Feedforward control of high-speed solid-rotor synchronous reluctance ...

Feedforward Control of High-Speed Solid-Rotor Synchronous Reluctance Machines With Rotor Dynamics Model Jae-Do Park

Heath Hofmann

Claude Khalizadeh

The Pennsylvania State University 121 Electrical Engineering East University Park, PA 16802 Email: [email protected]

The Pennsylvania State University 121 Electrical Engineering East University Park, PA 16802 Email: [email protected]

Pentadyne Power Corporation 20750 Lassen st. Chatsworth, CA 91311 Email: [email protected]

Abstract— An open-loop current regulator for a high-speed synchronous reluctance machine with a solid conducting rotor is presented. A rotor dynamic model is developed which is similar to an induction machine model yet includes a magnetic saliency of the rotor. The model is then used to calculate command voltages for a desired current in an open-loop current regulator. Techniques for parameter extraction and discrete-time models for digital implementation are discussed. Experimental results, including a 120kW discharge of a flywheel energy storage system, validate the performance of the controller.

N OMENCLATURE [Lr ] [Ls ] [M ] [Rr ] Rs ωre ωr λr s λr r irs iss ˜irs irr vsr v˜rs v˜rc L
s P td Ts Vbus ispk J

Rotor inductance matrix Stator inductance matrix Mutual inductance matrix Rotor resistance matrix Stator resistance Electrical rotor angular velocity Mechanical rotor angular velocity Stator flux linkage vector in rotor reference frame Rotor flux linkage vector in rotor reference frame Stator current vector in rotor reference frame Stator current vector in stationary reference frame Stator current command vector in rotor reference frame Rotor current vector in rotor reference frame Stator voltage vector in rotor reference frame Stator voltage command vector in rotor reference frame Stator voltage command vector (dead-time compensated) in rotor reference frame Stator leakage inductance Pole number of the machine Dead or blanking time Switching period DC bus voltage Stator current magnitude
 0 −1 Rotation matrix 1 0

IAS 2004

I. I NTRODUCTION Current regulators for electric machines are typically based upon feedback control [1]. Implementation of field-oriented feedback control can be problematic for high-speed machines, however, as the dynamics of the machine in a field-oriented reference frame are speed-dependent. In particular, it can be shown that some imaginary component of the poles of the machine model in the rotor reference frame are essentially equal to the electrical rotor speed at high speeds. As a result, the system dynamics in the rotor reference frame become more resonant at high speeds, and hence it becomes more difficult to design stable feedback algorithms with good performance. Possible solutions to this involve gain-scheduling based upon rotor speed, but even so it can still be difficult to obtain good performance due to the inherent delays associated with a discrete-time implementation of the control algorithm, and also due to the presence of noise in the current measurements. Provided a sufficiently accurate model of the machine is available and is sufficiently robust to parameter variations, an open-loop controller can provide good performance and also avoids stability issues associated with feedback control, as the machine dynamics are inherently stable. Synchronous reluctance machines have advantages in certain high-speed applications such as flywheel energy storage systems [3]. These machines have 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 materials can be chosen to have good mechanical properties. 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, under these conditions it is difficult to laminate the rotor, and therefore eddy currents can flow freely. As a result, the standard model for synchronous reluctance machines is inadequate, as it does not account for the resulting flux-linkage dynamics occurring in the rotor. In particular, when attempting a torque step from zero to full

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torque, the rate of change of the flux-linkage in the rotor is not instantaneous but determined by time constants. An open-loop controller based upon the standard synchronous reluctance machine model can therefore create a current overshoot during transients, as the predicted back-emf is much higher than the actual back-emf of the machine. In this paper we present an open-loop controller for synchronous reluctance machines which takes into account the flux-linkage dynamics in a solid rotor configuration. First, the dynamic model of a solid-rotor synchronous reluctance machine is presented. Techniques for parameter extraction and discrete-time models for digital implementation are then discussed. An open-loop current regulator which uses this discrete-time model is then proposed. This current regulator is used in conjunction with a feedback voltage regulator to regulate the DC bus voltage of a flywheel energy storage system. Experimental results of such a system are presented and discussed.

and λra . The dynamics can then be written as follows:    
−1 2 Lr dλra r λ + Rr M irs , =− (6) a dt Rr Lr 
−1   2  M dirs M2 irs = Ls − v rs − Rs + Rr dt Lr Lr 
 
  Lr  r M 2 r  r − Jωre Ls − is + λa + λ ,(7) Lr Rr a

II. F ULL -O RDER M ODEL OF S YNCHRONOUS R ELUCTANCE M ACHINE WITH ROTOR DYNAMICS

B. Parameter Extraction

2 are Both the direct and quadrature values of Ls − M Lr approximately equal to the stator leakage inductance, L
s , and hence can be estimated, as well as the stator resistance the Rs , through terminal measurements of the
stator with  2 

Lr M rotor removed. The parameters Rr and Rr Lr can

A. Continuous-time Model Although a conducting rotor of a synchronous reluctance machine is technically a continuum system [2], it can be simply modeled in the rotor reference frame with direct and quadrature windings on the rotor, similar to the case of squirrel-cage induction machines. The equivalent two-phase flux-linkage/current relationships of the rotor and stator in the rotor reference frame are given in vector notation as follows:  

r  λr is [Ls ] [M ] s = (1) r λ irr , [M ] [Lr ] r where


x =

xd xq




, [Y ] =

Yd 0

0 Yq

 ,

(2)

the superscript ’r’ represents the rotor reference frame and the ’d’ and ’q’ subscripts represent direct and quadrature values, respectively. The dynamic expressions for the machine in the rotor reference frame are provided by Faraday’s law: d r λ = vsr − Rsirs − Jωreλrs , dt s d r λ = −[Rr ]irr dt r where ωre = P2 ωr is the electrical rotor speed. By defining a new vector λra ,
 λr = M λr , a Lr r

(3) (4)

(5)

we will choose the states of the system to be the vectors irs IAS 2004

where


 2 λr = Ls − M ir + λr . s a Lr s

(8)

With this formulation the dynamics can be expressed in terms of three sets of direct and quadrature parameters: time
 rotor 2 

Lr M constants Rr , rotor excitation resistance Rr Lr , and

2 inductance Ls − M Lr , and a scalar parameter, the stator resistance Rs .

be determined from voltage and current measurements using the following procedure: • Using a feedback current regulator at medium speeds, command either a direct or quadrature current irsx to the machine, where the subscript ’x’ stands for direct or quadrature values. • Instantaneously turn off all transistors in the 3-phase inverter driving the machine at time t = 0. The stator current should quickly (ideally instantaneously) go to zero. In this case the stator voltage of the machine will be due solely to the flux generated by rotor currents:
 M r v rs = Jωre λ Lr r = Jωreλr (9) a

From voltage measurements we can therefore easily determine the flux linkage λra . From the exponential decays of the voltage

Lr waveforms we can also estimate the rotor time constants R . r This can best be done through a curve fitting of the measured data. From the conditions at the turn-off transition (t = 0) we can determine the rotor excitation resistances, for both direct and quadrature axes, as follows:  2 Mx λr (t = 0+ ) , = rax Lrx isx (t = 0− )  2  −1  2  Lrx Mx Mx Rrx = . (10) Lrx Rrx Lrx The resulting parameters of a 120kW, 55000rpm solid-rotor synchronous reluctance machine are shown in Table I.

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TABLE I S YNCHRONOUS R ELUCTANCE M ACHINE PARAMETERS Stator Resistance Rs Stator Leakage Inductance L
s L Direct Rotor Time constant Rrd

rd

Direct Rotor Excitation Constant Rrd Quadrature Rotor Time constant

Lrq Rrq

0.017 Ω 9.6 µH 4.5 msec

M 2

Quadrature Rotor Excitation Constant Rrq

Mq Lrq

can be minimized by choosing λrsd and λrsq to be equal. In terms of current, this results in the following relationship between irsd and irsq :  τ3ph Lsq Lsq r r i = isd = (15) 3P Lsd sq 4 Lsd (Lsd − Lsq )

0.0097 Ω

d Lrd



2) Minimum Flux-Linkage Operating Point: Likewise, the peak flux linkage  (14) λspk = λrsd2 + λrsq2

500 µsec

2

0.0098 Ω

4

x 10 1

This operating point is desirable if one wishes to minimize core losses, which are proportional to the square of fluxlinkage, or if one wishes to minimize flux levels to avoid saturation of the machine or to remain within voltage limitations of the inverter driving the machine. 3) Maximum Power Factor Operating Point: A third possible operating point is one which maximizes the displacement power factor, neglecting stator resistive drop. It can be shown that this operating point is achieved when    Lsq r τ3ph r  . (16) isq =  isd =  L Lsd sq 3P (L − L )

0.8 0.6 0.4

Im

0.2 0 −0.2 −0.4 −0.6

4

−0.8 −1 −1

−0.5

0 Re

0.5

1 4

x 10

Fig. 1. Root locus of the natural dynamics of the machine when the speed of the machine is increased from 0 to 50000rpm. Arrows denote increasing rotor speed.

sd

sq

This operating point is desirable if one is limited by both voltage and current constraints, as it generates the most torque for a given voltage-current product. It is also a reasonably efficient operating point. Other operating points than these can of course be chosen to achieve certain criteria, such as the maximization of efficiency [5].

C. Operating Points [4]

III. C ONTROL T ECHNIQUE

The steady-state torque of a three-phase synchronous reluctance machine can be written in terms of its equivalent two-phase parameters as follows: 3P (Lsd − Lsq ) irsd irsq . (11) 4 For a given torque, there are a number of different combinations of irsd and irsq that can be used to achieve that torque. Typical operating points are as follows: τ3ph =

1) Minimum Current Operating Point: For a given torque, the peak current:  (12) ispk = irsd2 + irsq2 can be minimized by choosing irsd and irsq to be equal:  τ3ph irsd = irsq = (13) 3P (L sd − Lsq ) 4 This is a desirable operating point if one wishes to minimize resistive losses in the machine, or if one is limited by the output current capability of the inverter. IAS 2004

Lsd

A. Open Loop Controller Because of the nature of a flywheel energy storage system (i.e., slowly changing rotor speed), it is straightforward to model the machine dynamics accurately. Hence, we can use the model developed above to determine the appropriate command voltages to be applied to the machine for a desired ˜ current. The voltages for a current irs and resulting air-gap flux ˜r λ a are given as follows:     2 M ˜ r r ˜irs + Jωre [L
s ]˜irs v s = Rsis + Rr Lr
 ˜ Rr ˜ r dir ˜r  (17) + Jωre λa − λa + L
s s Lr dt It will be shown that sufficient accuracy can be achieved by approximating the stator voltage as follows:   ˜ ˜ ˜ (18) v˜s ≈ Rsirs + ωre J L
sirs + λra ˜ The estimated vector λra is determined from the desired stator current vector by numerically integrating the following

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Rs Lls

Kd

~r isd

ispk 1 − K d2

~r isq

Rrd Lrd M Rrd  d  Lrd

  

 Mq   Rrq  L   rq 

+

-

2

+

1 s

+

1 s

~

λ sdr

+ +

v~sdr

+

v~sqr

+

ω re

2

-

+ +

Rrq

~r

λ sq

+

Lrq Lls Rs

Fig. 2. Feedforward current control algorithm in rotor reference frame

The second order approximation of eATs would require roughly five times more multiplications than the first. Fig. 3 shows the percentage difference of the second and the first-order model-based controller with 18kHz switching frequency in typical operating modes of a machine with parameters shown in Table I. For all significant operating points (minimum current, minimum flux-linkage and maximum power factor) with peak current command ispk ranging from 0 to 1500A and rotor speed from 25000 to 50000rpm, it can be seen that the difference is less than 5%, thus utilizing the first-order model for this controller is a reasonable choice to save system resources with acceptable loss of accuracy. C. Dead-Time Compensation

differential equations:








Rr ˜ r d ˜ r λa + Rr λ =− dt a Lr



M Lr

2 

˜irs

(19)

A schematic of this controller is shown in Fig.2. The parameter Kd determines the operating point of the synchronous reluctance machine. B. Implementation with Discrete-time Model Controller The continuous-time system model above in Eqs. (3), (4) can be represented in state space form as d x = A(ωre )x + Bu. (20) dt Assuming essentially constant rotor velocity during a switching period Ts due to large inertia, the system equation can be treated as linear time-invariant. To implement a model-based controller in a digital processor, the continuous-time model can therefore be transformed to discrete-time difference equations as follows [11]:

An open-loop controller will be sensitive to any deviations of the system from the model, so we must therefore model all significant phenomena. Hence we will need to compensate for the dead-time effect. The dead-time associated with a phase leg will alter the desired average-value output voltage of the phase as follows: < vout (t) >=< vcommand (t) > −

Vbus td iout (t) . Ts |iout (t)|

(24)

When calculating the command voltage in the rotor reference frame v˜rc , we compensate for the fundamental component of the deadtime voltage using the desired current as follows [10]: ˜ 4Vbus td irs v˜rc = v˜rs + . πTs ispk

(25)

D. Delay Compensation

Axis- and phase-transformations in the discrete-time domain cannot be ideally performed due to the continuous-time external system. The sample-and-hold effect in the stationary (21) reference frame generates disturbances in the rotor reference = F (ωre )x(k) + G(ωre )u(k). frame, which can be seen in Fig. 4. This disturbance could The matrix eATs can be approximated by using the power be neglected when the switching vs. fundamental frequency series expansion method. Although the accuracy can be im- ratio is large enough; however, this ratio cannot be sufficiently proved with a higher order approximation, this requires more large in a high-speed system due to hardware limitations. processing time and memory space. This can create problems Moreover, most hardware implementations require at least one when executing the interrupt service routine, because generally sampling time delay to update the actual PWM command the timing is very tight when it comes to a high-performance values. These delay factors make the estimated flux values and drive. Hence a first-order technique (i.e., Forward Euler) is the actual voltage commands received by gate drive circuitry typically used. However, it is appropriate to determine whether become significantly off from expected values, as shown in first-order techniques will be sufficient in this application. Figs. 4 and 5. This can be solved by phase-shifting the The discrete-time system equation with the first order ap- angular velocity feedback information. By compensating the proximation of eATs is given as Ts , as shown in Fig. 8, the phase angle rotor position by 3ωre 2 in the controller can be synchronized to the actual angle. x(k + 1) = (I + ATs )x(k) + Ts Bu(k). (22) This phase shift corresponds to the average phase for the next The second order equations are given as follows. sampling period after the update delay of PWM commands.   2 2 2 The compensated command voltages and the simulation results A Ts ATs x(k+1) = I + ATs + x(k)+ Ts + Bu(k) with compensated commands are shown in Figs. 6 and 7, 2 2 (23) respectively. x(k + 1) = eA(ωre )Ts x (k)  + A(ωre )−1 eA(ωre )Ts − I Bu(k)

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0 −2 −4

0 5 1500

4

1000 500 i [A]

1000 3

0

RPM

spk

0 5

2

3

0

4

x 10

500 ispk [A]

1000 3

0

RPM

(a)

4

1500

4

1000 3

RPM

0

3

4

x 10

500 ispk [A]

0

4

500 ispk [A]

1000 3

0

RPM

(a)

3

4

2

2 0 5

1500

4

4

x 10

500 ispk [A]

1000 500 ispk [A]

0 (d)

0 5

1500

4

1500

4 RPM

4

2 0 5

x 10

0 5 x 10

(c)

Error [%]

Error [%]

0 5

2

1500 1000

RPM

4

2

spk

(d)

4

4

x 10

500 ispk [A]

1000 500 i [A]

0

4

(b)

4

3

spk

2

1500

4

1500

4 RPM

0 5

0 5

RPM

4

500 i [A]

4

1500 1000

0

x 10

(c)

Error [%]

Error [%]

Error [%]

2

4

3 RPM

4

4

1000

(b)

4

x 10

0 5

spk

(a)

Error [%]

500 i [A]

2

1500

4

4

x 10

Error [%]

0

1500

4

Error [%]

3 RPM

4

x 10

2 0 5

5 4

x 10

4 Error [%]

2

Error [%]

4 Error [%]

Error [%]

4

1000 3

RPM

0

4

x 10

500 i [A]

1500

4 3

spk

spk

(c)

(b)

1000 500 i [A]

0

RPM

(d)

Fig. 3. Steady-state percent difference between the state variables of the first- and second-order approximated models when ispk varies from 0 to 1500A and the rotor speed ranges from 25000 to 50000rpm in typical operating modes. Upper row: Minimum current operating points, Middle row: Minimum Flux operating points, Lower row: Maximum power factor operating points. (a) Direct flux estimation (b) Quadrature flux estimation (c) Direct voltage command (d) Quadrature voltage command

Vrsd [V]

200

0.02

(b)

(a) λsd [A]

100 (a) 7.5

8

8.5

−0.02

−3

x 10

200

λr [A]

Vssd [V]

0

0.001

0.002

0.003

0.004

0.005

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0.007

0.008

0.009

0.01

0.007

0.008

0.009

0.01

0.007

0.008

0.009

0.01

(a)

−0.005

sq

(a)

(b)

7.5

8

8.5

−0.01

−3

x 10 200

(a)

100

r

0 7.5

8

8.5

0.002

0.006

(a) (b)

0 −500

−3

(a)

0.001

500

x 10

200

0

1000

(b) isd [A]

Vrsq [V]

0

0

(b)

−200

0

0.001

0

(b)

0

sq

ir [A]

Vssq [V]

(b)

r

0

0

0.002

0.003

0.004

0.005

0.006

(a)

−1000

(b)

−200 7.5

8 Time[sec]

8.5

−2000

−3

x 10

Fig. 4. Simulation: Disturbances in voltage commands by delay for the case of 15kHz sampling and 50000rpm rotation with ˜irsd = r s r s , v˜sd , v˜sq , v˜sq . Superscript ’s’ represents 500 A, ˜irsq = −500 A. v˜sd stationary reference frame. (a) Ideal (b) Actual (from top)

0

0.001

0.002

0.003

0.004

0.005 Time[sec]

0.006

Fig. 5. Simulation: Erroneous flux estimation and current regulation by delay for the case of 15kHz sampling and 50000rpm rotation with ˜ rsd , λ ˜ rsq , (a) Estimated (b)Actual, irsd , ˜irsd = 500 A, ˜irsq = −500 A. λ r isq . (a) Command (b) Actual (from top)

E. Stationary Feedback Regulator As the winding resistance of high-speed machines is quite low, asymmetries in the machine and applied voltage, though small, can generate significant low-frequency or DC currents in the stator. The purpose of the stationary regulator is to eliminate these currents by generating a feedback response voltage which cancels the low-frequency voltage component mentioned above. A block diagram of the entire current IAS 2004

regulator implementation is shown in Fig. 8. Provided the fundamental electrical frequencies generated by the feedforward controller are much higher than the bandwidth of the stationary regulator, the stationary regulator achieves its purpose of eliminating the low frequency currents without interfering with the feedforward controller.

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Vrsd [V]

Stationary Regulator

(a)

200

(b)

r is s

100 0 7.5

8

0

+

-

PI

8.5 −3

x 10

200 Vssd [V]

(b)

Deadtime Compensator

(a)

0

r ~r is

−200 7.5

8

8.5 −3

x 10 Vrsq [V]

200

ω re

0 7.5

8

8.5

r v~cr

+

+ Inverse Rotor Ref. Transformation

+

+

Complete controller, including dead-time compensation, phase-delay compensation, and stationary regulator.

Fig. 8.

−200 7.5

8 Time[sec]

8.5 −3

x 10

ω re

Fig. 6. Simulation: Phase-compensated voltage commands for the case of 15kHz sampling and 50000rpm rotation with ˜irsd = r s r s , v˜sd , v˜sq , v˜sq (a) Ideal (b) Actual (from 500 A, ˜irsq = −500 A. v˜sd top)

Bus Voltage Regulator

r ~r is

Current Regulator

(b)

+

Load

r

λsd [A]

(a) 0.01

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

(b)

Fig. 9.

0

r

vbus

External DC Bus

0.01

0.005 λsq [A]

r is s

rs v~cmd

0.02

0

rs v~cmd

+

(b)

(a)

0

3Ts 2

θ re

−3

x 10

200 Vssq [V]

+

(b) (a)

100

r v~sr

Feed Forward Controller

Inverter

M/G Synchronous Reluctance Motor/Generator, Flywheel

Capacitor Bank

Experimental setup of flywheel energy storage system

(a) 0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

500

sd

ir [A]

−0.005 0 1000

0 −500

(b)

(a) 0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

0.002

0.003

0.004

0.005 Time[sec]

0.006

0.007

0.008

0.009

0.01

sq

ir [A]

500 (b)

0 −500 −1000 −1500

(a) 0

0.001

Simulation: Compensated flux estimation and current regulation for the case of 15kHz sampling and 50000rpm rotation with ˜ rsd , λ ˜ ssq ,(a) Estimated (b)Actual, irsd , ˜irsd = 500 A, ˜irsq = −500 A. λ r isq (a) Command (b) Actual (from top) Fig. 7.

current during a 500A step command using the feedforward control approach and a model without rotor dynamics, and the equivalent response of phases A and B using a controller where the rotor dynamics have been included. A clear overshoot of the measured current can be seen in the case where the rotor dynamics are neglected. The approximate rotor speed during these experiments was 39krpm. It can be seen that the model with rotor dynamics does not experience significant oscillatory behavior in the step response as seen in the simulations of Figs. 5 and 7. This fortunate result is most likely due to unmodeled damping mechanisms, such as core losses. The

IV. E XPERIMENTAL VALIDATION The proposed controller was validated on a 120kW, 4-pole synchronous reluctance machine. This machine is capable of speeds of up to 55,000 revolutions per minute. The rotor consists of alternating layers of a ferromagnetic and nonmagnetic material. This machine is part of a flywheel energy storage system manufactured by Pentadyne Power Corporation that is capable of providing 120kW of DC electrical power for up to 20 seconds. The system block diagram is shown in Fig. 9. The flywheel is suspended in vacuum by magnetic bearings. A picture of the machine rotor and flywheel rim is shown in Fig. 10. Fig. 11 shows the measured phase A IAS 2004

297

Fig. 10.

4-pole synchronous reluctance rotor and flywheel

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Without Rotor Dynamics

With Rotor Dynamics

dynamics is a valid technique for high-speed control. Provided the model parameters agree well with the actual system, good performance can be achieved. The most significant deviation between the system and the model is the saturation of the machine iron at high torque levels, which causes an effective reduction in the machine inductances, particularly the direct inductance. However, this problem can be resolved with a more sophisticated model of the flux-linkage/current relationships of the machine.

600 600 400 400

200

Current (A)

200

0

0

−200

−200

R EFERENCES

−400 −400 −600 0

0.005 0.01 Time (s)

0.015

−600 0

0.005 Time (s)

0.01

Left: result of 500A current step command using synchronous reluctance machine feedforward controller without rotor dynamics, phase A current. Right: result of 500A current step command using synchronous reluctance machine feedforward controller with rotor dynamics, phases A and B. Both experiments are at minimumflux-linkage operating point of machine.

Fig. 11.

Bus Voltage

540

1.8

530

1.6

520

1.4

510

1.2

500

V

bus

(V)

Power (W)

2

0.8

480

0.6

470

0.4

460

0.2

0.5

1 Time (s)

1.5

2

x 10

1

490

450 0

DC Power

5

550

0 0

1

2

[1] T. Matsuo and T.A. Lipo. Field-oriented control of synchronous reluctance machine. In 24th Annual IEEE Power Electronics Specialists Conference Record, pages 425.31, June 1993. [2] J. Melcher. Continuum electomechanics. MIT Press, 1981. [3] H. Hofmann and S.R. Sanders. High speed synchronous reluctance with minimized rotor losses. IEEE Transactions on Industry Applications, 36(2):531.9, Mar.-Apr. 2000. [4] T.A. Lipo, A. Vagati, L. Malesani, and T. Fukao. Synchronous reluctance motors and drives-A new alternative. Presented at the 26th IEEE-IAS meeting, Oct.1992. [5] H. Hofmann, S.R. Sanders, A. El-Antably. Stator-flux-oriented vector control of synchoronous reluctance machines with maximized efficiency. To be published in IEEE Transactions on Industrial Electronics. [6] J.I. Ha, S.J. Kang, S.K. Sul. Position-controlled synchronous reluctance motor without rotational transducer. IEEE transactions on Industry Applications, 35(6):1393.8, Nov.-Dec. 1999. [7] R. D. Lorenz, D. B. Lawson. Performance of feedforward current regulators for field oriented induction machine controllers. IEEE Transactions on Industry Applications, 23(4), 142.50, Jan.-Feb. 1987. A [8] A. Chiba, T. Fukao. A closed-loop operation of super high-speed reluctance motor for quick torque response. IEEE Transactions on Industry Applications, 28(3), 600.06, May-June. 1992. [9] B. Kenny, P.E. Kascak, R. Jansen, and T. Dever. A flywheel energy storage system demonstration for space applications. In Proceedings of the International Electric Machines and Drives Conference, volume 2, pages 1314.1320. IEEE, June 1-4 2003. [10] R.S. Colby, A.K. Simlot, and M.A. Hallouda, Simplified model and corrective measures for induction motor instability caused by pwm inverter blanking time. In PESC ’90 Rec. 21st Annu. IEEE Power Electron. Spec. Conf., 1990, pp.678.683, 1990. [11] C.T. Chen, Linear system theory and design. CBS College Publishing, 1984.

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Fig. 12. Transient response of flywheel system when DC supply is disconnected and 120kW load is connected. Left: bus voltage Right: DC power provided by flywheel unit

current regulator is then used as an inner regulator in a bus voltage control algorithm, similar to that presented in [9]. The control logic initiates the regulation scheme when the DC bus voltage connected to the 3-phase inverter drops below 500V. Fig 12 presents the bus voltage and DC power supplied by the flywheel system when the DC power supply to the system is disconnected and a 120kW load is connected. The initial rotor speed during this experiment is 53krpm. It can be seen that the voltage regulator responds quite well to the application of an instantaneous load. V. C ONCLUSION It is shown that a feedforward controller of a solid-rotor synchronous reluctance machine which includes the rotor IAS 2004

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