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Abstract-- In order to boost up the calculation precision ofd-q space vector analysis, new approach for estimatingparameters of line-starting permanent magnet motors isdeveloped. Introducing leakage-flux and magnetizing-fluxvariations dependant on not only stator excitation but alsorotor one, transient characteristics and steady-stateperformance are calculated. Thorough the comparison withfinite element analysis, the validity of the proposed method isverified. Especially, it is notable that it can provide at shorttimes accurate quasi-steady-state average torque and precisecritical load torque for self-starting.

Index Termsline-starting, space vector analysis, leakageflux, magnetizing flux

I. INTRODUCTION

URING the design stage of line-starting permanent

magnet (PM) synchronous motors, it is indispensable

to ensure the sufficient starting characteristics as well

as the rated performance. From the viewpoint of both time

consumption and cost for constructing the test machine, the

analytical approach on a computer that can realize rapid

characteristic estimation and least expense is of importance.

Numerical analysis methods for transient-state

characteristics can be divided into two main groups: one is

to analyze the electromagnetic field with the finite element

method (FEM), and the other is to solve the basic equations

with direct- and quadrature-axis space vector. The former

can provide the accurate results including harmonic

components due to complicated motor geometry by

combining the electrical-circuit model and kinetic system

[1]. On the other hand, the latter can realize the short-time

analysis in exchange for less accuracy, and thus boosting up

its calculation precision has been an important challenge

and is the main aim of this paper. It should be noted that

there is also another noble method: reluctance network

analysis, which has been widely studied and used due to its

compatibility between accurate and short-time calculation

[2], [3], although it is outside the scope of this paper.

The d-q space vector analysis needs parameters, such asinductance and resistance, and hence numerous approaches

for the estimation of these values have been investigated

and reported. In the early 1980s, Honsinger accomplished

the first work introducing the constant parameters that

included saturation effect of iron core, although these

parameters were not analyzed but measured with a test

motor [4]. Afterwards, as the analysis approach with the

FEM had been improved [5], [6], it became possible to

calculate such constant parameters without any

measurement, taking into account the space harmonics [7]

and the magnetic saturation [8], [9]. However, parameters

A. Takahashi, S. Kikuchi, H. Mikami, and K. Ide are with HitachiResearch Laboratory, Hitachi, Ltd., 7-1-1, Omika-cho, Hitachi-shi, Japan(e-mail: akeshi.takahashi.hc@hitachi.com).

A. Binder is with the Institute for Electrical Energy Conversion,Darmstadt University of Technology, Landgraf-Georg-Strasse 4, D-64283,Darmstadt, Germany.

variations dependent on current changes had not been

considered until it was measured and introduced into the d-

q space vector equations by Consoli [10]. His work was

superior in terms of representing the flux-linkage variations

as the function of both d-axis and q-axis stator current. In

1990s, with the development of computer performance, one

became able to achieve the widely changing parameters

dependent on the current variations by using the finite

element analysis (FEA). Rahmans paper first introduced

not only the parameters variations on the direct and

quadrature axes but also d-q cross-coupling effect, and

finally predicted steady-state characteristics with high

accuracy [11]. Afterwards, the availability of transient-statecalculation was also studied and presented [12]-[14].

However, treating the transient state with the d-q space

vector analysis, one must pay attention to the fact that

stator-side and rotor-side excitation has more or less

different flux paths. This means that the magnetizing flux,

which would be inherently equivalent whether stator or

rotor excitation, can be dependent on its flux source (see

Figs. 2 and 3), and hence the interference of both excitation

in the magnetizing and leakage flux must be considered.

From this viewpoint, the former studies have deficit, only

dealing with the magnetizing-flux excited by the stator

current; in [12], magnetizing flux in air gap generated by

the stator excitation was adopted and leakage flux wasneglected; in [13] and [14], although the leakage reactance

attributed to the rotor excitation was calculated only for

each slip, neither leakage- nor magnetizing-flux maps

related to the rotor current were treated. Therefore, more

consideration about how far the flux variation can be

affected by the excitation is kind of needed.

It should be noted that combinations of stator-current

and rotor-current input are so myriad that the perfect map

for their whole variation is difficult to make. And also, such

complicated works should be avoided from the viewpoint

of the simple and short-time design of the d-q space vector

analysis. In this paper, the leakage-flux and magnetizing-

flux behavior are investigated by the provisional FEA, andit is discussed how the magnetizing-flux linkage, which

would be common between the stator and rotor sides,

should be assumed. And then, the obtained parameters are

used for the d-q space vector analysis. To verify the validity

of the introduced method, the transient-state performances

are calculated and compared with the FEA results. All

analyses are performed for a two-pole prototype motor with

PN= 5 kW, nN= 3000 min-1

, VN= 200 V, Y-connection (see

data in Table 1 and Fig. 1). Neither the skin effect nor the

d-q cross-coupling effect is taken into account, which will

be studied in a future report.

II. BASIC THEORY OF CONVENTIONALMETHOD

The transient-state equations for line-starting PM

synchronous motors are expressed in per-unit values in

the d-q-reference frame:

d-q Space Vector Analysis for Line-StartingPermanent Magnet Synchronous Motors

Akeshi Takahashi, Satoshi Kikuchi, Hiroyuki Mikami,Kazumasa Ide and Andreas Binder

D

978-1-4673-0141-1/12/$26.00 2012 IEEE 134

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qmd

dsd

d

diru

+= (1)

dm

q

qsqd

diru

++= (2)

d

dir

'D'

D'

D +=0 (3)

d

dir

'Q'

Q'

Q +=0 (4)

( ) pd'

Ddmdsdmd ixixx +++= (5)

( ) 'Qqmqsqmq ixixx ++= (6)

( ) pd'D'Ddmddm'D ixxix +++= (7)( ) 'Q'Qqmqqm'Q ixxix ++= (8)

Lem

J mmd

d=

(9a)

( ) ( ) ( ) ( ) ( ) qddqe iim = (9b)

The subscripts dand q represent direct- and quadrature-

axis stator quantities, respectively, whileD and Q represent

direct- and quadrature-axis rotor cage quantities, and s

represents stator. The primed values signify rotor quantities

related to the stator winding data via a transformer ratio. i, u

and are current, voltage and flux linkage space vector

components, respectively, ris winding resistance,xm andxare main and leakage inductance, respectively, p is PM

flux linkage of the stator winding, m is mechanical angularvelocity, me and mL are electromagnetic torque and load

torque, respectively, is per-unit time: = Nt, and J is

starting time constant: J = NTJ, where N = 2fN and TJ= 319.8 ms. Reference values for the per-unit system are

the peak values of the rated phase voltage 2 UN,ph =

2 115.5 V and of the rated current 2 IN= 2 14.5 A,

the rated frequencyfN= 50 Hz.

For simplicity, the symbol prime is omitted in the

following notation, and the rotor-side parameters arebasically represented only with the capital subscript.

In (5) to (8), one can redefine the magnetizing-flux

linkages dm and qm as the function of the currents:

( )DddmpdDdmddm iiixix +=++

(10)

( QqqmQqmqqm iiixix +=+ .(11)

On the other hand, the leakage flux is expressed as

( )dddbsds iixix += (12)

qqqbsqs iixix += (13)( )DDDbrDD iixix += (14)

QQQbrQQ iixix += (15)

where xsb and xrb represent the overhang leakage flux of

the stator and the rotor, respectively, and d, q, Dand Q represent the slot leakage flux. The reason toseparate the overhang leakage flux from the slot leakage

flux is that the former comes from the conventional

analytical formula, while the latter can be determined

directly from the provisional FEA.

In what follows, for example, the dm which adopts the id

input in the provisional FEA is expressed as dm(id), while

the d with the id input is expressed as d(id), and theothers are subject to the similar manner. The flux curves

used for the space vector analysis comprise fundamental

space fluxes. Fig. 2 shows physically what the d, D, dm ,

d and D represent.Fig. 2 also depicts the difference in flux linkage due to

the only stator excitation and the only rotor excitation,

where the overhang leakage flux xsb*id is neglected. The

magnetizing flux dm(id) and dm(iD) shown in (a) and (b),respectively, which would be inherently equivalent, can

flow more or less different flux paths, and hence can be

non-identical.Fig. 3 illustrates the flux line chart of the dm(id)

and dm(iD) generation, with the following conditions: a) id= -14.6 pu, b) iD = -14.6 pu. Obviously, the leakage flux

paths in (a) are different from those in (b); at the center of

pole, the leakage flux in (a) occurs over eight teeth, while

that in (b) occurs over ten teeth. This leads to the difference

in the magnetic resistance and hence in the total flux

generated by the same magnetomotive force.

Fig. 2 also implies that the slot leakage flux d might bedependent on not only id but also iD, because the fluxgenerated by the iD input causes the interference in the main

flux path and hence the leakage flux path in the stator.Therefore, the d should be expressed as the function ofidand iD. However, combinations of stator-current and rotor-

current input are so myriad that the perfect map for their

whole variation is difficult to make. And also, such

PM

Cage bar

Flux barrier

Rib

Fig. 1. Rotor cross section.

TABLE IDATA OF PROTOTYPE MOTOR

Outer diameter of stator 160 mm

Inner diameter of stator 90 mm

Axial length of iron core 90 mm

Number of poles 2

Number of slots per pole and phase 5

Stator slot type semi-closed

Stator slot height 13.5 mm

Stator teeth width 3.8 mm

Winding connection Y

Number of rotor slots 22

PM material Nd-Fe-B

PM remanent flux density 1.20 T

PM relative permeability 1.04

Rotor cage material aluminum

Output power 5 kW

Rated speed 3000 min-1

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complicated works should be avoided from the viewpoint

of the simple and short-time design of the d-q space vector

analysis. In the next chapter, it is discussed how the

magnetizing and leakage flux should be formulated.

III. PROPOSED METHOD

In the proposed method, the provisional FEA determines

the parameters d, q, D, Q, dm and qm accordingto the two postulates described in the following termsA and

B.

A. Leakage Flux

It is first assumed that the leakage flux d is onlydependent on id but not influenced by any other current

input. In the same way, q is only dependent on iq, D on

iD, and Qon iQ.

This postulate is derived from the original equations (5)to (8). For example, setting iD in (5) and (7) at zero, and

assigning (12) to (5), one can obtain

( ) ( ) ( )

( ) ( )ddmdd

dDdddd

ii

iii

=

=(16)

where the overhang leakage fluxxsb* id is neglected because

the provisional FEA is 2-D field solutions.

Although in reality the slot leakage flux d might bedependent on not only id but also iD, there is no means for

justifying the dbehavior in the case of the coupled inputsofidand iD.

The other leakage flux q(iq), D(iD), and Q(iQ) aresubject to the same manner:

( ) ( ) ( )( ) ( )qqmqq

qQqqqq

ii

iii

=

=(17)

( ) ( ) ( )

( ) ( )DdmDD

DdDDDD

ii

iii

=

=

(18)

( ) ( )QqmQQQqQQQQ

ii

iii

=

=

. (19)

In the FEA, varying the d-axis stator current id and

keeping the rotor current iD set at 0 pu, d(id) and dm (id)curves can be achieved as shown in Fig. 4. Calculating the

difference of these two curves, d(id) can be obtained.

As it is clear from Fig. 4(b), d(id) is not linear functionofid, but the saturated curve. Normally, the leakage flux is

represented by constant inductance, and hence is

proportional to the current input. However, one has to pay

attention to the fact that a strict linear characteristic of the

leakage flux is only based on the linear property of the

magnetic steel sheet. In other words, any saturation of iron

core expropriates the linearity of main-flux and leakage-

flux variation. This is because the saturation in the main

flux path increases a total magnetic resistance, and hence

the total flux generated under the constant magnetomotive

force is decreased, leading to the nonlinearity of the leakage

flux. More detailed explanation with the magnetic circuit

described in chapter 4 can help to understand this

phenomenon.

It should be noted that the minus value ofd at id = 0

originates in the fact that the rotor flux linkage D(id)comprises whole flux generated by PMs while the stator

flux linkage d(id) does not include the leakage flux in therotor.

(b) dm(iD)Fig. 3. Flux line chart (a): id= -14.6 pu, b): iD = -14.6 pu).

(a) dm(id)

Gap

Rotor

Stator

PM

dm (iD)

D(iD)

D (iD )Gap

Rotor

Stator

PM

dm (id)

d(id)

d (id)

(a) with id input (iD = 0) (b) with iD input (id= 0)

Fig. 2. Schematic of flux linkage.

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-15 -10 -5 0 5 10 15

id (p.u.)

yd,ydh

(p.u.)

d(id)dh(id)

d(id)

dm (id)

Fluxlinkaged,

dm

(pu)

(pu)

(b) d(id) curveFig. 4. FE Analysis results of direct-axis flux linkage with idinput.

(a) d(id) and dm (id) curves

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

-15 -10 -5 0 5 10 15

id (p.u.)

d

(p.u.)

Leakag

eFluxd

(pu)

(pu)

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Varying the d-axis rotor current iD and keeping the stator

current id set at 0 pu, D (iD) and dm (iD) curves can beachieved as shown in Fig. 5. Calculating the difference of

these two curves, D(iD) can be obtained. In this case

D(iD) is approximately the linear function ofiD, as is well

known. But it should be noted that the D variation is not

strictly linear. The detailed behavior of the D can also beexplained by the magnetic circuit as described in chapter 4.

In the same way, the q(iq) is not the linear function of

iq but the saturated curve, while the Q(iQ) isapproximately the linear function ofiQ.

B. Magnetizing Flux

This term investigates magnetizing flux behavior, and

introduces the second postulate fordm and qm.According to (5), (7) and (10), the FE analysis with a

single id input yields D (id) = dm (id), while a single iD

input yields d(iD) = dm (iD). Fig. 6 shows the FEA results

ofdm(id) and dm(iD). dm denotes the difference between

dm(id) and dm(iD) :

)()( Ddmddmdm ii = . (20)

Basically, dm(id) and dm(iD) should be identical and

hence dm should be constantly zero, but actual curves ofthem are not exactly identical because of the difference in

the local flux paths.

Aiming at the simple treatment of dm, it is secondly

assumed that the magnetizing flux dm is expressed by the

only one function ( )Dddm ii + dependent on the sum ofidand iD:

2

)()(

2

DdmddmDd

dm

iiii

+=

+

(21)

where id= iD.

This postulate arises one question: how widely the dm

can cover the actual dm generated by myriad combinationsofidand iD. According to (5) and (10), the magnetizing flux

generated by the simultaneous inputs of idand iD can be

separated from the total flux linkage d(id, iD):

( ) ( ) ( )ddDddDddm iiiii =+ , (22)

where the assumption defined in term A is still valid that

d(id) is only dependent on id but not influenced by any

other current input.

Fig. 7 shows FEA results of the dm calculated by (21)

and the dm by (22). Although some deviations are

recognized, it is possible to substitute the dm for dm

regardless of the combinations ofidand iD.

By the way, according to (7) and (10), the magnetizing

flux dm is expressed in another way:

( ) ( ) ( )DDDdDDddm iiiii =+ , . (23)

Fig. 8 shows the FEA results of the dm calculated by

(21) and the dm by (23). Although some deviations become

bigger than that in Fig. 6, the magnetizing flux defined in(21) is to be introduced in the proposed method.

In the same way, it is assumed that the magnetizing flux

qm is expressed by the only one function ( )Qqqm ii +

dependent on the sum ofiq and iQ:

2

)()(

2QqmqqmQq

qm iiii +

=

+(24)

where iq = iQ.

(b) D(iD) curveFig. 5. FE Analysis results of direct-axis flux linkage with iDinput.

(a) D (iD) and dm (iD) curves

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-15 -10 -5 0 5 10 15

iD (p.u.)

(p.u.)

D(iD)

dh(iD)

D (iD)dm(iD)

(pu)

FluxlinkageD

,

dm

(pu)

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-15 -10 -5 0 5 10 15

iD (p.u.)

D

(p.u.)

(pu)

Leak

ageFluxD

(pu)

0

0.05

0.1

0.15

0.2

-15 -10 -5 0 5 10 15

id, iD (p.u.)

dm(

p.u.)

(pu)

Deviation

dm

(pu)

(b) dm

Fig. 6. FE Analysis results of difference between dm (id) and dm (iD).

(a) dm (id) and dm (iD) curves

-2

-1.5

-1

-0.50

0.5

1

1.5

2

-15 -10 -5 0 5 10 15

id, iD (p.u.)

(p.u.)

dh(id)

dh(iD)

dm (id)

dm (iD)

(pu)

Fluxlinkagedm

(pu)

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IV. THEORETICAL PROOF OF PROPOSED MODEL

This chapter theoretically proves the nonlinear propertyof the leakage flux and the inconsistent property of the

magnetizing flux described in chapter 3.

A. Theoretical Leakage Flux

Fig. 9 shows the simple magnetic circuit for the line-

starting PM motor. R represents magnetic resistance, F

represents magnetomotive force, and represents flux. The

subscriptss is stator, ris rotor, is air gap,p is permanent

magnet, and is leakage.Applying the Kirchhoffs second law for the whole

closed loops and solving the equations, one can calculate .Assuming the linear case, i.e., infinite permeability of iron

core, the magnetic resistance Rs and R r can be neglected.

And more, setting the stator-side magnetomotive forceFsat

an arbitrary value except for zero and the rotor-side Fr at

zero, 1lrepresents

ld(id), while 3

lrepresents

lD (id),

and hence ld(id) is expressed as

p

rppr

s

srppr

p

lld

lDd

ldd

ld

FF

iii

++

+

++=

+==

RRRRRR

R

RRRRRRR

R 1

)()()( 31

(25)

where superscript l means the linear case. Since all the

magnetic resistance andFp

in (25) are constant,

l

d(id

) is

the linear function of magnetomotive forceFs or current.

Applying rough approximation ofR = 0.01Rs, Rp =

0.1Rs and Rr= Rs to (25), ld(id) can be calculated as

)09.09.1(1

)( pss

dld FFi =

R

. (26)

However, in reality, the magnetic saturation of the iron

core makes nonnegligible the magnetic resistance such as R

s. Assuming Rs = kRs, where k is nonlinear coefficient,

and applying the same conditions as the above linear case

to the other magnetic resistance, one can obtain

++

+=

+==

ps

s

nlnl

d

nl

Dd

nl

dd

nl

d

Fk

kF

k

iii

0.11.2

2

0.11.2

0.21

)()()( 31

R

(27)

where superscript nlmeans the nonlinear case.

When k= 0.1 orRs = 0.1Rs, nl

d(id) is

)0.91.910(1

)( pss

d

nl

d FFi =

R

(28)

Comparison of (26) with (28) clarifies that the nonlinear

case yields less leakage flux, and that the leakage flux is

dependent on the magnetic resistance Rs or the iron core

saturation. If the Rs increases due to more saturation, the

leakage flux will further decrease: for example, k= 0.5 or

Rs = 0.5Rs, which can be caused by huge magnetomotive

force Fs, leads to the significant saturation of the leakage

flux

)1.43(0.291

)( pss

d

nl

d FFi =

R

. (29)

Applying the same conditions as the above, and setting

the Fs at zero and the Fr at an arbitrary value except for

zero, D(iD) in the nonlinear case can be expressed as

)(0.11.2

21)()()( 13 pr

C

s

DdDDDD FFk

kiii +

+=+==

=

R

(30)Table 2 represents the relationship between k and the

coefficient C= 2k/(1.2k + 0.1). As is clear from (30) and

Table 2, the D is nonlinear function ofFr. However, one

Fig. 7. FE analysis results of direct-axis magnetizing-flux linkagedm

calculated by (21) and the dm calculated by (22).

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-15 -10 -5 0 5 10 15

id+ iD (pu)

dm(

id

+iD)(pu)

iD = -14.6 puiD = -9.8 puiD = -4.9 puiD = 0 puiD = 4.9 puiD = 9.8 pu

iD = 14.6 pudm (ave.)

iD

dm

Fig. 8. FE analysis results of direct-axis magnetizing-flux linkagedm

calculated by (21) and the dm calculated by (23).

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-15 -10 -5 0 5 10 15

id + iD (pu)

dm(

id

+iD)(pu)

id = -14.6 pu

id = -9.8 puid = -4.9 puid = 0 puid = 4.9 puid = 9.8 puid = 14.6 pudm (ave.)

id

dm

Fig. 9. Simple magnetic circuit for the line-starting PM motor (R:

magnetic resistance,F: magnetomotive force, : flux; subscriptss: stator,

r: rotor, : air gap,p: permanent magnet, : leakage).

Fs

RsRs Rr

R

Rp

Rr

Fr

Fp

1 2 3

Stator RotorAir gap

TABLE IIRELATIONSHIP BETWEENKAND C=2K/(1.2K+0.1).

k 0.1 0.2 0.3 0.5 1.0 1.5

C 0.91 1.18 1.30 1.43 1.54 1.58

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has to pay attention to the fact that the increasing rate of C

is much more moderate than that of k; for example,comparing k = 1.0 with k = 0.1, the k increases 10 times

while the C increases only 1.7 times, which results in the

apparent linear characteristic ofD.

B. Theoretical Magnetizing Flux

Setting the Fs at an arbitrary value except for zero and

theFrat zero, 3 is equal to D (id) ordm (id):

( )Rdet

)()(

)(

2

3

psrssssrs

ddm

FF

i

++++=

=

RRRRRRRR

(31)

where

22 )()(

)()()(

srprrss

rprrsssdet

RRRRRRR

RRRRRRRR

+++

+++++=R

(32)

Inversely, setting the Frat an arbitrary value except for

zero and theFs at zero, 1 is equal to d(iD) ordm (iD):

Rdet

)( 1

prsrrs

Ddm

FF

i

+=

=

RRRR (33)

Comparison of (31) with (33) clarifies that dm (id) and

dm (iD) are generated by the different flux paths.

V. VALIDITY OF PROPOSED METHOD

The obtained parameters in chapter 3 are used for the d-q

space vector analysis. In order to verify the validity of the

proposed method, the transient-state performances arecalculated and compared with the FEA results.

Fig. 10 shows the results of the d-q space vector analysis

during start up, with the following conditions; u = 1.00 pu,

fs = 1.00 pu, J= 100.48 pu, mL = 0 pu. For comparison, theFEA time-stepping results are also represented.

Due to the switching on of the stator voltage, the 50Hz

starting current and the DC component occur in the stator

winding, and results in the 50Hz-pulsating starting torque.

During the start-up, all results exhibit a good agreement.

There are some errors between the d-q space-vector-

analysis results and the FEA results, which is mainly

because the d-q space vector analysis takes into account

neither the d-q cross-coupling effect nor the influence of thecurrent displacement. Also, it may be another reason that

the provisional FEA determines the parameters according to

the two postulates described in chapter 3.

Fig. 11 shows the quasi-steady state characteristics. In

order to verify the advantages of the proposed method, the

results calculated with the conventional method are also

presented. The conventional method only considers the

magnetizing flux in the air gap generated by the stator

excitation, while the leakage flux is neglected, leading to

the big deviations as shown in Fig. 11(a). On the other hand,

the proposed method exhibits better agreement with the

FEA results, as shown in Fig. 11(b). Even in the proposed

method, the peak values around slip = 1 do not agree withthe FEA results. The reason of the errors is that the d-q

cross-coupling and harmonic effects contribute to

pulsating-torque generation. Table 3 represents the detailed

data of the quasi-steady state characteristics. The deviation

between the conventional method and the FEA becomes

more than 20 %, while the proposed method offers less

error within 10 %.

The calculation accuracy of the average torque in the

quasi-steady state results in the precision of critical loadtorque for the self-starting. It is 1.25 pu in the FEA

(starting-success up to this value) whereas 1.52 pu in the

proposed method. The deviation is 22%, which comes from

the calculation errors shown in Table 3. In the proposed

method, the critical load torque is 1.31 pu, which exhibits a

good agreement with the FEA.

These results indicate that the proposed method enables

one to estimate accurate slip-versus-torque curves and

starting capability at short times.

VI. CONCLUSION

In order to boost up the calculation accuracy of the d-q

space vector analysis, the leakage-flux and magnetizing-flux behavior were investigated and the obtained

parameters were used for analysis program.

First through the provisional investigation, it was found

-8-6

-4

-2

0

2

4

6

8

10

12

0 0.2 0.4 0.6

Time (s)

Torque(pu)

d-q space vector analysis

FEA

(c) U-phase current versus timeFig. 10. Computation of FEA and d-q space vector analysis results atno-load starting (u = 1.00 pu,fs = 1.00 pu, mL = 0 pu).

(b) Rotation versus time

(a) Torque versus time

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6

Time (s)

Rotation(pu)

d-q space vector analysis

FEA

-15

-10

-5

0

5

10

15

0 0.2 0.4 0.6

Time (s)

U-phasecurrent(pu)

d-q space vector analysis

FEA

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that

- leakage-flux curve of stator excitation is saturated dueto the magnetic resistance in the stator core, while thatof rotor excitation is nearly proportional to currentinput,

- the magnetizing flux, which would be inherentlyequivalent whether stator or rotor excitation, is not

always identical but dependent on its flux source.Second, in order to verify the validity of the proposed

method, simulation results were compared with the FEA

results. It was found that

- the quasi-steady state characteristics and the criticalload torque for self-starting exhibited the goodagreement with the FEA results, which indicted thatthe method enables one to estimate accurate startingcharacteristics at short times.

VII. REFERENCES

[1] K. Kurihara and M. A. Rahman, Steady-state performance analysisof permanent magnet synchronous motors including spaceharmonics, IEEE Trans. Magn., vol. 30, pp. 13061315, May 1994.

[2] V. Ostovic, Computation of saturated permanent magnet ac motorperformance by means of magnetic circuits, IEEE Trans. Ind. Appl.,vol. IA-23, no. 5, pp. 836-841, Sept./Oct. 1987.

[3] V. Ostovic, A simplified approach to the magnetic equivalent circuitmodeling of electric machines, IEEE Trans. Ind. Appl., vol. 24, no.2, pp. 308-316, Mar./Apr. 1988.

[4] V. B. Honsinger, Permanent magnet machine: asynchronousoperation, IEEE Trans. Power App. Syst., vol. PAS-99, pp. 15031509, July 1980.

[5] K. Miyashita, S. Yamashita, S. Tanabe, T. Shimozu and H. Sento,Development of a high speed 2-pole permanent magnetsynchronous motor, IEEE Trans. Power App. Syst., vol. PAS-99,pp. 2175-81, 1980.

[6] V. B. Honsinger, The fields and parameters of interior type of acpermanent magnet machines, IEEE Trans. Power App. Syst., vol.PAS-101, no. 4, pp. 867-876, Apr. 1982.

[7] A. Ishizaki and Y. Yamamoto, Asynchronous performanceprediction of ac permanent magnet motor, IEEE Trans. EnergyConv., vol. EC-1, no. 3, pp. 101-108, Sep. 1986.

[8] M. A. Rahman and A. M. Osheiba, Performance of large line-startpermanent magnet synchronous motors, IEEE Trans. Energy Conv.,vol. 5, pp. 211217, Mar. 1990.

[9] S. M. Osheba and F. M. Abdel-Kader, Performance analysis ofpermanent magnet synchronous motors part:II operation fromvariable source and transient characteristics, IEEE Trans. EnergyConv., vol. 6, no. 1, pp. 8389, Mar. 1991.

[10] A. Consoli and A. Abela, Transient performance of permanentmagnet AC motor drives, IEEE Trans. Ind. Appl., vol. IA-22, no.1,pp 32-41, 1986.

[11] M. A. Rahman and P. Zhou, Determination of saturated parametersof PM motors using loading magnetic fields, IEEE Trans. Magn.,vol. 27, no. 5, pp. 39473950, Sep. 1991.

[12] I. Iglesias, L. Garcia and J. Tapplrit, A d-q model for the self-comtated synchronous machine considering the effects of magneticsaturation, IEEE Trans. Energy Conv., vol. 7, no. 4, pp. 768776,Dec. 1992.

[13] P. Zhou, M. A. Rahman and M. A. Jabber, Field circuit analysis ofpermanent magnet synchronous motors, IEEE Trans. Magn., vol.30, no. 4, pp. 13501359, July 1994.

[14] M. A. Rahman and P. Zhou, Field-based analysis for permanentmagnet motors, IEEE Trans. Magn., vol. 30, no. 5, pp. 36643667,Sep. 1994.

VIII. BIOGRAPHIES

Akeshi Takahashi (M08) received the M. Eng. degree from HokkaidoUniversity, Sapporo, Japan, in 2004, and Dr.-Ing. (Ph.D.) degree fromDarmstadt University of Technology, Darmstadt, Germany, in 2010. Since2004, he has been with Hitachi Research Laboratory, Hitachi Ltd., wherehe is engaged in rotating machine research and development. He was a

Visiting Researcher in Darmstadt University of Technology from 2007 to2008.

Satoshi Kikuchi graduated Miyagiken Technical High School, Sendai,Japan, in 1988. Currently, he is with Hitachi Research Laboratory, wherehe is involved in rotating machine research and development as a SeniorResearcher. He has been with Hitachi Ltd. since 1988.

Hiroyuki Mikami (M95) received the M. Eng. degree from IbarakiUniversity, Hitachi, Japan, in 1990, and Ph. D. degree from TohokuUniversity, Sendai, Japan, in 2008. Currently, he is a Manager withHitachi Research Laboratory, where he is involved in rotating machineresearch and development. He has been with Hitachi Ltd. since 1990.

Kazumasa Ide (M94) received the M. Eng. and Ph. D. degrees fromTohoku University, Sendai, Japan, in 1988 and 1994, respectively.

Currently, he is a Manager with Hitachi Research Laboratory, where he isinvolved in electric power conversion system. He has been with HitachiLtd. since 1988.

Andreas Binder (M97SM04) received the Dipl.-Ing. (diploma) and Dr.Tech. (Ph.D.) degrees in electrical engineering from the University ofTechnology, Vienna, Austria, in 1981 and 1988, respectively. From 1981to 1983, he was with ELIN-Union AG, Vienna, where he worked on thedesign of synchronous generators. From 1983 to 1989, he was with theDepartment of Electrical Machines and Drives, Technical University,Vienna. After this, he joined Siemens AG, first in Bad Neustadt, Germany,then in Erlangen, Germany. His main tasks included the development of dcand inverter-fed ac drives. Since October 1997, he has been the Head ofthe Institute of Electrical Energy Conversion, Darmstadt University ofTechnology, Darmstadt, Germany, where he is also a Full Professor. Dr.Binder was the recipient of the Power Engineering Society (ETG)Literature Award in 1997.

TABLE IIIDETAILED DATA OF QUASI STEADY-STATE CHARACTERISTICS.

Ave. torque

(pu)

Deviation

(%)

Ave. torque

(pu)

Deviation

(%)

Ave. torque

(pu)

Deviation

(%)

FEA 2.89 100 2.24 100 0.73 100

Convent ional 4.11 142 3.00 134 0.87 120

Proposed 3.05 105 2.44 109 0.76 105

s = 0.1s = 1 s = 0.5

Fig. 11. Quasi steady-state characteristics (solid lines: d-q space vector

analysis, dotted line: FEA).

(b) Proposed method

(a) Conventional method-4

0

4

8

12

00.20.40.60.81

Electromagnetictorque(pu)

Slip (pu)

Maximum torque

Average torque

Minimum torque

-4

0

4

8

12

00.20.40.60.81

Electromagnetictorque(pu)

Slip (pu)

Maximum torque

Average torque

Minimum torque

140