3038
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 8, AUGUST 2008
Control of High-Speed Solid-Rotor Synchronous
Reluctance Motor/Generator for Flywheel-Based
Uninterruptible Power Supplies
Jae-Do Park, Member, IEEE, Claude Kalev, Member, IEEE, and Heath F. Hofmann, Member, IEEE
Abstract—A hybrid controller, consisting of a model-based feedforward controller and a proportional–integral feedback compensator, for a solid-rotor synchronous reluctance motor/generator
in a high-speed flywheel-based uninterruptible power supply application is proposed in this paper. The feedforward controller
takes most of the control output of the current regulator based
on the machine model, and the PI controllers compensate the
possible inaccuracies of the model to improve the performance
and robustness of the complete control system. The machine
current tracking error caused by parameter inaccuracy in the
model-based controller is mathematically analyzed and utilized to
dynamically compensate the estimated flux linkage to eliminate
the steady-state error in current regulation. Stability analysis is
also presented, and it can be seen that the regulation performance
and robustness of the system are improved by the proposed hybrid
controller. Simulation and experimental results consisting of a
flywheel energy storage system validates the performance of the
controller.
Index Terms—Flywheel, model-based control, synchronous
reluctance motor, uninterruptible power supply (UPS).
N OMENCLATURE
∆irs
∆λra
∆vsr
[Lr ]
[Ls ]
[M ]
[Rr ]
J
ωre
A
λr
r
λr
s
ĩr
s
ṽsr
irs
Current error vector in rotor reference frame.
Flux linkage estimation error vector in rotor reference
frame.
Voltage command error vector
in rotor reference frame.
Lrd
0
Rotor inductance matrix
.
0
Lrq
Stator inductance matrix.
Mutual inductance matrix.
Rotor resistance matrix. 0 −1
Rotation matrix
.
1 0
Electrical rotor angular velocity.
Full-order system matrix of the synchronous reluctance
machine.
Rotor flux linkage vector in rotor reference frame.
Stator flux linkage vector in rotor reference frame.
Stator current command vector in rotor reference frame.
Stator voltage command vector in rotor reference frame.
Stator current vector in rotor reference frame.
Manuscript received February 28, 2007; revised January 7, 2008. First
published February 22, 2008; last published July 30, 2008 (projected).
J. Park and C. Kalev are with Pentadyne Power Corporation, Chatsworth,
CA 91311 USA (e-mail: jaedo.park@pentadyne.com).
H. F. Hofmann is with The Pennsylvania State University, University Park,
PA 16802 USA.
Digital Object Identifier 10.1109/TIE.2008.918583
vsr
x
Ki
Kp
Ls
Rs
Stator voltage vector in rotor reference frame.
Machine state vector.
Integral gain in feedback compensator.
Proportional gain in feedback compensator.
Stator leakage inductance.
Stator resistance.
I. I NTRODUCTION
U
NINTERRUPTIBLE power supply (UPS) systems have
been widely utilized to improve the electric power quality
for critical loads. For anomalies such as interruptions or sags, a
UPS supports the load using its stored energy. The energy storage device for UPS systems has historically been the lead-acid
battery. However, recently, there has been great interest in finding alternatives for lead-acid batteries due to their operating/
maintenance cost and environmental impact. Advances in
power electronics, magnetic bearings, and high-strength carbon
fibers have resulted in flywheel energy storage systems that can
be used as a substitute or supplement for lead-acid batteries in
UPS systems [1]–[5].
High-power flywheels can provide backup power to handle
the majority of power disruptions that last for 5 seconds or less
[1] and still have time to cover longer outages until a backup
system can cover the full load. Flywheels can also be used
in conjunction with batteries. This can reduce the number of
short charge/discharge cycles of the batteries, which greatly
extends their lifetime. It also improves the battery reliability
and preserves the battery capacity for longer disturbances.
Synchronous reluctance machines have advantages as a
motor/generator in flywheel energy storage systems due to the
zero “spinning” losses when no torque is being generated by
the machine, as opposed to permanent magnet machines with a
stator iron. Furthermore, the rotor of a synchronous reluctance
machine design can possess excellent structural integrity if
the rotor saliency is created by alternating layers of magnetic
and nonmagnetic metals connected by a high-strength bonding
process, such as brazing. However, when such a rotor is utilized for the machine, the conventional synchronous reluctance
machine models become inaccurate, particularly for the case of
steep torque changes, because the flux dynamics of the rotor
due to eddy current flow are not taken into consideration [6].
Feedforward current regulators for electric machines are
one solution for high-speed applications, as typical feedback
regulators can be problematic in field-oriented control due to
the speed dependence of the machine dynamics. A sufficiently
0278-0046/$25.00 © 2008 IEEE
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PARK et al.: CONTROL OF SYNCHRONOUS RELUCTANCE MOTOR/GENERATOR FOR FLYWHEEL-BASED UPSs
accurate model of the machine can make a model-based feedforward controller a reasonable approach, as the stability issue
becomes avoidable due to the inherently stable machine dynamics. It has been shown that the conventional model of the
synchronous reluctance machine, which does not consider the
rotor flux dynamics, can create a current overshoot during
transients when used in a current regulator, as the predicted
back electromotive force (EMF) is much higher than the actual
back EMF of the machine. This makes it problematic to utilize
the conventional model to design a model-based controller for
a machine with a conducting rotor. This issue has been resolved
in the authors’ previous work [6].
Although the model utilized in the feedforward controller
describes the machine well, the feedforward controller relies
heavily upon accurate knowledge of the parameters for good
performance. However, practically, it is hard to measure all
parameters exactly. Some of them may be difficult to measure,
and initially measured parameters can easily vary with operating conditions such as temperature and the nonlinear magnetic
properties of the iron in the machine. A feedforward-controlled
system generates inaccurate output if the parameters are not
correct and does not take into account unmodeled dynamics or
disturbances. As a result, the efficiency will be non-optimal,
because the actual operating point of the machine will be off
from the commanded one if the parameters are inaccurate.
Furthermore, the inverter may trip at high power levels if the
erroneous operating point requires a higher than necessary
current to generate the desired torque. This can cause problems
for some critical operating conditions unless the current error is
eliminated properly.
A hybrid controller which incorporates a feedback PI compensator into a model-based feedforward controller to improve
the performance and robustness of current regulation for a highspeed solid-rotor synchronous reluctance machine is proposed
in this paper. The machine current tracking error caused by
the parameter mismatch is mathematically analyzed and is
utilized to dynamically compensate the estimated flux-linkage
to eliminate the steady state error in current regulation. Stability
analysis is also performed, and it will be shown that the regulation performance and robustness of the system are improved.
The proposed controller yields an improved transient response for a fast-changing torque command with the model, as
well as good tracking performance from the PI regulator. This
is particularly desirable for applications such as flywheel-based
or flywheel–battery hybrid energy storage systems, because fast
response is an important performance factor of UPS systems,
and improved tracking performance yields better efficiency.
The proposed controller has been experimentally validated with
a solid-rotor synchronous reluctance motor/generator based
flywheel energy storage system.
II. M ODEL -B ASED F EEDFORWARD C ONTROLLER [6]
A. Continuous-Time Model
The feedforward controller which is utilized in this paper is
based on the machine model presented in [6]. The equivalent
circuit model is shown in Fig. 1. Unlike the equivalent-circuitbased models in previous studies [7]–[9], this model takes the
3039
Fig. 1. Equivalent circuit model of synchronous reluctance machine in
synchronous reference frame.
dynamics of the rotor flux-linkage into account and, therefore,
better represents the flux behavior in the machine. This allows
a significant improvement on transient response, particularly
for the solid-rotor synchronous reluctance machine whose
rotor currents, generated by the flux-linkage dynamics, are not
negligible [6].
The machine is modeled in the rotor reference frame by
direct and quadrature windings and is similar to the case
of squirrel-cage induction machines, yet includes a magnetic
saliency of the rotor. The dynamic expressions for the machine
in the rotor reference frame are given as follows:
2
Rr r
M
dλra
irs
=−
(1)
λa + R r
dt
Lr
Lr
−1 2 dirs
M
M2
r
irs −ωre J
= Ls −
vs − Rs + Rr
dt
Lr
Lr
Rr r
M 2 r r
i + λa +
λa
× Ls −
Lr s
Lr
(2)
where
λr = M λr .
a
Lr r
(3)
B. Feedforward Controller Implementation
It is straightforward to build a sufficiently accurate machine
dynamics model for a flywheel system, due to its slowly varying
speed. Hence, a reasonably accurate command voltage for the
given current commands can be determined from the model.
The voltages for a current ĩrs and resulting flux linkage λ̂ra are
given as
2
ṽsr = Rs ĩrs + ωre J Ls − M ĩrs + ωre Jλ̂ra
Lr
d
M 2 r r
+
ĩs + λa . (4)
Ls −
dt
Lr
It has been found that sufficient performance can be achieved by
neglecting dynamic terms and approximating the stator voltage
as follows:
ṽsr = Rsĩrs + ωre J Lsĩrs + λ̂ra .
(5)
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 8, AUGUST 2008
Note that measured stator leakage inductance Ls is utilized
in the controller instead of [Ls − (M 2 /Lr )]. This is because
both the direct and quadrature values of [Ls − (M 2 /Lr )] are
approximately equal to the stator leakage inductance Ls and,
hence, can be estimated, as well as the stator resistance Rs ,
through terminal measurements of the stator with the rotor
removed.
The flux-linkage vector λ̂ra can be estimated by numerically
integrating (1) using command currents
t 2
Rr r
M
r
ĩr dt.
−
(6)
λ̂a =
λ̂a + Rr
s
Lr
Lr
−∞
The inverse of the rotor time constants [Rr /Lr ] and the rotor
“excitation” resistance [Rr (M/Lr )2 ] can be obtained experimentally, as discussed in [6].
When incorrectly estimated, flux-linkage values λ̂ra are utilized to calculate command voltage as in (5), an erroneous
command voltage ṽsr is generated
ṽsr = vsr + ∆vsr
M 2 r r
r
ĩ + λ̂a .
= Rs ĩs + ωre J Ls −
Lr s
(12)
(13)
This voltage error will result in a stator current error. The
relationship between flux-linkage estimation and the current
can be determined from the command values in (13) and the
actual values from the command in (5), and the steady-state
error of the machine current caused by mismatched parameters
can be represented as follows:
−1
M2
ωre J∆λra .
(14)
∆irs = Rs I + ωre J Ls −
Lr
III. PI F EEDBACK C OMPENSATOR
B. Feedback-Compensator Implementation
A. Error Caused by Parameter Mismatch
Among the three sets of direct and quadrature parameters
and the scalar parameter required for the model used in the
controller, it has been assumed that [Ls − (M 2 /Lr )], which
can be approximated by the stator leakage inductance Ls ,
and Rs have exact values in this paper. However, the other
parameters containing [Lr ] and [M ] and [Rr ] will vary due to
nonlinear magnetics and rotor temperature, respectively.
Equation (6) is used to estimate the flux-linkage. If an error
exists in the time constant and/or excitation resistance, the estimated flux-linkage will have the following additive error term:
r r
λ̂a = λ̂a0 + ∆λ̂ra
t Rr
−
+ ∆1 λ̂ra0 + ∆λra
=
Lr
−∞
2
M
+ ∆2 ĩrs dt
+ Rr
Lr
(7)
(8)
where λ̂ra0 represents the right amount of the flux linkage for
the given current command. Then, the error in the flux-linkage
estimation can be separated as
∆λ̂ra =
t
−∞
Rr
r
−[∆1 ]λ̂a0 −
+ ∆1 ∆λra + [∆2 ]ĩrs dt.
Lr
−1
where the term Rs ωre
J∆irs is included in an attempt to decouple the direct and quadrature dynamics. With the addition
of this feedback compensator, the control performance can be
improved by compensating the deviation of model parameters
from the actual machine. The model-based controller generates
most of the control output and has already resolved the overshoot issue of the solid-rotor synchronous reluctance machine
[6]. Hence, the feedback can have reduced gain so that it can
be less sensitive to noise or random errors and have less of an
impact on the stability of the system.
In order to reduce the number of states in the system, the
integral part of the PI regulator can be integrated into the flux
estimator (6) as follows:
r
λ̂a =
(9)
t
−∞
2
Rr r
M
ĩr + K ∆ir dt.
−
λ̂a + Rr
i
s
s
Lr
Lr
(16)
The block diagram of the feedback compensator with the
model-based feedforward controller is shown in Fig. 2.
Differentiating yields
Rr
d r
r
∆λa = −[∆1 ]λ̂a0 −
+ ∆1 ∆λra + [∆2 ]ĩrs .
dt
Lr
In steady-state, the error of the current is proportional to
that of the estimated flux-linkage, which comes in turn from
parameter errors, as shown in (14). Hence, a flux-linkage compensator using a PI regulator is given as follows:
Ki
r
−1
∆λa = Kp +
J∆irs
(15)
∆irs − Rs ωre
s
(10)
Assuming steady-state operation, the error terms of the fluxlinkage estimation become dc offsets. However, it is difficult
to tell which parameter is incorrect from the output, because
the errors are a combination of parameters, current, and
flux-linkage
−1 Rr
∆λra = −
[∆1 ]λ̂ra0 − [∆2 ]ĩrs .
(11)
+ ∆1
Lr
IV. S TABILITY A NALYSIS
A. Feedforward Control
The state variables of the machine are defined as
T
x = λrad λraq irsd irsq .
(17)
Moreover, the machine dynamics equations of (1) and (2) can
be represented in matrix form in (18)–(20), shown at the bottom
of the next page.
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PARK et al.: CONTROL OF SYNCHRONOUS RELUCTANCE MOTOR/GENERATOR FOR FLYWHEEL-BASED UPSs
Fig. 2.
Block diagram of the feedback compensated model-based control system.
Fig. 3.
State-space diagram of the feedforward control system.
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From the controller equations represented in (5) and (6), the
following matrix notation has been used:
Rr
 = −
(21)
Lr
2
M
(22)
B̂ = Rr
Lr
Ĉ = ωre J
(23)
M2
D̂ = Rs I + ωre J Ls −
.
Lr
(24)
Thus, the complete system dynamics are given by
x˙
x
A 04×2
B 04×2 ṽsr
=
+
˙r
ĩr . (25)
02×4 Â
02×2 B̂
λ̂ra
λ̂a
s
The state-space diagram is shown in Fig. 3.
Because the voltage command vector ṽsr is synthesized based
on the estimated flux-linkage vector λ̂ra and the current command vector ĩr
s
ṽsr = Ĉλ̂ra + D̂ĩrs .
(26)
Equation (25) can be further simplified as follows:
x˙
x
A
BĈ
BD̂ r
ĩs .
+
˙r = 02×4 Â
B̂
λ̂ra
λ̂a


A=
 − Ls −
B= 0
−
Rr
Lr
M2
Lr
(27)
Rr
Lr
The eigenvalues of (27) are shown in Fig. 4. The system is
stable, but it can be seen that the eigenvalues move toward the
origin and increase in the imaginary direction as the rotor speed
is increased.
2
Rr LMr
2 −1
M
Lr
Ls −
Fig. 4. Eigenvalues of the feedforward-controlled system when the speed of
the machine is increased from 0 to 50 000 r/min. Arrows denote increasing rotor
speed.
− ωre J
−1 2 M2
− Ls − Lr
Rs + Rr LMr
− ωre J Ls −
−1 T
C = [0 I]
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



2
(18)
M
Lr
(19)
(20)
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 8, AUGUST 2008
Fig. 5. State-space diagram of the feedback compensated system. Flux compensation.
B. Feedback Compensation
Actual measured current values are extracted from the
machine state vector x by matrix C; therefore, the current error
vector can be given as
∆irs = ĩrs − Cx.
(28)
Taking the PI-compensator output and decoupling term into
consideration, the system dynamics are given by
x˙ = Ax + Bṽsr
= (A − BĈFC)x + BĈλ̂ra + B(D̂ + ĈF)ĩrs
(29)
where
ṽsr = Ĉλ̂ra + ĈF∆irs + D̂ĩrs
−1
J.
F = Kp I − Rs ωre
(30)
(31)
The state-space diagram is shown in Fig. 5.
With the integrator part of the controller incorporated with
the flux estimator, as shown in (16), the complete control
system with the PI compensator can be represented in matrix
form, as shown as follows:
x˙
x
B(D̂ + ĈF) r
A − BĈFC BĈ
ĩs .
r +
˙r =
−Ki C
Â
λ̂a
B̂ + Ki I
λ̂a
(32)
Fig. 6 shows the eigenvalues of the compensated system with
Kp = Ls and Ki = Ls . It can be seen that the highly speeddependent eigenvalues of the system have significantly faster
decay rates than the feedforward system.
V. C OMPARISON W ITH
V OLTAGE -C OMPENSATION S CHEME
The estimated flux-linkage, including the PI-compensation
term, will eventually be utilized to determine the voltage command through the model in the feedforward controller. By
changing the placement of PI regulator and decoupling terms,
it is possible to implement a voltage-compensated current regulator. This configuration becomes a conventional feedback cur-
Fig. 6. Eigenvalues of the feedforward-controlled system with compensator
when the speed of the machine is increased from 0 to 50 000 r/min. Case of
Kp = Ls and Ki = Ls . Arrows denote increasing rotor speed.
rent regulator and additive feedforward compensation, which is
shown in Fig. 7.
The output of the PI feedback compensator, which is stator
voltage command, will be given as
M2
r
r = K + Ki
+
ω
J
L
−
(33)
ṽPI
∆irs
∆
i
p
re
s
s
s
Lr
where the term ωre J[Ls − (M 2 /Lr )]∆irs is included in an
attempt to decouple the direct and quadrature dynamics. As
well as this PI regulator output, the feedforward compensation
voltage calculated from the model is added to the command
ṽsr = ṽ PI + Rsĩrs + ωre J Lsĩrs + λ̂ra .
(34)
The state-space diagram is shown in Fig. 8. Taking the
PI-regulator output and decoupling term into consideration, the
system dynamics will be given as
x˙ = Ax + Bṽsr
= (A−BFC)x + BĈλ̂ra + B
p + B(D̂ + F)ĩrs (35)
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PARK et al.: CONTROL OF SYNCHRONOUS RELUCTANCE MOTOR/GENERATOR FOR FLYWHEEL-BASED UPSs
Fig. 7.
Block diagram of conventional current-feedback controller with feedforward compensation.
Fig. 8.
State-space diagram of the feedback-compensated system. Voltage compensation.
3043
where
ṽsr = Ĉλ̂ra + p + F∆irs + D̂ĩrs
M2
F = ωre J Ls −
+ Kp I.
Lr
(36)
(37)
The dynamics of the compensator can be derived as follows:
p˙ = Ki ∆irs = −Ki Cx + Kiĩrs .
(38)
Therefore, the complete control system with the PI compensator can be represented in matrix form as
 ˙  
 
x
x
A−BFC BĈ
B
 λ̂˙r  =  02×4
  λ̂r 
Â
0
2×2
a
a
−Ki C
02×2 02×2
p
p˙


B(D̂ + F)
ĩrs . (39)
+
B̂
Ki I
Note that the flux-compensation scheme, as opposed to
the voltage-compensation scheme, has two less integrators.
Figs. 9 and 10 show the eigenvalues of the flux-compensated
and voltage-compensated system at 50 000 r/min with varying
gains. Kp and Ki have been varied from zero to Ls and to
Rs for flux and voltage compensator, respectively. The poles
with zero gain of Figs. 9 and 10 are different because of the
decoupling terms. It can be seen that the oscillating mode in
the flux-compensation scheme has a lower oscillation frequency
and faster decay.
Fig. 9. Eigenvalues of the feedforward-controlled system with flux compensator when the PI gains are increased from 0 to Ls at 50 000 r/min. Arrows
denote increasing gain.
VI. E XPERIMENTAL R ESULTS
To validate the theory, experiments using the proposed fluxcompensated current regulator are performed on a 120 kW
4-pole solid-rotor synchronous reluctance machine. The rotor
consists of alternating layers of a ferromagnetic and nonmagnetic material. The machine parameters are shown in Table I.
This machine is a part of a flywheel energy storage system
manufactured by Pentadyne Power Corporation that is capable
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 8, AUGUST 2008
Fig. 11.
Experimental setup of flywheel energy-storage system.
Fig. 10. Eigenvalues of the feedforward-controlled system with voltage compensator when the PI gains are increased from 0 to Rs at 50 000 r/min. Arrows
denote increasing gain.
TABLE I
MACHINE/CONTROLLER PARAMETERS
Fig. 12. Experimentally measured flux linkages in synchronous reference
frame. Offsets due to the remanent magnetization can be seen. (a) λrsd . (b) λrsq .
of providing 120 kW of dc electrical power for up to 20 s over
a speed range of 25 000–54 000 r/min. The machine is driven
by a three-phase inverter, and the proposed control algorithm,
which has been shown in Fig. 2, is implemented in a DSP-based
controller.
Analog/digital converters sample machine currents synchronously with the center-based pulsewidth-modulated generator,
which operates at a switching frequency of 18 kHz. Analog
low-pass filters with 128 kHz bandwidth are applied to reduce
the effects of noise and ripple. The sampling/calculation delay and input/output filtering should be carefully considered
for discrete-time controller implementation, because these can
result in an inferior performance or poor stability margin,
particularly due to the low switching-to-fundamental frequency
ratio. Delays should be compensated properly, as discussed in
[6], for the feedforward controller.
The proposed current regulator is then used as an inner
regulator in a bus voltage control algorithm, similar to that
presented in [10]. The bus voltage regulator generates the
torque command for the machine so that the dc power to
the load can be controlled. It is not necessary to regulate the
machine speed in this configuration. The block diagram of the
experimental system is shown in Fig. 11.
The machine model utilized in the proposed controller accommodates the rotor flux dynamics to avoid the huge overshoot in fast torque transient [6]; hence, the model-based part
generates most of the control output, and the feedback compensator only generates a relatively small corrective component to
the command voltages. The feedback gains can be readily tuned
experimentally to obtain the desired performance. First, the
proportional gain that compensates about 80% of the error without integral gain was determined. Subsequently, the integral
gain was increased to find the value that eliminates the steadystate error properly. The controller was able to avoid too much
overshoot while quickly eliminating the offsets from parameter
inaccuracies.
The proposed model-based feedforward controller assumes
linear magnetic behavior, meaning that the flux-linkages of
the machine are linearly related to the currents. In practice,
however, this relationship is nonlinear. While saturation of the
machine iron is one possible nonlinear effect, in the system
under study, this effect is not significant in the operating range
of the machine due to the relatively large air gap. Another
nonlinear magnetic property which has more of an effect on
the system under study is the remanent magnetization of the
iron in the rotor of the machine, which is shown in Fig. 12.
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PARK et al.: CONTROL OF SYNCHRONOUS RELUCTANCE MOTOR/GENERATOR FOR FLYWHEEL-BASED UPSs
Fig. 13. Experiment: 150 A step commands in synchronous reference frame
at 35 000 r/min. Model-based controller. Offsets due to the remanent magnetization can be seen. Upper: direct-axis. Lower: quadrature-axis. (a) Command
current ĩrs . (b) Actual current irs .
Fig. 14. Experiment: 0–300 A ramp commands in synchronous reference
frame at 35 000 r/min. Model-based controller. Errors due to the remanent magnetization can be seen. Upper: direct-axis. Lower: quadrature-axis.
(a) Command current ĩrs . (b) Actual current irs .
This creates errors in the current tracking that are particularly
important at relatively low power levels. Although these errors
can be removed by incorporating the nonlinearity into the
machine model, this phenomenon is left unmodeled so that
it can be utilized to validate the performance of the feedback
compensator.
As expected, when using only the model-based controller,
the system shows offsets/errors in current tracking when a step
current command of 150 A and a ramp command from 0 to
300 A were applied to the system. The results are shown in
Figs. 13 and 14. This is most likely because the remanent
magnetization is not considered in the model. However, the
error can be effectively removed by the proposed hybrid controller, as shown in Figs. 15 and 16, because the PI controller
compensates the unmodeled nonlinearity.
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Fig. 15. Experiment: 150 A step commands in synchronous reference frame
at 35 000 r/min. Model-based controller with flux-based PI compensator.
The offsets are removed by the PI compensators. Upper: direct-axis. Lower:
quadrature-axis. (a) Command current ĩrs . (b) Actual current irs .
Fig. 16. Experiment: 0–300 A current commands in synchronous reference
frame at 35 000 r/min. Model-based controller with flux-based PI compensator.
The errors are removed by the PI compensators. Upper: direct-axis. Lower:
quadrature-axis. (a) Command current ĩrs . (b) Actual current irs .
VII. C ONCLUSION
In this paper, a hybrid controller consisting of a model-based
feedforward controller and a PI feedback compensator for a
solid-rotor synchronous reluctance motor/generator has been
proposed. The proposed control scheme has been applied to
a motor/generator in a high-speed flywheel-based UPS system. It has been shown that the proposed hybrid controller
with PI feedback compensator, in addition to the model-based
controller considering flux dynamics in the solid-rotor scheme,
easily compensates errors in the flux-linkage estimator caused
by inaccurate parameters or unmodeled dynamics, as well as
improves the regulation performance for the current commands
and the stability of the system.
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 8, AUGUST 2008
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Jae-Do Park (S’04–M’07) received the B.S. and
M.S. degrees in electrical engineering from Hanyang
University, Seoul, Korea, in 1992 and 1994, respectively, and the Ph.D. degree from The Pennsylvania
State University, University Park, in 2007.
From 1994 to 2001, he was a Research Engineer
with LG Industrial Systems, Anyang, Korea. Since
2004, he has been with Pentadyne Power Corporation, Chatsworth, CA, where he is currently a
Controls Software Engineer. His current interests
include flywheel energy storage systems, power converters, and ac machine drives.
Claude Kalev (M’93) received the degree in electronic engineering from California Polytechnic State
University, San Luis Obispo.
Since June 2002, he has been the Vice President
of the Electrical Engineering Department, Pentadyne Power Corporation, Chatsworth, CA, which
he cofounded when the company was incorporated
in 1998. His interests include high-speed rotating
machinery, magnetic-bearing-system development,
high-vacuum systems, and molecular drag pump
design.
Mr. Kalev is a member of Tau Beta Pi and the Golden Key Honor Society.
Heath F. Hofmann (M’89) received the B.S. degree
in electrical engineering from the University of Texas
at Austin in 1992 and the M.S. and Ph.D. degrees in
electrical engineering and computer science from the
University of California, Berkeley, in 1997 and 1998,
respectively.
He is currently an Associate Professor with
Pennsylvania State University, University Park. His
research area is in power electronics, specializing
in the design and control of electromechanical systems. His specific interests include energy harvesting
(i.e., the generation of electricity from one’s environment), flywheel energystorage systems, and electric drives for electric and hybrid electric vehicles.
Dr. Hofmann was the recipient of a Prize Paper Award (First Prize) by the
Electric Machines Committee at an IEEE Industry Applications Society Annual
Meeting in 1998.
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