SIMULATION OF SATURATED DEEP BAR INDUCTIONMOTORS IN THE PRESENCE OF IRON LOSS

M. Bakhtiari, A. Jalilian

Iran University of Science and Technology, Iran

ABSTRACT

The investigation of the performance of 3-phase induction motors requires reconsideration in their modeling. In this papertwo different models have been studied and three influential parameters on motor performance have been consideredaltogether for the first time. The first model uses variable rotor parameters for modeling the skin effect while the secondmodel applies constant parameters in a more complicated manner. Simulation results confirmed that both models have beenin good agreement. The skin effect, core losses and saturation have also been investigated and presented in this paper.

Keywords: Induction Motor Modeling, Iron Loss, Skin Effect, Saturation.

1. INTRODUCTION obtained by multiplying the modification factors of Kr andK, in rotor dc resistance and inductance values as:

Different models have been introduced for inductionmotor in the literature. Those who were interested in the Rac Kr Rdc (1)dynamic behavior of the induction motor have paid more L K L (2)attention to the skin effect [1]. However, there has been a ac x dcgroup who has considered the motor core losses in orderto predict the quality of the control system's performance These coefficients for rectangular bars are as follows [1]:[2, 3]. But it should be noted that any kind of partial viewand simplification in the induction motor models may lead k_ = sinh23 +sin ()to unpredictable errors in the final results. cosh 2, - cos 2,

3 sinh 2, - sin 2 4This paper is an attempt to achieve an accurate model of 24 cosh 24 - cos 24 (4)induction motor which may have the characteristics ofboth outlooks mentioned above simultaneously. where:Therefore, at first, two approaches for the modeling ofskin effect have been introduced to which the way of 4-h 0 (5)incorporating the core losses and saturation phenomenon phave been added. In these equations, h is the height of rotor bar, f is

frequency and s is fundamental slip and p is the resistivityThe choice of each method depends on the model's oftebrmeia.Tehgtofoorarcnepefrmne In no-aroi or lo-otg of the bar material. The height of rotor bar can beperformance. In non-harmonic or low-voltage THD cluae s

conditions the first model is preferred but in harmonic calculated as:

conditions the second model is easier to deal with. h(c_m) - 2(P(kW)/1O)/55 (6)

2. MODELING OF SKIN EFFECT where P denotes for motor power rating [4].

Skin effect or deep bar effect is one of the most effectivephenomena on the variation of induction motor's 1.8parameters. Investigation of two different methods of 1.6considering skin effect in motor models is consideredhere. 1.4

2.1 Modeling of skin effect using the modificationfactorIn this method coefficients for studying the changes of 0rotor resistance and inductance can be obtained using the 0i : ' . 1 i 1 yol0.mathematical relations and bar and slots forms. Therefore, slin this method there is no need for experimental tests to Figure 1. Variation of rotor impedance modificationdetermine these changes. The desirable variations can be factors (kr,kx) with slip, (1): Resistance, (2): Inductancee

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The profile of the mentioned coefficients against slip is The motor core loss is the sum of stator and rotor corepresented in Figure 1. losses. Even, the rotor core loss is negligible in the

sinusoidal voltage supplies, it is included for generality as:2.2 Modeling of skin effect using a multi-branch rotorIn this the method, the skin effect is modeled by adding s 2(02 \ 2222some resistive-inductive branches to the rotor as shown in Piron 7= mkee+khoe)- e (10)Figure 2. ike Rm

iron 4n(ke52W2 +khsw 2) ts2w22 w)21~2Ll L2 Lpr s2t)2 khste - em em (1 1)

A (7. Af~Y>~ ~Y~~ i/ke Rms2

where kh and ke are hysteresis and eddy-current lossR R R3 coefficients, s and r subscripts stand for the stator and

rotor respectively. Since 03e2m denotes the air gap voltage,B the dimension like ratio is resistive and therefore it is

Figure 2. A Multi-branch rotor modeling represented by R*m.Using equations (10) and (I1) the motor iron losses can be

In this method, practical test results are required to obtain modeled with an equivalent resistance R, as:

the changes of rotor parameters with frequency. The R R* // R,1 Rm (12)values for rotor branch parameters can be calculated using m m 52 s2 +Ithe laboratory results and minimizing the followingfunction [5]: It should be noted that considering iron losses in both

N single-branch and multi-branch rotor modeling leads to

F [( ) )]2 +[K2 ( ) K )]2 (7) adding one more state-space variable and consequently toF= 1,[K, ( fs )- K, ( I; )] +[Kx( I; ) - K1;)]|(7)amorecomplexmathematical model.

with 4. MODELING OF SATURATION

Kr' ( fi)=e ] (8) The saturation is an effective phenomenon in theRdc induction motor performance and to ignore it may lead to

Im[ZAB] considerable error particularly in motor loss estimation.Kr (f) = (9) The errors are usually due to the decrease in rotor leakage

x 2xTxfxdc inductance which leads to increased copper loss [8].

Recently, finite element method has been recommended Since the rotor inductance saturation is a rare phenomenonfor calculating Kr and Kx instead of using experimental and usually occurs in harmonic conditions, so in this paperusing ~~~we have been satisfied with considering the magnetizingresults [6]. In this paper, the use of equations (3) and (4) is i ane sation. in orderito ahe th rigrecommended.fo mor simplicity........ inductance saturation. In order to achieve the right

rcmendedlicatnofo molti-breaslci model for the rotor hasa dynamic response, the magnetizing inductance should beThe pplcatonf mltibrach mdelfortherotr hs a used and corrected continuously. For this purpzose, anweakness that for each branch, an additional state variable istdante no-loated curvei(Figus. Fr 3) s uldbe,uefor simulating the induction motor performance is needed. insteof rm-bad value whicare useful fo theThis makes the process of computer simulation more instead of rms-based values whlch are useful for the

complex and time-consuming. However, this method has y- popsome merits in harmonic conditions where constant simple multiplying of VE into rms values is not sufficientparameters can be used for a wide range of frequencies for this purpose. The method of calculating the[7]. instantaneous curve from rms curve is reported in [9].

3. MODELING OF IRON LOSSES

The iron losses in induction motors consist ofthree groups 5. DYNAMIC EQUIVALENT CIRCUITof hystersis losses, eddy current losses and stray losses. Inthis paper only the first two groups are considered and the The dynamic performance of an induction motor ismodeling of stray losses is neglected. generally studied by means of the equivalent circuits inConsidering iron losses in single-branch and multi-branch the dq (direct and quadrate) reference frame. In thisrotor models are the same and can be carried out by section the same approach has been used for motorparalleling the iron loss equivalent resistance (Rm) with models with single and multi-branch rotors.motor's magnetizing inductance. Therefore, the majorproblem is the calculation of Rm and its variations.

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20C kqsw (14)kqs Vqs - Cekds LRs (14)

150 -lIS'- /Xdr (°)e -O)r )Xqr -Rr (dr dm (15)

qr qm (16)-50-qr Lir

-100 ~~ ~ ~ ~ ~ ~ (cew)XrRrA --lao (~~~~~~~~~~~~~~~~~~kd kXdm~

-150 -dm LIS Lir LM)(7-200 lll

-0.8 -0.6 -0.4 -0.2 0 O.2 0 4 0 6 0.8. ACurrent(A) qs qr _ dm

Figure 3. Instantaneous no-load curve for an induction qm Lir LM (motor obtained from rms values where:

5.1 Single-branch rotor 1 = 1 1 + 1 (19)An induction motor dynamic model with single-branch LM LIS Lir Lmrotor has been presented in Figure 4: As it can be seen, Rmand Lm are chosen as variable parameters to show the loss The mechanical equation of the induction motor can bedependency (on slip) and magnetizing inductance changes given as:with saturation. It must be mentioned that the model is 2 Apresented in synchronous rotating frame. Ten TL K J dr (20)

(f)g00))qr In this equation Tem is the electromagnetic torque, TL is the

1+ + load torque, J is rotor moment of inertia and P is theLj

L i motor poles. To calculate the electromagnetic torque, the1+1 ~Liii following equation is used:a

Tem =3P Lm {2Udr(Iqs IqjRm)2uqr(Ids IdRP)}(21)4 Lm +Lr

A R, L + where Idph7 and 'qpn are the direct and quadrateAR, Lt R + L components ofthe current flowing through the Rm.Vq, R.I Lmj RrX

*- - - 'b5.2 Multi-branch rotorbFigure 4. Dynamic equivalent circuit of an induction The dynamic model of an induction motor with multi-motor in a synchronously rotating dq reference frame branch rotor in stationary frame is shown in Figure 5:

The flux equations of this model are as follows: , Lix _

Xds = LlsIds +LmIdm A qs LSiqs +Lml qm Liri L/2

Xdr = LlrIdr +LmIdm Xqr = Ljriqr +LmIqm Rm LittX~~~~~~~L - Rn Rr2Xdm LmIdm qqm qm

O -j@%pr~ -Jcopr2By choosing these fluxes as state-space variables andusing the Kirschoff Laws, the necessary state-spaceequations can be obtained to analyze the induction motor Figure 5. Equivalent circuit of a multi-branch

performance: ~~~~~~~~~~~induction motor in a stationary dq frame

As can be viewed the core losses are once again modeledXds- Vds + qs R ds - Vd(13 as a resistance in parallel with the magnetizingqs S L1s inductance. The flux equations for a two-branch rotor are

given as:

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6. SIMULATION RESULTS:Pds Llsids + Lmidm (Pqs Ljsiqs + Lmiqm

In this section, the described models have been simulated(Pdrl =Lmnidm] + Lirli drl (Pqrl = Lmiqm + Llr2'qrl using Matlab-Simulink software to prove their validity.

(Pdr2 Lmldm + Llr2 dr2 (Pqr2 Lmiqm + LJr2Iqr2 This process has been carried out in four stages:

6.1 Models cornparisonWhile p chosen as flux instead of X to avoid interferenceThe carried-out simulations show that the results obtained

wquatith s

the prevwrioustequations. Itimd thvlg from even a two-branch rotor model with constantequations can be written as:parameters are in a good agreement with those obtained

dPdS from a single-branch rotor with variable parameters. TheVds RSids + dt(22) reason could be using equations (3) and (4) as reference of

the second model.Vqs = Rsiq + qs(23)qs sqsdt (23) 6.2 Skin effect

O = Rrlid1 +ddrl + 0Pl (24) To study the influence of the skin effect on dynamicldrl dt r qr performance of an induction motor, the electromagneticd(Pqrl torque profile of the motor with and without considering

O = Rr 1qrl dt r (Pdrl (25) the skin effect has been simulated as shown in Figure 6.

O Rr2ldr2 + d +dt r(Pqr2 (26)

O = Rr2iqr2 + d(Pqr2 - (Pdr2 (27) 15dt

Now we can deduce the motor state-space equations: D 0

Pds J(Vds- Rsids)dt (28)

E

(Pqs s - Rsiqs)dt (29)

(Pdrl J(r°l(Pqrl Rrlidil)dt (30)0 01 02 03 04 05 06 07 0.8 09 1

Time(s)

(qr =|0-91-Rr i,j )dt (31) .TesPqrl JWr(Pdrl - Rriiqri ) dt (31) Figure 6. Torque profile of an induction motor duringstart-up: (l)skin effect not considered (2) skin effect

Pdr2 J0)7rPqr2 -Rr2 dr2)dt (32) considered

K( Pds Pdrl Pdr2 As it can be observed the skin effect has caused a(Pdm JRm + +dm dt (33) considerable increase in the start-up electromagnetic

V LIS L'-1LJr 2 LM J torque and some decrease in motor start-up time.

FR( )qsqr q

Pqm dt (34) 6.3 Core lossesLIS Lq- L L12 LM Simulated results show that the core losses have not such

a considerable effect on the motor performance as shownin which: in Figure 7, even if Rm has significant changes during the

l l l l l start-up (Figure 8).LM Lj~ L L (35) Ignoring Rm will cause at least three errors:M L1S Llrl Lr2 Lm * Error in rotor flux estimation

Finally the electromagnetic torque can be calculated from * Error in rotor flux phase anglethe following equation: * Error in electromagnetic torque estimation

Therefore, it's inclusion in the induction motors modelingTern= {(Pdslqs - Pqs1ds} (36) is highly recommend.

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7. CONCLUSION

. 4 1In this paper a new attempt has been made to achieve a12 more accurate induction motor dynamic model. Two10 different dynamic models of induction motors have been8 11 < developed. In the first one, the skin effect is modeled as6 l ll lllI|1\~ (2variable parameters in the rotor side. In the second

E24 approach, the modeling is carried out by adding moreutu2 branches to the rotor circuit. The magnetizing inductance

saturation and core losses have also been considered inboth models. It is the first time that all three phenomena

-2 l lhave been included in a motor equivalent circuit. The0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 validity of the proposed models and equations are proved

by performing simulations of an induction motor inFigure 7. Electromagnetic torque profile during start-up Matlab/Simulink environment. The skin effect, core

(1) R. not considered (2) Rm considered losses and saturation have also been investigated in this5000 paper where the results have been presented and

compared.4500

8. REFERENCES4000 i

[1] White, T.J.; Hinton, J.C.; "Improved dynamic performancep3500 of the 3-phase induction motor using equivalent circuit

parameter correction", Int. Conference on Control, 21-243000 March 1994, Volume 2, Page(s): 1210 - 1214.

[2] Levi, E.; "Impact of iron loss on behavior of vector2500 controlled induction machines", IEEE Trans. on IA, Nov.-

Dec. 1995, Volume 31, Issue 6, Page(s):1287 - 1296.20001 0.2 04 06 12 14 [3] Jinhwan Jung; Kwanghee Nam; "A vector control scheme

Time(s) for EV induction motors with a series iron loss model",

Figure 8. Motor losses equivalent resistance (Em) IEEE Trans. on IE, Vol 45, No 4, pp. 617 - 624 Aug. 1998.profile from start-up to steady-state [4] DeBuck et al.; "A simple but reliable loss model for

inverter-supplied induction motors", IEEE Transaction on

6.4 Saturation Industry Applications, VollA-20, No.1, Jan/Feb 1984.To Satudyathonsaturation phenomenon,stator'ssteadystate

[5] Alexander C. Smith, Russel C.Healey and StephenTo study the saturation phenomenon, stator' s steady state Williamson;"A Transient Induction Motor Model Includingcurrent has been simulated with and without considering Saturation and Deep Bar Effect", IEEE Transactions onsaturation. The results have been presented in Figure 9. Energy Conversion, Vol. 11, No. 1, March 1996.

[6] Jingchuan Li, Longya Xu, "Investigation of Cross-Saturation and Deep Bar Effects of Induction Motors by

4 Augmented d-q Modeling Method", IEEE Conference onS nnotCoded Satutio Cosided IA, Vol. 2, pp. 745-750, 30 Sep.-4 Oct. 2001.

[7] Retiere, N.; Foggia, A.; Roye, D.; Mannevy, P.;"Deep-bar2 Induction Motor Model for Large Transient Analysis under

Saturated Conditions", IEEE ICEMD, May 1997.[8] J. C. Clare, et al, "Additional Losses Due to Operation of

co;0 I I I \I\Machines from Inverters", IEE Half Day Colloquium onTesting of Electrical Machines, pages:5/1-5/8, June 1999.

[9] Ong, Chee-Mun, "Dynamic Simulation of ElectricMachinery Using Matlab/Simulink", Prentice Hall PTR,Chapter 4, 19 Sep. 1997.

-4 l l l l lL L L

APPENDIX 10.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6

Time(sec)

Figure 9. Stator's steady-state current Parameters ofthe simulated motor:Pn =0.75kW,220V,P= 4, f=50Hz

As it can be seen a considerable decrease in the stator's 10lO,L1= 43mH, Rr 6.3Q, Lir =40mHcurrent has been occurred because of the saturation. Rm 5 kQ, Lm =.421 H, Tn 5.15 Nm, f .01

h =0.012488 m, p =.02x 10-6Q.m

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