2154 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 15, NO. 2, JUNE 2005

Experimental Determination of Dynamic Parametersfor a Superconducting Machine

S. Woodruff, M. Steurer, and H. Boenig

Abstract—Superconducting electrical machines are increasinglyof interest for diverse applications such as generators, synchronouscondensers and motors. These machines’ dynamic behavior dif-fers from that of conventional machines in significant ways due tocertain time constants and reactances being very different. Thesedifferences can present difficulties when conventional testing pro-cedures are applied. A 5 MW superconducting rotor machine de-signed and built by American Superconductor Corporation is cur-rently being tested in the Advanced Test Facility of the Center forAdvanced Power Systems at Florida State University. A variety oftest procedures are being applied to determine the machine’s dy-namic performance and the effectiveness of these tests when ap-plied to a superconducting machine is being assessed. In this paper,two means of analysing test data and extracting machine parame-ters are described.

Index Terms—Electric machine testing, parameter estimation,superconducting motors.

I. INTRODUCTION

SUPERCONDUCTING synchronous machines have beenreceiving much attention for a variety of applications, in-

cluding generators, synchronous condensers and motors. Whendeveloping such applications, it becomes necessary to predictas accurately as possible how the machine will behave in its in-tended service environment. Such predictions are particularlydifficult in the case of novel machines such as these, becausethe experience that has been developed for conventional ma-chines over decades does not yet exist. How much of the expe-rience from conventional machines applies to superconductingmachines and how to characterize and predict the new featuresnot shared with conventional machines are questions that needto be answered as swiftly as possible.

These needs are especially acute in the case of super-conducting motors to be used for marine propulsion. Thedynamic requirements of this application are stringent andlittle experimental information on the dynamic behavior ofsuperconducting machines exists to date. For these reasons,the 5 MW high temperature superconducting (HTS) rotorprototype propulsion motor developed by American Super-conductor Corporation (AMSC) [1] is currently under test atthe Advanced Test Facility of the Center for Advanced PowerSystems (CAPS) at the Florida State University.

Manuscript received October 5, 2004. This work was supported by the U.S.Office of Naval Research under Grant N0014-02-1-0623.

The authors are with the Center for Advanced Power Systems at FloridaState University, Tallahassee, FL 32310 USA (e-mail: woodruff@caps.fsu.edu;steurer@caps.fsu.edu; boenig@ctesc.net).

Digital Object Identifier 10.1109/TASC.2005.849600

Fig. 1. Block diagram of the data acquisition and feedback system at CAPSutilizing the RTDS (from [2]).

The CAPS test facility was designed to provide a sophis-ticated testing environment for the characterization of novelpower-systems hardware in a systems context [2]. The 5 MWdynamometer capability of the test facility was the first tobe commissioned and is being used to test the HTS motor.Additional capabilities now being acquired include a 5 MWcontrollable AC/DC bus which will be used to apply arbitrarybus behavior to power-systems test equipment.

Central to the systems-oriented philosophy guiding CAPS’development of the test facility are provisions for conductinghardware-in-the-loop experiments [2], in which hardware undertest in the test facility is made to operate as part of a largersystem implemented in software on a real-time digital simulator(RTDS) [3]. As shown in Fig. 1, sensor signals from the hard-ware are passed to the simulator, which computes the behaviorof the simulated system in response to hardware dynamics andsends control signals back to the hardware reflecting the sim-ulated system’s effect on the hardware. Ongoing tests for theHTS motor at CAPS include both traditional tests and hard-ware-in-the-loop experiments.

In order to extract the maximum possible amount of informa-tion from the data recorded during testing, parameter-estimationtechniques are being adapted and developed for application totest results from the CAPS facility. Parameter estimation forelectrical machines is an active area of research [4]–[7]. In thecase of the HTS motor, traditional power-systems approachesto parameter determination for conventional synchronousmachines need to be evaluated in light of the differences indynamics between superconducting and conventional syn-chronous machines. Non-traditional approaches employingparameter-estimation technology from other areas also need tobe considered.

1051-8223/$20.00 © 2005 IEEE

WOODRUFF et al.: EXPERIMENTAL DETERMINATION OF DYNAMIC PARAMETERS FOR SUPERCONDUCTING MACHINE 2155

The present paper describes two approaches for parameterdetermination being examined at CAPS. After a brief descrip-tion of the testing and data acquisition facilities at CAPS, ananalysis of the short-circuit data obtained during factory testing[1] of the HTS motor is presented in which a traditional ana-lytical expression for the short circuit current is fit to observeddata to yield good results for motor parameters. A more numeri-cally oriented parameter-estimation approach is then discussed,in which a gradient-search optimization technique is used to fitmodel predictions to observed data. While more complex, thisapproach may be applied to any test (though accurate parameterestimation requires the parameter in question measurably affectthe results of the test) and permits observational data to be fittedto new machine models when traditional models prove inade-quate.

II. TESTING AND DATA ACQUISITION

CAPS’ test facility includes two 2.5 MW GE-Toshiba motorsand drives. The two motors may be operated against each otheras motor and dynamometer for experimentation, or the two to-gether may provide a 5 MW dynamic load to a test motor suchas the HTS motor. The dynamometer machines are controlledeither from the test facility distributed digital control system orfrom the RTDS.

Data acquisition is performed with several different sys-tems as appropriate for different signal bandwidths. The RTDSrecords signals with a bandwidth from DC to 6.7 kHz on dozensof 16-bit analog I/O channels. Data is taken in million-samplesnapshots on each RTDS processing module, or rack. The largecomputational capability of the RTDS provides opportunitiesfor doing extensive real-time signal processing.

Fig. 1 includes signal paths between the test equipment andthe RTDS. Optical analog-to-digital cards (OADC) providesimultaneous 16-bit sampling of 6 input channels without mul-tiplexing, with a fiber-optic link between the cards (mountednext to PLC’s on the test floor) and the simulator in a room150 feet away. Approximately ten fixed and portable OADCcards are used throughout the test facility. Digital-to-analogcards (FDAC) send control signals from the RTDS to the threevariable speed drives ( , , and ).

Voltages at the motor terminals and the 4.16 kV bus aresensed with Schaffner MD200 high voltage 7 kV differentialprobes with an accuracy of better than 2% and a bandwidth ofDC to 50 MHz. Currents at the motor terminals and the testmotor input transformer are measured to an accuracy of betterthan 0.2% with PEM CWT6LFR Rogowski type transducers(bandwidth of 0.3 Hz–3 MHz, range 0–1200 ).

Torque is measured by strain gauges on the shaft between thetest motor and the dynamometer machines. The strain gaugeshave been calibrated in situ to achieve an accuracy of 1%. Speedis measured with a resolver mounted on the unoccupied end of

’s shaft. These signals, as well as various outputs from thedrive control systems, are relayed to the RTDS by OADC cards.

National Instruments data acquisition cards record, everysecond, 30 temperature signals from sensors embedded in thetest motor stator winding. A second dedicated data acquisition

Fig. 2. Best fit of analytical fault-current expression to experimental dataassuming constant rotor speed.

system records temperatures from the HTS rotor every 3 sec-onds. Finally, a Bentley Nevada vibration monitoring system isused to detect undesirable vibration levels that may occur.

Tests being performed include steady-state running at variouspower levels, tests for parameter determination and dynamictests. The parameter-determination tests include a selection oftests used in the past for characterizing the behavior of conven-tional machines; comparison of the results from these tests willpermit good estimates of parameter values as well as an evalu-ation of the appropriateness of each test for a superconductingmachine. The extensive series of dynamic tests will characterizethe HTS motor under dynamic conditions that mimic maneuversat sea, that focus on the potential for ac losses and heating inthe rotor when the motor is disturbed dynamically and mappingout the dynamic performance characteristics of the machine. In-cluded will be tests involving torque and speed variations at dif-ferent rates, speed reversals and step-changes in speed, torqueand current.

III. SHORT-CIRCUIT ANALYSIS

Factory tests conducted prior to the HTS motor tests at CAPSincluded a short-circuit test reported in [1]. The current wave-form from one of the stator phases is shown in Fig. 2. The tra-ditional approach for estimating quantities such as the transientand subtransient reactances and the respective time constantsfrom a short-circuit test involves examining the degree to whicheach peak in the waveform is reduced in amplitude over the pre-vious one. In this case, the system reaches a steady state tooquickly for an accurate determination of parameters to be madein this fashion.

However, a more detailed analysis leads to better results. Ananalytical expression for the stator short-circuit current from asynchronous machines textbook [8] was employed to fit the ob-served current waveform as accurately as possible. The result ofthis calculation is also shown in Fig. 2. Although the fit initiallyis fairly good, the waveform deviates from the measured valuesin the later portion of the test record.

Careful examination of the test data reveals that the frequencyof the waveform (and thus the speed of the machine) variedslightly during the course of the test. Taking this speed variationinto account leads to the fit shown in Fig. 3, where the analyticalexpression is seen to fit the observed waveform quite well.

The machine parameters determined through the fit in Fig. 4are compared in Table I with the values from [1]. The values arenearly identical, except for the armature time constant, whichcomes out slightly higher in the present analysis. This simple

2156 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 15, NO. 2, JUNE 2005

Fig. 3. Best fit of analytical fault-current expression to experimental data withrotor speed varying as described in the text.

analysis is thus seen to be quite effective in extracting a greatdeal of information about the HTS motor.

IV. GRADIENT-SEARCH PARAMETER ESTIMATION

A second approach to analysing test data is being developedwhich involves minimizing the error between observed resultsand those computed numerically with a model. Parameter esti-mation involving optimizations, such as least-squares methods,are quite common in many areas. In the present application, themotor terminal voltage waveforms measured during a test areapplied to a standard d-q frame synchronous machine model andthe computed stator current waveforms are compared with thecurrent waveforms measured during the test. The mean-squareerror between the waveforms is used as a measure of the dis-crepancy between them and an optimization scheme is used toadjust the motor parameters in the model to minimize this error.

The computation of the model results is performed using theFortran package DASSL [9] for solving differential-algebraicequations [10]. Its use eliminates the need for putting theequations in the standard form required for most ordinary-dif-ferential equation solvers and it employs variable-order,variable-time-step integration algorithms. The optimizationprogram calls DASSL as a subroutine.

The minimization strategy employed here is based on acommon gradient-based line-search algorithm (see, for ex-ample, [11]). Starting at an initial set of parameter values, thegradient of the objective function (the mean-square error be-tween computed and observed current waveforms) is computedand a search for the minimum value of the objective functionis carried out along a line in the direction of the (negative)gradient. Once the minimum value is found, the process startsover at this new point with a new gradient computation. Thistechnique has been successfully used in a number of power-sys-tems applications for optimizing controllers and power-systemscomponents [12], [13].

Sample results of this parameter estimation procedure areshown in Table II. In this case, the “observed” data, for a short-circuit test, is computed from the model, rather than taken froma hardware test. The parameter values shown are the ratios of thetrial machine parameters (in this case the mutual inductance be-tween the field winding and the electromagnetically active rotorshield and the shield self-inductance) to the actual values usedin the computation of the “observed” data. As seen in the firstline of the table, the process is initiated with these parameters20% too low and 20% too high, respectively. All other motorparameters are held constant.

TABLE ISHORT-CIRCUIT RESULTS

TABLE IIGRADIENT-SEARCH RESULTS

The first line search takes two iterations and succeeds in re-ducing the objective function nearly by a factor of ten. Thesecond line search starts with the final set of parameters fromthe first line search and takes five iterations to reduce the mean-square error only by a factor of about three. It sets things up forthe third line search, though, which reduces the error by a factorof 20 in two iterations. The slight increase in the error from thefirst to second iteration indicates more tuning the of step sizeand tolerances is needed. After that, succeeding line searchesmake little difference and the procedure has reached the limitof its performance with the given tolerances. The final values ofthe parameters are both close to one, indicating the procedurehas recovered the parameter values used in the computation ofthe original “observed” data.

WOODRUFF et al.: EXPERIMENTAL DETERMINATION OF DYNAMIC PARAMETERS FOR SUPERCONDUCTING MACHINE 2157

The procedure thus successfully extracts these subtransientparameters in a few iterations of the optimization scheme. It hasalso been able to extract the field inductance, which, becauseit is so large in a superconducting machine, is very difficult todetermine experimentally.

The gradient-search approach has been applied to CAPS testdata (a speed ramp, as a short-circuit test has not yet been con-ducted at CAPS) and has successfully recovered the stator in-ductance and stator-field mutual inductance, with values veryclose to those determined by AMSC. However, as these valuesmay easily be computed with steady-state RMS voltage and cur-rent values, the value of this approach is in its capability to de-termine transient and subtransient parameters, as shown above.So far, we have not been able to reliably extract such parametersfrom the speed ramp data, but expect to be able to derive themfrom data from short-circuit tests (and possibly from data fromother tests), when they are performed at CAPS.

While certainly more complex than the method used in Sec-tion III, approaches like this one may be applied to any test andemploy any model. Not being limited to short-circuit tests (orother cases where an analytical solution is available) means pa-rameters may be extracted from any test data sufficiently richin dynamics that the parameters of interest are well representedin the data. Being able to experiment with new models (particu-larly nonlinear models) means that if traditional models do notadequately predict the behavior of the HTS motor, new modelsmay be developed and validated.

V. CONCLUSIONS

Two approaches for analysing HTS motor test data are pre-sented here. The detailed fitting of the short-circuit test data tothe analytical result for the stator current led to values in ex-cellent agreement with the values from [1] determined from fi-nite-element calculations and from other tests.

The gradient-search approach is more complex but is morewidely applicable. It may be applied to data from any test, withthe quality of results depending on the dynamic content of the

test. It may also be used in conjunction with any model, whethera traditional motor model or a model with new components tocapture uniquely HTS motor dynamics. The results describedhere using this technique are promising and it will be the subjectof further development.

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