Zero speed sensorless drive capability of fractional slot ...paduaresearch.cab.unipd.it/5230/1/2012_PEMD_Sensor... · Zero–speed sensorless drive capability of fractional–slot

Zero–speed sensorless drive capability offractional–slot inset PM machine

Adriano Faggion Nicola Bianchi Silverio BolognaniEmanuele Fornasiero

Electric Drives LaboratoryDepartment of Industrial EngineeringUniversity of Padova

PEMD 2012Power Electronics, Machines and Drives Conference

Bristol, 27-29 March 2012

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Introduction

Self sensingrotor positiondetection

Inset 12–slot8–pole PMmachine

Finite elementsimulations

Experimentalresults

Conclusions

This presentation refers to the paper:

Adriano Faggion, Nicola Bianchi, Silverio Bolognani andEmanuele Fornasiero

”Zero–speed sensorless drive capability offractional–slot inset PM machine”

IEEE – PEMD 2012Power Electronics, Machines and Drives Conference

Bristol (UK), 27-29 March 2012.

PEMD 2012 Zero–speed sensorless drive capability of fractional–slot inset PM machine 2

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Introduction




Experimentalresults

Conclusions

Outline

1 Introduction

2 Self sensing rotor position detection

3 Inset 12–slot 8–pole PM machine

4 Finite element simulations

5 Experimental results

6 Conclusions


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Introduction




Experimentalresults

Conclusions

Introduction

Sensorless control purpose

For the sensorless control purpose, three different rotorconfigurations are studied in a previous paper:(a) Interior,(b) Ringed–pole and (c) Inset Permanent Magnet (PM)Rotor.

(a) Interior PM motor (b) Ringed pole PMMotor

(c) Inset PM motor


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Introduction




Experimentalresults

Conclusions

Introduction

Sensorless control purpose

For the sensorless control purpose, three different rotorconfigurations are studied in a previous paper:(a) Interior,(b) Ringed–pole and (c) Inset Permanent Magnet (PM)Rotor.

⇒ Among these the inset PM machine results to have agood performance as far as the sensorless rotor positiondetection is concerned.Then in the paper a 12–slot 8–pole inset PMconfiguration is deeply studied.


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Introduction




Experimentalresults

Conclusions

Self sensing rotor position detection

Sensorless technique1 The detection of the rotor position by means of a high

frequency (HF) signal injection is a common sensorlessdetection technique.

2 It consists on the injection of a HF voltages in the statorwindings, which causes a HF currents.

3 HF current vector draws a figure that containsinformation of the rotor position.


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Rotation due to thecross-saturation effect

Rotating HF voltage vector⇓

Ellipse HF current vectortrajectory⇓

HF saliency can bedefined as:

ξHF =∆Imax∆Imin

⇓mutual inductance Ldqh

causes the ellipseinclination �


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HF rotating voltage, injected in a general rotating referenceframe dxqx , of the type:

uxdh = Uhcos(ωht)uxqh = Uhsin(ωht)

is adopted.It is assumed that the machine is standstill (electrical speedequal to zero).


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The magnetic model of the machine can be described bymeans of the matrix of differential HF inductances in eachoperating point, expressed by:

L =[

Ldh LdqhLqdh Lqh

] Lavg = Lqh + Ldh2Ldif =

Lqh − Ldh2

Ldh is the HF d–axis inductanceLqh is the HF q–axis inductanceLdqh is the HF cross saturation inductanceLavg is the HF average inductanceLdif is the HF difference inductance.


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High Frequency current vector results of two components:

īdqh = īcw + īccw

with

īcw = −Λh∆

Lavgej(ωht+π2 )

īccw = −Λh∆

√L2dif + L

2dqh

e−j(2(∆θ−�)+ωht+π2 )

where � is the displacement due to the presence ofcross-saturation between the d– and q–axis. It can becomputed as:

� =12

arctan(−

LdqhLdif

)and ∆ = LdhLqh − L2dqh ,∆θ = θ̃me − θme.


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HF voltage vector injection in the actual dq ⇒ ∆θ = 0 andthen:

īdqh = −Λh∆

Lavgej(ωht+π2 )︸︷︷︸

īcw

− Λh∆

√L2dif + L

2dqh

e−j(−2�+ωht+π2 )︸︷︷︸

īccw

ī cwī ccw

(d)

ī cw

ī ccw

(e)

ξHF =∆Imax∆Imin

=Lavg +

√L2dif + L

2dqh

Lavg −√

L2dif + L2dqh


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The HF current vector īdqh is used to recognize themaximum axis direction of the ellipse. This should coincidewith the d–axis.

x

x

(f) Ideal case Ldqh = 0

xx

(g) Real case Ldqh 6= 0

However, because of the cross–saturation the actual d–axisis not correctly recognized but an axis displaced of theangle error � with respect to the d–axis is found.


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Figure: Sensorless rotor position estimation scheme

Output of the estimation scheme is:

idemf = −Λh∆

√L2dif + L

2dqh

sin(2∆θ − 2�)

This quantity is manipulated in order to zeroing the term∆θ − �. The result is:

∆θ − � = 0 ⇒ θ̃me = θme + �


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Particular case ]1If the motor does not exhibit a cross–saturation between thed– and q–axis, the angle error � becomes equal to zero.The direction of maximum axis is along the d–axis.

⇒ Correct estimation of the rotor position.


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Particular case ]1No cross–saturation between the d– and q–axis. Angleerror � becomes zero.

ξHF =Lavg +

√L2dif + L

2dqh

Lavg −√

L2dif + L2dqh

⇒ ξHF =Lavg + LdifLavg − Ldif

=LqhLdh


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Particular case ]2If the d– and q–axis inductances are equal, the currentvariation on the d– and q–axis becomes equal.Anyway, the HF saliency remains, due to thecross-saturation.

⇒ Rotor position estimation with 45◦ angle error.


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Experimentalresults

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Particular case ]2d– and q–axis inductances equal. HF saliency remains, duethe presence of the cross-saturation.

ξHF =Lavg +

√L2dif + L

2dqh

Lavg −√

L2dif + L2dqh

⇒ ξHF =Lavg + LdqhLavg − Ldqh


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Particular case ]3In case of:• No cross–saturation between the two axes• d– and q–axis HF inductances equalthen the current ellipse degenerates into a circle.

⇒ Rotor position detection not allowable.


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Particular case ]3No cross–saturation and d– and q–axis inductances equal.The current ellipse degenerates in a circumference.

ξHF =Lavg +

√L2dif + L

2dqh

Lavg −√

L2dif + L2dqh

⇒ ξHF =LavgLavg

= 1


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Experimentalresults

Conclusions

Inset 12–slot 8–pole PM machine

Geometry of 12–slot 8–pole inset PM motor

(a) (b)

In red the coil of phase a. The stator exhibits afractional–slot non–overlapped coil winding.

Variable Dimension measure unity

Stack length 90 (mm)External stator diameter 133.6 (mm)Inner stator diameter 71.5 (mm)PM thickness 4.95 (mm)PM width 16 (mm)


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Id = 0 and Iq = 0.Without the current the flux due to the PMs practicallydoesn’t flow through the tooth.


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(c) Id = I and Iq = 0 (d) Id = 0 and Iq = I

FE simulation have been done excluding the effect of themagnet.In the case of Fig.(d) there is a more density of the flux lines.Then the Lq inductance results greater than the Ld one.


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Finite element simulations

FE Simulations

The FE simulations have been carried out with the aimof determining the main characteristics of the motor.Some simulations have been done for different (Id , Iq)currents, to cover a wide range of operating points.Nominal current is IN = 10 A.The current limits are −20 A ≤ Id ≤ 20 A and0 A ≤ Iq ≤ 20 A.The differential inductances are computed and themagnetic saliency of the motor is derived.


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Experimentalresults

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Map of the magnetic saliency ξHF

• It is worth noticing that the saliency is sufficientlyhigh in the whole second half plane. It remains aroundξHF = 1.6.


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Map of the ratio Ldif /Lavg .

• The difference inductance Ldif is greater than zero inthe whole Id–Iq plane.⇒ The rotor position is detected even under overload.


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Experimentalresults

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Map of the ratio Ldqh/Lavg

• The cross–saturation inductance Ldqh is negligiblealong the MTPA trajectory.⇒ The angle error � is very low.


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Map of the error |�| due to cross–coupling (deg)

• � remains lower than 1 el .deg. up to the nominalcurrent.• � increases for higher currents, however remaininglower than 10 el .deg. along the MTPA trajectory.


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Inset 12–slot 8–pole rotor configuration

Summary of the motor characteristicsX A difference inductance Ldif is always greater

than zero in a whole plane, since Lqh > Ldh.X The mutual differential inductance is negligible,

since it is quite similar to that on a SPM motor.X The angle error due to the cross–saturation is

very low, especially along the MTPA trajectory.


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Experimentalresults

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Experimental results

Test bench setup

Some experimental tests have been carried out in order toverify the self–sensing motor capability in all the dq currentplane.

INVERTER


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Experimental setup

• The machine under test is coupled to a master drive.• The master drive can be speed– or torque–controlled byan industrial inverter.• The inset PM machine is controlled by a laboratoryinverter monitored by an acquisition system.• A rotating voltage vector, with amplitude Uh equal to 20 V ,is added to the reference power voltages u∗d and u

∗q given by

the current regulators.• The injection frequency is set to 500 Hz.• The tests have been carried out locking the inset PMmachine by the master one.


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High frequency currents at two different working pointsalong the MTPA trajectory

time (s)

i d(A

)

0 0.002 0.004 0.006 0.008 0.01−2

0

2

time (s)

i q(A

)

0 0.002 0.004 0.006 0.008 0.01−2

0

2

(e) id = 0 and iq = 0

0 0.002 0.004 0.006 0.008 0.018

10

12

0 0.002 0.004 0.006 0.008 0.01−4

−2

0

time (s)

i d(A

)

time (s)

i q(A

)

(f) id = −2 and iq = 10

X Each current is given by the sum of a constant value anda sinusoidal signal due to the HF voltage injection.X The amplitude of the iq current oscillation is lower thanthat of the id current, being Lqh > Ldh .


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High frequency ellipses in the id –iq plane

−8 −6 −4 −2 0 2 4 6 8 10 12 14−8

−6

−4

−2

0

2

4

6

8

10

12

14MTPAHF Ellipse

Rotation due to thecross-saturation effect

X The HF saliency is obtained applying: ξhf = ∆Imax/∆Imin.


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HF Saliency

−8 −6 −4 −2 0 2 4 6 8 10 12 14−8

−6

−4

−2

0

2

4

6

8

10

12

14MTPAHF Ellipse

X ξHF for each ellipse are slightly lower to those estimatedby FE simulation.X ξHF remains equal to 1.6 in all the left dq half–plane.X FE simulations highlight that the saliency remains also inoverload conditions.


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Angle error �

−8 −6 −4 −2 0 2 4 6 8 10 12 14−8

−6

−4

−2

0

2

4

6

8

10

12

14MTPAHF Ellipse

X All the ellipses have the maximum axis practically parallelto the d–axis.X This means that the error � is very low.X With |̄i | ≤ IN the � remains lower than 1 el .deg..X A low error confirms the low cross–saturation effect.X This confirms the results given by the FE simulation.


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Conclusions

Conclusions

X The 12–slot 8–pole inset PM motor results to be verysuitable for the sensorless rotor position detection, based onthe HF voltage injection.X The iron tooth introduced between each couple of PMsyields a proper HF rotor saliency.X This magnetic behaviour results to be slightly affected byiron saturation and cross–saturation phenomena.X This characteristics remain also under overloadoperations.


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Related Papers by the Authors

S. Bolognani, S. Calligaro, R. Petrella, and M. Tursini,”Sensorless control of ipm motors in the low–speedrange and at stand–still by hf–injection and dftprocessing.”,In in IEEE International Electric Machines and DrivesConference, 2009. IEMDC ’09., May 2009, pp.1557–1564.

N. Bianchi, S. Bolognani, J.–H. Jang, and S.–K. Sul,”Advantages of inset pm machines for zero–speedsensorless position detection”,IEEE Trans. on Industry Applications, vol. 44, no. 4, pp.1190 –1198, 2008.


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Experimentalresults

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Related Papers by the Authors (cont.)

N. Bianchi, S. Bolognani, and A. Faggion,”Predicted and measured errors in estimating rotorposition by signal injection for salient-pole pmsynchronous motors”,in IEEE International Electric Machines and DrivesConference, 2009. IEMDC ’09., May 2009, pp.1565–1572.

A. Faggion, S. Bolognani, and N. Bianchi,”Ringed–pole permanent magnet synchronous motor forposition sensorless drives”,in IEEE Energy Conversion Congress and Exposition,2009. ECCE 2009., 2009, pp. 3837 –3844.


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Experimentalresults

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Related Papers by the Authors (cont.)

A. Faggion, N. Bianchi, and S. Bolognani,”A ringed–pole spm motor for sensorless drives –electromagnetic analysis, prototyping and tests”,in IEEE International Symposium on IndustrialElectronics, ISIE 2010, Bari, IT, Jul. 4–7, 2010.

A. Faggion, E. Fornasiero, N. Bianchi and S. Bolognani,”Sensorless capability of fractional-slot surface-mountedPM motors”,in Electric Machines Drives Conference (IEMDC), 2011IEEE International, 2011, pp. 593 –598


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Thank you for the attention.


IntroductionSelf sensing rotor position detectionInset 12–slot 8–pole PM machineFinite element simulationsExperimental resultsConclusions

Zero speed sensorless drive capability of fractional slot ...paduaresearch.cab.unipd.it/5230/1/2012_PEMD_Sensor... · Zero–speed sensorless drive capability of fractional–slot

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