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Self-sensing Control of the Externally-ExcitedSynchronous Machine for Electric Vehicle Traction

ApplicationMohamad Koteich, Amir Messali, Simon Daurelle

To cite this version:Mohamad Koteich, Amir Messali, Simon Daurelle. Self-sensing Control of the Externally-ExcitedSynchronous Machine for Electric Vehicle Traction Application. SLED 2017 8th IEEE InternationalSymposium on Sensorless Control for Electrical Drives, Sep 2017, Catania, Italy. �hal-01573060�

Self-sensing Control of the Externally-Excited Synchronous Machinefor Electric Vehicle Traction Application

Mohamad Koteich1, IEEE Member, Amir Messali2, Student Member, Simon Daurelle2, Student Member

Abstract—This paper studies the possibility of removing theposition sensor from electric vehicles (EVs) powertrains thatemploy the externally-excited synchronous machine (EESM)for traction. Three position estimation approaches are studied:back-electromotive-force integration, state-observer and high-frequency voltage injection approaches. Theoretical backgroundis presented, a comparative performance analysis is performed,and experimental results on a 65-kW EESM drive test bench areshown. Some requirements for EV powertrains are emphasized.

I. INTRODUCTION

The electric vehicle (EV) market is expected to growincreasingly in the next decade. Most of nowadays EVsuse inset permanent-magnet synchronous machine (IPMSM)drive for traction. The main challenge of the IPMSM inthe automotive industry is the dependence on the rare-earthmarket. Several alternative solutions have been studied inorder to remove magnets from EV drives without increasingtheir volume and their mass [1]. One potential alternative isthe externally-excited synchronous machine (EESM) which isbeing successfully used in Renault Zoe, Fluence and KangooEVs.

The present paper studies the possibility of removing theposition sensor from the EESM drive system, using self-sensing control techniques [2], in order to reduce the cost andincrease both the reliability and the mechanical robustness ofthe drive. Compared to the IPMSM, very few papers havestudied the self-sensing capabilities of the EESM [3]–[7],especially that several designs of the latter have been proposed:if the Zoe traction drive is taken as example, there exist at least3 different EESM powertrains, the first two generations aremanufactured by Continental, and the latter ones are Renaultin-house manufactured machines.

This paper is aimed at presenting a primary study of thefeasibility of self-sensing control for EESM traction drives.Three broad approaches for position estimation are testedand compared: 1) back-electromotive force (EMF) integra-tion approach [8], presented in Section III, 2) state-observerapproach [6], in Section IV, and 3) high-frequency (HF)injection approach [9], in Section V. The performance of thefirst approach are presented for medium and high speed. Thelimitations of the second approach are analyzed. The thirdapproach has two major advantages over the first two ones: 1)it works stably at low speed and standstill and 2) it does notrequire the knowledge of any machine parameter.

Experimental tests have been performed on a 4-poles, 65-kW EESM, the results are presented in Section VI.

1 Groupe Renault, Technocentre, Guyancourt, France2 Ecole Centrale Nantes, LS2N Laboratory, Nantes, France

II. EESM MATHEMATICAL MODEL

The schematic representation of the EESM is shown onFig. 1: a three-phase stator, with an externally DC-excitedwinding in the rotor [6].

A. NotationsThe complex space vector notation is used to model the

revolving electromagnetic stator quantities [10]. Let xrs be astator quantity in the rotor reference frame, it can be expressedas

xrs = xsse−jθ

or equivalently

xsd + jxsq = (xsα + jxsβ)(cos θ − j sin θ)

Subscripts s and f stand for stator and rotor (field) quantitiesrespectively, whereas superscripts s and r tell whether thequantity is expressed in the stator (αβ) or the rotor (dq)reference frame. θ is the angle between the stator and therotor reference frames. The fluxes, currents, voltages andback EMFs are denoted by ψ, i, v and e, respectively. Theinductance and the resistance of a given circuit are denoted byL and R respectively, and M denotes the mutual inductancebetween the stator and rotor circuits.

B. Stator equationsThe stator voltage equation in the stator coordinates can

be written as:

vss = Rsiss +

dψss

dt(1)

In the rotor reference frame, the previous equation becomes:

vrs = Rsirs +

dψrs

dt+ jωψr

s(2)

Neglecting the cross-saturation inductances, the stator flux canbe expressed in the rotor coordinates as:

ψrs

=Ld + Lq

2irs +

Ld − Lq2

ir∗s +Mf if (3)

= L0irs + L2i

r∗s +Mf if (4)

where ir∗s denotes the complex conjugate of irs.

C. Rotor equationsThe rotor scalar equations are expressed in the rotor

reference frame. The voltage equation is:

vf = Rf if +dψfdt

(5)

with

ψf = Lf if +Mf isd (6)

va

vb

v cvf

d

q

θ

a

b

c

Fig. 1: The EESM schematic representation

III. EQUIVALENT-FLUX BASED ESTIMATION

This section describes a unified position estimator for ACmachines. It is designed by merging of the contributionsof several papers including [8], [11]–[15]. The followingestimator consists of two parts: stator flux estimation basedon a programmable statically-compensated (PSC) low-passfilter (LPF), and rotor flux position estimation based on theEquivalent Flux, or Active Flux, concept described below.

A. Stator flux estimation

The stator flux vector can be estimated by integrating theback-EMF (ess):

ψss

=

∫(vss −Rsiss)dt =

∫essdt (7)

where vss is the command voltage estimated using an invertermodel, Rs is considered to be fairly accurately known, and issis the measured stator current.

The implementation of a pure integrator is prone to driftproblems due to inverter nonlinearities, current measurementnoises, unbalanced gains and DC offset. Furthermore, an initialcondition error would result in a DC-offset in the integra-tor output. To overcome these problems, various algorithmshave been reported in the literature, including adaptive fluxobservers [13], which require the knowledge of the machineinductances. Nevertheless, it can be argued that if the (open-loop) integration function is optimized, the use of adaptive(closed-loop) estimation structure would not be easily justi-fiable. Thus, an optimized modified integration algorithm isdesigned for stator flux estimation.

To remove the error due to the DC-offset at the input ofthe integrator, a high-pass filter, with a corner frequency ωc,is implemented in series with the input of the pure integrator.This results in a low-pass filter (LPF) approximated integrator:

Ψs(s)

es(s)=

1

s.

s

s+ ωc=

1

s+ ωc(8)

The filter generates both magnitude distortion and phase lag,which can be compensated for, in steady-state, by multiplying

the filter by the following function, in order to bring the LPFresponse closer to the pure integrator response [11]:

jωs + ωcjωs

= 1− j ωcωs

(9)

Furthermore, the tunning of the filter cut-off frequency is atrade-off between the offset rejection dynamics and the steady-state accuracy: for example, higher corner frequency ωc en-sures faster DC-offset rejection, however, it introduces higherdistortion in the output signal due to increasing attenuationand phase lag. Therefore, an adaptive corner frequency tuningshould be adopted: ωc is chosen in a way to be dependent onthe stator angular frequency ωs as follows [8]:

ωc = λ|ωs| (10)

where λ is a positive real number smaller than one. At lowspeed, λ can be tuned to a low value, e.g. 0.1, whereas forhigher speeds, it can take higher values. In this case, the time-constant of the LPF, 1/(λ|ωs|), is decreased with the increaseof the stator frequency. The time-domain expression of sucha PSC-LPF is [8]:

ψs

s=

∫ (−λ|ωs|ψ

s

s+ [1− jλsign(ωs)] e

ss

)dt (11)

The performance of the PSC-LPF depends on the statorresistance, the accuracy of the inverter model, and the choiceof λ. Furthermore, it heavily relies on the accuracy of the statorflux angular frequency (ωs) estimate. A PLL-based estimationscheme, applied to the command voltage, is implemented toestimate the stator angular frequency [12], as shown in Fig. 2.

B. Equivalent-flux concept and position estimation

The stator back-EMF integration is valid for all AC ma-chines, since they all have the same voltage structure. Therotor position estimation based on the stator flux relies on theinteraction between the stator and the rotor fields, which isdependent on the rotor structure. Nevertheless, a unified fluxmodel can be developed in view of rotor field-oriented controlof AC drives, by introducing the Equivalent Flux concept ψeqand an equivalent stator inductance Leq [14]:

ψss

= Leqiss + ψs

eq(12)

ψseq

= ψeqejθ (13)

with Leq = Lq for synchronous machines and Leq = σLsfor inductions machines (IMs), and the equivalent flux ψeq isexpressed for the EESM, IPMSM and the IM as the following:

EESM : ψeq = (Ld − Lq)isd +Mf if

IPMSM : ψeq = (Ld − Lq)isd + ψr

IM : ψeq = krψrd

(14)

The rotor position of the EESM can be estimated from thestator flux by evaluating the phase angle of the equivalent fluxvector using the arctangent function for example.

The complex signal flow of the equivalent-flux-based po-sition estimator is shown on Fig. 2.

iss

vss

jλ

ψs

sess

sign

ejθvsq

ωs

θv

PLL

ψs

eq

θCompensation Low-pass filter

Kp

Ki

s

λ

ω

s1

s1

Rs Lq

Fig. 2: Equivalent-flux based Estimator

IV. STATE-OBSERVER BASED ESTIMATION

The state-space model of the EESM can be deduced fromSection II, by incorporating the mechanical model equations[6]. A state-observer, such as the extended Kalman filter (EKF)can be designed to estimate the rotor position and speed basedon the stator and rotor currents measurement. Nevertheless,a state observer requires the system to satisfy the so-calledobservability conditions, in order to ensure stable and accurateestimation. The observability of the EESM is studied in [6],where it is shown that at standstill, the observability is notguaranteed, unless some varying (high-frequency) voltage isinjected in the machine.

According to the authors experience, a full-order observer,such as the EKF, is not a practical solution for EV’s EESMself-sensing control, for the following reasons:

• Observer-based estimation fails at very low-speed, unlessan HF voltage is injected. In the case of the studiedEESM, the injection in the rotor winding is not helpfulbecause of the low bandwidth of the rotor circuit. A lowamplitude HF signal will be filtered if injected to therotor, and lower frequency signal would generate torqueripple. On the other hand, if the HF signal is to be injectedin the stator, then HFI techniques would be preferredthanks to their robustness and simplicity.

• The model does not only rely on the knowledge of Ld andLq , but also on Lf and Mf . These inductances cannotbe accurately known due to nonlinear saturation phe-nomenon that occur in the machine. Therefore, apart fromobservability problems at low speed, a state-observer,such as the EKF, would fail to accurately estimate theposition over the whole operating range, due to theabsence of an accurate linearized model.

• the EKF implementation requires high computationalburden.

As a conclusion, state observers that rely on the knowledgeof the inductances are less likely to work on the EESM, where

α

jβ

djq

θ

d

θ

jq

vsdc

vsqcvsdc = Vc cosωct

vsqc = ωωcVc sinωct

Injected Voltage

Resulting Flux

ψsdc = Vcωc

sinωct

ψsqc = 0

Fig. 3: HF voltage injection principle.

magnetic saturation phenomena are more complex than theIPMSM. More robust methods are to be sought.

V. PULSATING HF INJECTION BASED ESTIMATION

The pulsating HF injection (HFI) position estimation hasbeen proposed for the IPMSM by Corley and Lorenz [9]. Itis based on the property of the d- and q- axes flux beingdecoupled: if the following HF voltage vector, at ωc angularfrequency (ωc >> ωs)

vrsc = Vc cos(ωct) + jVcωsωc

sin(ωct) (15)

is injected to the drive, in the estimated rotor referenceframe (Fig. 3), it is expected to induce HF current only onthe estimated d-axis. The measured HF current through theestimated q-axis is driven to zero via a PI mechanism in orderto make the estimated position track the actual position. TheHF resistive drop voltage can be neglected. The induced HFflux in the estimated position coordinates is

ψrsc

=Vcωc

sin(ωct) (16)

it can be expressed in the stationary coordinates as follows:

ψssc

=Vcωc

sin(ωct)ejθ (17)

The induced HF current in the stationary coordinates can bewritten as (by inverting equation 4 and transforming it into thestator reference frame):

issc =1

L20 − L2

2

(L0ψ

s

sc− L2ψ

s∗scej2θ

)(18)

= Icpejθ sin(ωct)− Icnej(2θ−θ) sin(ωct) (19)

Icp and Icn denote the maximum magnitude positive- andnegative-sequence components of the HF currents respectively:

Icp =Vcωc

L0

L20 − L2

2

=Vcωc

L0

LdLq(20)

Icn =Vcωc

L2

L20 − L2

2

=Vcωc

L2

LdLq(21)

The HF q-axis current component is extracted using afirst order high-pass filter (HPF), and the following positionestimation error signal, ε, is evaluated by low-pass filteringthis HF component multiplied by sin(ωct):

ε = LPF[sin(ωct)Im

(issce

−jθ)]

(22)

isαisqc

isβ

LPF

θ

cos θsin θ

s1

s1

εKi

Kp

ω

sinωct

PLL

Demodulation

HPF

isq

Carrier Extraction

Fig. 4: Demodulation signal processing for HFI sensorless control

which finally yields:

ε =Icn2

sin 2(θ − θ) ≈ Icn(θ − θ) (23)

This signal is then fed to a PLL tracking mechanism thatoutputs the position. The demodulation process is illustratedin Fig. 4. For more details about the PLL tuning refer to [16].

The Pulsating HFI is also a generic estimation techniquethat can be applied to AC drives. It only required a magneticanisotropy in the flux path. In the case of the EESM, the statorHF current can generate a rotor HF current due to the couplingbetween the two circuits. Nevertheless, as mentioned earlier,the rotor bandwidth is much lower than the stator one for thestudied EESM, and the HF signal is chosen in a way to befiltered by the rotor circuit.

VI. EXPERIMENTAL RESULTS

This section presents the results of the experimental teststhat have been performed on the 4-poles 65-kW Renaultmanufactured EESM drive that is used on the Zoe electric car.The drive is operated in sensorless configuration, the positionsensor is used for comparison. A 10 kHz switching frequencyPWM voltage source inverter is used, with a 400 Volt DC bus.

A. Flux-based position estimation

The Equivalent-flux-based position estimator presented inSection III has been tested under self-sensing control con-figuration, for a speed ramp, from 1000 to 9000 rpm, withno- and full-load. The results are shown on Fig. 7. Thevalue of Lq is generated based on a look-up table with twoinputs (for simplicity): the estimated speed and estimatedtorque. The look-up table is filled based on experimental tests.Other techniques can be used for Lq identification, such aspolynomial identification using the stator current as input. Tothe best of the knowledge of the authors, the adaptive, robustestimation of Lq is still an open problem, and no promisingsolutions have been proposed yet.

The position estimation error depends mainly on the valuesof Lq . Higher accuracy and higher precision look-up table isneeded to ensure better estimation quality. Position estimationbased on flux estimation is not stable at low speed, due to thelow amplitude range of the back-EMF.

The speed estimation using the stator voltage PLL seem tobe fairly accurate. Its dynamical performance can be furtherimproved by fine tuning the PLL or by incorporating themechanical model and the torque request.

B. Kalman Filter based position estimation

The extended Kalman filter (EKF) algorithm shown in Fig.5 has been tested, using the stationary αβ electromechanicalmodel of the EESM [6]. System linearization matrices and ma-trix inversion calculation had been done analytically, off-line,in order to reduce computational burden. The HF injection inthe rotor winding proposed in [6] has been implemented. Fig.6 shows that at very low speed, when a HF current is injectedto the rotor winding, the position estimation error is aroundzero, which is not the case when no HF current is injected. Thisis consistent with the observability analysis results presentedin [6]. On the other hand, the EKF performance dependson the accuracy of the machine model; due to magneticsaturation phenomena, which are significant in traction drives,the position estimation error varies significantly dependingon the operating point. The tests show that an EKF with asimple EESM model cannot provide an accurate estimationfor different operating points.

C. HFI-based position estimation

HFI-based position estimation is tested for speeds lowerthan 1000 rpm. The injected voltage amplitude is 30 V, at 1.5kHz. A very challenging torque-speed profile is used for thetest (see Fig. 8); it includes situations that are not likely tohappen in practice.

The pulsating HFI-based self-sensing control seems to berobust enough, especially that no parameters are needed forestimation. It should be noted that the steady state estimationerror increases as the speed increases. As for the speedestimation, it seems to be accurate enough.

The dynamical performance of this estimation techniquecan be improved by fine-tuning the filters and the PLL band-widths. The EESM under study seems to have advantageoussaliency characteristics.

VII. CONCLUDING REMARKS

The electric vehicle traction drive is a very challengingapplication for the self-sensing control, because it requires

x0

P0

x0

Prediction / Estimation

Linearization

;

Pk+1/k+1 = Pk+1/k −KkCkPk+1/k

Correction / Innovation

Kk = Pk+1/kCTk

(CkPk+1/kC

Tk +R

)−1

Observer Gain

xk+1/k = xk/k + Tsf(xk/k, uk

)

xk+1/k+1 = xk+1/k +Kk

(yk − h(xk+1/k)

)

∂f(x,u)∂x

∣∣∣∣xk/k,uk

Ak =∂h(x)∂x

∣∣∣∣xk/k

Ck =

Pk+1/k = Pk/k + Ts(AkPk/k +Pk/kA

Tk

)+Q

Fig. 5: Extended Kalman Filter estimation algorithm

1.7

1.8

1.9

2

2.1

2.2

2.3

0 5 10 15 20 25

0

50

100

150

200

250

300

350

Fig. 6: EKF experimental results.

very accurate position estimation with high dynamical per-formance, including critical situations such as high-torquezero-speed operation. In addition, the AC machines used intraction have high power-to-volume ratio, with a complexmagnetic (saturation) behavior. Throughout this paper, threeposition estimation approaches have been studied and testedon an EESM traction drive: the equivalent-flux, the state-observer and the high-frequency injection approaches. Thefirst approach can be applied to all AC machines. Its mainlimitations are the stability at low speed and the dependenceon the accuracy of the inductance Lq estimation. The secondapproach highly relies on the machine inductances, and re-quires higher computation complexity. The latter approach isaccurate and robust enough at low speed, and can be applied

for all salient AC machines. However, it suffers from limiteddynamical performance at higher speeds. Combining the first(or second) and the latter approaches is a viable estimationstrategy that is well known and often used [17]. Furtherinvestigations of the rotor winding injection characteristics andbenefits [4]–[6] are to be carried out in the future.

REFERENCES

[1] T. Jahns, “Getting rare-earth magnets out of ev traction machines: Areview of the many approaches being pursued to minimize or eliminaterare-earth magnets from future ev drivetrains,” IEEE ElectrificationMagazine, vol. 5, pp. 6–18, March 2017.

[2] J. Holtz, “Sensorless control of induction machines with or withoutsignal injection?,” IEEE Transactions on Industrial Electronics, vol. 53,pp. 7–30, 2 2006.

[3] A. Griffo, D. Drury, T. Sawata, and P. H. Mellor, “Sensorless starting ofa wound-field synchronous starter/generator for aerospace applications,”IEEE Transactions on Industrial Electronics, vol. 59, pp. 3579–3587,Sept 2012.

[4] J. Choi, I. Jeong, K. Nam, and S. Jung, “Sensorless control forelectrically energized synchronous motor based on signal injection tofield winding,” in IECON 2013 - 39th Annual Conference of the IEEEIndustrial Electronics Society, pp. 3120–3129, Nov 2013.

[5] A. Rambetius and B. Piepenbreier, “Carrier signal based sensorlesscontrol of wound field synchronous machines using the rotor winding asthe receiver: Rotating vs. alternating carrier,” in Proceedings of PCIMEurope 2015; International Exhibition and Conference for Power Elec-tronics, Intelligent Motion, Renewable Energy and Energy Management,pp. 1–8, May 2015.

[6] M. Koteich, A. Maloum, G. Duc, and G. Sandou, “Observability analysisof sensorless synchronous machine drives,” in 2015 European ControlConference (ECC), pp. 3560–3565, IEEE, 7 2015.

[7] A. Beciu, E. Godoy, P. Rodriguez-Ayerbe, I. Bahri, and A. Maalouf,“High frequency impedance analysis for sensorless starting of woundrotor synchronous machines,” in IFAC 2017, Toulouse, July 2017.

[8] M. Hinkkanen and J. Luomi, “Modified integrator for voltage modelflux estimation of induction motors,” IEEE Transactions on IndustrialElectronics, vol. 50, no. 4, pp. 818–820, 2003.

[9] M. Corley and R. Lorenz, “Rotor position and velocity estimation for asalient-pole permanent magnet synchronous machine at standstill andhigh speeds,” Industry Applications, IEEE Transactions on, vol. 34,no. 4, pp. 784 – 789, 1998.

[10] J. Holtz, “The representation of ac machine dynamics by complex signalflow graphs,” IEEE Transactions on Industrial Electronics, vol. 42,pp. 263–271, 6 1995.

[11] N. Idris and A. Yatim, “An improved stator flux estimation in steady-state operation for direct torque control of induction machines,” IEEETransactions on Industry Applications, vol. 38, no. 1, pp. 110–116, 2002.

[12] M. Comanescu, L. Xu, and S. Member, “An improved flux observerbased on pll frequency estimator for sensorless vector control of in-duction motors,” Industrial Electronics, IEEE Transactions on, vol. 53,no. 1, pp. 50–56, 2005.

[13] I. Boldea, G. D. Andreescu, C. Rossi, A. Pilati, and D. Casadei, “Activeflux based motion-sensorless vector control of dc-excited synchronousmachines,” in Energy Conversion Congress and Exposition, 2009. ECCE2009. IEEE, pp. 2496–2503, 2009.

[14] M. Koteich, G. Duc, A. Maloum, and G. Sandou, “A unified model forlow-cost high-performance ac drives: the equivalent flux concept,” inThe Third International Conference on Electrical, Electronics, ComputerEngineering and their Applications (EECEA), Apr. 2016.

[15] M. Koteich, “Flux estimation algorithms for electric drives: a compar-ative study,” in International Conference on Renewable Energies forDeveloping Countries 2016 (REDEC2016), July 2016.

[16] L. Harnefors and H.-P. Nee, “A general algorithm for speed and positionestimation of ac motors,” IEEE Transactions on Industrial Electronics,vol. 47, no. 1, pp. 77–83, 2000.

[17] C. Silva, G. M. Asher, and M. Sumner, “Hybrid rotor position observerfor wide speed-range sensorless pm motor drives including zero speed,”IEEE Transactions on Industrial Electronics, vol. 53, no. 2, pp. 373–378,2006.

Measured and Estimated Electrical Position (Degree)

Rotor current if

Time (sec)

10 15 20 25 30 35

2000

4000

6000

8000

Measured and Estimated Mechanical Speed (RPM)

10 15 20 25 30 35

−20

0

20

40

Mechanical Speed estimation error (RPM)

10 15 20 25 30 35−5

0

5Electrical position estimation error (Degree)

Time (sec)

10 20 30 40

2000

4000

6000

8000

Measured and Estimated Mechanical Speed (RPM)

10 20 30 40

−20

0

20

40

Mechanical Speed estimation error (RPM)

10 20 30 40−10

−5

0

5

Electrical position estimation error (Degree)

Time (sec)

Fig. 7: Flux-based sensorless experimental results: no-load (left) and full-load (right) speed ramp from 1000 to 9000 rpm.

25 30 35 40 45 50 55 60

0

1 pu

Torque (N.m.)

25 30 35 40 45 50 55 60−500

0500

1000

Measured and Estimated Mechanical Speed (RPM)

25 30 35 40 45 50 55 60−100

0

100Mechanical Speed estimation error (RPM)

25 30 35 40 45 50 55 600

100200300

Measured and Estimated Electrical Position (Degree)

25 30 35 40 45 50 55 60

−100

10

Electrical position estimation error (Degree)

Time (sec)

Fig. 8: HFI sensorless experimental results.