CC BY
42
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2014, № 2 (50)
ЕЛЕКТРИЧНИЙ ТРАНСПОРТ
UDC 629.423.31-048.24
A. M. AFANASOV1*, A. YE. DRUBETSKIY1, S. V. ARPUL1, A. P. KHVOROSTYANKINA1
1 Dep. «Electric Rolling Stock of Railways», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 373 15 31, e-mail afanasof@ukr.net 'Dep. «Electric Rolling Stock of Railways», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 373 15 31
ENERGY EFFICIENCY DETERMINATION OF LOADING-BACK SYSTEM OF ELECTRIC TRACTION MACHINES
Purpose. Acceptance post-repair tests of electric traction machines are conducted on loading-back stands that reduce the overall power costs for the tests. Currently a number of possible circuit designs of loading-back systems of electric machines are known, but there is no method of determining their energy efficiency. This in turn makes difficult the choice of rational options. The purpose of the article is the development of the corresponding methodology to make easier this process. Methodology. Expressions for determining the energy efficiency of a stand for testing of electric traction machines were obtained using the generalized scheme analysis of energy transformations in the loading-back systems of universal structure. Findings. The technique was offered and the analytical expressions for determining the energy efficiency of loading-back systems of electric traction machines were obtained. Energy efficiency coefficient of loading-back system is proposed to consider as the ratio of the total action energy of the mechanical and electromotive forces, providing anchors rotation and flow of currents in electric machines, which are being tested, to the total energy, consumed during the test from the external network. Originality. The concept was introduced and the analytical determination method of the energy efficiency of loading-back system in electric traction machines was offered. It differs by efficiency availability of power sources and converters, as well as energy efficiency factors of indirect methods of loss compensation. Practical value. The proposed technique of energy efficiency estimation of a loading-back system can be used in solving the problem of rational options choice of schematics stands decisions for electric traction machines acceptance tests of main line and industrial transport. Keywords: electric traction machines; tests; loading-back; power losses; energy efficiency
Introduction
Requirements of the relevant standards and regulations for repair of locomotives provide for
acceptance testing of each newly manufactured
electric traction machine or machine after repair [3]. These tests are an important and integral part of technical process of production or repair of electric traction machine, the material costs for which are included in the cost of final product [10].
Technical quality control, which is conducted during the acceptance tests of electric traction machines, ultimately determines the reliability and dependability of the hauling plant as a whole and,
consequently, the cost-effectiveness of railway transportations of mainline and industrial vehicles.
The loading-back systems (where the energy exchange between the tested machines takes place) provide high energy efficiency of the tests with relatively low total power of power supply sources. External power sources in such loading-back systems are needed only to cover the power losses in the tested electric machines [4].
Reduction of power consumption for acceptance post-repair tests of electric traction machines is one of the urgent problems on repair enterprises of traction rolling stock of mainline and industrial
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2014, № 2 (50)
vehicles. Thermal tests of electric traction machines on the test bench of loading-back are the most energy-intensive part of the entire test program. Energy consumption for this type of tests can be reduced both by increasing the energy efficiency of the loading-back system and by optimizing the mode of loading of electric traction machines [11, 13, 12].
Purpose
The purpose of this research is to develop the methods for determining the energy efficiency of loading-back systems of electric traction machines.
Methodology
The term energy efficiency is generally understood as the rational use of energy resources during some technological process.
The most known index of energy efficiency of a device performing useful work is its efficiency coefficient. That is the ratio of this useful work to the energy consumption from the network.
Despite the fact that the loading-back system does not perform useful work, the fact of the load current flow of electric machines and rotation of their anchors is the purpose of loading-back process, namely, providing the tests of electric machines tests under loading [9].
Thus, the energy efficiency of the loading-back system can be considered as the ratio of the total energy of mechanical and electromotive forces providing anchors rotation and the flow of currents in tested electric machines to the total energy consumed during the test from the external network.
In general, the energy efficiency coefficient of loading-back system can be represented as
*эфс _
4
атр
where Anon h A,, are the useful and consumed
energy accordingly.
Consumed energy A3aTp does not require detailed explanation, but, nevertheless, one should note that it will be considered as the total amount of electricity consumed during the test of electric traction machines by all the sources of system from the three-phase AC network.
The issue of what should be considered as a useful energy consumed for the test requires de-
tailed observation. If the purpose of loading-back is to ensure the load current flow and anchors (rotors) rotation, the useful power is the total power of all kinds of losses in the tested electric machines. Covering all the power losses in electric machines is the main purpose of energy sources in the system of loading-back [8]. From this point of view, the useful power of sources of loading-back system is
P™ =lAPflr ,
where ^APgr is the total power losses in the
tested electric machines (engine and generator).
Then the energy efficiency coefficient of the loading-back system is
iE
AP
k =-0_
кэфс t1
i E
0
where V P - the total power consumed by the loading-back system from the network; t1 - is the testing time.
Total power consumption V P is consumed to cover the total power losses in the tested electric machines ^APflr and the total losses in regulators
and converters V APpn
¿—l pn
V P = V APgr + V APpn .
The energy efficiency of the loading-back system, as it was shown above, is the ratio of the total power losses in the tested electric traction machines meeting the parameters of adopted loading mode to the total power consumed by the power supply sources of loading-back system from the network. The nature of dependence of this indicator on the structure of the loading-back system can be determined by the universal scheme of energy transformations shown in Fig. 1.
This scheme is universal and takes into account all the possible options to cover the power losses in the tested electric machines [9]:
- direct covering of electric losses;
- indirect covering of electric losses;
- direct covering of idling losses;
- indirect covering of idling losses.
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2014, № 2 (50)
power converter and the MPC. Transmission of mechanical power Pg from the tested engine E to
the tested generator G is carried out through the MPC converter; when transmission of the electric power Pr from the tested generator G to the engine E is carried out though the EPC converter.
Energy transformation loop, including the conditional part of engine E, conditional part of generator G, and the converters MPC and EPC is the main one. Total losses in the tested engine and generator caused by transformations in this loop, represent a useful power of the loading-back system.
I
ДРдг =ДРд + Д.
Fig. 1. Universal scheme of energy transformations in the loading-back system of electric traction machines
The scheme provides the variants of electrical and mechanical power transmission in the main power conversion loop using converters of electric and mechanical power, respectively.
Electric power source ES compensates electric losses in loading-back system by direct process, when the electric power source ES' compensates idling losses by indirect way. The source of mechanical power MS covers idling losses in the system directly, when the source of mechanical power MS' covers electrical losses indirectly. All four possible power sources are connected to the network «N».
The tested engine is conventionally divided into two parts: fl and fl'. A conditional part fl is included into the main loop of power transformations, and the part D' is a conditional converter of ES' source electric power into mechanical power transmitted to generator G [5]. The tested generator is also conditionally divided into two parts: G and G'. Conditional part G is included into the main loop of power transformations, when the part G' is a conditional converter of MS' source mechanical power into electric power transmitted to the engine E.
Transmission of power PH3 of ES source to the engine E is carried out directly, when the transmission of power P^ of the ES' source to generator G is carried out through the engine E' and mechanical
Total power, consumed by loading-back system from the network,
IP = P + P2 + P3 + P4,
where P1, P2, P3, P4 are the powers, consumed from the network by the sources ES, ES', MS, MS' accordingly.
In accordance with the energy transformation scheme shown in Fig. 1, the power balance can be represented as
IP = IAP +AP + AP' +AP +
/ v / v gr H3 H3 hm
+AP' +AP +AP +AP' + AP",
hm npM np3 g r '
where APH3, AP' , APhm , AP' are the power
H3 ' H3 ' hm ' hm r
losses in the sources ES, ES', MS, MS' accordingly; APnpM, APnp3 are the losses in converters of
mechanical and electric power accordingly; APg', AP" are the additional power losses in the tested engine and generator accordingly.
Findings
Coefficient of energy efficiency of loading-back system can be represented as
I AP
Lu g"_
¿эфс =
ЕДРдг +1ДРрп '
where
YAP =AP +AP' +AP
/ у рп иэ иэ им
+AP' + AP + AP
им прм прэ
■ap;+ap; .
Наука та прогрес транспорту. Вкник Дншропетровського нащонального ушверситету з^зничного транспорту, 2014, № 2 (50)
Power losses in the sources and converters are determined by their efficiency and net power at the output required for the operation of loading-back system in the set mode [7].
Note that the diagram in Fig. 1 is universal and takes into account all possible energy transformations in the loading-back system. For a particular electromechanical loading-back system most of elements of the given energy scheme will be absent. The coefficient of energy efficiency k3^c will
be determined by the efficiency of the sources of ES, ES', MS, MS', converters EPC, MPC, and by the energy efficiency coefficients of power transformations in the conventional parts E' and G'.
The energy efficiency coefficient of transformation of electric power PH'3 into mechanical one Pg' in the engine E' can be represented as [2]
= P
nnpi p,
H3
or
=1-APL
nnp1 = 1 P, •
H3
The energy efficiency coefficient of mechanical power Ph'm transformation into electrical one Pr' in the generator G' can be represented as [1]
nnp 2 = pi
hm
or
= 1-AP
nnp 2 = 1 P, ■
hm
It should be noted that the additional losses APg' and APr' are connected with energy process parameters in the main loop, i.e. they are dependent on Pg and Pr correspondingly. Also note that
in almost all variants of loading-back systems at least one of the indirect compensation methods of at least one of the loss types in the tested electric machines is used [9].
Coefficients nnp1 and nnp2 together with efficiency of all power sources and converters determine the total energy efficiency of loading-back
system k3^c .
Originality and practical value
It was introduced the concept and proposed the method of analytical determination of the energy efficiency of the loading-back system of traction electric machines. It differs by considering the efficiency of power sources and converters, as well as energy efficiency coefficient of indirect methods to cover losses.
The proposed evaluation methodology of energy efficiency of loading-back system can be used to solve the choice problem of rational circuit design of stands for acceptance testing of electric traction machines of mainline and industrial vehicles.
Conclusions
Energy efficiency of loading-back system is determined by efficiency of power sources and converters, as well as the energy efficiency of indirect methods of loss cover. The losses depend on the share of particular type of loss in the total power loss in the tested electric traction machine.
Reduction of electric energy consumption for electric traction machines testing can be achieved by means of both the choice of rational loading modes [6], and the optimization of the structure of loading-back system.
Minimization of total energy consumption for testing of electric traction machines can be achieved by reducing the number of successive power transformations in auxiliary devices or refusal from such transformations. The most rational seems to be a solution to cover all the losses by a single source of energy. This can be a source of both electrical and mechanical power [9]
LIST OF REFERENCE LINKS
1. Афанасов, А. М. Энергетические показатели механического способа компенсации электрических потерь в тяговых электродвигателях при их взаимной нагрузке / А. М. Афанасов // Вюн. Дншропетр. нац. ун-ту залiзн. трансп. iM. акад. В. Лазаряна. - Д., 2010. - Вип. 35. -С. 69-73.
2. Афанасов, А. М. Энергетические показатели электрического способа компенсации магнитных и механических потерь в тяговых электродвигателях при их взаимной нагрузке / А. М. Афанасов // Вкн. Дншропетр. нац. ун-ту залiзн. трансп. iM. акад. В. Лазаряна. - Д., 2010. - Вип. 34. - С. 65-68.
Наука та прогрес транспорту. Вкник Дншропетровського нащонального ушверситету залiзничного транспорту, 2014, № 2 (50)
3. ГОСТ 2582-81. Машины электрические вращающиеся тяговые. Общие технические условия. - Введ. 1983-01-01. - М. : Изд-во стандартов, 1981. - 34 с.
4. Жерве, Г. К. Промышленные испытания электрических машин / Г. К. Жерве. - Л. : Энерго-атомиздат, 1984. - 408 с.
5. Захарченко, Д. Д. Тяговые электрические машины : учеб. пособие для вузов / Д. Д. Захарченко, Н. А. Ротанов. - М. : Транспорт, 1991. -343 с.
6. Лоза, П. О. Визначення е^валентного струму навантаження при випробовуванш тягових електродвигушв на названия без вентиляцп / П. О. Лоза, Л. В. Дубинець, Д. В. Устименко // Вюн. Дншропетр. нац. ун-ту залiзн. трансп. iм. акад. В. Лазаряна. - Д., 2008. - Вип. 25. -С. 26-29.
7. Лоза, П. О. Покращення енергетичних власти-востей стенда для випробувань колекторних тягових двигушв локомотивiв / П. О. Лоза // Вюн. Дншропетр. нац. ун-ту залiзн. трансп. iм. акад. В. Лазаряна. - Д., 2008. - Вип. 22. -С. 69-71.
8. Лоза, П. О. Покращення енергетичних та ш-ших показнишв приймально-здавальних ви-
пробувань тягових двигушв електровозiв / П. О. Лоза // Вюн. Дншропетр. нац. ун-ту за-лiзн. трансп. iM. акад. В. Лазаряна. - Д., 2009. -Вип. 27 - С. 81-83.
9. Магистральные электровозы. Тяговые электрические машины / В. И. Бочаров, Г. В. Василенко, А. Л. Курочка, В. П. Янов. - М. : Энер-гоатомиздат, 1992. - 464 с.
10. Правила ремонту електричних машин електро-возiв i електропо1здв : ЦТ-0204. - К. : Вид. дiм «САМ», 2012. - 286 с.
11. Castaneda, C. E. Discrete-Time Neural Sliding-Mode Block Control for a DC Motor With Controlled Flux / С. Е. Castaneda, A. G. Loukianov, E. N. Sanchez // IEEE Transactions. Industrial Electronics. - 2012. - Vol. 59. - Iss. 2. -P.1194-1206.
12. El Hayek, J. Experiences with a traction drive laboratory model / J. El Hayek, T. J. Sobczyk, G. Skarpetowski // Electromotion. - 2010. -Vol. 17. - Iss. 1. - P. 30-36.
13. Liu, Y. Developments in Switching Mode Supply Technologies / Y. Liu, W. Eberle // IEEE Canadian Review. Switching Mode Power Supplies. Fall. - 2009. - № 61. - P. 9-14.
А. М. АФАНАСОВ1*, А. Е. ДРУБЕЦКИЙ1, С. В. АРПУЛЬ1, А. П. ХВОРОСТЯНКИНА1
1 Каф. «Электроподвижной состав железных дорог», Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (056) 373 15 31, эл. почта afanasof@ukr.net
'Каф. «Электроподвижной состав железных дорог», Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (056) 373 15 31
ОПРЕДЕЛЕНИЕ ЭНЕРГЕТИЧЕСКОЙ ЭФФЕКТИВНОСТИ СИСТЕМЫ ВЗАИМНОГО НАГРУЖЕНИЯ ТЯГОВЫХ ЭЛЕКТРИЧЕСКИХ МАШИН
Цель. Приёмо-сдаточные послеремонтные испытания тяговых электромашин проводятся на стендах взаимной нагрузки, которые позволяют снизить общие затраты электроэнергии на испытания. В настоящее время известен целый ряд возможных схемных решений систем взаимного нагружения электромашин, однако отсутствует методика определения их энергетической эффективности. Это, в свою очередь, затрудняет выбор рациональных вариантов. Целью работы является разработка подходящей методики, которая упростит соответствующий процесс. Методика. Выражения для определения энергетической эффективности стенда для испытания тяговых электромашин получены путем анализа обобщенной схемы энергетических преобразований в системе взаимного нагружения универсальной структуры. Результаты. Предложена методика и получены аналитические выражения для определения энергетической эффективности системы взаимного нагружения тяговых электромашин. Коэффициент энергетической эффективности системы взаимного нагружения предложено рассматривать как отношение общей энергии действия механических и электродвижущих сил, обеспечивающих вращение якорей и протекание токов в испытуемых электромашинах, к суммарной энергии, потребленной за время испытания из внешней сети. Научная новизна. Введено понятие и предложен метод аналитического определения энергетической эффективности системы взаимного нагружения тяговых электрических машин, отличающийся учётом в нем к. п. д. источников и преобразователей мощности, а также коэффициентов энергетической эффективности косвенных методов ком© А. М. Afanasov, А. Уе. Бпи^Ыу, 8. V. Агри1, А. Р. Khvorostyankina, 2014
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2014, № 2 (50)
ЕЛЕКТРИЧНИИ ТРАНСПОРТ
пенсации потерь. Практическая значимость. Предложенная методика оценки энергетической эффективности системы взаимного нагружения может быть использована при решении задачи выбора рациональных вариантов схемных решений стендов для проведения приёмо-сдаточных испытаний тяговых электромашин магистрального и промышленного транспорта.
Ключевые слова: тяговые электромашины; испытания; взаимная нагрузка; потери мощности; энергетическая эффективность
А. М. АФАНАСОВ1*, А. е. ДРУБЕЦЬКИЙ1, С. В. АРПУЛЬ1, А. П. ХВОРОСТЯНК1НА1
1 Каф. «Електрорухомий склад затзниць», Дтпропетровський нацюнальний ушверситет з^зничного транспорту iменi академiка В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Украша, 49010, тел. +38 (056) 373 15 31, ел. пошта afanasof@ukr.net
'Каф. «Електрорухомий склад залiзниць», Дтпропетровський нацiональний унiверситет залiзничного транспорту iменi академiка В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Украша, 49010, тел. +38 (056) 373 15 31
ВИЗНАЧЕННЯ EHEPrETO4HOÏ ЕФЕКТИВНОСТ1 СИСТЕМИ ВЗАеМНОГО НАВАНТАЖЕННЯ ТЯГОВИХ ЕЛЕКТРИЧНИХ МАШИН
Мета. Приймально-здавальт пiсляремонтнi випробування тягових електромашин проводяться на стендах взаемного навантаження, як1 дозволяють знизити загальш витрати електроенергiï на випробування. Сьогодш ввдомий цiлий ряд можливих схемних рiшень систем взаемного навантаження електромашин, проте вiдсутня методика визначення 1'х енергетично1 ефективностi. Це, в свою чергу, ускладнюе вибiр рацюнальних варiантiв. Метою роботи е розробка пiдходящоï методики, яка спростить вщповвдний процес. Методика. Вирази для визначення енергетичноï ефективностi стенда для випробування тягових електромашин отримано шляхом аналiзу узагальнено1' схеми енергетичних перетворень у системi взаемного навантаження унiверсальноï структури. Результата. Запропоновано методику й отримано аналггичш вирази для визначення енергетично1' ефективностi системи взаемного навантаження тягових електромашин. Коефщент енергетично1' ефективностi системи взаемного навантаження рекомендовано розглядати як вщношення загально1' енергп дiï мехашчних та електрорушiйних сил, що забезпечують обертання якорiв i протiкання струмiв у випробовуваних електромашинах, до сумарно1' енергiï, спожшш за час випробування iз зовнiшньоï мереж1. Наукова новизна. Введено поняття й запропоновано метод аналггачного визначення енергетично1' ефективностi системи взаемного навантаження тягових електричних машин, який вiдрiзняеть-ся урахуванням у ньому к. к. д. джерел i перетворювачiв потужностi, а також коефiцiентiв енергетично1' ефективностi непрямих методiв компенсацiï втрат. Практична значимiсть. Запропонована методика оцiнки енергетично1' ефективностi системи взаемного навантаження може бути використана при виршенш задачi вибору рацюнальних варiантiв схемних рiшень стендiв для проведення приймально-здавальних випробувань тягових електромашин мапстрального й промислового транспорту.
Ключовi слова: тяговi електромашини; випробування; взаемне навантаження; втрати потужностi; енерге-тична ефективнiсть
REFERENCES
1. Afanasov А.М. Energeticheskiye pokazateli mekhanicheskogo sposoba kompensatsii elektricheskikh poter v tyagovykh elektrodvigatelyakh pri ikh vzaimnoy nagruzke [Energy indicators of compensation mechanical method of electric losses in traction motors at their mutual load]. Visnyk Dnipropetrovskoho natsionalnoho universytetu zaliznychnoho transportu imeni akademika V. Lazariana [Bulletin of Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan], 2010, issue 35, pp. 69-73.
2. Afanasov А.М. Energeticheskiye pokazateli elektricheskogo sposoba kompensatsii magnitnykh i mekhani-cheskikh poter v tyagovykh elektrodvigatelyakh pri ikh vzaimnoy nagruzke [Energy indicators of compensation mechanical method of magnetic and mechanical losses in traction motors at their loading back]. Visnyk Dnipropetrovskoho natsionalnoho universytetu zaliznychnoho transportu imeni akademika V. Lazariana [Bulletin of Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan], 2010, issue 34, pp. 65-68.
Наука та прогрес транспорту. Вкник Дншропетровського нащонального ушверситету залiзничного транспорту, 2014, № 2 (50)
3. GOST 2582-81. Mashiny elektricheskiye vrashchayushchiyesya tyagovyye. [State Standard 2582-81. Rotating electrical machines for rail and road vehicles]. Moscow, Standartinform Publ., 1981. 34 p.
4. Zherve G.K. Promyshlennyye ispytaniya elektricheskikh mashin [Industrial testing for electrical machines]. Leningrad, Energoatom Publ., 1984. 408 p.
5. Zakharchenko D.D., Rotanov D.D. Tyagovyye elektricheskiye mashiny [Traction electric machines]. Moscow, Transport Publ., 1991. 343 p.
6. Loza P.O., Dubynets L.V., Ustymenko D.V. Vyznachennia ekvivalentnoho strumu navantazhennia pry vyprobovuvanni tiahovykh elektrodvyhuniv na nahrivannia bez ventyliatsii [Determination of equivalent current load under traction electric motors tests for heating without ventilation]. Visnyk Dnipropetrovskoho natsionalnoho universytetu zaliznychnoho transportu imeni akademika V. Lazariana [Bulletin of Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan], 2008, issue 25, pp. 26-29.
7. Loza P.O. Pokrashchennia enerhetychnykh vlastyvostei stenda dlia vyprobuvan kolektornykh tiahovykh dvy-huniv lokomotyviv [Improving of stand energy properties for collector locomotive traction motors test]. Visnyk Dnipropetrovskoho natsionalnoho universytetu zaliznychnoho transportu imeni akademika V. Lazariana [Bulletin of Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan], 2008, issue 22, pp. 69-71.
8. Loza P.O. Pokrashchennia enerhetychnykh ta inshykh pokaznykiv pryimalno-zdavalnykh vyprobuvan tiahovykh dvyhuniv elektrovoziv [Improving energy and other indicators of acceptance tests of electric locomotives traction motors]. Visnyk Dnipropetrovskoho natsionalnoho universytetu zaliznychnoho transportu imeni akademika V. Lazariana [Bulletin of Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan], 2009, issue 27, pp. 81-83.
9. Bocharov V.I., Vasilenko G.V., Kurochka A.L., Yanov V.P. Magistralnyye elektrovozy. Tyagovyye elek-tricheskiyye mashiny [Mainline electric locomotives. Traction electric machines]. Moscow, Energoatom Publ., 1992. 464 p.
10. Pravyla remontu elektrychnykh mashyn elektrovoziv i elektropoizdiv. [Repair rules of electric machines of electric locomotives and electric trains]. Kyiv, Vydavnychyi dim «SAM», 2012. 286 p.
11. Castaneda C.E., Loukianov A.G., Sanchez E.N. Discrete-Time Neural Sliding-Mode Block Control for a DC Motor With Controlled Flux. IEEE Transactions. Industrial Electronics, 2012, vol. 59, issue 2, pp. 1194-1206.
12. El Hayek J., Sobczyk T., Skarpetowski G. Experiences with a traction drive laboratory model. Electromotion, 2010, vol. 17, issue 1, pp. 30-36.
13. Liu Y., Eberle W. Developments in Switching Mode Supply Technologies. IEEE Canadian Review. Switching Mode Power Supplies. Fall, 2009, no. 61, pp. 9-14.
Prof. Mukha A. N., D. Sc. (Tech.); Prof. Skrabets F. P., D. Sc. (Tech.) recommended this article to be
published
Received: Jan. 31, 2014
Accepted: March 17, 2014
