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1692 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 18, NO. 3, SEPTEMBER 2008

Transient Capability of Superconducting Devices onElectric Power Systems

Kiruba Sivasubramaniam, Senior Member, IEEE, Tao Zhang, Antonio Caiafa, Xianrui Huang,Minfeng Xu, Member, IEEE, Liang Li, E. T. Laskaris, and J. W. Bray

Abstract—Superconducting devices operating within a powersystem are expected to go through transient overload conditionsduring which the superconducting coil has to carry currents abovethe rated values. Designing the coil to remain superconductingthrough any possible fault scenario can be cost prohibitive, neces-sitating operation beyond the critical current for short periods. Inorder to set operating limits and design adequate protection sys-tems for superconducting devices connected to a power system, theregion of safe operation of these devices has to be described withgeneral capability curves. Existing standards that define limitsfor these over-current situations are based on copper windingexperience that do not apply to devices with superconductingcomponents because of the highly nonlinear interaction betweenmagnetic fields, operating temperature, and current density in thesuperconductor, and the rapidly varying material properties atcryogenic temperatures. In this paper, the behavior of supercon-ducting coils during over-currents is discussed and a simplifiedcapability curve is described to help standardize device capabil-ities. These curves are necessary to aid power system designersin appropriately designing the system and associated protectionsystems.

Index Terms—High-temperature superconductor (HTS) coil,over-current, quench protection, stability criterion, supercon-ducting generator.

I. INTRODUCTION

S UPERCONDUCTING coils are generally designed to berobust against disturbances utilizing one of the following

stability criteria: critical current margin, or cryostability throughaggressive cooling. These design practices allow the coil to ac-commodate small disturbances, like those that cause training orspontaneous quenches in low-temperature superconductor mag-nets, but not necessarily for an extended period of normal op-eration. With the advent of high-temperature superconductor(HTS) conductors and operation at significantly higher temper-atures, greater stability is possible due to the increased heat ca-pacity available. The actual level of over-current the coils canwithstand is a function of the heat capacity, cooling, and thecurrent/field profile. Several papers discuss how to analyze this

Manuscript received February 18, 2008; revised March 3, 2008. First pub-lished June 27, 2008; current version published September 4, 2008. This paperwas recommended by Associate Editor P. Masson.

K. Sivasubramaniam, T. Zhang, A. Caiafa, X. Huang, M. Xu, E. T. Laskaris,and J. W. Bray are with the General Electric Global Research Center,Niskayuna, NY 12309 USA (e-mail: [email protected]).

L. Li was with the General Electric Global Research Center, Niskayuna, NY12309 USA. He is now with the College of Electrical Engineering, HuazhongUniversity of Science and Technology, Wuhan 430000, China.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TASC.2008.2000902

TABLE IANSI C50.15 THERMAL STABILITY REQUIREMENTS

capability [1], [2]. This, unfortunately, is highly dependent onthe coil and cooling design, and will not be unique to any givendevice and current waveform.

Mature industries, like the electric utilities, demand generalcapability curves for devices being hooked up to their systemfor system design, integration studies, and protection schemes.While a general set of curves is hard to obtain for practical su-perconducting coils, if we recognize that most HTS magnets areconduction cooled with a cryocooler, and the transients of con-cern are short lived [2], then a conservative set of curves can beobtained based on adiabatic operation of each basic conductortype. These curves can be obtained either analytically or empir-ically. In this paper, we describe a format for representing thisdata, and how to obtain them analytically. This has been vali-dated with some experiments.

II. TRANSIENT REQUIREMENTS

Electrical apparatus for power applications are routinely ex-pected to go through transient fault conditions which can re-sult in significant over-currents compared to steady-state oper-ation. Such transients are rare and short-lived, but may resultin a coil quench and thermal run-away [2]. IEEE and ANSIstandards give generic specifications for the required short-termcurrent-carrying capability of these devices, which flow downto the superconducting components. For example, the require-ments for the field coil in synchronous generators is shown inTable I [3]. These requirements are generally based on (

; ) measurement for the coil capability, andare applicable to apparatus utilizing conventional conductors,such as copper, and operating at around room temperature. Atthese time-scales, the temperature is determined mainly by theamount of heat dumped into the coil in an adiabatic mode, sincecooling is not a significant factor. With an assumption of linearmaterial properties, which is reasonable for conventional con-ductors at these temperatures, the product becomes the lim-iting quantity regardless of the time duration.

For superconducting coils, however, the strong coupling be-tween the electromagnetic and thermal conditions, coupled withthe highly nonlinear properties at low temperatures means thata simple product cannot be used to gauge the coil capa-bility. The more complex behavior of superconducting coils re-quires a rigorous analysis to qualify the coil for operation under

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SIVASUBRAMANIAM et al.: TRANSIENT CAPABILITY OF SUPERCONDUCTING DEVICES 1693

Fig. 1. Data organization relative to an SC coil.

Fig. 2. Definition of parameters.

various fault scenarios. Such a model needs to incorporate de-tails of the coil assembly, the cryogenic cooling circuit, jouleheating of the wire splices, and heat transfer through radiationand conduction to the rest of the system. Numerical analysis canbe performed with these models to see if the coils can satisfyspecific over-current profiles [1], [2], with the coil returning tothe superconducting state at the end of the over-current situa-tion (when it returns to the rated current). In other words, thecoil should be equal to or below the current sharing temper-ature, , at the rated current after the over-current incident.While these methods allow us to qualify the coils for specificfault conditions, their general overload capability is not easilycompared with other devices in the system. For example, eventhe two current waveforms have the same values, they willhave significantly different impact on the temperature of the su-perconducting coil. There is, thus, a need for a different way toexpress the transient capability of superconducting coils.

III. CAPABILITY CURVES

The objective of having the transient capability of supercon-ducting coils organized in a generic manner is to give the de-signer a helpful tool that can help avoid over-sizing the super-conducting coil during the design phase, as well as to providedata for system designers to implement system-wide protectionschemes. One way to represent the transient capability of su-perconducting coils is to define a safe operating area (SOA)for a given coil, in the form of the curves shown in Fig. 1.Given the operating temperature , and the operating current

, the quantities mentioned in Fig. 1 are defined as follows,and are represented in Fig. 2. The critical current dependingboth on the local magnetic field and the operating temper-ature can be obtained from the look-up table generated by

Fig. 3. Schematic of conductor cross section.

the measured versus data. The quantity iscalculated as and the quantity is calcu-lated as . The quantity is the max-imum time that the coil can support the over-current andstill being able to return in superconducting state when the cur-rent falls back to . Referring to Fig. 1, is biggerthan , and is bigger than .In other words, is bigger than , and is bigger than

.

IV. ANALYTICAL MODEL

A numerical transient analysis is used to calculate the Jouleheating, the temperature, and the resistance of the coil at everytime-step. The current and magnetic field results are the inputs.During an over-current fault, the current and the magnetic fieldof the field coil may exceed its normal operation values and theconductor becomes normal for a short period of time. Considersuperconducting coils using the HTS conductor, like that fromthe American Superconductor Corporation. The conductor con-tains mainly BSCCO, silver, Pb–Sn solder, and stainless steel.A schematic of a typical HTS BSCCO conductor is shown inFig. 3.

During over-current situations, with a given current throughthe HTS tape, , a portion of it, , will go through the super-conducting component while the remaining, ,through the silver matrix. The resulting voltage across a unitlength of the tape can be obtained from the superconductor’scharacteristic as

(1)

where V/m is the regular constant to define the crit-ical current of HTS material, the critical current, and isusually a large number between 10 and 20 depending on thequality of HTS materials. Apparently, the same voltage will ap-pear across a unit length of the silver matrix, therefore, the cur-rent through the silver can be obtained from Ohm’s law as

(2)

where and are, respectively, the electric resistivity andcross section area of the silver substrate contained in the tape.

Considering the current sharing, i.e., , (1)and (2) can be combined to solve for and for any oper-ating current during the over-current situations, and the totalheat generation rate per unit length can be simply calculated as

. The high nonlinearity of (1) makes the explicit solu-tion impossible. A simplification can be made, however, by as-suming a very high -value such that the current through the su-perconducting component remains constant as for all .In this case, the voltage drop across the HTS tape depends on

1694 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 18, NO. 3, SEPTEMBER 2008

Fig. 4. Heat capacities as a function of temperatures.

the silver matrix as and the total Joule lossesper unit length can be estimated as

(3)

In case that the operating current is less than the critical cur-rent, i.e., , the total Joule losses can be simply estimatedby the losses in the superconducting component only

(4)

Knowing the losses, a simple time-stepping model underideal adiabatic conditions can be implemented on a spreadsheetas follows:

1) Select coil temperature, and operating current/field and ini-tialize model.

2) Look-up (or interpolate) critical current based on mea-sured data of critical current versus temperature and fielddata. In most power applications, the peak field is domi-nated by the self-field of the coil, and the field has to bescaled by the coil current as it goes through the over-cur-rent pulse.

3) Compare the local coil temperature with the critical tem-perature, , which is a function of the local magnetic field( . When , the heat generationper unit length can be obtained from either (3) or (4) de-pending on the operating current. Here, is a function oflocal magnetic field and temperature , and

is based on the measured curve of the HTStape. When , there is no current sharing and all thecurrent will go through the silver matrix, therefore, the heatgeneration can be calculated as

(5)

It should be noted that, in this step, the local magnet fieldand temperature are functions of both time and locationdefined as and .

4) Compute temperature rise using heat-load from aboveand heat capacity of conductor obtained by summing uptemperature-dependent heat capacities of the constituentmaterials. The data used for our analysis are shown in theFig. 4.

Fig. 5. 50% over-current pulses with different duration resulting in (a) recovery(shown on the top with pulse duration = 6 s); and (b) thermal runaway (shownon the bottom with pulse duration = 6:3 s).

5) Update temperature and progress to the next time step. Thecritical pulse duration is the time at which the operatingcurrent is equal to the critical current at the end of thepulse.

Fig. 5 below shows typical results for an over-current pulse.On the top, the coil temperature rises from 36 K to 41.5 Kfor a 50% over-current (normal operating current of 125 A and

SIVASUBRAMANIAM et al.: TRANSIENT CAPABILITY OF SUPERCONDUCTING DEVICES 1695

Fig. 6. Capability curve from analytical model.

Fig. 7. Long over-current pulse with 40% over-current.

over-current of 187.5 A) lasting just under 6 s. After the pulse,the operating current returns to below the critical currentand the coil can continue operating indefinitely. If the over-cur-rent pulse lasts any longer, as shown on the bottom of the figure,

would be greater than at the end of the pulse, so the coilcontinues heating up and can thermally run way without suffi-cient cooling.

A set of such analyses can be performed to generate the ca-pability curves described in Section IV. Fig. 6 shows the curvesfor a coil operated at 55 K and under a 6-T background mag-netic field.

To illustrate why such detailed capability curves are impor-tant, consider another over-current pulse as shown in Fig. 7.Compared to the pulses in Fig. 5, it has the same normal oper-ating current of 125 A, but a lower level over-current of 175 A,

Fig. 8. Two typical temperature profiles under over-current pulses (top: coilrecovers; bottom: coil thermally runs away).

i.e., 40% over-current, and a much longer duration of 38 s. Thispulse raises the coil temperature from 36 K to 37 K, and thecoil recovers to the superconducting state after the pulse. Thisis in spite of the fact that the product of this transient pulseis four times that of the short pulse on the top of Fig. 5.

V. EXPERIMENTAL VALIDATION

To verify the analytical predictions and confirm that it is pos-sible to organize data as shown in Fig. 1, a series of tests onan HTS superconductive coil were performed. The purpose ofthis set of measurements is to determine the maximum time thatan over-current can be sustained by the coil and still be able toreenter the superconducting state when the current goes back tothe operating conditions (see Fig. 2). The known parameters arethe normal operating current, the initial temperature, the mag-netic field, and the current overshoot. Figs. 8 and 9 show a fewsets of measurements.

The tests proceeded as follows: the value of the operating cur-rent is set, and a single pulse of current is superimposed on theoperating current. The temperature is monitored. If, at the endof the pulse, the temperature starts to decrease immediately (asshown on the top of Fig. 8), the test is repeated with a pulseof the same amplitude but increased duration. If, at the end ofthe pulse, the temperature still rises (as shown on the bottom ofFig. 8), the measurement is repeated with the same pulse am-plitude but decreased duration. If, at the end of the pulse the

1696 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 18, NO. 3, SEPTEMBER 2008

Fig. 9. Coil at the limit of thermal run away.

Fig. 10. Measured capability curve for coil having critical currentI = 46:5 A.

temperature tends to stay constant (as shown in Fig. 9), the du-ration of the pulse is recorded as the maximum duration of thepulse current the coil can support and still be able to reenterthe superconductive state. Once the maximum pulse duration isdetermined, one of the known parameters is changed and the de-scribed procedure is repeated.

The parameter values kept constant are: magnetic field at 6 T,and initial temperature at 55 K. The critical current of the coilunder these conditions is 46.5 A. The parameters modified arethe operating current (or base current), and the amplitude andduration of the over-current pulse. These data, plotted accordingthe procedure indicated above, are shown in Fig. 10. It can beseen that the data measured are consistent with what was ex-pected (Fig. 6). But the test coil has much higher capability thanthe predictions under adiabatic conditions. This discrepancy ismainly because of the way the test coil was cooled. In the ex-periment, the coil was placed inside a liquid helium dewar witha certain distance above the liquid level. The convection of coldhelium gas keep the coil cool, and a temperature controller wasused to drive a heater so that the coil temperature can be main-tained constant. Right before the over-current pulse was applied,

Fig. 11. Temperature versus time for test coil.

however, the temperature controller had to be turned OFF other-wise it will try to adjust the heater output to control the coil tem-perature at constant. This apparently resulted in an extra coolingeffect during the over-current pulse, compared to the adiabaticcondition. As shown in Fig. 11, the coil temperature was keptconstant at 50 K before s. After that, the temperaturecontroller was turned OFF, and the coil temperature immediatelydropped, indicating a significant cooling effect.

VI. CONCLUSION

This work proves that superconducting coils can be safely op-erated for a limited amount of time outside the superconductingstate in a reliable, repeatable manner, as long as operation is lim-ited to a well-defined safe operating region. Defining this SOAin the form of simple, yet conservative, capability curves as de-scribed in this paper can be useful in designing system-wide re-laying and protection. These results are important because theycan be used to dramatically reduce the size of superconductingcoils, while maintaining the reliability required in mature indus-tries. This generic SOA establishes the minimum over-currentcapability for electrical devices using HTS conductors. In elec-trical devices in which the cooling is significant, the capabilitycan be higher, as demonstrated in the tests described above. En-gineers can take advantage of the increased capability based onthe confidence in the cooling conditions.

REFERENCES

[1] A. Ishiyama and H. Asai, “A stability criterion for cryocooler-cooledHTS coils,” IEEE Trans. Appl. Supercond., vol. 11, no. 1, pp.1832–1835, Mar. 2001.

[2] K. Sivasubramaniam, X. Huang, E. T. Laskaris, T. Zhang, J. W. Bray,J. M. Forgarty, and R. A. Nold, “Performance of an HTS generator fieldcoil under system fault conditions,” IEEE Trans. Appl. Supercond., vol.16, no. 4, pp. 1971–1975, Dec. 2006.

[3] American National Standard Requirements for Synchronous Machines,ANSI Standard C50.

[4] J. W. Lue, M. S. Lubell, D. Aized, J. M. Campbell, and R. E. Schwall,“Spontaneous quenches of a high temperature superconducting pan-cake coil,” IEEE Trans. Magn., vol. 32, no. 4, pp. 2613–2616, Jul. 1996.

SIVASUBRAMANIAM et al.: TRANSIENT CAPABILITY OF SUPERCONDUCTING DEVICES 1697

Kiruba Sivasubramaniam (S’96–A’00–M’02–SM’05) received the B.S. degree in electronic andelectrical engineering, from Obafemi AwolowoUniversity, Nigeria, and the Ph.D. degree in electricpower engineering from Rensselaer PolytechnicInstitute, in 2000.

He works in the Electromagnetics and Super-conductivity Laboratory, General Electric GlobalResearch Center, Niskayuna, NY. Kiruba’s recentresearch activities include the development of ad-vanced superconducting generators, next-generation

MRI magnets, and other electromagnetic equipment. He is currently thelead technologist for a high-power density superconducting multimegawattgenerator for the AFRL.

Tao Zhang received the B.S. and M.S. degrees inpower and energy engineering from Shanghai JiaoTong University, China, and the Ph. D. degree in me-chanical engineering from Florida State University,in 2004.

He is currently working at the Electromag-netics and Superconductivity Laboratory, GeneralElectric Global Research Center, Niskayuna, NY.His research interests include the developmentand research on advanced cryogenic technologiesand the applications of superconductivity, e.g.,

superconducting high-power density generators, MRI magnets, and otherelectromagnetic devices. He has published over 20 peer-reviewed technicalpapers.

Antonio Caiafa received the Laurea degree in elec-trical engineering from the Politecnico di Milano,Milan, Italy, in 1999, and the M.S. and Ph.D. degreesfrom University of South Carolina, Columbia, in2003 and 2004, respectively.

In 2000, he joined the R&D group of ST Mi-croelectronics as a Simulation Software Developer.Since October 2004, he has been a Lead Engineer inthe Electronic Power Conversion Laboratory, Gen-eral Electric Research Center, Niskayuna, NY. Hismain interests are semiconductor device modeling

and characterization, soft-switching topologies, and high voltage applications.

Xianrui Huang received the B.S. degree in mechan-ical engineering from the Nanjing Aeronautical Insti-tute, Nanjing, China, in 1975, and the Ph.D. degree inmechanical engineering from the University of Wis-consin-Madison, in 1984.

His research activities are focused on the develop-ment and application of superconducting magneticresonance imaging systems and other electric de-vices. He has written over 50 technical papers andhas been awarded over 32 patents.

Minfeng Xu (M’06) received the B.S. degree in elec-trical engineering from Nanjing University, China, in1982, and the Ph.D. degree in physics from the Uni-versity of Wisconsin-Milwaukee, in 1990.

He worked in the fields of condensed matterphysics and ultra-low temperature research, and inthe design and engineering of power electronics andsuperconducting magnets for high-energy physicsand utility applications. He is currently a SeniorScientist in General Electric Global Research Center,Niskayuna, NY. His research areas include the de-

velopment of superconducting magnets and systems for magnetic resonanceimaging and for other applications.

Liang Li received the B.Sc. degree in electrical en-gineering from Huazhong University of Science andTechnology (HUST), Wuhan, China, in 1985, and theM.Eng. degree in fusion engineering from the PlasmaPhysics Institute, Chinese Academy of Science, in1988. He received the Ph.D. degree from KathliekeUniversity Leuven, Belgium, in 1998.

From 1988 to 1991, he was a Research Scientistdeveloping electromagnets for fusion research withthe Plasma Physics Institute, Chinese Academy ofScience. From 1997 to 2000, he was an Associate Re-

searcher with the National High Magnetic Field Laboratory (NHMFL), Talla-hassee, FL, engaging high field pulsed magnet development. He succeeded inthe development of a pulsed magnet reaching 78.8 T nondestructively. FromOctober 2000 to April 2007, he was a Senior Electrical Engineer with Gen-eral Electric Global Research Center (GE GRC). His research areas are pulsedmagnets, permanent magnetic (PM) and superconducting MRI, high-tempera-ture superconducting generator, and wind generator. In April 2007, he joinedHuazhong University of Science and Technology (HUST), Wuhan, China, asa Professor in the Electrical Engineering College, where he is the Director ofthe Pulsed High Magnetic Field Laboratory and the General Manager of theNational “Big Science Project” of Pulsed High Magnetic Field Facility. He isthe author and coauthor of more than 55 publications. He is the holder of threepatents.

E. T. Laskaris received the M.S. degree in mechan-ical engineering, and the Ph.D. degree in mechanicalengineering from Rensselaer Polytechnic Institute, in1971 and 1974, respectively.

He joined the General Electric (GE) Large SteamTurbine Generator Department in 1967, and trans-ferred to GE Corporate Research and Developmentin 1973. He held several technical leadership andmanagement positions related to applied research insuperconductivity and was responsible for severaltechnology developments including: a 20 MVA

superconducting generator, 0.5–1.5 T superconducting MRI magnet prototypesfor the GE Signa magnetic resonance imaging products, 0.7 and 1.2 T openMRI magnets for diagnostic and interventional applications, and the technologyof cryogen-free, conduction-cooled superconducting magnets for image-guidedtherapy.

Dr. Laskaris was elected to the National Academy of Engineers in 2004.

J. W. Bray received the B.S. degree in physicsfrom Georgia Institute of Technology, in 1970. Hereceived the M.S. and Ph.D. degrees in physicsfrom the University of Illinois, in 1971 and 1974,respectively. While at Illinois, he worked underProfessor John Bardeen on unusual mechanisms forsuperconductivity.

He joined General Electric Corporate Researchand Development after graduation in September,1974. He has held several technical and managementpositions supervising R&D on various physical

science topics, biotechnology, electronic materials processing (e.g., molecularbeam epitaxy, chemical vapor deposition), electronic devices, electronicpackaging, and high-temperature superconductivity.