Sensor Less Control of IM Using Natural Variables With Loss Minimization

8/14/2019 Sensor Less Control of IM Using Natural Variables With Loss Minimization

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Sensorless Control of Induction Motor Using NaturalVariables with Loss Minimization

Olorunfemi Ojo and Ga nDongDepartment of Electrical and Computer EngineerindCenter for Electric PowerElectric Machine and Power Electronics LaboratoryTennessee Technological University, Cookeville, T N 38505Phone : (931)-372-3869, Fax : (931)-372-3436, E-mail :oio(@tntech.edu

Absiruct - This paper presents an approach to sensor-less speed control an efficiency-optimized induction motorusing natural and reference frame independent quantitiesas state variables - the square of the magnitude of rotorflux linkage, active and reactive torques and rotor speed.Utilization of the nonlinear geometric control methodologyof input-output linearization with decoupling permits theimplementation of the control in the stationary referenceframe. This approach eliminates the use of synchronousreference transformation and flux alignment required inclassical vector control schemes. The proposed sensor-lessspeed method uses both the rotor voItage equations, whichare shown to provide a good rotor speed estimation. Theefficiency of the induction motor is realized by choosingthe optimal reference rotor flux linkage using an efficiencyoptimizing formulation. 'The proposed scheme and theiradvantages are demonstrated both by computersimulations and som e experimental results for motor speedcontrol.

I, INTRODUCTIONInduction machines have been widely used in the industry,consuming a significant percentage of electric power

generation. Much research work has been done to improvetheir design and enhance steady-state operation whileefficiency improvement of motor drives has been an area ofactive resear ch within the last twenty five years occasioned bythe increasing need to better utilize electric power. Theefficiency can be improved through an appropriate control ofmotor excitation to reduce various kinds of losses includingthe copper and core losses, which are the dominant electricallosses, Copper loss reduces with decreasing stator and rotorcurrents while the core loss essentially increases withincreasing air-gap flux density. A study of the copper and coteloss components reveals that their trends conflict - when thecore loss increases, the copper loss tends to decrease for agiven torque. However, there is an air-gap flux density atwhich the sum of copper a nd core losses is minimized. Hence,electrical loss minimization process ultimately comes down tothe selection of the appropriate air-gap flux density when themotor is operating at a particular speed or torque. Since theair-gap flux density must be variable when the load ischanging, control schemes in which the (rotor, air-gap) fluxlinkage is constant will yield sub-optimal efficiency operationespecially when the load is light.

The vector control of induction machines emerges with thedevelopment of modem power electronics. The fast-switchingdevices and the DSP provide the convenient ways to realizethe complex control scheme through voltage source inverters,There has been some work done on the efficiencyoptimization of high performance drives. The classical vectorcontrol algorithms need some modifications to include coreloss effect and in the determination of the reference currents orflux linkages, without which the decoupling between the fluxand torque current components are compromised [ I ] . A mostrecent proposal in a series of papers dealing with the speed-sensor-less vector control of induction machines, operating athigh efficiency in which core loss is accounted for, showswith simulation and experimental results, that in th e sensor-less mode o f operation, high agility and high efficiency arefeasible 123. Recently, papers have been presented dealingwith loss minimization and high performance speed (torque)control of synchronous and permanent magnet machines usingnon-linear control schemes based on feedback linearizationand decoupling methods using motor models in which coreloss is represented with core loss resistances [3-51.From the application point of view, quantities such as rotorflux linkage, torque, active and reactive powers etc are whatcan be easily related to rather than reference frametransformed variables. These quantities are all naturalvariables which are independent of any referen ce frame. Usingthese quantities as the control variables leads to the scalarcontrol and they are directly useable for the loss minimizationcontrol scheme since the power and losses are also scalarquantities.A speed sensor-less control algorithm is used to eliminatethe speed sensor and or encoder. This hardware eliminationresults in total cost reduction of the drive system. It isbasically the algorithm of speed estimation that infers themeasurement required from other more easily availablemeasurements including motor voltages and currents. Thetechniques that have been developed so far can be classifiedinto three categories: using motor back EM F for the flux andspeed estimation, detecting rotor slot harmonics in the statorcurrents and detecting the saliency in the rotor 16-81, Since thefluxes have to be estimated fo r the calculation of those naturalvariables, the speed estimation using the fluxes and rotorvoltage equations in the stationary reference frame becomesexplicit, which belongs to the first category of speedestimation technique. Either one of the two rotor voltage

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equations can be used to calculate the rotor speed information.However, the calculation using sinusoidal rotor fluxes causesthe problem of division by zero and induced possibleoscillations. These problems can be solved with a high degreeof accuracy of rotor speed estimation when both rotorequations are used.There are two main approaches presented in the literaturefor the loss minimization of electric machines: - model basedand on-line power search optimization methods. In the modelbased scheme, the loss is defined in terms of measuredmachine parameters which is minimized using what is calledthe loss model controllers [9-111. The on-line power searchoptimization method uses the measured input power to themotor and perturbs control variables until the measured poweris minimized for a particular operating condition [12-131. Itwould appear with good justification that these efficiencyimprovement schemes find their greatest utility under steadyand quasi-steady-state operating conditions.The organization of the paper is as following. In Section 11the induction motor model with loss consideration isintroduced while in Sections 111 an d IV the loss minimizationscheme is laid out. The speed estimation algorithm is set forthin Section V while simulation and experimental results arepresented in Section VI.

II . INDUCTiON MOTOR M ODE L WITH LOSS CONSIDERATION

0.20- .15 -E.EJ 0.10 -

0.05 -he q-d equivalent circuit for the induction machine isshown in Fig. 1in which the core loss is represented by a coreloss resistance.

r,

0 I 1 0(a) q-axisT F Y *v* L(b) d-axisFig. 1 . Equivalent q-d axis circuit of the induction motor.

The voltage equations for the induction machine in thearbitrary reference frame speed w are :

Define L = L -& and k = 1 + 5 , the stator voltageequations can be expressed in terms of 1' I ; and l g r , A d asfollows.

a L, r cqr

(2)Th e model equations contain the mutual inductance and thecore loss resistance which are changing with the stator fluxlinkage. These changes are accounted for in both computersimulations and experimental implementation of thecontrollers by updating them as the stator flux linkage varies.

Figure 2 illustrates these parameter changes for a 1 hpmachine, in which the measured mutual inductance and coreresistance are plotted as the function of the stator flux linkage.

0.W 4 I I I 1U a i 0.2 0 .3 0.4

stai.x nLuW)(a)

1000800

E 6000 40 0

Izoo

00 0.1 0.2 0. 3 0.4

Stitwflux (Wb)(b)Fig. 2. Measured parameters of the induction machine as afunction of stator flux linkage magnitude. (a) Mutualinductance, @) core loss resistance.

111. NATURAL VARIABLEMODEL A N D LOSS MINIMIZATIONThe variables of the natural variable model of the inductionmachine chosen ate the developed electromagnetic torque q ,

the developed reactive torque T , , the rotor speed U , and thesquare of the magnitude of the rotor flux linkage Am . Thevariables are the same in all transformation reference framesThey are defined in terms of the axis currents and flux linkageas :

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IV . FORMULATION OFCONTROL SCHEMEThe total loss minimization is achieved through appropriatecommand of the q-d axis machine voltages by closed-loopcontrollers using a voltage source inverter. Since the model ofthe machine is nonlinear and coupled, the principles ofnonlinear control of the input-output linearization with

decoupling are used to rem uve the nonlinearity and decoupledterms thereby enabling classical linear system controlmethodology to be used to determine both the constant gainparameters and the structure of the controllers. This is possiblesince the input-output linearization and decoupling strategyensures linear relationship between the input control variablesand the controlled variables with each output-input pairdecoupled from each other.Th e control scheme can be derived through differentiatingthe control variables. The command for the flux is given fromthe loss minimization function.

The losses consisting of copper and core losses expressed interms of natural variables are given as:

(4)

The total electrical loss is to be minimized when the motori s subject to the operating load torque condition, re= T ~ ' ,Wecan choose either or T, as the other control variable toform the loss minimization function y ,

Equation (5) is determined from (4).

(7 )Under steady-state operation, the total loss is minimizedwhen :

'.(a' +T 2 )2k 2

The quantities m, an d m, are calculated using the outputsof the controllers for r, an d Tr. Then the voltages commandsare calculated by solving (13).

Popular PI controllers are applied for the control of;2,,Te, and U, , Their corresponding transfer functions arederived as follows.

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Fig. 3 . Control scheme of induction motor with electrical loss minimization strategy.

The controller parameters are determined fiom the transferfimctions by tuning the denominators to be Butterworthpolynomial compliant, which is to optimize the closed-loopeigen-values to be uniformly located in the left half plane onthe circle of the resonant frequency. Buttenvorth polynomialfor a transfer function with a second order polynomial is givenby

Comparing the coefficients of the denominators of the transferfunctions obtained from (15) and (16) gives the controllers'gains for a chosen resonant frequency Q.The seIection of the,resonant frequency is such as to ensure the closed-looptransfer functions of the controIIed variables have minimum-phase characteristics [13]. The controller structure for themotor speed control is shown in Fig. 3.V. SPEED ESTIMATION

The rotor voltage equations are used in the proposed speedsensor-less approach, making the estimation method part ofthe category using the motor back EMF. The complex-formrotor voltage eq uations in the stationary reference frame are :0 = rJ, , +PA, + N r J q d r (16)Eliminating the rotor curre& using (17) and resolving thevoltage equ ations into real and imaginary parts, the

expressions for the estimated speeds ate given in (1 8).I 1=- (Aq&- J q d 9 14+

The rotor flux are calculated from the stator flux linkagesand stator currents using (19)

The stator flux linkages are estimated by integrating thestator back-EMF using a low pass filter and a compensationscheme to eliminate magnitude and phase errors in (20) .

In (20) a is the cut-off frequency. Extensive simulation resultsshow that using either equation in (18) results significant errorin the speed estimation. A better estimation results areobtained using both equations in (18) as in (2 1).U, =-d Jqrli+yzAir2

VI. SlMULATlON AND EXPERIMENTAL RESULTSFigure 4 gives the no-load starting transient of anexperimental 1 hp induction machine whose parameters areshown in Fig. 2 and the Appendix. The reference speed isramped from zero to 300 radlsec while seeking to minimizethe total electrical loss. The simulation results show that therotor flux linkage quickly builds up and maintains an almost

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constant rated value and becomes small at steady-state. Thetotal loss reduces as the developed torque becomes zero.In Fig. 5, the speed is maintained at 300 radsec, but theload torque is changing. As expected, the rotor flux respondsto the changing load demand resulting in the minimization ofthe losses. As the load demand decreases, the rotor flux alsodecreases resulting in a lower loss. In Fig. 6, the rotor speed ischanged with time and it is seen that both the rotor fluxlinkage as the loss seeks the minimum level. In these figures,the square of the rated flux linkage is about 0. 2 Wb'.

I,, , .*,,,,-: 50-

Fig. 4. Speed regulation and loss minimization for motorstarting from zero speed to 300 rad sec. (a) developed torque,@) actual and command rotor speed, (c) square of rotor fluxlinkage, (d) total electric loss.s - , - ? - - - - V I -- --

.....t'- -4 -

\L-1 1 2 U L . U I 5 2 a . I I s r L

[\( c ) . n1 -I "

.... ~ . . . . . . . . . . . . . . . . ~ ....... ;... .... +- ,_AhL

1 -- i' I- - - 7 TAdl 8 %I ' I4 4 1 U il A : $2 z1 *I S I IFig. 5. Speed regulation and loss minimization for changingload torque (a) developed torque, (b) actual and commandrotor speed, (c) square of rotor flux linkage, (d) total electricloss.

Figures 4-6 demonstrate the possibilities that this controlscheme presents , with changing load or reference speedcommands an appropriate rotor flux linkage is determined tominimize the electnc loss while simultaneously giving highperformance speed controlThe proposed speed estimation method has also beensimulated in Fig. 7 Figure 7(a) shows the steady-state speedof reference and actual speeds after the reference speed isramped from zero to 150 rad/sec, in which the steady-stateerror IS very small Figure 7(b) shows the speed response for aconstant flux reference when the load is under step change. It1s seen that the estimated speed is almost identical to the

I@.=dl

Ia 30 12 11 I S1 4 L a g l l

Fig. 6. Speed regulation and loss minimization for changingrotor speed. (a) developed torque, (b) actual and commandrotor speed, (c) square of rotor flux linkage, (d) total electricloss.Actual speed. This simulation result verifies the effectivenessof the proposed sensor-less approach. Figure 8 gives thesimulation results when only one of the rotor voltageequations is used. Compared with the proposed method, theoscillation in the estimated speed is significant and it causesproblems when the estimated speed is used as the actual speedfeedback.

I . . . . . . . i. .- 8I'5 0 6 ; 1'5 2 ; 1 I; ; 4s it


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i . - - 1_ .

IL

Fig. 8. Reference and estimated speed at steady-state usingone of the rotor voltage equations in (18)The speed sensor-less method has been implemented withthe proposed control scheme. Figure 9 below showsexperimentally the no-load speed response of the motor whenthe speed is changing. The estimated speed and actualmeasured speeds track the reference speed very well. Then themotor is driven to 600 rpm using the same speed estimationmethod. From the starting condition to steady-state speed, therotor flux is set at rated condition after which the lassminimization algorithm is applied, which is shown in Fig. 10.The reference speed tracks the actual speed closely and the

TekPrevu I t I , , ,T " "

. . . . .. . .rr.. . . : . . . . . . . . . +. . . . . : . . . . . . .1 : . : . t-. .. . :. + .. : . . . : . : . . . . . . + . . . . . . . . . . . j .J.: ..(b) 300 - 600rpmFig. 9. Experimental results for speed sensor-less control.From Top : (1) Reference speed, (2) measured speed, (3 )estimated speed.

Fig. 10 . Speed regulation from zero to 600 rpm. From top: ( I )command rotor speed, (2) actual rotor speed, (3) square ofrotor flux linkage, (4) phase 'a' current

Fig. 1 Speed regulation ( 300 - 600 pm ) showing rotor fluxvanation. From top ' (1) Reference speed, (2) Estimatedspeed, (3) Rotor flux linkage.

magnitude square of flux linkage reduces after the lossminimization algorithm kicks in. There is however an initialdivergence between the actual and estimated speed at thestarting condition when the rotor flux linkage is kept constant.Finally, figure 11 displays the changing rotor flux linkageprofile for the loaded motor under changing rotor speedcondition. This graph succinctly demonstrates how theoptimum rotor flux linkage command is changing whichshould consequently affect the loss in the machine -improving overall motor efficiency.VII. CONCLUSIONS

The approach of induction motor speed sensor-less controlusing natural and reference Frame independent quantities asstate variables is presented. The nonlinear geometric controlmethodology of input-output linearization with decoupling isused for the implementation of the control in the stationary

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reference fiame. This technique eliminates the need ofsynchronous reference transformation and flux alignmentrequired in classical vector control schemes. Both rotorvoltage equations are used for the estimation of rotor speed toachieve the speed sensor-less control scheme. Simulation andsome experimental results show that the efficiency ofinduction motor drives can be optimized by choosing theoptimal rotor flux linkage reference from the efficiencyoptimizing formulation while simultaneously achieving rotorspeed sensor-less control. The proposed loss minimizing,sensor-less speed regulation scheme and their advantages aredemonstrated both by computer simulations and someexperimental results.

REFERENCES[ l ] E. Levi, Impact of iron loss on the behavior of vectorcontroHed induction machines, IEEE Trans. on Indus tyApplications, vol. IA-31, no. 6, pp. 1287-1296,November/December 1995.[2J K. Matsuse, S. Tanguchi, T. Yoshizumi and K. Namiki, Aspeed-sensor-less vector control of induction motoroperating at high efficiency taking core loss into account,

IEEE Trans. on Industry Applicafions, vol. IA-37, no , 2,pp. 548- 558, MarcWApril2001.[ 3 ]D. Grenier, L. A. Dessaint, 0 .Akhrif, Y . Bonnassieux andB. Le Pioufle, Experimental nonlinear control of apermanent magnet synchronous motor using saliency,IEEE Trans. on Industrial Elecfronics, vol. 44, no. 10, pp.680-697, October 1997.[4] H. Lee, S.Kang and S . Sul, Efficiency-optimized directtorque control of synchronous reluctance motor usingfeedback linearization, ZEEE Trans. on IndustrialElectronics,vol. 46, no . 1, pp. 192 - 198, February 1999.

[5] 0. Ojo, F. Osaloni and Z . Wu, A control strategy foroptimum efficiency operation of high performance interiorpermanent magnet motor drives, Conference Record o jthe 2003 IEEE industvyApplications Conference, pp. 604-610, October 2003.[6] M-H Shin, D-S Hynn, S-B Cho and S-Y Choe, Animproved stator flux estimation for speed sensorless statorflux orientation control of induction motors, IEEE Trans.on Power Elecfronics, vol. 15, no. 2, pp. 312-317, March2000.[7] M. W. Degner and R. D. orenz, Position estimation ininduction machines utilizing rotor bar slot harmonics andcarrier frequency signal injection, ZEEE Trans. on

Industry Applications, vol. 36, No. 3, pp. 736-142,May/June 2000.[8] M. J. Corly and R. D. orenz, Rotor position and velocityestimation for a salient-pole permanent magnetsynchronous machine at standstill and high speeds, IEEETrans. on Zndustvy Applications, vol. 34, No. 4, pp . 784-789, July/August 1998.[9] A . Kusko and D.Galler, Control means for minimizationof losses in ac and dc motor drives, ZEEE Trans. onIndusfry Applications, vol. IA-19, pp. 561-570,JulyIAugust 1983.[ l o ] D. . Kirschen, D.W. Novotny and W. Suwanwissot,Minimizing induction motor losses by excitation controlin variable frequency drives, IEEE Trans. on IndustrySeptemberiOctober 1984.[ l l ] C. Mademlis, J. Xypteras and N.Margaris, Lossminimization in surface permanent-magnet synchronousmotor drives, IEEE Trans. on Industry Application s, vol.IA-47, pp . 115 -122, February 2000.[121 T. Matsuo, A. El-Antably an d T. A. Lipo, A new controlstrategy for optimum efficiency operation of asynchronous reluctance motor, IEEE Trans. on IndustryApplications, vol. 33, no. 5, pp. 1146-1153,SeptembedOctober 1997.[13] ff.G. Kim, S. K. Sul and N. H. Park, Optimal efficiencydrive of a current source inverter fed induction motor byflux control, IEEE Trans. on I n du s f v Applicarions, vol.20, no. 6, pp.1453-1459, NovemberDecember 1984.[141 B. Friedland, Control System Design, An Introductionto State-Space Methods, McGraw-Hill, New York,1986.

[15] Kazmierkowski M.P, Krishnan R, BIaabjerg F, Controlin Power Electronics: Selected Problems, AcademicPress, Boston, 2002.

AppZica t i~~~ ,vol. IA-20, pp. 1244- 1250,

APPENDIXThe parameters of the 230V, 4-pole, 1 hp induction machineused for this experiment are:

Stator resistance = 1.98OhmsStator leakage inductance = 0.0091 HMagnetizing inductance = 0.1986 H - See Figure 2(a)Core loss resistance = 850 Ohms - See Figure 2(b)Rotor per phase resistance = 1.85 OhmsRotor per phase leakage inductance = 0.0091 HThe moment of inertia = 0.089 kg-m2

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Sensor Less Control of IM Using Natural Variables With Loss Minimization