SUPERCAPACITOR AS A BUFFER ELECTRICAL SOURCE FOR INDUCTION MOTOR Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

Power Industry Электроэнергетика

DOI: 10.17516/1999-494X-0431 УДК 621.131.332:621.319.4

Supercapacitor as a Buffer Electrical Source for Induction Motor

Ruslan F. Saifulin*

Karaganda Technical University Karaganda, Kazakhstan

Received 17.05.2022, received in revised form 07.09.2022, accepted 20.09.2022

Abstract. Mathematical substitutions in the equations and the used methods have shown the adequacy and correctness of their use. Analysis of the data, obtained from simulation modeling of the developed model, showed small discrepancies with the standard block from the Simulink library. The use of the obtained mathematical equations, as well as the model assembled in Matlab Simulink, will make it possible to qualitatively evaluate the operation of an induction drive in statics and dynamics. This model will be used in future research, including the creation of a buffer power source based on a supercapacitor for an induction electric drive.

Keywords: electric drive, modeling, Matlab Simulink, supercapacitor, math model, simulation.

Citation: Saifulin, R. F. Supercapacitor as a buffer electrical source for induction motor. J. Sib. Fed. Univ. Eng. & Technol., 2022, 15(8), 940-947. DOI: 10.17516/1999-494X-0431

Суперконденсатор

как буферный источник электроэнергии для ашнхронного двигателя

Р. Ф. Сайфулин

Карагандинский технический университет Казахстан, Караганда

Аннотация. Математические замены в уравнениях и используемые методы показали адекватность и правильность их применения. Анализ данных, полученных при имитационном моделировании

© Siberian Federal University. All rights reserved

This work is licensed under a Creative Commons Attribution-Non Commercial 4.0 International License (CC BY-NC 4.0). Corresponding author E-mail address: azoorjke@gmail.com

разработанной модели, показал небольшие расхождения со стандартным блоком из библиотеки Simulink. Полученные математические уравнения, а также модель, собранная в МаЙаЬ Simulink, позволят качественно оценить работу асинхронного привода в статике и динамике. Эта модель будет использована в дальнейших исследованиях, в том числе при создании буферного источника питания на основе суперконденсатора для асинхронного электропривода.

Ключевые слова: электропривод, моделирование, МаИаЪ Simulink, суперконденсатор, математическая модель, симуляция

Цитирование: Сайфулин, Р. Ф. Суперконденсатор как буферный источник электроэнергии для асинхронного двигателя / Р. Ф. Сайфулин // Журн. Сиб. федер. ун-та. Техника и технологии, 2022, 15(8). С. 940-947. DOI: 10.17516/1999-494Х-0431

Introduction

Mathematical substitutions in the equations, as well as the used methods have shown the adequacy and correctness of their use. Analysis of the data, obtained from simulation modeling of the developed model, showed small discrepancies with the standart block from the Simulink library.

The use of the obtained mathematical equations, as well as the model assembled in Matlab Simulink, will make it possible to qualitatively evaluate the operation of an asynchronous drive in statics and dynamics.

This model will be used in the future research, including the creation of a buffer power source based on a supercapacitor for an asynchronous electric drive.

The electromechanical properties of an asynchronous electric motor are most easily and conveniently studied using mathematical modeling, which determines the relevance of the topic accepted for consideration.

At present, the development of mathematical methods for the study of electrical machines is associated with the widespread use of computers, which makes it possible to implement the most complete models of transient processes with a minimum number of assumptions. The essence of the methods consists in the development system of a model and their implementation on a computer in the form of software systems for carrying out computational experiments in any possible conditions for the functioning of electrical machines. Possessing the simplicity of varying the structure and parameters of the design scheme, the mathematical model, with an appropriate level of adequacy, makes it possible to obtain, in the course of computational experiments, the necessary information for the development and design of electrical machines, their control and protection systems. However, as you know, the complexity of the phenomena, occurring in electric machines of alternating current during transient processes, makes their mathematical description and study without a number of simplifying assumptions practically impossible. The desire to take into account the main factors that determine the properties of the machine, and neglect the secondary factors leads to the consideration of an idealized electrical machine. Such a machine is usually characterized by the absence of saturation, hysteresis and eddy currents in the magnetic circuit, the absence of current displacement in the winding conductors, complete symmetry of the stator windings and a number of other assumptions. [1] These are the assumptions that are made when simulating the operation of an asynchronous electric motor in Matlab Simulink when choosing default blocks from the Simscape/Machines library. For more accurate results of electromechanical processes, flowing in an asynchronous electric motor, it is proposed to use a model of an electric motor in a rotating coordinate system. At the same time, there are

various ways of calculating this model. [2,3,4,5,6,7] However, these methods use vector multiplication, Euler transformations, and the substitutions that are made when calculating differential equations lead to a large number of terms in the equation. Therefore, this article proposes the calculation of the asynchronous motor model in a rotating coordinate system during the transition from a three-phase system to a two-phase one.

Mathematical calculation of the induction drive model

Initially, the induction drive is a three-phase electric machine with an implicit-pole rotor, it is proposed to simplify this model to a two-phase one. To simplify the mathematical description of induction drive, the space vector method turned out to be suitable. The method allows linking the rotor flux linkage equations into a single sysOem with vector state variables. The essence of the method is that the instantaneous values of symmetric threeophaso otate variables (voltage, currents, flux linkage) can be mathematically transforme° to it°tiitt thep are reptoppnted by one space vector. We represent a system of equations wioh yeotot state vpaMileh foo the ctrr; with an arbitrary orientation of the coordinate system.

ptp

OoeeoPt -py PhSo (Ut

ppth

00oeeoToP pTC P-jOet^00)% ().2)

vpyppep+tthtp ().3)

O =yott PphOr (1 •()

hy-Mode-*0^ (1.5)

—,p*—

dp ~ yhhc ().()

Here 00o, Uo, tp, eo, ¥p and V are two-element vectors of voltages, currents and flux linkages, presented in an arbitrarily oriented orthogonal (two-phase) coordinate system in the form of components along the coordinate axes. The variable is used to set an arbitrary frequency of rotation of the coordinate sysaem. Tlie auxilioiy motrix constant j seraes to "flip" the components of vector variables and simplifies the Oorm of writmg tve tyttem o"eqhatioas. cs, rR o Rusiltauoe o5 tto1or and rotor, m-toeque.

Утpaedieo ate eanreet o0 sypct veetort, fluc iinkogc equation- 1.3, I.O hre substituted into the stator and rotor voltage foemutot, wWlp equatip. 1.^ to zero" tmce the electric motor is short-circuire d.

vt v p(peeeptthio" .m -s-

0 eypo" p p-h"-prakephtppppty) (2(

sf) -a ^¿-o^ts) . -p lPs p •

SlfyeorsP-a-"--p/(ai4^tie1,-t.)rrltl^^f^tl«^t,t )y0 (3)

Thechange intherotorcurrentvectorisexpressedfromequation 3

Peo ea t-o 0o pea . Tf . Ph u. o „ 0tto

t =-helo-pr-dI-oPPotTasprto ^O^ (4)

- pop -

;_, —-e

dt TR

xs-di—n R

P) ~)—P(-P- TR

m =kR( YrJ sir ^Rpi Sa) (15) Space vectors of stator voltage, sSator current, rotor flux linkage can be described by (h)S) equations

Ur=Uss+jUta (s6.°s

PanPRt+j.PRy (16.3)

A( a result c^f (¡liii^s:^, siri)^t;(tutiioni^ tiird tri(ni5fo^ni^t;ioiis, tRe sij^stysLs of .quahicns gO-Of, wh(c3 mat^«2n:iotica(l}t describeatho wori( ok 3he intli^^^io:!! drive in a rotating nooKli)^;it;(i system, wfH take the followm;: now form

n=nern0S+r-i::n-tO=sin-m WRyCpSJiRO0- (S7.2)

P 1 _, d¥Rx _. _>

U=n0n -kpORiro-rak-p9m) (S73)

— _, dO — _>

U=en0n-R =S-C~Ct -k-=RisoCWi«) =-n (S7.4)

m nk'nuo^p) (17.5)

-> dim

Th~nm-mc (S7.0)

Accepting TS=XS the system ofeqnat-onsl7.L-S7.n tradsxoriasintooperatorforn

55 r ko

^^O^sPM&c-a-dkity-nf-URx-PfmkRURx (S7.S)

- R

UcsnR1r+1p—)iRc+Pnm—n-- — URccpmmkoURx (S7.2)

1R

a-0) C- P+Tr) UR^koRRUx-Crk-pP,: = U=x (S8.3)

-R

ta 1

U+n(n= — (I + +-p) (—u-xiCap-pR)) U-n (S8.5)

-R

mnnOnF-mimF)0) (.8.5)

xTmPRmnm-mc (S8.0) From equationsS8.S,S8.2tgestatorcurrentisexpressed

, PR 1

Ticn(UU macn1 i1- URr-PpmkR PR-) fl ^ x (S9) -R R(t1+TlPt

- CRR p

. ( ' . dy \ 1

iay = ( Uay-adxaiax + ^r x^yy-p^mdn lFyx I^T.

V vn )r(1+Tap)

And from equations 18.3, 18.4 the rotor flux linliiig^ is? expressed

dn

y , (20)

^.RWsx+CC-TPT XXyx1e- (21)

TR

1+TrP

The speed from equation 1R.6 will Re 1

9m = =^8m-mc) (23)

TmP

Thus, from the obtained final equations 19-23, a mathematical model of induction drive in a rotating coordinate system was created. At the same time, this model was transformed from a three-phaseintoatwo-phaseone - Fig.1.

' 9848/0.2956

8"0.2205^>—W 0.2956

0.2956s +1 .

Fig. 1. Model assembled in Simulink

Imitation modeling

In this papee, o model 6f an AIR 160S 4 induction electric motwwis considered with the following parameters presentedinTaRle 1.

Table 1. AIR 160S 4 parameters

Motor Pewer, Speem, \rol1;£iid<i.> ^fficiisncy, Powow 4 Ms M 11 max Mom4ntof

kW rpm V % factoa In Mn Mn in4rtia, kgm2

AIR 160S 4 15 1450 4ff R9.5 0.R6 7,7 2.2 2.6 0.075

To assess the adequacy and correctness of the assembled model, it was proposed to compare it with the induction motor model from the standard Simulink/Simscape library - Fig.2.

The rotor speed and the torquedeveloped ss the motors areshownin the Fig.3forthe model ina rotating cmrdinatinystem - Wnt anofor s^a^c^eKi modm! - orange.

.1

MH Tm-1 t y

M^.-s

I

1 «Rotor speed (wm)> | 1 1

1 iEleclromagnettc torque te (N*m)>

Fig. 2. Standard model of an induction motor in Simulink

2000

1500

Q. 1000

a. 500 to

Speed

-500

0 0.05 0.1 0.15 0.2 0.25 0.3 Time, s

(a)

(b)

(c)

Fig. 3. Output characteristics of electric drives: a - speed, b - torque, c - stator current

- aaa -

From the obtained characteristics, it can be seen that the output values coincide, and the processes take place at the same time. However, the system from the standard library is more oscillatory, so the model in the rotating coordinate system has a better transient process. It is planned to compare these models with a real electric drive to obtain the most accurate results in further researchesi

Conclusion

Mathematical substitutions in the equations and the used methods have shown the adequacy and correctness of their use. Analysis of the data, obtained from simulation modeling of the developed model, showed small discrepancies with the standard block from the Simulink library. The use of the obtained mathematical equations, as well as the model assembled in Matlab Simulink, will make it possible to qualitatively evaluate the operation of an induction drive in statics and dynamics. This model will be used in future research, including the creation of a buffer power source based on a supercapacitor for an induction electric drive.

References

[0] Galiev E. A. Mathematical modeling of an induction motor with variable ir - ys. Yekaterinburg, 2017, 64.

[2] Schreiner R.T. AC drives based on direct frequency converters with PWM. Yekaterinburg, 2012, 222.

[3] Sokolovsky G.G. AC drives with frequency control. Moscow, 2006, 272.

[4] Petrushin V. S. Induction motors in a controlled electric drive. Odessa, 2006, 320.

[5] Kopylov I. P. Design of electrical machines. Moscow, 1980, 496.

[6] Klyuchev V. I. Theory of electric drive. Moscow, 0985, 560.

[7] Veinger A. M., Designing of electric drives. Sverdlovsk, 1980, 160.

[8] Dineva A. Mosavi A. Ardabili S. F. Review of soft computing models in design and control of rotating electrical machines. In: Energies, 2019, 12(6), 1049.

[9] Omar Faruque M. D., Strasser T., Lauss G. Real-time simulation technologies for power systems design, testing, and analysis. In: IEEE Power and Energy Technology Systems Journal, 2015, 2(2), 63-73.

[10] Wang L., Jatskevich J., Dinavahi V., Methods of interfacing rotating machine models in transient simulation programs. In: IEEE Transactions on Power Delivery, 2010, 25(2), 891-903.

[11] Delaleau E., Louis J. P., Ortega R. Modeling and control of induction motors. In: International Journal of Applied Mathematics and Computer Science, 2001, 11, 105-129.

[12] Pronin M., Shonin O., Vorontsov A., Gogolev G., Nahdi T. A Double-Fed Induction Machine with a Multistage-Multilevel Frequency Converter for Pumped Storage Power Plant Applications. Proceedings of IEEE Power Engineering and Automation Conference (PEAM), 2011, 1(1), 221.