Design optimization of high-temperature superconducting power

Design Optimization of High-Temperature
Superconducting Power Transformers
Thomas L. Baldwin, John I. Ykema, Cliff L. Allen, and James L. Langston
Abstract—As HTS transformers begin to move into utility and
commercial applications, engineering must optimize the designs
for AC losses and total ownership costs while meeting the performance criteria and application requirements. Transformer manufacturers use cost optimization techniques during the design phase
to minimize material costs and satisfy the utility’s loss evaluation
requirement. This paper presents the modifications necessary in
transformer design and optimization to handle high-temperature
superconductors as the winding material. These changes include
AC losses, short-circuit stresses, and cooling loads. Design results
are presented for a five-legged core, three-phase, 3.5-MVA power
transformer optimized for reduced weight and footprint space for
electrical distribution onboard ships.
Index Terms—High-temperature superconductors, optimization
methods, power transformers.
HE development of high-temperature superconducting
power apparatus has made remarkable progress during
the last several years. The advantages and potential applications of the new technology to the utility industry have been
demonstrated in laboratories and with industrial prototypes [1].
The next step leading to commercialization is developing good
design techniques and manufacturing processes. The future
success of HTS power apparatus depends on achieving lower
AC losses and reducing the total ownership costs. Optimized
design techniques play an important role in minimizing cost
and losses [2].
On the surface, transformer, design especially for small power
transformers, appears to be a simple and rudimentary task. Wire
sizes are chosen based on current ratings, core dimensions are
selected according to peak flux densities, and so forth [3]. While
it is true that transformers can be designed using simple rules,
followed by design optimization, care must be taken when migrating from copper or aluminum conductors to HTS materials.
Major differences that must be accounted for include the AC
loss mechanism, critical currents, and mechanical limits of the
Manuscript received August 5, 2002. This work was supported in part by the
U.S. Department of Defense and by the Office of Naval Research.
T. L. Baldwin is with the Center for Advanced Power Systems and the
FAMU-FSU College of Engineering, Tallahassee, FL 32310 USA (e-mail:
to[email protected]).
J. I. Ykema is with SPD Technologies Inc., L-3 Communications, Philadelphia, PA 19116 USA (e-mail: [email protected]).
C. L. Allen is with the Ship Systems, Nothrop Grumman Corporation,
Pascagoula, MS 39568 USA (e-mail: [email protected]).
J. L. Langston is with the FAMU-FSU College of Engineering, Tallahassee,
FL 32310 USA (e-mail: [email protected]).
Digital Object Identifier 10.1109/TASC.2003.813123
The aim of this paper is to consolidate considerations required
in HTS transformer winding design and optimization from various works that have been reported in the literature.
In this paper, we focus the design scope by considering a
class of medium-power, three-phase transformers that are used
in shipboard applications. Typical power ratings range from 0.5
MVA to 5.0 MVA, and the nominal primary voltages ratings are
4.16 kV and 6.6 kV at 60 Hz. The nominal secondary voltage
ratings range from 120 V to 600 V, representing the utilization voltages. The transformers are located within ship compartments where oil-filled transformers are necessarily prohibited.
Ship distribution networks use both three-leg core and five-leg
core transformers.
In this investigation we use a five-leg warm core with cylindrical windings in individual cryostats. The water-cooled iron
core operates at room temperature. The warm-bore cryostat contains the HTS windings. Bi-2223 tape windings are cooled by
two cryo-coolers for each of the three phases with conductive
metal cooling strips running axially through the coils. The windings are kept under vacuum with no liquid cryogen, which could
pose a safety issue in confined spaces. This cooling system permits the winding to operate over a 35 K to 80 K temperature
range without substantial design changes.
HTS transformer designs must be concerned about the
quenching phenomena. Coil quenching may be actively utilized to provide fault current limiting. Otherwise, the design
should not allow coil quenching under any expected operating
condition. In this design, the operation of the transformer is not
interrupted due to coil quenching by short-circuit and inrush
Every transformer must meet performance requirements
without damaging itself or the surrounding system when abnormal events occur. Such constraints are generally nonlinear
functions of the design variables. The major design constraints
for a HTS transformer are discussed next.
A. Coil Design
We selected concentric cylindrical coils for the windings. The
advantage over pancake shape windings is a higher critical current density due to a lower radial flux density of the stray magnetic field. The critical current also increases by a factor of 3.5
when the operating temperature is lowered to 35 K. Achieving
1051-8223/03$17.00 © 2003 IEEE
Fig. 1. Critical current ratio as a function of the magnetic flux density parallel
to the Bi 2223 tape surface.
Fig. 3. Transformer leakage flux of a LH winding transformer. Only the
lower half of the windings are shown. The winding and core are cylindrically
symmetrical about the core centerline.
is the ampere-turns of the coil and is the coil
length. The peak radial magnetic flux density is traditionally not
considered, but can be approximated at the end of a coil by
Fig. 2. Critical current ratio as a function of the magnetic flux density
perpendicular to the Bi 2223 tape surface. Note how rapidly the critical current
decreases with increasing flux density when compared with Fig. 1.
higher current densities effectively reduces the conductor AC
In a concentric winding, the conductor is exposed to a magnetic field oriented perpendicular to the current path. The field
, flux compocontains both parallel, , and perpendicular,
nents with reference to the tape’s surface. To obtain the needed
current density in the Bi-2223 tape, the magnetic design must
not exceed a combination of perpendicular and parallel stray
flux densities as established from Figs. 1 and 2, which graph
the tape’s characteristics [4]. For much of the winding’s length,
particularly near the axial center, the flux lines in the leakage
channel are parallel to the core axis, as shown in Fig. 3. Near
the ends of the windings, some of the flux lines turn and cross
into the windings, so that the flux component at the conductor
has a radial component.
The tape is wound with the wider edge oriented in the axial direction as shown in the insert of Fig. 3. Consequently, the coil’s
for the tape. Likewise, the coil’s radial
axial field becomes
. The peak axial flux density is found in the
field becomes
middle of the coil’s height and is approximated by
where is the width of the tape.
The conductor losses are dependent on the transport current
and the transversal magnetic fields, and are dominated by hysteresis at 60 Hz. From the self, parallel, and perpendicular magnetic fields three loss components are summed to give the total
loss. The self-field loss is given by the Norris equation for a superconductor with elliptical cross-section [5]
is the critical current of the
where is the frequency and
tape. The loss due to the magnetic field parallel to the width of
the tape is described by [6];
is the
where is the coefficient of effective conduction area,
is the full penetration field flux
tape cross-sectional area, and
have been fitted to experimental
density. Parameters and
test data. The loss due to the perpendicular magnetic field is
described by [6];
is a geometrical parameter, and
is a critical magwhere
netic field. Table I gives values for the Bi-2223 tape.
As a comparison, the current density for copper and aluminum conductors ranges from 1 to 4.5 A/mm (rms) with
losses on the order of 15 to 60 mW/A-m. To be competitive,
As faults can happen during any part of the cycle, the
worst-case transient fault current is used to determine the
mechanical stress. From the transformer standards [10],
is the open-circuit coil voltage,
- and
are the real and reactive components of the complex impedance,
is the transformer leakage inductance. The resulting
asymmetrical fault current is used to obtain the magnetic
leakage field surrounding the coils and the resulting mechanical
forces on the windings.
C. Leakage Reactance
the AC losses in HTS tapes operating at 77 K must be approximately 100 times smaller. The larger factor addresses the
coefficient of cooling for removing the heat.
B. Conductor Stresses From Large Currents
Conductors may experience large electromagnetic and mechanical forces during short-circuit faults and energization conditions. Bi-2223 tapes experience a reduction in the critical current when placed under tension as indicated in Table I. The critical current is reduced by 5% at the critical stress point [4].
The vector product of the leakage flux density and the current
flowing in a conductor results in a radial force on the conductor.
The inner concentric winding is compressed with a radial inward force, while the outer winding is expanded with an outward force. The outward radial force is transferred into the con,
ductor as a tensile hoop stress. The maximum stress,
happens in the innermost turn of the outer coil [8]
As the ac resistance of the superconducting wire is small,
the series impedance of the HTS transformer is almost entirely
made up of the leakage reactance. In power system operation
the impedance serves to limit the short-circuit current. The
impedance is specified by the utility or by industry standards.
HTS transformers will likely be designed to meet such a
constraint if it lacks active fault-current limiting technology.
The leakage reactance between any two windings can be calculated by finite element methods that directly solve Maxwell’s
equations. In practice, simplified calculations have proven
adequate, which assume that the amp-turns are uniformly
distributed along the windings, and the magnetic field only
contains axial components [11]. The leakage reactance is found
to be in terms of the winding dimensions, defined in Fig. 4, and
number of turns,
is the ampere-turns in the primary winding, is the
axial length of the primary coil, is the rms current in the outer
coil under tension, and is the diameter of the innermost conductor turn under tension. The maximum applied stress, which
may be caused by the inrush or fault current, should not approach the critical stress of the tape [9].
Whenever a transformer is re-energized, the flux change must
match the voltage according to Faraday’s law. Compounded by
the residual (or remanent) flux, the core is driven strongly into
saturation, requiring a very large excitation or inrush current.
The inrush can be many times the normal load current, and is
approximated by
for a two-coil, LH arranged transformer. For a three-coil, LHL
winding arrangement, we assume that the widths of the two lowvoltage windings are equal and that the two leakage channels
have equal gap distances,
is the residual flux density,
is the saturation flux
is the effective cross-sectional area of the core, and
is the area inside the mean turn of the primary coil. For
3% silicon steel, the remanence is close to 90% of the peak
. Most transformers designs normally choose
flux density,
in the range of 1.6 to 1.8 T, about 10% to 20% below the
saturation flux density.
D. Cooling System
The performance of the winding conductors is temperature
dependent. Generally, we can achieve reduced AC losses by
lowering the operating temperature, but we are penalized with
an increased cooling cost for removing the heat.
A comprehensive thermal design optimization is presented in
[12], which balances the compactness of the windings with the
efficiency of the cooling system. The procedure includes a heat
transfer analysis for cooling load estimate and a thermodynamic
evaluation for cryogenic refrigeration. An optimum operating
temperature exists that minimizes the overall power consumption. The optimal temperature for conduction-cooled concentric
the windings. The designs differ fundamentally in the winding
configuration, one being a LH design and the other as a LHL
design. The LHL provides a lower electrical length and reduced
leakage channel flux, resulting in lower AC conductor losses.
In addition, the hoop stress on a conductor is reduced considerably with the LHL design, whereas the LH design exceeds the
mechanical limit, and therefore not a feasible design.
Fig. 4. Relevant dimensions of the LHL concentric windings for calculating
the leakage impedance.
The success of high-temperature superconducting power
transformers depends on finding the niche opportunities
where the performance is superior to conventional oil-filled or
cast-coil power transformers to justify the higher costs. The
changes to the design optimization presented in this paper
permit tailoring HTS power transformer for special application
at the lowest possible cost. A computer-aided design program
implements a transformer optimization while incorporating
these concepts. The techniques will be expanded to include
new characteristics of HTS transformers such as fault current
At present, the techniques are used to develop theoretical designs of HTS transformers for research purposes. These techniques can be applied directly to transformer manufacturing
computer-aided design systems.
coil windings is in the range of 65 K to 75 K at the cold head
of the cryo-cooler. Cooler temperatures are justified, only if the
amount of AC loss is substantially reduced.
Transformer design optimization is a minimization of the cost
of materials and losses. The flux density, current density, mechanical force, and size limits, along with having the required
leakage impedance, add constraints to the minimization.
In classical transformer optimization, a designer uses four to
seven independent variables. Common quantities selected are
the core induction, number of turns, current densities for the
high and low windings, electrical length, and cooling channel
size. In HTS transformer designs, the current densities should
be maximized for optimal conductor utilization due to the high
cost of the conductor. We selected the winding temperature to
replace the current density as an independent variable in the
Table II presents two trial design results for a 3.5 MVA transformer. The Bi-2223 tape, characterized in Table I, is used in
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