EVS28 KINTEX, Korea, May 3-6, 2015

Study on Permanent Manget Temperature Estimation of PMSM for

EV Traction

Suyeon Cho1, Donghyun Seo2, Waegyeong Shin2, Ju Lee3 1(corresponding author) Convergent System Safety Technology R&D Center, Reliability & Safety R&D Division, Korea Automotive

Technology Institute, 303 Pungse-ro, Pungse-myeon, Dongnam-gu, Cheonan-si, Chungnam, 330-912, Korea, sycho@katech.re.kr 2Convergent System Safety Technology R&D Center, Reliability & Safety R&D Division, Korea Automotive Technology Institute, 303

Pungse-ro, Pungse-myeon, Dongnam-gu, Cheonan-si, Chungnam, 330-912, Korea 3Department of Electrical Engineering, Hanyang Univrtsity, 222 Wangsimni-ro, Seongdong-gu, Seoul, 133-791, Korea

Introduction

Rotor Magnet Temperature Effect[1][2]

Demagnetization Curve of NdFeB Magnet

2

,,

,

( )100

( 25)r r RT

C Brr RT

B T BT

T B−

= ×−

,,

( 25)( ) 1

100C Br

r r RT

T TB T B

− = +

,C BrT

( )rB T

,r RTB

,,

,

( )100

( 25)ci

ci ci RTC H

ci RT

H T HT

T H−

= ×−

,,

( 25)( ) 1

100ciC H

ci ci RT

T TH T H

− = +

, ciC HT

( )ciH T

,ci RTH

Material Temperature Coefficient, [%/℃] Curie

Temp., ℃ Residual flux density Intrinsic coercivity,

Alnico 5 -0.02 +0.01 900

Alnico 8 -0.02 +0.01 860

Sm2Co17 -0.03 -0.20 800

SmCo5 -0.045 -0.40 700

NdFeB(Bonded) -0.07 -0.40 470

NdFeB(Sintered) -0.11 -0.60 310

Ferrite 8 -0.20 +0.27 450

: Temperature Coefficient of Residual Flux Density

: Residual Flux Density @ Temperature

: Residual Flux Density @ Room Temperature(25℃)

: Temperature Coefficient of Intrinsic Coercive Force

: Intrinsic Coercive Force @ Temperature

: Intrinsic Coercive Force @ Room Temperature(25℃)

Introduction

Rotor Magnet Temperature Effect[1][2] Change of Operation Point on Demagnetization Curve

3

Max. Operating Temp. = 150°C

Permeance Line

Applied field

Change of Operation Point Reduced Magnet Flux

Introduction

Rotor Magnet Temperature Effect[1][2] Change of Inductance

4

Finite element analysis results against rotor permanent magnet temperature of PMSM

(a) Room temperature condition(25℃) (b) High temperature condition(125℃)

Parameter Estimation Model

5

Discrete Z-domain PMSM voltage equation[3]-[6]

2

1

[ ( ) ( )]( ) d dd

d v z e zi zz d

−=

−

2

1

[ ( ) ( )]( ) q q

q

q v z e zi z

z q−

=− 1 2

1,

a sa s q

q

R TR T LL

a

eq e qR

−− −

= =

1 21,

a sa s dd

R TR T LL

a

ed e dR

−− −

= =

Z-domain equations(Zero-Order-Hold)

1 211 ,

a sa s dd

R TR T LL a s s

d a d

R T Ted e dL R L

−− −

= − =

1 211 ,

a sa s q

q

R TR T LL a s s

q a q

R T Teq e qL R L

−− −

= − =

Euler Approximation

Time sequence form

{ }*1 2( ) ( 1) ( 1) ( 1)d d d di n d i n d v n e n= − + − − −

( 1) ( 1)d r q qe n L i nω− = − −

1 21 ,a s s

d d

R T Td dL L

−

{ }*1 2( ) ( 1) ( 1) ( 1)q q q qi n q i n q v n e n= − + − − −

1 21 ,a s s

q q

R T Tq qL L

−

( 1) ( 1)q r d d r fe n L i nω ω φ− = − +

Online - Parameter Estimation

I. Magnetic Flux Estimation[7],[8]

Steepest Descent Method

{ }*1 2( ) ( 1) ( 1) ( 1)q q q qi n q i n q v n e n= − + − − −

1 21 ,a s s

q q

R T Tq qL L

−

{ }*1 2

ˆ ˆ( ) ( 1) ( 1) ( 1)q q q qi n q i n q v n e n= − + − − −

ˆ( ) ( ) ( )f q qe n i n i nφ = −

21( ) ( )2f f

V n e nφ φ =

2

ˆ( ) ( ) ( )( )ˆˆˆ( ) ( )( )

f f

f

q

q qq

V n V n i nJ q e n

e n e ni nφ φ

φ

∂ ∂ ∂= = =∂ ∂∂

ˆˆˆ ( 1) ( 1) ( 1) ( 1)q r d d r fe n L n i n nω ω φ− = − − + −

Magnet Flux Estimator

: Estimation Error

: Error Function

2ˆˆ(̂ 1) ( ) ( ) ( )fq q qe n e n J e n q e nφγ γ+ = − = −

,ˆ(0) (0) (0)q r d d r f inite L iω ω φ= +0 :n =

0 :n > 2ˆˆ(̂ 1) ( ) ( ) ( )fq q qe n e n J e n q e nφγ γ+ = − = −

√ Stability condition in selecting adaptation gain

22,max

20q

γ< <

( ) ( 1) ( ) 0f f f

V n V n V nφ φ φ + − <

ˆ ( )ˆ ˆ( ) ( ) ( )qf d d

r

e nn L n i nφ

ω= −

Online - Parameter Estimation

II. Inductance(Ld, Lq) Estimation[7],[8]

Affine Projection Algorithm(Adaptive Filter)

( ) ( ) ( )Ty n R n nθ=

ˆ( ) [ ( ) ( 1) ( 1)]Te n y n R n nθ= − − −

( 1) ( )ˆ(̂ ) ( 1) , {0,2}, 0( 1) ( 1)T

R n e nn nR n R nµθ θ µ δ

δ−

= − + ∈ ≈+ − −

{ }*1 2( ) ( 1) ( 1) ( 1)d d d di n d i n d v n e n= − + − − −

{ }*1 2( ) ( 1) ( 1) ( 1)q q q qi n q i n q v n e n= − + − − −

1 21 ,a s s

d d

R T Td dL L

−

1 21 ,a s s

q q

R T Tq qL L

− 1 2ˆˆ 1 ,ˆˆa s s

q q

R T Tq qL L

− =

1 2ˆˆ 1 ,ˆˆ

a s s

d d

R T Td dL L

−

ˆˆ( ) ( ) ( )Ty n R n nθ= Estimator

APA algorithmUpdate equation ( )e n

( )TR n

ˆˆ( ) ( 1) ( 1)Ty n R n nθ= − −

( 1) ( )ˆ(̂ ) ( 1)( 1) ( 1)T

R n e nn nR n R nµθ θ

δ−

= − ++ − −

( )y n

ˆ( )nθ

ˆ( )y n

Z-1

Online - Parameter Estimation

II. Inductance(Ld, Lq) Estimation[7],[8]

Affine Projection Algorithm(Adaptive Filter)

{ }*1 2( ) ( 1) ( 1) ( 1)d d d di n d i n d v n e n= − + − − −

1 2ˆˆ( 1) 1 , ( 1)ˆˆ ( 1) ( 1)

a s s

d d

R T Td n d nL n L n

− − −− −

ˆ( ) ( ) ( )dL d de n i n i n= −

{ }*1 2

ˆˆˆ ˆ( ) ( 1) ( 1) ( 1) ( 1) ( 1)d d d di n d n i n d n v n e n= − − + − − − −

ˆˆ ( 1) ( 1) ( 1)d r q qe n L n i nω− = − − −

* ˆ( 1) [ ( 1), ( 1) ( 1)]d

TL d d dR n i n v n e n− = − − − −

1 2ˆˆˆ ( 1) [ ( 1), ( 1)]

d

TL n d n d nθ − = − −

{ }*1 2( ) ( 1) ( 1) ( 1)q d q qi n q i n q v n e n= − + − − −

{ }*1 2

ˆ ˆˆˆ( ) ( 1) ( 1) ( 1) ( 1) ( 1)q q q qi n q n i n q n v n e n= − − + − − − −

ˆˆˆ ( 1) ( 1) ( 1) ( 1)q r d d r fe n L n i n nω ω φ− = − − + −

ˆ( ) ( ) ( )qL q qe n i n i n= −

* ˆ( 1) [ ( 1), ( 1) ( 1)]q

TL q q qR n i n v n e n− = − − − −

1 2ˆ ˆˆ( 1) [ ( 1), ( 1)]

q

TL n q n q nθ − = − −

1 2ˆˆ( 1) 1 , ( 1)ˆˆ( 1) ( 1)a s s

q q

R T Tq n q nL n L n

− − −− −

Verification by Simulation

9

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 5 10 15 20 25 30 35 40 45 50

Est

. PM

flux

link

age[

Wb]

N Step

Motor Speed = 1000RPMCurrent = 6A@15degPhi_init=0.1WbPhi_real = 0.189WbTs = 0.001sec

-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

25 30 35 40 45 50

Est

imat

ion

Err

or [W

b]

N Step

Motor Speed = 1000RPMCurrent = 6A@15degPhi_init=0.1WbPhi_real = 0.189WbTs = 0.001sec

0

0.0025

0.005

0.0075

0.01

0.0125

0.015

0.0175

0.02

0 10 20 30 40 50 60 70 80 90 100

Est

. Ind

ucta

nce

[H]

N Step

Motor Speed = 1000RPMCurrent = 6A@15degLd_init=0.0045HLq_init=0.006HTs = 0.0002sec

Ld_est

Ld_real = 0.006H

Lq_real = 0.009H

Lq_est

-0.002

-0.0015

-0.001

-0.0005

0

0.0005

0.001

0.0015

0.002

20 30 40 50 60 70 80 90 100

Est

imat

ion

Err

or [H

]

N Step

Ld_est_error Lq_est_error

Motor Speed = 1000RPMCurrent = 6A@15degLd_init=0.0045HLq_init=0.006HTs = 0.0002sec

Experiment

I. IPMSM Specifications and Test Bench for Experiment

10

Parameter Value Unit

Motor Type Interior PM Synchronous Motor

Rated Output 750 WRated Torque 3.58 NmRated Speed 2000 rpmMax Speed 3000 rpmDC Voltage 200 V

Phase Curent max 6 ApeakBack EMF coefficient@25℃ 39.634 Vpeak/krpm

No. of phase 3No. of Pole 4No. of Slot 24Silicon Steel S60(0.5t)Magnet Type NdFeB/Parallel Magnetization

Magnet Thickness 3 mmMagnet Length 38 mm

Stator Outer Diameter 60.9 mmStator Inner Diameter 35 mm

Rotor Outer Diameter(max) 34.4 mmAirgap Length 0.6 mmStack Length 90 mm

Dynamo Controller

DC Power Supply

Dynamo Set(Torque Tranducer+Servo Motor)

OscilloscopeComputer

Mobile Recoder(Temperature monitor)

Motor Controller(DSP + Power Stack)

Motor Controller(DSP + Power Stack)

IGBT Module

Gate Driver TMS320F28335DSP Board

Dynamo Set(Torque Tranducer+Servo Motor)

Torque Tranducer

Servo Motor

PMSM

(a) (b)

Experiment

II. Rotor magnet temperature variation

11

0.193Wb 0.184Wb 0.177Wb

Experiment

III. Parameter estimation results

12

Ld_est_Flag

Ld_init=0.003H

5V/divDA_out = 1.358VDA_scale = 1/200

Ld_est Ld_est=0.00679H

Lq_est_Flag

Lq_init=0.012H

5V/divDA_out = 1.820VDA_scale = 1/200

Lq_est Lq_est=0.0091H

Phi_est_Flag

Phi_estPhi_init=0.1Wb

Phi_est=0.189Wb

5V/divDA_out = 3.784DA_scale = 1/20

Experiment

IV. Control results by proposed method

13

0

0.6

1.2

1.8

2.4

3

3.6

4.2

4.8

5.4

6

-3 -2.7 -2.4 -2.1 -1.8 -1.5 -1.2 -0.9 -0.6 -0.3 0

Q-a

xis c

urre

nt [A

]

D-axis current [A]

Idq_fdb@Medium rotor temperature Idq_fdb@High rotor temperature

(1)(2)

4.8

5.1

5.4

5.7

6

-2.7 -2.55 -2.4 -2.25 -2.1

Q-a

xis c

urre

nt [A

]

D-axis current [A]

Idq_fdb@Medium rotor temperature Idq_fdb@High rotor temperature

β=22.4°Ia=5.97A

3

3.25

3.5

3.75

4

4.25

4.5

-0.4 -0.35 -0.3 -0.25 -0.2 -0.15

Q-a

xis c

urre

nt [A

]

D-axis current [A]

Idq_fdb@Medium rotor temperature Idq_fdb@High rotor temperature

β=4.21°

β=3.47°

Ia=3.86A

Ia=3.72AMedium rotor temp.

High rotor temp.

Traces of current at medium and high rotor temperature

Conclusion

14

Parameters affected by the rotor temperature variation of the IPMSM were analyzed. In addition to demagnetization characteristics of the permanent magnet, Parameters of IPMSM was estimated by proposed method(numerical technique and adaptive filter) for compensating rotor magnet temperature. From the experiment results of parameter estimation and torque control, the proposed method was verified.

Acknowledgments & References

15

This research was financially supported by the “Green electronic car component development and research foundation construction program” through the Ministry of Trade, Industry & Energy(MOTIE) and Korea Institute for Advancement of Technology(KIAT)

ACKNOWLEDGMENT

REFERENCES [1] Tomy Sebastian, "Temperature Effects on Torque Production and Efficiency of PM Motors Using NdFeB Magnets,"

IEEE Transactions on Industry Applications, Vol. 3 1, No. 2, pp. 353~357, 1995. [2] PD002 VACODYM-VACOMAX, 2007, VACUUMSCHMELZE社 [3] Henrik Neugebauer, "Parameter Identification of a Permanent Magnet Synchronous Motor," Master's Thesis,

Department of Signals&Systems, Chamers University of Technology, 2012. [4] D. S. Oh, K. Y. Cho, and M. J. Youn, “A discretized current control technique with delayed input voltage feedback

for a voltage-fed PWM inverter,” IEEE Trans. Power Electron., vol. 7, no. 2, pp. 364–373, Apr.1992. [5] T. H. Liu, C. M. Young, and C. H. Liu, “Microprocessor-based controller design and simulation for a permanent

magnet synchronous motor drive,” ZEEE Trans. Industrial Electronics, vol. 1E-35, no. 4, November 1988, pp. 516-523.

[6] B. K. Bose and P. M. Szczesny, "A microcomputer based control and simulation of an advanced IPM synchronous machines drive system for electric vehicle propulsion," IEEE Trans. IE, vol. 35, no. 4, pp. 547-559, 1988. [7] Yasser Abdel-Rady Ibrahim Mohamed, Member, IEEE,and Tsing K.Lee, "Adaptive Self-Tuning MTPA Vector

Controller for IPMSM Drive System", IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 21, NO. 3, SEPTEMBER 2006.

[8] Donald W. Marquardt, "An Algorithm for Least-Squares Estimation of Nonlinear Parameters" Journal of the Society for Industrial and Applied Mathematics, Vol.11, No.2, pp.431-441, Jun, 1963.