Produção Nacional
Revisado por pares
Magnetic properties of an ACSR conductor steel core at temperatures up to 230 ∘C and their impact on the transformer effect
2021; Institution of Engineering and Technology; Volume: 15; Issue: 2 Linguagem: Inglês
10.1049/smt2.12016
ISSN1751-8830
AutoresRuyguara A. Meyberg, Farith M. Absi Salas, Luis Adriano M.C. Domingues, Márcio Antônio Sens, Maria Teresa Correia de Barros, Antonio C. S. Lima,
Tópico(s)High voltage insulation and dielectric phenomena
ResumoIET Science, Measurement & TechnologyVolume 15, Issue 2 p. 143-153 ORIGINAL RESEARCH PAPEROpen Access Magnetic properties of an ACSR conductor steel core at temperatures up to 230 ∘ C and their impact on the transformer effect Ruyguara A. Meyberg, Corresponding Author Ruyguara A. Meyberg ruyguara@poli.ufrj.br orcid.org/0000-0002-5907-996X COPPE/UFRJ, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil CEPEL/ELETROBRAS, Electrical Energy Research Center, Rio de Janeiro, Brazil Correspondence Ruyguara A. Meyberg, COPPE/UFRJ, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil. Email: ruyguara@poli.ufrj.brSearch for more papers by this authorFarith M. Absi Salas, Farith M. Absi Salas CEPEL/ELETROBRAS, Electrical Energy Research Center, Rio de Janeiro, BrazilSearch for more papers by this authorLuis Adriano M. C. Domingues, Luis Adriano M. C. Domingues CEPEL/ELETROBRAS, Electrical Energy Research Center, Rio de Janeiro, BrazilSearch for more papers by this authorMárcio A. Sens, Márcio A. Sens CEPEL/ELETROBRAS, Electrical Energy Research Center, Rio de Janeiro, BrazilSearch for more papers by this authorMaria Teresa Correia de Barros, Maria Teresa Correia de Barros orcid.org/0000-0003-2494-5511 IST/ULisboa, University of Lisbon, Lisbon, PortugalSearch for more papers by this authorAntonio C. S. Lima, Antonio C. S. Lima orcid.org/0000-0001-8671-4271 CEPEL/ELETROBRAS, Electrical Energy Research Center, Rio de Janeiro, BrazilSearch for more papers by this author Ruyguara A. Meyberg, Corresponding Author Ruyguara A. Meyberg ruyguara@poli.ufrj.br orcid.org/0000-0002-5907-996X COPPE/UFRJ, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil CEPEL/ELETROBRAS, Electrical Energy Research Center, Rio de Janeiro, Brazil Correspondence Ruyguara A. Meyberg, COPPE/UFRJ, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil. Email: ruyguara@poli.ufrj.brSearch for more papers by this authorFarith M. Absi Salas, Farith M. Absi Salas CEPEL/ELETROBRAS, Electrical Energy Research Center, Rio de Janeiro, BrazilSearch for more papers by this authorLuis Adriano M. C. Domingues, Luis Adriano M. C. Domingues CEPEL/ELETROBRAS, Electrical Energy Research Center, Rio de Janeiro, BrazilSearch for more papers by this authorMárcio A. Sens, Márcio A. Sens CEPEL/ELETROBRAS, Electrical Energy Research Center, Rio de Janeiro, BrazilSearch for more papers by this authorMaria Teresa Correia de Barros, Maria Teresa Correia de Barros orcid.org/0000-0003-2494-5511 IST/ULisboa, University of Lisbon, Lisbon, PortugalSearch for more papers by this authorAntonio C. S. Lima, Antonio C. S. Lima orcid.org/0000-0001-8671-4271 CEPEL/ELETROBRAS, Electrical Energy Research Center, Rio de Janeiro, BrazilSearch for more papers by this author First published: 12 January 2021 https://doi.org/10.1049/smt2.12016Citations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The current density distribution between layers of steel-reinforced conductors having an odd number of aluminum layers is modified by the transformer effect, as a result of the steel core magnetisation. This redistribution of current affects the conductor alternating current resistance, the transitory temperature radial distribution, and depends on the total current intensity, and the core permeability, which varies with temperature. Although some steel-cored conductors are designed to operate at high temperatures to maximise their current capacity, the core magnetic properties in this scenario need to be further investigated. This paper presents the results of experimental work on an ACSR conductor, and on its steel core to investigate the steel core magnetic properties over an extended temperature range, and how they affect the transformer effect. Results show an unexpected hump-shaped variation of the permeability with temperature in a specific range of magnetic field strength, with maximum permeability values occurring at a temperature ranging from 150 to 170 ∘ C , which were not covered in previous studies. A similar behaviour is seen in the variation of the axial magnetic flux with increasing conductor temperature, causing the flux to decrease at high temperatures, and thus weakening the transformer effect during the conductor operation. 1 INTRODUCTION Most overhead line conductors consist of several concentric layers of aluminum strands helically wound over a core of galvanised steel strands. The steel core is designed to support the mechanical strength while the aluminum strands provide current conduction with low resistivity and losses. Since the interstrand contact resistance is much higher than the resistance of the strands themselves, the current tends to flow through its spiral path [1-3] producing an internal axial component of the magnetic field, similarly to a solenoid. However, due to the alternation of the stranding directions between layers, the axial component produced by currents in adjacent layers has opposite directions, which tends to cancel the resulting field [4]. In this way, conductors with an even number of aluminum layers have the same number of layers producing the longitudinal component in opposite directions and, therefore, the resulting field in the steel core tends to be canceled [5]. In conductors with an odd number of aluminum layers, the resulting longitudinal component causes hysteresis and eddy current losses, and modifies the current distribution between layers, known as the transformer effect [6-9]. This current redistribution, in turn, increases the conductor alternating current resistance and modifies the transitory temperature radial distribution [10-12]. The magnitude of the transformer effect depends on the resulting axial magnetic flux in the core and therefore varies with the intensity of the current carried by the conductor and the steel core permeability, which depends on the temperature and tensile stress [13]. The magnetic properties of the steel core must then be known for any temperature and tensile stress of the core over the range of possible operating conditions for the study of the transformer effect. The permeability variation with temperature, at constant magnetic field strength and tensile stress, was measured by several authors on steel strands of different diameters and over different temperature ranges. Double [14] carried out the measurements on a single galvanised steel strand of 4.5 mm diameter taken from an ACSR conductor (aluminum conductor steel reinforced), in the range from 16 ∘ C to 52 ∘ C . Matsch and Lewis [15] measured the variation of the permeability on galvanised steel strands of diameter from 1.61 mm to 4.79 mm, over the range from 20 ∘ C to 100 ∘ C . The same variation was measured by Morgan and Price [3] on strands of 2.69 mm, 3.12 mm and 3.56 mm diameter, over the range from 20 ∘ C to 130 ∘ C . Later, the measurement was made by Riaz [16] on strands of diameter from 2.36 mm to 4.78 mm, over the range from 0 ∘ C to 150 ∘ C , and Morgan et al. [13], on a steel core of 2.24 mm diameter strands taken from a "Grackle" ACSR conductor, in the range from 25 ∘ C to 120 ∘ C . All authors reported the increase of permeability with temperature, which was attributed to a reduction in the internal strains in the crystals and in the anisotropy of the crystal structure with increasing temperature [13]. It should be noted that the temperature range covered by the authors was from 0 ∘ C to 150 ∘ C , which even exceeds the maximum emergency overload temperatures of conventional conductors. However, with the increasing demand for electricity, environmental and economic factors restricting the construction of new transmission lines (TL), the use of technologies aimed at up-rating the overhead lines ampacity, such as the Dynamic Line Rating (DLR) [17-21] and improved current capacity conductors [22-24] has gained attention. Such conductors are designed so that they can be operated at higher temperatures [22-24]. The typical ACSR maximum operating temperature, for example, is about 90 ∘ C , while an ACSS conductor (for aluminum conductor steel supported), having the same steel core and annealed aluminum strands, can operate up to 200 ∘ C [25]. The magnetic properties of the steel core at these higher temperatures, which the improved current capacity conductors may reach, should be investigated. This paper presents the results of extensive laboratory work on both a three-layer ACSR "Duck" conductor and its steel core, in order to investigate how the magnetic properties of the core influence the transformer effect observed in the whole conductor. An extended temperature range was considered. Variations of the complex permeability, hysteretic angle, loss tangent and power losses of the steel core were measured for different magnetic field strengths and temperatures from 40 ∘ C to 230 ∘ C . The current distribution between aluminum layers of the "Duck" conductor and its axial magnetic flux were measured for different currents carried by the conductor and during the increase in its temperature. Currents up to 6 kA were supplied to the conductor and the measurements were carried out considering the maximum temperature of 200 ∘ C on the conductor surface. 2 MAGNETIC PROPERTIES OF THE STEEL CORE 2.1 Experimental procedure The measurements were made on two galvanised steel strands of 220 mm length and 2.68 mm diameter taken from the steel core of the ACSR "Duck" conductor described in Appendix. A pair of spools made of polyester with fiberglass, as shown in Figure 1, was built for the experiment. On each coil were coaxially wound a magnetising coil of 150 turns and a search coil of 10 turns, both of enameled-copper strands. FIGURE 1Open in figure viewerPowerPoint Spool built for the experiment. (a) Side view, (b) front view The steel strands were placed inside one of the spools and their ends were compressed between two U-shaped laminated silicon steel cores, as shown in Figure 2. The arrangement sets a magnetic circuit with 81 mm length of the steel strands and two parallel magnetic paths formed by the U-shaped cores. As the area of the U-shaped steel core is much larger than that of the steel strands, its reluctance may be neglected and the length of the steel strands within the coil (81 mm) may be considered as the effective length of the magnetic circuit. FIGURE 2Open in figure viewerPowerPoint Arrangement of the magnetic circuit To compensate for the air gap between the search coil and the steel strands, another similar arrangement was build using two aluminum strands of the same diameter of the steel strands. The arrangement with the steel strands was placed inside a controlled ambient chamber, whose temperature ranged from 40 to 230 ∘ C , at intervals of 10 ∘ C . The magnetising coils of both arrangements were connected in series and supplied with sinusoidal currents at 60 Hz from a double Variac and a mercury switch. The search coils were connected in series, in opposite directions, in order to subtract the voltage induced by the magnetic flux in the air gap between the steel strands and the search coil. The resulting voltage from the search coil was supplied to an analog integrator to obtain the magnetic induction, which was recorded on a digital oscilloscope along with the magnetising current and the search coil voltage. Measurements were made for a wide range of magnetising current at each temperature in the controlled ambient chamber. The magnetic field strength H is calculated from the magnetising current I m as follows: H = N m I m / ℓ , (1)where N m is the number of turns of the magnetising coil and ℓ is the magnetic path length. The magnetic induction B, obtained by an analog integrator, is calculated by integrating the search coil voltage divided by its number of turns N s and the cross-sectional area of the steel strands. The relative complex permeability, which is used in electromagnetic models [6, 7], describes the B–H relation by an equivalent complex value μ ¯ r , given by μ ¯ r = B p μ 0 H p e − j δ , (2)where μ 0 is the magnetic permeability of free space, H p and B p are the peak value of the magnetic field strength and induction, respectively, and δ is the hysteretic angle, that is, phase shift between B and H. In this representation H and B are linearly related and the B–H loop is elliptical, with an area A e l l i p s e = π B p H p sin δ , (3)which represents the energy losses per unit volume in one cycle. The imaginary part of the complex permeability ( B p / H p sin δ ) is then related to these losses, while the real part ( B p / H p cos δ ) is related to the stored energy [26], [27]. The hysteretic angle δ is calculated from (3), that is, δ = arcsin A e l l i p s e π B p H p , where A e l l i p s e is the area of the measured B–H loop [27-29]. 2.2 Results and discussion 2.2.1 Relative permeability and power losses The modulus of the relative permeability measured for different magnetic field strength and temperatures is shown in Figures 3 and 4. Figure 3(a) shows the variation with magnetic field strength with the maxima heavily influenced by the temperature. The permeability maximum value for each temperature is depicted in Figure 3(b). As plotted results show, that maximum value occurs at decreasing values of magnetic field strength, for temperatures up to 130 ∘ C . This has been reported in literature [13]. However, a different behaviour is found in results for temperatures above 160 ∘ C . This change of behaviour implies that, well below the Curie temperature, a maximum value of the magnetic permeability exists, for a specific range of the magnetic field strength. This is shown in Figure 4 where the variation of the relative permeability with temperature for different magnetic field values is plotted, showing a hump shape for magnetic field strength ranging from 1.0 to 2.4 kA/m. Furthermore, the temperature at which the permeability reaches its maximum value depends on the magnetic field strength, occurring at increasing temperatures, ranging from 150 ∘ C to 170 ∘ C , with increasing magnetic field strength. It should be noticed that these maximum permeability values are found far below the steel Curie temperature, which is above 700 ∘ C and at which the permeability was only expected to reach its maximum value. FIGURE 3Open in figure viewerPowerPoint Variation of the relative permeability modulus ( μ r ) with magnetic field strength for different temperature values (a) and respective maximum values (b), showing their ascending and descending behaviour FIGURE 4Open in figure viewerPowerPoint Variation of the relative permeability modulus ( μ r ) with temperature for different magnetic field strength To the authors' best knowledge, the existence of a maximum permeability value below Curie temperature for the steel used in conductor cores was never reported. However, previous measurements were carried out up to 150 ∘ C [16], thus slightly bellow the temperature at which these maximums are found. The existence of a maximum permeability value below Curie temperature is also found in other magnetic materials such as many ferrites, occurring mainly at the temperature that the crystal anisotropy goes through zero [30, 31]. This secondary permeability maximum (SPM) depends on the chemical composition of the material and coincides with a minimum power loss [32, 33]. In order to check if similar conclusion can be drawn for the tested steel, the power losses were calculated considering the hysteresis loop area, for different values of induction and temperature. Results in Figure 5 depict power losses as a function of induction for several temperature values, showing the same type of behaviour as reported in literature for ferrites. In the case of the tested steel, the losses curves move down for temperatures up to 130 ∘ C and then up from 160 to 230 ∘ C . As mentioned before, only the behaviour up to 130 ∘ C was already known [3], thus the analysis of the behaviour at higher temperatures represents an important contribution of this work. The temperature at which the losses reach their minimum, for different induction values, can be seen in Figure5(b) and corresponds to the temperature range in which the SPM is found, that is, from 150 to 170 ∘ C - see in Figure 4. FIGURE 5Open in figure viewerPowerPoint Variation of power losses with induction for different temperature values (a) and with temperature for different induction values (b) The observed permeability variation will certainly influence the transformer effect in ACSR conductors, which is commonly experimentally studied up temperatures around 130 ∘ C [34]. A study on the transformer effect for higher temperatures is presented in Section 3, based on experimental results obtained for a "Duck" conductor. 2.2.2 Hysteretic angle, loss tangent and complex relative permeability These quantities were computed from experimental results, according to Equations (2) and (3). Figure 6 shows the variation of the hysteretic angle δ with magnetic field strength, for different temperatures. The variation of the corresponding loss tangent ( tan ( δ )) is shown in Figure 7. The real and imaginary parts of the complex relative permeability are shown in Figure 8, for different magnetic field strength and temperature. In all figures, two distinct behaviours of the magnetic characteristic with increasing temperature are observed: one behaviour up to 130 ∘ C and another above 160 ∘ C , as observed in the permeability modulus. All obtained results up to 130 ∘ C are similar to those reported in [13], which were carried out on a steel core taken from an ACSR "Grackle" conductor at temperatures up to 120 ∘ C . FIGURE 6Open in figure viewerPowerPoint Variation of hysteretic angle δ with magnetic field for different values of temperature FIGURE 7Open in figure viewerPowerPoint Variation of loss tangent with magnetic field strength for different values of temperature FIGURE 8Open in figure viewerPowerPoint Variation of the complex relative permeability with magnetic field strength for different values of temperature. (a) Real part, (b) imaginary part 3 IMPACT ON THE TRANSFORMER EFFECT As the permeability variation influences the transformer effect in ACSR conductors and experimental results are only known at temperatures up to 130 ∘ C [34], a study for higher temperatures was carried out in order to identify the influence of the new findings on the permeability variation reported in Section 2. 3.1 Experimental procedure The present study was carried out using the same experimental arrangement as in [35]. A 10.4 m span of a three-layer ACSR "Duck" conductor was tested, which has 54 aluminum strands and a 7-strand steel core. The strand diameter of both materials is 2.68 mm. A 590 mm length section of this conductor was dismantled (the aluminum strands were sectioned, unwrapped to place current transformers and then reconnected) in order to allow simultaneous measurement on each aluminum strand. The uncertainties of the current transformers are about 2%. Further details on the arrangement are given in [35]. Conductor details are given in Appendix. The conductor surface temperature was measured using J-type thermocouples, insulated with Teflon, named from Tc1 to Tc6, at six different locations along its length, as shown in Figures 9 and 10. Thermal paste was used to improve their contact with the conductor surface. Thermocouples uncertainties after calibration were ±0.1%. FIGURE 9Open in figure viewerPowerPoint Arrangement of the ACSR "Duck" conductor (Tc: thermocouple, Sc: search coil) FIGURE 10Open in figure viewerPowerPoint Arrangement of the ACSR "Duck" conductor - schematic illustration The axial magnetic flux was measured using 100-turn search coils, made of 22 AWG tinned copper wires, named Sc1 to Sc3, wound over the conductor at three different points along the span. The total current and tensile stress were measured using a window-type current transformer and a dynamometer, respectively. The current transformer is calibrated with accuracy of 0.3%. The conductor was supplied with currents at 60 Hz and root mean square (RMS) value ranging from 600 to 6000 A, from a system of transformers and a reactor bank, fed by a 138 kV TL. The conductor was at room temperature (around 23 ∘ C ) before each current was supplied. The intensity of the total current was kept within a range of 0.9%, by means of transformer tap changes, until the monitored temperature on the conductor's surface became steady or reached 200 ∘ C . All currents and voltage at the search coils were monitored and recorded by a digital system called IMA-DP [36, 37], which stored the RMS, max, min and mean values every 5 s, and 9-cycle samples of the waveform at intervals of 30 s. The conductor surface temperature was monitored and recorded by a second digital system, with a 7-s storage interval. Both systems were placed in a separated room, over 3 m away from the experiment. Conductive objects were also kept at a distance greater than 1.7 m from the energised conductor. 3.2 Results and Discussion Results previously obtained using this experimental arrangement were presented in [35] for a total current up to 1100 A, showing that the concentration of current in the middle layer increases with the intensity of the current carried by the conductor, as a result of the transformer effect. Furthermore, a current redistribution was found with increasing conductor temperature. This newly found phenomenon was accounted for by the presence of a radial gradient of temperature, whose effect prevails over the effect of the steel core permeability increasing with temperature. For the present study, the values of the total current supplied to the conductor were increased (up to 6 kA) so that an extended range of temperature and magnetic field are reached. Figures 11 and 12 show the temperature measured by the six thermocouples along several time frames for different total current intensities. For currents up to 1100 A the steady-state temperature was below 200 ∘ C . For higher current intensities the temperature exceeded 200 ∘ C and the power supply was turned off. A difference in the temperatures measured by the thermocouples is observed, which was attributed to the non-uniform heat dissipation. To represent the temperature on the conductor surface, the average temperature measured from thermocouple Tc2 to Tc5 was taken, thus disregarding the temperatures at the ends of the conductor. The initial and final representative times ( t i and t f ) are indicated in Figures 11 and 12. For total currents from 1000 to 2300 A, an intermediate time ( t m ) is also indicated, at which a maximum magnetic flux value was found. FIGURE 11Open in figure viewerPowerPoint Variation of the temperature on the conductor surface along time, measured by thermocouples Tc1 (), Tc2 (), Tc3 (), Tc4 (), Tc5 () and Tc6 (), with total current intensities of 900 A (a), 1000 A (b) and 1100 A (c) FIGURE 12Open in figure viewerPowerPoint Variation of the temperature on the conductor surface along time, measured by thermocouples Tc1 (), Tc2 (), Tc3 (), Tc4 (), Tc5 () and Tc6 (), with total current intensities of 1600 A (a), 2300 A (b) and 2700 A (c) The axial magnetic flux is calculated by integrating the measured search coil voltages divided by its number of turns N s . Figures 13 and 14 present the variation of the RMS value of the axial magnetic flux along time, corresponding to each coil, for the six total current intensities. The difference between the values measured by the three search coils can be attributed to the temperature variation in the conductor along the span, measured by the thermocouples (see Figure 10), higher flux values corresponding to higher temperatures. FIGURE 13Open in figure viewerPowerPoint Variation of the axial magnetic flux along time, measured by search coil Sc1 (), Sc2 () and Sc3 (), with total current intensities of 900 A (a), 1000 A (b) and 1100 A (c) FIGURE 14Open in figure viewerPowerPoint Variation of the axial magnetic flux along time, measured by search coil Sc1 (), Sc2 () and Sc3 (), with total current intensities of 1600 A (a), 2300 A (b) and 2700 A (c) For the different total current intensities, results in Figures 13 and 14 show two distinct behaviours of the magnetic flux along time and thus during the conductor heating process. For total current intensities bellow 1000 A, the magnetic flux continuously increases with temperature, as noted in [35], where the magnetic flux was analysed for a total current of 900 A. However, from 1000 A up to 2300 A, the magnetic flux along time presents a hump shape, that is, it increases with temperature, reaches a maximum value at the intermediate time ( t m ), marked in Figures 13 and 14 with a vertical line, and then decreases. Figures 11 and 12 show that the conductor surface temperatures measured at t m increase with increasing total current intensity and therefore with increasing magnetic field strength in the core, such as that observed in the variation of permeability with temperature in Section 2. The temperature on the conductor surface at t m ranges from 134 ∘ C to 168 ∘ C , while the maximum permeability value of the steel core was found at temperatures from 150 ∘ C to 170 ∘ C . It should be noticed that the temperature in the steel core may be higher than that on the conductor surface, depending on the conductor radial temperature gradient, which occurs for current densities greater than 1 A/mm 2 [5]. For total current higher than 2.3 kA, the magnetic flux maximum value with increasing temperature no longer exists, meaning that the strength of the magnetic field in the core must be above 2.4 kA/m and so the permeability monotonically increases (see Figure 4). Considering the current measured on each aluminum strand and their cross-sectional area (5.64 mm 2 each), the corresponding values of current density were calculated. The current density in each aluminum layer was calculated as the mean value of its strands. The variation along time of the current density in each aluminum layer and the mean value in these three layers were computed for a large range of total current intensities (up to 6 kA). Figures 15 and 16 depict results for the six total current intensities considered in Figures 11-14. The current density in each layer, the magnetic flux measured by each search coil and the corresponding temperature on the conductor surface for the six total current intensities and for the representative times ( t i , t m and t f ) are given in Table 1. The variation of magnetic flux and current density in each interval is given in Table 2. TABLE 1. Conductor surface temperature, axial magnetic flux and current density in each aluminum layer for different intensities of total current and representative times Magnetic Flux Current Density ( 10 − 6 Wb) (A/mm 2 ) Search Coil Layer Total Current (A) Conductor Surface Temperature ( ∘ C ) Sc1 Sc2 Sc3 Inner Middle Outer 900 50.32 5.43 5.89 6.45 2.915 3.100 2.869 125.54 7.57 8.74 9.47 2.857 3.136 2.869 1000 33.85 5.38 6.55 7.30 3.219 3.451 3.172 134.38 8.49 10.30 11.01 3.139 3.500 3.157 155.03 7.92 9.59 10.69 3.122 3.506 3.177 1100 38.42 6.22 7.59 8.59 3.547 3.825 3.461 135.27 9.97 12.35 13.22 3.470 3.901 3.479 179.43 7.02 8.97 9.71 3.408 3.883 3.524 1600 42.97 11.70 13.42 14.84 5.065 5.717 4.984 147.64 19.08 21.69 23.17 4.910 5.797 4.992 187.29 14.95 17.84 19.25 4.854 5.722 5.059 2300 67.99 21.84 23.68 25.79 7.081 8.160 6.932 168.43 31.32 35.32 37.16 6.974 8.186 7.109 221.76 28.40 32.79 35.17 6.980 8.042 7.186 2700 76.90 27.52 29.54 31.69 8.435 9.619 8.247 195.75 38.20 42.78 44.70 8.223 9.425 8.413 TABLE 2. Variation of the axial magnetic flux and current density in each layer during intervals Variation of Magnetic Flux Variation of Current Density ( 10 − 6 Wb) (A/mm 2 ) Search Coil Layer Total Current (A) Interval Sc1 Sc2 Sc3 Inner Middle Outer 900 [ t i , t f ] 2.14 2.85 3.01 −0.058 0.036 0.000 1000 [ t i , t m ] 3.11 3.78 3.71 −0.080 0.049 −0.015 [ t m , t f ] −0.57 −0.74 −0.32 −0.017 0.006 0.020 1100 [ t i , t m ] 3.75 4.76 4.63 −0.077 0.076 0.018 [ t m , t f ] −2.95 −3.38 −3.51 −0.062 −0.018 0.045 1600 [ t i , t m ] 7.38 8.27 8.33 −0.155 0.080 0.008 [ t m , t f ] −4.13 −3.85 −3.92 −0.056 −0.075 0.067 2300 [ t i , t m ] 9.48 11.64 11.37 −0.107 0.026 0.177 [ t m , t f ] -2.92 −2.53 −1.99 0.006 −0.144 0.077 2700 [ t i , t f ] 10.68 13.24 13.01 −0.212 −0.194 0.166 FIGURE 15Open in figure viewerPowerPoint Variation of current density along time in the inner (), middle () and outer () layers of aluminum strands, and the mean value in these three layers (), with total current intensities of 900 A (a), 1000 A (b) and 1100 A (c) FIGURE 16Open in figure viewerPowerPoint V
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