differential-evolution-based parameter identification of a line-start ipm synchronous motor

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 11, NOVEMBER 2014 5921

Differential-Evolution-Based ParameterIdentification of a Line-Start IPM

Synchronous MotorTine Marcic, Member, IEEE, Bojan Štumberger, Member, IEEE, and Gorazd Štumberger, Member, IEEE

Abstract—This work deals with the differential-evolution(DE)-based method for simultaneous identification of the electric,magnetic, and mechanical subsystem parameters of a line-startinterior permanent magnet synchronous motor (LSIPMSM). Theparameters are determined in the optimization procedure usingthe dynamic model of the LSIPMSM; the time behavior of volt-ages, currents, and speed measured on the tested LSIPMSM; andthe DE, which is applied as the optimization tool. During theoptimization procedure, the DE changes the parameters of theLSIPMSM dynamic model in such a way that the differencesbetween the measured and calculated time behaviors of individualstate variables are minimized. This paper focuses on the objectivefunction definition, the constraint settings for individual parame-ters, the normalization of parameters, and, above all, the test andmeasurement procedures performed on the LSIPMSM, which alltogether make it possible to determine the LSIPMSM dynamicmodel parameters valid for a broad range of operation, thus ensur-ing proper evaluation of the LSIPMSM’s line-starting capability.Some of the LSIPMSM parameters that can be determined byfinite-element analysis and experimental methods are comparedto the values obtained by the DE, thus validating the DE-basedapproach.

Index Terms—AC motors, differential evolution (DE), line-start interior permanent magnet (IPM) synchronous motor(LSIPMSM), modeling, optimization, parameter estimation, tests.

I. INTRODUCTION

THE ANALYSIS of transient behavior for translatory androtary electromechanical devices demands the usage of a

reliable dynamic model of the device. These models consist ofthe electric and mechanical subsystems, which are most oftencoupled by the magnetic subsystem [1], [2]. In order to attainreliable performance, the respective subsystem model parame-ters have to be identified. Different computational methods [3]–

Manuscript received May 23, 2013; revised November 5, 2013; acceptedJanuary 10, 2014. Date of publication February 26, 2014; date of currentversion June 6, 2014. This work was supported in part by the SlovenianResearch Agency under Project L2-1180, Project L2-2060, Project L2-4114,Project L2-5489, and Project P2-0115.

T. Marcic and G. Štumberger are with TECES, Research and DevelopmentCentre for Electric Machines, 2000 Maribor, Slovenia, and also with the Facultyof Electrical Engineering and Computer Science, University of Maribor, 2000Maribor, Slovenia (e-mail: [email protected]; [email protected]).

B. Štumberger is with the Faculty of Energy Technology, University ofMaribor, 8270 Krško, Slovenia, with the Faculty of Electrical Engineering andComputer Science, University of Maribor, 2000 Maribor, Slovenia, and alsowith TECES, Research and Development Centre for Electric Machines, 2000Maribor, Slovenia (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIE.2014.2308160

[12] are applied when detailed data of the employed materialsand geometry are available. However, when coping with analready manufactured device in a specific application, thenexperimental methods are applied. These describe the devicebehavior by means of measurable parameters on the deviceterminals [1], [2], [13]–[20]. Such experimental methods areindispensable in cases when the exact geometry or materialdata for a particular device are not known since the model withcorresponding parameters provides an integral view into thedevice’s behavior. Unfortunately, in certain cases, some of theparameters for the dynamic model, which reflect the modeleddevice’s physical characteristics, are difficult to identify by bothof the aforementioned methods.

Line-start interior permanent magnet synchronous motors(LSIPMSMs) [3]–[6], [8], [9], [12], [17]–[19] are most oftenused in fan, pump, and compressor drives without any powerelectronics and therefore have to be able to start from standstilland accelerate the drive up to rated speed when they arefed from a constant-amplitude and constant-frequency voltagesource. A short-circuited rotor winding, the so-called squirrel-cage known from induction motors [5], [6], [20], provides theaforementioned line-starting capability. The line-starting tran-sient [3]–[6], [8], [9], [12], [21], [22] represents one of the mosttroublesome transients known in the field of electric drives.Fig. 1 shows that the LSIPMSM rotor consists of a magneticallysalient iron core with flux barriers [10], [11], permanent magnetsegments, and a squirrel-cage. Its steady-state performance isdirectly related to exploitation of the permanent magnet torqueknown from permanent magnet synchronous motors [7], [13],[16], [17], [19] and the reluctance torque due to inherent ironcore saliency known from synchronous reluctance motors [7],[14]. Although otherwise advantageous [12], [23], the squirrel-cage and saliency aggravate the determination of all neededLSIPMSM dynamic model parameters by using finite-elementanalysis (FEA) [3]–[6], [8], [9], [12], [13], [19] or experimentalmethods [15], [17]–[19].

In this paper, the needed (electric, magnetic, and mechanicalsubsystems) parameters for an LSIPMSM model are simultane-ously identified by employing the stochastic search algorithmdifferential evolution (DE) [18], [20], [24]–[36] along withsome specific tests performed on the LSIPMSM. By using suchan approach, the LSIPMSM’s parameters can be adequatelyidentified without any prior knowledge of its properties incontrast to, for example, the FEA-based approach. Althoughit was applied before in the field of electric motors [26],

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5922 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 61, NO. 11, NOVEMBER 2014

Fig. 1. Principal cross section of the LSIPMSM.

[28], [29], the DE-based approach for determining LSIPMSMparameters was first presented in [18], but a comprehensive andstructured evaluation of its effectiveness has not been done.Besides the steady-state efficiency, for an LSIPMSM, its line-starting capability is the most important attribute. Therefore,the LSIPMSM dynamic model, along with its correspondingparameters, has to be able to correctly simulate line-startingtransients. This integral work presents for the first time thefollowing:

1) appropriate test signals and their measurement proce-dures needed for the DE-based LSIPMSM parameteridentification;

2) sets of optimized LSIPMSM parameters and their iden-tification procedure by employing DE along with theLSIPMSM dynamic model and aforementioned testsignals;

3) comprehensive evaluation of the proposed DE-basedmethod, test signals, and obtained parameter sets suitablefor effectively simulating line-starting performance withthe LSIPMSM dynamic model.

For the sake of completeness, Section II presents the usedLSIPMSM dynamic model along with its parameters that canbe determined by FEA and experiments. Sections III–V presentthe gist of this work, where the employment of DE in con-junction with the LSIPMSM dynamic model is introducedand the preparation of input data needed in the optimizationprocess is described in detail. Section VI presents the resultingparameter sets obtained using DE and their value discrepanciesto results obtained by other methods; most importantly, theireffectiveness of simulating line-starting transients is evaluatedas well. Section VII concludes this paper.

II. TWO-AXIS LSIPMSM DYNAMIC MODEL

The LSIPMSM is made like a hybrid (Fig. 1) between asquirrel-cage induction motor, a synchronous reluctance motor,and a permanent magnet synchronous motor. Thus, a squirrel-cage, flux barriers (saliency), and permanent magnets are im-plemented in its rotor. Its magnetically linear lumped parametermodel written in the d−q reference frame [5], [18] is defined byalignment of the model d-axis with the axis of the permanentmagnet flux linkage. The q-axis is placed electrical π/2 ahead.In the LSIPMSM dynamic model, the different inductances inthe d- and q-axes account for effects of saliency. A set of two

short-circuited and perpendicular model windings with theirresistance and inductance in the d- and q-axes accounts forthe squirrel-cage effects, respectively. Permanent magnet fluxlinkage vector accounts for the permanent magnet effects.

The LSIPMSM model is defined by the set of (1)–(6). Statorvoltage balance is described by (1) and (2), while rotor voltagebalance is described by (3) and (4). The torque (5) neatly de-picts the hybrid nature of LSIPMSMs by listing different torqueproducing components originating from squirrel-cage, saliency,and permanent magnet effects, respectively. Mechanical motionis described by (6)

ud=Rsid+Lsddiddt

+Lmddikddt

+dθ

dt(−Lsqiq−Lmqikq) (1)

uq=Rsiq+Lsqdiqdt

+Lmqdikqdt

+dθ

dt(Lsdid+Lmdikd+ψm) (2)

0 = Rkdikd + Lrddikddt

+ Lmddiddt

(3)

0 = Rkqikq + Lrqdikqdt

+ Lmqdiqdt

(4)

te=p(Lmdiqikd−Lmqidikq)+p(Lsd−Lsq)idiq+pψmiq (5)

J

p

d2θ

dt2= te − tl −

f

p

dθ

dt− TC . (6)

In (1)–(6), the subscripts d and q denote variables in the d-and q-axes, respectively, u• represents the stator voltages, i•represents the stator currents, Rs represents the stator resis-tance, ik• represents the cage currents, Rk• represents the cageresistances, Ls• represents the stator self-inductances, Lm•represents the mutual inductances, Lr• represents the rotor self-inductances, θ is the electrical rotor position, ψm is the lengthof the permanent magnet flux linkage vector, J is the momentof inertia, te is the electromagnetic torque, p is the number ofpole pairs, tl is the load torque, f is the coefficient of viscosefriction, and TC is the Coulomb friction torque. Parameters Rs,Rk•, Ls•, Lm•, and Lr• are considered as constants in (1)–(6).

Some of the electromagnetic parameters used in the previ-ously described LSIPMSM dynamic model can be determinedby experiments or by postprocessing of FEA output data. Rs

is relatively straightforward to measure; thus, it is customarythat it is determined in that way. ψm and Ls• can be determinedexperimentally and by FEA, which will be shown in the fol-lowing section. Although not done in this work, the mechan-ical parameters (J, f, TC) can be determined by experimentalmethods [2] as well. Contrarily, the parameters that relate to thesquirrel-cage (Rk•, Lm•, Lr•) cannot be determined directly.For the aforementioned reason and because strongly coupledfinite-element models [3], [4], [6], [8] are computationallyvery complex for line-starting analysis, the authors proposed toefficiently employ the previously described lumped parameterdynamic model in combination with the DE algorithm forsimultaneous identification of all of the needed dynamic modelparameters valid for a broad range of LSIPMSM operation.

A. Results From FEA and Measurements

Some of the LSIPMSM magnetic subsystem parameters thatcan be determined by using FEA and experimental methods

MARCIC et al.: DE-BASED PARAMETER IDENTIFICATION OF A LINE-START IPM SYNCHRONOUS MOTOR 5923

Fig. 2. No-load back EMF at 157 rad/s and comparison of ψm valuesdetermined by different methods.

have been determined for evaluation and validation of the DE-based method. In [18], the parameters Rs and ψm were de-termined from measurements with a simple multimeter, whichafterward proved to be disadvantageous because the othermodel parameters determined by DE were adjusted consideringthose aforementioned values. In this paper, Rs was measured bya more precise ohmmeter GW Instek GOM-802.

A 2-D nonlinear time-stepped finite-element solver in com-bination with multislice rotor representation was used in theFEA of magnetic conditions. The mesh of each rotor sliceconsists of 37 432 first-order triangular elements. The nonlin-earity of the used iron core material was accounted for witha single-valued B−H curve. The magnetic conditions over acomplete cycle of magnetic field variation were calculated in126 discrete equidistant time steps by shifting the rotor positionand simultaneously changing the current excitation. For eachrotor position, the phase flux linkages were obtained from theaverage value of the magnetic vector potential in stator slots inaccordance with the winding arrangement scheme. The averagevalues of the d- and q-axis flux linkages over one electricalcycle were obtained from phase flux linkages by applyingabc → dq0 transformation for each set of (id, iq) excitation.The parameter ψm has been obtained without stator currentexcitation. The d- and q-axis apparent and incremental self-inductance characteristics have been obtained from the current-dependent characteristics of the d- and q-axis magnetic fluxlinkages. The apparent inductance is defined as the slope of thelinearized characteristic of flux linkage versus current throughthe origin and the particular operating point on the flux linkageversus current characteristic. The incremental inductance isdefined as the slope of the tangential line at the particular pointon the flux linkage versus current characteristic.

The actual finite-element software package is in-house de-veloped software and is commercially not available. However,it has proven reliable in a series of electric motor designproblems; some published in [5], [13], and [16]. The neededcomputational time for computation of magnetic conditionsover one electrical cycle depends on the saturation level andtypically takes between 8 and 10 min for one rotor slice(data used for a PC with Intel(R) Core(TM) i5-2400S CPU @2.50 GHz).

On the other hand, the length of the permanent magnet fluxlinkage vector ψm can be determined from the measured back-electromotive force (back EMF) [2], [16] at a certain rotorspeed with open LSIPMSM terminals (no load). Fig. 2 presentsa comparison of the no-load back EMF obtained by experiments

Fig. 3. Comparison of Lsd and Lsq values determined by different methods.

at the mechanical rotor speed of 157 rad/s and by FEA bypostprocessing of finite-element output data. It can be notedthat they correspond to each other very well. Fig. 2 summarizesthe ψm values obtained from experiments and FEA. The valuesdetermined by DE and presented in Fig. 2 will be discussedlater in Section VI.

The apparent stator self-inductances Lsd and Lsq can bedetermined from the measured current-dependent magnetic fluxlinkage characteristics in the d- and q-axes, respectively [13]–[17], [19]. The current-dependent characteristics of Lsd andLsq obtained by experiments and FEA are shown in Fig. 3.By comparison of Lsd and Lsq curves, respectively, whichwere obtained by experiments and FEA, one can note that theycorrespond to each other very well, respectively. The valuesdetermined by DE and presented in Fig. 3 will be discussedlater in Section VI.

At this point, it should be noted that the aim of the DE-based parameter identification is to find all of the neededconstant parameter values in the previously described dynamicmodel, which are suited for correctly simulating transients ina broad range of operation of the LSIPMSM, e.g., simulatingline-starting transients. A previously performed comparisonof dynamic models, based on incremental inductances [30]as well as on apparent variable inductances, has shown thatthe LSIPMSM dynamic model based on constant apparent(large signals) single-value inductances is sufficient to properlyevaluate the start-up capabilities of LSIPMSMs [18] in spite ofless accurate and only in average considered saturation effects.This drawback is effectively minimized by a proper selectionof the supply voltages (detailed in Section IV-C), where theresultant effects of saturation in the measured currents and shaftspeed are implicitly accounted for by DE-determined constantsingle-value inductances. The other aforementioned models aresimply too complex and too time-consuming to be suitable fortheir use in DE-based parameter identification.

In the given case, DE identifies the constant inductancevalues simultaneously with all other constant model parametersin such a way that the resultant effects of all constant parameterscombined produce such a response from the dynamic modelthat corresponds best to the actual LSIPMSM response. Fig. 3shows current-dependent characteristics of inductances deter-mined experimentally and by FEA. They are compared withthe DE-determined constant-value inductances where differentsupply voltages are applied. The DE-determined constant val-ues of inductances are then used in the LSIPMSM dynamicmodel calculation presented in Figs. 5– 7 and discussed later


in this paper. Although, the presented LSIPMSM dynamicmodel can be adapted to accept both constant and variableparameters, throughout this work, only constant parametershave been applied in the model.

III. EMPLOYMENT OF THE DE ALGORITHM

DE is a fast and robust population-based direct-searchstochastic optimization algorithm which mimics Darwinianevolution, and it was first introduced by Storn and Price [24].Since its introduction, its popularity has grown in the engineer-ing audience [18], [20], [25]–[36], and many authors regard itas one of the best stochastic optimization methods for solvingreal-life engineering problems because of its favorable assets.

1) It is robust in attaining global minima.2) It is appropriate for solving nonlinear and constrained

optimization problems.3) It needs only a few control parameters to be defined.4) It does not require a starting point but boundaries of

expected solutions.

In this paper, a MATLAB implementation of the variantDE/rand-to-best/1/exp based on the publicly available originalsource code from [24] was employed in identifying the param-eters of the magnetically linear lumped parameter LSIPMSMdynamic model elucidated in the previous section. Descriptionsof the actual DE algorithm at work are available from [18], [20],[24], [25], [28], [31], and [32]; add-ons to the original algorithmare available from [33], [34], and [36]. The optimization objec-tive was the best possible agreement between the measured anddynamic-model-calculated time behaviors of model variables.In order to reach the objective, the DE was changing values ofthe model parameters during the optimization procedure, thusminimizing the squared differences between the measured andcalculated variables. The adopted DE settings were based onprevious experiences [18], [27], [30], [32]. The usage of DE inthe process of identification of the LSIPMSM dynamic modelparameters required the following:

1) appropriate tests performed on the tested LSIPMSM;2) simultaneous measurements of the time behavior of

model variables, which are used in the objective function;3) derivation of the magnetically linear lumped parameter

LSIPMSM dynamic model [5], [18], which is used tocalculate the time behavior of the model variables;

4) definition of the objective function [18], whose value isminimized during the optimization process;

5) definition of individual model parameter constraints,which ensure that parameter values are in accordancewith basic laws of physics;

6) normalization of model parameters in the optimizationprocedure because the values of individual model param-eters might differ in the range of millions.

Having in mind the identification of model parameters whichare suitable for LSIPMSM drive simulations in a wide range ofoperation, this work focuses on the six aforementioned require-ments, the preparation of input data needed in the optimizationprocess, and, above all, the comprehensive evaluation of theemployed procedures and test signals.

IV. MODEL VARIABLES, TESTS,AND EXPERIMENTAL SETUP

A. Model Variables Used in the Optimization Process

During the optimization process, in which the model param-eters are determined by the DE, the differences between theindividually measured and model-calculated variables are usedin the objective function. By examining the derived LSIPMSMmodel (1)–(6), the stator currents in the d- and q-axes, namely,id and iq , and the electrical motor speed ω = dθ/dt were identi-fied as the model variables which have to be measured and usedin the objective function. This is mainly because the appliedvoltages ud and uq depend on the electrical rotor position θ,while the cage currents ikd and ikq cannot be measured [19].

B. Tests Performed on the LSIPMSM

The DE was used in the identification of LSIPMSM pa-rameters by using three different sets of measured variables.The motor was voltage-fed in open-loop control by a volt-age source inverter (VSI), where the motor’s rated voltage tofrequency ratio (380 V at 50 Hz) has been maintained in alltests in order to achieve similar magnetic conditions in its ironcore. The LSIPMSM’s rotor speed was zero prior to the startof all of the tests. The VSI output voltages and frequencieswere set in a stepwise manner to different values during thetest, provoking different LSIPMSM transients. During the test,recorded simultaneous measurements of the time behavior ofLSIPMSM model variables id, iq , and ω have been used in theobjective function in the process of identification of LSIPMSMparameters using DE.

The first set of model parameters was determined by theDE based on recorded variables from the here-called 506-V/66-Hz test, where the LSIPMSM was supplied by the VSIwith four simultaneous stepwise voltage and frequency changes(126 V/16 Hz, 253 V/33 Hz, 380 V/50 Hz, and 506 V/66 Hz).The measured transients of the currents id and iq and the speedω during the 506-V/66-Hz test are presented in Fig. 4(a). Thesecond set of model parameters was determined by the DE forthe here-called 380-V/50-Hz test where only one output voltageof one output frequency (380 V/50 Hz) was generated by theVSI. This test could be performed by supplying the LSIPMSMdirectly from the grid as well. However, in order to facilitate adirect comparison, the VSI was employed in this test also. Themeasured transients during the 380-V/50-Hz test are presentedin Fig. 4(b). The third set of model parameters was determinedby the DE for the here-called 126-V/16-Hz test where againonly one output voltage of one output frequency (126 V/16 Hz)was generated by the VSI. The measured transients during the126-V/16-Hz test are presented in Fig. 4(c).

C. Experimental Setup

The tested motor was an IEC frame size 90 four-pole three-phase LSIPMSM with stator windings in wye-connection andrated for 380-V terminal voltage at 50-Hz frequency. The exper-imental setup consisted of the tested LSIPMSM, controlled VSISemikron, LC filter Siemens, control system dSpace 1103 PPC,current measurement chains based on LEM current sensors,


Fig. 4. Measured transients of LSIPMSM currents and speed during the (a) 506-V/66-Hz test, (b) 380-V/50-Hz test, and (c) 126-V/16-Hz test.

TABLE ILSIPMSM MODEL PARAMETER SETS IDENTIFIED BY THE DE

voltage measurement chains with Hameg differential probes,and Iskra position sensor. During the test, all signals weresampled with a sampling time of 100 μs.

V. NORMALIZATION, CONSTRAINTS,AND OBJECTIVE FUNCTION

The LSIPMSM dynamic model is given by (1)–(6), while thelist of its parameters to be determined by the DE is given at theleft column of Table I; the fixed model parameters have beenp = 2 and Rs = 7.198 Ω. During the optimization process, theDE generates the parameters from Table I. They are used inthe dynamic model to calculate responses on supply voltagesapplied during the test. The quality of model parameters isevaluated by the objective function, where the measured andcalculated stator currents and motor speed are compared. Theoptimization goal is to find that set of model parameters,which ensures the best agreement between the measured andcalculated variables.

A. Normalization of Parameters

Individual parameters of the LSIPMSM dynamic model candiffer in the range of more than 106. In the given case, the DE

generates normalized parameters whose values are between 0and 1. For use in the dynamic model, the normalized parametersare transformed to the physical interval of individual parame-ters. According to experiences from [25] and [27], normalizedparameters can converge faster.

B. Definition of Constraints

The values of the model parameters, which are adjustedduring the optimization procedure, have to be constrained toadequate values. This ensures that values of individual pa-rameters are in accordance with basic laws of physics, whilethe DE is forced to search for the solution in the appropriatedirection. Apart from the most obvious that all parameters musthave a positive value, the following parameter constraints weredefined:

(Lsd < Lsq)∧ (Lmd < Lmq) ∧ (Lrd < Lrq) (7)

(Lmd < Lsd)∧ (Lmd < Lrd) (8)

(Lmq < Lsq)∧ (Lmq < Lrq). (9)

The constraint (7) emerges from the definition of the d−q ref-erence frame used in the derivation of the two-axis LSIPMSMmodel. The d-axis is aligned with the permanent magnet fluxlinkage vector; therefore, the d-axis is the axis with higherreluctance, and consequently, the values of the model in-ductances in the d-axis must be lower than the ones in theq-axis. The constraints (8) and (9) emerge from the definition ofself-inductances. The stator self-inductances Ls• and rotor self-inductances Lr• have higher values than the mutual inductancesLm• for the value of individual leakage inductances [1], [2],respectively. If any of the constraints given by (7)–(9) areviolated, a very high value of penalty function pf is added tothe value of objective function q defined in the next section.

C. Objective Function

During the optimization process, the DE is searching forvalues of individual model parameters by minimizing the value


TABLE IIDE SETTINGS

of the objective function q defined in (10), where pf denotes thepenalty function value

q = kidqid + kiqqiq + kωqω + pf . (10)

An acceptable agreement between the measured and calculatedvalues of currents and motor speed simultaneously has beenassured by defining individual objective functions qid, qiq , andqω as the mean square difference between the measured andcalculated values of the stator current in the d-axis qid(11),the stator current in the q-axis qiq(12), and the electrical motorspeed qω(13) for the given time interval t ∈ [t1, t2]

qid =1

t2 − t1

t2∫t1

(imd (τ)− id(τ))2 dτ (11)

qiq =1

t2 − t1

t2∫t1

(imq (τ)− iq(τ)

)2dτ (12)

qω =1

t2 − t1

t2∫t1

(ωm(τ)− ω(τ))2 dτ. (13)

The superscript m indicates measured variables. Weighting fac-tors kid, kiq , and kω with values of 20, 20, and 1, respectively,have been utilized in order to balance the impact of individualobjective functions on the combined one. In general, weightingfactors can be set as ratios of peak values of variables recordedduring the test.

VI. RESULTS AND DISCUSSION

A. Parameters Obtained by the DE

The recorded transients from tests in Fig. 4 have been usedin the DE optimization process for identifying LSIPMSM pa-rameter values as previously described. During the optimizationprocess, the LSIPMSM model had been imposed with themeasured motor terminal voltages in the α−β reference frameuα and uβ , which are independent of the model-calculatedelectrical rotor position θ. The relation between the statorvoltages written in the α−β (stationary) reference frame andthe stator voltages written in the d−q (rotating) reference frameis provided by transformation matrix TR

TR=

[cos(θ) − sin(θ)sin(θ) cos(θ)

];

[uα

uβ

]=TR

[ud

uq

];T−1

R

[uα

uβ

]=

[ud

uq

].

(14)

Table I presents the LSIPMSM parameters identified by theDE based on the three tests from Fig. 4, while Table II presentsthe used DE settings. The mechanical subsystem parameter(J, f, TC) values obtained by the DE do not differ much

whether the 506-V/66-Hz or 380-V/50-Hz test is employed;however, they differ when the 126-V/16-Hz test is employed.This can be mainly attributed to the steady-state rotor speed inthe 126-V/16-Hz test, which is significantly lower than thosein the other two tests. Consequently, the electric and magneticsubsystem parameters based on the 126-V/16-Hz test have beenadjusted during the optimization process to accommodate thoseparticular mechanical conditions. This resulted in a low valueof ψm and mismatched relations between Rkd and Rkq, andLrd and Lrq , respectively, which could have been mitigatedby higher values of pf in combination with the 126-V/16-Hztest. However, this has not been employed here because a directcomparison between the DE-obtained values was the primaryaim of this work.

Overall, the resulting parameters from the 506-V/66-Hz and380-V/50-Hz tests presented in Table I show good agreementbetween LSIPMSM model parameters determined by the DEand those determined by experiments and FEA presented inSection II-A. The values presented in Fig. 2 show that, althoughthere is a small difference, the DE-determined value of ψm byemploying the 380-V/50-Hz test is a bit closer to the measuredvalue when compared to the 506-V/66-Hz test. This affectsalso the DE-determined value of Lsd which is very similar forthe 506-V/66-Hz and 380-V/50-Hz tests; note the overlappinglines of DE-506/66 Hz and DE-380 V/50 Hz for Lsd in Fig. 3.On the other hand, the DE-determined value of Lsq is quitedifferent for the 506-V/66-Hz and 380-V/50-Hz tests, whichmay be attributed to the fact that in the 380-V/50-Hz test onlyone steady-state saturation condition was recorded. Thus, itseems that the DE-identified values of Lsd and Lsq based on the506-V/66-Hz test may be applicable for the complete observedcurrent interval. This implies that the set of parameters basedon the 506-V/66-Hz test may be more suitable for analyzing abroad range of LSIPMSM operation.

B. Evaluation of the Proposed DE-Based Method

When analyzing LSIPMSM dynamic performance, the maininterest is their ability to start from zero rotor speed directlyfrom line and to synchronize to the feeding voltage frequency.Therefore, in order to evaluate the LSIPMSM dynamic modelperformance, the three previously presented sets by the DE-identified model parameters (Table I) were used to calculatemodel responses for a series of direct line-start tests at 50 Hzwith different voltage values at no load. There, the LSIPMSMmodel had been imposed with the measured motor phase volt-ages in the a, b, c reference frame ua, ub, and uc. The relationbetween the stator voltages written in the a, b, c (natural) refer-ence frame and the stator voltages written in the α−β referenceframe is provided by transformation matrix T32 (15), where u0

can be neglected because it cannot influence the results in (1)–(6)

T32=

√2

3

⎡⎢⎣

1 0√22

− 12

√32

√22

− 12 −

√32

√22

⎤⎥⎦;

⎡⎣ua

ub

uc

⎤⎦=T32

⎡⎣uα

uβ

u0

⎤⎦;

T−132

⎡⎣ua

ub

uc

⎤⎦=

⎡⎣uα

uβ

u0

⎤⎦ . (15)


Fig. 5. (a) Measured variables and LSIPMSM dynamic-model-calculated variables for the line-start at 200 V/50 Hz (200 V was the line-to-line rms voltage onthe LSIPMSM terminals) using parameters identified by the DE based on the (b) 506-V/66-Hz test, (c) 380-V/50-Hz test, and (d) 126-V/16-Hz test.

Fig. 6. (a) Measured speed and LSIPMSM dynamic-model-calculated speed for the line-start at 220 V/50 Hz (220 V was the line-to-line rms voltage on theLSIPMSM terminals) using parameters identified by the DE based on the (b) 506-V/66-Hz test, (c) 380-V/50-Hz test, and (d) 126-V/16-Hz test.

Fig. 5(a) presents the measured voltages, currents, and speedduring the direct line-start transient at 200-V line-to-line rmsterminal voltage and 50-Hz frequency, whereas Fig. 5(b)–(d)presents the LSIPMSM dynamic-model-calculated transientsby employing parameter sets identified by the DE based onthe 506-V/66-Hz test, 380-V/50-Hz test, and 126-V/16-Hz test,respectively. Fig. 5(a) shows that the tested LSIPMSM was notable to start and run up to synchronism at 200 V. Comparisonof Fig. 5(b)–(d) reveals that the dynamic model was able topredict the unsuccessful line-start only if the parameter setidentified by the DE based on the 506-V/66-Hz test has beenemployed [Fig. 5(b)]. Contrarily, the dynamic model was notable to predict the unsuccessful line-start if the parameter setsidentified by the DE based on the 380-V/50-Hz [Fig. 5(c)]or 126-V/16-Hz [Fig. 5(d)] tests have been employed. Thisshows the utmost importance of employing tests which coverthe broadest range of different LSIPMSM operating states.Such tests provide the DE the necessary input data so that itcan identify parameters which enable good correlation of themeasured and LSIPMSM dynamic-model-calculated transientsover a broad range of LSIPMSM operation—this includes line-starting transients as well. Such a parameter set has beenobtained based on the 506-V/66-Hz test.

Fig. 6(a) presents the measured speed during the direct line-start transient at 220-V line-to-line rms terminal voltage and50-Hz frequency, where the LSIPMSM started and synchro-nized successfully. Comparison of Fig. 6(b)–(d) shows that,although the LSIPMSM dynamic model predicted a successfulline-start regardless of the employment of different parametersets, the measured LSIPMSM speed transient and run-up timeis different when different parameter sets are used in the model.Although not further investigated, the mechanical parametervalues obtained based on the 506-V/66-Hz [Fig. 6(b)] and

380-V/50-Hz [Fig. 6(c)] tests do not differ much, but in calcula-tion of the LSIPMSM run-up time, these may be of significantimportance. However, from the results, it seems again that theparameters identified by the DE based on the 506-V/66-Hz testmay be the most suitable ones.

Fig. 7(a) presents the measured voltages, currents, and speedduring the direct line-start transient at 380-V line-to-line rmsterminal voltage and 50-Hz frequency, whereas Fig. 7(b)–(d)presents the LSIPMSM dynamic-model-calculated transientsby employing parameter sets identified by the DE based onthe 506-V/66-Hz test, 380-V/50-Hz test, and 126-V/16-Hz test,respectively. Although differences are small, comparison ofFig. 7(a)–(d) shows that, in this case, the dynamic model incombination with the parameter set identified by the DE basedon the 380-V/50-Hz test [Fig. 7(c)] is the most suitable one. Theother two sets of parameters seem to produce a longer lasting dccomponent in the voltage ud, which depends on the dynamic-model-calculated electrical rotor position θ and, consequently,on the correctness of the model parameters.

C. Summary

To sum up, the presented results show that the LSIPMSMparameter set identified by the DE based on the 506-V/66-Hztest is most suitable for simulations of the very important line-start transients. Although the results show that the parameter setidentified by the DE based on the 380-V/50-Hz test is certainlythe most suitable for simulating the rated test case (380 V/50 Hz), the results also show that the other two parameter setsbased on the 506-V/66-Hz test and the 126-V/16-Hz test maybe usable for the rated test case as well. Thus, the parameterset obtained by the DE based on the 506-V/66-Hz test is suit-able for simulations in a wide range of LSIPMSM operation.


Fig. 7. (a) Measured variables and LSIPMSM dynamic-model-calculated variables for the line-start at 380 V/50 Hz (380 V was the line-to-line rms voltage onthe LSIPMSM terminals) using parameters identified by the DE based on the (b) 506-V/66-Hz test, (c) 380-V/50-Hz test, and (d) 126-V/16-Hz test.

Furthermore, the resulting magnetic parameters from the506-V/66-Hz test show overall agreement between LSIPMSMmodel parameters determined by the DE and those determinedby experiments and FEA presented in Section II-A, despitethe fact that the DE determines the model parameters by con-sidering the resultant effects of all constant model parameterscombined. This is a consequence of the actually conductedtests presented in Fig. 4 because the signals measured dur-ing the transients and steady states are then used as inputfor the DE parameter identification, and thus, they signifi-cantly affect the resulting values of the LSIPMSM parameters.The 506-V/66-Hz test covered several transients and severalsteady states; therefore, the DE identified parameters that in-clude electric, magnetic, and mechanical conditions for a widerange of LSIPMSM operation. Contrarily, the 380-V/50-Hz and126-V/16-Hz tests, respectively, covered only one transient andonly one steady state; thus (although perfectly optimized), theDE identified parameters that included electric, magnetic, andmechanical conditions for one operating point only.

Again, it should be pointed out that the main aim of theDE-based approach for determining LSIPMSM parameters isto find all of the needed constant parameter values of thedynamic model, which are suited for correctly simulating line-starting transients over a broad range of LSIPMSM operation.Thus, the model parameters identified by the DE are to beregarded as “equivalent parameter values quasi-averaged overseveral different operating points” of the LSIPMSM, of whichvariable magnetic, electric, and mechanical conditions are tobe simultaneously included in appropriate test signals as inputfor the DE procedure—as shown previously by the exemplary506-V/66-Hz test.

VII. CONCLUSION

In this paper, the DE has been applied in identifying pa-rameters of the LSIPMSM dynamic model with constant pa-rameters. As it was shown in this work, in order to obtaina set of LSIPMSM parameters suitable for predicting a widerange of operation and most importantly adequately predictingline-starting capability of LSIPMSMs, employment of the DE

requires adequate tests to be performed on the LSIPMSM.These tests have to excite the broadest range of differentLSIPMSM operating states so that they enable the identificationof a suitable set of constant parameters applicable for a widerange of LSIPMSM operation. Thus, the tests have to coverseveral transients and several steady states so that adequateelectric, magnetic, and mechanical conditions are recorded andconsequently included in the parameter optimization procedure.The proposed procedure required measurement of voltages,currents, and motor speed during the test. Furthermore, theproposed DE-based method enables the identification of severalparameters which cannot be determined by FEA or experi-mental methods. The performance of the DE-based methodwas evaluated by comparison of the DE-obtained results andthe results that can be obtained from measurements and FEAas well.

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Tine Marcic (S’04–M’09) was born in Maribor,Slovenia, in 1978. He received the B.Sc. degree inindustrial engineering and the Ph.D. degree in elec-trical engineering from the University of Maribor,Maribor, Slovenia, in 2002 and 2008, respectively.

Since 2003, he has been with TECES, Researchand Development Centre for Electric Machines,Maribor, where he is currently a Researcher in theProject Office. In 2012, he joined the Faculty ofElectrical Engineering and Computer Science, Uni-versity of Maribor. His research interests include

electromechanical design, modeling, analysis, and testing of electric rotatingmachines.

Bojan Štumberger (M’99) received the B.Sc.,M.Sc., and Ph.D. degrees in electrical engineeringfrom the University of Maribor, Maribor, Slovenia,in 1993, 1997, and 1999, respectively.

Since 1993, he has been with the Faculty of Elec-trical Engineering and Computer Science, Universityof Maribor, where he was an Assistant Professor ofElectrical Engineering from 2001 to 2010. In 2010,he moved to the Faculty of Energy Technology, Uni-versity of Maribor, where he has been an AssociateProfessor of Electrical Engineering since 2011. His

research interests include electromechanical design and modeling of electricalmachines, CAD of electromagnetic devices, and magnetic material modeling.

Dr. Štumberger is a member of the International Compumag Society, theIEEE Industry Applications Society, and the IEEE Power and Energy Society.

Gorazd Štumberger (M’92) was born in Ptuj,Slovenia, in 1964. He received the B.Sc., M.Sc.,and Ph.D. degrees in electrical engineering from theUniversity of Maribor, Maribor, Slovenia, in 1989,1992, and 1996, respectively.

In 1989, he joined the Faculty of Electrical Engi-neering and Computer Science, University of Mari-bor, where he is currently a Professor of ElectricalEngineering. He was a Visiting Researcher with theUniversity of Wisconsin, Madison, WI, USA, in1997 and 2001, and with Katholieke Universiteit

Leuven, Leuven, Belgium, in 1998 and 1999. His current research interestsinclude power system research and design, modeling, analysis, and control ofelectrical machines and drives.

Dr. Štumberger is a member of the International Compumag Society and theSlovenian Committee of the International Council on Large Electric Systems(CIGRE).

differential-evolution-based parameter identification of a line-start ipm synchronous motor

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