finite element estimation of induction motor parameters for sensorless applications

Finite element estimationof induction motor parametersfor sensorless applications

Luigi Alberti and Nicola BianchiDepartment of Electrical Engineering, University of Padova, Padova, Italy, and

Samad Taghipour BoroujeniDepartment of Engineering, Shahrekord University, Sharekord, Iran

Abstract

Purpose – To purpose of this paper is to introduce a procedure to compute the d- and q-axisparameters of the induction motor.

Design/methodology/approach – A finite element procedure, based on the d- and q-axis model ofthe induction motor is adopted.

Findings – Such a procedure is well suited to analyse IM with anisotropic rotor, where anintentionally created saliency is introduced in the rotor bar geometry, so as to detect the IM rotorposition without sensor.

Originality/value – The proposed procedure allows one to evaluate the sensorless control capabilityof the IM. It will be useful for both analysis of the IM performance and design of the machine itself.

Keywords Induction motor, Sensorless control, Equivalent circuit, Finite element analysis,Induction machine parameters, Magnetic devices

Paper type Research paper

1. IntroductionThe permanent magnet (PM) machine is adopted in several applications, thanks to itshigh-torque density and high efficiency. The PM is a key element of the machine whichis also the more expensive component. In addition, particular care has to be givenduring operating conditions so as to avoid to demagnetize it. On the other hand, theinduction motor (IM) represents the workhorse of electrical machines thanks to itsrobustness and reliability (Alberti et al., 2009). Moreover, the absence of expensivecomponents makes it cheap and easy of being manufactured. However, there are notonly advantages. When an IM drive is compared with a PM motor drive, the powerelectronic has to be slightly oversized due to the lower power factor of the IM.

In large-scale production, the absence of the position sensor implies a worthwhilecost reduction. In addition, the presence of a position sensor represents a possiblesource of fault. This is not desirable in applications like transportation systems andelectrical vehicles, in which a high grade of fault tolerance is required. Therefore, asensorless IM drive is the candidate to compete with the PM drive in traction systems.

This paper focuses on a finite element (FE) procedure to compute the IM sensorlesscapability. A rotating field is imposed adopting a d-q model of the IM. The proposedmethod allows to identify the rotor parameter along the d- and the q-axis from thefield solutions. Therefore, the equivalent circuits exhibit different rotor parametersaccording to the considered axis, highlighting the sensorless capability of the IM.

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Induction motorparameters

191

COMPEL: The International Journalfor Computation and Mathematics inElectrical and Electronic Engineering

Vol. 31 No. 1, 2012pp. 191-205

q Emerald Group Publishing Limited0332-1649

DOI 10.1108/03321641211184913

In addition, the proposed method allows to compute the d- and q-axis parameters fromthe same field solution, reducing the computation time.

2. Sensorless control of IMThe sensorless control of IM has been widely investigated in literature. Differenttechniques and solutions have been proposed and discussed extensively (Jansen andLorenz, 1996; Cilia et al. 1997; Degner and Lorenz, 1998; Holtz, 1998; Vas, 1998; Ha andSul, 2000; Holtz, 2002; Carmeli et al., 2005; Duran et al., 2005; Boussak and Jarray, 2006;Holtz, 2006; Iwanski and Koczara, 2007; Pena et al., 2008). In this section, the principlesof sensorless control of IM by means of signal injection are summarized. In particular,a rotating high-frequency signal is considered for the detection of the rotor saliencyfollowing the approach described in Degner and Lorenz (1998) and Holtz (2002).The injection of a carrier signal, in addition to the fundamental excitation, provides apersistent excitation that allows for the continuous estimation of the rotor position andflux angle.

Figure 1 shows a diagram of the control technique. In the left part of the figure, the

reference frame is fixed to the rotor flux. Starting from the stator current reference i*s ,

the current error is computed and the stator voltage reference v*s is generated.Then, a change of reference frame is operated and the voltage reference is reported to

the stator frame by means of the operator e j~qlr , where ~qlr is the estimated rotor flux

angle computed from the estimated rotor position angle ~qe

m (the symbol over a letterindicates the estimated quantities, and superscript e means electrical quantity).

A high-frequency carrier signal vðsÞsc is added to the fundamental excitation using thePWM voltage source inverter. The high-frequency voltage can be written in the statorreference frame as:

vðsÞsc ¼ Vsc ejvct ¼ vðsÞscd þ jvðsÞscq ð1Þ

Figure 1.Diagram of the controlscheme for sensorlesscontrol of IM

Rotor flux reference frame Stator reference frame

IMPWMPI

LPF

is * us

*

is

BPF

Modelsand PLL

+

–

Jl°~

e–jJl°~

ejJl°~ +

+

usc = Vsc ejwct– (s)

wc

Je~m

~wme

Notes: The symbol “ ~ ”over a letter indicates estimated quantities; superscript emeans electrical

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where the carrier voltage components along the two axes are:

vðsÞscd ¼ Vsc · cosðvctÞ

vðsÞscq ¼ Vsc · sinðvctÞ

8<: ð2Þ

With a properly high-carrier frequency vc, the IM is modeled for the high-frequencysignal, considering only the total leakage inductance (Degner and Lorenz, 1998), andthe voltage equation can be written as:

vðsÞsc . jvc LðsÞs

iðsÞ

sc ð3Þ

where ½LðsÞs is the inductance matrix in the stator reference frame. For a rotor with a

single sinusoidally distributed magnetic saliency, the inductance matrix can be writtenin the rotor reference frame as:

LðrÞs

¼

Lsd 0

0 Lsq

" #ð4Þ

where Lsd and Lsq are the two leakage inductances along the d- and q-axis,respectively. Various rotor geometries can be used to achieve such magnetic saliency.Two different examples will be considered in Section 4.

Then the inductance matrix is transformed to the stator reference frame as:

LðsÞs

¼ T LðrÞ

s

T 21 ¼

Lsavg 2 Lsdif cos 2qem 2Lsdif sin 2qe

m

2Lsdif sin 2qem Lsavg þ Lsdif cos 2qe

m

" #ð5Þ

where qem is the rotor position in electrical radians, and the leakage inductances Lsavg

and Lsdif are defined as:

Lsavg ¼Lsq þ Lsd

2Lsdif ¼

Lsq 2 Lsd

2ð6Þ

The interaction between the carrier voltage vðsÞsc , and the rotor saliency produces acarrier signal current that contains information relating to the position of the rotor.Solving equation (3), the carrier current results in:

iðsÞ

sc ¼ 2jI cpejvct þ jI cne

j 2qem2vctð Þ ð7Þ

where:

I cp ¼Lsavg

LsdLsq·Vsc

vcI cn ¼

Lsdif

LsdLsq·Vsc

vcð8Þ

The carrier current is composed by a positive- and negative-sequences component.As shown in equation (7), the negative-sequence component contains informationabout the rotor position qr in its phase and it is generated by the difference of theleakage inductance along the two rotor axes.

In order to extract the rotor position information from the negative-sequencecomponent, the motor current is processed by the two blocks in the bottom-right cornerof Figure 1. At first, the carrier current is multiplied by e2jvct and filtered to eliminatethe positive-sequence component, as:


193

HPF iðsÞ

sc · e2jvctn o

¼ jI cnej 2qe

m22vctð Þ ð9Þ

Then this signal is elaborated by means of a vector product “ £ ” with a signal

e jð2~qe

m22vctÞ which contains the estimated rotor position ~qe

m. In this way, the error signalis obtained as:

1 ¼ I cnej 2qe

m22vctð Þ £ e j 2 ~qe

m22vct

¼ I cn · sin2 ~qe

m 2 qem

¼

Vsc

vc·

Lsdif

LsdLsq· sin2 ~q

e

m 2 qem

ð10Þ

When the error signal 1 is zero, the estimated rotor position ~qe

m is equal to the actualrotor position qe

m, and the sensorless detection of the rotor position of the IM rotor isachieved. Then, the flux angle ~qlr is computed elaborating ~q

e

m (Novotny and Lipo,1996).

It is worth noticing that equation (10) also shows the dependence of the error signalon the difference leakage inductance defined in equation (6). In order to get the errorsignal 1, a proper value of Lsdif has to be achieved by introducing a variation in therotor slot geometry (Degner and Lorenz, 1998).

3. Parameter estimation based on d-q modelAs illustrated in the previous section, it is possible to track the IM rotor position thanksto the introduction of a rotor saliency, that is a difference in the d- and q-axis leakageinductances Lsd and Lsq.

A rotor with an intentionally introduced saliency is considered. Some examples ofrotor structures will be considered in Section 4. The procedure to compute the IMparameters is based on the two-axis IM model. The analysis is carried out in the rotorreference frame, that is, the reference frame rotating at the same speed of the rotor,i.e. ve

m, in electrical radians per second. The reference frames are shown in Figure 2.The electrical angle between the rotor d (r)-axis and the stator d (s)-axis is indicated asqem. Both d- and q-axis are excited together, since a rotating magnetic field is imposed

in the simulations. Therefore, the parameters of both d- and q-axis are obtainedsimultaneously from the same field solution.

In the considered reference frame, the stator voltages are:

vsd ¼ Rsisd þdlsddt

2 vemlsq

vsq ¼ Rsisq þdlsq

dtþ ve

mlsd

ð11Þ

The corresponding d-q model of the IM machine is shown in Figure 3, where allparameters are referred to the stator. The G-type equivalent circuits are used, with allleakage inductances considered on the rotor side. The stator resistances are omitted inthe circuits of Figure 3. Such stator resistance as well as all 3D parameters are notincluded in the FE model of the motor, and they are computed analytically and addedto the circuits in a second time (Alberti et al., 2008; Dolinar et al., 1997).

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At steady state, the voltages and currents can be considered to be sinusoidal with timeso that the complex representation can be used. In the d (r)-q (r) reference frame, theyvary at the electrical speed (v2 ve

m), where v ¼ 2pf , with f the stator frequency.Overline symbols will be used to highlight complex phasors. Thus, equation (11) arerewritten as:

Vsd ¼ RsIsd þ Œ v2 ve

m

Lsd 2 ve

mLsq

Vsq ¼ RsIsq þ Œ v2 ve

m

Lsq þ ve

mLsd

ð12Þ

A. Magnetizing inductancesFor the computation of the magnetizing inductances, it is convenient to simulate therotor at synchronous speed that is, ve

m ¼ v. It results that the electrical quantities(currents, voltages, flux linkages) in the d (r)-q (r) reference frame exhibit zero frequency,i.e. they are constant (upper case letters, without overlines are used in this case).The voltage equations (12) are rewritten as:

Vsd ¼ RsI sd 2 vLsq

V sq ¼ RsI sq þ vLsd

ð13Þ

Figure 2.A sketch of the considered

IM with the adoptedreference frame

Figure 3.Dynamic two-axis

equivalent circuits ofthe IM


195

Since the frequency is zero, there are no rotor currents. The d-q flux linkagescorrespond to the magnetizing d-q flux linkages of the motor. They depend on the d-qcurrents imposed in the stator, since the iron is non-linear.

It is worth noticing that d- and q-axis currents can be imposed simultaneously.Then, both d-q flux linkages, and d-q inductances, can be computed from the same fieldsolution. Therefore, not only the saturation effect is considered, but also the mutualeffect between the d (r)- and the q (r)-axis, that is the d-q cross-saturation effect. In thiscondition, the d-q circuits of IM model (Figure 3) are not independent.

Starting from the d-q axis magnetizing currents, i.e. Id and Iq, the phase currents areobtained from the Park transformation as:

I a ¼ I d cos qem

þ I q sin qe

m

I b ¼ I d cos qe

m 22p

3

þ I q sin qe

m 22p

3

I c ¼ I d cos qem 2

4p

3

þ I q sin qe

m 24p

3

ð14Þ

The magnetizing inductances result in:

LmdðI sd; I sqÞ ¼LsdðI sd; I sqÞ

I sd

LmqðI sd; I sqÞ ¼LsqðI sd; I sqÞ

I sq

ð15Þ

and they are functions of both magnetizing currents. Of course, without consideringcross-saturation effect, the magnetizing inductances are simplified as:

Lmd ¼Lsd

I sd

I sq¼0

Lmq ¼Lsq

I sq

I sd¼0

ð16Þ

B. Rotor parametersFor the computation of the rotor parameters, the analysis is carried out again in therotor reference frame. At steady state, all electrical quantities vary at the rotorfrequency which is v2 ve

m.Neglecting the stator resistance, Rs, the voltages (equation 12) are rewritten as:

Vsd ¼ þŒ v2 vem

Lsd 2 ve

mLsq

Vsq ¼ þŒ v2 vem

Lsq þ ve

mLsd

ð17Þ

and they vary at the electrical frequency (v2 vem).

Therefore, in order to compute the rotor parameters, time harmonic FE simulationsare carried out, setting the frequency f r ¼ ðv2 ve

mÞ=2p. Both rotor and stator arefixed (as at standstill), and the d-q stator windings are supplied at the rotor frequencyfr. The two-axis circuits of Figure 3 reduce to those shown in Figure 4. Since rotorparameters depend on the rotor frequency, they are obtained from various timeharmonic FE simulations imposing different rotor frequencies. A linearized iron

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196

lamination is considered in the FE time harmonic simulations, assigning a properconstant value to the relative magnetic permeability in the various machine parts.Hence, superposition of the effects can be applied.

In order to estimate the rotor parameters, the d-q stator currents in the simulationsare fixed to:

Isd ¼ I

Isq ¼ 2ŒIð18Þ

where jIj ¼ffiffiffi2

pI rms is the current amplitude.

Thus, the magnetic field is rotating, but modulated by the rotor anisotropy.Currents are induced in the rotor bars, and the rotor parameters of the two-axis modelof Figure 4 can be computed. The flux linkages Lsd and Lsq are determined from thefield solution and the voltages are achieved from equation (17). Therefore, the d-axisequivalent parameters are computed from flux linkages, as:

Leq;d ¼ Real

Lsd

Isd

Req;d ¼ 2 v2 vem

Imag

Lsd

Isd

ð19Þ

so that the d-axis rotor parameters Rrd and Lsd of the circuits of Figure 4 are computed as:

Lsd ¼ Lmd

Leq;dðLmd 2 Leq;dÞ2 ðReq;d=ðv2 vemÞÞ

2

ðLmd 2 Leq;dÞ2 þ ðReq;d=ðv2 ve

mÞÞ2

Rrd ¼ Req;dðLmd þ LsdÞ

Lmd 2 Leq;d

ð20Þ

Similar computations are adopted for the q-axis parameters Rrq and Lsq of the circuit ofFigure 4(b).

It is worth noticing that jI sdj ¼ jI sqj are imposed in the time-harmonic FEsimulation. As a consequence, jVsdj – jVsqj, since the flux linkages and thecorresponding voltages are modulated by the rotor anisotropy. In the actual operatingconditions, it is jVsdj ¼ jVsqj, while jI sdj – jI sqj.

The described technique allows the computation of the IM parameters along thed (r)- and q (r)-axis. Since the possibility to achieve information about the rotor positionfrom the carrier signal depends on the difference in the d- and q-axis inductances,i.e. on Lsdif as in equation (10), this procedure is an useful tool to investigate thesensorless control capability of the IM. Computing the machine parameters fordifferent frequency it is also possible to study the impact of the carrier frequency.

Figure 4.Steady-state two-axis

equivalent circuits(a) d-axis (b) q-axis


197

4. Different rotor geometriesIn this section, the procedure illustrated above is adopted to compute the parameters ofthree IMs with different rotor geometry. The motor is a 2-pole machine with Qs ¼ 24stator slots and Qr ¼ 28 rotor slots. At first, a rotor without any introduced saliency,i.e. a standard rotor, is considered. Then, two different modifications in the rotorlamination is considered.

A. Regular rotor slotsIn this subsection, a standard IM is considered. The rotor has a standard laminationgeometry, with regular rotor slots. Since there is not intentionally introduced magneticsaliency in the rotor, equal parameters are expected along the d (r)- and q (r)-axis.The computed parameters are reported in Figure 5 versus the rotor position.A frequency of 50 Hz has been considered even though this frequency is low for carriersignal injection in sensorless control, but such a simulation allows to get the typicalvalues of the machine parameters at standstill. Figure 5(a) shows the rotor resistancealong the two axes and Figure 5(a) shows the total leakage inductance. It can be notedthat both the two-axis parameters Rr and Ls have the same average value. The periodicvariation of the parameters with the rotor position is due to the slot harmonics and it isinvestigated in detail later on.

Figure 6 shows the same parameters, computed setting a rotor frequency equal to300 Hz which is a frequency more suitable for signal injection in sensorless control ofIM. Considering the average values, it can be noted that there is significant increasingof the rotor resistances while the leakage inductances decreases. Also in this case thereis a variation of the parameters with the rotor position.

Figure 7 shows the flux linkages computed during the simulations at 300 Hz.Figure 7(a) and (b) shows the flux linkage of the phase a and of the d-axis versus the

Figure 5.Simulations at 50 Hz, rotorwithout saliency

1.30

1.40

1.50

1.60

1.70

11.0

11.5

12.0

12.5

0 12 18 24 30 36 42 48 54 60

Rotor position (deg)

100 20 30 40 50 60


(a) Rotor resistance (b) Leakage inductance

6

d-axis q-axis d-axis q-axis

Rr (

Ω)

Lσ

(mH

)

Figure 6.Simulations at 300 Hz,rotor without saliency

0 12 18 24 30 36 42 48 54 6010.5

11.0

11.5

12.0

1.50

2.00

2.50

3.00

3.50

4.00

Rr (

Ω)


100 20 30 40 50 60


d-axis q-axis

(a) Rotor resistance

Lσ

(mH

)

d-axis

(b) Leakage inductance

q-axis

6

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198

rotor position, respectively. Both the real and imaginary values achieved by the timeharmonic simulations are reported.

As expected, the phase a flux linkage, la, varies as a cosine function with therotor position. The d-axis flux linkage is almost constant with the rotor position. Both laand ld exhibit a superimposed high-frequency components. Figure 8 shows theharmonic content of the phase a flux linkage. Besides, the main harmonics of orderp ¼ 1, the higher harmonics are those of orderQr ^ 1 (they are the harmonics of order 27and 29 for the considered machine). There are also the harmonics of order Qr ^ 3 (i.e. 25and 31 but their amplitude is lower (a semilogarithmic scale is adopted in Figure 8).

In order to reduce the slot harmonic effects, the rotor is skewed. In order to considerthe rotor skewing in the FE analysis, for each rotor position, a set of simulations iscarried out considering a skewing step of one mechanical degree. Then, the resultsare averaged and the IM parameters computed. Figure 9 shows the phase a fluxlinkage computed according to two different skewing angles. For the sake ofcomparison, the flux linkage without skewing is also reported. In Figure 9(a), askewing angle of 11 8 is considered. With such a skewing angle the slotting effects

Figure 7.Simulations at 300 Hz,rotor without saliency

–20

–10

0

10

20

0 30 60 90 120 150 180

λ a (

mV

s)


0 30 60 90 120 150 180


λ d (

mV

s)

realimag

(a) Phase a flux linkage

–4048

121620

realimag

(b) d-axis flux linkage

Figure 8.Harmonic content of thephase a flux linkage la

0.1

1

10

100

0 10 15 20 25 30 35

Am

plitu

de (

mV

s)

harmonic order5

Figure 9.Phase a flux linkages

considering two differentskewing angles in the

rotor

4.06.08.0

10.012.014.016.018.0

4.06.08.0

10.012.014.016.018.0

0 10 20 30 40 50 60 70 80

l a (

mV

s)

l a (

mV

s)


0 10 20 30 40 50 60 70 80


no skewing11 degskewing

(a) 11 deg skewing

no skewing15 degskewing

(b) 15 deg skewing (one stators lot)


199

is almost completely canceled. Figure 9(b) shows la when the rotor skewing angleis equal to the stator slot angle, which is 15 8. In this case the slotting effects is notcompletely canceled, and the high-frequency components in the flux linkage due to theslotting is in opposition with respect to the original component.

B. Variation in the rotor slot opening heightA modified rotor is now considered. The rotor geometry is modified in order tointroduce a magnetic saliency. In particular, the rotor slot geometry remains the same,but a modulation in the rotor slot opening height is introduced, as shown in Figure 10.The width of the rotor slot openings are equal for all the slots.

The adopted rotor reference frame is reported in Figure 10. The d (r)-axis is fixed ona rotor slot with the higher slot opening. Figure 11 shows the flux lines of a simulationwith only d-axis current at 300 Hz. As can be noted, the flux lines do not enter deeply inthe rotor, but they are mainly concentrated in the upper part of the rotor where therotor slot openings height is lower. Similarly, Figure 12 shows the flux line when onlyq-axis current is imposed. In this case, the flux lines are concentrated where the rotorslot openings height is higher. This means that a lower d-axis inductance is expectedwith respect to the q-axis.

The IM parameters are computed as described above but without considering rotorskewing. Figure 13(a) shows the rotor resistance at 300 Hz. Comparing Figures 6(a)and 13(a), there is not a significant variation in the rotor resistance since the rotorshape is not changed.

Figure 13(b) shows the leakage inductances at 300 Hz. In this case the mean valueof the two-axis parameters are not equal, due to the introduced magnetic saliency.As expected, the d-axis inductance is lower than the q-axis inductance.

In both (a) and (b) of Figure 13, the slot harmonics effect is visible. It represents adisturbance in the detection of the rotor position, since it influences the inductance Lsdifand the error signal 1 given in equation (10). Therefore, the rotor skewing represents abenefit according to this sensorless technique.

Figure 10.Rotor structure of the firstrotor (rotor no. 1)

q(r)

d (r)

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200

C. Variation in the rotor slot opening widthA different rotor slot modification is now analyzed. The rotor slot geometry remainsagain the same, a modulation is introduced in the slot opening width, as shown inFigure 14 while the heights of the slot openings are equal for all the slots.

The adopted rotor reference frame is reported in Figure 14. The d (r)-axis is fixed ona rotor slot with the thinnest slot opening. Also in this case, similarly to the simulationreported in Figures 11 and 12, when only d-axis current is imposed the flux lines aremainly concentrated in the upper part of the rotor, and so a lower d-axis inductance isexpected as well.

Figure 15(a) shows the rotor resistance computed at 300 Hz. As above, there is not asignificant variation in the rotor resistance with respect to the previous rotor geometries.

Figure 15(b) shows the leakage inductances at 300 Hz. The mean value of the d- andq-axis parameters are not equal due to the introduced magnetic saliency. As expected,the d-axis inductance is lower than the q-axis inductance. Finally, Figure 15(a) and (b)highlights again the disturbance due to the rotor slot harmonics.

Comparing the results shown in Figures 13(b) and 15(b), it can be noted that in rotorno. 2 the difference of the d- and q-axis inductances is lower with respect to the rotorno. 1. So that it results:

Lsdif ðrotor#1Þ . Lsdif ðrotor#2Þ ð21Þ

From equation (20) a better sensorless capability is expected from an IM with a rotor oftype no. 1.

5. ConclusionsA FE procedure is presented to compute the high-frequency parameters of an IM. Sucha procedure is based on the two-axis IM model. A machine with an intentionallyintroduced saliency in the rotor has been studied. Two different magnetic geometrieshave been analyzed in the paper. The proposed procedure helps to evaluate the

Figure 11.Flux lines when only

d-axis current is imposed(rotor no. 1)


201

sensorless capability of the IM and to predict the variation of the machine parameters.In addition, the effect of slot harmonics is highlighted and the skewing is takeninto account in the simulations. It is a helpful tool during the design of the rotorgeometry.

Figure 13.Simulations at 300 Hz,rotor no. 1

12.0

13.0

14.0

15.0

16.0

17.0

1.50

2.00

2.50

3.00

3.50

4.00

0 10 20 30 40 50 60

Rr (

Ω)

Rotor position (deg)0 10 20 30 40 50 60


d-axis q-axis


Lσ

(mH

)

d-axis


q-axis

Figure 12.Flux lines when onlyq-axis current is imposed(rotor no. 1)

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Figure 15.Simulations at 300 Hz

(rotor no. 2)

1.50

2.00

2.50

3.00

3.50

4.00

0 10 20 30 40 50 60

Rr (

Ω)


0 10 20 30 40 50 60


d-axis q-axis


Lσ

(mH

)

7.0

8.0

9.0

10.0

11.0

12.0300 Hz

d-axis


q-axis

Figure 14.Rotor structure of the

second rotor (rotor no. 2)

q (r)

d (r)


203

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Vas, P. (1998), Sensorless Vector and Direct Torque Control, Oxford Science Publications, Oxford.

About the authors

Luigi Alberti received the Laurea and PhD degrees in Electrical Engineering fromthe University of Padova, in 2005 and 2009, respectively. Currently he is aResearch Assistant at the University of Padova. His research activities areconcentrated on the electromechanical analysis and design of electrical motors,in particular, for electric drives applications. He is also a Consultant to variouselectromechanical industries.

Nicola Bianchi received the Laurea and PhD degrees in Electrical Engineeringfrom the Department of Electrical Engineering, University of Padova, Padova,Italy, in 1991 and 1995, respectively. In 1998, he joined the Department ofElectrical Engineering of the same University, as Assistant Professor inElectrotechnique. Since 2005 he has been an Associate Professor in ElectricalMachines, Converters and Drives. He works at the Electric Drive Laboratory,Department of Electrical Engineering at the University of Padova. His teaching

activity deals with the design methods of electrical machines, where he introduced the finiteelement analysis of the machines. His research activity is in the field of the design of electricalmachines especially for drives applications. In the same field, he is responsible for variousprojects for local and foreign industries. He is a member of IEEE IAS and IEEE PES. He is amember of the Electrical Machines Committee and the Electrical Drives Committee of the IEEEIA Society. He is author and co-author of several scientific papers on electrical machines and

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drives, and two international books on the same subject. Nicola Bianchi is the correspondingauthor and can be contacted at: [email protected]

Samad Taghipour Boroujeni was born in 1981. He received the BSc., MSc, andPhD degrees in Electrical Engineering from the University of Amirkabir (TehranPolytechnic), Iran, in 2003, 2005, and 2010, respectively. He is currently AssistantProfessor at the Electrical Engineering Faculty of Shahrekord University (SKU),Shahrekord, Iran. He is working on the design, analysis and optimization ofelectric machines.


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finite element estimation of induction motor parameters for sensorless applications

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