Negative Consequence of Motor Voltage Asymmetry and Its Influence to the Unefficient Energy Usage

Transcription

1 Negative Cosequece of Motor Voltage Asymmetry ad Its Ifluece to the efficiet Eergy sage Electrical egieerig istitute "Nikola esla" Koste Glaviica 8a, Belgrad Serbia Web: Abstract: - Aalysis of the effect of ubalaced voltages o the three-phase iductio motor is preseted i the paper. Sice the ubalaced voltage of %, 3.5% ad 5% icrease i losses could reach, i the same order, the amout of 8%, 5% ad 50% of omial power losses i the motor, it is reasoable requiremet to permit voltage asymmetry %, so this is the upper limit i most atioal ad iteratioal stadards. he truth is that with a smaller load, the motor could safely work also at higher values of ubalaced voltage. he literature states that the iformatio give previosly is determied from measuremets ad that they are higher tha calculated values. However, it is explaied here by the fact that the rotor iverse resistace is higher by 1.4 times compared to the rotor resistace i short circuit mod sice curret frequecy of the egative sequece i the rotor widig is two times higher (f r, f 1 =f r, ), i.e. it is higher for 1.41 times tha correspodig values give i the literature hus it is icreasigly coviced that the requiremets which are give i most appropriate stadards are justified. Performed aalysis show that there are some cosideratios that could be icluded i curret stadards. Motor operatio is ot geerally allowed whe the values of the coefficiet of ubalaced voltage are 1 / 5%, because i the (rare) case whe the direct ad iverse compoet of the stator currets i (a) phase matchig, icrease of the curret i that phase would be 1.38 times, ad the icrease of the losses i the widigs of that phase would be 90%. Key-Words: - egative sequece voltag asymetry, power losses, iductio motor, eergy efficiecy, stadard 1 Itroductio Electrical eergy savigs i the drive could be realized by improvemets of power quality i the cosumer etwork. Power losses ad reactive loads are icreased additioally due to the voltage asymmetry ad (or) existece of high-order harmoics i supply voltage. Voltage asymmetry could appear due to the existece of larger moophase loads or asymmetrical capacitor bak with damaged or switched of capacitor because of blow fuse i oe phase. oday, existece of highorder harmoics i supply voltage is frequet due to the icreased umber of cosumers supplied over rectifiers ad iverters like electrical drives, electrothermal loads, etc. erm power quality [1-3] mostly meas quality of supply voltage that should meet followig requiremets: - voltage value (permissive variatios are i the rage of ±5% of omial voltage), - permissive total harmoics distortio of voltage is HD 3 8% (higher value is for low voltage etworks), - permissive voltage asymmetry is 3% ad has higher ifluece o accurate ad ecoomical motor operatio. Effect of voltage asymmetry to the three phase iductio motor is equivalet to the appearace of egative sequece voltage system that create rotatig field which rotates cotrary to the rotatio of the positive sequece field ad motor rotatig directio. Cosequece is that small values of egative sequece voltage produce relatively high values of egative sequece currets. Per defiitio, coefficiet of asymmetry (K %) is ratio of egative sequece voltage ( ) ad positive sequece voltage ( DS ). For the simplificatio, Stadard NEMA MG1 determies coefficiet of asymmetry i such a way that at first average arithmetical value of lie voltages is determied. For istac for measured voltages of 396V, 399V ad 405V average value is 400V. ha, the highest variatio from average voltage is determied (405V 400V = 5V). At the ed, coefficiet (percet) of voltage asymmetry is calculated as quotiet of highest variatio ad average value: K % = 100(5/400) = 1.5%. ISSN: Issue 8, Volume 9, August 010

2 Sice percetages of egative sequece currets are higher 6-10 times, tha uder such a low voltage asymmetry egative sequece currets could reach up to te percet. his causes additioal motor heatig ad appearace of iverse torque that relates to the startig ad maximum motor torque decrease ad smaller icrease of motor slip durig operatio. Because power losses ad motor heatig are icreased, tha allowable motor loadig is decreased. As percet of asymmetry rises, deratig factor of omial power decreases (show i Fig. 1 per NEMA MG1 [1]). voltages) will be i detail preseted i the paper as follows. At first, a procedures for calculatio ad aalysis of egative sequece currets ad correspodig power losses ad iverse motor torques will be show. ha, evaluatio of egative sequece voltage values that could be arrised i cosidered cosumer etworks is preseted. Equivalet circuit ad motor parameters for egative sequece voltage system.1 Equivalet circuit of iductio motor for egative sequece Whe iductio motor is supplied from etwork with asymmetrical voltages, tha three phase voltage system should be decomposed to positiv egative ad zero sequece. Further, usig equivalet motor circuits [4-8] separately for positive (Fig. 3a) ad for egative sequece (Fig. 3b), calculatios ad aalyses of motor eergy ad operatio characteristics (currets, power losses, torques) are performed. Fig. 1. Relatio betwee deratig factor ad voltage asymmetry With icrease of voltage asymmetry coefficiet, motor efficiecy decreases uder all load levels. Depedece of motor efficiecy is give i Fig. for voltage asymmetry coefficiet of 0.00%,.50%, 5.00% ad 7.50% [1]. Fig.. Motor efficiecy i depedece of motor load for differet voltage assymetries Electrical eergy cosumptio is uecessarily icreased due to the lower motor efficiecy (Fig. ), so maiteace of low voltage asymmetry ( %) is a measure of efficiet eergy usage. I that cas the ifluece of voltage asymmetry (egative sequece Fig. 3. Equivalet circuits of iductio motor a) positive sequece voltage (upper), b) egative sequece voltage (middle) c) etire circuit for egative sequece voltage (lower) ISSN: Issue 8, Volume 9, August 010

3 At the ed, with correspodig superpositio of relevace values their overall values are obtaied. Oly i that way a real (overall) values of motor power losses could be determied.. Parameters of equivalet circuit for egative sequece voltage Stator widig resistace (R s ) ad reactace (X s ) are almost the same for positive ad egative voltage sequece. Parameters of equivalet circuit that are correlated to the rotor side ad egative sequece voltage system (resistace R r, ad reactace X r, ) are substatially differet tha those for positive voltage sequec because the frequecy of the rotor currets i egative sequece are multiple higher: f = f 1 (-s) f 1 >> sf 1 (1) Values of resistace R r, ad reactace X r, are determied from the correspodig parameters i short-circuit regim R r, ad X r,. It is show i [4-6] that values of correspodig resistaces ad reactaces are approximatelly equal i those regimes: R r, R r, ad X r, X r,. If we look carefully, we could fid that this statemet is ot correct. hose parameters chages are depedet o the ratio of the rotor coductor height (H) ad field peetratio ( r, = /(f 1 )), i.e. the quotiet = H/ r, ; where: f1 frequecy of supply voltage first order harmoic, - coductor specific resistac = 0 magetic coductace of coductor. Fig. 4 is give for ζ = H/ = 1. 3: R r,sc (f)=1 3R r ad L r,sc (hf)=1 0.50L r, where R r ad L r are resistace ad iductace i low slip regim respectively, for istace i omial regime. Sice curret frequecy of the egative sequece i the rotor widig is two times higher (f r, f 1 =f r, ), tha field peetratio of those currets are lower for times, so correspodig values of reactace are lower ad resistace higher for times: R r, Rr, () X r, X r, / (3) he explaatio is based o the fact that for the motors larger tha 5 kw (or for relative field peetratio ζ ScC = H/ 1) i the short circuit regime (f = f), it is start ot to use the whole sectio (or height H) of the rotor bar [8]. Fig. 4. Relatio betwee coductor chamfer resistace ad iductace ad relative field peetratio From that it could be cocluded that for the egative sequece (f =f) it is used for times lower part of the rotor coductor height ad also sectio of the rotor coductor. Sice usually values of rotor resistace (R r ) ad reactace (X r ) are kow i the omial regim tha it is ecessary to kow values of coefficiet of rotor resistace icrease (k R >1) ad coefficiet of rotor reactace decrease (k X < 1), both i the short circuit regime. From () ad (3), the values for R r, ad X r, could be calculated as: Rr, kr, Rr (4) X r, k X, X rc (5) where values of coefficiets k R, ad k X, are determied from Fig. 4 for previosly established value of relative field peetratio ζ = H/. I such a maer are determied approximate values of coefficiets k R ad k X, for differet rotor slot deep H (mm)= 15; 0; 30; 40; 50 ad give i able 1. From the quatitative review of correspodig values for k R, ad k R,, ad k X, ad k X,, it could be see that valid relatios are: k R, 1.41k R, ad k X, k R, /1.41, ad it could be cocluded that relatios () ad (3) are correct. I that way it is cofirmed author s state that it is ot correct to believe that values of correspodig resistaces ad reactaces for egative sequece currets are approximately equal to those for motor short ISSN: Issue 8, Volume 9, August 010

4 circuit regime as refered i the literature [4-6]. Cotrary, it is oly correct that those values are i relatio by () ad (3). It is usefull to specify commo values for rotor slot deep H (mm) ad frame sizes for stadard iductio motors, as give i able. From these facts more precisely calculatios ad aalyses of egative sequece voltage (ad egative sequece currets) ifluece to the motor operatio could be performed. able 1: Coefficiets k R ad k X i short circuit regime ad egative sequece currets Rotor slot deep H (mm) Al, = 10 mm; Al, = 7 mm K R, K R, K X, K X, able : sual values for rotor slot deep H (mm) ad frame sizes for stadard iductio motors P (kw) Axial heigh Rotor slot deep, H (mm) Negative sequece currets ad power losses Negative effect to the motor operatio due to the presece of egative sequece voltage is obvious for two reasos: - it iduces occuerece of egative sequece currets that produces losses i the stator ad rotor widigs, i.e. o the stator (R s ) ad rotor (R r, ) resistac ad - appearace of iverse torque opposite to the motor operative torque that origiates from direct voltages ad currets system. It is usefull to express the value of egative sequece curret (I 1, ) i the uits of omial positive sequece curret I 1,PS : I1, 1, / Z M, I1 1 / Z M, 1, / X 1, 1 (6) 1, / Z M, 1 X 1, (6 8) 1 sice egative sequece impedace Z M, X M, ( )X M,, where X M, is motor short circuit reactace ad X M, ( )Z M, (Z M, - motor impedace i omial regime). It could be see from (6) that egative sequece currets i stator ad rotor widigs are 5 8 times higher from the values of egative sequece voltage coefficiets ( 1, / ). Sice egative sequece currets are ot depedet o motor load ad slip, tha we suggest to calculate the coefficiet of assymetry i the uits of omial motor voltage. I the followig calculatios ad aalyses the value X =0.13 (or X = 0.16, i.e. I /I =6.5) is used, so: I1, 1, 7.7 I1 1 (7) Value of icreased losses i the phase widigs of stator is proportioal to the square of egative sequece currets, tha from (7) it could be calculated as: P Cus, /P Cu =(I 1, /I 1 ) =60 ( 1, / ) (8) Percet of losses i rotor coductors could be higher up to 3-6 times (-5 times due to the higher rotor resistace for egative sequece currets ad further up to 1. times due to the additioal icrease of rotor widig temperature uder such a high power losses), i.e. R r, R r, =( 6) R r. Equatio for losses calculatio i the rotor widigs for R r, =5R r, is: P Cu,r, /P Cu,r =5 (I 1 /I 1 ) =300 ( 1, / ) (9) ISSN: Issue 8, Volume 9, August 010

5 Assumig that egative sequece impedace is Z, X, = 0.13 (or I /I =7.7) ad egative sequece rotor resistace is R r, =5 R r, the power losses values are calculated for voltage assymetry of.5%, 3.5% ad 5%. Such a calculated values from (6.7) ad (6.8), i percet of omial losses, for particular motor parts (stator, rotor) ad whole motor, are give i able 3. Similar data are give i [] otig that there were based o measuremets that are larger tha calculated values is explaied by the icrease resistace rotor for iverse power by 1.5 times because of the additioal icrease i temperature of the rotor coductor, which is ot possible at this scale. his ca oly be explaied by sigificat icrease of rotor resistace for aother 40% (), compared to what is stated i the literature. O this basis, the obtaied values for the permitted egie load P / P (%) also were similar to those provided to the appropriate stadards (Fig. 1). Give the pessimistic assumptio, especially for smaller egie power (up to 10 kw) whe the rotor reсistace icreased oly by -3 times (up to times higher due to the iverse resistace rotor currets ad eve up to 1. times for a additioal icrease i temperature of the coductor rotor i such a large loss of power), ie R r, 1.4R r, = ( 3) R r. Calculatio of losses i the rotor coductors, for R r, = 3R r, was coducted by the expressio: P Cu, R, / P Cu, r = 60 (I 1, / I 1 ) = = 180 ( 1, / ) (10) sice the iverse of impedace Z 1, X 0.9X = 0.13 (i.e., whe the motor short circuit reactace X =0.143, or I /I = 7). hus obtaied data are give i able 4. hese data are reliable egie power below 10kW ad these parameters, compared to those i able 4 ad the relevat literature []. able 3: Icreased power losses i % of omial losses for particular motor parts ad motors over 100kW (or R r, =5 R r ) Voltage assymetry (%) Negative sequece curret (%) Stator curret (RMS) (%) Icreased losses (%) Average value for stator widig Rotor Motor (overall) Icreased temperature (C 0 ) Isolatio class A Isolatio class B Permissible motor load P/P (%) For motors of isolatio class A or B ISSN: Issue 8, Volume 9, August 010

6 able 4: Icreasig the power losses i % of omial loss of some parts of the motor, over For motor power below 10 kw (or R r, = 3 R r ) Voltage assymetry (%) Negative sequece curret (%) Stator curret (RMS) (%) Icreased losses (%) Average value for stator widig Rotor Motor (overall) Icreased temperature (C 0 ) Isolatio class A Isolatio class B Permissible motor load P/P (%) For motors of isolatio class A or B Based o data give i able 4, it is cocluded that the effects of ubalaced icrease i electricity ad power loss is less whe it comes to motor power 10 kw, compared to the data specified i the relevat stadards. hus, the above icreas the asymmetry of 3%, approximately equal to those which are listed i able 3 for the asymmetry of %, so the etworks with motors below 10 kw may be eligible asymmetry coefficiet of egative sequece voltage ( 1, / ) 3%. I practic allowed the omial load of the motor, up to 1, / 3% (able 4). Although the ubalaced voltage losses i the rotor coductors is much higher tha the correspodig losses i the stator widig, but icrease the losses of oe phase of the stator ca be the greatest. Specifically, ufavorable is i case whe the direct ad iverse curret compoet could be the same i oe phase. Curret i this phas at the voltages ubalace of 5% would be: - At omial load I = I PS + I = I N N = 1.38 N, while - At 80% of the motor load: I = I PS + I = 0.8I N N = 1.18 N, while the correspodig power losses, respectively, were higher tha the omial 100% (1.38-1) = 90% ad 100% (1.18-1) = 39%. he the curret icrease i that phase would be 1.38 times at the egative sequece voltage 1, / = 5% ad icrease of the losses i the widigs of that phase could reach 90% = 100% (1.38-1). Otherwis i the practice it could be rarely the case whe direct ad iverse compoet of the curret matchig phase agle. For exampl it is ecessary to stress that the asymmetry is a cosequece of oly oe phase voltage deviatio of the values (ot phased by the agle) ad the phase agles of the direct ad iverse impedace a little differet, which is rarely filled because ta(φ )= But it is possible that the phase agle betwee these compoets is about 30 0, ad a correspodig icrease i this phase will be lower: - curret icrease would be i the aalyzed cases 1.35I N ad 1.079I N, respectively ad - correspodig icrease i losses i this phase would be 5.5% ad 16.4%. For these reasos, the motor operatio is ot allowed whe the values of the coefficiet of egative sequece voltage is 1, / 5%. Iterestigly, moder motors of higher efficiecy (IE3 or premium efficiecy motors ) have less iverse power) [7], at the same values of egative sequece voltag ad therefore less additioal losses due to the ubalac compared to a stadard motors (Fig. 5). ISSN: Issue 8, Volume 9, August 010

7 Fig. 6: Depedece of the losses i iro (W) of the percetage of ubalaced voltage (%) at omial voltag higher (for 10%) ad reduced (for 10%) voltage. 4 Motor iverse torque he system of egative sequece voltages leads to the appearace of the iverse torque ( ), which is opposed to the torque that drives the motor (the torque that comes from the direct system voltages ad currets, PS ). Resultat drivig torque is reduced, e = PS - ad the direct torque must be icreased to compesate that decrease. herefor the slip ad direct curret systems are icreased, ad also the correspodig power losses. Direct ( PS ) ad iverse ( ) electromagetic torques are calculated usig the equatio: Fig. 5. Depedece of iverse currets of ubalaced voltage motors for: a) stadard motor (class IE1) ad b) premium efficiecy motors class (IE3) Experimetal measuremets [3] showed that the effect of ubalaced voltages o the iro losses icrease more if the motor is powered with high voltage. hus, Fig.6 shows: - losses icrease i iro is 5W, ad the ubalaced voltage of 5% ad omial voltag while - losses icrease i iro is 35W whe the ubalaced voltage of 5% ad the voltage of 110%. his additioaly ifluece o reducig the coefficiet of omial power (deratig factor), as well as reducig motor efficiecy ad icreasig power cosumptio. PS 3 1PSRr s ( R R / s) X (10) s r 3 1Rr /( s) (11) s ( R R /( s)) X s r assumig that R R =R RPS =R r ad R r / (-s) = R r / ad with less eglect, leads to a relatioship: Z 1 PS ( ) (1) PS 1PS X Sometimes it is coveiet to express the iverse torque i uits of the omial torque ad the ( 1 1 ) Z X (13) ISSN: Issue 8, Volume 9, August 010

8 his meas that, for the coefficiet of ubalaced voltage 1, / = 0.04, would be / = 3 00:04 = Slip ad power losses will also be icreased for times, or 0.5%. But if we assume that the iverse rotor resistace for -5 times higher (up to -4 times higher because of the iverse rotor resistace currets ad eve up to 1. times for a additioal icrease i temperature of the rotor coductor i such a large loss of power), the the expressio for the relative values of the iverse torque is: (6 15) 1 1 (14) where the lower value of the coefficiet related to the motor power up to 10 kw, ad the upper value for motor power above 100 kw. Whe coefficiet of ubalaced voltage 1, / = 0.05, iverse torque i uits of the omial torque could be at / = 10 1:05 = Slip ad power losses will be icreased also for 0.05 times, or.5% P. As this is a medium power motor, with η 90% or with losses of P γ 10% P power losses are icreased by ΔP γ = 5% P γ, which is less tha half of the determied value of icreasig losses ΔP γ, = 50%. he explaatio lies i the fact that i this way (i.e. through the power that is allocated to resistace R r, /, Fig.3c) covers oly half the power losses i resistace R r, while the remaiig half of the compesated part of mechaical power (P m ), which is obtaied through the axis of direct voltage system, Fig. 7. hus, aother procedure cofirmed adequate accuracy of quatitative estimates give i able 4. 5 balaced voltage iflueces to the power factor Lee have show i [1] a compariso betwee differet kids of ubalace voltage (magitude ad agle]) ad their effects o the losses, efficiecy ad power factor, for a three phase iductio motor of 3 HP. It is show that, if DS is costat ad icreases, the power factor will be reduced less tha the efficiecy. I a recetly work [13], authors give a mathematical equatio with efficiecy ad power factor as a fuctio of DS ad. With that equatio it is cofirmed a qualitative descriptio i [1] about lower ifluece of ubalace voltage o the power factor valu ad this is reaso why it is ot ivestigated i the paper. Figure 7: Electromagetic torque characteristics ( m ) ad the electromagetic power (P em ) i the followig regimes: geerator (s <0), motor (0 s 1) ad brakig (s> 1), as well as at poit s = (for the iverse voltage). ISSN: Issue 8, Volume 9, August 010

9 6 Causes ad evaluatio of iverse voltage values By defiitio, the coefficiet of asymmetry is relatioship betwee the iverse system voltage ( ) ad direct voltage systems ( PS ). hus, the percetage of ubalaced voltage is calculated usig the formula: K % 100 DS (15) where the direct ad iverse system voltage compoet are calculated usig the formula ab a bc a ca PS 3 (16) ab a bc a ca 3 (17) hus, i the case of balaced (simetrical) voltages at the motor ab =a bc =a ca, - we get that PS = ab = bc = ca (1), ad - =0 (13). Asymmetry ca arise for several reasos. Oe is the joiig of large cosumers to oe or two phases. hus, if a cosumer who coected to oe phas e.g. phase "a", creates a voltage drop Δ = 3%, the it causes the asymmetry of 1% ( = 1%), sice the usymmetrical voltage system ca be preseted as the sum of the symmetric system voltage ( ab = bc = ca ) ad ubalaced system voltages ( ab = Δ = 3%, bc = 0, ca = 0). o this secod voltage system, accordig to (17), correspods he ubalaced system voltage of = 1%. If purely iductive cosumer is coected betwee two phases, so that the voltage levels o each phase of the impedace etwork is 3%, the a similar aalysis leads to the coclusio that this causes the asymmetry of % ( = %), at the motor coectios. hese cases are possible i practic ad rarely exceed the specified quatitative values. Asymmetry may be a cosequece of fuse capacitor burig. he fall out of codeser part ad reductio of capacitive power is equivalet to appear of iductive loads betwee the two correspodig phases. his results i the appearace of the iverse voltage value which is equal to / 3 reductio of the phase voltage betwee phases i which the reduced capacitive load. he geeral assessmet is that it is almost always the asymmetry coefficiet K <%, except for the iterruptio of oe phase i the etwork, or iterruptio i ay of the motor phase widigs. 7 Coclusio Results of aalysis preseted i the paper could be summarized i followig: 1. he effect of ubalaced voltages o the threephase asychroous motor is equivalet to the appearace of a iverse system voltage creates a rotatig field that rotates i the opposite directio with respect to the rotatio of the direct field ad the directio of rotatio machies. he cosequece is that the low value of the iverse voltage is iverse curret relatively high values. By defiitio, the asymmetry coefficiet (K % = 100 1, / ) is a iverse relatioship betwee the system voltage ( ) ad direct voltage systems ( DS ). Sice the ubalaced voltage of %, 3.5% ad 5% icrease i losses could reach, i the same order, the amout of 8%, 5% ad 50% of omial power losses i the motor, it is reasoable requiremet to permit voltage asymmetry %, so this is the upper limit i most atioal ad iteratioal stadards. he truth is that with a smaller load, the motor could safely work also at higher values of ubalaced voltage. 3. he literature states that the iformatio give uder. is determied from measuremets ad that they are higher tha calculated values. It is, however, here explaied by the fact that the rotor resistace higher by 1.4 times compared to the rotor resistace i short circuit mod ad ot to equal to the same value as described i the literature. hus it is icreasigly coviced that the requiremets which are give i most appropriate stadards are justified. 4. Voltage ubalace causes further icrease of the motor heatig, as well as the occurrece of iverse torques which leads to a reductio of the startig ad maximum torqu ad a smaller icrease i motor slip i operatio. Sice by the icrease of ubalaced voltage power losses are icreased ad motor heatig, tha allowed motor load decreases more with higher percetage of ubalace. hus, for the ubalaced voltage of %, 3%, 4% ad 5%, values of deratig factor are 0.95, 0.93, 0.87, ad 0.81, respectively, accordig to NEMA stadards. 5. Based o the actual calculatio ad aalysis, it was foud that the effects of ubalaced icrease i electricity ad power loss is less whe it comes to motor power 10 kw, compared to the data referred to the appropriate stadards. hus, the above icreas the asymmetry of 3%, approximately equal to those referred to i the stadards for asymmetry ISSN: Issue 8, Volume 9, August 010

10 of %, so the etworks with motors below 10 kw may be acceptable voltage asymmetry with asymmetry coefficiet ( 1, / ) 3%. 6. Motor operatio is ot geerally allowed whe the values of the coefficiet of ubalaced voltage are 1, / 5%, because i the (rare) case whe the direct ad iverse compoet of the stator currets i (a) phase matchig, icrease of the curret i that phase would be 1:38 times, ad the icrease of the losses i the widigs of that phase would be 90%. Refereces: [1] A.H.Boett, A overview of how AC Iductio motors performace has bee affected by the October 4,1997 Implemetatio of the Eergy policy act of 199, IEEE rasactio o Idustry Applicatios, Vol.36, No 1, 000, pp [] J.R. Liders, Effects of Power Supply Variatios o AC Motor Characteristics, IEEE rasactio o Idustry Applicatios, Vol. IA-8", No 4, July/August 197, pp [3] P. Pyllay, P. Hofma, M. Mayag Deratig of Iductio Motors Operatig with a Combiatio of balaced Voltages ad Over or dervoltages, IEEE rasactio o Idustry Applicatios, Vol. I7, No 4, December 00, pp [4] I. Boldea, S. A. Nasar, he Iductio Machie Hadbook, 00 by CRC Press LLC. [5] A.Ivaov-Smolesky, Electrical Machies, Vol., Mir Publishers, 198, pp [6] V. I. Radi, D. E. Bruski, A. E. Zorohovič, Electrical machies: Iductio machies (i Russia), Moscow, 1989, pp. 38. [7] A.E. Kravčik, et al., Iductio machies Hadbook vol.4a (i Russia), Eergoizdat, Moscow, 198. pp [8] M. Kostic, Parameters of equivalet circuit of saturated iductio motors with squirell-case rotor i short circuit regim ehika, chapter Elektrotehika (i Serbia, to be published). [9] M.Kostic, Equivalet circuits of saturated iductio motors ad evaluatio of calculatio accuracy accordig to -schem ehika, chapter Elektrotehika 5/009 (i Serbia), pp.7e-18e. [10] J. Keck, D.A. Casada, P.J. Otday, A Comparisio of wo Eergy Efficiet Motors, IEEE rasactios o Idustry Applicatios, Vol.EC 13, No.., 1998, pp [11] K.Barra,.Bouktir, K.Bemahammed, Optimal Efficiecy based Predictive Cotrol Of Iductio Machie Icludig Magetic Saturatio ad Ski effect, WSEAS RAACIO o CIRCIS ad SYSEMS, Issue 6, Volume 3, August 004, pp [1] Chig-Yi Le Effects of balaced Voltage o Operatio Performace of a hree-phase Iductio Motor, IEEE rasactio o Eergy Coversio, Vol.14, No., 1999, pp [13] E.Quisp P.Viego, J.Cogollos, Statistical Equatios to Evaluate the Effects of Voltage balace o the Efficiecy ad Power Factor of a hree-phase Iductio Motors, WSEAS RAACIO o CIRCIS ad SYSEMS, Issue 4, Volume 4, April 005, pp [14] H.Mabrouk, A.Rachid, Ifluece of the Rotor Dimesios ad the Supply Voltage o the Performaces of Solid Rotor Asychroous Motor, WSEAS RAACIO o CIRCIS ad SYSEMS, Issue 3, Volume 5, March 006, pp [15] M.Chafai, L.Refoufi, H.Betarzi, Medium Iductio Motor Widig Isulatio Protectio System Reliability Evaluatio ad Improvemet sig Predictive Aalysis, 6th WSEAS Iteratioal Coferece o CIRCIS, SYSEMS, ELECRONICS, CONROL & SIGNAL PROCESSING, Cairo, Egypt, Dec 9-31, 007, pp ISSN: Issue 8, Volume 9, August 010