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Comparison of electric and calorimetric measurements of AC losses in HTS wires and bulks
Physica C 445–448 (2006) 701–706 www.elsevier.com/locate/physc
Comparison of electric and calorimetric measurements of AC losses in HTS wires and bulks O. Tsukamoto
*
Tsukamoto Laboratory, Faculty of Engineering, Yokohama National University, 79-5, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan Available online 14 June 2006
Abstract We developed electric methods to measure total AC losses in an HTS wire carrying a transport current in an AC magnetic field, AC transport current losses in a wire subjected to magnetic fields generated by AC currents in adjacent wires and AC magnetization losses in a bulk. The validity of those methods was investigated by comparison of the data measured by calorimetric methods. In the paper, the electric and calorimetric measurement methods are explained and their validity is discussed based on the experimental data. 2006 Elsevier B.V. All rights reserved. PACS: 74.25.Ha Keywords: HTS wire; HTS bulk; AC loss measurement; Calorimetric method; Electric method
1. Introduction Owing to recent progress of high temperature superconductor (HTS) technology, hundreds km Bi2223/Agsheathed wires are produced in production scale and an over 200 m long YBCO wire with more than 200 A of transport critical current has been developed [1]. Using those wires R&Ds of various HTS power apparatuses are ongoing in many countries and technical feasibility of HTS applications is being demonstrated. Of those applications AC power apparatuses such as power transmission cables, transformers and current limiters are most promising. HTS bulk technology also has progressed greatly and various applications, e.g. motors, non-contact bearings for flywheel energy storage systems and motors, magnetic levitation systems, are being developed also in many countries. In those applications, the HTS wires and bulks are subjected to AC magnetic fields. Energy is dissipated in a *
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0921-4534/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2006.05.008
superconductor when it is used in AC conditions. This energy dissipation, the AC loss, directly affects the efficiency and economic feasibility of HTS applications. Moreover in the case of bulks, the AC losses decay and possibly erase the trapped magnetic field [2]. Therefore, knowledge on AC losses in HTS wires and bulks is important to design HTS AC power apparatuses and develop low AC loss HTS wires, coils and bulks. Measurement methods of AC losses are divided in two categories, electric and calorimetric methods. Generally speaking, the electric methods have high sensitive and resolution. However, their validity needs to be verified, because the results may not be proper if the electromagnetic environments of the superconductors are not well defined. On the other hand, the calorimetric methods can measure the real losses. However, they are much time consuming and not so sensitive or of high resolution as the electric methods. They also need verification of the calibration method. Therefore, the electric measurement methods are preferable, if their validity is proven. We have conducted experiments to measure the AC losses in HTS wires and bulks by the electric and calorimetric methods simultaneously. Based on the experimental
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O. Tsukamoto / Physica C 445–448 (2006) 701–706
results, the validity of the measurement methods is discussed. 2. AC losses in wires AC losses are generated in a wire when AC transport current and/or external AC magnetic field are applied to the wire. The loss due to the AC transport current is the AC transport current loss and the energy dissipated in the wire is supplied by a current source connected to the wire. The loss due to the external field is the AC magnetization loss which is supplied by the external field. In an AC superconducting apparatus, generally, the losses combined by the transport current and magnetization losses are generated. 2.1. Measurements of AC losses in a single wire Fig. 1 shows an arrangement to measure the AC losses in HTS wires by electric and calorimetric methods. Each of the methods is explained separately in the following. 2.1.1. Electric methods The AC losses in the wires are affected by magnetic environments around the wires. Therefore, methods to correctly measure the AC losses in various magnetic environments need to develop. In principle, methods for AC loss measurement of HTS wires are the same as those for LTS wires. However, special cares are necessary for the measurement arrangements of AC losses in HTS wires because of a specific aspect of HTS wires, i.e. tape-shaped with high aspect ratio. 2.1.1.1. Transport current losses. A transport current loss is usually measured by measuring a resistive voltage component in the signal from voltage taps attached to the conductor. The resistive component which is in phase with the transport current is measured by a lock-in amplifier. However, special cares are necessary for arrangements of voltage leads from the voltage taps. In a commonly used rectangular lead arrangement, the leads from the taps need to be apart enough from the wire to make errors negligibly
small [3]. However, a wide voltage lead loop picks up a large inductive voltage which causes errors in various manners. In a spiral leads arrangement shown in Fig. 1, the voltage leads are spirally wound on a cylindrical surface surrounding the wire. This arrangement clears problems of the rectangular loop arrangements [4]. The transport current loss in the section between the voltage taps can be measured correctly with this arrangement even if the wire is subjected to external magnetic field in phase with the transport current. With this arrangement, the loss of a wire in tight space can be measured and inductive components in the voltage signal are remarkably suppressed. The transport current loss Qt [J/m/cycle] is given: Qt ¼ I tm V tl =2lp f ;
ð1Þ
where Itm is the amplitude of transport current and Vtl is the amplitude of the loss component of the voltage between the voltage taps. lp is the distance between the voltage taps and f is frequency. 2.1.1.2. Magnetization losses. The magnetization losses are measured by use of a pick-up coil applying AC external field to the wire. There are various shapes of pick-up coils. A simple one is an in-plane rectangular pick-up coil as illustrated in Fig. 1. Magnetization losses can be measured by this rectangular pick-up coil for the case that the external field is perpendicular to the face of the wire. The magnetization losses Qm [J/m/cycle] are given by the following equation when the width of the pick-up coil is wider enough than that of the wire (more than 3 times wider than the wire width) [5] Qm ¼ pwV ml Bm =2Lc f ;
ð2Þ
where Lc and w were the length and width of the pick-up coil, respectively. Vml is the magnetization loss voltage component of the pick-up coil that is in phase with the external magnetic field. There are other pick-up coil configurations which can measure the magnetization losses for various angles between the external magnetic field and the tape face of the wire [6]. 2.1.1.3. Total losses. The total losses can be measured by the combination of the methods to measure Qt and Qm applying the transport current and the external magnetic field, only if the transport current and external magnetic field are in the same phase. The total losses Qtotal [J/m/ cycle] are given by [7] Qtotal ¼ Qt þ Qm :
ð3Þ
It is difficult to measure Qtotal electrically when the phases of the transport current and external magnetic field are different.
Fig. 1. Sample arrangement to measure the AC losses in a wire subject to external magnetic field Bm by electric and calorimetric method.
2.1.2. Calorimetric methods In a calorimetric method, the losses are measured by detecting temperature rise of the thermally insulated wire due to the losses. There are various methods of the calori-
O. Tsukamoto / Physica C 445–448 (2006) 701–706
2.1.3. Verification of the measurement methods An experiment was conducted to investigate the validity of the measurement methods described above using an YBCO conductor arranged as shown in Fig. 1. With this arrangement where all of the voltage leads, pick-up coil and thermo-couple were put together, the total AC losses in the same part of an HTS wire were simultaneously measured by the electric and calorimetric methods. In this experiment, Qt without the external magnetic field measured by the electric method was used as the heat input for the calibration. The results are shown in Fig. 2 for the case that the external AC magnetic field was perpendicular to the wire face and in phase with the transport current. The errors between the data measured by both methods were around 20% of the values measured by the electric method in the range of Qtotal > 3 · 105 J/m/ cycle. In the range of Q < 3 · 105 J/m/cycle the calorimetric method did not have enough sensitivity and the errors became larger. Considering the loss values themselves varied by the 3 order of magnitude, the data obtained by the both methods agreed with each other. Thus, the validity of the both of the measuring method was verified [7].
-1
10
Electric
YBCO f=64.1Hz
0.0Ic 0.19Ic -2
10
0.39Ic 0.58Ic
(J/m/cycle)
0.77Ic -3
total
10
0.97Ic
Brandt eq. Calorimetric
-4
10
0.19Ic
Q
metric [7–9] measurement. A compact and versatile method developed by Ashworth [9] is illustrated in Fig. 1. The wire is thermally insulated with stylus form and the temperature rise is detected by a thermo-couple. With this method Qtotal can be measured even if the phases of the transport current and external magnetic field are different. In this method, a calibration curve of known value of heat input to a wire Q [W/m] vs. the duration time of heating Dt for the wire temperature to rise by a given value DT is made at the first step. Several ways can be considered to put the heat to the wire. The best way is that the wire itself generates the heat. By applying DC current Idc over the critical currents Ic and measuring a voltage Vdc [V/m] along the wire, the value of Q = IdcVdc is given [9]. Electric measurement methods of Qt in the wire without the external magnetic field and Qm without the transport current are well established. Therefore, as an alternative, electrically measured Qt or Qm also can be used as the value of the heat-input Q. Using the obtained calibration curve, Qtotal can be measured by measuring the duration time Dt of application of the transport current and external magnetic field for the wire temperature to rise by DT [7].
703
0.39Ic Bm
-5
10
0.58Ic
α =90deg
0.77Ic 0.97Ic
-6
10
0.001
0.01
0.1
Bm(T)
Specifications of sample YBCO wire Conductor dimensions
10.0 mm×0.15 mm
Critical current Ic at 0T and 1 μV/cm (77K)
51.7 A
n value at 0T
33.1
Thickness of Ag layer
50 μm
Thickness of YBCO layer
1.0 μm
Fig. 2. Total AC losses Qtotal in YBCO wire measured by electric and calorimetric methods are plotted against Bm for various values of Itm. The external magnetic field is perpendicular to the wide face of the wire.
picks up the losses in other wires if proper cares to exclude the loss components due to the other wires are not taken. We developed an electric method to measure the transport current losses in a wire of three wires arranged parallel on a flat plane by a measurement arrangement using spiral and rectangular voltage lead loops as shown in Fig. 3 [10]. Two large spiral voltage loops and three small spiral loops are set in addition to the rectangular loops from pairs of voltage taps attached to the wires w1, w2 and w3. Each of the small spiral loops is wound on the cylindrical surface enclosing the wire to which the potential taps are attached. One of the large spiral loops is wound on a cylindrical
v2R v1
R
v1S
v2S v3S
v1-2S v S 3-2
2.2. Measurements of AC losses in wires with adjacent wires v3R
In assembled conductors, e.g. power cables, HTS wires are affected by magnetic fields produced by currents in adjacent wires. Therefore, the losses in the wires should be measured as they are assembled. 2.2.1. Electric method When the AC transport current losses in a wire in an assemble conductor are measured, the voltage lead loop
w1 w2 w3 Fig. 3. Arrangements of potential leads loops to measure the transport current losses in wires in a three wire array.
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surface enclosing the wires w1 and w2 with its center axis on the center of the wire w1 and the other large spiral loop on a cylindrical surface enclosing w2 and w3 with its center axis on the center of w3 (in Fig. 3). With this arrangement, the power dissipated in each of the wires can be measured because the spiral loops do not pick up the magnetic fluxes generated outside of the loops and the rectangular loops pick up the fluxes around the wires to which the voltage taps are attached including the fluxes due to the other wires. vSi is the voltage of the small spiral loop enclosing wi (i = 1–3) and QSi the average power per unit length of the wire wi measured by the small spiral loops given by hvSi ii i=lp , where ii is the current of wi and lp the distance between the voltage taps. vS12 and vS32 are the voltages of the large spiral loops enclosing w1 and w2, w2 and w3, respectively and the averaged powers per unit length of the wire measured by the large spiral loops QS12 and QS32 are given by hvS12 i1 i=lp and hvS32 i3 i=lp , respectively. Then, Q0i the power dissipated in the wire wi is given as follows: Q02 ¼ QS2 QS1 QS3 þ QS12 þ QS32 :
ð4Þ
If i1 and i3 are equal and w1 and w3 are geometrically symmetric, then, we can assume Q01 ¼ Q03 , and Q01 and Q03 are given by R R 0 Q01 ¼ Q03 ¼ ðQR 1 þ Q2 þ Q3 Q2 Þ=2;
QR i
hvR i
ð5Þ
vR i
where ¼ ii i=lp and is the voltage between the taps on wi measured by the rectangular voltage loop [10]. 2.2.2. Measurement by calorimetric method and verification of the measurement methods The transport currents losses in Bi/Ag sheathed wires (4 mm wide and 0.24 mm thick) arranged in the same way as shown in Fig. 3 were measured by a calorimetric method to investigate the validity of the electric method described above. The experimental arrangement is shown in Fig. 4. The measurement method is similar to that of Ashwarth [9]. The wires were thermally insulated locally by polystyrene foam plates and the temperature rises of the wires due to AC losses were measured by thermo-couples. Rectangular lead loops were attached to the wires for
DC measurement for the calibration. Calibration was done as follows. The whole measurement arrangement was put in a DC magnetic field to reduce the critical currents of the wires for the calibration. Applying a DC transport current exceeding the critical currents Ici to the wire wi individually, the Joule heat in the wire was measured by measuring the DC current and voltage between the voltage taps. It was found that the temperature rises of the other wires than the wire to which the DC current was applied were not negligibly small. Therefore, temperature rise of all the wires were measured in the steady state. Coefficients of the heat conduction from a wire to the ambience and the other wires were determined from the measured data assuming the linearity. Using the thus determined heat conduction coefficients, the transport current losses in each of the wires were calculated from the data of the temperature rise of the wires and the calibration curve. Experiments were performed to compare the data measured by both of the electric and calorimetric methods explained above. Critical currents Ici of the Bi/Ag sheathed wires were 97.5 A, 96.5 A and 99.0 A for i = 1, 2, 3, respectively for the electric measurement and 96.0 A, 94.6 A and 99.4 A for i = 1, 2, 3, respectively for the calorimetric measurements. The transport current losses of each wire of the three wires were measured in the two modes, individual and series modes. In the individual mode, the transport current was put in only one wire individually. In the series models the three wires were connected in series and the same transport current was put in the three wires. In Fig. 5, QCi normalized by QCI i is plotted against the amplitude of the transport current Itm for i = 1–3, where QCi and QCI are the transport current losses in unit length of wi i measured by the calorimetric method in the series and individual modes, respectively. In Fig. 5, the electrically measured data Q0i normalized by QSi are also plotted for the comparison of the electric and calorimetric methods, where QSi is the transport current losses in w1 measured by the electric method in the individual mode. The critical currents of the wires used in the electric and calorimetric
1.6
Electric
1.4
Q10 / Q1S
1.2
Q20 / Q2S
Thermo couple Ratio
30mm Polystyrene thermal insulator Rectangular voltage loop
w1
Gap
w2
Gap
Gap=1mm
w3
1
60mm
Fig. 4. Experimental arrangement for calorimetric method to measure the transport current losses in wires in a three wire array.
Q30 / Q3S Calorimetoric
0.8
Q1C / Q1CI
0.6
Q2C / Q2CI
0.4
Bi/Ag wire
60Hz
50
60
70 I [A]
80
90 100
Q3C / Q3CI
tm
Fig. 5. Comparison of losses in the wires in the three wire array obtained by the electric and calorimetric methods.
O. Tsukamoto / Physica C 445–448 (2006) 701–706
experiments were not exactly the same but close to each other. Therefore, we consider that the direct comparison of the data obtained by both methods is reasonable and the agreement of the both data is good. Based on this result we consider that our electric method gives valid data of the transport current losses in the wires. Obviously from Fig. 5, the measurement results show that the losses in the series mode were reduced in the wire w2 and increased in the wires w1 and w3 compared with those in the individual mode. This is because the perpendicular magnetic field components to the wire surface which dominates the losses were reduced for w2 and increased for w1 and w3 because of the magnetic field produced by the adjacent wires. 3. AC losses in bulks Fig. 6 shows an arrangement to measure the AC losses in an HTS bulk by an electric method together with a calorimetric method [11]. A pair of pick-up coils surrounding the bulk, the inner and outer, are for the electric method. Number of turns of the inner and outer pick-up coils are ni and no and wound on co-centric cylindrical surfaces of radii ri and ro, respectively. The turns and radii of the inner ro ri CFRP rod
HTS bulk
h0
Bm
Heater Thermo-meter
Inner pick-up coil (ni, ri)
Thermal insulator Outer pick-up coil (no, ro)
a
105 104
Electric Calorimetric
103 102 f =62.32Hz 101 0.01
and outer pick-up coils are so adjusted that ni pr2i ¼ no pr2o and the pick-up coils are connected to each other differentially to cancel inductive voltage induced in the pick-up coils. Heights of the pick-up coils 2h are the same. The resistive voltage component of the signal from the pair of the pick-up coils are measured by a lock-in amplifier. The AC loss per cycle per until volume Qb [J/m3/cycle] is given by the following equations [12]: Qb ¼
0.1 B m [T]
1 KV R Bm h ; 2 ðni no Þl0 vb f
ð6Þ
where Bm and f are the amplitude and frequency of the external AC magnetic field, respectively. VR is the amplitude of the resistive component of the voltage signal from the pair of the pick-up coils and vb is the volume of the bulk. K is the correction factor and K = 1, if the heights of the pick up coils are larger enough than the height of the bulk and the radii of the pick-up coils ri and ro. A heater of a Manganin wire is placed on the peripheral area of the bottom surface of the bulk and a semiconductor temperature sensor at the center of the bottom surface for the calorimetric measurement. The bulk sample is thermally insulated by stylus-form as show in Fig. 6. The measurement arrangement is put in vacuum space in a cryostat and the bulk is cooled by a cryo-cooler connecting its cold head to the bulk with a CFRP rod. In this arrangement, it is considered that whole of the heater power is put into the bulk and that the bulk temperature Tb increases linearly for a stepwise heating. Getting a calibration curve of the heater power vs. dTb/dt at a fixed temperature rise of the bulk DT0, the AC losses is measured from the value of dTb/dt at DT0 applying a stepwise AC magnetic field of constant amplitude. AC losses in an YBCO bulk of 31.0 mm dia. and 15.0 mm high measured by the electric and calorimetric methods are show in Fig. 7 [11]. In this measurement, DT0 was 1 K. Both of the AC loss data agree with each other with errors around 20% of the electrically measured values. These results show that both the electric and calorimetric methods are valid and that the measured data are valid.
Magnetization loss Q[W/m3]
Magnetization loss Q[W/m3]
Fig. 6. Sample arrangement to measure AC losses in HTS bulk subjected to an external AC magnetic field Bm by electric and calorimetric methods.
705
b
105 10
4
Electric Calorimetric
103 102 f =62.32Hz 101 0.01
0.1 B m [T]
Fig. 7. AC losses in the bulk measured calorimetric and electric methods at different values of bulk temperature Tb0 are plotted against the amplitude of the external AC field Bm. (a) Tb0 = 60 K, (b) Tb0 = 70 K.
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4. Concluding remarks Validity of the electric measurement methods of AC losses in HTS wires and bulks which we developed was investigated by conducting calorimetric measurements simultaneously. The results of the experiments are summarized as follows: (a) Total AC losses in an HTS wire: There was some uncertainty in determination of the total losses by adding the transport current and magnetization losses which were measured by the electric method separately and also in the calibration method of the calorimetric method. It was shown that the total losses measured simultaneously by the electric and calorimetric methods well agreed with each other, which proved that the electric method together with the calorimetric method including the calibration method were valid. (b) Transport current losses in a wire with adjacent wires: An electric method to measure AC transport current losses in HTS wires placed parallel on a flat plane was developed, and its validity was investigated by conducting a calorimetric measurement. The loss data obtained by the electric and calorimetric methods well agreed with each other, which demonstrates the validity of the electric method. It was shown in our experiment that the AC transport current losses in an HTS wire was significantly affected by the magnetic field produced by the adjacent wires and that the transport current losses in a wire with adjacent wires carrying the same current at the both side was smaller than those in the case that there were no current in the adjacent wires. (c) Magnetization losses in bulk: AC losses in a bulk HTS subjected to an AC external field were simultaneously measured by the calorimetric and electric methods which we developed. The data measured by both methods well agreed with each other. Thus, the validity of both methods was proven. Generally, electric methods are much less time consuming than the calorimetric methods. Therefore, when an elec-
tric method whose validity is proven is developed, we can measure the losses efficiently with high sensitivity and resolution. However, there are some limitations in the electric measurements, e.g. the total losses in a wire carrying AC transport current in an AC magnetic field of different phase and losses in a bulk or a wire subjected to non-sinusoidal alternate magnetic field. The electric methods are difficult to be applied to those cases but the calorimetric methods are applicable. Acknowledgements This work was supported in part by METI through ISTEC as the US–Japan Joint study of AC Losses in HTS and in part by MEXT Grant-in-Aid for Scientific Research (S) (14102019). References [1] Y. Shiobara, presented at EUCAS2005, MO-PL-3, 2005. [2] O. Tsukamoto, K. Yamagishi, J. Ogawa, M. Murakami, M. Tomita, J. Mater. Proc. Technol. 161 (2005) 52. [3] M. Ciszek, A.M. Campbell, B.A. Glowacki, Physica C 233 (1994) 203. [4] S. Fukui, Y. Kitoh, T. Numata, O. Tsukamoto, J. Fujikami, K. Hayashi, Adv. Cryo. Eng. 44 (1998) 723. [5] E. Martinez, Y. Yang, C. Beduz, Y.B. Huang, Physica C 331 (2000) 216. [6] Z. Jiang, N. Amemiya, N. Ayai, K. Hayashi, IEEE Trans. ASC 13 (2003) 3557. [7] J. Ogawa, H. Nakayama, S. Odaka, O. Tsukamoto, Cryogenics 45 (2005) 23. [8] C. Schmidt, Cryogenics 41 (2001) 393. [9] S.P. Ashworth, Physica C 315 (1999) 79. [10] O. Tsukamoto, Y. Yamato, S. Nakamura, J. Ogawa, IEEE Trans. ASC 15 (2005) 2895. [11] K. Yamagishi, S. Sekizawa, J. Ogawa, O. Tsukamoto, presented at EUCAS2005, MO-M-O2-3, 2005. [12] J. Ogawa, M. Iwamoto, O. Tsukamoto, M. Murakami, M. Tomita, Physica C 372–376 (2002) 1754.
Comparison of electric and calorimetric measurements of AC losses in HTS wires and bulks O. Tsukamoto
*
Tsukamoto Laboratory, Faculty of Engineering, Yokohama National University, 79-5, Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan Available online 14 June 2006
Abstract We developed electric methods to measure total AC losses in an HTS wire carrying a transport current in an AC magnetic field, AC transport current losses in a wire subjected to magnetic fields generated by AC currents in adjacent wires and AC magnetization losses in a bulk. The validity of those methods was investigated by comparison of the data measured by calorimetric methods. In the paper, the electric and calorimetric measurement methods are explained and their validity is discussed based on the experimental data. 2006 Elsevier B.V. All rights reserved. PACS: 74.25.Ha Keywords: HTS wire; HTS bulk; AC loss measurement; Calorimetric method; Electric method
1. Introduction Owing to recent progress of high temperature superconductor (HTS) technology, hundreds km Bi2223/Agsheathed wires are produced in production scale and an over 200 m long YBCO wire with more than 200 A of transport critical current has been developed [1]. Using those wires R&Ds of various HTS power apparatuses are ongoing in many countries and technical feasibility of HTS applications is being demonstrated. Of those applications AC power apparatuses such as power transmission cables, transformers and current limiters are most promising. HTS bulk technology also has progressed greatly and various applications, e.g. motors, non-contact bearings for flywheel energy storage systems and motors, magnetic levitation systems, are being developed also in many countries. In those applications, the HTS wires and bulks are subjected to AC magnetic fields. Energy is dissipated in a *
Tel.: +81 45 339 4121; fax: +81 45 338 1157. E-mail address: [email protected]
0921-4534/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2006.05.008
superconductor when it is used in AC conditions. This energy dissipation, the AC loss, directly affects the efficiency and economic feasibility of HTS applications. Moreover in the case of bulks, the AC losses decay and possibly erase the trapped magnetic field [2]. Therefore, knowledge on AC losses in HTS wires and bulks is important to design HTS AC power apparatuses and develop low AC loss HTS wires, coils and bulks. Measurement methods of AC losses are divided in two categories, electric and calorimetric methods. Generally speaking, the electric methods have high sensitive and resolution. However, their validity needs to be verified, because the results may not be proper if the electromagnetic environments of the superconductors are not well defined. On the other hand, the calorimetric methods can measure the real losses. However, they are much time consuming and not so sensitive or of high resolution as the electric methods. They also need verification of the calibration method. Therefore, the electric measurement methods are preferable, if their validity is proven. We have conducted experiments to measure the AC losses in HTS wires and bulks by the electric and calorimetric methods simultaneously. Based on the experimental
702
O. Tsukamoto / Physica C 445–448 (2006) 701–706
results, the validity of the measurement methods is discussed. 2. AC losses in wires AC losses are generated in a wire when AC transport current and/or external AC magnetic field are applied to the wire. The loss due to the AC transport current is the AC transport current loss and the energy dissipated in the wire is supplied by a current source connected to the wire. The loss due to the external field is the AC magnetization loss which is supplied by the external field. In an AC superconducting apparatus, generally, the losses combined by the transport current and magnetization losses are generated. 2.1. Measurements of AC losses in a single wire Fig. 1 shows an arrangement to measure the AC losses in HTS wires by electric and calorimetric methods. Each of the methods is explained separately in the following. 2.1.1. Electric methods The AC losses in the wires are affected by magnetic environments around the wires. Therefore, methods to correctly measure the AC losses in various magnetic environments need to develop. In principle, methods for AC loss measurement of HTS wires are the same as those for LTS wires. However, special cares are necessary for the measurement arrangements of AC losses in HTS wires because of a specific aspect of HTS wires, i.e. tape-shaped with high aspect ratio. 2.1.1.1. Transport current losses. A transport current loss is usually measured by measuring a resistive voltage component in the signal from voltage taps attached to the conductor. The resistive component which is in phase with the transport current is measured by a lock-in amplifier. However, special cares are necessary for arrangements of voltage leads from the voltage taps. In a commonly used rectangular lead arrangement, the leads from the taps need to be apart enough from the wire to make errors negligibly
small [3]. However, a wide voltage lead loop picks up a large inductive voltage which causes errors in various manners. In a spiral leads arrangement shown in Fig. 1, the voltage leads are spirally wound on a cylindrical surface surrounding the wire. This arrangement clears problems of the rectangular loop arrangements [4]. The transport current loss in the section between the voltage taps can be measured correctly with this arrangement even if the wire is subjected to external magnetic field in phase with the transport current. With this arrangement, the loss of a wire in tight space can be measured and inductive components in the voltage signal are remarkably suppressed. The transport current loss Qt [J/m/cycle] is given: Qt ¼ I tm V tl =2lp f ;
ð1Þ
where Itm is the amplitude of transport current and Vtl is the amplitude of the loss component of the voltage between the voltage taps. lp is the distance between the voltage taps and f is frequency. 2.1.1.2. Magnetization losses. The magnetization losses are measured by use of a pick-up coil applying AC external field to the wire. There are various shapes of pick-up coils. A simple one is an in-plane rectangular pick-up coil as illustrated in Fig. 1. Magnetization losses can be measured by this rectangular pick-up coil for the case that the external field is perpendicular to the face of the wire. The magnetization losses Qm [J/m/cycle] are given by the following equation when the width of the pick-up coil is wider enough than that of the wire (more than 3 times wider than the wire width) [5] Qm ¼ pwV ml Bm =2Lc f ;
ð2Þ
where Lc and w were the length and width of the pick-up coil, respectively. Vml is the magnetization loss voltage component of the pick-up coil that is in phase with the external magnetic field. There are other pick-up coil configurations which can measure the magnetization losses for various angles between the external magnetic field and the tape face of the wire [6]. 2.1.1.3. Total losses. The total losses can be measured by the combination of the methods to measure Qt and Qm applying the transport current and the external magnetic field, only if the transport current and external magnetic field are in the same phase. The total losses Qtotal [J/m/ cycle] are given by [7] Qtotal ¼ Qt þ Qm :
ð3Þ
It is difficult to measure Qtotal electrically when the phases of the transport current and external magnetic field are different.
Fig. 1. Sample arrangement to measure the AC losses in a wire subject to external magnetic field Bm by electric and calorimetric method.
2.1.2. Calorimetric methods In a calorimetric method, the losses are measured by detecting temperature rise of the thermally insulated wire due to the losses. There are various methods of the calori-
O. Tsukamoto / Physica C 445–448 (2006) 701–706
2.1.3. Verification of the measurement methods An experiment was conducted to investigate the validity of the measurement methods described above using an YBCO conductor arranged as shown in Fig. 1. With this arrangement where all of the voltage leads, pick-up coil and thermo-couple were put together, the total AC losses in the same part of an HTS wire were simultaneously measured by the electric and calorimetric methods. In this experiment, Qt without the external magnetic field measured by the electric method was used as the heat input for the calibration. The results are shown in Fig. 2 for the case that the external AC magnetic field was perpendicular to the wire face and in phase with the transport current. The errors between the data measured by both methods were around 20% of the values measured by the electric method in the range of Qtotal > 3 · 105 J/m/ cycle. In the range of Q < 3 · 105 J/m/cycle the calorimetric method did not have enough sensitivity and the errors became larger. Considering the loss values themselves varied by the 3 order of magnitude, the data obtained by the both methods agreed with each other. Thus, the validity of the both of the measuring method was verified [7].
-1
10
Electric
YBCO f=64.1Hz
0.0Ic 0.19Ic -2
10
0.39Ic 0.58Ic
(J/m/cycle)
0.77Ic -3
total
10
0.97Ic
Brandt eq. Calorimetric
-4
10
0.19Ic
Q
metric [7–9] measurement. A compact and versatile method developed by Ashworth [9] is illustrated in Fig. 1. The wire is thermally insulated with stylus form and the temperature rise is detected by a thermo-couple. With this method Qtotal can be measured even if the phases of the transport current and external magnetic field are different. In this method, a calibration curve of known value of heat input to a wire Q [W/m] vs. the duration time of heating Dt for the wire temperature to rise by a given value DT is made at the first step. Several ways can be considered to put the heat to the wire. The best way is that the wire itself generates the heat. By applying DC current Idc over the critical currents Ic and measuring a voltage Vdc [V/m] along the wire, the value of Q = IdcVdc is given [9]. Electric measurement methods of Qt in the wire without the external magnetic field and Qm without the transport current are well established. Therefore, as an alternative, electrically measured Qt or Qm also can be used as the value of the heat-input Q. Using the obtained calibration curve, Qtotal can be measured by measuring the duration time Dt of application of the transport current and external magnetic field for the wire temperature to rise by DT [7].
703
0.39Ic Bm
-5
10
0.58Ic
α =90deg
0.77Ic 0.97Ic
-6
10
0.001
0.01
0.1
Bm(T)
Specifications of sample YBCO wire Conductor dimensions
10.0 mm×0.15 mm
Critical current Ic at 0T and 1 μV/cm (77K)
51.7 A
n value at 0T
33.1
Thickness of Ag layer
50 μm
Thickness of YBCO layer
1.0 μm
Fig. 2. Total AC losses Qtotal in YBCO wire measured by electric and calorimetric methods are plotted against Bm for various values of Itm. The external magnetic field is perpendicular to the wide face of the wire.
picks up the losses in other wires if proper cares to exclude the loss components due to the other wires are not taken. We developed an electric method to measure the transport current losses in a wire of three wires arranged parallel on a flat plane by a measurement arrangement using spiral and rectangular voltage lead loops as shown in Fig. 3 [10]. Two large spiral voltage loops and three small spiral loops are set in addition to the rectangular loops from pairs of voltage taps attached to the wires w1, w2 and w3. Each of the small spiral loops is wound on the cylindrical surface enclosing the wire to which the potential taps are attached. One of the large spiral loops is wound on a cylindrical
v2R v1
R
v1S
v2S v3S
v1-2S v S 3-2
2.2. Measurements of AC losses in wires with adjacent wires v3R
In assembled conductors, e.g. power cables, HTS wires are affected by magnetic fields produced by currents in adjacent wires. Therefore, the losses in the wires should be measured as they are assembled. 2.2.1. Electric method When the AC transport current losses in a wire in an assemble conductor are measured, the voltage lead loop
w1 w2 w3 Fig. 3. Arrangements of potential leads loops to measure the transport current losses in wires in a three wire array.
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surface enclosing the wires w1 and w2 with its center axis on the center of the wire w1 and the other large spiral loop on a cylindrical surface enclosing w2 and w3 with its center axis on the center of w3 (in Fig. 3). With this arrangement, the power dissipated in each of the wires can be measured because the spiral loops do not pick up the magnetic fluxes generated outside of the loops and the rectangular loops pick up the fluxes around the wires to which the voltage taps are attached including the fluxes due to the other wires. vSi is the voltage of the small spiral loop enclosing wi (i = 1–3) and QSi the average power per unit length of the wire wi measured by the small spiral loops given by hvSi ii i=lp , where ii is the current of wi and lp the distance between the voltage taps. vS12 and vS32 are the voltages of the large spiral loops enclosing w1 and w2, w2 and w3, respectively and the averaged powers per unit length of the wire measured by the large spiral loops QS12 and QS32 are given by hvS12 i1 i=lp and hvS32 i3 i=lp , respectively. Then, Q0i the power dissipated in the wire wi is given as follows: Q02 ¼ QS2 QS1 QS3 þ QS12 þ QS32 :
ð4Þ
If i1 and i3 are equal and w1 and w3 are geometrically symmetric, then, we can assume Q01 ¼ Q03 , and Q01 and Q03 are given by R R 0 Q01 ¼ Q03 ¼ ðQR 1 þ Q2 þ Q3 Q2 Þ=2;
QR i
hvR i
ð5Þ
vR i
where ¼ ii i=lp and is the voltage between the taps on wi measured by the rectangular voltage loop [10]. 2.2.2. Measurement by calorimetric method and verification of the measurement methods The transport currents losses in Bi/Ag sheathed wires (4 mm wide and 0.24 mm thick) arranged in the same way as shown in Fig. 3 were measured by a calorimetric method to investigate the validity of the electric method described above. The experimental arrangement is shown in Fig. 4. The measurement method is similar to that of Ashwarth [9]. The wires were thermally insulated locally by polystyrene foam plates and the temperature rises of the wires due to AC losses were measured by thermo-couples. Rectangular lead loops were attached to the wires for
DC measurement for the calibration. Calibration was done as follows. The whole measurement arrangement was put in a DC magnetic field to reduce the critical currents of the wires for the calibration. Applying a DC transport current exceeding the critical currents Ici to the wire wi individually, the Joule heat in the wire was measured by measuring the DC current and voltage between the voltage taps. It was found that the temperature rises of the other wires than the wire to which the DC current was applied were not negligibly small. Therefore, temperature rise of all the wires were measured in the steady state. Coefficients of the heat conduction from a wire to the ambience and the other wires were determined from the measured data assuming the linearity. Using the thus determined heat conduction coefficients, the transport current losses in each of the wires were calculated from the data of the temperature rise of the wires and the calibration curve. Experiments were performed to compare the data measured by both of the electric and calorimetric methods explained above. Critical currents Ici of the Bi/Ag sheathed wires were 97.5 A, 96.5 A and 99.0 A for i = 1, 2, 3, respectively for the electric measurement and 96.0 A, 94.6 A and 99.4 A for i = 1, 2, 3, respectively for the calorimetric measurements. The transport current losses of each wire of the three wires were measured in the two modes, individual and series modes. In the individual mode, the transport current was put in only one wire individually. In the series models the three wires were connected in series and the same transport current was put in the three wires. In Fig. 5, QCi normalized by QCI i is plotted against the amplitude of the transport current Itm for i = 1–3, where QCi and QCI are the transport current losses in unit length of wi i measured by the calorimetric method in the series and individual modes, respectively. In Fig. 5, the electrically measured data Q0i normalized by QSi are also plotted for the comparison of the electric and calorimetric methods, where QSi is the transport current losses in w1 measured by the electric method in the individual mode. The critical currents of the wires used in the electric and calorimetric
1.6
Electric
1.4
Q10 / Q1S
1.2
Q20 / Q2S
Thermo couple Ratio
30mm Polystyrene thermal insulator Rectangular voltage loop
w1
Gap
w2
Gap
Gap=1mm
w3
1
60mm
Fig. 4. Experimental arrangement for calorimetric method to measure the transport current losses in wires in a three wire array.
Q30 / Q3S Calorimetoric
0.8
Q1C / Q1CI
0.6
Q2C / Q2CI
0.4
Bi/Ag wire
60Hz
50
60
70 I [A]
80
90 100
Q3C / Q3CI
tm
Fig. 5. Comparison of losses in the wires in the three wire array obtained by the electric and calorimetric methods.
O. Tsukamoto / Physica C 445–448 (2006) 701–706
experiments were not exactly the same but close to each other. Therefore, we consider that the direct comparison of the data obtained by both methods is reasonable and the agreement of the both data is good. Based on this result we consider that our electric method gives valid data of the transport current losses in the wires. Obviously from Fig. 5, the measurement results show that the losses in the series mode were reduced in the wire w2 and increased in the wires w1 and w3 compared with those in the individual mode. This is because the perpendicular magnetic field components to the wire surface which dominates the losses were reduced for w2 and increased for w1 and w3 because of the magnetic field produced by the adjacent wires. 3. AC losses in bulks Fig. 6 shows an arrangement to measure the AC losses in an HTS bulk by an electric method together with a calorimetric method [11]. A pair of pick-up coils surrounding the bulk, the inner and outer, are for the electric method. Number of turns of the inner and outer pick-up coils are ni and no and wound on co-centric cylindrical surfaces of radii ri and ro, respectively. The turns and radii of the inner ro ri CFRP rod
HTS bulk
h0
Bm
Heater Thermo-meter
Inner pick-up coil (ni, ri)
Thermal insulator Outer pick-up coil (no, ro)
a
105 104
Electric Calorimetric
103 102 f =62.32Hz 101 0.01
and outer pick-up coils are so adjusted that ni pr2i ¼ no pr2o and the pick-up coils are connected to each other differentially to cancel inductive voltage induced in the pick-up coils. Heights of the pick-up coils 2h are the same. The resistive voltage component of the signal from the pair of the pick-up coils are measured by a lock-in amplifier. The AC loss per cycle per until volume Qb [J/m3/cycle] is given by the following equations [12]: Qb ¼
0.1 B m [T]
1 KV R Bm h ; 2 ðni no Þl0 vb f
ð6Þ
where Bm and f are the amplitude and frequency of the external AC magnetic field, respectively. VR is the amplitude of the resistive component of the voltage signal from the pair of the pick-up coils and vb is the volume of the bulk. K is the correction factor and K = 1, if the heights of the pick up coils are larger enough than the height of the bulk and the radii of the pick-up coils ri and ro. A heater of a Manganin wire is placed on the peripheral area of the bottom surface of the bulk and a semiconductor temperature sensor at the center of the bottom surface for the calorimetric measurement. The bulk sample is thermally insulated by stylus-form as show in Fig. 6. The measurement arrangement is put in vacuum space in a cryostat and the bulk is cooled by a cryo-cooler connecting its cold head to the bulk with a CFRP rod. In this arrangement, it is considered that whole of the heater power is put into the bulk and that the bulk temperature Tb increases linearly for a stepwise heating. Getting a calibration curve of the heater power vs. dTb/dt at a fixed temperature rise of the bulk DT0, the AC losses is measured from the value of dTb/dt at DT0 applying a stepwise AC magnetic field of constant amplitude. AC losses in an YBCO bulk of 31.0 mm dia. and 15.0 mm high measured by the electric and calorimetric methods are show in Fig. 7 [11]. In this measurement, DT0 was 1 K. Both of the AC loss data agree with each other with errors around 20% of the electrically measured values. These results show that both the electric and calorimetric methods are valid and that the measured data are valid.
Magnetization loss Q[W/m3]
Magnetization loss Q[W/m3]
Fig. 6. Sample arrangement to measure AC losses in HTS bulk subjected to an external AC magnetic field Bm by electric and calorimetric methods.
705
b
105 10
4
Electric Calorimetric
103 102 f =62.32Hz 101 0.01
0.1 B m [T]
Fig. 7. AC losses in the bulk measured calorimetric and electric methods at different values of bulk temperature Tb0 are plotted against the amplitude of the external AC field Bm. (a) Tb0 = 60 K, (b) Tb0 = 70 K.
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4. Concluding remarks Validity of the electric measurement methods of AC losses in HTS wires and bulks which we developed was investigated by conducting calorimetric measurements simultaneously. The results of the experiments are summarized as follows: (a) Total AC losses in an HTS wire: There was some uncertainty in determination of the total losses by adding the transport current and magnetization losses which were measured by the electric method separately and also in the calibration method of the calorimetric method. It was shown that the total losses measured simultaneously by the electric and calorimetric methods well agreed with each other, which proved that the electric method together with the calorimetric method including the calibration method were valid. (b) Transport current losses in a wire with adjacent wires: An electric method to measure AC transport current losses in HTS wires placed parallel on a flat plane was developed, and its validity was investigated by conducting a calorimetric measurement. The loss data obtained by the electric and calorimetric methods well agreed with each other, which demonstrates the validity of the electric method. It was shown in our experiment that the AC transport current losses in an HTS wire was significantly affected by the magnetic field produced by the adjacent wires and that the transport current losses in a wire with adjacent wires carrying the same current at the both side was smaller than those in the case that there were no current in the adjacent wires. (c) Magnetization losses in bulk: AC losses in a bulk HTS subjected to an AC external field were simultaneously measured by the calorimetric and electric methods which we developed. The data measured by both methods well agreed with each other. Thus, the validity of both methods was proven. Generally, electric methods are much less time consuming than the calorimetric methods. Therefore, when an elec-
tric method whose validity is proven is developed, we can measure the losses efficiently with high sensitivity and resolution. However, there are some limitations in the electric measurements, e.g. the total losses in a wire carrying AC transport current in an AC magnetic field of different phase and losses in a bulk or a wire subjected to non-sinusoidal alternate magnetic field. The electric methods are difficult to be applied to those cases but the calorimetric methods are applicable. Acknowledgements This work was supported in part by METI through ISTEC as the US–Japan Joint study of AC Losses in HTS and in part by MEXT Grant-in-Aid for Scientific Research (S) (14102019). References [1] Y. Shiobara, presented at EUCAS2005, MO-PL-3, 2005. [2] O. Tsukamoto, K. Yamagishi, J. Ogawa, M. Murakami, M. Tomita, J. Mater. Proc. Technol. 161 (2005) 52. [3] M. Ciszek, A.M. Campbell, B.A. Glowacki, Physica C 233 (1994) 203. [4] S. Fukui, Y. Kitoh, T. Numata, O. Tsukamoto, J. Fujikami, K. Hayashi, Adv. Cryo. Eng. 44 (1998) 723. [5] E. Martinez, Y. Yang, C. Beduz, Y.B. Huang, Physica C 331 (2000) 216. [6] Z. Jiang, N. Amemiya, N. Ayai, K. Hayashi, IEEE Trans. ASC 13 (2003) 3557. [7] J. Ogawa, H. Nakayama, S. Odaka, O. Tsukamoto, Cryogenics 45 (2005) 23. [8] C. Schmidt, Cryogenics 41 (2001) 393. [9] S.P. Ashworth, Physica C 315 (1999) 79. [10] O. Tsukamoto, Y. Yamato, S. Nakamura, J. Ogawa, IEEE Trans. ASC 15 (2005) 2895. [11] K. Yamagishi, S. Sekizawa, J. Ogawa, O. Tsukamoto, presented at EUCAS2005, MO-M-O2-3, 2005. [12] J. Ogawa, M. Iwamoto, O. Tsukamoto, M. Murakami, M. Tomita, Physica C 372–376 (2002) 1754.