research article simple hybrid model for efficiency...

Hindawi Publishing CorporationAdvances in Power ElectronicsVolume 2013 Article ID 371842 8 pageshttpdxdoiorg1011552013371842

Research ArticleSimple Hybrid Model for Efficiency Optimization of InductionMotor Drives with Its Experimental Validation

Branko Blanuša1 and Bojan Knezevic2

1 Faculty of Electrical Engineering University of Banja Luka Patre 5 78000 Banja Luka Bosnia and Herzegovina2 Faculty of Mechanical Engineering University of Banja Luka Bulevar Stepe Stepanovica 75 78000 Banja LukaBosnia and Herzegovina

Correspondence should be addressed to Branko Blanusa bbrankoetfblnet

Received 28 December 2012 Revised 14 February 2013 Accepted 14 February 2013

Academic Editor Jose Pomilio

Copyright copy 2013 B Blanusa and B Knezevic This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

New hybridmodel for efficiency optimization of inductionmotor drives (IMD) is presented in this paper It combines two strategiesfor efficiency optimization loss model control and search control Search control technique is used in a steady state of drive andloss model during transient processes As a result power and energy losses are reduced especially when load torque is significantless related to its rated value Also this hybrid method gives fast convergence to operating point of minimal power losses and showsnegligible sensitivity to motor parameter changes regarding other published optimization strategies This model is implemented invector control induction motor drive Simulations and experimental tests are performed Results are presented in this paper

1 Introduction

Induction motor is a widely used electrical motor and agreat energy consumerThe vast majority of induction motordrives are used for heating ventilation and air condition-ing (HVAC) These applications require only low dynamicperformance and in most cases only voltage source inverteris inserted between grid and induction motor as cheapestsolution The classical way to control these drives is constantVf ratio and simple methods for efficiency optimizationcan be applied [1] From the other side there are manyapplications where like electrical vehicles electric energy hasto be consumed in the best possible way and use of inductionmotors These applications require an energy optimizedcontrol strategy [2]

One interesting algorithmwhich can be applied in a drivecontroller is algorithm for efficiency optimization

In a conventional setting the field excitation is keptconstant at rated value throughout its entire load range Ifmachine is underloaded this would result in overexcitationand unnecessary copper losses Thus in cases where a motordrive has to operate in wider load range the minimizationof losses has great significance It is known that efficiency

improvement of IMD can be implemented via motor fluxlevel and this method has been proven to be particularlyeffective at light loads and in a steady state of drive Alsoflux reduction at light loads gives less acoustic noise derivedfrom both converter and machine From the other side lowflux makes motor more sensitive to load disturbances anddegrades dynamic performances [3]

Drive loss model is used for optimal drive control inloss model control (LMC) [3ndash7] These algorithms are fastbecause the optimal control is calculated directly from theloss model But power loss modeling and calculation of theoptimal control can be very complex Often the loss model isnot accurate enough

Search strategy methods have an important advantagecompared to other strategies [8ndash11] It is completely insen-sitive to parameter changes while effects of the parametervariations caused by temperature and saturation are veryexpressed in two other strategies The online efficiencyoptimization control on the basis of search where the flux isdecremented in steps until the measured input power settlesdown to the lowest value is very attractive Algorithm isapplicable universally to any motor Besides all good charac-teristics of search strategy methods there is an outstanding

2 Advances in Power Electronics

problem in its use For many applications flux convergence toits optimal value is too slowly Also flux is never reached itsoptimal value then in small steps oscillates around it

For electrical drives that work in periodic cycles it ispossible to calculate the optimal trajectory of magnetizationflux using optimal control theory so that power losses inoneworking cycle areminimal [12]Thesemethods give goodresults if the working conditions do not change

Hybrid method combines good characteristics of twooptimization strategies SC and LMC [3 13ndash15] It wasenhanced attention as interesting solution for efficiencyoptimization of controlled electrical drives During tran-sient process LMC is used so fast flux changes and gooddynamic performances are kept Search control is usedfor efficiency optimization in a steady state of drive Lossmodel of IM in d-q rotational system and procedure forparameter identification in a loss model based on Moore-Penrose pseudoinversion is given in Section 2 New hybridmodel is presented in Section 3 Qualitative analyses of thismethod with simulation and experimental results are givenin Section 4 At the end obtained results are presented inConclusion

2 Power Loss Modeling

The process of energy conversion within motor drive con-verter and motor leads to the power losses in the motorwindings and magnetic circuit as well as conduction andcommutation losses in the inverter [6]

The losses in the motor consist of hysteresis losses andeddy current losses in a magnetic circuit (iron losses) lossesin the stator and rotor windings (copper loss) and straylosses In nominal operating conditions the iron losses aretypically 2-3 times smaller than the copper losses but atlow loads these losses are dominant These losses consistof hysteresis and eddy current losses Eddy current lossesare proportional to the square of supply frequency andhysteresis losses are proportional to supply frequency Bothcomponents of iron losses are dependent of stator flux levelso next expression is suitable to represent these losses

119875120574Fe = 119888eddy1205952

1199041198891205962

119904+ 119888hys120595

2

119904119889120596119904 (1)

where 119888eddy is eddy current and 119888hys is hysteresis loss coeffi-cients

Copper losses are appeared as a result of the passing theelectric current through the stator and rotor windings Theselosses are proportional to the square of current through statorand rotor windings and they are given by

119901120574Cu = 1198771199041198942

119904+ 1198771199031198942

119904119902 (2)

The total additional losses typically do not exceed 5when the drive works with light loads This case is the mostimportant for the power loss minimization algorithms sostray losses are not considered as a separate loss component

Losses in the drive converter consist of the losses inthe rectifier and the conductive and switching losses in theinverter The losses in the rectifier are independent of the

magnetizing flux and not specifically taken into accountOnly conductive losses in the inverter are dependent on themagnetizing flux and these can be presented in the next form

119875INV = 119877INV1198942

119904= 119877INV (119894

2

119904119889+ 1198942

119904119902) (3)

Based on the previous considerations the losses in theinduction motor drive dependent on the magnetizing fluxcan be expressed as follows

119875120574 = (119877INV + 119877119904) 1198942

119904119889+ (119877INV + 119877119904 + 119877119903) 119894

2

119904119902

+ 119888eddy1205962

1199041205952

119904119889+ 119888hys120596119904120595

2

119904119889

(4)

Take into account expression for output power119875out = 119889120596120595119904119889119894119904119902 (5)

where 119875out is output power and 119889 is constant which dependson the characteristics of Parkrsquos rotating transformation (inthis case it is 15) and the relation

119875in = 119875120574 + 119875out (6)

expression for input power can be written in the next form

119875in = 1198861198942

119904119889+ 1198871198942

119904119902+ 11988811205962

1199041205952

119904119889+ 1198881120596119904120595

2

119904119889+ 119889120596120595119904119889119894119904119902 (7)

where 119886 = 119877119904 + 119877INV 119887 = 119877119904 + 119877INV + 119877119903 1198881 = 119888eddy 1198882 = 119888hysand 119889 is positive constant

Two typical cases are differed(1) linear dependence of magnetizing flux from the mag-

netizing current(2) nonlinear dependence of magnetizing flux from the

magnetizing currentIn the algorithms for loss minimization magnetizing flux

is less than or equal to the nominal value so it is used in thelinear part of magnetization characteristics

Starting from the expressions (4) and taking into accountexpression (5) the power losses can be expressed as a functionof 119894119904119889 119879em and 120596119904 as follows

119875120574 (119894119904119889 119879em 120596119904) = (119886 + 11988811198712

1198981205962

119904+ 11988821198712

119898120596119904) 1198942

119889+

1198871198792

em

(119889119871119898119894119904119889)2

(8)

Slip angular speed can be defined as follows

120596119904119897 = 120596119904 minus 120596 asymp

119894119904119902

119879119903119894119904119889

(9)

where 119879119903 is time rotor constantBased on expression (8) power losses can be given as

function of magnetizing current 119894119904119889 and operating conditions(120596 119879em)

119875120574 (119894119904119889 119879em 120596) = (119886 + 11988811198712

1198981205962+ 11988821198712

119898120596) 1198942

119904119889

+(2120596119871119898 + 1198882119871119898) 119879em

119889119879119903

+1198792

em1198892

(119887

1198712119898

+1198881

1198792119903

)1

1198942

119904119889

(10)

Advances in Power Electronics 3

Putting 1198961 = 119886 + 11988811198712

1198981205962+ 11988821198712

119898120596 1198962 = (119879

2

em1198892)(1198871198712

119898+

11988811198792

119903) and 1198963 = (2120596119871119898 + 1198882119871119898)119879em119889119879119903 (10) can be written

as follows

119875120574 (119894119889 119879em 120596) = 11989611198942

119904119889+

1198962

1198942

119904119889

+ 1198963 (11)

Parameter 1198963 is a function of 119879119903 which is time variantespecially due to temperature changes Time rotor constantis continuously updated in the algorithm for parameteridentification so the parameter 1198963 too

First and second derivations of 119875120574 in a function of 119894119904119889 are

120597119875120574

120597119894119889

= 21198961119894119904119889 minus 21198962

1198943

119904119889

1205972119875120574

1205972119894119904119889

= 21198961 + 61198962

1198944

119904119889

1198961 gt 0 1198962 gt 0

1205972119875120574

1205972119894119904119889

gt 0

for 119894119904119889min le 119894119904119889 le 119894119904119889max

(12)

Value 119894119904119889max is chosen to be 119868119889119899 and 119894119904119889min is determinedbased on characteristics of drive and requirements for elec-tromagnetic torque reserve In this case 119894119904119889min = 05119868119889119899 where119868119889119899 is nominal value of 119894119904119889 current On the basis of expressionsin (12) it can be concluded that in the steady state of drive andknown operating conditions exists accurate value of 119894119904119889 whichgives minimal losses as follows

119894lowast

119904119889LMC =4radic

1198962

1198961

(13)

Based on the specified optimal value of 119889 component statorcurrent vector and command of electromagnetic torque 119902component of the stator current is determined as follows

119894lowast

119904119902LMC =119879em

119889119871119898119894lowast

119904119889LMC (14)

21 Parameter Identification in a Loss Model This proce-dure of parameter identification is a mainly based on theprocedures described in [6 7] In order to determine theparameters in the model losses 119886 119887 1198881 and 1198882 it is necessaryto measure the input power and know the exact value of theoutput power The exact value of the output power is neededto determine correct information of the losses in the driveand to avoid coupling between load pulsation and work ofoptimization controller Also the samples of the values thatdefine input powers VDC 119894DC (119875in = VDC119894DC) are availablein the controller and these values are used for protect andcontrol functions (dynamic braking the soft-start operationPWM compensation etc)

The proposed procedure of parameter identification isshown in Figure 1 The samples that exist in the expres-sion (7) are memorized at each period Usually the 119879119878

is 100ndash200 120583s Due to high-frequency components that donot contribute to identification of the relevant parameters

119882 = [119886 119887 1198881 1198882 119889]119879 input signal and the input power are

averaged in the period 119879 = 119876119879119878

int

(119899+1)119879

119899119879

119875in (119905) 119889119905 = 119886int

(119899+1)119879

119899119879

1198942

119889(119905) 119889119905 + 119887int

(119899+1)119879

119899119879

1198942

119902(119905) 119889119905

+ 1198881 int

(119899+1)119879

119899119879

[1205952

119889(119905) 1205962

119904(119905) 119889119905]

+ 1198882 int

(119899+1)119879

119899119879

[1205952

119889(119905) 120596119904 (119905) 119889119905]

+ 119889int

(119899+1)119879

119899119879

[120596 (119905) 119894119902 (119905) 120595119904119889 (119905) 119889119905] 997904rArr

119884119873 = 119886119860119873 + 119887119861119873 + 11988811198621198731 + 11988821198621198732 + 119889119863119873

(15)

Values 119860119873 119861119873 1198621198731 1198621198732 and 119863119873 119873 = 1 119872 suc-cessively form the columns 119875( 1) 119875( 2) 119875( 3) 119875( 4) and119875( 5) of matrix 119875119872times5

Vector 119884 is formed from 119872 averaged values of inputpower 119884119873119873 = 1 119872 Vector119882119892 is calculated by applyingMoore-Penrose pseudoinversion (Figure 1) as follows

119882119892 = [119886119892 119887119892 1198881198921 1198881198922 119889119892]119879= (119875119879119875)minus1

119875119884 (16)

That is119882119892 is approximate solution of thematrix equations119875119882 = 119884 which gives a minimum value 119875119882 minus 119884 orminimummean-square error

The choice of 119876 is of great importance for the process ofparameters identification (see (15)) because the input powerfluctuations should be sufficient in the period 119879 = 119876119879119878Otherwise 119875

119879119875 matrix will be singular or aspire singularity

that is det (119875119879119875)will be close to 0Theprocess of determiningthe parameters in the loss model is repeated during theoperation of electric drive

3 Hybrid Model for Efficiency Optimization

Electrical drive with block for efficiency optimization isshown in Figure 2 Electric drive is supplied from the primarypower network 3times380VThis voltage is rectified and the volt-age and current in DC link are measured The drive inverteris current regulated (CR) voltage three-phase inverter Refer-ence and measured 119889 and 119902 components of stator current arekept in the current controllers These controllers are realizedin rotational 119889 119902 coordinate system as a linear PI controllerOutputs of controller are 119889 and 119902 component of stator voltageThese voltages are transformed (B-transformation) in three-phase reference voltages Vlowast

119886 Vlowast119887 and Vlowast

119888 These voltages are

scaled and lead to PWM modulator where control signalsof inverter switches are generated This drive works as speedcontrolled drive Speed reference and measured speed areled into speed controller Speed controller is realized as PIcontroller in incremental form with proportional coefficientin a feedback local branch The output of speed controlleris reference value of electromagnetic torque Reference valueof stator current 119889 component is determined in a block forefficiency optimization and 119902 component of stator current


1198942119904119889

1198942119904119902

1199061

1199062

1199063

1199064

1199065

1199066

119875( 1)

119875( 2)

119875( 3)

119875( 4)

119875( 5)

119860119899

119861119899

1198621198991

1198621198992

119863119899

119884119899

minus1119875119879119884

119875

119884

119875 (119872

times5)M

ATRI

CA

119875( 1) =

119875( 2) =

119875( 3) =

119875( 3) =

119875( 4) =

119884 =

∣det(119875119879119875)∣025

119894119904119902

sum119895=1

119895=1198761199061(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199062(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199063(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199064(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199065(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199065(119899119879 + 119895)120591119876

(119875119879119875)

1205952119904119889120596

2119904

1205952119904119889120596

120595119904119889120596

119904

(DC)119875in

[1198601198990 middot middot middot 1198601198990+119872]119879





[1198631198990 1198631198990+119872]119879

119882119892 = [119886119892 119887119892 1198881119892 1198882119892 119889119892]119879

[119886119892 119887119892 1198881119892 1198882119892 119889119892]119879=

Figure 1 A method for determining the parameters 119886 119887 1198881 1198882and 119889 from the input signal

vector on the basis of 119889 stator current vector component andelectromagnetic torque reference (see (14)) Position of rotorflux vector is determined in indirect vector control block(IVC)

Hybrid model for efficiency optimization consists from3 blocks LMC SC and steady state control (SSC) blockLMC is used during transient states caused of external speedor torque demand [3] Optimal control (119894lowast

119904119889LMC 119894lowast

119904119902LMC) iscalculated directly from loss model for a given operationalconditions what obtains power loss optimization and gooddynamic performances SC is used in a steady state for aconstant output power

On the basis of speed reference and measured speed SSCblock defines its output and controls switches (Figure 2) Iftransient states is detected LMC is active and its outputs areforwarded to indirect vector control (IVC) block and currentregulators When steady state is detected in SSC block lastvalue of magnetizing current during transient state is used asstarting point for search algorithm

31 Loss Model Controller Optimal control calculation inLMC for a given operational conditions is described inSection 2

Expressions for 119889 and 119902 component of stator current aredefined by (8) and (10)

This method is sensitive to parameter changes due totemperature changes and magnetic circuit saturation whatconsequently leads to error in a current references calcu-lation So algorithm for parameter identification is alwaysactive and parameters in the loss model are continuouslyupdated (Figure 2)

32 Search Controller Search algorithm is used in steadystate which is detected in the SSC block Error that existsbetween the current reference 119894119889 that is generated in the LMCmodel and in the search model appears as a consequence ofinverter and stray losses which are not included in the modelThe applied search algorithm is simple Since the current 119894119904119889is very close to the value which gives minimal losses smallstep of magnetization current Δ119894119904119889 = 001119868119889119899 is chosen

For two successive values of the 119894119904119889 current power lossesare determined Sign of Δ119894119904119889 is maintained if power losses arereduced Otherwise the sign of Δ119894119904119889 is opposite in the nextstep

119894119904119889 (119899) = 119894119904119889 (119899 minus 1) minus sgn (Δ119875120574 (119899 minus 1)) Δ119894119904119889 (17)

When the two values of magnetization current 1198941199041198891 and1198941199041198892 were found so the sign of power loss is changed betweenthese values and new reference of 119894119904119889 current is specified as

119894lowast

119904119889SC =1198941199041198891 + 1198941199041198892

2 (18)

In this way there are no oscillations of 119894119904119889 current air gapflux and electromagnetic torque which are characteristics ofthe search algorithm

4 Simulation and Experimental Results

41 Simulation Results Hybrid method for efficiency opti-mization of IMD has been studied through computer sim-ulation in MATLAB-Simulink

Speed reference and load torque are shown in Figure 3The steep change of load torque appears with the aim


119875in

119875in

119875out = 120596 lowast119894lowast119904119902119878119862

119894lowast119904119889119878119862

119894lowast119904119889

119894lowast119904119902

119878119862

1119911

120596120596lowast

120596lowast

119894lowast119904119902119871119872119862

119894lowast119904119889119871119872119862119871119872119862

119886 119887 1198881 1198882 119889

119894119904119889 119894119904119902120596 120596119904 119875in

lowast

Δ120596

120596

120596

+

Steadystate

control

Speedreference

PI speedcontroller

119889 PI currentcontroller


119868119881119862120579lowast119904

1198941199041198891198941199041199023Φ 2Φ

2Φ 3Φ

120579119904119861

119894119886 119894119887 119894119888

119907119886119907119887119907119888

119907lowast119889119907lowast119902

119907lowast119889

119907lowast119902

119907lowast119886119907lowast119887119907lowast119888120579119904

123

1

2

3

Rectifier

Powercalculation

119860119872Encoder

Incrementalencoderinterface

CRPWMVSI

Power supply3 times 230V

50 Hz

Loss model

Torque

SW3 SW1

SW2

estimator

parameteridentification

120595119904119889

minus

119879em

119879em

lowast119879em

119894DC119907DC

119861minus1

Figure 2 Overall proposed block diagram of efficiency optimization controller in IMD

of testing the drive behavior in the dynamic mode andits robustness for a sudden load perturbations Graphs ofmagnetization current (119894119904119889) and active component (119894119904119902) ofstator current vector for a given operating conditions andapplied hybrid method are shown in Figure 4

Graphs of power loss for nominal flux and hybridmethodare given in Figure 5 It is obvious that the use of hybridmethods gives significantly less power losses than when theflux is maintained at nominal value for a light load of drive

42 Experimental Results The experimental tests have beenperformed on the setup which consists of the following

(i) induction motor (3 phases Δ380V119884220V37212 A cos120601 = 071 1410 rmin 50Hz)

(ii) incremental encoder connected with the motor shaft(iii) three-phase drive converter (DCAC converter and

DC link)(iv) PC and dSPACE1102 controller board with

TMS320C31 floating point processor and peripherals(v) interface between controller board and drive con-

verter

0 2 4 6 8 10 120

02

04

06

08

1

Time (s)

Speed reference pu

Load torque pu

Figure 3 Speed reference and load torque [pu]

Parameters of used induction motor are given in theappendix of the paper


0 2 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

119894 119889an

d119894 119902

stat

or cu

rren

ts

Current 119894119889 puCurrent 119894119902 pu

Figure 4 Graphs of 119889 and 119902 component of stator current for a givenoperating conditions

0 2 4 6 8 10 120

20

40

60

80

100

120

140

160

Time (s)

Pow

er lo

sses

(W)

Hybrid method

Nominal flux

Figure 5 Graph of power loss for nominal flux and applied hybridmethod

The algorithm observed in this paper used theMATLAB-Simulink software dSPACE real-time interface and C lan-guage Handling real-time applications is done in ControlD-esk

All experimental tests and simulations have been donein the same operating conditions of the drive and somecomparisons between algorithms for efficiency optimizationare made through the experimental tests Graphs of powerlosses for nominal flux and when the hybrid method isapplied are shown in Figures 6 and 7 respectively Graphs ofmagnetization current for a given operational conditions areshown in Figure 8 and speed response is shown in Figure 9

200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)

Figure 6 Power losses for nominal magnetization flux and opera-tional conditions shown in Figure 3

200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)

Figure 7 Power losses when the hybrid method is applied andoperational conditions shown in Figure 3

Based on graph in Figure 6 it can be concluded thatthe speed drop for a step change of load is small and speedresponse is strictly aperiodic

5 Conclusion

Algorithms for efficiency optimization of induction motordrive are briefly described Detailed theoretical analysis ofpower losses in induction motor is presented Algorithm forparameter identification in the loss model based on Moore-Penrose pseudoinversion is presented Also hybrid algorithmfor efficiency optimization has been applied According to thetheoretical analysis performed simulations and experimen-tal tests we have arrived to the following conclusions

If load torque has a value close to nominal or highermagnetizing flux is also nominal regardless of whether analgorithm for efficiency optimization is applied or not


25

2

15

1

05

0 0 2 4 6 8 10 12Time (05 sdiv)

Curr

ents119894 119889

119894119902

(01

Ad

iv)

119894119889

119894119902

Figure 8 Magnetization current 119894119889and active current when the

hybrid method is applied and operational conditions shown inFigure 3

0 2 4 6 8 10 12Time (05 sdiv)

160

120

80

40

0

Spee

d (r

ads

)

Figure 9 Speed response when the hybrid method is applied andoperational conditions shown in Figure 3

For a light load hybrid method for efficiency optimiza-tion gives significant power loss reduction (Figures 5 6 and7)

There is no oscillation of magnetization flux which ischaracteristic of the search algorithms (Figures 4 and 8)

Also this hybrid method shows good dynamic perfor-mances and no sensitivity to parameter changes (Figure 9)

Implementation of presented algorithm is simple and itcan be universally applied to any electrical motor Changesare only related to different models of power losses

Appendix

Parameters of used induction motor

3 phase Δ220Y380V (supply voltage)

37212 A (nominal stator current)

075 kW (nominal mechanical power)cos120601 = 0 71 (power factor)1410 rmin (nominal mechanical speed)119877119904 = 104 Ω (stator resistance)119877119903 = 116 Ω (rotor resistance)119871120574119904 = 22mH (stator leakage inductance)119871120574119903 = 22mH (stator leakage inductance)119871119898119899 = 0 557H (magnetization inductance)

119869119898 = 0 0072 kgm2 (inertia moment)119868119889119899 = 1501A (nominal value of 119894119904119889 current)119868119902119899 = 2093A (nominal value of 119894119904119902 current)

Nomenclature

119877119904 119877119903 Resistance of stator and rotor winding119871 119904 119871119903 Self-inductance of stator and rotor119871119898 Magnetizing inductance120590 Leakage factor1198711015840

119904 Stator transient inductance

119875 Number of pole pairs120599119904 120596119904 Rotor flux angle and angular speed120599 120596 Rotor angle and angular speed120596119904 slip speed119879em Elektromagnetic torque120595119904119889 Magnetizing flux119894119904119889 119894119904119902 119889 and 119902 components of stator current vector

References

[1] F Abrahamsen F Blaabjerg J K Pedersen P Z Grabowskiand P Thgersen ldquoOn the energy optimized control of standardand high-efficiency induction motors in CT and HVAC appli-cationsrdquo IEEE Transactions on Industry Applications vol 34 no4 pp 822ndash831 1998

[2] M Chis S Jayaram and K Rajashekara ldquoNeural network-based efficiency optimization of EV driverdquo in Proceedings of theCanadian Conference on Electrical and Computer Engineering(CCECE rsquo97) pp 454ndash457 May 1997

[3] E S Sergaki and G S Stavrakakis ldquoOnline search based fuzzyoptimum efficiency operation in steady and transient statesfor DC and AC vector controlled motorsrdquo in Proceedings ofthe International Conference on Electrical Machines (ICEM rsquo08)Vilamoura Portugal September 2008

[4] F Abrahamsen J K Pedersen and F Blaabjerg ldquoState-of-Art ofoptimal efficiency control of low cost induction motor drivesrdquoin Proceedings of Conference on Fuzzy Systems (PESC rsquo96) pp920ndash924 1996

[5] M N Uddin and S W Nam ldquoDevelopment of a nonlinear andmodel-based online loss minimization control of an IM driverdquoIEEE Transactions on Energy Conversion vol 23 no 4 pp 1015ndash1024 2008

[6] B Blanusa P Matic Z Ivanovic and S N Vukosavic ldquoAnimproved loss model based algorithm for efficiency optimiza-tion of the induction motor driverdquo Electronics vol 10 no 1 pp49ndash52 2006


[7] S N Vukosavic and E Levi ldquoRobust DSP-based efficiencyoptimization of a variable speed induction motor driverdquo IEEETransactions on Industrial Electronics vol 50 no 3 pp 560ndash570 2003

[8] G C D Sousa B K Bose and J G Cleland ldquoFuzzy logicbased on-line efficiency optimization control of an indirectvector-controlled induction motor driverdquo IEEE Transactions onIndustrial Electronics vol 42 no 2 pp 192ndash198 1995

[9] D de Almeida Souza W C P de Aragao Filho and G C DSousa ldquoAdaptive fuzzy controller for efficiency optimization ofinduction motorsrdquo IEEE Transactions on Industrial Electronicsvol 54 no 4 pp 2157ndash2164 2007

[10] S Ghozzi K Jelassi and X Roboam ldquoEnergy optimization ofinductionmotor drivesrdquo inProceedings of the IEEE InternationalConference on Industrial Technology (ICIT rsquo04) pp 602ndash610December 2004

[11] Z Liwei L Jun W Xuhui and T Q Zheng ldquoSystematic designof fuzzy logic based hybrid on-line minimum input powersearch control strategy for efficiency optimization of IMrdquo inProceedings of the CESIEEE 5th International Power Electronicsand Motion Control Conference (IPEMC rsquo06) pp 1012ndash1016August 2006

[12] B Blanusa and S N Vukosavic ldquoEfficiency optimized controlfor closed-cycle operations of high performance inductionmotor driverdquo Journal of Electrical Engineering vol 8 pp 81ndash882008

[13] C Chakraborty and Y Hori ldquoFast efficiency optimizationtechniques for the indirect vector-controlled induction motordrivesrdquo IEEE Transactions on Industry Applications vol 39 no4 pp 1070ndash1076 2003

[14] B Blanusa P Matic and B Dokic ldquoNew hybrid model forefficiency optimization of induction motor drivesrdquo in Proceed-ings of 52nd International Symposium ELMAR-2010 pp 313ndash3172010

[15] PWas Electrical Machines and Drives Oxford University Press1992

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



problem in its use For many applications flux convergence toits optimal value is too slowly Also flux is never reached itsoptimal value then in small steps oscillates around it

For electrical drives that work in periodic cycles it ispossible to calculate the optimal trajectory of magnetizationflux using optimal control theory so that power losses inoneworking cycle areminimal [12]Thesemethods give goodresults if the working conditions do not change

Hybrid method combines good characteristics of twooptimization strategies SC and LMC [3 13ndash15] It wasenhanced attention as interesting solution for efficiencyoptimization of controlled electrical drives During tran-sient process LMC is used so fast flux changes and gooddynamic performances are kept Search control is usedfor efficiency optimization in a steady state of drive Lossmodel of IM in d-q rotational system and procedure forparameter identification in a loss model based on Moore-Penrose pseudoinversion is given in Section 2 New hybridmodel is presented in Section 3 Qualitative analyses of thismethod with simulation and experimental results are givenin Section 4 At the end obtained results are presented inConclusion

2 Power Loss Modeling

The process of energy conversion within motor drive con-verter and motor leads to the power losses in the motorwindings and magnetic circuit as well as conduction andcommutation losses in the inverter [6]

The losses in the motor consist of hysteresis losses andeddy current losses in a magnetic circuit (iron losses) lossesin the stator and rotor windings (copper loss) and straylosses In nominal operating conditions the iron losses aretypically 2-3 times smaller than the copper losses but atlow loads these losses are dominant These losses consistof hysteresis and eddy current losses Eddy current lossesare proportional to the square of supply frequency andhysteresis losses are proportional to supply frequency Bothcomponents of iron losses are dependent of stator flux levelso next expression is suitable to represent these losses

119875120574Fe = 119888eddy1205952

1199041198891205962

119904+ 119888hys120595

2

119904119889120596119904 (1)

where 119888eddy is eddy current and 119888hys is hysteresis loss coeffi-cients

Copper losses are appeared as a result of the passing theelectric current through the stator and rotor windings Theselosses are proportional to the square of current through statorand rotor windings and they are given by

119901120574Cu = 1198771199041198942

119904+ 1198771199031198942

119904119902 (2)

The total additional losses typically do not exceed 5when the drive works with light loads This case is the mostimportant for the power loss minimization algorithms sostray losses are not considered as a separate loss component

Losses in the drive converter consist of the losses inthe rectifier and the conductive and switching losses in theinverter The losses in the rectifier are independent of the

magnetizing flux and not specifically taken into accountOnly conductive losses in the inverter are dependent on themagnetizing flux and these can be presented in the next form

119875INV = 119877INV1198942

119904= 119877INV (119894

2

119904119889+ 1198942

119904119902) (3)

Based on the previous considerations the losses in theinduction motor drive dependent on the magnetizing fluxcan be expressed as follows

119875120574 = (119877INV + 119877119904) 1198942

119904119889+ (119877INV + 119877119904 + 119877119903) 119894

2

119904119902

+ 119888eddy1205962

1199041205952

119904119889+ 119888hys120596119904120595

2

119904119889

(4)

Take into account expression for output power119875out = 119889120596120595119904119889119894119904119902 (5)

where 119875out is output power and 119889 is constant which dependson the characteristics of Parkrsquos rotating transformation (inthis case it is 15) and the relation

119875in = 119875120574 + 119875out (6)

expression for input power can be written in the next form

119875in = 1198861198942

119904119889+ 1198871198942

119904119902+ 11988811205962

1199041205952

119904119889+ 1198881120596119904120595

2

119904119889+ 119889120596120595119904119889119894119904119902 (7)

where 119886 = 119877119904 + 119877INV 119887 = 119877119904 + 119877INV + 119877119903 1198881 = 119888eddy 1198882 = 119888hysand 119889 is positive constant

Two typical cases are differed(1) linear dependence of magnetizing flux from the mag-

netizing current(2) nonlinear dependence of magnetizing flux from the

magnetizing currentIn the algorithms for loss minimization magnetizing flux

is less than or equal to the nominal value so it is used in thelinear part of magnetization characteristics

Starting from the expressions (4) and taking into accountexpression (5) the power losses can be expressed as a functionof 119894119904119889 119879em and 120596119904 as follows

119875120574 (119894119904119889 119879em 120596119904) = (119886 + 11988811198712

1198981205962

119904+ 11988821198712

119898120596119904) 1198942

119889+

1198871198792

em

(119889119871119898119894119904119889)2

(8)

Slip angular speed can be defined as follows

120596119904119897 = 120596119904 minus 120596 asymp

119894119904119902

119879119903119894119904119889

(9)

where 119879119903 is time rotor constantBased on expression (8) power losses can be given as

function of magnetizing current 119894119904119889 and operating conditions(120596 119879em)

119875120574 (119894119904119889 119879em 120596) = (119886 + 11988811198712

1198981205962+ 11988821198712

119898120596) 1198942

119904119889

+(2120596119871119898 + 1198882119871119898) 119879em

119889119879119903

+1198792

em1198892

(119887

1198712119898

+1198881

1198792119903

)1

1198942

119904119889

(10)


Putting 1198961 = 119886 + 11988811198712

1198981205962+ 11988821198712

119898120596 1198962 = (119879

2

em1198892)(1198871198712

119898+

11988811198792


as follows

119875120574 (119894119889 119879em 120596) = 11989611198942

119904119889+

1198962

1198942

119904119889

+ 1198963 (11)



120597119875120574

120597119894119889

= 21198961119894119904119889 minus 21198962

1198943

119904119889

1205972119875120574

1205972119894119904119889

= 21198961 + 61198962

1198944

119904119889

1198961 gt 0 1198962 gt 0

1205972119875120574

1205972119894119904119889

gt 0

for 119894119904119889min le 119894119904119889 le 119894119904119889max

(12)


119894lowast

119904119889LMC =4radic

1198962

1198961

(13)


119894lowast

119904119902LMC =119879em

119889119871119898119894lowast

119904119889LMC (14)






int

(119899+1)119879

119899119879

119875in (119905) 119889119905 = 119886int

(119899+1)119879

119899119879

1198942

119889(119905) 119889119905 + 119887int

(119899+1)119879

119899119879

1198942

119902(119905) 119889119905

+ 1198881 int

(119899+1)119879

119899119879

[1205952

119889(119905) 1205962

119904(119905) 119889119905]

+ 1198882 int

(119899+1)119879

119899119879

[1205952

119889(119905) 120596119904 (119905) 119889119905]

+ 119889int

(119899+1)119879

119899119879

[120596 (119905) 119894119902 (119905) 120595119904119889 (119905) 119889119905] 997904rArr

119884119873 = 119886119860119873 + 119887119861119873 + 11988811198621198731 + 11988821198621198732 + 119889119863119873

(15)



119882119892 = [119886119892 119887119892 1198881198921 1198881198922 119889119892]119879= (119875119879119875)minus1

119875119884 (16)











1198942119904119889

1198942119904119902

1199061

1199062

1199063

1199064

1199065

1199066

119875( 1)

119875( 2)

119875( 3)

119875( 4)

119875( 5)

119860119899

119861119899

1198621198991

1198621198992

119863119899

119884119899

minus1119875119879119884

119875

119884

119875 (119872

times5)M

ATRI

CA

119875( 1) =

119875( 2) =

119875( 3) =

119875( 3) =

119875( 4) =

119884 =

∣det(119875119879119875)∣025

119894119904119902

sum119895=1

119895=1198761199061(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199062(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199063(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199064(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199065(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199065(119899119879 + 119895)120591119876

(119875119879119875)

1205952119904119889120596

2119904

1205952119904119889120596

120595119904119889120596

119904

(DC)119875in






[1198631198990 1198631198990+119872]119879

119882119892 = [119886119892 119887119892 1198881119892 1198882119892 119889119892]119879

[119886119892 119887119892 1198881119892 1198882119892 119889119892]119879=




119904119889LMC 119894lowast










119894lowast

119904119889SC =1198941199041198891 + 1198941199041198892

2 (18)






119875in

119875in


119894lowast119904119889119878119862

119894lowast119904119889

119894lowast119904119902

119878119862

1119911

120596120596lowast

120596lowast

119894lowast119904119902119871119872119862

119894lowast119904119889119871119872119862119871119872119862

119886 119887 1198881 1198882 119889

119894119904119889 119894119904119902120596 120596119904 119875in

lowast

Δ120596

120596

120596

+

Steadystate

control

Speedreference

PI speedcontroller



119868119881119862120579lowast119904

1198941199041198891198941199041199023Φ 2Φ

2Φ 3Φ

120579119904119861

119894119886 119894119887 119894119888

119907119886119907119887119907119888

119907lowast119889119907lowast119902

119907lowast119889

119907lowast119902


123

1

2

3

Rectifier

Powercalculation

119860119872Encoder


CRPWMVSI


50 Hz

Loss model

Torque

SW3 SW1

SW2

estimator


120595119904119889

minus

119879em

119879em

lowast119879em

119894DC119907DC

119861minus1









verter

0 2 4 6 8 10 120

02

04

06

08

1

Time (s)

Speed reference pu

Load torque pu




0 2 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

119894 119889an

d119894 119902

stat

or cu

rren

ts



0 2 4 6 8 10 120

20

40

60

80

100

120

140

160

Time (s)

Pow

er lo

sses

(W)

Hybrid method

Nominal flux




200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)


200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)



5 Conclusion




25

2

15

1

05

0 0 2 4 6 8 10 12Time (05 sdiv)

Curr

ents119894 119889

119894119902

(01

Ad

iv)

119894119889

119894119902



0 2 4 6 8 10 12Time (05 sdiv)

160

120

80

40

0

Spee

d (r

ads

)






Appendix






Nomenclature




References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Putting 1198961 = 119886 + 11988811198712

1198981205962+ 11988821198712

119898120596 1198962 = (119879

2

em1198892)(1198871198712

119898+

11988811198792


as follows

119875120574 (119894119889 119879em 120596) = 11989611198942

119904119889+

1198962

1198942

119904119889

+ 1198963 (11)



120597119875120574

120597119894119889

= 21198961119894119904119889 minus 21198962

1198943

119904119889

1205972119875120574

1205972119894119904119889

= 21198961 + 61198962

1198944

119904119889

1198961 gt 0 1198962 gt 0

1205972119875120574

1205972119894119904119889

gt 0

for 119894119904119889min le 119894119904119889 le 119894119904119889max

(12)


119894lowast

119904119889LMC =4radic

1198962

1198961

(13)


119894lowast

119904119902LMC =119879em

119889119871119898119894lowast

119904119889LMC (14)






int

(119899+1)119879

119899119879

119875in (119905) 119889119905 = 119886int

(119899+1)119879

119899119879

1198942

119889(119905) 119889119905 + 119887int

(119899+1)119879

119899119879

1198942

119902(119905) 119889119905

+ 1198881 int

(119899+1)119879

119899119879

[1205952

119889(119905) 1205962

119904(119905) 119889119905]

+ 1198882 int

(119899+1)119879

119899119879

[1205952

119889(119905) 120596119904 (119905) 119889119905]

+ 119889int

(119899+1)119879

119899119879

[120596 (119905) 119894119902 (119905) 120595119904119889 (119905) 119889119905] 997904rArr

119884119873 = 119886119860119873 + 119887119861119873 + 11988811198621198731 + 11988821198621198732 + 119889119863119873

(15)



119882119892 = [119886119892 119887119892 1198881198921 1198881198922 119889119892]119879= (119875119879119875)minus1

119875119884 (16)











1198942119904119889

1198942119904119902

1199061

1199062

1199063

1199064

1199065

1199066

119875( 1)

119875( 2)

119875( 3)

119875( 4)

119875( 5)

119860119899

119861119899

1198621198991

1198621198992

119863119899

119884119899

minus1119875119879119884

119875

119884

119875 (119872

times5)M

ATRI

CA

119875( 1) =

119875( 2) =

119875( 3) =

119875( 3) =

119875( 4) =

119884 =

∣det(119875119879119875)∣025

119894119904119902

sum119895=1

119895=1198761199061(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199062(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199063(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199064(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199065(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199065(119899119879 + 119895)120591119876

(119875119879119875)

1205952119904119889120596

2119904

1205952119904119889120596

120595119904119889120596

119904

(DC)119875in






[1198631198990 1198631198990+119872]119879

119882119892 = [119886119892 119887119892 1198881119892 1198882119892 119889119892]119879

[119886119892 119887119892 1198881119892 1198882119892 119889119892]119879=




119904119889LMC 119894lowast










119894lowast

119904119889SC =1198941199041198891 + 1198941199041198892

2 (18)






119875in

119875in


119894lowast119904119889119878119862

119894lowast119904119889

119894lowast119904119902

119878119862

1119911

120596120596lowast

120596lowast

119894lowast119904119902119871119872119862

119894lowast119904119889119871119872119862119871119872119862

119886 119887 1198881 1198882 119889

119894119904119889 119894119904119902120596 120596119904 119875in

lowast

Δ120596

120596

120596

+

Steadystate

control

Speedreference

PI speedcontroller



119868119881119862120579lowast119904

1198941199041198891198941199041199023Φ 2Φ

2Φ 3Φ

120579119904119861

119894119886 119894119887 119894119888

119907119886119907119887119907119888

119907lowast119889119907lowast119902

119907lowast119889

119907lowast119902


123

1

2

3

Rectifier

Powercalculation

119860119872Encoder


CRPWMVSI


50 Hz

Loss model

Torque

SW3 SW1

SW2

estimator


120595119904119889

minus

119879em

119879em

lowast119879em

119894DC119907DC

119861minus1









verter

0 2 4 6 8 10 120

02

04

06

08

1

Time (s)

Speed reference pu

Load torque pu




0 2 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

119894 119889an

d119894 119902

stat

or cu

rren

ts



0 2 4 6 8 10 120

20

40

60

80

100

120

140

160

Time (s)

Pow

er lo

sses

(W)

Hybrid method

Nominal flux




200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)


200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)



5 Conclusion




25

2

15

1

05

0 0 2 4 6 8 10 12Time (05 sdiv)

Curr

ents119894 119889

119894119902

(01

Ad

iv)

119894119889

119894119902



0 2 4 6 8 10 12Time (05 sdiv)

160

120

80

40

0

Spee

d (r

ads

)






Appendix






Nomenclature




References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1198942119904119889

1198942119904119902

1199061

1199062

1199063

1199064

1199065

1199066

119875( 1)

119875( 2)

119875( 3)

119875( 4)

119875( 5)

119860119899

119861119899

1198621198991

1198621198992

119863119899

119884119899

minus1119875119879119884

119875

119884

119875 (119872

times5)M

ATRI

CA

119875( 1) =

119875( 2) =

119875( 3) =

119875( 3) =

119875( 4) =

119884 =

∣det(119875119879119875)∣025

119894119904119902

sum119895=1

119895=1198761199061(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199062(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199063(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199064(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199065(119899119879 + 119895)120591119876

sum119895=1

119895=1198761199065(119899119879 + 119895)120591119876

(119875119879119875)

1205952119904119889120596

2119904

1205952119904119889120596

120595119904119889120596

119904

(DC)119875in






[1198631198990 1198631198990+119872]119879

119882119892 = [119886119892 119887119892 1198881119892 1198882119892 119889119892]119879

[119886119892 119887119892 1198881119892 1198882119892 119889119892]119879=




119904119889LMC 119894lowast










119894lowast

119904119889SC =1198941199041198891 + 1198941199041198892

2 (18)






119875in

119875in


119894lowast119904119889119878119862

119894lowast119904119889

119894lowast119904119902

119878119862

1119911

120596120596lowast

120596lowast

119894lowast119904119902119871119872119862

119894lowast119904119889119871119872119862119871119872119862

119886 119887 1198881 1198882 119889

119894119904119889 119894119904119902120596 120596119904 119875in

lowast

Δ120596

120596

120596

+

Steadystate

control

Speedreference

PI speedcontroller



119868119881119862120579lowast119904

1198941199041198891198941199041199023Φ 2Φ

2Φ 3Φ

120579119904119861

119894119886 119894119887 119894119888

119907119886119907119887119907119888

119907lowast119889119907lowast119902

119907lowast119889

119907lowast119902


123

1

2

3

Rectifier

Powercalculation

119860119872Encoder


CRPWMVSI


50 Hz

Loss model

Torque

SW3 SW1

SW2

estimator


120595119904119889

minus

119879em

119879em

lowast119879em

119894DC119907DC

119861minus1









verter

0 2 4 6 8 10 120

02

04

06

08

1

Time (s)

Speed reference pu

Load torque pu




0 2 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

119894 119889an

d119894 119902

stat

or cu

rren

ts



0 2 4 6 8 10 120

20

40

60

80

100

120

140

160

Time (s)

Pow

er lo

sses

(W)

Hybrid method

Nominal flux




200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)


200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)



5 Conclusion




25

2

15

1

05

0 0 2 4 6 8 10 12Time (05 sdiv)

Curr

ents119894 119889

119894119902

(01

Ad

iv)

119894119889

119894119902



0 2 4 6 8 10 12Time (05 sdiv)

160

120

80

40

0

Spee

d (r

ads

)






Appendix






Nomenclature




References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










119875in

119875in


119894lowast119904119889119878119862

119894lowast119904119889

119894lowast119904119902

119878119862

1119911

120596120596lowast

120596lowast

119894lowast119904119902119871119872119862

119894lowast119904119889119871119872119862119871119872119862

119886 119887 1198881 1198882 119889

119894119904119889 119894119904119902120596 120596119904 119875in

lowast

Δ120596

120596

120596

+

Steadystate

control

Speedreference

PI speedcontroller



119868119881119862120579lowast119904

1198941199041198891198941199041199023Φ 2Φ

2Φ 3Φ

120579119904119861

119894119886 119894119887 119894119888

119907119886119907119887119907119888

119907lowast119889119907lowast119902

119907lowast119889

119907lowast119902


123

1

2

3

Rectifier

Powercalculation

119860119872Encoder


CRPWMVSI


50 Hz

Loss model

Torque

SW3 SW1

SW2

estimator


120595119904119889

minus

119879em

119879em

lowast119879em

119894DC119907DC

119861minus1









verter

0 2 4 6 8 10 120

02

04

06

08

1

Time (s)

Speed reference pu

Load torque pu




0 2 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

119894 119889an

d119894 119902

stat

or cu

rren

ts



0 2 4 6 8 10 120

20

40

60

80

100

120

140

160

Time (s)

Pow

er lo

sses

(W)

Hybrid method

Nominal flux




200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)


200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)



5 Conclusion




25

2

15

1

05

0 0 2 4 6 8 10 12Time (05 sdiv)

Curr

ents119894 119889

119894119902

(01

Ad

iv)

119894119889

119894119902



0 2 4 6 8 10 12Time (05 sdiv)

160

120

80

40

0

Spee

d (r

ads

)






Appendix






Nomenclature




References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 2 4 6 8 10 120

02

04

06

08

1

12

14

Time (s)

119894 119889an

d119894 119902

stat

or cu

rren

ts



0 2 4 6 8 10 120

20

40

60

80

100

120

140

160

Time (s)

Pow

er lo

sses

(W)

Hybrid method

Nominal flux




200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)


200

150

100

50

00 2 4 6 8 10 12

Time (05 sdiv)

Pow

er lo

sses

(10 W

div

)



5 Conclusion




25

2

15

1

05

0 0 2 4 6 8 10 12Time (05 sdiv)

Curr

ents119894 119889

119894119902

(01

Ad

iv)

119894119889

119894119902



0 2 4 6 8 10 12Time (05 sdiv)

160

120

80

40

0

Spee

d (r

ads

)






Appendix






Nomenclature




References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










25

2

15

1

05

0 0 2 4 6 8 10 12Time (05 sdiv)

Curr

ents119894 119889

119894119902

(01

Ad

iv)

119894119889

119894119902



0 2 4 6 8 10 12Time (05 sdiv)

160

120

80

40

0

Spee

d (r

ads

)






Appendix






Nomenclature




References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article simple hybrid model for efficiency...

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