Sensorless Control at High Starting Torque of a 4000 NmTraction Drive With Permanent Magnet Synchronous

Machine

F. Demmelmayr, M. Susic, M. SchroedlVIENNA UNIVERSITY OF TECHNOLOGY

INSTITUTE OF ENERGY SYSTEMS AND ELECTRICAL DRIVESGusshausstrasse 25-29 / E370-2

Vienna, AustriaE-Mail: florian.demmelmayr@tuwien.ac.at

URL: http://www.ieam.tuwien.ac.at

Keywords<<sensorless control>>, <<permanent magnet synchronous machine>>, <<electric drive>>

AbstractThis paper presents numerical torque simulations and sensorless control of a permanent magnet syn-chronous machine (PMSM). The machine was developed for a wheel-hub traction drive with a maximumtorque of 4000 Nm. The Indirect Flux detection by Online Reactance Measurement (INFORM) methodprovides control at standstill and low speed without a rotor position sensor. A back electromotive force(EMF) model handles the operation at higher speed. The structure of the control and the load behaviourof INFORM are shown. The torque characteristic is calculated by numerical simulation and comparedwith recorded values. An additional curve depicts the influence of the INFORM test signals on machinetorque.

IntroductionDirect traction drives with wheel-hub machines require high starting torque and wide speed range. Highdynamic space vector control of permanent magnet synchronous machines (PMSMs) fulfils these de-mands. Vector control requires the knowledge of the actual rotor angular position. The rotor angle can bereceived by special sensors such as encoders or resolvers. But these sensors have some drawbacks: Theyincrease the total cost of electric machines and decrease the reliability. Sensorless techniques overcomethese weaknesses. The properties of sensorless control mostly depend on the machine speed. At highspeed, back electromotive force (EMF) methods are state-of-the-art [1], [2]. But they fail at standstillor very low speed [3]. At this operating range, most methods base on tracking the position of magneticsaliencies [4]. The presented Indirect Flux detection by Online Reactance Measurement (INFORM)model estimates the rotor angular position by special test signals [5]. The control of the regarded PMSMdrive deals with two sensorless techniques. Below a rated engine speed of 10 % INFORM calculates therotor position. Above that speed, the back-EMF model is used.

Figure 1: Stator (left) and rotor (right) of the PMSM

The presented PMSM prototype was developed, constructed (fig. 1) and tested with the support ofour industrial partner Voith Turbo GmbH (St. Polten, Austria). A numerical simulation calculates therequired starting torque. The result is compared with recorded values of two different control methods.These methods present the torque behaviour with position estimation from encoder and from sensorlesscontrol. The second method examines the influence of the test signals on torque characteristic.

Sensorless control of the PMSMThe machine speed usually influences the quality of sensorless control methods. At high speed, beyondabout 10 % of rated speed, back-EMF methods handle the position detection. They are based on theinduced voltage and appropriate models of the machine. The induced voltage decreases with reducingrotor speed and vanishes at machine standstill. Therefore the back-EMF model becomes worse withdecreasing rotor speed. In this operation range the INFORM method supplies applicable position infor-mation.

The INFORM methodThe implemented encoderless INFORM method for standstill and low speed utilizes varying magneticproperties depending on the angular rotor position. These properties arise from saturation and/or reluc-tance effects [5].INFORM uses test signals for position calculation. These voltage space phasor test pulses (us) inter-rupt the inverter-fed current control of the machine at certain time slices. In the meantime, the resultingcurrent-change space phasors (∆is/∆τ) are measured. Both, the test signals and their results define incre-mental ”inductances“ (linc). These position-varying inductances are used for rotor angular determination.

linc :=us

∆is/∆τ(1)

Following considerations are based on the inverse of these inductances

yINF

:=1

linc. (2)

Reluctance and saturation effects have an electrical angular symmetry of 180◦. Therefore also the com-plex quantity y

INFdisplays this characteristic. It describes a circle in the Gaussian plane if the fundamen-

tal harmonic of the signal is considered only.

yINF

:= y0 +∆y · e j(2γINF−2γU) (3)

The function can be expressed by an offset y0 and the radius of the circle ∆y. The position on the circleis a function of the angle of the test pulse stator voltage space phasor γU and the searched rotor positionγINF. Usually a three phase traction inverter offers voltage space phasors in six different directions

γU = kπ

3, k = 0, 1, 2... (4)

The presented INFORM method uses test signals in all of these directions. Figure 2 sketches the voltageund current behaviour of phase U during a U+, V+ and W+ test sequence. Current changes of the testsignals are measured in all three phases.Each of the three complex current changes ∆i|u, ∆i|v and ∆i|w from figure 3 yield two different results,one from its real and one from its imaginary part. Therefore six equations for the three unknown valuesy0, ∆y and 2γINF are available. The components from equation (3) can be calculated by real or imaginarypart consideration.

Implementation of the sensorless controlThe implemented sensorless control uses INFORM below a rated speed of about 10 % and the back-EMFmethod at higher speed [10].

6

-

-� tsequencet

Iu

6

?

∆iu|u6?

∆iu|v

∆iu|w6?

-

6U

t

Uu V W

6?≈ 1

3Udc

6

?

≈ 23Udc

. . . current measuring points

Figure 2: Voltage test signals Uu and current responses Iu during the INFORM measurement in phase u with threecyclic voltage signals U, V and W [8]

Figure 3: Rotor position dependent current changes [9]

The Back-EMF modelFigure 4 shows the structure of the sensorless calculation. At the top left, the machine model for theback-EMF estimation is depicted. The components of the stator voltage space phasor (uS,α, uS,β) andthe stator current space phasor (iS,α, iS,β) define the actual operating point. The complex stator voltageequation of a PMSM in the αβ stator-oriented reference frame

uS,αβ = rS iS,αβ +d ΨS,αβ

d τ(5)

represents the model of the machine with the per unit stator resistance (rS) and the time derivative of thecomplex stator flux linkage (ΨS). Equation 6 calculates the complex flux linkage due to the permanentmagnets (ΨM,αβ) with the stator inductance lS.

ΨM,αβ = ΨS,αβ− lS iS,αβ (6)

The argument of ΨM,αβ corresponds with the searched rotor position γEMF. The small feedback com-ponent KΨ (figure 4) stabilises the two digital integrators and prevents drift effects due to parameteruncertainties and measuring errors.

?

switchINFORM/EMF

2

2γINF

γEMF

Kγ

-?

qz−1

-

mechanical observer

γ

jKω

-

-q ω

- e z−1 q�?

tct

?

- qj?- -

j

-qa aa ?ω

?

j6

γ∗

∆γq

tan−1( cimag

creal

)jjiw -

iu -

iv -

INFORM method

cimag

crealj -

--

ΨM,β

ΨS,β

ΨS,α

KΨ

KΨ

iS,β

j6q6

rs

?

uS,α - j?

iS,α

6

q?

rs

back EMF method

j6

6

ls

q

j?ls?

ΨM,α

�

q

�

- e -q6

z−1�

- e z−1

-q�?

uS,β -

tan−1(

ΨM,βΨM,α

)?

6

Figure 4: Structure of the sensorless INFORM/EMF estimation

The INFORM methodThe INFORM method is pictured at the bottom left of figure 4. The changes of the phase currents (iU, iVand iW) during the test signals define a complex function cINF with its real (creal) and imaginary (cimag)part

cINF = ∆y · e j 2γINF = creal + j cimag (7)

This function is called Characteristic INFORM curve. Its argument (2γINF) is twice the searched rotorposition.

Switch between back EMF and INFORM methodA speed-dependent switch decides which sensorless method (2γINF or γEMF) will be used. It has a smallhysteresis to prevent unwanted toggle.

Observer structureA mechanical observer improves the sensorless position information and determines the actual rotorspeed (ω). The input of the observer (∆γ) is the difference between sensorless estimation (γEMF or 2γINF)and the actual observed rotor position (γ∗ or 2γ∗),

EMF method: ∆γ = γEMF− γ∗ (8)

or

INFORM method: ∆γ = 2γINF−2γ∗. (9)

This value affects the outcome of the speed and the angle calculation with the two constants Kω and Kγ.The constants quantify the values from sensorless estimation and the observer.The whole structure from figure 4 is implemented by using the microcontroller of the drive inverter. Eachsoftware task of the controller calculates a new position value. The actual rotor speed (ω) influences theangle estimation of the next task. The normalized dead time tct considers the time between two tasks ofthe used controller. Equations 10 and 11 describe the oberserver structure in the discrete z-domain.

γ = Kγ ·∆γ+ z−1 · (ω · tct + γ) (10)

ω = Kω ·∆γ+ z−1 · ω (11)

Control structure of the traction driveThe control structure of the traction drive is depicted in figure 5 [11]. The torque and field weakeningcontroller determines the reference stator current components (id,ref and iq,ref). The two componentsdepend on the reference torque (tref) from a tramway cab, the actual rotor speed (ω) and the componentsof the voltage space phasor (uα and uβ). The current controller works with two separated PI structures indirect and quadrature direction. Current and voltage space phasors are transformed from stator orientedto rotor oriented reference frame and vice versa using the estimated rotor angle (γ).

wvu

-id,ref

�d, q

�

iw

phase currentmeasurement

q

iviu

�

6qγ

id,meas

iq,measu,v,w

���

PMSM

???

sensorless position estimation - INFORM/EMF

uα

uβ

+d, q

∆id

∆iq

-m-

-

-

-

-

-iq,ref -

6

6

transformation - dq/αβ

reference framedq - current controller

q qm PWM

γ

α,β inverter

b bUDC

---

---

6

uβuαω 666tref 6

torqueandfield

weakeningcontroller

uSα

uSβ

�

�

uSα

uSβ

ω

Figure 5: Control structure

Numerical torque calculationNumerical simulation with the finite element method (FEM) provides appropriate results of the producedtorque of the PMSM. The presented calculation expects vector oriented control, with a quadrature currentcomponent only.The Maxwell stress (−~n · p) can be expressed by the magnetic flux density (~B) along the cylindricalair-gap between stator and rotor of the machine [6], [7].

−~n ·p =1µ0

((~n ·~B

)~B− 1

2

(~B ·~B

)~n)

(12)

Analizing the Maxwell stress yields to an electromagnetic torque vector (~T ) on a cylindrical surface (∂V )in the air-gap with the radius r and the normal vector~n.

~T =∮

∂V

~r× 1µ0

((~n ·~B

)~B− 1

2

(~B ·~B

)~n)

dΓ (13)

The calculation assumes constant flux density along the active iron length (lfe) and therefore a two-dimensional design (Bz = 0). Cylindrical coordinates (r,ϕ) with the normal unit vectors (~er and ~eϕ) areused. dΓ denotes the surface element of the integral.

~n =−~er, ~B = Br~er +Bϕ~eϕ, dΓ = rlfedϕ (14)

Tz =−r2lfeµ0

2π∫0

Br(r,ϕ)Bϕ(r,ϕ)dϕ (15)

The flux density (Br, Bϕ) in the air-gap is evaluated using the software tool Ansys V12.1. The resultingtorque (eq. 15) over quadrature stator current magnitude is shown in figure 7.

(a) iq = 0 (b) iq = 1

(c) iq = 2 (d) iq = 3

Figure 6: Flux lines of the magnetic field from FEM calculation at different quadrature stator current (iq)

Figure 6 depicts the magnetic flux lines of a 60◦ anti-periodic section of the PMSM at different quadraturestator currents (iq). The section of the PMSM represents the whole machine due to its specific symmetry.The coloured lines represent isolines of the magnetic vector potential. Two adjacent flux lines representa magnetic flux of 0.84 mWb. The torque is derived from results of the magnetic flux density from theFEM.

Measurements and Results

Torque characteristicFigure 7 illustrates the torque over the normalized stator current. The top curve describes the result of thenumerical simulation. Below, two measured graphs are displayed. The encoder control graph shows theproduced torque of the drive, using a position sensor. It is compared to the encoderless INFORM controlwhich includes short interruptions of the pulse width modulation (PWM) for the active test pulses. Thesensorless method has only little influence. The numerical simulation provides a good agreement withthe recorded values.The figure also depicts the Characteristic INFORM curves (eq. (7)) at no-load, iq = 1, iq = 2 and iq =3. The size of the loci and therefore the signal to noise ratio of the rotor position calculation increasewith rising stator current up to twice current magnitude. The curves are similar to triangles instead ofestimated circles because of higher harmonics [9].

Machine efficiency curveThe machine efficiency curve (Fig. 8) shows the produced torque over machine speed. Each point isrecorded at steady state. The colour fields represent various efficiency values of the fundamental wave.The figure includes the reluctance torque, produced by a negative direct current component besides themain current component in quadrature axis. Also the lines of constant power are plotted from 5 kW to140 kW mechanical output power. The machine provides high efficiency over a wide operation rangeand wide field weakening range.INFORM is used below a rated machine speed of 10 %. In this operation range the machine efficiency isnot significant. Therefore this paper does not regard the influence of the INFORM test sequence on theefficiency.

Figure 7: Torque over stator current magnitude with Characteristic INFORM curves at selected operation pointsat ω = 5%

Figure 8: Machine efficiency curve of the PMSM

ConclusionThe presented PMSM drive reaches high starting torque up to 4000 Nm. Measurements and numericalsimulations of produced torque show a good agreement. The sensorless control operates from standstillto maximum speed. It works with a combined INFORM/back-EMF model. The quality of the INFORMcalculation increases with rising load and works well up to high starting torque.

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Dynamic Performance PMSM, IEEE Transactions on Industrial Electronics, Page(s): 2092 - 2100,June 2010

[2] D. Paulus, J.-F. Stumper, P. Landsmann, R. Kennel, Robust Encoderless Speed Control of a Syn-chronous Machine by direct Evaluation of the Back-EMF Angle without Observer, Sensorless Con-trol of Electrical Drives (SLED), Padova, Italy, 2010

[3] F. Briz, M.W. Degner, P. Garcia, R.D. Lorenz, Comparison of saliency-based sensorless controltechniques for AC machines IEEE Transactions on Industry Applications, Page(s): 1107, July 2004

[4] A. Consoli, G. Scarcella, A. Testa, Sensorless Control of PM Synchronous Motors at Zero Speed,IEEE-IAS Conf. Rec. pp. 1033-1040, 1999.

[5] M. Schroedl, Sensorless control of AC machines at low speed and standstill based on the ”INFORM”method, IEEE IAS Conference, San Diego, Proc. 1: 270-277, 1996

[6] J. Jackson, Classical Electrodynamics, John Wiley, New York (USA), 1962

[7] P. Penfield, H.A. Haus Electrodynamics of Moving Media, Cambridge, Mass.: M.I.T. Press, 1967

[8] A. Eilenberger, Permanent Magnet Synchronous Machines With Tooth Coils for Sensorless ControlIncluding Overload Range, Doctoral thesis, Vienna University of Technology, 2011

[9] F. Demmelmayr, A. Eilenberger, M. Schroedl, Sensorloser Betrieb von PM-Außenlaufermaschinenmit konzentrierten Wicklungen, E&I Elektrotechnik und Informationstechnik, 3 (2011), Page(s): 68- 74., 2011

[10] M. Schroedl, M. Hofer, W. Staffler, Combining INFORM method, Voltage model and mechani-cal observer for sensorless control of PM Synchronous Motors in the whole speed range includingstandstill, Power Conversion Intelligent Motion (PCIM), Nurnberg, Germany, 2006

[11] M. Schroedl, W. Staffler, Sensorless Control of a Double-Stator Disc Rotor PM Synchronous MotorUsing a Combined INFORM R©/EMF Model, Power Conversion Intelligent Motion (PCIM), Nurn-berg, Germany, May 2009