Loss Minimization in Vector-controlled Interior Permanent-magnet

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1344 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 49, NO. 6, DECEMBER 2002

Fig. 6. Output waveform under one-cycle control.

Fig. 7. FFT result of PWM output.

Fig. 8. FFT result of one-cycle output.

2) One-cycle is better than PWM control in tracing transient wave-

forms. Through the experiments, one-cycle control shows its

better performance than PWM control in the dynamic response.There exists shorter delay between reference signal and output

than that in the PWM control.

3) One-cycle is more general than PWM control. One-cycle control

can approximate arbitrary waveforms that can be dc, ac, or those

strange waveforms without any regulation such as transient fault

voltages in power systems. PWM control depends on the mod-

ulation signal requiring specific consideration. The generality

of one-cycle control is also tightly connected to its high-speed

response.

4) One-cycle is more complex than PWM control in hardware. To

realize the algorithm of one-cycle control, a high-speed inte-

grator, either digital or analog, should be used. However, PWM

control does not need any integrators.

REFERENCES

[1] F. Ertl, J. W. Kolar, and F. C. Zach, Basic considerations and topolo-gies of switched-mode assisted linear power amplifiers, in Proc. IEEE

APEC96, vol. 1, 1996, pp. 207213.[2] K. Nielsen, PEDECA Novel pulse referenced control method for

highquality digital PWMswitchingpower amplification, in Proc. IEEEPESC98, vol. 1, 1998, pp. 200207.

[3] Z. Lai and E. M. Smedley, A new extension of one-cycle control andits application to switching power amplifiers, IEEE Trans. Power Elec-tron., vol. 11, pp. 99105, Jan. 1996.

[4] G. Carrara and S. Gardella, A new multilevel PWM method: A theoret-ical analysis, IEEE Trans. Power Electron., vol. 7, pp. 497505, May1992.

[5] V. Agelidis and M. Calais, Application specific harmonic performanceevaluation of multicarrier PWM techniques, in Proc. IEEE PESC98,1998, pp. 172178.

[6] Y. F. Liu et al., A novel three-phase multilevel voltage source con-verter, in Proc. IPEMC, vol. 1, 2000, pp. 231238.

Loss Minimization in Vector-Controlled Interior

Permanent-Magnet Synchronous Motor Drives

Christos Mademlis and Nikos Margaris

AbstractAn efficiency optimization method for vector-controlledinterior permanent-magnet synchronous motor drives is presented. Basedon theoretical analysis, a loss minimization condition that determines theoptimal -axis component of the armature current is derived. Selectedexperimental results are presented to validate the effectiveness of the

proposed control method.

Index TermsAdjustable-speed drives, efficiency optimization, interior

permanent-magnet (PM) motor, loss minimization.

I. INTRODUCTION

Improvement of permanent-magnet (PM) motor efficiency is a most

important priority, hence, several control methods have been proposed

in order to reduce the loss of PM motor drives and improve their per-

formance. This can be realized by an online control of thed

-axis com-

ponent of the stator current (I

d

). In surface PM motor drives, copper

loss is minimized by keeping thed

-axis componentof thestator current

equal to zero (I

d

= 0

) [1], [2]. Thus, a maximum torque-per-ampere

current control is accomplished. Since the I

d

= 0

control prevents

the demagnetization of the PM, it is often employed in interior PM

motor drives. However, in I

d

= 0

control method the reluctance

torque is not produced. Contrarily, reluctance torque can be producedby controlling the

I

d

current according to load conditions. Thus, the

I

d

current that provides maximum torque-per-ampere current ratio in

interior PM motor drives, is a function of theI

q

current and opposes

the excitation field of the PM [1][4].

Manuscript received February 2, 2001; revised April 16, 2002. Abstract pub-lished on the Internet September 13, 2002.

The authors are with the Department of Electrical and Computer Engi-neering, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece(e-mail: [email protected]; [email protected]).

Digital Object Identifier 10.1109/TIE.2002.804990

0278-0046/02$17.00 2002 IEEE
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 49, NO. 6, DECEMBER 2002 1345

Fig. 1. Optimal vector-controlled interior PM synchronous motor drive.

A method for both copper and iron loss minimization of an interiorPM motor based on flux-weakening control is presented in [5]. How-ever, the proposed condition is complex and cannot be easily imple-mented. Finally, a control method for efficiency improvement of PMmotors, by keeping power factor equal to unity, is described in [6].However, although the real to apparent power ratio (kW/kVA) of thePM motor is maximized, power losses are not minimized.

In this letter, a loss minimization method for vector-controlled in-terior PM synchronous motor drives is presented. From the theoreticalanalysis, a condition that specifies the optimal

d

-axis component of thestator current for minimizing interior PM motor losses is derived. Theexistence of the loss minimum in interior PM motors and the fact thatthe minimum loss operating points satisfy the optimal

I

d

current con-dition are experimentally verified.

The block diagram of the optimal PM motor drive is shown in Fig. 1.The loss model controller (LMC) measures the speed (

!

r

) and theI

q

current and specifies the optimal I d current by means of the optimalefficiency condition.

II. BASIC EQUATIONSLOSS MODEL

Fig. 2(a) and (b) shows thed

- andq

-axes equivalent circuits, re-spectively, of the interior PM synchronous motor in a synchronouslyrotating reference frame [7]. The equivalent circuits are given in theper-unit system and referred to balanced steady-state operation. Effectsof iron and stray losses are ignored. The phasor diagram in a synchro-nously rotating

d

q

reference frame is illustrated in Fig. 2(c). In thefigure, the

I

d

current is negative (demagnetizing current) and resultsin field weakening. The

d

- andq

-axes components of the magnetizingcurrent are given, respectively, by

I

m d

= I

0

f

+ I

d (1)

and

I

m q

= I

q

:

(2)

Since the magnetic permeability of the PM is close to air, theq

-axisreactance (

X

m q

) of the interior PM motor exceeds thed

-axis reactance(

X

m d

) [1]

X

m q

> X

m d

:

(3)

The electromagnetic torque of the motorT

e

is given by [1]

T

e

= X

m d

I

0

f

I

q

0 ( 0 1 ) X

m d

I

d

I

q

(4)

(a)

(b)

(c)

Fig. 2. (a)d

-axis per-unit equivalent circuit. (b)q

-axis per-unit equivalentcircuit. (c) Phasor diagram of interior PM synchronous motor.

where

is the saliency ratio

=

X

m q

X

m d

> 1 :

(5)

The electrical losses of a PM synchronous motor that can be mini-mized by flux weakening are copper, iron, and stray-load losses. Ironlosses are due to hysteresis and eddy currents, and are given by the fol-lowing formula [1], [8]:

P

F e

= c

F e

!

e

8

2

m

= c

F e

!

e

I

0

f

+ I

d

2

+

2

I

2

q

:

(6)

Stray-load losses arise on the copper and iron of the motor, due to the

nonuniform current distribution and the distortion of the magnetic fluxby theload current, respectively. Stray-load lossesare givenby [9], [10]

P

s t r

= c

s t r

!

2

e

I

2

s

:

(7)

The electrical losses, expressed ind

-q

axes components, are given by,

P

l

= P

C u

+ P

F e

+ P

s t r

= a ( I

2

d

+ I

2

q

) + b ( I

0

f

+ I

d

)

2

+

2

I

2

q

(8)

where

a = r

s

+ c

s t r

!

2

e

(9)

and

b = c

F e

!

e

X

2

m d

:

(10)
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1346 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 49, NO. 6, DECEMBER 2002

Fig. 3. Power loss versus I current in a 3.4-kW interior PM motor drive(experimental results).

III. LOSS MINIMIZATION CONDITION

The loss minimization condition at steady state (T

e

and!

e

constant)with respect to

I

d

is given by

@ P

l

@ I

d

T ; !

= 0 :

(11)

Using (8), condition (11) is satisfied when

I

d

( a + b ) + b I

0

f

+ ( a + b

2

) I

q

@ I

q

@ I

d

= 0 :

(12)

Since the electromagnetic torque is kept constant, it is deduced that

@ T

e

@ I

d

!

= 0 :

(13)

From (4) and (13), we obtain

@ I

q

@ I

d

=

( 0 1 ) I

q

I

0

f

0 ( 0 1 ) I

d

:

(14)

Substituting (14) in (12) yields

I

2

d

0 I

d

I

0

f

( a + 2 b 0 b )

( 0 1 ) ( a + b )

0

b I

0 2

f

+ I

2

q

( 0 1 ) ( a + b

2

)

( 0 1 ) ( a + b )

= 0 :

(15)

The solution of (15) is as follows:

I

d

= G

d

a + b ( 2 0 )

a + b

6 G

d

a + b

a + b

2

+ I

2

q

a + b

2

a + b

(16)

where

G

d

=

I

0

f

2 ( 0 1 )

:

(17)

Substituting (16) in (4) and after some algebraic operations, theelec-tromagnetic torque for the two solutions of (15) is respectively givenby

T

e

= X

m d

I

0

f

I

q

a + b

2 ( a + b )

2 1 7 1 + 4

I

2

q

I

0 2

f

( a + b ) ( a + b

2

) ( 0 1 )

2

( a + b )

2

:

(18)

From (18), it is evident that the solutionI

d

results in negative elec-tromagnetic torque and, therefore, it is rejected. On the contrary, the

TABLE I3.4-kW INTERIOR PM MOTOR PARAMETERS

(a)

(b)

Fig. 4. Performance of optimal PM motor drive with LMC. (a) I current andinput power. (b) I current and stator voltage (experimental results).

solutionI

d

is acceptable. The second derivative ofP

l

with respectto

I

d

@

2

P

l

@ I

2

d

T ; !

= 2 ( a + b ) + 6 I

2

q

( a + b

2

) ( 0 1 )

2

I

0

f

0 ( 0 1 ) I

d

2

(19)

is always positive. Therefore, the loss minimization of the interior PM

motor is obtained from the I d current, as given by

I

d

= G

d

a + b ( 2 0 )

a + b

0 G

d

a + b

a + b

2

+ I

2

q

a + b

2

a + b

:

(20)

The parameters of the proposed controller, required for the im-plementation, are obtained from the motor model and determinedexperimentally [11].

IV. EXPERIMENTAL RESULTS

The existence of the loss minimum is experimentally verified. Fig. 3

shows the loss reduction versusd

-axis current, measured in a 3.4-kW

interior PM synchronous motor. For the points noted by asterisk, the

loss minimization is achieved and these operating points satisfy the
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 49, NO. 6, DECEMBER 2002 1347

second solution (I

d

) of condition (16). Note that the loss minimum

curves are smooth and flat around the minimum. The parameters of the

interior PM motor are given in Table I.

Fig. 4(a) and (b) illustrates the performance of the suggested LMC.

Although the optimalI

d

current is a priori known from (20), theI

d

command decreases at a low rate in order to avoid strong armature

current and torque disturbances.

V. CONCLUSION

In this letter, a loss minimization method for vector-controlled in-

terior PM synchronous motor drives has been presented. Based on the

motor loss model,a conditionto obtainthe optimum valueof theI

d

cur-

rent for accomplishing loss minimization of interior PM synchronous

motor drives was derived. The suggested controller uses the signals of

the rotating speed andI

q

current, and the optimalI

d

current is speci-

fied by means of the loss minimization condition. Experimental results,

taken from a three-phase 3.4-kW interior PM motor, were presented to

confirm the high performance of the drive.

REFERENCES

[1] S. A. Nasar, I. Boldea, and L. E. Unnewehr, Permanent Magnet, Re-luctance and Self-Synchronous Motors. Boca Raton, FL: CRC Press,1993.

[2] S. Morimoto, Y. Takeda, T. Hirasa, and K. Taniguchi, Expansion ofoperating limits for permanent magnet motor by current vector controlconsidering inverter capacity, IEEE Trans. Ind. Applicat., vol. 26, pp.866871, Sept./Oct. 1990.

[3] T. M. Jahns, G. B. Kliman, and T. W. Neumann, Interior permanent-magnet synchronous motors for adjustable-speed drives, IEEE Trans.

Ind. Applicat., vol. IA-22, pp. 738747, July/Aug. 1986.[4] B. J. Chalmers, L. Musaka, and D. F. Gosden, Variable-frequency syn-

chronous motor drives for electric vehicles, IEEE Trans. Ind. Applicat.,

vol. 32, pp. 896903, July/Aug. 1996.[5] S. Morimoto, Y. Takeda, and T. Hirasa, Loss minimization control ofpermanent magnet synchronous motor drives, IEEE Trans. Ind. Elec-tron., vol. 41, pp. 511517, Oct. 1994.

[6] Y. Nakamura, T. Kudo, F. Ishibashi, and S. Hibino, High-efficiencydrive due to power factor control of a permanent magnet synchronousmotor, IEEE Trans. Power Electron., vol. 10, pp. 247253, Mar. 1995.

[7] P. C. Krause, Analysis of Electric Machinery. New York: McGraw-Hill, 1986.

[8] V. B. Hosinger, Performance of polyphase permanent magnet ma-chines, IEEE Trans. Power App. Syst., vol. PAS-99, pp. 15101518,July/Aug. 1980.

[9] S. A. Nasar, Handbook of Electric Machines. New York: McGraw-Hill, 1987.

[10] J. K.GierasandM. Wing,Permanent Magnet MotorTechnology:Designand Applications. New York: Marcel Dekker, 1997.

[11] F. Fernndez-Bernal, A. Garca-Cerrada, and R. Faure, Determination

of parameters in interior permanent-magnet synchronous motors withiron losses without torque measurement, IEEE Trans. Ind. Applicat.,vol. 37, pp. 12651272, Sept./Oct. 2001.

Documents

Loss Minimization in Vector-controlled Interior Permanent-magnet