130132222 measurement of three phase transformer derating and reactive power demand under nonlinear...
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7/29/2019 130132222 Measurement of Three Phase Transformer Derating and Reactive Power Demand Under Nonlinear Loading Conditions
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IEEE TRANSACTIONS ON POWER DELIVERY 1
Measurement of Three-Phase TransformerDerating and Reactive Power Demand
under Nonlinear Loading ConditionsEwald F. Fuchs, Fellow, IEEE, Dingsheng Lin, and Jonas Martynaitis
AbstractThe measurement of real and apparent power der-ating of three-phase transformers is important for transformersfeeding nonlinear loads. This paper presents a new digital data-ac-quisition method for measuring derating and reactive power de-mand of three-phase transformers under full or partial load con-ditions. The accuracy requirements of the instruments employed(potential, current transformers, shunts, voltage dividers, optocou-plers volt- and current meters) are addressed. Application exam-ples demonstrate the usefulness of this new digital data-acquisitionmethod.
Index TermsHarmonics, nonsinusoidal operation, reactivepower demand, real and apparent power derating, transformerlosses.
I. INTRODUCTION
MEASURING the real and apparent power derating of
three-phase transformers is desirable because additional
losses due to power quality problems (e.g., harmonics, dc exci-
tation) can be readily limited before any significant damage due
to additional temperature rises occurs.
Measuring transformer losses from the input power minus the
output power in real time is inaccurate because the losses are thedifference of twolarge values; this approach results in maximum
errors in the losses of more than 60% for high-efficiency
% transformers [1]. The usually employed indirect method
consisting of no-load (iron-core loss) and short-circuit (copper
loss) tests [2] cannot be performed on-line while the transformer
is partially or fully loaded.
IEEE Recommended Practice C57.110 computes the trans-
former derating based on for various harmonics , which is
derived from the dc winding resistance and the rated load loss
[3]. Kelly et al. [4] describe an improved measuring technique of
the equivalent effective resistance as a function of frequency
of single-phase transformers, which allows the direct calcula-
tion of transformer loss at harmonic frequencies from
Hz up to 100 kHz. This equivalent effective resistance takes into
Manuscript received April 23, 2004; revised June 9, 2005. This work wassupported in part by the U. S. Department of Energy, Office of Energy Manage-ment, under Contract 19X-SK205V, and in part by the EPRI under Contract No.2951-07 and 4887-01. Paper no. TPWRD-00187-2004.
E. F. Fuchs is with the University of Colorado, Boulder, CO 80309 USA(e-mail: [email protected]).
D. Lin is with Ansoft Corporation, Pittsburgh, PA 15219 USA (e-mail:[email protected]).
J. Martynaitis is with the Department of Electrical and Lighting Engineering,Kaunas University of Technology, Kaunas LT-44244, Lithuania (e-mail:[email protected]).
Digital Object Identifier 10.1109/TPWRD.2005.858744
account the total lossesof the transformer: the copper losses plus
the iron-core losses. Based on the fact that the iron-core losses
do not depend on harmonic currents, but depend on harmonic
voltages (amplitudes and phase shifts) [5], the total losses deter-
mined by [4] are not accurate. In addition, temperature-depen-
dent operating conditions cannot be considered in [4]. Mocci
[6] and Arri et al. [7] present an analog measurement circuit
to directly measure the total losses for single- and ungrounded
three-phase transformers. However, employment of many PTsand CTs in the three-phase transformer measuring circuits [7]
decreases the measurement accuracy.
This paper presents a direct method for measuring the
derating of three-phase transformers while transformers are
operating at any load and any arbitrary conditions. The mea-
suring circuit is based on potential transformers (PT) current
transformers (CT), shunts, voltage dividers or Hall sensors
[8], A/D converter and computer (microprocessor). Using a
computer-aided testing (CAT) program [1], [9] losses, effi-
ciency, harmonics, derating and wave shapes of all voltages and
currents can be monitored within a fraction of a second. The
maximum errors in the losses are acceptably small and depend
mainly upon the accuracy of the sensors used.
II. APPROACH
A. Three-Phase Transformers in or Y-Y Ungrounded
Connection
For - or ungrounded Y-Y connected three-phase trans-
formers (see Figs. 1, and 2 for using shunts, voltage dividers
and optocouplers), one obtains with the application of the two-
wattmeter method at the input and output terminals by inspec-
tion
(1)
The term represents
the instantaneous iron-core loss, and
is the instantaneous copper loss.
B. Three-Phase Transformers in - Connection
Fig. 3 illustrates the application of the digital data-acquisition
method to a - connected transformer bank.
0885-8977/$20.00 2006 IEEE
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2 IEEE TRANSACTIONS ON POWER DELIVERY
Fig. 1. Eight-channel CAT circuit for accurate - or ungrounded Y-Yconnected three-phase transformer loss monitoring using PTs and CTs.
Fig. 2. Eight-channel CAT circuit for accurate - or ungrounded Y-Yconnected three-phase transformer loss monitoring using shunts, voltage
dividers, and optocouplers.
Forungrounded - connectedthree-phasetransformers, the
currents of the Y side must be referred to the line currents of the
side, as shown in Fig. 3. The lossof the transformer isgiven by
(2a)
Fig. 3. Eight-channel CAT circuit for accurate -Y three-phase transformerloss monitoring using PTs and CTs.
where and are input line currents of phases and
, respectively; and are the
two-wattmeter secondary currents; and are the output
line-to-neutral voltages of phases and respectively.
Because the neutral of the Y-connected secondary winding
(N) is not accessible, the secondary phase voltages are measured
referred to the neutral of the Y-connected PTs (see Fig. 3).
This does not affect the accuracy of loss measurement, whichcan be demonstrated below. The output power is
(2b)
where denotes the neutral of the Y-connected secondary
winding. Because , the measured output power
referred to the neutral of PTs is the same as that referred to
the neutral of the secondary winding.
III. ACCURACY REQUIREMENTS FOR INSTRUMENTS
The efficiencies of high-power electrical apparatus such
as single- and three-phase transformers in the kVA and MVA
ranges are 97% or higher. For a 15 kVA three-phase transformer
with an efficiency of 97.02% at rated operation, the total losses
are W, copper and iron-core losses
W and W at V and A,respectively, as listed in Table VII(a).
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FUCHS et al.: THREE-PHASE TRANSFORMER DERATING AND REACTIVE POWER DEMAND 3
TABLE IINSTRUMENTS AND THEIR ERROR LIMITS FOR FIGS. 1 AND 2
The determination of the losses from voltage and current dif-
ferences as described in Fig. 1-where differences are calibrated-
greatly reduces the maximum error in the loss measurement.
The series voltage drop and exciting current at rated operation
referred to the primary of the 15 kVA, 240 V/240 V three-phase
transformer are V, A, re-
spectively (Table VII(a)). The instruments and their error limits
are listed in Table I. In Table I, ,
and stand for the relevant calibrated voltmeters and am-
meters. Because all voltage and current signals are sampled via
PTs, CTs (or optocouplers) and current shunts, the error limits
for all instruments are equal to the product of the actually mea-
sured values and their relative error limits, instead of full-scale
errors, as shown in Table I. All error limits are referred to the
meter side.
In Fig. 2, the voltage divider combined with
an optocoupler emulates the function of a PT without
hysteresis. The optocoupler can alter the amplitude of a signaland provide isolation without affecting the phase shift of the
signal as it is corrupted by PTs. The current shunt and
optocouplers emulate that of a CT without
hysteresis and parasitic phase shift. The prime indicates that
is about of the same magnitude as , this is accomplished
by the adjustment of the amplifier gain(s) of the optocoupler(s).
The line-to-line voltage is measured with the maximum error
of (taking into account the maximum errors of and volt-
meter)
(3)
The difference current is measured with the maximum error of
(4)
Therefore, the loss component in (1) is measured
with the maximum error of
(5)
TABLE IIMEASURED IRON-CORE AND COPPER LOSSES OF 9 kVA YY-CONNECTED
TRANSFORMER
The series voltage drop is measured with the maximum error
of
(6)
The output current is measured with the maximum error of
(7)
and the loss component in (1) is measured with
the maximum error of
(8)
Thus, the total loss is measured with the maximum error of
% (9)
The above error analysis employs PTs and CTs. If these de-
vices generate too-large errors because of hysteresis, voltage di-
viders and shunts combined with optocouplers can be used, as
indicated in Fig. 2, [10]. A similar error analysis using shunts,
dividers and optocouplers leads to the same maximum error in
the directly measured losses, provided the same standard max-
imum errors (0.1%) of Table I are assumed. The factor 2 in (9) is
employed because loss components in (5) and (8) are only halfof those in (1).
IV. COMPARISON OF DIRECTLY MEASURED LOSSES WITH
RESULTS OF NO-LOAD AND SHORT-CIRCUIT TESTS
A computer-aided testing program (CATEA) [9] is used to
monitor the iron-core and copper losses of three-phase trans-
formers. The nameplate data of the tested transformers are given
in the Appendix.
The results of the on-line measurement of the iron-core and
copper losses for a Y-Y connected 9 kVA three-phase trans-
former (consisting of three 3 kVA single-phase transformers,
Appendix A.1) are given in Table II for sinusoidal rated line-to-line voltages of 416 V, where the direct (on-line) measurement
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4 IEEE TRANSACTIONS ON POWER DELIVERY
TABLE IIIMEASURED DATA OF 4.5 kVA TRANSFORMER BANK #1
data are compared with those of the indirect (separate open-cir-
cuit and short-circuit tests) method.
The iron-core loss of the indirect method is larger than that
of the direct method because the induced voltage of the former
is larger than that of the latter. The copper loss of the indirectmethod is smaller than that of the direct method because the
input current of the former (which is nearly the same as the
output current) is smaller than that of the latter.
V. APPLICATIONS
A. 4.5-kVA Three-Phase Transformer Bank #1 Feeding
Full-Wave Rectifier
A 4.5 kVA, 240 V/240 V, - -connected three-phase trans-
former (Fig. 1) consisting of three single-phase transformers
(bank #1, Appendix A.2) is used to feed a full-wave diode rec-
tifier (see Appendix A.5) with an LC filter connected across the
resistive load (see Figs. 6-5 of [11]). In Table III, measured dataare compared with those of linear load condition. The measured
wave shapes of input voltage , exciting current ,
series voltage drop and output current of phase
A are shown in Figs. 4(a), (b) for linear and nonlinear load con-
ditions. The total harmonic distortion -factor and har-
monic components of the output current are listed in Table IV.
Table III compares measured data and shows that the trans-
former is operated at nonlinear load with about the same losses
occurring at linear load (261.3 W). With the apparent power de-
rating definition
(10)
the derating at the nonlinear load of Table III is 99%. The real
power delivered to the nonlinear load is 91.4% of that supplied
at linear load.
B. 4.5 kVA Three-Phase Transformer Bank #2 Supplying
Power to Six-Step Inverter
A 4.5 kVA transformer bank #2 (Appendix A.3) supplies
power to a half-controlled six-step inverter (Appendix A.6),
which in turn powers a three-phase induction motor. The motor
is controlled by adjusting the output current and frequency of
the inverter. The transformer is operated at rated loss at variousmotor speeds. Rated loss of bank #2 is determined by a linear
(a)
(b)
Fig. 4 (a) Measured wave shapes of 4.5 kVA three-phase transformer bank #1feeding linear load (see rms values of Tables III and IV). (b) Measured wave
shapes of 4.5 kVA three-phase transformer bank #1 feeding full-wave dioderectifier load (see rms values of Tables III and IV).
TABLE IVOUTPUT CURRENT HARMONIC COMPONENTS, ,
AND -FACTOR [Fig. 4(b)]
(resistive) load at rated operation. The iron-core and copper
losses are measured separately and are listed in Table V(a).
Measured wave shapes of input voltage, exciting current, se-
ries voltage drop and output current of phase A are shown in
Figs. 5(a), (b) for linear and nonlinear conditions. The output
current includes both odd and even harmonics due to the half-
controlled input rectifier of the six-step inverter. Dominant har-
monics of input voltage and output current are listed for different
motor speeds in Table V(b). The total harmonic distortion of
the input voltage and output current as well as the -factor are
listed in Table V(c) for the speed conditions of Tables V(a), (b).
C. 15 kVA Three-Phase Transformer Supplying Power to
Resonant Rectifier
A 15 kVA, 240 V/240 V, - connected three-phase trans-
former (Appendix A.4) is used to supply power to a resonant
rectifier [12] (Appendix A.7). The transformer is operated withthe resonant rectifier load at the same total loss generated by a
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FUCHS et al.: THREE-PHASE TRANSFORMER DERATING AND REACTIVE POWER DEMAND 5
TABLE V(a)MEASURED IRON-CORE AND COPPER LOSSES OF 4.5 kVA, - CONNECTED
TRANSFORMER BANK #2 FEEDING A SIX-STEP INVERTER AT VARIOUSMOTOR SPEEDS [FIG. 5(b)]
(a)
(b)
Fig. 5 (a) Measured wave shapes of 4.5 kVA three-phase transformer bank #2
feeding linear load [see rms values of Tables V(a), (b), and (c)]. (b) Measuredwave shapesof 4.5 kVA three-phasetransformerbank #2 feeding half-controlledsix-step inverter [see rms values of Tables V(a), and (b), (c)].
three-phase linear (resistive) load. Measured data are compared
in Table VI. Measured wave shapes of input voltage, exciting
current, series voltage drop and output current of phase A are de-
picted in Figs. 6(a), (b). The fundamental phase shift between
output transformer line-to-line voltage and phase current
of the resonant rectifier is 67.33 , and the output displace-
ment factor (within transformer phase) is therefore
. The fundamental phase shift between outputline-to-line voltage and phase current for the linear resistive
TABLE V(b)INPUT VOLTAGE (IN rms VOLTS) AND OUTPUT CURRENT (IN rms AMPERES)
HARMONICS OF PHASE A [Figs. 5(a) AND (b)]
TABLE V(c)
MEASURED THD-VALUES AND -FACTOR [FIG. 5(a) AND (b)]
load is 30.95 , and the output displacement factor (within trans-
former phase) is, therefore, . Note that
the wave shapes of the output currents of Figs. 6(a), (b) are about
sinusoidal.
If the transformer with the resonant rectifier load is operated
(see Table VI) at about the same loss as linear load (233.9 W),
the output current of the transformer with the resonant recti-
fier load is 26.94 A, which corresponds to the copper loss of
192.2 W ( W W). Therefore, the transformer ap-
parent power derating of the transformer for the nonlinear load
is 99.7%. The real power supplied to the nonlinear load is 78.5%
of that of the linear load.
D. 15 kVA Three-Phase Transformer Bank Absorbing Power
From a PWM Inverter
The same transformer of Section V-C absorbs power from
a PWM inverter [12] (Appendix A.8) and supplies power to a
resistive load (case #1) and to a utility system (case #2). The
transformer losses are also measured when supplying a linear
resistive load fed from sinusoidal power supply (linear load).All measured data are compared in Table VII(a).
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6 IEEE TRANSACTIONS ON POWER DELIVERY
(a)
(b)
Fig. 6 (a) Measured wave shapes of 15 kVA three-phase transformer feeding
linear load (see rms values of Table VI). (b) Measured wave shapes of 15 kVAthree-phase transformer feeding resonant rectifier (see rms values of Table VI).
TABLE VIMEASURED DATA OF 15 kVA THREE-PHASE TRANSFORMER WITH
RESONANT RECTIFIER LOAD [FIG. 6(a) AND (b)]
Measured wave shapes of input voltage, exciting current, se-
ries voltage drop and output current of phase A are shown in
Figs. 7(a)(c). The total harmonic distortion -factor
and harmonic amplitudes of the transformer output current are
listed in Table VII(b).
Fig. 8 summarizes the total harmonic distortion , ap-
parent power (kVA) derating, and real power (kW) derating for
uncontrolled (a, b), half-controlled (c) and controlled (d, e) con-
verter loads of transformers. In particular the graphs of Fig. 8
can be identified [11] as follows:
a) 25 kVA single-phase pole transformer [13], [17], [14],[18], [15] feeding uncontrolled full wave rectifier load;
TABLE VII(a)MEASURED DATA OF 15 kVA THREE-PHASE TRANSFORMER CONNECTED
TO PWM INVERTER [FIG. 7(a)(c)]
b) 4.5 kVA three-phase transformer feeding uncontrolled full
wave rectifier load;
c) 4.5 kVA three-phase transformer feeding half-controlled
rectifier load;
d) 15 kVA three-phase transformer absorbing power fromPWM inverter (14 kW);
e) 15 kVA three-phase transformer feeding resonant rectifier
load (8 kW).
VI. DISCUSSION OF RESULTS AND CONCLUSIONS
A. Discussion of Results
A new approach for the measurement of the derating of three-
phase transformers has been described and applied under non-
sinusoidal operation. It extends the measurement approach of
single-phase transformers [1], [9], [12], [13], [17], [14], [18],
[15] to three-phase transformers [11], [15], [16].The apparent power (kVA) derating, (10), of three-phase
transformers is not greatly affected by the . Even for
values of about 70%, derating is about 99%.
The real power (kW) derating is greatly affected (see Fig. 8)
by the current wave shape generated by solid-state converters, in
particular by the phase shift of the fundamental current compo-
nent. Therefore, inverters and rectifiers should be designed such
that they supply and draw power, respectively, at a displacement
(power) factor of about 1.
Three-phase transformers have similar derating properties as
single-phase transformers [1], [9], [12], [13], [17], [14], [18],
[15].The maximum error in the directly measured losses is about
15%, which compares favorably with the maximum error of
more than60% [1] for loss measurement based on the difference
between input and output powers as applied to high-efficiency
% transformers.
Transformers of the same type may have significantly dif-
ferent iron-core losses as measured in Table III (261.3 W) and
Table V(a) (220.6 W).
Small transformers (kVA-range) have relatively small wire
cross-sections resulting in small skin-effect losses. Large trans-
formers (MW-range) have aluminum secondary windings with
relatively large wire cross-sections resulting in relatively large
skin-effect losses. For this reason substation transformers canbe expected to have larger apparent power derating than the
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FUCHS et al.: THREE-PHASE TRANSFORMER DERATING AND REACTIVE POWER DEMAND 7
(a)
(b)
(c)
Fig. 7(a) Measured wave shapes of 15 kVA three-phase transformer feedinglinear load [see rms values of Tables VII(a) AND (b)]. (b) Measured wave
shapes of 15 kVA three-phase transformer fed by a PWM inverter (case #1)[see rms values of Tables VII(a) AND (b)]. (c) Measured wave shapes of 15kVA three-phase transformer fed by a PWM inverter (case #2) [see rms valuesof Tables VII(a) AND (b)].
TABLE VII(b)OUTPUT CURRENT HARMONICS, AND -FACTOR [FIG. 7(b) AND (c)]
ones measured in this paper. Unfortunately, transformers in the
MW-range cannot be operated in a laboratory under real-life
conditions. Therefore, it is recommended that utilities sponsor
the application of the method of this paper and permit on-sitemeasurements.
Fig. 8. Total harmonic distortion of current , apparent power (kVA)derating, and real power (kW) derating for uncontrolled (a, b), half-controlled(c) and controlled (d, e) converter loads.
B. Comparison With Existing Techniques
The maximum error in the directly measured losses is about
15% (using potential and current transformers), which compares
favorably with the maximum error of more than 60% [1] (em-
ploying shunts and voltage dividers) for loss measurement based
on the difference between input and output powers as applied to
high-efficiency % transformers.
The technique of [4] uses the pre-measured transformer ef-
fective resistance as a function of frequency to calculate
transformer total losses for various harmonic currents. This
method can be classified as an indirect method because the
transformer losses are obtained by computation, instead of
direct measurement. In addition, the approach of [4] neglects
the fact that the iron-core losses are a function of the harmonic
phase shift [5], in other words the values are not constantfor any given harmonic current amplitude but vary as a function
of the harmonic voltage amplitude and phase shift as well.
Finally, temperature-dependent operating conditions, for ex-
ample, cannot be considered in [4]. For the above reasons, the
method of [4] must be validated by some direct measurements,
such as the method presented in this paper.
The method of Mocci [6] and Arri et al. [7] has not been prac-
tically applied to three-phase transformers. The presented mea-
surement circuit for three-phase transformers [7] uses too many
instrument transformers (e.g., 9 CTs and 9 PTs), and therefore,
the measured results will be not as accurate as those based on
the measurement circuits of this paper, where only 4 CTs and 5PTs are used as shown in Fig. 3.
APPENDIX
1) 9 kVA Three-Phase Transformer Bank: Y-Y connected
three-phase transformer bank with V of rated line-to-
linevoltagesconsistsofthreesingle-phasetransformers.Thetype
numbers of the threesingle-phase transformers are J7065, J7610,
and J7065 (bank #1), and the nameplate data of which are:
Powerformer Dry-type transformer
CAT. no.: 211-101, 3 kVA, single-phase, 60 Hz;
High voltage 240/480 V; Low voltage 120/240 V.
2) 4.5 kVA Three-Phase Transformer Bank #1: Single-phase transformers with the nameplate data listed in A.1 are
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8 IEEE TRANSACTIONS ON POWER DELIVERY
used in this bank #1 and are connected in such way that the rated
line-to-line voltages are V. Only the two high-voltage
windings of each single-phase transformer are employed as
primary and secondary, and the rated apparent power of the
three-phase transformer bank is therefore 4.5 kVA.
3) 4.5 kVA Three-Phase Transformer Bank #2: Single-
phase transformers with the nameplate data listed in A.1 havingthe type numbers J7605, J7606, and J7605 are used in this bank
#2, and are connected in such way that the rated line-to-line
voltages are V. Only the two high-voltage windings
of each single-phase transformer are employed as primary and
secondary, and the rated apparent power of the three-phase
transformer bank is therefore 4.5 kVA.
4) 15 kVA Three-Phase Transformer Bank: 15 kVA,
- connected bank consists of three 5 kVA trans-
formers. The original rated apparent power of the single-phase
units is 10 kVA. The two high-voltage windings were used
as primary and secondary, and the rated power of the bank is
therefore 15 kVA. The nameplate data are:
Westinghouse Type: EP transformer
Frame no.: 179, 10 kVA, single-phase, 60 Hz;
High voltage: V Low voltage: V.
5) Three-Phase Diode Bridge: A,
V.
6) Half-Controlled Three-Phase Six-Step Inverter: General
Electric AC adjustable frequency drive
Model no.: 6VGAW2007CI
Input: Output:
Volts: 230 HP: 7.5, kVA: 8.8;
Hertz: 50/60 Volts: variable;
Amps: 22 Hz: 660;
Phase 3 Amps ac: variable;
Phase 3.
7) Controlled Three-Phase Resonant Rectifier
[12]: University of Colorado
ID no.: 5484
Input: Output:
Volts: 340600 ac 20 kW;
Hertz: 1260 Volts: 380 dc;
Amps: 45 Amps: 60 dc.
Phase 3
8) Controlled Three-Phase PWM Inverter [12]: University
of Colorado
ID no.: 5485
Input: Output:
Volts: 360 dc 20 kW;
Amps: 70 dc Volts: 240 ac;
Amps: 80 ac;
Power factor: 0.7 (lead) to 1.0 p.u.;
Hertz: 50/60.
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[18] E. F. Fuchs, D. Yildirim, and W. M. Grady, Corrections to Measure-ments of eddy-current loss coefficient - derating of single-phasetransformers, and comparison with K-factor approach, IEEE Trans.Power Del., vol. 15, no. 4, p. 1357, Oct. 2000.
Ewald F. Fuchs (F90) received the Dipl.-Ing. degree in electrical engineeringfrom the University of Stuttgart, Stuttgart, Germany, and the Ph.D. degree inelectrical engineering from the University of Colorado, Boulder, in 1967 and1970, respectively.
Currently, he is a Professor of Electrical Engineering at the Universityof Colorado.
Dingsheng Lin received the B.Sc. and M.Sc. degrees in electrical engineering
from the Shanghai University of Technology, Shanghai, China, in 1982 and1987, respectively.
Currently, he is a Senior Research and Development Engineer with Ansoft
Corporation, Pittsburgh, PA. He was promoted to Associate Professor of Elec-trical Engineering with Shanghai University of Technology in 1991. His maininterests are the design and optimization techniques of electrical machines andelectromagnetic field calculation.
Mr. Lin received the third prize of the Chinese National Award of Scienceand Technology in 1987, and two second prizes of the Shanghai City Award ofScience and Technology in 1986 and 1989.
Jonas Martynaitis received the Dipl.-Eng. degree from Kaunas PolytechnicInstitute, Lithuania, in 1969, and the Ph.D. degree in lighting engineering andelectronics from the Moscow Institute of Energy, Moscow, Russia, in 1980.
Currently, he is an Associate Professor with the Department of Electrical En-
gineering, Kaunas University of Technology, Lithuania. During the 1980-1981academic year, he was with the University of Colorado at Boulder performingresearch.