Mining and Metallurgy Engineering Bor site/Radovi_TR33016/2014/M24 Bor 2014 Vukic.pdfBOR is a journal based on the rich tradition of expert and scientific work from the field of mining,

Mining and MetallurgyEngineering Bor

UDC 622 ISSN 2334-8836 (Štampano izdanje)

ISSN 2406-1395 (Online)

Published by: Mining and Metallurgy Institute Bor

4/2014

MINING AND METALLURGY INSTITUTE BOR

MINING AND METALLURGY ENGINEERING BOR is a journal based on the rich tradition of expert and scientific work from the field of mining, underground and open-pit mining, mineral proce-ssing, geology, mineralogy, petrology, geomecha-nics, metallurgy, materials, technology, as well as related fields of science. Since 2001, is published twice a year, and since 2011 four times year.

Editor-in-chief Academic Ph.D. Milenko Ljubojev, Principal Reasearch Fellow, Associate member of ESC Mining and Metallurgy Institute Bor E-mail: [email protected] Phone: +38130/454-109, 435-164

Editor Vesna Marjanović, B.Eng.

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ISSN 2334-8836 (štampano izdanje)

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Published by Mining and Metallurgy Institute Bor 19210 Bor, Zeleni bulevar 35 E-mail: [email protected] Phone: +38130/454-110 Scientific – Technical Cooperation with the Engineering Academy of Serbia

Editorial Board Prof.Ph.D. Tajduš Antoni

The Stanislaw University of Mining and Metallurgy, Krakow, Poland

Prof.Ph.D. Mevludin Avdić MGCF-University of Tuzla, B&H

Prof.Ph.D. Vladimir Bodarenko National Mining University, Department of Deposit Mining, Ukraine

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Prof.Ph.D. Kemal Gutić MGCF-University of Tuzla, B&H

Ph.D. Miroslav R.Ignjatović, Senior Research Associate Chamber of Commerce and Industry Serbia

Prof.Ph.D. Vencislav Ivanov Mining Faculty, University of Mining and Geology "St. Ivan Rilski" Sofia Bulgaria

Academic Prof.Ph.D. Jerzy Kicki Gospodarkl Surowcami Mineralnymi i Energia, Krakow, Poland

Ph. D., PEng. Dragan Komljenović Hydro-Quebec Research Institute Canada

Ph. D. Ana Kostov, Principal Research Fellow Mining and Metallurgy Institute Bor

Prof. Ph. D. Nikola Lilić Faculty of Mining and Geology Belgrade

Ph.D. Dragan Milanović, Research Associate Mining and Metallurgy Institute Bor

Prof.Ph.D. Vitomir Milić Technical Faculty Bor

Ph.D. Aleksandra Milosavljević, Research Associate Mining and Metallurgy Institute Bor

Ph.D. Dragoslav Rakić Faculty of Mining and Geology Belgrade

Prof.Ph.D. Rodoljub Stanojlović, Technical Faculty Bor

Academic Prof.Ph.D. Mladen Stjepanović Engineering Academy of Serbia

Ph.D. Vlastimir Trujić, Principal Research Fellow Mining and Metallurgy Institute Bor

Ph.D. Biserka Trumić, Senior Research Associate Mining and Metallurgy Institute Bor

Prof.Ph.D. Nebojša Vidanović Faculty of Mining and Geology Belgrade

Prof.Ph.D. Milivoj Vulić University of Ljubljana, Slovenia

Prof.Ph.D. Nenad Vušović Technical Faculty Bor

JOURNAL OF INTERNATIONAL IMPORTANCE, VERIFIED BY A SPECIAL DECISION ON THE MINISTRY OF EDUCATION, SCIENCE AND TECHNOLOGICAL DEVELOPMENT

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INSTITUT ZA RUDARSTVO I METALURGIJU BOR

MINING AND METALLURGY ENGINEERING BOR je časopis baziran na bogatoj tradiciji stručnog i naučnog rada u oblasti rudarstva, podzemne i površinske eksploatacije, pripreme mineralnih sirovina, geologije, mineralogije, petrologije, geomehanike, metalurgije, materijala, tehnologije i povezanih srodnih oblasti. Izlazi dva puta godišnje od 2001. godine, a od 2011. godine četiri puta godišnje.

Glavni i odgovorni urednik Akademik dr Milenko Ljubojev, naučni savetnik Institut za rudarstvo i metalurgiju Bor E-mail: [email protected] Tel. 030/454-109, 435-164

Urednik Vesna Marjanović, dipl.inž.

Prevodilac Nevenka Vukašinović, prof.

Tehnički urednik Suzana Cvetković, teh.

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ISSN 2334-8836 ISSN 2406-1395 (Online) Indeksiranje časopisa u SCIndeksu i u ISI. Sva prava zadržana.

Izdavač Institut za rudarstvo i metalurgiju Bor 19210 Bor, Zeleni bulevar 35 E-mail: [email protected] Tel. 030/454-110 Naučno - tehnička saradnja sa Inženjerskom Akademijom Srbije

Uređivački odbor Prof. dr Tajduš Antoni

Stanislavov univerzitet za rudarstvo i metalurgiju, Krakov, Poljska

Prof. dr Mevludin Avdić RGGF-Univerzitet u Tuzli, BiH

Prof. dr Vladimir Bodarenko Nacionalni rudarski univerzitet, Odeljenje za podzemno rudarstvo, Ukrajina

Dr Mile Bugarin, viši naučni saradnik Institut za rudarstvo i metalurgiju Bor

Prof. dr Kemal Gutić RGGF-Univerzitet u Tuzli, BiH

Dr Miroslav R. Ignjatović, viši naučni saradnik Privredna komora Srbije

Prof. dr Vencislav Ivanov Rudarski fakultet Univerziteta za rudarstvo i geologiju "St. Ivan Rilski" Sofija Bugarska

Prof. dr Jerzy Kicki Državni institut za mineralne sirovine i energiju, Krakov, Poljska

Dr Dragan Komljenović Istraživački institut Hidro-Quebec, Kanada

Dr Ana Kostov, naučni savetnik Institut za rudarstvo i metalurgiju Bor

Prof. Dr Nikola Lilić Rudarsko geološki fakultet Beograd

Dr Dragan Milanović, naučni saradnik Institut za rudarstvo i metalurgiju Bor

Prof. dr Vitomir Milić Tehnički fakultet Bor

Dr Aleksandra Milosavljević, naučni saradnik Institut za rudarstvo i metalurgiju Bor

Dr Dragoslav Rakić, docent Rudarsko geološki fakultet Beograd

Prof. dr Rodoljub Stanojlović Tehnički fakultet Bor

Akademik Prof. dr Mladen Stjepanović Inženjerska akademija Srbije

Dr Vlastimir Trujić, naučni savetnik Institut za rudarstvo i metalurgiju Bor

Dr Biserka Trumić, viši naučni saradnik Institut za rudarstvo i metalurgiju Bor

Prof. dr Nebojša Vidanović Rudarsko geološki fakultet Beograd

Prof. dr Milivoj Vulić Univerzitet u Ljubljani, Slovenija

Prof. dr Nenad Vušović Tehnički fakultet Bor

ČASOPIS MEĐUNARODNOG ZNAČAJA VERIFIKOVAN POSEBNOM ODLUKOM MINISTARSTVA ZA PROSVETU, NAUKU I TEHNOLOŠKI RAZVOJ

REPUBLIKE SRBIJE - M24

CONTENS SADR@AJ

Gordana Milentijević, Blagoje Nedeljković, Miljan Jakišić

POSSIBILITY OF Pb-Zn ORE EXPLORATION IN THE DISTRICT PLAKAONICA II OF THE MINE CRNAC .............................................................................. 1

MOGUĆNOSTI ISTRAŽIVANJA Pb-Zn RUDE NA REVIRU PLAKAONICA II RUDNIKA CRNAC .......................................................................................... 9

Radmilo Rajković, Ljubiša Obradović, Daniel Kržanović, Miomir Mikić

APPLICATION THE SOFTWARE PACKAGES GEMCOM AND MINEX FOR DESIGN THE WASTE LANDFILL – AN EXAMPLE OF CONSTRUCTION THE CASSETTE III PHASE 3 OF ASH AND SLAG LANDFILL OF THE THERMAL POWER PLANT GACKO .................... 17 PRIMENA SOFTVERSKIH PAKETA GEMCOM I MINEX ZA PROJEKTOVANJE DEPONIJE OTPADA - PRIMER KONSTRUKCIJE KASETE III FAZE 3 DEPONIJE PEPELA I ŠLJAKE TE GACKO ........................................................................................................................... 25

Daniel Kržanović, Radmilo Rajković, Miomir Mikić, Milenko Ljubojev

EFFECT OF STAGE DEVELOPMENT OF MINING OPERATIONS ON MAXIMIZATION THE NET PRESENT VALUE IN LONG-TERM PLANNING OF OPEN PITS .............................................. 33

EFEKAT FAZNOG RAZVOJA RUDARSKIH RADOVA NA MAKSIMIZACIJU NETO SADAŠNJE VREDNOSTI KOD DUGOROČNOG PLANIRANJA POVRŠINSKIH KOPOVA ................... 41

Rodoljub Stanojlović, Jovica Sokolović, Nikola Ćirić

TECHNOLOGICAL REQUIREMENTS OF THE NEW COPPER SMELTER OF RTB BOR, A GREAT CHALLENGE FOR THE MINING PROFESSION AND SCIENCE ............................................ 49 TEHNOLOŠKI ZAHTEVI NOVE TOPIONICE BAKRA RTB-A BOR, VELIKI IZAZOV ZA RUDARSKU STRUKU I NAUKU ................................................................................. 57

Dragan Zlatanović, Marija Ilić, Vladimir Milisavljević, Dragan Ignjatović

RESULTS OF EXPERIMENTAL INSTALLATION OF ROOFBOLTING SYSTEM IN THE MINES ....................................................................................................... 65

REZULTATI EKSPERIMENTRALNE UGRADNJE AT VISEĆE PODGRADE U RUDNICIMA ........................................................................................................ 75

Miomir Mikić, Radmilo Rajković, Daniela Urošević, Ivana Jovanović

RECLAMATION THE ASH AND SLAG LANDFILL CASSETTE No. III OF THE TPP ''GACKO'' AFTER PHASE 3 ....................................................................... 85

REKULTIVACIJE DEPONIJE PEPELA I ŠLJAKE KASETA BR. III TE ''GACKO'' NAKON FAZE 3 ............................................................................................................... 95

Miomir Mikić, Daniela Urošević, Vojka Gardić, Borislav Petrović

MONITORING THE QUALITY OF WATER, AIR AND SOIL OF THE ASH AND SLAG LANDFILL OF TPP GACKO CASSETTE III, PHASES 1 AND 2 ................................................................. 105 MONITORING KVALITETA VODE, VAZDUHA I ZEMLJIŠTA DEPONIJE PEPELA I ŠLJAKE TE GACKO KASETE 3, FAZE 1 I 2 .................................................................................................. 115

Radmila Marković, Vojka Gardić, Branimir Jugović, Marija Stevanović

DEWATERING OF SLUDGE OBTAINED BY NEUTRALISATION FROM SULFURIC-ACID WASTE SOLUTIONS ......................................................................................................... 125

ODVODNJAVANJE MULJA DOBIJENOG NEUTRALIZACIJOM SUMPORNO-KISELIH OTPADNIH RASTVORA ......................................................................................... 131

Dejan Bogdanović, Ljubiša Obradović, Slavica Miletić

SELECTION THE OPTIMUM METHOD OF REHABILITATION THE DEGRADED AREAS AROUND THE BOR RIVER DOWNSTREAM FROM THE FLOTATION TAILING DUMP BOR ................................................................................................................. 137 IZBOR OPTIMALNE METODE SANACIJE DEGRADIRANIH POVRŠINA OKO BORSKE REKE NIZVODNO OD FLOTACIJSKOG JALOVIŠTA BOR ..................................................... 147

Mile Dimitrijević, Daniela Urošević, Snežana Milić, Tamara Urošević

COPPER EXTRACTION FROM COPPER SMELTER SLAG WITH PYRITE OR FLOTATION TAILINGS FOLLOWED BY WATER LEACHING ............................................................... 157

EKSTRAKCIJA BAKRA IZ TOPIONIČKE ŠLJAKE PRŽENJEM SA PIRITOM ILI FLOTACIJSKOM JALOVINOM I LUŽENJEM VODOM .............................................................................. 165

Đukan Vukić, Saša Štatkić, Žarko Milkić

HARMONICS ASYNCHRONOUS TORQUES IN WOUND ROTOR INDUCTION MOTOR WITH FREQUENCY CONVERTER IN THE ROTOR .................................................................................... 173

HARMONIJSKI ASINHRONI MOMENTI ASINHRONOG MOTORA SA NAMOTANIM ROTOROM SA FREKVENTNIM PRETVARAČEM U ROTORU ................................................................ 179

Slađana Krstić, Miomir Mikić, Vesna Ljubojev, Boško Vuković

PHYSICAL AND GEOCHEMICAL SOIL CHARACTERISTICS FOR REMEDIATION THE ASH LANDFILL OF THE OPEN PIT GRAČANICA ............................................................................. 185

FIZIČKE I GEOHEMIJSKE OSOBINE ZEMLJIŠTA ZA REKULTIVACIJU DEPONIJE PEPELA PK GRAČANICA ............................................................................................................. 189

Gordana Milentijević, Blagoje Nedeljković, Jelena Đokić

IMPLEMENTATION THE ENVIRONMENTAL PROTECTION SYSTEM IN THE TERRITORY OF THE KOSOVSKA MITROVICA AND ZVEČAN MUNICIPALITIES ........................... 193

SPROVOĐENJE SISTEMA ZAŠTITE ŽIVOTNE SREDINE NA TERITORIJI OPŠTINA KOSOVSKA MITROVICA I ZVEČAN ............................................................................................................ 205

No. 4, 2014 Mining & Metallurgy Engineering Bor 173

MINING AND METALLURGY INSTITUTE BOR ISSN: 2334-8836 (Štampano izdanje) UDK: 622 ISSN: 2406-1395 (Online)

UDK: 621.313.333(045)=111 DOI:10.5937/MMEB1404173V

Đukan Vukić*, Saša Štatkić**, Žarko Milkić**

HARMONICS ASYNCHRONOUS TORQUES IN WOUND ROTOR INDUCTION MOTOR WITH FREQUENCY

CONVERTER IN THE ROTOR***

Abstract

The subject of this paper is the harmonics asynchronous torqueses which appear due to the presence of high time harmonics in the voltage and current of wound rotor induction motor whose speed is regu-lated by frequency converter in the rotor circuit. Theoretical and experimental analysis was carried out in the case when the waveform of voltage, obtained from frequency converter, is rectangular.

Keywords: harmonics asynchronous torques, induction motor, high harmonics, belt-drive

* Faculty of Agriculture, University of Belgrade, Serbia ** University of Priština, Faculty of Technical Sciences, Kosovska Mitrovica, Kneza Miloša 7,

38220 Kosovska Mitrovica, Serbia, e-mail: [email protected] *** These results are a part of the Project TR 33016, “Research, Development and Implementation of

Programs and Procedures Energy Efficiency of Electric Drives” funded by the Ministry of Educa-tion, Science and Technological Development of the Republic of Serbia.

1 INTRODUCTION

In various branches of the industry, where bulk materials are produced or transported, various types of belt convey-ors, with various constructions and drive systems, are used for transport of materi-als. A characteristic place for application the belt conveyors is mines, especially the open-pit mines. For the operation of belt conveyors, the most important component is the belt drive. Belt conveyors which are used for transport of bulk materials most often have a large capacity, which means driving them requires drives with signifi-cant power. With belt conveyors, it is es-pecially necessary to highlight the need for a high torque during starting the belt, i.e., a high starting torque. A drive with

wound rotor induction motor is often used for belt-drive solution at the open-pit mines [1].

In the case when the speed of wound rotor induction motor is regulated by fre-quency converter in the rotor circuit, in the stator and rotor voltages and currents, in addition to the fundamental harmonic, the high time harmonics appear as well. The spectrum of high time harmonics de-pends on the type of used converter, motor construction and mode of drive operation. High harmonics have a negative influence on regulated motor characteristics. This negative influence is manifested in the appearance of additional iron and copper loss and asynchronous torques [2, 5].


Figure 1 The rectangular waveform of the rotor phase voltage

Asynchronous harmonic torques, which

are analyzed in this paper, are produced by interaction of rotor flux high time harmonics and corresponding stator current harmonics in the case when voltage static converter is used. The rectangular voltage waveform, controlled by the frequency converter in rotor circuit, is shown in Figure 1.

Periodic voltage waveform shown in Figure 1, in addition to the fundamental, con-sists of high harmonics in order =5, 7, 11, 13,…. as well. Due to the presence of high

harmonics in the rotor voltage, the rotor and stator currents are not sinusoidal, i.e. in addi-tion to the fundamental, high harmonics ap-pear. Frequencies of these harmonics are given by the following equations:

11 )1(1 fsf

12 fsf (1)

With symbol s is marked a slip, while the f1 represents the network frequency at the stator side.

Figure 2 Equivalent circuit of wounded rotor induction motor for high time harmonics

High voltages and currents time har-

monics in the stator and rotor circuits, as well as asynchronous harmonic torques, can be analyzed and calculated according to the equivalent circuit of wounded

rotor induction motor for high harmonics [4], shown in Figure 2. Symbol designa-tions used in the equivalent circuit are taken from the basic theory of induction motors.

30 150 210

u

t

dU

360

11 (1 )s R

s

1sX 2sX 2R

sX

U 1I

2I

mI


2 GENERAL EQUATIONS

Harmonic asynchronous torque of th high time harmonic is:

21

1

1 I

sRqM

(2)

For the th harmonic of the stator current speed of the rotating field is 1=s1, while slips is given with the expression

1 (1 )sss

[4]. According to equiva-

lent circuit which is shown in Figure 2, the th harmonic of the stator current can be

expressed through the th harmonic of the rotor current.

21

21

21

)()1(1

XX

sR

XII

(3) where is =5, 7, 11, 13, … the harmonic order.

Substitution equation (3) in the equation (2), expression for harmonic asynchronous torque of the th high time harmonic re-ceives the following form:

2

212 2

1 211

1 (1 )( )

1 (1 )

XRqM Is R X X

s

(4)

Relative value of the harmonic asynchronous torque of th high time harmonic is:

21

21

2

21

2

12

2

1)(

)1(1)1(1

XX

sR

sR

XsR

I

I

MM

m (5)

Maximum value, hence most im-

portant significance, has the asynchronous torque of the 5th harmonic, which according to exp. (5) is:

251

21

2

251

2

12

525

)(61

)61(

XXs

RsR

XsR

I

Im (6)

Maximum value of the asynchronous

torque of the 5th harmonic is for s = 1/6. In order to estimate value of this torque we are taking that s = 1/6 – Δs. Considering that Δs << 1/6, it is obtained that:

2152

25

2

12

52max5

)(12 XXR

X

I

Im

(7)


3 THEORETICAL ANALYSIS

From the expression (5), it can be seen that asynchronous high harmonic torques value depends on a sort of the used static semi-conductor frequency converter and the order of high time harmonic, where with the increase of the order of harmonic, that value rapidly decreases. For the given value of higher harmonic, character and the value of higher harmonics asynchro-nous torques depend on the slip, i.e. of the rotation speed. So, the 5th harmonic torque is resistive in the region 0 < s < 1/6, i.e. for speed in the interval 5/6n1 <n<n1 while it is driven one in the region 1/6 < s < 1, i.e. for speed 0 < n < 5/6n1. The torque of the 7th harmonic is resistive at all speeds. The torque of the 11th harmonic is driven in the region 0 < n < 11/12n1 and resistive one afterwards, etc.

According to the expressions (6) and (7), it could be concluded that maximum value of the 5th harmonic asynchronous

torque, appearing at s = 1/6 is much higher than at the other values and that it has high relative value. Actually, it was stated in some previously published studies. How-ever, that is not so, owing to the following reasons:

Firstly, reactance 5X is lower than corresponding reactance for fundamental harmonic ),( 151 XXX because of saturation due to the field fundamental harmonic [3].

Secondly, at the slip of s = 1/6 5th har-monic of the stator current is equal zero

),0( 51 I because then the flux of that harmonic is highly increased, as there is no damping effect of stator current. This results in a significant increase of corre-sponding equivalent reactance, and direct-ly comes from equivalent circuits for the 5th harmonic at s = 1/6 and at s 1/6, shown in Figures 3 and 4.

Figure 3 Equivalent circuit of wounded rotor induction motor for the 5th harmonic at s = 1/6

Consequently, the 5th harmonic of ro-

tor current at s = 1/6 is lower than at s 1/6 because:

5( 1/6 ) 5

5( 1/6 ) 5 5

2 2

2 2

(1 )( )

s

s

I X cI c X X

(8)

2X

5X 52U 52I


Figure 4 Equivalent circuit of wounded rotor induction motor for the 5th harmonic at s 1/6

Where 5

515

X

XXc

is the Hop-

kins leakage coefficient of the 5th harmon-ic which amounts 3.115.15 c for recent induction motors, and

,)63( 25 XX i.e.:

)6/1(52)6/1(52 ss II (9)

Since the 5th harmonic of rotor current has a ignificant effect on maximum value of corresponding harmonic asynchronous torque (according to expression (8)), it can be concluded that this value is much lower than it would be if the facts, mentioned above, were neglected.

Asynchronous harmonic torque of the 7th harmonic has no maximum in motor working domain. The maximum value of the 11th harmonic appears at the slip s = 1/12 and it is much lower than maxi-mum value of the 5th harmonic torque.

4 RESULTS OF MEASUREMENTS AND CALCULATIONS

In order to verify the derived conclu-sions and insight into relative values of the asynchronous harmonic torques experi-mental tests have been carried out for three-phase wound rotor induction motor

made by “Rade Končar”, of 6.4 kW rated output, which parameters are determined by previous experimental tests and which amount:

41.01R 60.02R 25.11X 25.12X 6.45X

Feeding from rotor’s side was through semi-conductor converter type VF-6 made by GEC, whose output was voltage shape shown in Fig. 1. Measuring of harmonic stator’s and rotor’s currents was carried out using electronic Wave analyzer FRA-2d made by “Radiometar”- Copenhagen. The following results were obtained:

- at slip of 6/1s %1152 I

- at slip of 5,0s %2852 I

By calculation, according to (8), max-imum value of the asynchronous torque of 5th harmonic is obtained:

%81,0max5 m

For medium and high power motors, re-lative value of stator resistance is very low, because higher value of m is obtained which, however do not exceed the value of 5%. Value of torque at other slips is lower than 1% .

1X 2X

5X

52U 51I

52I

5mI


5 CONCLUSION

Harmonic asynchronous torques appear due to the presence of high time harmonics in voltages and currents of wound rotor in-duction motor whose speed is regulated by the static frequency converter in the rotor circuit. They are produced by the interaction between the high time harmonics rotor flux and corresponding stator current harmonics. Theoretical analysis, calculations carried out and experimental test results, which are giv-en in this paper, have shown that they are small, including maximum value of the 5th harmonic torque, which appears at the slip of

6/1s and that they have no significant effect on motor behavior.

The described method is considered the most unfavorable voltage waveform at the output of the frequency converter, and it is a rectangular voltage waveform, and showed that the asynchronous torques cannot have a significant impact on the value of the motor torque. Further shaping the voltage wave-form can completely eliminate the presence of asynchronous components of the motor torque.

Appendix

s slip 1 speed of stator rotated field f1 network frequency at the stator’s side f2 frequency at the rotor’s side ordinal number of harmonics 1 speed of the th harmonic of stator

rotated field s slip of the th harmonic R1 stator resistance per phase R2 rotor resistance per phase X1 stator leakage reactance per phase X2 rotor leakage reactance per phase X magnetization reactance for the base

frequency X magnetization reactance of the th

harmonic U1 stator voltage per phase for the th

harmonic

U2 rotor voltage per phase for the th

harmonic I1 rms stator current for the base frequency I2 rms rotor current for the base frequency I1 rms stator current for the th harmonic I2 rms rotor current for the th harmonic

REFERENCES

[1] B. Jeftenić, M. Bebić, L. Ristić, S. Šta-tkić, "Design and Selection of Belt Conveying Equipment & Systems," Chapter 2 in Book - Design and Selec-tion of Bulk Material Handling Equip-ment and Systems: Mining, Mineral Processing, Port, Plant and Excavation Engineering. vol. I, Edited by Prof. Jayanta Bhattacharya, ISBN: 9788190904377, pages in Book: 254, pages in Chapter 2: 60, Publisher: Wide Publishing, Kolkata, West Bengal, India, 2011.

[2] A. Lavi, R.J. Polge: Induction Motor Speed Control with Static Inverter in the Rotor, IEEE Trans, PAS-85, No 1, 1987, pp. 76-84.

[3] M. Petrović: The Behavior of Asyn-chronous Machine in the Regulation Using the Thyristor Recovery of Slip Energy, Publications of Faculty of Electrical Engineering, University of Belgrade, Series Electro Energy, No. 63, 1976 (in Serbian);

[4] Dj. Vukić: Harmonic Equivalent Cir-cuits of Induction Motor with Semi-conductor Converter in the Rotor, Re-view of research work at the Faculty of Agriculture, Vol. 38, 1993, pp. 119-127.

[5] Dj. Vukić: D. Stojanović, N. Mitrović: The Effect of Higher Harmonics on Operation the Asynchronous Motor with Semiconductor Converter in the Rotor Circuit, Proceedings, VIII Sym-posium “Power Electronics”, Novi Sad, September 1995, pp. 343-350 (in Serbian).

Broj 4, 2014. Mining & Metallurgy Engineering Bor 179

INSTITUT ZA RUDARSTVO I METALURGIJU BOR ISSN: 2334-8836 (Štampano izdanje) UDK: 622 ISSN: 2406-1395 (Online)

UDK: 621.313.333(045)=163.41 DOI:10.5937/MMEB1404173V

Đukan Vukić*, Saša Štatkić**, Žarko Milkić**

HARMONIJSKI ASINHRONI MOMENTI ASINHRONOG MOTORA SA NAMOTANIM ROTOROM SA

FREKVENTNIM PRETVARAČEM U ROTORU***

Izvod

Predmet ovog rada su harmonijski asinhroni momenti koji nastaju kao posledica postojanja vremenskih harmonika napona i struje kod asinhronog motora sa namotanim rotorom kod koga se upravljanje brzinom vrši frekventnim pretvaračem u kolu rotora. Sprovedena je teoretska i ekspe-rimentalna analiza za slučaj kada je talasni oblik napona na izlazu iz frekventnog pretvarača pravo-ugaoni.

Ključne reči: harmonijski asinhroni momenti, asinhroni motor, viši harmonici, pogoni traka

* Poljoprivredni fakultet, Univerzitet u Beogradu, Srbija ** Fakultet tehničkih nauka, Univerzitet u Prištini, Kosovska Mitrovica, Kneza Miloša 7,

38220 Kosovska Mitrovica, Srbija, e-mail: [email protected] *** Ovi rezultatu su deo projekta TR33016 “Istraživanje, razvoj i primena programa i mera energetske

efikasnosti elektromotornih pogona” finansiranog od Ministarstva prosvete, nauke i tehnološkog razvoja Republike Srbije

1. UVOD

U različitim granama industrije gde se rastresiti materijali proizvode ili prevoze, za transport materijala upotrebljavaju se raz-ličiti tipovi transportera sa gumenom tra-kom, različitih konstrukcija i pogonskih sistema. Karakteristično mesto za primenu transportera sa gumenom trakom su rudnici, posebno rudnici sa površinskim kopom. Za rad transportera sa gumenom takom najvaž-nija komponenata je pogon trake. Trans-porteri sa gumenom trakom koji se koriste za prevoz rastresitih materijala često su velikog kapaciteta, što za njihovo pokretanje zahteva pogone značajnih snaga. Kod trans-portera sa gumenom trakom neophodno je posebno naglasiti potrebu za velikim mo-mentom u toku polaska trake, tj. velikim

polaznim momentom. Pogon sa asinhronim motorom koji ima namotani rotor se često koristi kao rešenje za pogone traka na površinskim kopovima [1].

U slučaju kada se upravljanje brzinom asinhronog motora sa namotanim rotorom vrši pomoću frekventnog regulatora u kolu rotora, pored osnovnih harmonika struja i napona statora i rotora postoje i viši vre-menski harmonici. Sadržaj viših vremenskih harmonika zavisi od vrste upotrebljenog pre-tvarača, konstrukcije motora i režima rada pogona. Viši harmonici imaju negativan uti-caj na karakteristike upravljanja motora. Ovaj negativan uticaj ispoljava se u pojav-ljivanju dodatnih gubitaka u gvožđu i bakru i harmonijskih asinhronih momenata [2, 5].


Sl. 1. Pravougaoni talasni oblik faznog napona rotora

Harmonijski asinhroni momenti koji su

analizirani u ovom radu, nastaju usled među-sobnog delovanja viših vremenskih harmo-nika fluksa rotora i odgovarajućih harmo-nika statorskih struja u slučaju kada se kori-sti statički naponski pretvarač. Pravougaoni talasni oblik napona upravljan od strane frekventnog pretvarača u kolu rotora prika-zan je na slici 1.

Periodični talasni oblik napona prikazan na slici 1, pored osnovne komponente tako-đe sadrži i više neparne harmonike prema redosledu =5, 7, 11, 13,…. Kao posledica

prisustva viših harmonika napona rotora, struje rotora i statora nisu sinusoidalne, tj., pored osnovne sinusne komponente, sadrže i više harmonike. Frekvencije ovih viših har-monika date su sledećim jednačinama:

11 )1(1 fsf

12 fsf (1)

Klizanje je označeno sa simbolom s, dok f1 predstavlja frekvenciju mrežnog napajanja sa strane statora.

Sl. 2. Ekvivalentna šema asinhronog motora sa namotanim rotorom za više vremenske harmonike

Viši vremenski harmonici napona i

struja u kolima statora i rotora, kao i har-monijski asinhroni momenti, mogu se ana-lizirati i izračunavati na osnovu ekviva-lentne šeme asinhronog motora sa namo-

tanim rotorom za više harmonike [4], koja je prikazana na Slici 2. Primenjeno ozna-čavanje simbola u ekvivalentnoj šemi pre-uzeto je iz osnovne teorije asinhronih motora.

30 150 210

u

t

dU

360

11 (1 )s R

s

1sX 2sX 2R

sX

U 1I

2I

mI


2. OPŠTE JEDNAČINE

Harmonijski asinhroni moment za -ti viši vremenski harmonik je:

21

1

1

IsRqM

(2)

Za -ti harmonik struje statora brzina obrtnog polja statora je 1 1s

, dok

je klizanje dato izrazom 1 (1 )ss

s

,

[3]. Prema ekvivalentnoj šemi koja je pri-kazana na Slici 2. -ti harmonik struje sta-

tora se može izraziti preko -tog harmonika struje rotora:

21

21

21

)()1(1

XX

sR

XII

(3) gde je = 5, 7, 11, 13,… red harmonika.

Zamenom jednačine (3) u jednačinu (2) izraz za harmonijski asinhroni moment za -ti viši vremenski harmonik dobija sledeći oblik: 2

212 2

1 211

1 (1 )( )

1 (1 )

XRqM Is R X X

s

(4)

Relativna vrednost harmonijskog asin-

hronog momenta za -ti viši vremenskiharmonik je:

21

21

2

21

2

12

2

1)(

)1(1)1(1

XX

sR

sR

XsR

I

I

MM

m (5)

Maksimalnu vrednost, a stoga i naj-

važniji značaj, ima asinhroni moment 5-tog harmonika, koji prema izrazu (5) iznosi:

251

21

2

251

2

12

525

)(61

)61(

XXs

RsR

XsR

I

Im (6)

Maksimalna vrednost asinhronog mo-

menta 5-tog harmonika ima se pri klizanju s=1/6. U cilju procene vrednosti ovog asinhronog momenta smatraćemo da je s=1/6 – Δs. Uzimajući u obzir da je Δs << 1/6, dobija se:

2152

25

2

12

52max5

)(12 XXR

X

I

Im

(7)


3. TEORIJSKA ANALIZA

Iz izraza (5), može se videti da vrednost viših harmonijskih asinhronih momenata zavisi od vrste korišćenog frekventnog pretvarača i reda vremenskih viših harmo-nika, gde sa porastom reda harmonika, ova vrednost amplitude naglo opada. Za datu vrednost višeg harmonika, karakter i vrednost višeg harmonijskog asinhronog momenta zavisi od klizanja, t.j. od brzine obrtanja. Tako, 5-ti harmonik momenta je otporan (protivi se kretanju) u oblasti klizanja 0 < s < 1/6, t.j. za opseg brzina 5/6n1 < n < n1, dok je pogonski (podržava kretanje) u oblasti klizanja 1/6 < s < 1, t.j. za opseg brzina 0 < n < 5/6n1. Sedmi harmonik asinhronog momenta je otporan pri svim brzinama. Jedanaesti harmonik asinhronog momenta je pogonski u oblasti 0 < n < 11/12n1, i otporan nakon toga, itd.

Prema izrazima (6) i (7), može se zaključiti da maksimalna vrednost 5-tog harmonika asinhronog momenta, koja se

pojavljuje pri s = 1/6, je mnogo viša od vrednosti drugih komponenti i da zato ima i visoku relativnu vrednost. Zapravo, ovo je izloženo u nekim ranije objavljenim istraži-vanjima. Medjutim, to nije tako, zbog sle-dećih razloga:

Prvo, reaktansa 5

X magnećenja petog harmonika je manja od odgovarajuće reak-tanse osnovnog

1 5 1( )X X X harmonika,

zbog zasićenja od stranje polja osnovnog harmonika [4].

Drugo, pri klizanju s = 1/6, 5-ti har-monik struje statora je jednak nuli (I15=0), zbog čega se peti harmonik fluksa naglo povećava, jer pri tome nema efekta priguši-vanja od strane struje statora. Ovo dovodi do značajnog povećanja odgovarajuće ekviva-lentne reaktanse, i direktno proizilazi iz ekvivalentnih šema za 5-ti harmonik pri s = 1/6 i pri s 1/6, kao što je prikazano na slikama 3 i 4.

Sl. 3. Ekvivalentna šema asinhronog motora sa namotanim rotorom

za 5-ti harmonik pri 6/1s

Sledstveno, 5-ti harmonik struje rotora pri s = 1/6 je manji od vrednosti pri s 1/6 jer je:

5 ( 1/ 6 ) 5

5 ( 1/6 ) 5 5

2 2

2 2

(1 )( )

s

s

I X cI c X X

(8)

2X

5X 52U

52I


Sl. 4. Ekvivalentna šema asinhronog motora sa namotanim rotorom

za 5-ti harmonik pri 1 / 6s

Gde je 5

5

5

1X Xc

X

Hopkinsov

koeficijent rasipanja za 5-ti harmonik koji za današnje asinhrone motore iznosi

51, 15 1,3c , i reaktansa magnećenja 5-

tog harmonika je5 2(3 6)X X , t.j.:

)6/1(52)6/1(52 ss II (9)

Kako 5-ti harmonik struje rotora ima značajan efekat na maksimalnu vrednost odgovarajućeg harmonijskog momenta (prema izrazu (8)), može se zaključiti da je ova vrednost mnogo manja od one koja bi bila da su zanemarene prethodno nave-dene činjenice

Harmonijski asinhroni moment 7-og har-monika nema maksimalnu vrednost u mo-tornom radnom području (oblasti). Maksi-malna vrednost 11-tog harmonika asinhro-nog momenta pojavljuje se pri klizanju s = 1/12 i ona je mnogo značajno niža od maksimalne vrednosti 5-tog harmonika asinhronog momenta.

4. REZULTATI MERENJA I PRORAČUNI

U cilju potvrđivanja izvedenih zaklju-čaka i uvida u relativne vrednosti harmo-nijskih asinhronih momenata, eksperimen-talna ispitivanja su izvršena na trofaznom

asinhronom motoru sa namotanim rotorom, proizvodnje “Rade Končar”, nazivne snage 6,4 kW, čiji su parametri određeni u ranije izvršenim ogledima i koji iznose:

41,01R 60,02R 25,11X 25,12X

6,45X

Napajanje sa rotorske strane ostvareno je preko pretvarača tipa VF-6 proizvodnje General Electric, čiji izlaz talasni oblik na-pona prikazana na Slici 1. Merenje harmo-nijskog sadržaja struja statora i rotora izvr-šeno je pomoću elektronsko talasnog anali-zatora FRA-2d proizvodnje “Radiometar”- Copenhagen. Dobijeni su sledeći rezultati:

- pri klizanju 6/1s %1152 I

- pri klizanju 5,0s %2852 I

Izračunavanjem prema izrazu (8) dobi-jena je maksimalna vrednost 5-tog harmo-nika asinhronog momenta:

%81,0max5 m Za motore srednjih i velikih snaga,

relativna vrednost otpora statora je veoma mala, zbog čega se dobijaju veće vrednosti relativnog harmonijskog momenta m, koji međutim ne prelazi vrednost od 5%. Vred-nosti asinhronih momenata pri drugim klizanjima je manja od 1%.

1X 2X

5X

52U 51I

52I

5mI


5. ZAKLJUČAK

Harmonijski asinhroni momenti nastaju usled prisustva viših vremenskih harmonika u naponima i strujama asinhronog motora sa namotanim rotorom kod koga se brzina reguliše primenom frekventnih pretvarača u kolo rotora. Proizvodi ih međusobno delo-vanje između viših vremenskih harmonika rotorskog fluksa i odgovarajućih harmonika struje statora. Teorijska analiza, izvršeni proračuni i eksperimentalni rezultati, koji su prikazani u ovom radu, pokazuju da su oni mali, uključujući maksimalnu vrednost 5-tog harmonika asinhronog momenta, koji nastaje pri klizanju s = 1/6 i kao takav nema značajan efekat na karakteristike motora.

Opisana metoda je razmatrala najne-povoljniji talasni oblik napona na izlazu iz frekventnog pretvarača, a to je pravougaoni talasni oblik napona, i pokazala da pri tome harmonijski asinhroni momenti nemaju značajan uticaj na vrednost momenta mo-tora. Daljim oblikovanjem talasnog oblika napona može se potpuno eliminisati pri-sustvo asinhronih komponenti momenta.

Dodatak

s klizanje 1 brzina obrtnog polja statora f1 frekvencija mrežnog napajanja sa

statorske strnae f2 frekvencija sa rotorske strane redni broj harmonika 1 brzina -tog harmonika obrtnog polja

statora s klizanje -tog harmonika R1 otpornost statora po fazi R2 otpornost rotora po fazi X1 reaktansa rasipanja statora po fazi X2 reaktansa rasipanja rotora po fazi X reaktansa magnećenja za osnovnu

frekvenciju X reaktansa magnećenja za frekvenciju

-tog harmonika U1 napon statora po fazi za -ti harmonik U2 napon rotora po fazi za -ti harmonik

I1 efektivna vrednost struje statora za

osnovnu frekvenciju I2 efektivna vrednost struje rotora za

osnovnu frekvenciju I1 efektivna vrednost struje statora za

frekvenciju -tog harmonika I2 efektivna vrednost struje rotora za

frekvenciju -tog harmonika

LITERATURA

[1] B. Jeftenić, M. Bebić, L. Ristić, S. Šta-tkić, "Design and Selection of Belt Conveying Equipment & Systems," Chapter 2 in Book - Design and Sele-ction of Bulk Material Handling Equi-pment and Systems: Mining, Mineral Processing, Port, Plant and Excavation Engineering. vol. I, Edited by Prof. Jayanta Bhattacharya, ISBN: 9788190904377, pages in Book: 254, pages in Chapter 2: 60, Publisher: Wide Publishing, Kolkata, West Bengal, India, 2011.

[2] A. Lavi, R.J. Polge: Induction motor speed control with static inverter in the rotor, IEEE Trans, PAS-85, No 1, 1987, pp. 76-84.

[3] M. Petrović: Ponašanje asinhrone ma-šine pri regulaciji pomoću tiristorske rekuperacije energije klizanja, Publi-kacije Elektrotehničkog fakulteta Uni-verziteta u Beogradu, serija Elektro-energetika, No 63, 1976.

[4] Dj. Vukić: Harmonic equivalent cir-cuits of induction motor with semicon-ductor converter in the rotor, Review of research work at the Faculty of Agri-culture, Vol. 38, 1993, pp. 119-127.

[5] Dj. Vukić, D. Stojanović i N. Mitro-vić: Uticaj viših harmonika na rad asinhronog motora sa poluprovod-ničkim pretvaračem u kolu rotora, Zbornik VIII Simpozijuma “Ener-getska elektronika”, Novi Sad, sep-tembar 1995, pp. 343-350.

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