain equal, the greater thermal elongation of the aluminium must be offset by reduced elastic elongation and the lesser thermal elongation of the steel core must be increased by increased elastic elongation. In other words, as the conductor temperature increases, the percentage of total tension in the aluminium must decrease. At a temperature referred to as the knee-point temperature (KPT), the tension in the aluminium layers of the ACSR conductor has decreased to zero (see Figure 1) and all of the conductor tension is in the steel core. Above the KPT, the aluminium wire layers go into compression. If the elastic modulus of the aluminium layers in compression is equal to that in tension (think of the behaviour of Aluminium-clad steel wire), then the CTE remains equal to that at temperatures below the KPT. If the elastic modulus of the aluminium wire layers is zero, then the conductor s composite thermal elongation rate decreases to that of the steel core alone, depending upon the compression modulus of the aluminium layers. In any stranded aluminium conductor, the aluminium wires undergo both elastic and plastic elongation. With an all-aluminium conductor, plastic elongation due to high load events and metallurgical creep, cause both the everyday sag and the high temperature sag to increase over the life of an overhead line. With ACSR, the core usually undergoes only a small amount of plastic elongation during high load events and the impact of plastic elongation in the aluminium layers is different. Using the EPE stress-strain model, the amount of plastic elongation in the aluminium layers can be calculated as a function of both high tension load events and creep elongation over time. All three stress-strain models allow one to calculate the KPT of ACSR, but LE assumes that it remains constant over time and loads, SPE assumes that KPT decreases a set amount over time, and EPE can be used to calculate the KPT of ACSR for user-specified loading events and, given creep elongation models, the variation of KPT over the life of the line. Other factors can also influence the KPT. The initial KPT of ACSR (or other reinforced conductors) can be reduced by pre-stressing the conductors prior to sagging and clipping. Rawlins [7] suggests in some detail that the KPT can be higher than expected due to residual stranding stresses in the aluminium wires of ACSR made in modern rigid-frame stranding machines, which effectively makes the zero-stress aluminium wire layers shorter than the zero stress length of the core. Finally, long pulls and high tensions during tension stringing can produce nonnegligible plastic elongation of the aluminium prior to sagging. These phenomena are best studied using the EPE model. Above the KPT, the continued thermal expansion of aluminium yields increasing aluminium compression but, if the aluminium compression modulus is low, the rate of sag increase with temperature is sharply reduced to near that of the steel core alone as shown in Figure 2. The advantage of using the EPE conductor model is that it yields lower calculated high temperature sags (about a meter less at 150 o C as shown in Figure 2). On the other hand, because it is not as conservative as the LE/SPE conductor model, there must be increased concern with those factors that affect the modelling. 42

5 Figure 2: Sag vs temperature for ACSR with LE/SPE and EPE conductor models There are three primary concerns with regard to sags calculated by the EPE conductor model. They involve the conductor manufacturing details (lay lengths and bobbin tension), the conductor installation procedures, and the occurrence of severe mechanical ice & wind load events prior to the field sag measurements of the existing line. The KPT depends on the ACSR stranding (Figure 3) and the effective span length (Figure 4) as summarized in Table 2. Table 2: Final knee-point temperature as a function of ACSR steel content and ruling span length. Ruling Span Length - meters Type* of ACSR (e.g. 45/7) 90 C 130 C 160 C 14 (e.g.54/7) 75 C 95 C 110 C 23 (e.g. 30/7) 30 C 30 C 40 C * - Type = 100*[A S /A A ] Clearly, high-temperature sag accuracy is more of an issue with existing lines having relatively short spans and for any line having high steel content ACSR (e.g. 30/19). 6. Compression of helical aluminium strand layers For single-layer and multi-aluminium layer ACSR conductors, at conductor temperatures above the KPT, the aluminium wires continue to expand faster than the steel core wires putting the aluminium layers into compression and increasing the elastic elongation of the steel core. Given the physics of the ACSR conductor, aluminium compression must occur above the KPT. The aluminium wires in each layer are helices. Under tension, the modulus of the aluminium wires is close to 10 Mpsi and the strength of these layers is a significant portion of the composite conductor s tensile strength. Under compression, an unconstrained aluminium wire helix produces a much lower modulus because the wire bends rather than compresses. That is, the helix expands radially and the resistance to axial strain is about 5% of that in tension. Rawlins paper on High Temperature Sag Calculation [7] derives the axial compression modulus (spring constant Figure 3: Comparison of sag vs temperature for 45/7, 54/7, and 30/19 ACSR with a 300 m ruling span. Figure 4: Sag vs conductor temperature for 180, 300, and 425 m spans. 43

6 Figure 6: Radial expansion of unrestrained helical aluminium wire layers of Drake ACSR as a function of axial strain. per unit area of strand), E ff for a free helically-wound aluminium strand layer as follows: Where: E is the axial elastic modulus of aluminium (slightly less than 60 GPa). n is the number of strands in the layer. α is the lay angle of the layer. E ff is a weak function of the lay angle and is typically slightly less than 4 GPa. Therefore, the axial modulus of the aluminium layers in compression is less than 10% of the axial modulus in tension unless the layers are constrained radially. The relationship between the total length (L) of a strand and its lay length (λ) is shown in the following diagram. Figure 5: Two-dimensional representation of aluminium wire helix dimensions Where: θ = Lay angle R = Radius of strand helix L = Helical wire length λ = Axial length of one turn of the helix (the lay length) Now, The conductor strain, S, is defined as the ratio of the change in lay length divided by the lay length and the radial expansion of the strand layer due to a change in lay length due to conductor strain is: Where: D = Overall diameter of strand layer d = Strand diameter in layer R = Radial expansion of the strand layer Considering the number of strands in the layer, n, as a function of strand and layer diameters: Then: The strain, S, is the same for all layers of the conductor, so a comparison between the radial expansion rates of each layer can be made by using: Where subscript i denotes the specific strand layer. For an ACSR conductor with two layers of aluminium wires, if the radial expansion rate of the outer layer is greater than or equal to that of the inner layer, then both are free to expand radially and the modulus of each in compression is low. Given the range of recommended lay ratios from IEC or ASTM production standards, use of preferred ratios will allow free expansion of the aluminium layers. With 2 or more layers of aluminium, each layer will expand similarly if free to do so. Figure 6 shows the dependence of inner and outer aluminium layer expansion for 26/7, 2-layer Drake ACSR as a function of lay ratio. At the preferred ratio, the layers are free to expand radially. 44

7 Figure 7: Influence of aluminium compression force and residual aluminium layer stress on EPE high-temperature sag calculations Rawlins developed an approximate aluminium layer compression modulus for multi-layer ACSR which was implemented in the SAG10 numerical sag-tension calculation method. Using the maximum recommended inner layer lay ratio (16) and the minimum recommended outer lay ratio (10) for 2-layer, 26/7 Drake ACSR, the compression modulus was sufficiently high to change the thermal elongation rate beyond the KPT as shown in Figure 7. Note that the existence of significant axial aluminium layer compression stress changes the slope of the sag versus temperature curve beyond the KPT while the existence of residual stress from manufacturing shifts the KPT value itself but does not change the slope. Higher than estimated plastic elongation of the aluminium layers would have an effect similar to that of residual stress but would reduce the KPT rather than increasing it. 7. Experimental measurements of High Temperature Sag Field measurements of high temperature sag in operating lines are extraordinarily difficult primarily because very few lines carry currents close the line thermal rating under normal system conditions and because weather conditions are normally more favourable to heat loss than those assumed for thermal line rating calculations. In addition, the small differences in sag produced by variation in CTE at high temperature are easily overwhelmed by small variations in end-point movement. Consequently, experimental measurements have been attempted for indoor and outdoor test spans. The point of this paper is to explain and quantify how the user s choice of conductor model (LE, SPE, and EPE) influences the calculation of ACSR sag at high temperature based on field survey measurements. The result of these Figure 8: Comparison of measured and calculated sag vs temperature for 26/7 ACSR 45

8 Figure 9: Comparison of experimental measurements of sag vs temperature vs conductor average temperature. calculations can be important in establishing the thermal capacity of existing clearance-limited overhead lines and in determining the best method for increasing the thermal capacity of such lines. Two careful laboratory experiments are discussed in the following paragraphs. Figure 8, shown in Reference [7], is based on tests performed as part of a study of high temperature thermal elongation with an indoor, 90 meter test span. The conductor is 26/7 Hawk (240 mm2) and it was pre-stressed to simulate the aluminium layer plastic elongation that would occur as a result of creep and high load events in an installed line. This experimental data was analysed by Rawlins [7] and presented in an IEEE paper which elicited a good deal of interesting discussion. In essence, Rawlins proposed that the experimental data could best be explained by residual stress in the aluminium layers produced as a result of stranding in a rigid-frame stranding machine. He supplemented this data by measurements of residual stress in various ACSR conductors prior to installation and concluded that the KPT should be adjusted upward by assuming a residual stress of 15 MPa. A second experimental study was performed in an outdoor test line (2 spans) at the Oakridge National Laboratory in Oakridge, Tennessee. The analysis was reported by Seppa [8] and his plot of the test data is reproduced in Figure 9. The test facility consisted of two 180 m spans, carefully terminated to allow accurate sag measurement and with many thermocouples embedded in the conductors. The laboratory experiments demonstrate that the measured sags are less than those calculated with the LE or EPE, constant CTE model and greater than that calculated with the EPE/Graphical method where residual stress is ignored. The experiments at both locations indicate that high temperature sag calculations using the EPE conductor model should use an assumption of 15 to 20 MPa for residual aluminium stress to be conservative on the basis of this limited experimental data. 8. High Temperature Sag in new and existing lines it may be observed that sag at high temperature is seldom measured in either new or old lines. In both cases, high temperature sag is calculated based upon sag measurements made at everyday line currents and weather conditions. For new lines, field measurements are made after tension stringing as part of line construction. For existing lines, measurements are made with the line carrying normal current (or none), by LiDAR or conventional survey methods. With new and existing lines, given non-homogeneous conductors (both conventional ACSR and HTLS), the tension distribution between core and aluminium layers is estimated at the time of measurement. The EPE analysis presented in this paper is also applicable to the analysis of high-temperature, low-sag conductors having either zirconium or annealed aluminium layers surrounding a core which has high strength and low thermal elongation. 9. Selection of High-Temperature Sag model for new lines when designing new overhead transmission lines, the height and the placement of support structures is dependent on wind and ice loads (primarily on the conductors) and on the sag of the phase conductor at the templating temperature. If the reduction in slope of sag 46

9 versus temperature beyond the knee-point temperature is neglected, then the structure attachment heights and spacing will be somewhat higher than need be. The added cost of somewhat higher sag clearances may be less onerous in new lines compared to reconductoring existing lines. For example, the difference in total line cost when increasing the templating temperature from 50 C to 80 C has been found to be around 5% in certain projects in Eskom, South Africa. This is not a generic finding and the cost will differ depending on the terrain, tower family being used, conductor types, etc. In determining the model to use, it is important to determine the application of the conductor and the likely operating temperature. If the power on the line has a fairly flat load profile, the cost of losses will likely lead the designer to select a larger aluminium area. This will imply that the operating temperature of the conductor will be quite low. In this case the linear model may suffice as it will result in a slightly conservative sag but will not result in high line costs as the difference between the models below the knee point is small. If the line is used to supply a peak load for a short duration or is designed to operate at a high temperature under n-1 conditions, it is important to understand the exact sagtemperature relationship of the conductor. If the linear model is adopted, the cost of the line may be excessive due to the conservative sag calculation, because it ignores the non-linear CTE behaviour of ACSR. 10. Selection of High- Temperature Sag calculation method for existing lines The initial step in evaluating methods of uprating existing overhead lines consists of making detailed measurements of conductor position and terrain survey for the entire line. Increasingly, this is done with airborne LiDAR, though traditionally, by conventional survey methods. In most cases, these older HV lines are lightly loaded (electrically) when the system is operating normally, so the measured conductor position in each span corresponds to a conductor temperature within 5 o C to 15 o C of air temperature. It is necessary to calculate the conductor sag for the line s maximum conductor design ( templating ) temperature and for any higher temperature considered for uprating purposes. In this case, the choice of high temperature sag model can be quite important. If the knee-point behaviour is ignored altogether, then the resulting conservative calculation of sag at high temperature may rule out the use of existing ACSR conductors at higher temperature and reconductoring may seem to be the only choice. If the reduced thermal elongation beyond the knee-point temperature is considered and properly modelled, then it may be possible to choose a relatively inexpensive method of uprating the line by raising certain supports or re-tensioning the line. On the other hand, when doing calculations to allow thermal uprating of an existing line without reconductoring, one must be careful to recognize the need to model the sag behaviour correctly and to allow for both calculation errors and measurement tolerances, both of which are impossible to avoid. If the thermal rating is to be determined in real time, it is important that the actual sag-temperature relationship is determined by calibration and measurement. This is covered in TB 498 [9]. 11. Use of High Temperature Low Sag (HTLS) conductors High temperature low sag conductors are often designed so that the conductor operates above the knee-point under normal conditions. This is the case with annealed aluminium, gapped and some polymer cored conductors. The rate of sag as a function of temperature is therefore dependent on the core only and not the aluminium component. This allows for a high temperature of operation without exceeding the permissible sag. If the linear model is chosen with regard to HTLS conductors, it may indicate that the conductor is not suitable for certain applications which may not be the case. This is demonstrated in Technical Brochure 244 [2]. The type of HTLS also needs to be chosen to suit the application. In determining the initial cost of the HTLS installation it is important that an accurate sag-temperature model be used. This should take the knee-point into account. Failing to do this may result in the HTLS option being found less than optimal as the increase in thermal rating may not negate the higher initial cost. 47

10 12. Conclusions When calculating the sag of ACSR at conductor temperatures above 75 C, the thermal elongation rate of the conductor should model the mechanical and thermal behaviour of the aluminium layers and the steel core separately. If the conventional ACSR temperatureindependent CTE formula is used, the sag at maximum line temperature will be overestimated. In designing new lines, allowing for the modest amount of excess high temperature sag which results from the linear CTE method is of minor importance. However, in evaluating options for thermal uprating of existing lines, the difference in the linear and non-linear CTE methods can have a large impact on the uprating method chosen. If the conductors are intended to operate at temperatures above 75 C, it is recommended that a model be used that takes into account the knee-point of the conductor. Failure to do this may result in a suboptimal conductor being chosen for the line. The temperature gradient also needs to be considered as the average temperature determines the conductor sag and not the surface temperature [10]. As the conductor temperature increases above ambient, the aluminium layer thermal expansion rate is twice that of the steel core and at the knee-point temperature (KPT), the tension in the aluminium layers is zero and all the tension is in the steel core. Beyond the KPT, the CTE of the conductor is reduced and the conductor sag which corresponds to the line s maximum temperature is reduced. The issue of KPT and its impact on the line sag at high temperature depends on a number of line design factors. The issue is of minimal concern when: 1. The maximum operating high temperature of the line is determined by loss of strength in the aluminium layers rather than sag. 2. The spans are long (>400 m). 3. The conductor has a steel core area less than 7% that of the aluminium layers. 4. Compression modulus of the aluminium layers is negligible. The issue is of primary concern when: 1. The maximum operating high temperature of the line is determined by the clearances produced when the conductor is at the templating temperature. 2. The spans are short (<400m). 3. The conductor has a steel core area greater than 10% that of the aluminium layers. 4. Lay ratios are near recommended values. When the sag of ACSR at high temperature is essential to the selection of line uprating method, the KPT should be determined by use of the EPE mechanical conductor model (including the impact of metallurgical creep of aluminium and plastic elongation for high tension load events) and a residual stress of 15 to 20 MPa should be specified for the aluminium layers. 13. Bibliography [1] CIGRE Task Force B2.12.3, Sag-tension Calculation Methods for Overhead Lines, Technical Brochure 324, June, [2] CIGRE Task Force B2.12, Conductors for Uprating of Overhead Lines, Technical Brochure 244, April, 2004, [3] IEEE Subcommittee 15.11, Limitations of the Ruling Span Method for Overhead Line Conductors at High Operating Temperatures. Report of IEEE WG on Thermal Aspects of Conductors, IEEE WPM 1998, Tampa, FL, Feb. 3, 1998 [4] CIGRE WG B2.12, Alternating Current (AC) Resistance of Helically Stranded Conductors, Technical Brochure 345, April, [5] IEC 1597, Overhead electrical conductors Calculation methods for stranded bare conductors, First Edition, [6] Varney T., Aluminium Company of America, Graphic Method for Sag Tension Calculations for A1/S1A (ACSR) and Other Conductors, Pittsburg, 1927 [7] Rawlins, C.B., Some Effects of Mill Practice on the Stress Strain Behavior of ACSR, IEEE Transactions on Power Systems, Vol. 14, No. 2, April, [8] T. Seppa Fried Wire? (Public Utilities Fortnightly, December 2003, pages 39-41) [9] CIGRE Working Group B2.36, Guide for Application of Direct Real- Time Monitoring Systems, Technical Brochure 498, June, [10] Clairmont, B, Douglass, D., Radial and Longitudinal Temperature Gradients in Bare Stranded Conductors with High Current Densities, CIGRE Paper B2-108, Paris,