SCIENCE CHINA Technological Sciences • Article •
March 2015 Vol.58 No.3: 545–550 doi: 10.1007/s11431-014-5749-0
An applicable calorimetric method for measuring AC losses of 2G HTS wire using optical FBG WANG YinShun1*, ZHOU WeiWei2 & DAI JingShu3 1
State Key Laboratory of New Energy Power System, North China Electric Power University, Beijing 102206, China; 2 Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190, China; 3 Beijing Key Laboratory of High Voltage & Electromagnetic Compatibility, North China Electric Power University, Beijing 102206, China Received September 26, 2014; accepted December 11, 2014; published online January 7, 2015
We present a new calorimetric method for measuring alternative current (AC) losses of high-temperature superconducting (HTS) tapes by optical fiber Bragg grating (FBG), which is particularly well suited for the AC loss measurement of ReBCO wires, so-called the second generation (2G) HTS wires. Compared with conventional calorimetric methods, the suggested method is both free of electromagnetic disturbance, magnetic field, and fast as well as simple. Self-field AC losses are measured by the optical FBG method and the conventional lock-in-amplifier (LIA) technique, respectively. The results show that the measured AC loss is in good agreement with those measured by the electric method, thus the presented calorimetric method would be available for measuring the AC loss of 2G wire and is expected to be generalized for the measurement of AC loss or thermal performances of HTS bulk. AC losses, calorimetric method, 2G HTS wire, calibration, optical fiber Bragg grating (FBG) Citation:
Wang Y S, Zhou W W, Dai J S. An applicable calorimetric method for measuring AC losses of 2G HTS wire using optical FBG. Sci China Tech Sci, 2015, 58: 545550, doi: 10.1007/s11431-014-5749-0
1 Introduction Coated conductor (CC), so-called the second generation HTS tapes coated ReBCO (rare earth barium cuprate) thin film on metal tape, have potential in a variety of existing applications, such as power application in low magnetic field at higher operating temperature such as cable, fault current limiter (FCL), transformer, and in high magnetic field at low temperature, for instance the magnet, motor or generator. Most of those potential applications require those 2G HTS wires to manifest well upon the application of an alternative current (AC) and AC magnetic field. Therefore, when superconductor carries AC current or is exposed to AC magnetic field, some power loss will generates, namely *Corresponding author (email:
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2015
AC loss, which is thus one of the important performances of practical superconductors. Even in nominally “direct current (DC)” applications and process of exciting and demagnetizing of high field magnets, the current ripple or filed will be imposed on HTS tapes in which AC loss then generates. Thus, the AC losses of HTS tapes is one of the most important factors in evaluating their economic viability, stability, security, and must be fully understood. The AC loss measurement principles of superconductors traditionally include electrical techniques and calorimetric techniques [1,2]. The former techniques include magnetization method and transport method. Magnetization method essentially measure m-H loops by means of some magnetometers such as vibrating sample magnetometer (VSB) and superconducting quantum interference device (SQUID) or pick-up coils, the transport method measures the voltage developed along superconductor carrying AC transport curtech.scichina.com link.springer.com
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rent. The calorimetric techniques have been widely used in low-temperature superconductor (LTS) mainly with two methods, one is liquid helium (LHe) boiling-off calorimetry in which the vapor created from liquid bath is used to determine the generated heat and is proven useful for LTS samples, coils or devices with good sensitivity. Unfortunately, this method is ineffective in liquid nitrogen (LN2) for small samples except for HTS devices since LN2 has high latent heat which thus results in low measurement accuracy. Other calorimetric methods are realized by measuring the T caused by the AC loss generated in sample [3]. The electrical methods of magnetic and electrical techniques are the most commonly used for extracting the power loss. In the magnetic method, induced current appears in the superconductor when it is placed to an AC magnetic field, a voltage is simultaneously created in a pickup coil which surrounds the superconducting sample [4,5]. In the electrical method, AC current is supplied in the sample and the generating longitudinal voltage is measured with voltage taps attached to the sample [6]. In the latter case, the AC loss is determined by the part of the voltage in-phase with the transport current. Although electrical techniques by lock-in-amplifier (LIA) and pick-up coils method for measuring AC losses in superconductor are relatively mature and applicable for fast measurement of AC loses with low level, they have a number of drawbacks in some cases [7]: 1) Not available if there are phase difference between magnetic field and transport current; 2) ineffective when superconductor carries nonsinusoidal AC current or is exposed to non-sinusoidal AC magnetic field; 3) the technique is very difficult to apply experimentally due to subtle and sophisticated circuit; 4) deeply and easily affected by electromagnetic environment disturbances; 5) phase sensitive. In order to overcome these difficulties, some authors suggested calorimetric techniques to obtain the AC losses by directly measuring temperature rise T created by AC losses in HTS tape regardless of sophisticated electromagnetic without environment modification under atmosphere pressure. Originally, temperature change is measured by using differential thermocouple (DTC) [8], this calorimetric method can be used to obtain AC losses in HTS tapes for a wide range of conditions without imposing any preconceived model on current patterns or magnetic flux penetration into superconducting sample. More importantly, the AC loss resulting from any complicated waveform of AC current or applied AC magnetic field, DC magnetic field superposed with AC ripple current component, combination of AC magnetic field and AC current with or without phase differences, can be measured. However, the DTC has disadvantages of low precision resulting from noises created in the measuring circuit due to AC magnetic field and thermal noise. In order to improve the measuring precision, Cernox thermometer was chosen as temperature sensor. Nevertheless, its precision depends on its resistance measured by
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different current forms. There are some potential drawbacks in Cernox: 1) Conduction extra heat into measuring system; 2) a longer response time than thermocouples due to its big mass; 3) measurement system is much more complex [9]. In addition, the magnetic field particularly at high magnetic field has obvious effect on resistance of thermocouple and Cernox thermometer, so called magnetoresistance effect, so that both of methods are not available for measuring AC loss of HTS tapes. Based on these considerations we presented a new passive calorimetric method by suing optical FBG to measure AC losses of HTS tapes, which is particularly suitable for ReBCO tapes. We demonstrate that this technique is well applicable for a fast and accurate characterization as well as simple comparing with the above two calorimetric techniques by using DTC and Cernox thermometer. The YBCO coated conductor (CC) was only used to validate our measurement method.
2 Model of calorimetric measuring AC losses Figure 1 schematically shows the schematic geometry of a ReBCO CC, width and thickness as well as length of the CC sampe are w and d as well as 2L, respectively; ReBCO film is at top; temperatures of both ends are constant Tb, the ambient temperature (referring to gas nitrogen GN2, thereafter) is T0. The principle of the optical FBG is to measure the temperature rise T based on the temperature distribution generated within a tape which is exposed to temperature T0 on its surroundings and cooled at both ends with constant temperature Tb, when the superconductor sample is exposed to an internal heat generation (Joule heat). The steady-state heat conduction equation due to uniform Joule heat is kA
d 2T Pc ph T T0 0, dx 2
(1)
where A and k are cross-sectional area and thermal conductivity, respectively; T stands for temperature distribution along the coated conductor; p and h separately represent the cooling perimeter of the coated conductor and heat transfer coefficient between the conductor and environment, and Pc (W/m) refers to the AC loss created by the conductor when it carries AC current. With assuming that k and h are constant and independent of temperature, the solution of eq. (1) is
Figure 1
Schematic geometry of a coated conductor.
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x ch Pc Pc T x T x T0 Tb T0 , ph ph L ch 2
(2)
where
kA . ph
(3)
At the central point, the temperature difference between the conductor and environment is Pc Tb T0 ph P . Tm T 0 T0 c ph L ch 2
(4)
Figure 2 illustrates temperature profile predicted by eq. (4) for a conductor with its end temperature Tb and environment temperature T0. In principle, AC loss per unit length is found if the temperature rise Tm is measured according to eq. (4) which is just approximate in that we assume that k and h are independent of temperature, actually we can not know those parameters accurately. In practice, we need not know these two parameters, the AC loss can be obtained by internal calibration eq. (4).
3 Temperature dependence of optical FBG Optical FBG is a sensor to measure micro-strain, its gross diameter is smaller than 100 m which is so thin that the temperature equilibrium between optical FBG and specimen reaches easily and quickly. Dependence of its wavelength variance on temperature can be described by B =αT T ,
(5)
Figure 2 Typical temperature profile of coated conductor: Tb=78 K, T0= 78.5 K, L=200 mm, h=15 W/(m2 K), k=20 W/(m K), p=2(w+d) = 2×(4.8+0.2) mm=10 mm, A=0.96 mm2, Pc=101 W/m.
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where T is temperature-dependent sensitivity coefficient and T=λB(ξ+α), B and B denote the wavelength and its shift of optical FBG due to temperature variation. In this paper, optical fiber grating modulator with wavelength of 1510–1590 nm, that is, Fiber sensors system (Sm225) manufactured by Micron Optical Int., is used to measure the wavelength of optical FBG. In order to obtain the relation of wavelength shift B with temperature T, an optical FBG anchored to cold-head by thermal conductive adhesive was calibrated by Cernox thermometer at reference temperature 6 K by means of G-M cryo-cooler in processes of cooling-down and heating-up. Figure 3 indicates the dependence of wavelength shift B on temperature with three cycles of cooling and heating process, which shows that the repeatability is good enough and hence the optical FBG can be used to measure temperature rise T in temperature range of LN2 with a resolution of 170 pm/K in region of 77.3 K.
4 Experimental setup The arrangement of set-up is schematically shown as Figure 4. The copper box is immersed in LN2 bath which fills the cryostat. The sample locates in the copper box and its both ends are soldered to massive copper cone blocks, which has enough heat sink and gives a large surface area for cooling such that keeps the temperature constant. The current leads firstly go from the copper box filling LN2 and then enter the LN2 bath of cryostat and then contact with power supply rather than directly contact with the power supply. It is noteworthy that special care must be taken when we solder sample tape to massive copper cone blocks since thermal stress acted on the sample is probably inhomogeneous and possibly results in degradation of its superconducting characteristics. The level of boiling LN2 in cryostat is much higher than that of copper box, as shown in Figure 4, there is a little fluctuation on LN2 surface in cryostat but there is almost flat on LN2 surface of copper box under atmosphere pressure. As a consequence, this procedure ensures that the LN2
Figure 3
Plot of FBG wavelength shift against temperature.
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evaporation and heat-leak into LN2 of copper box are minima. The one end of the optical FBG is attached to central part on HTS upper surface by thermal conductive adhesive and the other end is free. It is not necessary for the optical FBG to insulate electrically. Care measures must be taken so that the optical FBG maintains good thermal contact with sample tape. The couple of inner current leads should be soldered to massive copper blocks in order to avoid their thermal disturbing the measurement. In order to suppress critical current during DC calibration, a pair of magnets made of 12 permanent NdFeBs are arranged for providing perpendicular magnetic field. The gap between them for sample is about 5 mm and the magnetic field is up to 0.5 T, so that the sample can be heated uniformly along the whole length which is in the gap of the pair of permanent magnets if the DC transport current exceeds its critical current. The sample is cooled by conduction-cooling since it is directly soldered by its both ends to the massive copper cone blocks part of which immerses into LN2. The temperature of massive copper cone blocks are almost constant with 78 K, the temperature of sample is equal to that of cone blocks because the LN2 level of copper box is just 3 mm below the sample tape which is just only 0.2 mm thickness, other reason is that the LN2 evaporation is minimum due to our arrangements where inner and outer current leads are respectively attached on two terminals of specimen and power supply, thus the heat leakage into inner LN2 by a pair of inner current leads is so small that it has little effect on the temperature of YBCO CC sample. Voltage taps, used to measure critical current and AC losses, were softly attached to the tape within the central segment and then tightly twisted to minimize the induced voltages by the AC self magnetic field before inputting measuring instruments (Voltmeter for DC and LAP for AC measurements).
5 Calibration
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various transfer properties at any temperature are exactly known. However, the transfer properties are difficult to measure. Here, we adopt a more pragmatic method and an internal calibration. A direct calibration of optical FBG response as a function of the power loss created in the YBCO CC sample can be obtained by using a DC current and perpendicular magnetic field which can effectively reduce the critical current in that the sample has strong anisotropy. If a DC current higher than the critical current flows along the sample, a voltage and then power loss is produced. Consequently, the AC losses are thus obtained accurately if the DC voltage between two voltage tapes is measured. Calibration is the most important step in any kind of calorimetric methods. Ideally, the measurement approach should not depend on thermal characteristics of materials such as thermal conductivities, thermal capacities. Generally, these parameters are usually difficult to know accurately at low temperature and the thermal resistances are different with orders of magnitude if extreme care is not taken in assembly. Principally, these uncertainties can be minimized by calibrations with an exact known power source. Unfortunately, this method probably introduces errors if a small electrical heater is used as calibration power source. It is generally necessary to use a calibration heater to find thermal parameters according to some models. HTS sample itself is used as the calibration heater in order to avoid these problems. Here, we perform these by providing a DC transport current (little lower than the critical current) for the sample after applying a DC magnetic field with perpendicular to the wide sample surface. The critical current can be suppressed, a DC voltage and dissipation losses are hence generated in the sample. Since both of the DC voltage and DC current are measured with good accuracy, the DC loss distribution in the sample is in just the same manner as the measured AC loss. It only needs to assume that the temperature rise T resulting from a given DC dissipation is same as that from AC one. The DC calibration is carried out in exactly the same
According to eq. (4), calculation of the power loss in HTS sample would be possible if the temperature rise T and its
Figure 4 (Color online) Schematic arrangement of set-up for calibration and AC loss measurements by electric method and FBG.
Figure 5 Calibration curve between energy loss and FBG response in DC magnetic field.
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manner as one used in AC loss measurement steps. The sample whose both sides are covered by brass layers is YBCO CC with 4.8 mm width and 0.2 mm thickness manufactured by American Superconductor Company (AMSC). It had an initial critical current higher than 103 A at self-field over the whole length of the 100 m tape. Firstly, we measure the temperature and critical current at self field after removing the permanent magnets. The temperature on sample is about 78.5 K and its critical current is 98 A. If the perpendicular magnetic field is 0.5 T, its critical current reduces to about 20% of that at self field, that is, 19.6 A. It must be noted that the HTS film should be upward and contact with the optical FBG directly. Then, after moving back the permanent magnets into its position, the profile of temperature T and wavelength shift B was recorded for a given DC transport current supplying to sample (little larger than 20 A). It is assured that the tape temperature rise T by more than 0.5 K from the 78.5 K starting temperature is not allowed in all the measurements, which ensures the critical current approximate constant. The variation in critical current of YBCO CC between 78.5 and 79.5 K, and thus in losses, is small sufficiently and neglected. We take this temperature rise T to be enough small into consideration so that the loss does not need to correct during temperature variation, and is thus sufficiently high to be reliably measured. A YBCO CC with larger critical current and a lower thermal conductivity substrate would only need a shorter test segment in order to keep the temperature rise T as small enough as possible. Due to this rigors restriction, it is assured that all the related thermodynamic parameters are approximately constant in duration of the measurement. As a consequence, any correction to the measuring data is not necessary in the critical current of the YBCO CC sample during the measurement. Thus, the DC dissipation equals to the product of DC voltage and current. In this manner, a single calibration curve which is the optical FBG wavelength shift B generated by dissipation in the YBCO CC sample is obtained after a defined time of heating (usually 5 s). Duration of at least 20 s was permitted between supplying DC currents for the YBCO CC sample to be cooled back to its surrounding temperature. Figure 5 indicates a representative set of calibrated data in measurements on a single YBCO CC sample. In these cases, DC currents lower than the self field critical current are supplied to the YBCO CC sample which is simultaneously exposed to a perpendicular DC magnetic field for generating a loss voltage, the sensitivity is about 103 W/m/pm. For the cases including a higher temperature rise T or larger power loss, it is essential for the measurement system to be calibrated correspondingly even the calibration is much more sophisticated. The wavelength shift B should be compared with a calibrated curve obtained between loss and optical FBG response. It is assumed that the temperature rise T resulting from power loss does not depend on the waveform of
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AC current if the frequency is much higher than the thermal time constants. Therefore, it is not essential for the measuring system to reach steady-state by using this method. It is just supposed that the temperature rise T after a period of time is same for the same energy loss and does not has dependence on the mechanism creating the losses. The calibration curve then describes the dependence of wavelength shift B on a loss generation P in a certain standard time. Actually, it is not necessary to know the actual temperature rise T. In this method, the loss generated along the whole YBCO CC sample is uniform just as the case during the AC measurements. Consequently, the calibrated curve can be used to convert optical wavelength shift B to AC losses. When this calorimetric method is used, each YBCO CC sample needs to calibrate for obtaining different calibration curve which depends on the details of sample assembling, thermal conductivity, heat transfer, thermal capacity, size, etc. The AC losses can be obtained by comparing the temperature rise T after a heating duration of unknown AC power loss with that after the same duration of known DC power loss. Therefore, it is not necessary for us to assume any values such as heat transfer, thermal conductivity, the temperature profile along the YBCO CC sample. It is only assumed that there is a corresponding relation between power loss P and temperature rise T after a fixed heating duration.
6 Measurement of AC losses As for any new measurement approach, it needs to firstly show that it should produce the same results with the more widely used methods at least in the ranges where the two methods can be compared with each other. The optical FBG is used to produce wavelength shift B, yielding maximum wavelength shift B in our measurement of pm. In the setup used, DC perpendicular magnetic field up to 0.5 T is available from a pair of permanent magnets made of 10 NdFeB rectangular magnets. Again, after moving away the pair of permanent magnet from the setup system, we energized the sample by supplying AC transport current, the self field AC losses measured by both this calorimetric with an optical FBG and conventional electrical (lock-in-amplifier) techniques [4], respectively, as shown in Figure 6. These measurements were for a single YBCO CC in LN2 with exciting a frequency of 60 Hz AC transport current. The agreement between the two methods is good enough with normalized transport current at i0.2 because of the limited sensitivity of this method. However, this does not affect the effectiveness of this method since the aim of experiment is just to verify the availability of this measurement method. Furthermore, the experimental data was between a strip and rod with circular or elliptical cross sections according to the critical state model [10] for self field AC losses predicted by Norris [11].
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thus no exception. Although we do not accurately expect that this calorimetric method can be widely used to measure AC losses of full-scale devices made from 2G wire, it is possibly significant in improving our understanding of AC losses in model systems especially when it is used in combination with numerical simulation which accordingly permits us to understand the effect of AC losses in practical applications. This work was supported by the National Natural Science Foundation of China (Grant No. 51477053), and the Beijing Education Commissions (Grant No. GJ2013009).
Figure 6
Self AC losses of YBCO CC at frequency 60 Hz.
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With validating the calorimetric technique, it can be then generalized in a wide range of AC measurements where the electrical techniques would be extremely difficult to use since the optical FBG is not affected by any electromagnetic environments, such as AC current, AC magnetic field, phase, field angle, waveforms.
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7 Conclusions
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We have demonstrated that the calorimetric measurement by the optical FBG a fast, accurate and electromagnetic disturbance free method is an available for determining AC losses of 2G wire (ReBCO CC). In order to validate the method, the self field loss of a YBCO CC sample exposed to perpendicular DC magnetic field was measured and compared with the electrical measurement method, both of them are good agreement. This technique can be generalized to measure AC losses in a wide range of sophisticated electro-magnetic conditions and is able to measure the local power loss or heat generation in coils and HTS bulk, respectively. Few new experimental techniques in any field have no drawbacks and the calorimetric method by optical FBG is
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