Permanent Magnet Synchronous Machine Parameters

Zdenek Cerovský, Miroslav Lev

Permanent Magnet Synchronous Machine ParametersIdentification for Load Characteristics Calculation

DOIUDK

10.7305/automatika.2015.07.813621.313.32:621.313.8; 621.317

Original scientific paper

Self reactanceXd in direct axis ’d’ and self reactanceXq in quadrature axis ’q’ influence the load characteristicsof the permanent magnet machine. Their calculation methods are known. All calculations should be verified bymeasurements. Measurement with AC variable voltage and frequency source applied on stator winding is correctwhen eddy currents do not exist. Other methods evaluate the DC current decay after initial direct current was appliedon the stator winding. Accuracy of these methods is lowered because of the numerical evaluation of current decaycurve. Another method performs the measurement on the machine loaded as a motor. The load angle β is measuredby a machine set of four machines. The accuracy is lowered by higher harmonics induced in no load in the helpingsynchronous machine. The load angle can be also obtained by geometrical construction of the vector diagram. Inthis paper the evaluation of the generator steady state regime of the machine is used. The generator works withdifferent loads consisting of capacitance, inductance or arbitrary impedance or resistance. When the generatortransfers from no load to load regime the rotor is shifting and the load angle changes. This angle is measured.The newly proposed measurement methods are simple in special cases of loads. Results of measurements and theirexperimental verification are published in the paper.

Key words: Electric machines, Parameter identification, Permanent magnet machinery, Synchronous machines,Variable speed drive

Identifikacija parametara sinkronog stroja s permanentnim magnetima za proracun karakteristikaopterecenja. Reaktancija Xd u uzdužnoj ’d’ osi i reaktancija Xq u poprecnoj ’q’ osi utjecu na karakteri-stike opterecenja stroja s permanentnim magnetima. Metode za njihov izracun su poznate. Svaki izracun trebaobi se potvrditi mjerenjima. Mjerenje korištenjem izmjenicnog izvora s promjenjivim naponom i frekvencijomprikljucenim na statorske namote prikladno je kada nema vrtložnih struja. Druge metode procjenjuju opadanjeistosmjerne struje nakon što je prethodno narinuta struja u uzdužnoj osi. Tocnost ovih metoda umanjena je zbognumericke evaluacije krivulje opadanja struje. Takoer se koristi i metoda koja vrši mjerenja na opterecenom strojuu motorskom režimu rada. Kut opterecenja β mjeri se korištenjem skupa od cetiri stroja. Tocnost je smanjena zboginduciranih viših harmonika u praznom hodu zbog pomocnog sinkronog stroja. Kut opterecenja može se takoerdobiti geometrijskim pristupom iz faznog dijagrama. U ovom radu korištena je procjena u stacionarnom stanju uzgeneratorski režim rada. Generator je opterecen razlicitim trošilima koja ukljucuju kapacitivno, induktivno, otpornoili s proizvoljnom impedancijom. Prijelaznu pojavu generatora iz praznog hoda u optereceni režim rada prati pro-mjena rotorskih velicina i kuta opterecenja. Ovaj kut je moguce izmjeriti. Predložena metoda mjerenja jednostavnaje uz posebne vrste opterecenja. U radu su prikazani rezultati mjerenja uz eksperimentalnu potvrdu metode.

Kljucne rijeci: Elektricni strojevi, identifikacija parametara, stroj s permanentnim magnetima, sinkroni stroj, elek-tromotorni pogon promjenjive brzine

1 INTRODUCTION

Progress in power electronic converters brought radi-cal change of synchronous machine usage area. They op-erated with constant frequency usually [1,2]. Synchronousmachines supplied by electronic converters are first of allwidely used as permanent magnet synchronous machine(PMSM) in variable speed drives [3–8]. New application

field lies also in electric vehicle drives [9] and aircraft [10].Permanent magnet synchronous machines have influencedthe usage of electronic converters on the other hand too[11–13].

Synchronous machine usage area caused constructionmodifications according to different technologies and areaswhere machines are used. Other changes in construction

Online ISSN 1848-3380, Print ISSN 0005-1144ATKAFF 56(2), 217–225(2015)

217 AUTOMATIKA 56(2015) 2, 217–225

Permanent Magnet Synchronous Machine Parameters Identification for Load Characteristics Calculation Z. Cerovský, M. Lev

were caused by permanent magnet development [14]. Selfreactance Xd and Xq depend not only on machine con-struction but also on the permanent magnet material qual-ity. Classical salient-pole synchronous machines with rotorwinding for field current have Xd > Xq and their ratio isusually

Xd

Xq∈ 〈1.3; 2.5〉.

This proportion changes in PMSM sharply. ManyPMSM have Xd and Xq nearly the same. But indispens-able number of PMSM has the ratio

Xd

Xq∈ 〈0.5; 1.5〉.

That means that Xd < Xq is also possible [8, 11, 15–17]. The calculation methods of direct axis reactance Xd

and quadrature axis reactance Xq are known. Also the fi-nite element method is possible. All calculations surelycontain uncertainty caused by nonlinear iron features, ge-ometrical complexity, permanent magnet material featuresand by accepted presumptions [18]. That means calcula-tions should be verified by experiments any case. Reac-tances of variable speed PMSM are usually expressed asinductances for practical reasons. There were used differ-ent measurement methods for direct axis inductance Ld

and quadrature axis inductance Lq in literature. In [19]two methods are used. The first method is using an AC-source with variable voltage and frequency applied on sta-tor winding for synchronous inductances measurement.The rotor must be fixed in the phase axis on which thedirect inductance Ld is measured and then shifted 90

electrical degrees for Lq measurement. The method is cor-rect when in the machine eddy currents do not exist. Thesecond method, described also in [20], evaluates the DCcurrent decay after initial direct current was applied. In[15] a similar voltage step method was used. Accuracy ofthese methods is lowered because of the numerical evalua-tion of the current time curve. Current decay can last sev-eral minutes in turboalternators as mentioned in [20]. Pa-per [3] uses the steady state working when the machine isloaded as a motor. Under this condition the magnetic fluxesin ’dq’ axes are constant. The torque angle (load angle) βis measured by a machine set of four machines. The accu-racy is lowered by higher harmonics induced in no load inthe helping synchronous machine. Paper [17] uses also thesteady state analysis. The load angle is obtained by geo-metrical construction which lowers the accuracy too.

2 MEASUREMENT OF PMSM PARAMETERS INSTEADY-STATE CONDITION

The newly proposed measurement methods are de-scribed in this section. They are simple and accurate. They

can be used also for machines where eddy currents inthe ’dq’ axes exist and cannot be omitted.

In this paper the evaluation of steady state of themachine working as generator is used. The generator isloaded with capacitance or inductance when Ld induc-tance is measured. The generator is loaded with arbitraryimpedance or resistance when Lq inductance is measured.This load causes that the torque angle (load angle) β oc-curs. When the machine transfers from no load to loadregime the rotor is shifting and the torque angle changesfrom zero to β. This angle can be measured by the posi-tion sensor or by the stroboscope. The vector diagram insteady state is depicted in Fig. 1. The angle β is the an-gle between stator voltage U1 and voltage Ub induced bypermanent magnet flux.

To construct the diagram following values must beknown:

R1 stator resistance

Xd stator self reactance in ’d’ axis

Xq stator self reactance in ’q’ axis

U1 stator voltage

I1 stator current

ϕ phase angle.

2.1 Measurement of stator self inductance in ’d’ axis

Vector diagram in Fig. 1 will change when the PMSMis loaded as generator by capacitance or inductance only.For the case of the capacitance load see Fig. 2.

The stator current vector I1 = IC is situated in thedirect axis ’d’ as its magnetic flux linkage Ψc = Ld · I1.Voltage Ub is induced by the permanent magnet flux.

The magnetic flux linkage Ψc = Ld · I1 will be addedto the magnetic flux linkage of the permanent magnetwhich induces the voltage Ub. It holds exactly when R1 iszero or very small. For the case of inductance load the mag-netic flux linkage Ψ will be subtracted from the magneticflux linkage of the permanent magnet. The direct axis in-ductance is the function of the magnetic circuit and perma-nent magnet quality. We can measure the voltage Ub of thePMSM in no load. The direct axis reactance X1d +X1σ

can be calculated from the difference of no load voltageand load voltage. It holds when we omit the resistance R1.The voltage drop on the resistance R1 is small when com-pared with the stator voltage U1. The calculation can becorrected with respect to the voltage dropR1 · IC. The cor-rection is usually not needed. The vector diagram is shownin Fig. 2 for the case when the machine was loaded withcapacitance. Voltage drop R1 · IC is assumed as very low.

AUTOMATIKA 56(2015) 2, 217–225 218


Fig. 1. Vector diagram of salient pole synchronous machineloaded by inductance in steady state generator regime,Xd > Xq

Fig. 2. Vector diagram of PMSM loaded by capacitance.Voltage vector U1 was laid into the real axis.

We can calculate:

X1d +X1σ =U1 − Ub · cos ε

Ic, (1)

L1d + L1σ =X1d +X1σ

ω. (2)

It holds for the angle ε:

sin ε =R1 · IcUb

. (3)

For R1 · Ic = 10 V and Ub = 220 V, ε ≈ 2.60 andcos ε = 0.9989.

The correction is not necessary even if it is possible.

We can calculate the time constant knowing the statorphase resistance R1 = Rd.

Td =L1d + L1σ

Rd, (4)

Td =U1 − Ub · cos ε

Rd · ω · Ic. (5)

Procedure is the same when we load the machine with in-ductance.

2.2 Measurement of stator self inductance in ’q’ axis

Measurement may be performed on the machine loadedas generator. The load can be arbitrary combination of re-sistance, inductance and capacitance.

Directly measurable values are:

R1 = Rd stator phase resistance

U1 stator voltage

Ub voltage induced by the permanent magnet in noload regime

Z loading impedance

ϕ phase angle

Ld = L1d + L1σ Direct axis inductance is knownfrom previous measurement

ω electrical angular frequency.

We use for the measurement evaluation the vector dia-gram in Fig. 3 which is drawn for the case that Ld < Lq.

The position and the length of the vector |A| · e α canbe calculated from (6).

~A = ~U1 −R1 · ~I1 − (X1d +X1σ) · ~I1 = |A| · e α. (6)

The value Ld = L1d + L1σ was measured and isknown. The length of the vector and its angle α can becalculated from (6). The length of the vector |B| · e β de-pends on L1q + L1σ .

~B = ~U1 −R1 · ~I1 − (X1q +X1σ) · ~I1. (7)

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Fig. 3. Vector diagram of salient pole synchronous machineloaded by inductance in generator regime X1d < X1q

We can write for the angle γ between vectors ~A and ~B:

cos γ =Ub

A. (8)

We can write for the angle β:

β = α± γ. (9)

Sign plus holds for the case Ld < Lq. Compare Fig. 1and Fig. 3.

Sign minus holds for the case Ld > Lq. CompareFig. 1 and Fig. 3.

For this decision the measurement of the angle β isneeded. It is possible to measure it by the position sensoror by the stroboscope as shifting the axes when the ma-chine rotor transfers from no load to load regime or on thecontrary.

• In case if Ld > Lq it holds β < α.

• In case if Ld = Lq it holds β = α.

• In case if Ld < Lq it holds β > α.

The decomposition of the current ~I1 into ’d’ component~I1d and ’q’ component ~I1q depends on the angle β.

Voltage Ub induced by the permanent magnet is con-stant and does not depend on the load of the PMSM.

Voltage Ub in Fig. 3 and Fig. 1 is determined by theperpendicular line from the vector ~A on the vector ~B.

Procedure of the quadrature axis inductance calculationcan be performed by following equations:

Angle δ between stator current ~I1 and ’d’ axis is:

δ = 90− ϕ− β. (10)

Current components in ’q’ and ’d’ axis I1q and I1d are:

I1q = I1 · sin δ = I1 · sin(90− ϕ− β) = I1 · cos(ϕ+ β),(11)

I1d = I1 · cos δ = I1 · cos(90− ϕ− β) = I1 · sin(ϕ+ β).(12)

We get from the vector diagram:

~C = ~Ub + (X1d +X1σ) · ~I1d, (13)

(X1q +X1σ) · ~I1q = ( ~U1 −R1 · ~I1)− ~C. (14)

We obtain for the quadrature axis reactance and quadra-ture axis inductance finally:

X1q +X1σ = − ( ~U1 −R1 · ~I1)− ~C

~I1q, (15)

L1q + L1σ =X1d +X1σ

ω. (16)

The computation will be very simple if the measure-ment on the PMSM is performed in the regime of re-sistance load only. In such a case the angle ϕ = 0, thecurrent vector ~I1 is a real negative number and the vec-tor ~U1 −R1 · ~I1 = U1 +R1 · I1. We get from Fig. 3 andϕ = 0 for ~C = (U1 +R1 · I1) · e β · cosβ.

We get from (15):

X1q +X1σ = − (U1 +R1 · I1)− C · e β~I1q

=

= − (U1 +R1 · I1)− (U1 +R1 · I1) · e β cosβ

−e β · I1q=

= − (U1 +R1 · I1) · (1− e β cosβ)

−e β · I1q=

= U1 +R1 · I1

I1q· (e− β − cosβ) =

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= U1 +R1 · I1

I1q· (cosβ − sinβ − cosβ) =

=U1 +R1 · I1I1 · cosβ

· sinβ =

=U1 +R1 · I1

I1· tanβ. (17)

It holds for the stator self reactance in quadrature axisand stator self inductance in quadrature axis simple (18)and (19) finally.

X1q +X1σ =U1 +R1 · I1

I1· tanβ, (18)

L1q + L1σ =X1q +X1σ

ω=U1 +R1 · I1

I1 · ω· tanβ.

(19)

It is only the measurement in the regime of resistanceload needed. Only voltage U1, current I1 and angle β be-tween U1 and Ub are needed. The angle β can be mea-sured by the position sensor or by the stroboscope. Angle βmarks the ’dq’ axes shifting when the machine rotor trans-fers from no load to load regime or on the contrary.

3 PERFORMED MEASUREMENTS

Measurements were performed according to the Chap-ter 2. Measured machine was: Synchronous machine1 kW, 140 V, star connected, 3 phases, 4.6 A, 133.33 Hz,2000 min−1, pole number 2p = 8, with buried permanentmagnets symmetrically distributed. Photo of the measuredmachine is in Fig. 4. Measurement arrangement is in Fig. 5.

Fig. 4. PMSM 1 kW, 140 V, star connected, 3 phases,4.6 A, 133.33 Hz, 2000 min−1, pole number 2p = 8, withburied permanent magnets symmetrically distributed

Fig. 5. Measurement arrangement

3.1 Influence of saturation in the machine duringmeasurement

Saturation of the magnetic circuit in PMSM is causedby two factors. The first factor is the permanent magnet initself and the second factor is the armature reaction causedby load. Permanent magnets have good quality nowadays.Nevertheless the coercive field strength Hc and remanentmagnetic flux density Br are limiting factors for the ma-chine design. Therefore the saturation level of the magneticcircuit at no load is rather low. The influence of the arma-ture reaction on the magnetic saturation in PMSM is loweras in machines using excitation winding. Let us compare itusing the magnetic circuit in Fig. 6. The reluctance of thearmature stack is assumed to be much smaller than the re-luctance of the air gap. Let us consider the case when thearmature reaction is zero. It means that the armature coil inFig. 6 is without current.

Fig. 6. Magnetic circuit with permanent magnet, armaturereaction and the demagnetization curve H = f(B)

It holds between the air gap magnetic flux density Bδ ,coersive field strength HC and the remanent magnetic fluxdensity Br (20) .

Bδ = Br −Br ·Bδg ·Hc · µ0

· δ, (20)

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from which we get:

Bδ =Br

1 + Br·δg·Hc·µ0

. (21)

When the armature coil current is present and causesthe MMF it will hold:

Bδ = Br −Br

g ·Hc·(Bδµ0· δ ∓MMF

), (22)

from which we get:

Bδ =Br ·

(1± MMF

g·Hc

)

1 + Br·δg·Hc·µ0

. (23)

The sign ’+’ holds in case when the MMF supportsthe permanent magnet. The sign ’-’ holds in case whenthe MMF acts against the permanent magnet.

Let us assume that the magnetic circuit is magnetizedonly with excitation winding (not depicted in Fig. 6). Thepermanent magnet is not used and the armature reactioncauses additionally the same MMF as in the previouscase. The armature reaction MMF causes additional air gapmagnetic flux density Bδ:

∆Bδ = µ0 ·MMF

δ. (24)

Let us calculate the increasing of the air gap mag-netic flux density ∆Bδ caused by armature windingMMF 100 A.

Parameters of the magnetic circuit are listed in Table 1.The magnetic flux density in the air gap when the cir-

cuit is magnetized only by permanent magnet is given by(21) Bδ = 0.7020 T.

The magnetic flux density in the air gap when the cir-cuit is magnetized by permanent magnet and by armaturereaction with MMF 100 A is given by (23)Bδ = 0.7207 T.

The increasing of the magnetic flux density in the airgap is ∆Bδ = 0.0187 T.

The increasing of the magnetic flux density in theair gap when the magnetic circuit is magnetized by ex-citation winding and additionally by armature reaction

Table 1. Parameters of the magnetic circuitLength of the permanent magnet g = 0.005 mLength of the air gap δ = 0.002 mCoercive field strength

Hc = 750 000 Am−1

of the permanent magnetPermanent magnet

Br = 1 Tremanent magnetic flux density

with MMF 100 A is given by (24) ∆Bδ = 0.0628 T. Thatmeans that the influence of the armature reaction is in ma-chine with excitation winding 3.358 times stronger then inPMSM.

In all these cases were the air gap magnetic flux densi-ties Bδ calculated under the assumption that the reluctanceof the armature stack is negligible. Nevertheless the resultsshow that the saturation effect can appear in PMSM only atvery high loads and is much more weaker then in machineswith exciting windings. Approximately similar results holdin ’q’ axis because also here the magnetic flux crosses thepermanent magnet material. Magnetic flux crosses in thiscase the side extension parts of permanent magnet poles.Therefore the measured values can be used in prevailingloads. When we want to calculate load characteristics ofthe machine at high loads it is better to measure the selfinductances at high currents but with attension not to de-magnetize the permanent magnet.

3.2 Measurement of stator self inductance in ’d’ axis.

Machine was loaded with capacitive current.

3.2.1 Values measured

Stator effective phase voltage U1 = 58.38 V, phasevoltage induced with permanent magnets Ub = 55.71 V.Capacitive current IC = 1.117 A. Frequency dur-ing measurement f = 99.16 Hz, angular velocityω = 623.04 s−1, revolutions 1487.4 min−1, phase re-sistance R1 = Rd = 0.963 Ω.

3.2.2 Results obtained

Using (1) we obtain the reactance Xd at frequencyf = 99.16 Hz:

Xd = X1d+X1σ =U1 − Ub

Ic=

58.38− 55.71

1.117= 2.39 Ω.

(25)Using (2) we get stator self inductance:

Ld = L1d+L1σ =X1d +X1σ

ω=

2.39

623.04= 0.003836 H.

(26)Using (4) we get the time constant:

Td =0.003836

0.963= 0.003983 s. (27)

The angle ε can be omitted because:

sin ε = Rd·IcUb

= 0.963·1.11755.71 = 0.0193, (28)

ε = 1.106 ,

cos ε = 0.9998.

AUTOMATIKA 56(2015) 2, 217–225 222


3.3 Measurement of stator self inductance in ’q’ axis.

Machine was loaded with resistance only.

3.3.1 Values measured

Stator effective phase voltage U1 = 25.92 V. Cur-rent IR = 2.265 A. Frequency during measurementf = 52.5 Hz. Angular velocity ω = 329.87 s−1, revolu-tions 787.5 min−1. Phase resistance R1 = Rd = 0.963 Ω.Angle β = 8.510 was measured with position sensor.Graph of voltage Ub is measured in no-load and is depictedin Fig. 7.

Fig. 7. Shifting angle β between terminal voltage U1 andvoltage Ub induced with permanent magnets. One periodof the 8 pole machine.

In the Fig. 7 the position sensor pulse ’R’ is writtendown. Position sensor does not mark the ’d’ or ’q’ axis withits pulse ’R’ but voltage Ub does it. Voltage graph de-termines in no-load with its zero value the ’d’ axis posi-tion and with its maximum value the ’q’ axis position. Thegraph Ub is recorded and then the machine is loaded withthe resistance at the same velocity. Voltage graph U1 dur-ing full load is recorded too. Both oscillograms (Ub andU1) were put one on each other with position sensor pulsesaligned. Angle between them is angle β.

Using (18) we get for Xq (29) at frequencyf = 52.5 Hz.

Xq = X1q +X1σ =U1 +R1 · I1

I1· tanβ, (29)

Xq =25.92 + 0.963 · 2.265

2.265· tan(8.51) = 1.856 Ω.

Using (19) we get for Lq (30).

Lq = L1q + L1σ =X1q +Xσ1

ω, (30)

Lq =1.856

329.87= 0.005626 H.

Measured machine has (L1q + L1σ) > (L1d + L1σ)with the ratio:

L1q + L1σ

L1d + L1σ= 1.47.

4 EXPERIMENTAL CONFIRMATION OF MEA-SURED PMSM PARAMETERSMeasured parameters can be used for PMSM charac-

teristics prediction. Let us use the experimentally obtainedinductances Ld, Lq and calculate the voltage characteris-tics of the permanent magnet generator. Let us load thegenerator with a circuit formed with different impedancesZZ = RZ + ω · LZ orZZ = RZ − 1

ω·CZwhere the resis-

tance RZ will be several times changed.Calculation results are shown in Fig. 8 and Fig. 9.

Fig. 8. Calculated voltage characteristic compared withmeasurement. Three phase symmetrical load is inductivewith constant LZ = 23.9 mH and changing resistance RZ

from 6.04 Ω to 30.0 Ω, f = 101.2 Hz. Points measured aremarked with symbols ’+’, full line holds for calculated val-ues, dash line holds for no load regime RZ →∞.

Parameters used for calculated characteristics in Fig. 8are: machine phase resistance R1 = 0.963 Ω machine in-ductances Ld = 3.836 mH and Lq = 5.626 mH and fre-quency f = 101.2 Hz. Calculations were performed forsymmetrical impedance Z = RZ + ω · LZ. InductanceLZ was used constant LZ = 23.9 mH while the resis-tance RZ has been changed from RZ from 6.04 Ω to30.0 Ω. Then the experiment was performed on machineloaded in turn with impedance ZZ = RZ + ω · LZ un-der the same conditions. Inductance LZ was hold con-stant LZ = 23.9 mH while the value of resistance RZ wasfour times changed RZ = 6.0 Ω; 14.58 Ω; 18.54 Ω; 24.7 Ω.The calculation result is in Fig. 8 compared with measure-ments. Points measured are marked with symbols ’+’.

Parameters used for calculated characteristics in Fig. 9are: machine phase resistance Rd = 0.963 Ω, machineinductances Ld = 3.836 mH, Lq = 5.626 mH and fre-quency f = 106.6 Hz. Calculation was performed for

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Fig. 9. Calculated voltage characteristic compared withmeasurement. Three phase symmetrical load is capacitivewith constantCZ = 0.032 mF and changing resistanceRZ

from 6.00 Ω to 30.0 Ω, f = 106.6 Hz. Points measured aremarked with symbols ’+’, full line holds for calculated val-ues, dash line holds for no load regime RZ →∞.

symmetrical impedance ZZ = RZ − 1ω·CZ

. CapacitanceCZ was hold constant CZ = 0.032 mF while the resis-tance RZ was changed from RZ from 6.00 Ω to 30.0 Ω.Then the machine was loaded in turn with impedanceZZ = RZ − 1

ω·CZunder the same conditions.

Capacitance CZ was hold constant CZ = 0.032 mFwhile the value of resistance RZ was three times changedRZ = 5.67 Ω; 13.14 Ω; 19.89 Ω. The calculation result is inFig. 9 compared with measurements. Points measured aremarked with symbols ’+’.

It can be seen from Fig. 8 and Fig. 9 that the generatorinductive current demagnetizes permanent magnets of thegenerator. The voltage drop is relatively high. The capaci-tive generator current acts positively with permanent mag-net orientation. The outgoing generator voltage is higherthen is the voltage in no load.

5 CONCLUSION

Modern electric drives very often use permanent mag-net synchronous machines (PMSM). Parameters of thesemachines influence the drive features. The saliency ofPMSM has often high importance for the drive and its con-trol. The saliency is influenced by machine constructionand by permanent magnet material quality. Measurementmethods for PMSM parameters identification are impor-tant. New methods are described in the paper. They aresuitable for stator self inductances in direct and quadratureaxes identification. They can be used for all constructionvariation of PMSM and for all permanent magnet mate-rials. Results of measurement methods and their experi-mental verification are published in the paper. Performedexperiments acknowledge the measurement methods.

ACKNOWLEDGMENT

Paper was supported by Josef Božek Research Centerof Engine and Automotive Technology at Czech TechnicalUniversity in Prague.

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Zdenek Cerovský was born in Czech RepublicFeb. 1, 1930. He graduated from Czech Tech-nical University in Prague. He started his car-rier with CKD factory as DC/AC machine de-signer. He projected hoisting engines, mill standengines, ship engines, drives for street cars, locosand electric vehicles. He changed for Czechoslo-vak Academy of Sciences, worked as head ofPower Electronics Department in the Institute forElectrical Engineering. Projected the first streetcar with induction motors in CSR together with

CKD. Received Dr.Sc. degree. Later on was director of the Institutefor Electrical Engineering. Changed for Czech Technical University inPrague as Professor. Was visiting professor at the UNI in Hannover Ger-many. Is member of the Research Center JB of Automotive Technology.He was member of Executive Council of the European Power ElectronicAssociation EPE Brussels and member of EPE-PEMC Council Budapest.He worked in many grants and projects like: Project NATO High Technol-ogy No 950918, Grant MPO IMPULS. SATREMA, Grant FI-IM5/171.He works for Italy grant agency. He is emeritus professor at Czech Tech-nical University in Prague.

Miroslav Lev was born in Czech Republic Sept.20, 1958. He graduated from Czech TechnicalUniversity in Prague. He graduated from two fac-ulties of the UNI in Prague. He finished at theFaculty of Electrical Engineering the specializa-tion Technical Cybernetics and at the Faculty ofMechanical Engineering the specialization Pro-duction Machines and Equipment. He was greatdeal of his technical activity employed by the Re-search Institute of Machine Tools and Machin-ing VUOSO, by the factory KONE Lifts and

ITI TÜV Group Süddeutschland. At the present time he is employed byCzech Technical University in Prague, Faculty of Electrical Engineering,Department of Electric Drives and Traction. His current interests includemathematical simulation and programming of systems working in realtime.

AUTHORS’ ADDRESSESProf. Zdenek Cerovský, Dr.Sc.Miroslav Lev, M.Sc.Department of Electric Drives and Traction,Faculty of Electrical Engineering,Czech Technical University in Prague,Technicka 2, CZ-16627, Prague, Czech Republicemail: [email protected], [email protected]

Received: 2014-03-18Accepted: 2014-07-04

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Documents

Permanent Magnet Synchronous Machine Parameters