ASSESSMENT OF THE THREE-PHASE INDUCTION MOTORS CHARACTERISTCS AIMING TO SAVE ENERGY: AN ERROR ANALYSIS

Antonio Tadeu Lyrio de Almeida ( 1,2 ) Afonso Henriques Moreira Santos (1)

Jo~o Lopes Ferreira Neto (1) Edson da Costa Bortoni (1)

( 1) EFEI - Escola Federal de Engenharia de Itajuba Av. BPS, 1303 - Pinheirinho

(2) UNITAU - Universidade de Taubate R. Daniel Daneli, s i n. - Jd. Morumbi 'Taubate . - S.P. 37500 - Itajuba - M.G.

ABSTRACT

This work aims to carry out a critical analysis of the errors resulting from the application of several methodologies employed to evaluate the characteristcs of induction motors in laboratory and in field.

to - INTRODUCTION

The electrical sector has adopted in the last years an attitude of energy saving. The identification of saving potentials and the technical and economical evaluation of the replacement of certain equipaments, as well as the consumer faculty in adopting other attitudes are largely fruits of optimization studies and of energetic diagnostics.

In such activities , many attention has been paid to the three-phase induction motors, seeking to obtain their performance characteristics; this f act rises from their massive presence in industrial processes in which they are often inadequate for the l oad they drive (mainly while moving fluids in pumps and fans, which respond for the most part of the demand) and they also often operate with low efficiencies.

Many procedures have been employed to determine such characteristcs . These procedures, however, are grouped in two basic levels, namely: the procedures performed in laboratory and the ones perfomed in the very work site.

The laboratory tests are based upon several standards [1,2,3,4,5] and they employ equipments hardly applicable in field; thus, the so-called "type c haracteristics " are obtained, which, in principle, are considered identical for the many units manufac tured based upon a design, even though there is a diversity in the quality of the material used and in the workmanship.

On the oher hand, the motors evaluation in site has been the object of several studies (12-17] with many methodologies and formulations resulting from them; the emphasis given is justified or the necessity to examine the real operational situations of the motor-load group, preventing from only theoretical simualations (closed upon the type characteristics like the statement) wich may disguise results.

In both situations, uncertainties in the methodologies employed are found out, in tests and in measurements and extrapolations as well. The literature has many examples of

these features, mainly on the achievement of the motors efficiency. As the electrical sector is acknowledge of, the some motor tested with different standards presents efficiency values strongly divergent to each other [6-8]. It is worth mentioning that even methods considered accurate (as in the case of the dynamometer method) present several soucers of errors.

Thus, it is evident that the economics of an eventual replacement can be seriously impaired, because the results obtained in laboratories and in field are not thoroughly sure.

With regards the previously mentioned and aiming to allow for to decrease the uncertainty rate in using the test data, a critical analisys of the errors inherent in the various standardized and expeditious methods is carried out.

2.0 - DISCUSSION ABOUT STANDARDS AND TEST

PROCEDURES

The internationally accepted standards with respect to the efficiency tests of induction motors are the IEEE std 112 [1], IEC Pub. 34-2 [2], JEC std 37 [3] and NEMA std MG 1 [4], the Brazilian standard ~ the NBR 5383 [5]. A$

The IEEE std 112 has two test categories : the tests with straight forward measurement and the ones with losses addition. In the first category are the A (brake), B (dynamometer) and C (back-to-back) methods; in the second are the E (losses segregation) and F (equivalent circuit).

The IEC-34-2 methods are basically the mentioned ones; the preferred one, however, is the losses segregation one, making it different in the way it corrects the temperature and evaluates the stray load losses. The JEC-std-37 methods are similar to the IEEE-std 112 ones, and they are note applicable to the method C. The method that the standard prefers is the circle diagram one, requiring tests with frequencies lowers than nominal. NEMA adopts as standardized procedure the IEEE std 112's method E, including a specific treatment of the stray load l osses.

The determination of the motor efficiency by the avaiable methods is a problem in itself, because all of them are faulty and present divergences in the results. With this respect, the references [6-8] gives many examples of the differences

"

} ~ ')

which exist in the efficiency values when one motor is tested by using different procedures.

As claimed by Andreas [6], the disagreements in the results are due to the stray load losses calculations; consequently, NEMA has adopted in its standards [4J, the recommendation that the polyphase induction motors be specified with the rated efficiency NEMA (or NEMA NOMEFF) when tested according to the IEEE-std 112 [lJ, dynamometer method, treating the stray load losses and admits a range of efficiency values for a given motor, based upon a statistical distribution, resulting in differences of up to 4.5 per cent points.

With respect to JEC std 37, Ishizaki and Hiragama [9J propose changes in some of its procedures, aiming to achieve a greater accurateness in the calculated characte­ristics.

It must be observed that, even in tests using the dynamometer (IEEE 112, method B) there are several sources of imprecision, such as the instruments, the dynamometer and instruments calibration [6J.

3.0 - METHODOLOGIES TO ASSESS THE MOTORS

CHARGING

The standardized procedures are more applicable to laboratories than in field, due to the necessity of suitable equipments and facilities.

With this regard, many methodologies and formulations have appeared which seek to determine the charging of the motors in their own site. Usually, they are based on measurements of easy accomplishment and on nameplate data or on manufacturer's data sheets.

Some of generically methodologies follows:

these methods assigned by

in this work, are

3.1 - Kloss Formula:

wich will be expeditous

analysed as

The Kloss formula permits to obtain the relationship between the torque (M) for a slip (s) and the maximum torque (Mk), that is:

M ~=

2 (1+ ~/R2 Sk)

~+~+2~slc: Sk s R2

(1 )

According to Kostenko [10J, when the relationship between the stator resistances (~) and the rotor resistence refered to the stator (Rz) cannot be determined with more precision, it is admitted that Rl=R2. In the equation (1), " Sk" is the slip corresponding to the pull-out torque "M)c", wich is obtained by taking the values given in catalogues for the rated conditions (MN, TJIoI) and the relationship Mk/MN.

3.2 - Linearization of the characte­ristic M=f(n):

The basic principle of this method is the linearization of the characteristic "torque x rotor speed", in the so-called operating region, that is, between slip zero and "sic" . The pair MN and TJIoI is considered as a point of the curve, wich given and taken as true. So, the load on the motor shaft is given by:

M n - n" TJIoI - ns . MN (2)

In wicp: ns is the synchronous speed; and n is the speed corresponding to the motor load (t1l.

The speed can be obtained directly or through measurement of the current absorved into the grid [11].

3.3 - Inverse Circle Diagram

The mounting of the Circle Diagram is possible through data obtained by performing the tests with free rotor and locked rotor under reduced voltage [10]; with the mentioned diagram and the plate-given rated values in hands, all the characteristic curves are obtained.

On the other hand, not always the tests mentioned in field are possible to be carried out; so, the authors have developed a computer program wich, inputed from simple measurements of active electric power, voltage and current taken "in loco" plots the circle diagram, in a form inverse to what is usually done. It is necessary to know the rated values.

3.4 - Methodology Developed by sa: [12]

Dr. sa has developed in his Phd thesis a methodology, also presents in the reference [12J, based on the solution of the equivalent circuit in "T" of the induction motor, calculating the parameters from manufacturers data sheets. The rotor reactance and the resistance are considered varying with the slip (or with the rotor frequency) between the start-up and Sk. So, the employment of the skin effect in the mentioned range is incorporated, but not the saturation influence. In the so-called operating region the parameters are kept constant. As the torque and start-up current values are used, it is hardly applicable to motors with wound rotors without adaptations.

3.5 - Other Methodologies:

There are others methodologies, as the is one mentioned in [13], in wich the power

obtained from three other values taken from manufacturer data sheets, corresponding to 50%, 75% and 100% of full load.

Goldenberg and Lobosco [14] use these data with the power factor and the speed for the same conditions; besides, the equationing include other data as full load and locked current, full load and locked rotor torque and the maximum torque. Fourteen equations are obtained wich only six unknowns, with an analytical solution resulting. Additionally, an adjustment is done through numerical processes to minimize the deviation between

the values claimed by the manufacturer the values calculated through Form F.3 IEEE std 112 [1] .

and from

The utilization of an accelerometer [15] allows for the achievement of the M=f(n) curves; but it requires the motor disconnection and it is more applicable to laboratories. With this respect, Szabados et alIi [16] develops improvements in the traditional accelerometers [15] and obtains the motor ' s characteristics based upon the measurement of the stator currents and speeds during the start-up, employing a data acquisition board together with the device. These techniques have their attraction in the possibility of performing, later, an on-line monitoring by using a microcomputer or through measurement of conventional currents. Artime and Sanz [16] presented another methodology wich employs the electric quantities measurement in two operating points, but it needs a value of the torque developed in the shaft for one of these points.

4.0 - STATISTICAL MODELS

The methods presented in the previous section for calculation of the developed torque and, consequently, of the power given in the motor shaft, have a deterministic character. It is known, however, that such procedures are subject to errors incurred from the achievement of the measurements to the practice of the mathematic models, these err ors accumulating during the applications.

One of the main restrictions presented to them is the utilization of data sheets or nameplate data; as a matter of fact, the diversity of the quality of the material used and of the workmanship leads to distinct performances for motors with the same design and rated characteristics.

With respect to these data, it is necessary to verify if they are typical, mean or guaranteed, if the stray load losses and the bearing ones are included in their determination, what is the test method used to obtain them and what is the trust level the motor ' s user wishes. This way, naturaly, there is a great uncertainty in the results obtained with the methodologies employing data sheets or nameplate data.

However, even when employing established methods in the sundry outstanding international standards, concerning questions arise, that is: What is the efficiency correct value? What results must be adopted to evaluate technically and economically the fewibility of replacing a motor? Is there any practical fewibility in the standardized methodologies?

The uncertainties are present in achievement and in the use of the results as well, and not only in expeditious methodologies. The fact that questions are the same done for these ones must be enhanced .

the test the the

last

Upon the exposed, there is a necessity of statistical treatment of any results obtained, so as to check out the inherent (or systematic) errors to the test or expeditous

methods, to the measurements and extrapolations. It must be observed that the NEMA recommendations [4] follow this findi ng.

The data consistency can be achieved through adjustments to statistical models [18] , which must reflect, however, the physical behavior of the motor to make them valids ; among them, the one presenting the least standard deviation must be used.

Based upon the theory of the three-phase induction motors and on the equationing of their ' equivalent circuit [10], three statistical models applicable to the region of steady operation of the motor were developed which are outlined.

a) Modell:

In this model, as simplification, the parameters are considered not to vary in the motor ' s operating region; so,

1 t1 (3)

in wich: C1 and Cz are constants which aggregate the motor's parameters, applied voltage and synchronous speed, quantities considered invarying in the analysis.

By means of a linear regression of multiple variables, along the origin a straight line best adjusted to the test points is obtained.

b) Model 2:

In this case, the interception was introduced in the linear regression by adding a new constant (~) to the expression (3), so as to consider the systematic errors.

The representative expression of the model is:

(4)

c) Model 3:

As, a matter of fact, some of the machine parameters vary with the speed along the operation [10], a new term was added to the expression (4) trying to represent this feature, that is:

1 t1 =

C1 S

+Czs+OI+ c;..

2 S

5,0 - TEST OAT A AND ADJUSTMENT OF THE MODELS

(5)

To illustrate the adjustments procedures with the statistic models test results of motors performed by different methodologies and obtained with various manufacturers are presented in the tables 1, 2 and 3.

Among more than two dozens of test sheets, the study of three motors, whose basic characteristic and standards employed in their tests are given in the Appendix.

For any test method, the best adjustment was up to mode l 3. The expressions for the motors' models are presents in the next page.

I

TABLE 1: Comparison f or the statistic mode ls - Motor 1

Torque in Cpu] Error r elative based on the to the t est rated torque data [% ]

Speed Te st Hode l Hodel Hode l Hodel [rpm] data 1 3 1 3 1714 1.85 1.66 1. 84 10 . 3 0 .54 1738 1. 39 1.37 1. 41 1.44 -1.44 1746 1. 25 1. 2 4 1. 24 0 . 80 0 . 80 1753 1.09 1.11 1. 09 1.83 0.00 1760 0.93 0 . 97 0 .93 -4 . 30 0.00 1767 0.78 0.82 0.77 -5.13 1.28 1778 0.53 0.56 0.53 5.66 0.00 1790 0.26 0.26 0 .26 0.00 0 .00

STANDARD DEVIATION 4 . 86 0 . 76

TABLE 2: Comparison fo r the statistic mode l s - Motor 2

Torque in Cpu] Er ror relative based on the to the test rated torque data [%]

Speed Test Hodel Hodel Hodel Model [rpm] data 1 3 1 3 3560 1.31 2.169 1. 239 69.90 -5.20 3573 1. 00 2.087 1.030 108.1 2.69 3581 0.75 1.791 0.802 138.2 6.65 3589 0 . 51 0.377 0.495 26 . 8 -3.88 3594 0 . 27 0.206 0 . 273 24 . 5 0 . 00

STANDARD DEVIATION 85 . 4 4 . 33

TABLE 3: Comparison for the stati stic models - Motor 3

Torque in Cpu] Error relativ e based on the to the test rated torque data [%]

Speed Test Model Model Hodel Mode l [rpm] data 1 3 1 3 874 1. 29 1.261 1.265 2 . 047 1.712 880 1.02 0.995 0.994 2.718 2.874 885 0.50 0.512 0.512 0.470 0.765 890 0.50 0.512 0.512 1 . 332 -1.387

STANDARD DEVIATION 0 . 039 0 . 038

a) Motor 1: -3

~ = 4.277 + 457.2 s _ 23.49 _ 4.68x:0 n s s

1 H

(6) b) Hotor 2 :

-2 - 5 = 2.06x10 + 394 . 6 s _ 10.27 _ 4.97x10

s S 2

(7) c) Motor 3:

- 5 ---H1 = 0 . 352 + 20.0 s _ 2.5x10- 5 - 8 . 46x10

S S 2

( 8)

Model 2 was neglected because in more than twenty motors evaluated it did not have physical significance . Model 1 presented a standard deviation superior to Hodel 3 in every case; this way, expressions (6), (7) and (8) are employed as the best approach to the motor performance, preventing from introducing systematic errors (mainly resulting from the use of the dynamometer method) as, for example; decrease of the speed when the load on the motor shaft

decreases, i n relat ion to t he previous measurement; speed constant with l oad i ncrease; speed constant with brutal r eduction of load in relation to the previous measurement, with the mo tor not operating with l ight load on the shaft; or, different speeds for equal l oads on the shaft, t he speed contro l being non- existent.

6 .0 - THE EXPEDITIOUS PROCEDURES AND THE

ADJUSTED STATISTICAL MODEL

The use of model 3 was best adjusted to the test data, making them consistent; now, any extrapolation almlng t o obtain othe r points in t he "torque related to speed" characteristic can be c alculate d through expressions (6) , (7) and (8) for motors 1, 2 and 3, r espectively . Again , it is enhanced that all the analysis of this work hold for the region between the speed corresponding to the maximum torque and the synchronous speed.

Only the procedures with easy application in field will be considered, that is, the Kloss formula [10J, the linearization of H=f(n), the inverse circle diagram, and the Dr. sa ' s [12] . The procedures mentioned in [13] and [14] will not be assessed because not always there are avaiable data about the operating conditions at 50% and 75% of full load of an operating motor. The Szabados' digital a ccelerometer [ 16] requires a tachogenerator coupled in the axie shaft what, many times, is not possible in industrial plants and, therefore, is not applicable to every case o f evaluation in field.

Within this scope, an error evaluation is carried out between the expeditous procedures and the statistical model adjusted for each case. The comparisons, are illustrated in correspondence to figures 1, 2 and 3, for motors 1, 2 and 3, respectively. The table 4 presents theirs standard deviations .

TABLE 4: Comparasion among methods Standard Deviation

kloss linear . inverse Method c ircle sa formula

diagram Hotor1 26.40 26.60 18 . 40 ---- -

Hotor2 15 . 50 18.50 -- - -- 15.90

Hotor3 0.262 2. 367 0.724 4 . 86

7.0 - CONCLUSIONS

It has been found that the most suitable statistical adjustment was the one performed through model 3. It is observed that i n the motors tested through JEC std 37 , the standard deviat ion is minimal, indicating that, even though using the ci r c le diagram and extrapolations to obtain the rotor parameters at low fre quenc y (12 [HzJ ) , the data present statistical consistency. The application of the IEEE-B/ NEMA method, also has resulted in good conformity of the data .

TABLE 1: Comparison for the statistic models - Motor 1

Torque in Cpu] Error r elative based on the to the test rated torque data [% ]

Speed Te st Hodel Hodel Model Model [rpm] data 1 3 1 3 1714 1.85 1.66 1.84 10.3 0 .54 1738 1. 39 1.37 1. 41 1.44 -1. 44 1746 1. 25 1. 24 1.24 0 . 80 0 .80 1753 1. 09 1.11 1. 09 1. 83 0.00 1760 0.93 0 . 97 0 . 93 -4.30 0 .00 1767 0 .78 0.82 0 . 77 -5.13 1.28 1778 0.53 0.56 0.53 5.66 0.00 1790 0.26 0.26 0 . 26 0.00 0 .00

STANDARD DEVIATION 4 . 86 0.76

TABLE 2 : Comparison fo r the statistic models - Motor 2

Torque in [pu] Error relative based on the to the test rated torque data [%]

Speed Test Hodel Hodel Hodel Hodel [rpm] data 1 3 1 3 3560 1. 31 2.169 1. 239 69.90 5.20 3573 1.00 2 . 087 1.030 108.1 2.69 3581 0.75 1.791 0.802 138.2 6.65 3589 0.51 0.377 0 . 495 26 . 8 -3 . 88 3594 0.27 0 .206 0 . 273 24 . 5 0 . 00

STANDARD DEVIATION 85.4 4 . 33

TABLE 3: Comparison fo r the statistic models - Hotor 3

Torque in [pu] Error relative based on the to the test rated torque data [%]

Speed Test Hode l Model Model Hode l [ rpm] data 1 3 1 3 874 1. 29 1.261 1.265 2.047 1.712 880 1.02 0.995 0.994 2.718 2.874 885 0.50 0.512 0.512 0.470 0.765 890 0.50 0.512 0.512 -1 . 332 -1.387

STANDARD DEVIATION 0 . 039 0 . 038

a) Motor 1:

1 t1"

-3 = 4.277 + 457 . 2 s _ 23.49 _ 4.68x10

1 t1"

s S2

( 6) b) Hotor 2:

-2 - 5 = 2.06x10 + 394 . 6 s _ 10 . 27 _ 4 . 97x10

s 5 2

(7 ) c) Motor 3 :

-5 ~ = 0 . 352 + 20 . 0 s _ 2 . 5x10- 5 - 8 . 46x10

S 8 2

(8)

Model 2 was neglected because in more than twenty motors evaluated it did not have physical significance . Hodel 1 presented a standard deviation superior to Model 3 in every case; this way, expressions (6), (7 ) and (8) are employed as the best approach to the motor performance, preventing from introducing systematic errors (mainly r e sulting from the use of the dynamometer method) as, for example; decrease of the speed when the load on the motor shaft

decreases, in relation to the previous measurement; speed constant with load increase; speed constant wi th brutal reduction of load i n relation to the previous measurement, with the mo tor not operating with l ight load on the shaft ; or, different speeds fo r equal l oads on the shaft, the speed control being non-ex i stent.

6.0 - THE EXPEDITIOUS PROCEDURES AND THE

ADJUSTED STATI STICAL MODEL

The use of mode l 3 was best adjusted to the test data, making them cons istent; now, any extrapolation a1m1ng t o obtain other points in the "torque related to speed" characteristic can be c alculated through expressions (6) , (7) and ( 8 ) for motors 1, 2 and 3, r espectively . Again, it is enhanced that all the analysis of this work ho ld for the region between the speed corr esponding to the maximum torque and the synchronous speed.

Only the procedures wi t h easy application in field will be considered, that is, the Kloss formula [10], the linearization of H=f(n), the inverse circle diagram, and the Dr. sa "s [12] . The procedures mentioned in [13J and [14] will not be assessed because not always there are avaiable data about the operating conditions at 50% and 75% of full load of an operating motor. The Szabados' digital a ccelerometer [ 16J requires a tachogenerator coupled in the axie shaft what, many times, is not possible in industrial plants and, therefore, is not applicable to every case of evaluation in field.

Within this scope, an error evaluation is carried out between the expeditous procedures and the statistical model adjusted for each case. The comparisons, are illustrated in correspondence to figures 1, 2 and 3, for motors 1, 2 and 3, respectively. The table 4 presents theirs standard deviations.

TABLE 4: Comparasion among Standard Deviation

kloss linear. inverse Method

formula circle . diagram

Motor1 26 . 40 26.60 18.40

Hotor2 15.50 18.50 -----

Motor3 0.262 2.367 0.724

7.0 - CONCLUSIONS

methods

sa

- --- -

15 . 90

4 . 86

It has been found that the most suitable statistical adjustment was the one performed t hrough model 3. It is observed that in the motors tested through JEC std 37, the standard deviation is minimal, indicating that, even though using t he ci r cle diagram and extrapolations to obtain the rotor parameters at low frequenc y (12 [Hz] ) , the data present statistical consistency. The application o f the IEEE-B/ NEMA method, also has resulted in good conformity of the data .

(pu)

~ = "EA5~RE"ENTS -- "'.~nSilCAl VODEL - KLOSS i'C·Ro,cULA .- - UNEAAlZATION - - - SA'

FIGURE 1: M = f(n) characteristic obtained through different methods, Motor 1_

et=J f.lEASUREMENTS _ STAnSilCAl MODEl - - KLOSS fORf.lULA .- - UNe:-RIZATION - - - CIRCLE DIAGRAI.I

'i596' , n (rpm)

'isba FIGURE 2: M = f(n) characteristic obtained

through different methods, Motor 2_

1.40 11.1 (pu)

1.20

,001

0.90 I 0.60

~ J.4O ]

= MEASUREM~NTS -- STAnSilc:Al MODEL -- KLOSS fORf.lULA . - - UNEARIZATION • - - CIRCLE OIAGRAI.! - SA'

G.20 1." "';;~o' " '815"' " aeo""" '~e5"" " 'B~b'" ., 'a~5", . n 'g~:m) FIGURE 3: M = f(n) characteristic obtained

through different methods, Motor 3 .

On the other hand, the IEC-34-2 methodology employed gave the largest error among all methods; it can be supposed that such a fact is because of the stray load losses calculation as being 0 _5 % of the active power absorbed from the grid for a de terminated load on the shaft, which causes distortions _

From the expeditious methodologies, only the Kloss formula and the linearization of M=f(n) were applic able to all the motors _ The

Dr. sa-s and the Inverse Circle method not even presented results cases and, therefore, their restricted_

Diagram in some

use is

The two first methods present as a f law the dependence on the catalogue or name plate data . It is observed that such data were supposed as the test ones and, even so, the errors were rather significant; it is likely that the imprecision would be much greater if this . was not done . Besides, the results obtained do not incorporate any conditions adverse to the network, such as voltage unbalance or presence of harmonics.

The other methodologies, as shown, not that applicable to evaluation operating motors, since the available are not much reliable or non-existent .

a re of

data

The identification of saving potentials and the technical and economical evaluation of replacing the motors requires swift methodologies for application in field; yet, as analysed, these are not enough_ The test procedures , which might supply this necessity, are of difficult application, they present divergent results according to the standard (and many . times, discrepants for motors of a same design) and, dependins upon the size, they are more expensive than the motor itself.

Within this evaluating the charging becomes there are high course, results damages) .

scope, the philosophy of efficiency or the motor a dangerous fact, because

mistake risks (what, of in considerable financial

The term "oversized motor" is very relative, because it depends on the requirements imposed by the load (work cycle), on the room conditions and on the supply network; besides, not always the products "efficiency per power factor" are the largest for full load conditions. The real situation of a motor, and the convenience of an eventual replacement, must be evaluated from the binomial "heating-energetic efficiency", these features being obtained through the typical work cycle_

Anyway, it can be concluded that the expeditious methods to evaluate the load of motors are subject to the reliability of data and characteristics supplied by manufacturers, this one holding for test results from the manufacturer . With this respect, it is interesting to notice that the expeditious methodologies have a great correspondence with the results obtained through application of the JEC-std 37; in other words, it can be said that all the methods are applicable because there are no certainty and that the validity depends on the standard through which the motor was originally tested .

REFERENCES

[1] Test Procedure for Polyphase Induction Motors and Generators IEEE Standard .l.l2, 1984_

[2] "Methods for determining losses and

[3]

efficiency of rotating machinery from tests" Electrical Machines Part Publication ~. (1972) Induction Machine, Standard QI Electrotechinical Committee, 1961.

electrical Rotating

2 IEEE

Japanese JEC 37,

[4] American Nacional Standard for Motors and Generators, NEMA MG ~- 1978.

[5] NBR 5383 HAquinas polifasicas de Indu~~o - Metodo de Ensaio - ABNT.

[6] Andreas, J.C.; ~ Efficient Electric ~ - Selection And Aplications Marcel Deckker, Inc, New York, 1982.

[7] Cumings, P.G.; Bowers, W.D.; Martiny, W.J. - "Induction motor efficiency test methods" - IEEE T.r.arul Q.Il lA, vol. lA-I?, no 3, may/june 1981, pp 253-272.

[8] Cummings, P.G. - "Comparison of IEC and NEHA/IEEE motor standards - part I" IEEE ~ Q.Il .Irui APP.L., vo 1. IA-18 , n 2 5, sep/out - "1982 - pp 471-478.

[9] Ishizaki, A.; Hirayama, K.; "Deter-mination of equivalent circuit parameters for performance calculation of polyphase induction machines Electrical Engineering in ~ - 87 (1) 1967 - pp 71-75.

[10] Kostenko, M.; Piotrovski, I. - Electri ~ Machines. - Mir Publ., Moscou.

[11] Ferreira Neto, J.L.; Santos, A.H.M; "Metodologia expedita de avalia~~o tecnica e econ6mica de substitui~~o de motores em operac;:~o" Winner of Pirelli"s ~ SaYing~, 1988.

[12] Ruppert Fo, E.; Arango, H.; sa; J.S. "Analysis of Squirrel Cage Induction Motor Rotor Bars Thermal Behavior" ~ ~ ~ Q.Il Electrical Machines (ICEM) - Cambridge; 1990, pp 245-250.

[13] Woodham, J.B.; "Motor loading for lowest losses" EQ1 - feb 1979, pp 66-69.

[14] Go ldemberg , C.; Lobosco, O.S. "Determination of Induction Motor Characteristics form manufacturers data sheets" - £I:o.Q.... In:t.... QQn:L. Q.Il Electrical Machines (ICEM) - Cambridge, 1990, pp 458-463.

[15] Cristofides, N.; Adkins, B.; - "Determi­nation of load losses and torques in squirrel-cage induction motors" - ~ lEE, vol 113, no 2, Dec. 1966 pp 1995-2005.

[16] Szabados, B.; Findlay, R.D.; Obermeyer, G.M.; Drapher, R.E. "Measurement of the torque-speed characteristics of induction motors using an improved new digital approach" - IEEE Trans Q.Il En.... ~,vol 5, no 3, sept. 1990, pp 565-571.

[17] Artime, J.; Sanz, J. - "A new proposed method for the determination of circuit parameters in squirrel-cage induction motors by steady-state tests". £I:o.Q.... In:t.... ~ Q.Il Electrical Machines (ICEM) - Cambridge, 1990, pp 522-526.

[18] Davies, O.L.; Goldsmith, P.L. - Stat is­~ methods in research And production. Hafner Pub. Co, New York, 1972.

APPENDIX

MOTOR"S TEST REPORT: A.1 - Motor 1:

, Test method: IEEE std 112 / B (dynamome t er) / NEMA MG 1. PN = 11 kW; ON = 1730 0.45945 0 /

0-. = 440 V; IN = 22 A; rpm& stator resistence 20 C;

I [A] 11.46 17.68 19.99 22.36 24.76 Pel[kW] 7.57 10.46 12.34 14 . 19 15.99 n [rpm] 1778 1767 1760 1753 1746 M [kgf] 3.22 4.76 5.75 6.72 7.66 p . [kW] 5.88 8.64 10.40 12.10 13.74

n 0.78 0.83 0.84 0.85 0.86 co/W 0 . 69 0.78 0.81 0.83 0.85

A.2 - Motor 2: Test method: IEC - 34 - 2

60 Hz; (Rt) =

22.17 17.75

1738 8.57

15.30 0.86 0.86

PN = 450 cv; UN = 4000 V; IN = 59. 1 A; 60 Hz; ON = 3570 rpm; 2 poles; MK/MN 2.63; HI'/MN = 1.39; Ip/IN = 6.32

LOAD % 125 100 75 50 25 Pel[kW] 455.0 350.0 264.0 183.5 101.5 S [kVA] 516.1 396.3 311.8 228.6 159.3 co/W 0.882 0.883 0.847 0.803 0.637 s% 1.111 0.750 0.528 0.306 0.167 PJ1.[kW] 7.40 4.36 2.69 1.44 0.70 PH [kW] 4.92 2.56 1.36 0.54 0.16 PsL [kW] 2.28 1.75 1.32 0.92 0.51 Total 23.97 18.04 14.74 12.27 10.74 P [kW] 431.03 331.96 249.26 171.23 90.76 T/ 0.947 0.948 0.944 0.933 0.894 I [A] 74.5 57.2 45.0 33.0 23.0

A.3 - Motor 3: Test Method: JEC - std 37; PN = 55 kW; UN = 440 V; IN = 96.0 A; 60 Hz; ON=880 rpm; 8 poles; = 3.10; HI'/MN=1.007; Ip/IN =

Test f [Hz] Free Rotor 60 Locked Rotor 60

Load Test (Circle Diagram Method)

LOAD % 125 100 75 50 co/W 0.844 0.813 0.757 0.643 s% 2.87 2.24 1.64 1.07 T/ 0.924 0.927 0.924 0.909 I [A] 115.6 95.6 77.4 61.8

A.4 - NOMENCLATURE

Pel - Active electric power; S - Total elec­tric power; I - L~ne current; P - Mechanical power; PJ1, PJ2 - I R losses (stator and rotor ); PsL - Stray load losses; s Slip; n Efficiency; M - Developed torque.

Antonio T. L. Almeida Elec. Eng. (EFEI/ 1980); Msc in Elect. Eng. (EFEI/1986). Currently the is working toward his Phd degree in elec. eng. at Universidade Estadual de Campinas (UNICAMP). He is presently professor of Electrical Machines at EFEI and UNITAU.

Afonso H. M. Santos - Elec. Eng. (EFEI/1978); Msc in Elec. Eng. (EFEI/1980); Phd (UNICAMP/ 1987). He works at EF~I, but presently is a Postdoctoral FellowautClRED, FRANCE.

Jo~o L. F. Neto Elec. Eng. (EFEI/1989); currently he is working toward his Msc degree at EFEI. He is the 1988 recipient of the Pirelli"s Energy Saving Award.

Edson C. Bortoni - Elec. Eng. (EFEI/1990); Presently he is working toward his Msc degree at UNICAMP.