Bromberg, L.

Michael, P.

Minervini, J.

DSpace@MIT

                                      PSFC-JA-08-9Current Lead Optimization forCryogenic Operationat Intermediate TemperaturesL. Bromberg, P. Michael and J. MinerviniMIT Plasma Science and Fusion CenterApril 1, 2008Supported in part by a grant from the MIT Energy InitiativeAbstractCurrent leads to low temperature environments represent a large heat input to thecryogenic environment. For cases that require large currents, such as in powerdistribution in intermediate voltages, the current leads represent, by far, the largestrefrigeration requirement.  Means of decreasing the refrigerator power when thecryogenic temperature is around liquid nitrogen temperature, or at temperatures that areoptimized for high temperature superconductors, are discussed in this paper.  The use ofmultiple cooling stages is described.I.  IntroductionProgress in high temperature superconductors has opened up superconductingapplications that otherwise have been economically unattractive. [Navigant] One suchapplication is power transmission, where the use of liquid nitrogen coolant substantiallysimplifies the cryogenic requirements.  The US Department of Energy has co-fundedthree substantial demonstrations of the use of HTS in AC transmission lines. [Haught]For transmission applications, the losses in the current leads are small compared withdistributed losses along the superconducting line which are dominated by thermalradiation (cryostat losses) and by the AC losses in the cable.  Minimization of the currentlead losses is not important.  In these applications the lines operate at relatively highvoltages and relatively low currents, compared with distribution cables. [McGuire,Weber, Demko, Sohn]As an example of a superconducting distribution system, several teams, including ours,have been looking at the possibility of using HTS distribution systems in data servers andsupercomputing centers. [Furuse] These centers have large power consumption, usuallymore than 10 MW, with very high power distribution density. [Prat] Normal conductorsare being used, with large cross section and substantial power dissipation, even atreduced current densities.A small program at the Plasma Science and Fusion Center at MIT is looking at thepotential of using DC distribution, using HTS cables, in data centers.  In this application,the use of relatively low voltages (~ 400 V DC) results in substantial currents to bedistributed, on the order of 20 kA. Under these circumstances, current leads represent asubstantial and dominant heat input to the cryogenic environment.Means of optimizing current leads have been discussed in the past, mainly forapplications to cryogenic environments around 4 K.  Recently, the development of HTScurrent leads that can transfer currents between 77 K and 4 K have been developed withseveral companies selling commercial components.  There has been little priordevelopment of methods to minimize the heat input to the liquid nitrogen environment, asthe requirements are significantly reduced compared with the more severe requirementsto 4 K.  However, in some potential applications, as in the data serer or supercomputercenters, means of minimization of the cryogenic refrigeration load is desired.In this paper, the minimization of the refrigeration power for current leads between roomtemperature (298 K) and 65 K are discussed.  The use of multiple intermediate stages isanalyzed. This method has proven very useful to minimization of the coolingrequirements when operating from room temperature to 4 K. [McFee]II. ModelThe methodology developed by McFee [McFee] has been used in this analysis.  Itprovides a general methodology to optimize current leads, even with temperaturedependent thermal and electrical properties.The  McFee formulism can be reduced to three equations. The minimum energytransmitted from temperature TH  to cold temperature T is given bywhere k(T) and ()  are the  temperature dependent thermal and electrical conductivitiesof the conductor, and I is the transport current. The ratio of length to cross sectional areaof the current lead that results in minimum thermal loss is given by(3)(1)(2)andwhere TL is the low temperature. Since Q(T) is proportional to the current I by equation(1), the ratio IL/A is independent of current and only depends on the high temperature TH,the low temperature TL and the material properties of the current lead.A case of special interest is the heat (and associated electrical power requirement for therefrigerator) that is transmitted from one temperature to another when a current leadoptimized for a given current is operated without current, such as during idle times of amagnet or no power transfer in a distribution or transmission line.  Once the optimumIL/A is identified for a given temperature difference and material properties, the powertransmitted from one temperature to the next when there is no current flowing isdetermined fromIt has been assumed that the current lead is made from copper with RRR =100.  Theassumed thermal and electrical properties of copper are shown in Figure 1.  It is possibleto decrease the thermal load through the use of alternative materials for the current leadsby about 10% [Rasmussen], but for simplicity copper is used in this study.In order to determine the electrical power requirement for the refrigerator system, anassumption needs to be made with respect to the efficiency of the refrigerators.  In thispaper, it is assumed that the refrigerator efficiency is a constant fraction of the Carnotefficiency between room temperature and the operating temperature or the refrigerator.This is a simplifying assumption as the efficiency drops (compared with Carnot) forsmall capacity units and for lower temperatures.  A relatively conservative multiple of 9(i.e., 11% of Carnot efficiency) is used in Section III for all refrigerators, independent oftemperature and capacity.The normalized electric power requirement for an individual refrigerator PE is thus,(PE /I)  = 9 (Q/I) /Carnotwhere Carnot  = TL/(TH – TL) is the Carnot efficiency of the refrigerator operating betweenupper temperature TH and lower temperature TL. The total electrical power is the sum ofthe electrical power of the individual refrigerators.Figure 1.  Assumed copper properties for the current lead with RRR = 100.III. Copper lead optimizationThe power requirement has been calculated for three cases when the leads aremanufactured from copper: a single stage current lead (cooling only at the operatingcryogenic temperature), one with cooling at an intermediate temperature, and finally onewith two intermediate cooling temperatures.  The temperature of operation has beenvaried in the second and third cases such that the total electrical power of the refrigeratorsis minimized.01002003004005006007000 100 200 300 400Temperature (K)Thermal conductivity (W/m K)1.E-091.E-081.E-07Electrical resistivity (Ohm m)The minimization function is the electrical power.  Alternatively, the minimizationfunction could be the capital cost of the overall refrigeration system, or the cost ofownership (capital and operating costs).Figure 2 shows the results of the calculations for the single stage, two-stage and three-stage current leads.  The calculated normalized electrical power PE of the refrigerator orrefrigerator set, assuming the model described in the previous section, are shown as afunction of the lower temperature of the upper stage (first stage), for two-stages andthree-stages systems. Also shown in the normalized electrical power for the single stage.For the single stage case, the normalized electrical power is 1.36 WE/A, (WE is electricalWatt) which decreases to about 0.92 WE/A for two stages, for a one third reduction ofelectrical power.  The gain of going from two-stages to three-stages is minimal, with anadditional electrical power reduction of about 6%.Figure 2. Normalized refrigerator system electrical power as a function of thetemperature of the intermediate stage for two and three stage refrigeration systems.298K - 65K0.80.911.11.21.31.4120 170 220 270 320First stage temperature (K)Power_e/I (W/A)2-stages8090100110120130140Two stagesThree stagesOne stageSecond stage temp 80K10011012090The case of two-stages has a broad optimum around an intermediate temperature of 145K.  At this temperature, the normalized thermal input at the first (145 K) and second (64K) stages are 0.039 and 0.017 WT/A, respectively.  The corresponding electrical power ofthe respective refrigerators are 0.37 and 0. 55 WE/A.The corresponding values of IL/A at the electrical power minimum are 3.7 106 A/m forthe single stage case, and for the two stage current lead, IL/A ~ 2.83 106 A/m for the hightemperature side and 1.48 106 A/m for the low temperature side.Figure 3 shows the value of IL/A required for the single and two stage current leads, as afunction of the cold stage temperature.  Note that the overall values of IL/A for the twostage current lead is about double that of the single stage current lead.Figure 3.  Values of IL/A for optimized single-stage and two-stages current leads.The properties of the optimized current leads, including the thermal loading in the case ofno current, are shown in Table 1 for both the single and two stage current leads.2.0E+062.2E+062.4E+062.6E+062.8E+063.0E+063.2E+063.4E+063.6E+063.8E+064.0E+0650 60 70 80 90 100 110Cold temperature (K)IL/A_optimum (A/m)single stageupper stagelower stagetwo-stageTable 1.  Characteristics of the optimized single and two stages current leadIt is interesting to note the thermal power loading at the different temperatures.  For thecase of two stages, the power loading at the 64 K station and at the intermediatetemperature stage is shown in Figure 4 as a function of the intermediate stagetemperature.  As the temperature of the intermediate stage increases, the individuallyoptimized thermal loading to the upper stage decreases while the thermal loading to thelower stage increases.  At the system optimum intermediate temperature (around 145 Kas shown in figure 2), the thermal loading to the low temperature is slightly less than halfthe thermal loading of the intermediate stage. At this optimum, the electrical power of the64 K temperature refrigerator is, however, about 50% larger than that of the intermediatetemperature refrigerator.Figure 4. Normalized thermal loads at the 64 K and intermediate-stage temperature as afunction of the intermediate temperature, for optimal individual leadsSingle stage Upper stage Lower stageQ_dot W/A 0.042 0.039 0.017IL/A A/m 3.73E+06 2.83E+06 2.73E+06Q_dot no current W/A 0.027 0.022 0.014Double stage00.0050.010.0150.020.0250.030.0350.040.045100 120 140 160 180 200Intermediate stage temperature (K)Normalized thermal load (WT/A)64 K stageIntermediate temperature stageTable 2.  Characteristics of optimized current leads with two stages as a function of thelower temperatureTable 2 shows the results of the calculations for the two-stage system as a function of thecold temperature.  The system performance has been evaluated for cold temperature of64K, 70K, 80K and 90K.  The associated value of the intermediate temperature thatminimizes the electrical power consumption of the refrigerator system is shown toincrease faster than the cold temperature.Also shown in Table 2 are the system-optimized values of the normalized heat flow whenoperating at full current and the associated value of IL/A of the optimized system.  Table2 shows these values for both the upper stage and the lower stage. The impact on thesystem of operating without current, especially during extended periods, as in caseswhere a load such as a bank of computers in the data center have been disconnected, asalso shown in Table 2 for the case of optimized two-stages current lead.IV. Non-copper current leadsIt is well known that it is possible to decrease the thermal loading with single stagecurrent leads through the use of materials other than copper.  In particular, aluminumLower temperature K 64 70 80 90Intermediate temperature K 145 155 165 180Upper stageQ_dot W/A 0.039 0.038 0.037 0.036IL/A A/m 2.83E+06 2.72E+06 2.61E+06 2.44E+06Q_dot no current W/A 0.022 0.021 0.021 0.020Lower stageQ_dot W/A 0.017 0.018 0.020 0.022IL/A A/m 2.73E+06 2.88E+06 2.96E+06 2.91E+06Q_dot no current W/A 0.014 0.014 0.013 0.014leads have about 10% lower thermal loading for single stage.  In this section, thepossibility of using multiple materials in different sections of the current lead isdiscussed, and the optimized parameters for multiple stage non-copper leads arepresented.Using the formalism by McFee, from equation (1) it is easy to see that for a giventemperature span, the thermal loading is minimized for those materials with the lowestratio between thermal and electrical conductivities.  Figure 5 shows the parameter k/s as afunction of temperature for 4 different materials:  copper (as in the previous section), andthree aluminum alloys: 1100, 5083 and 6061. [Nist1, Nist2]Figure 5. Ratio of thermal to electrical conductivity for copper and several aluminumalloys as a function of temperature.From Figure 5, it is clear that over the entire span, with the exception of a very smallregion near 65K, the use of 1100-series aluminum minimizes the thermal loading, for anytemperature span and irrespective of the number of stages.  In the rest of this section, theimplications of using one and two stages with 1100 series aluminum is presented.01002003004005006007008000 50 100 150 200 250 300 350Temperature (K)k/ (W/mK * m *10^6)copper508311006061Table 3 shows the results from the optimization of a single stage and two-stages currentleads, between 298 K and 65 K. The intermediate temperature of the optimum system hasincreased to about 150 K.  As in the case of copper, the optimum is quite broad.Table 3.  Optimized current leads with 1100 series aluminumThe two-stage system decreases the electrical power requirement by about 1/3.Single stageTwo stagesIntermediate temperature (K) 150Upper stageQ_dot/I W/A 0.039 0.035IL/A A/m 2.18E+06 1.62E+06Q_dot/I no Current W/A 0.024 0.020Lower StageQ_dot/I W/A 0.017IL/A A/m 1.85E+06Q_dot/I no Current W/A 0.011P_e/I W/A 1.278 0.867V. ConclusionsThis works summarizes efforts to decrease the refrigerator power requirements forcurrent leads operating between room temperature and near liquid nitrogen temperatures.This work is relevant to systems operating at temperatures around liquid nitrogen, as wellas to systems operating at lower temperature that use low-thermal conduction HTScurrent leads, as the overall electrical power requirement of these current are dominatedby the stages between room temperature and around 70K.It is shown that it is possible to decrease the electrical power requirements of therefrigerator by about 1/3 through the use of two-stages current leads, using refrigeratorperformance that is conservative.  With real systems, with higher temperaturerefrigerators running at higher fractions of their Carnot efficiencies, it is suggested thatthe refrigerator electrical power requirement can be decreased by 1/2.Not analyzed in this document is the impact of the optimization on capital cost, or, moreimportantly, on the cost-of-ownership.  Only the electrical power requirement wasminimized.  The higher temperature refrigerators are cheaper that comparable lowtemperature refrigerators, but the fact that each individual refrigerator of a multi-stageunit has smaller capacity increases the cost per unit (refrigerators show a decrease in costper watt that scales as C-0.3 where C is the capacity of the refrigerator).We are starting a compilation of state-of-the-art cryogenic refrigerators in order toprovide information required in order to repeat the exercise for capital cost minimizationas well as operating cost minimization using realistic temperature/capacity dependence ofrefrigeration efficiency.AcknowledgementsThis work has been carried partly under the auspices of the MIT Energy Initiative.References[Demko] Demko, J.A. I. Sauers, D.R. James, et al. Triaxial HTS Cable for the AEP BixbyProject, IEEE Transactions on Applied Superconductivity 17 2047-2050 [Haught] Haught D., et al., Overview of the U.S. Department of Energy (DOE) High-Temperature Superconductivity Program for Large-Scale Applications, International JApplied Ceramic Tech 4 197-202, July 2007 [Navigant] Navigant Consulting,http://www.energetics.com/meetings/supercon06/pdfs/Plenary/07_Navigant_HTS_Market_Readiness_Study.pdf[Furuse] Furuse, M, S. Fuchino, N. Higuchi and I. Ishii Feasibility Study of Low-VoltageDC Superconducting Distribution System,  IEEE Trans Applied Superconductivity 151759 (2005)[Maguire] Maguire, J.F, F. Schmidt, S. Bratt, T.E. Welsh et al., Development AndDemonstration Of A HTS Power Cable To Operate In The Long Island Power AuthorityTransmission Grid, IEEE Transactions on Applied Superconductivity 17 2034-7 (2007)[McFee] McFee, R., Optimum Input Leads for Cryogenic Apparatus, Rev Scientific Instr.,30 (1959).[NIST1] The thermal conductivity of the aluminum alloys and copper was obtained fromNIST database: http://cryogenics.nist.gov/MPropsMAY/material%20properties.htm[NIST2] The electrical conductivity of aluminum alloys was obtained from NIST,Cryogenic Properties of Materials (1973)[Rasmussen] C. N. Rasmusses et al., Optimization Of Termination For A High-Temperature Superconducting Cable With Room Temperature Dielectric Design, IEEETrans. Appl. Supercond. 9 45–49 (1999).[Pratt] Pratt, A. and P. Kumar, Evaluation of Direct Current Distribution in Data Centersto Improve Energy Efficiency, INTEL Corporate Technology Group; available athttp://hightech.lbl.gov/documents/DATA_CENTERS/DC-Journal-March07.pdf[Sohn] Sohn, S.H., J.H. Lim,  S.W. Yim et al., The Results of Installation andPreliminary Test of 22.9 kV, 50 MVA, 100 m Class HTS Power Cable System at KEPCO,IEEE Transactions on Applied Superconductivity 17 2043-2046[Weber] Weber, C.S, R. Lee, S. Ringo, T. Masuda, et al., Testing and DemonstrationResults of the 350 m Long HTS Cable System Installed in Albany, NY, IEEE Transactionson Applied Superconductivity 17 2038-42 (2007)

Current Lead Optimization for Cryogenic Operation at Intermediate Temperatures

http://dspace.mit.edu/bitstream/1721.1/94233/1/08ja009_full.pdf

Current Lead Optimization for Cryogenic Operation at Intermediate Temperatures

Abstract

Similar works

Full text

Available Versions

DSpace@MIT