104 IEEE Transactions on Encrgy Conversion, Vol. 5, No. 1, March 1990

PEAKED-MMF SMOOTH-TORQUE RELUCTANCE MOTORS

John S. Hsu (Htsui), Member, IEEE Shy-Shenq P. Liou, Student Member

Center for Energy Studies The University of Texas at Austin

10100 Burnet Road, Austin, Texas 78758

Herbert H. Woodson, Fellow, IEEE

Abstracl - This study investigates the steady-state torque characteristics of reluctance motors with nonsalient stator punchings, but with peaked rotating mmf s. The torque calculation includes the influences of saturation and fringing and groove fluxes. The peaked rotating mmf is produced by properly coordinated current waveforms and winding. Peaked-mmf reluctance motors have two major advantages: the torque is smooth and the flux per pole required to produce a given torque is lower than that of conventional reluctance motors. This property is most beneficial to 2-pole reluctance motors, for a given frame whose bore diameters and slot areas can be increased significantly for higher ratings or better performance. Unlike switched reluctance motors, a shaft encoder is not required for peaked-mmf motors.

INTRODUCTTO N

Reluctance motor drives have drawn the attention of investigators in the past several decades. From the late fifties to the early seventies, various segmental-type reluctance motors, which were evolved from the Kostko arrangement [ 11, were the center of interest [2-41. At present, switched reluctance motors, with high efficiency and torque, attract significant notice [5 , 61. The switching of power fed to individual coils of a switched reluctance motor is controlled by the shaft position encoders. Because of the salient structure of the stator punching and the switching of power, the motor's air-gap torque is generally fluctuous. Driven equipment with high-enough inertials is well suited for the switched reluctance motor drive. However, improvement of torque quality [7] is of general interest to prevent possible mechanical oscillation.

Unlike the switched reluctance motor, the peaked-mmf reluctance motor studied here has a nonsalient stator bore. The peaked stator mmf is produced by the proper arrangement of the stator winding and the current fed to the winding. The peaked-mmf reluctance motor does not require a shaft position encoder. Furthermore, there is no abrupt change of power from one salient pole to the other; the air-gap torque is smooth.

As compared with conventional induction or reluctance motors, for a given maximum stator-tooth flux density in a given frame, the peaked stator mmf substantially reduces the flux per pole. The lower core flux results in a larger stator bore or bigger slots, an arrangement that is most significant for 2-pole motors. This characteristic enables peaked-mmf reluctance motors to have higher ratings.

The focus of this paper is the general property and torque characteristics of peaked-mmf reluctance motors under the influence of (1) saturation and (2) fringing and groove fluxes. It predicts how the reluctance motor behaves with a rotating peaked air-gap mmf. Practical conclusions on peaked-mmf reluctance motors are obtained to improve future designs. The inverter or other arrangements between windings and current waveforms are not included in this paper; they will be discussed in a future paper. Extensive experimental work has been conducted to verify the accuracy of the analysis.

SAMPLE PEAKED-MMF RELUCTANCE MOTOR

The following arrangement between winding and current waveforms serves as one example to illustrate that the rotating peaked mmf can be produced. Figure 1 shows that when there is a third- harmonic rotating mmf revolving at the same speed as the fundamental mmf, the resultant air-gap mmf is the sum of these two mmf s. The resultant peaked mmf depends upon the relative third- harmonic phase angle as well as the relative amplitude of the third- harmonic mmf with respect to the fundamental's. Figure 2 shows the resultant mmf corresponding to various third-harmonic relative amplitudes. The rotor pole arc corresponding to the narrower peaked mmf is smaller than those of the conventional reluctance motors. This study uses a 60" (elechical degrees) and a 90" pole arc.

Two current waveforms in this case containing fundamental and third-harmonic components are shown in Fig. 3. The phase displacements between third-harmonic and fundamental are 45' (third- harmonic degrees) leading in Fig. 3a, and 45" lagging in Fig. 3b, respectively.

For a given frame the peaked-mmf winding is wound in the slots of a nonsalient stator core. The winding of a peaked-mmf motor can be designed for any number of poles. Figure 4a shows the grouping of conductors of a 2-pole, 36-slot, peaked-mmf reluctance motor. Conductors A-A, B-B', and C-C represent a set of 3-phase winding, and a-a', b-b, and c-c' represent another set of 3-phase winding. The phase displacement of these two sets of 3-phase windings is 30". Figure 4b shows that each of the two fundamental winding sets, (i.e., A-A', B-B', C-C', and a-a', b-b', c-c') can be considered as a phase of the 2-phase (D-D', and E-E), 6-pole, third-harmonic winding. (Figure 3a refers to phase A-A' current, and Fig. 3b refers to phase a-a' current.) The 3-phase fundamental components in the current waveforms are supplied to these two sets of fundamental windings and create a fundamental rotating field. Since the space displacement of these two sets of 3-phase windings is 30" apart, or 3 x 30" = 90' apart from the third-harmonic standpoint, the 2-phase, third-harmonic components in the current waveforms fed to the same two sets of fundamental, 3-phase windings, create a third-harmonic rotating mmf.

Re I a t ive 1.6 Resu I tant

1.5

I MMF

Fig. 1 Fundamental, third harmonic, and resultant mmfs 0885-8969/90/0300-0104$01 .OO 0 1990 IEEE

1.5

1 .o

0.5

0 .o

-0.5

-1 .o

-1.5

With Relative Third Harmonic MMF

Resu I tant MMF

and 1 .O Fundamental

Relative - Third Harmonic Phase Angle =

Fig. 2 Resultant mmfs corresponding to various third harmonic mmf's

Fig. 3 Current waveforms containing third harmonic components (a) 45" (third harmonic degrees) leading, (b) 45" lagging

TOROUE ANALYSIS

In this section, the first step to analyze the steady-state, air-gap torque of a peaked-mmf reluctance motor is to simplify the problem under an ideal situation. It is assumed that there is no saturation and no mmf drops in iron portions; the tooth harmonics are neglected; the fringing and groove air-gap fluxes are not considered; a n i the conductor distributions are represented in simple cosine functions.

The second step is to estimate the reduction of torque caused by fringing and groove air-gap fluxes. The third step is to consider the magnetic saturation influence on torque. The analytical method derived for the peaked mmf can be followed to analyze other arrangements between windings and current waveforms.

Air-Gau Toraue under Ideal Situation

Flux Distribution in Air GaD: Figure 5 shows the distributions of the current densities and mmf's for both fundamental and third harmonic within a pole. The rotor pole arc, y, and the load angle 6, are given in electrical degrees.

1 os

7 r 3 6 ' 4

A 2-pole, 36-slot, single-winding arrangement; (a) two sets of 3-phase windings (A-A', B-B', C-C' and a-a', b-b', c-c'), (b) same windings supplied with 2-phase (D-D' and E-E') third-harmonic currents

The current loading, A, which is the effective amperes per meter of the periphery of the stator bore, is defined as

2mNIKpKd

XD A =

where D = stator bore diameter in meters m = numberofphases N p n T = tumsper coil I = rmsphasecurrent Kp = pitch factor Kd = distribution factor

The peak of fundamental air-gap mmf wave, in ampere-tums per

= 2pnT/(no. of parallels) =turns in seriedphase = number of pole pairs = slots per phase belt per pole

pole, is given with subscript 1

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The air-gap flux density in teslas at location 8 is

Fundmental Fundamental Third

I Fig. 5 Distributions of current densities and mmf s

Fig. 6 Flux per pole at 6 = 30 electrical degrees

Similarly, the peak of air-gap third-harmonic mmf wave is given with subscript 3

fi DA3 F, = -

6P (3)

[F sin(p0) - F3 sin(3pB)I 4n 1 0-7 G

B = - (4)

where G is the effective air gap in meters; the minus sign in front of the third-harmonic mmf indicates that for the current density distributions as shown in Fig. 5, there is a 180' phase shift between fundamental and third harmonic mmf s.

Referring to Fig. 5, at a given load, the rotor location is 6/p mechanical degrees away from the stator pole center. The flux per pole, which is the integration of air-gap flux densities over the rotor pole arc area, is proportional to the integration of the total mmf along the rotor pole arc. As an example, Fig. 6 shows that under the same peak mmf and torque, the ratio of flux per pole of peaked-mmf over conventional reluctance motors is approximately 0.6.

Mametic Enerev Stored in Air Gap: Under the ideal situation, flux only goes through the air gap between stator bore and rotor pole arcs; the ideal energy [8, 91, WO, stored in the air gap in watt-seconds is

(volume of air gap)(average value of B 3 l o7

8n WO =

(5 )

Air-GapToraue: The ideal air-gap torque, TRQo, in watt-seconds is

The identical ideal air-gap torque can also be obtained from

T R Q o = - e - - Energy change at rotor pole arc

A(:)-.[.(:)l - A(:)-O A(:)

- (7)

t Energy loss at Energy gain at rotorpolefront - rotorpolead - -

This means that regardless of how wide the rotor pole arc is, the ideal torque depends upon the energy loss and gain at only two points--the rotor pole front, and the rotor pole end--, while the load angle 6/p tends to have a minor increment.

Influence of Fringing and Groove Air-Gau Fluxes

The air gap along the rotor groove is nonuniform due to fringing fluxes in the groove near the front and the end of the rotor pole arc. If the gap around these two points can be approximately considered as a constant value, G/KfG, where KfG must be less than 1 and greater than the ratio of air gap at the rotor pole arc over the gap at the groove,

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the torque caused by the fringing and groove fluxes can be expressed through the energy change at the front and the end of the groove adjacent to the rotor pole arc.

KfG can be obtained either through flux plotting or by statistical approach based on actual machines.

Influence of Magnetic Saturation

Reluctance motors have no rotor current to offset the stator mmf; the entire stator current is used to produce the air-gap mmf. The torque is calculated according to the flux densities at the rotor pole front and pole end. When saturation occurs, the pole front tends to saturate faster than the pole end. This accelerates the reduction in torque. Saturation increases the effective air gap. Let CG denote the multiplier of the air gap at a given location, 8,

Total ampere turns Air gap ampere tums C G =

G 7 - 10 + Stator tooth length turns per meter at (471

stator tooth pitch stator tooth width)] (

+ Rotor tooth length ampere turns per meter at I L

rotor tooth pitch rotor tooth width

GB~o’ 471 (9)

In order to calculate CG, the dimensions of the stator and rotor punchings and the magnetization curves of the punchings are needed. For a given load angle 6, Q-j can be calculated and labeled as CGf for the front and CGe for the end of the pole arc. Fquation(6) can be modified by CGf and CGe to include the saturation effect. The final torque including effects of saturation and fringing and groove fluxes is

71D ’L I o - ~ Torque= --

PG

[(Alsin (5 - z - 6) - % sin [ 3( 5 - f - 6)]f/CG

- (Alsin(;+$- 6) - $si{ 3(:+;-6)]f/CGf

+ K G { A l s i n ( 5 + f - 6 j - ?sin[3(;+$-6)l)*

The maximum torque or pull-out torque, observed from (lo), is proportional to the air-gap area, nDL, the bore current square, @A)2, and the reciprocal of pole pair times air gap, l/(pG).

SAMPLE CALCULATION

The parameters of a 3-phase, 6-pole, I-hp, peaked-mmf reluctance motor wound on a conventional induction motor stator core are given as follows, where subscripts 1 and 3 represent fundamental and third-harmonic, respectively.

p = 3 L = 0.1254m D = 0.1135m KG = Carter coefficent = 1.17 ml = 3 G = K<(30.000432 = 0.000505 m m3 = 2 Kdl = 0.966 Kpl = 1.0 Kp3 = 1.0 KfG = 0.15 assumed (gap/groove = 0.034) Rotor tooth pitch/Rotor tooth width = 1.9 Stator tooth pitch/Stator tooth width = 1.9

The rotor grooves are milled on a squirrel-cage rotor. The torque- versus-load-angle characteristics of the sample peaked-mmf reluctance motor are shown in Fig. 7, with y = 60°, I1 = 4.25 amps, and I3 = 3.33 amps (total rms current = 5.4 amps). The reductions in torques due to saturation and to fringing and groove fluxes are clearly shown by the three curves. Comparison between the second and third curves

Kd3 = 1.0 No. of parallels = 1

- 200 c .- n - I

(U 3 0- L 0 + U 3 a U 3 0

100

0

11.4.25 amps I3=3.33 amps T o t a l RMS c u r r e n t = 5.4 amps Po le arc=60 e l e c t r i c a l degrees

(a) ....... . . . .

. . . . . . . . . . . . . . . . . . . . . I dea l . . . . ...... [b) .......... / F r i n g e

. . ...... J S l t w a t ion ’ . /and F r i n g e

....................... J. . . . . . . . .... . . . ( c ) . .

. . - . . . . ... ... ... 1 : . .

EO 40 60 80 4

Load Angle 6 [ E l e c t r i c a l ~ e g r e e s ]

0

Fig. 7 Calculated torque vs. load angle, 6, curves; (a) ideal curve, (b) with influence of fringing and groove fluxes, (c) with influences of saturation and fringing and groove fluxes

- 1 -7 - T

108

shows that the torque reduction due to saturation is severe. The pull- out (or maximum) torque varies; for this motor i t occurs around 33", which is different from the 45" of conventional reluctance motors.

EXPERIMENTAL RESULTS

Extensive tests have been conducted on the motors specified for the sample calculations. The connection of the experimental motor is shown in Fig. 8. The current waveform source, which is not the focus of this paper, consists of a synchronized third- harmonic source injected to the fundamental source [10-13). This source can be replaced by an adjustable frequency source with the waveform property shown in Fig. 3. Different inverters are required for other arrangements between waveforms and windings.

A Lebow (Eaton) shaft torque sensor (model 1104-lk), coupled between the shafts of the motor and the loaded dc generator, is used for the torque measurement. A full-pitch search coil located on tops of slots, and a search conductor with return path outside the stator frame placed at the bottom of a stator slot are used for air-gap and core flux density measurements.

Two torque-versus-load-angle characteristics are tested under constant currents. One corresponds to a peaked mmf with I1 = 3.0 amps and I3 = 1.9 amps (total rms current = 3.5 amps); the other corresponds to a fundamental current 11 = 3.5 amps only. The test results are plotted in Fig. 9 to compare with the calculated results. Figure 10 shows the air-gap fluxes (upper traces), and the core fluxes (lower traces), under the same maximum air-gap flux and load, of a peaked-mmf (Fig. loa) and a conventional (Fig. lob) reluctance motor, respectively. A significant 40% reduction of the core flux in a peaked-mmf reluctance motor is clearly shown. The general agreement between analytical and test results as shown in Figs. 6,9, and 10 indicates that the analysis is on the right track.

CONCLUS IONS

The sample arrangement between current waveforms and winding shows that smooth torque can be produced by a peaked-mmf rotating field. One significant property of the peaked-mmf reluctance motor is that the flux per pole for the same amount of torque and maximum tooth flux density is significantly lower than that of a conventional reluctance motor. As a result, particularly for 2-pole motors, the rating of the motor for a given frame can be increased through a bigger bore or deeper stator slots.

The torque analysis with respect to the peaked mmf under the influences of saturation and fringing and groove fluxes is derived. The pull-out torque is proportional to the air-gap area, the bore current square, and the reciprocal of pole pair times air gap. Torque reduction is particularly severe for reluctance motors when the teeth are magnetically saturated. It is important that the saturation effect be considered seriously in punching designs. The air-gap fringing and groove fluxes in the grooved sections also reduce the torque, but this

@- Three

Power SUPP I Y

@-

Current Waveform Source

I I

Fig. 8 Connection of experimental motor

50 - c .r(

n I

40

2 30 U L 0 + 4-J

2 2 0 4-J 3 0

10

0

Peaked-HHF Data for RMS current \ ,_. (...., . = 3.5 amDs 3..:- ..._

.... '.. ... ' . '... . Theoretical 0

.. Conventiona

. .

. .

. .

20 40 60 BO ! 0

Fig. 9 Torque vs. load angle, 6, of peaked-mmf (11 = 3.0 amps, I3 = 1.9 amps) and conventional (11 = 3.5 amps) reluctance motors

Fig. 10 Air-gap flux (upper trace) and core flux (lower trace) of (a) peaked-mmf, (b) conventional reluctance motors (Both with 90' pole arcs and under the same load)

109

effect is not as severe as the results of saturation. The analytical method derived for the peaked mmf can be followed to analyze other arrangements between windings and current waveforms; the general conclusions obtained on this sample study can also be used for other arrangements. Investigation on various windings and their corresponding current waveforms is underway and the results will be discussed in the near future. Test results obtained from the sample motor agree with the calculated results.

ACKNOWLEDGEMENTS

The authors would like to thank the State of Texas for financial support through a grant under Texas Advanced Technology Program, Grant No. 1591. This work has been partially supported by NSF Grant No. ECS-880884, which is gratefully acknowledged. Thanks are due to the Center for Energy Studies, The University of Texas at Austin, for the support staff and facilities provided for the research work.

REFERENCES

J. K. Kostko. "Polvuhase Reaction Svnchronous Motors," Journal of the Ame;i'can Institute of Electrical Engineers,

P. J. Lawrenson and S. K. Guota. "Develooments in the vol. 45, pp. 1162-1168, NOV. 1923.

Performance and Theory of Se'gmental-Rotor Reluctance Motors," Proceedings IEE, vol. 114, no. 5, pp. 645-653, 1967. W. Fong and J. S. C. Htsui, "New Type of Reluctance Motor," Proceedines IEE, vol. 117, no. 3, pp. 545-551, Mar. 1970. W. Fong and J. S. C. Htsui, "Circle Diagram of the Polyphase Reluctance Machine," Conference Record of IASDEEE, Eighth Annual Meeting, pp. 137-142, 1973. P. J. Lawrenson, J. M. Stephenson, P. T. Blenkinsop, J. Corda, and N. N. Fulton, "Variable-Speed Switched Reluctance Motors," Proceedings IEE, vol. 127, pt. B, no. 4,

J. F. Lindsay, R. Arumugam, and R. Krishnan, "Finite-Element Analvsis Characterisation of a Switched Reluctance Motor with

pp. 253- 265, July 1980.

Multitooth per Stator Pole," Procedings IEE, vol. 133, pt. B, no. 6, pp. 347-353, Nov. 1986. J. S. Hsu and A. M. A. Amin. "Freauencv- and Time-Domain Torque Calculations of Current-Sdurce 'Induction Machines Using the 1-2-0 Coordinate System," IEEE Transactions on Industrial Electronics, in review: H. H. Woodson and J. R. Melcher. Electromechanical Dynamics. Part I: Discrete Svstems. New York: John Wiley & Sons. 1968. P. L.'Alger. The Nature of Induction Machines. New York: Gordon and Breach, 1965.

H. H. Woodson and J . S. C. Hsu (Htsui), "Method and Apparatus for Improving Performance of AC Machines," U.S. Patent Application, 1986. J. S. Hsu (Htsui), H. H. Woodson, and S-S. P. Liou, "Experimental Study of Harmonic-Flux Effects in Ferromagnetic Materials," IEEE Transactions on Mametics, accepted for publication. J. S. Hsu (Htsui) and R. Sharma, "Gate Signals for an M- phase, Nth-odd-harmonic Power Electronics Generator with Adjustable Phase Angle Capability," IEEE Transactions on Power Electronics, in review. A. M. A. Amin and J. S. Hsu (Htsui), "Digital-Type Firing Circuit for a Third Harmonic Generator," IEEE Transactions on Power Electronics, in review.

John S. Hsu (or Htsui) (M '64) was born in China. He received a BS degree from Tsing-Hua University, Beijing, China, and a PhD degree from Bristol University, England, in 1959 and 1969, respectively. He joined the Electrical and Electronics Engineering Department of Bradford University, England, serving there for nearly two years.

After his amval in the United States in 1971, he worked in research and development areas for Emerson Electric Company and later for Westinghouse Elecmc Corporation. Presently he is head of the Rotating Machines and Power Electronics Program, Center for Energy Studies, The University of Texas at Austin. Dr. Hsu is a chartered engineer in the United Kingdom and a registered professional engineer in Texas, Missouri, and New York.

Shy-Shenq P. Liou, born i n Tainan, Taiwan, Republic of China, received a BSEE degree from National Taiwan University in 1981 and an MS degree from The University of Texas at Austin in 1985. He served in the Chinese Air Force for two years. At present he is a PhD candidate i n the Electrical and Computer Engineering Department, The University of Texas at Fustin, and works as a research assistant for the Center for Energy Studies.

Herbert H. Woodson (F '70) earned SB, SM, and ScD degrees in electrical engineering from the Massachusetts Institute of Technology, graduating in 1956. He taught at MIT from 1954 to 1971 and at The University of Texas at Austin from 1971 to the present.

At The University of Texas Dr. Woodson is Dean of the College of Engineering, former Director of the Center for Energy Studies, and former Associate Director of the Center for Electromechanics. He has been active i n the IEEE Power Engineering Society, serving as its president from 1978 to 1980. I n 1984 IEEE honored him with the Nikola Tesla Award and the Centennial Medal. He has served on thirteen major governmental committees, published numerous technical papers and reports, and received four patents on electrical machines. Dr. Woodson is a Fellow of the American Association for the Advancement of Science and a Member of the National Academy of Engineering.