In this article the main stages of the formation and development of the department «Automation and Telemechanics», celebrating the 60th anniversary of its founding, are presented. The history and people who made the most significant contribution to the creation of the department are described. A brief description of the areas and specialties of training implemented at the department, as well as the main results of educational and research activities are presented.

Keywords: automation and telemechanics, control, telecommunications, information security.

Zanevskii Eduard Slavomirovich (Perm, Russian Federation) is a Ph.D. in Technical Sciences, Associate Professor, Professor Department of Automation and Telemechanics Perm National Research Polytechnic University (614990, Perm, 29, Komsomolsky pr., e-mail: zanevskii38@mail.ru).

Freyman Vladimir Isaakovich (Perm, Russian Federation) is a Doctor of Engineering Sciences, Professor, Deputy of the Head of the Chair «Automatic and Telemechanics» Perm National Research Polytechnic University (614990, Perm, 29, Komsomolsky pr., e-mail: vfrey@mail.ru).

Yuzhakov Alexander Anatolevich (Perm, Russian Federation) is a Doctor of Technical Sciences, Professor, Head of the Department of Automation and Telemechanics Perm National Research Polytechnic University (614990, Perm, 29, Komsomolsky pr., e-mail: uz@at.pstu.ru).

1. Matushkin N.N., Freiman V.I., Iuzhakov A.A., Danilov A.N., Kon E.L., Lobov N.V. Praktika razrabotki i primeneniia samostoiatel'no ustanavlivaemykh obrazovatel'nykh standartov i programm vysshego obrazovaniia [Practice of independently established standards for higher education and programs development and application]. Vysshee obrazovanie v Rossii, 2014, no. 6, pp. 5-13.

2. Kon E.L., Matushkin N.N., Freiman V.I., Iuzhakov A.A. Proektiro­vanie i realizatsiia setevykh magisterskikh programm po perspektivnym napravleniiam nauki, tekhniki i tekhnologii [Designing and realization of network master programs by science, technique and technology perspective directions]. Distantsionnoe i virtual'noe obuchenie, 2014, no. 8(86), pp. 79-89.

3. Danilov A.N., Kon E.L., Iuzhakov A.A., Andrievskaia N.V., Bezukladnikov I.I., Freiman V.I., Kon E.M. K voprosu o podgotovke i otsenke kompetentsii vypusknikov vysshei shkoly s ispol'zovaniem modulei «Vektor razvitiia napravleniia» i «Kvalifikatsionnye trebovaniia rabotodatelei» [To the question of preparing and evaluating the competencies of high school graduates using the modules “Vector of direction development” and “Qualification requirements of employers”]. Otkrytoe obrazovanie, 2012, no. 3, pp. 20-32.

4. Kon E.L., Freiman V.I., Iuzhakov A.A. Novye podkhody k podgotovke spetsialistov v oblasti infokommunikatsii [New approaches to preparing of specialists in infocommunications]. Vestnik Povolzhskogo gosudarstvennogo tekhnologicheskogo universiteta. Radiotekhnicheskie i infokommunikatsionnye sistemy, 2015, no. 1(25), pp. 73-89.

5. Freiman V.I. Organizatsiia izucheniia podkhodov k proektirovaniiu telekommunikatsionnykh setei [Organization of studying approaches to the design of telecommunication networks]. Vestnik Permskogo gosudarst­vennogo tekhnicheskogo universiteta. Elektrotekhnika, informatsionnye tekhnologii, sistemy upravleniia, 2011, no. 5, pp. 254-257.

6. Gavrilov A.V., Kon E.L., Freiman V.I. K voprosu ob upravlenii raspredelennymi geterogennymi mul'tivendornymi infokommunikatsionnymi sistemami [To the question of managing distributed heterogeneous multi-wender infocommunication systems]. Vestnik Permskogo gosudarstvennogo tekhnicheskogo universiteta. Elektrotekhnika, informatsionnye tekhnologii, sistemy upravleniia, 2011, no. 5, pp. 264-270.

7. Kon E.L., Freiman V.I., Iuzhakov A.A. K 60-letnemu iubileiu kafedry «Avtomatika i telemekhanika» Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta [To the 60th anniversary of the Department of Automation and Telemechanics of Perm National Research Polytechnic University]. Vestnik Povolzhskogo gosudarstvennogo tekhnologicheskogo universiteta. Radiotekhnicheskie i infokommuni­katsionnye sistemy, 2019, no. 4(44), pp. 85-91.

In connection with the development of the industrial complex, the development of new technologies, the increase in the extraction and processing of natural resources, as well as the study of new territories, there is a widespread use of a controlled electric drive and various types of electric energy converters in the world electric power industry, as well as a steady growth trend in their installed power. For these reasons, the issues of electromagnetic compatibility of the load with the supply network and ensuring the required quality of the converted electricity are particularly acute. A decrease in the quality of the converted electricity leads to a deterioration in energy performance, a decrease in productivity, a reduction in the life of electrical equipment, as well as an increase in the likelihood of an emergency. One of the effective ways to solve this problem is to use a cascade frequency converter, which allows the synthesis of high quality output voltage. Purpose: the development of circuit solutions and control algorithms for a cascade frequency converter that will allow the synthesis of high quality output voltage. Methods: on the basis of number-theoretic methods, theoretical foundations of electrical engineering, fundamentals of power electronics and positional number system, the study of options and ways to increase the possible number of levels of instantly synthesized voltage at the output of a cascade frequency converter was carried out. Results: proposed circuit solutions and control algorithms for a cascade frequency converter, which will improve the quality of the synthesized voltage. A mathematical description of the control algorithms of the unit cells of the cascade frequency converter, allowing to synthesize the required voltage. A quantitative and qualitative comparison of ways to improve the quality of the synthesized voltage at the output of a cascade frequency converter is presented, a histogram of the dependence of the number of synthesized voltage levels on the unit cell construction scheme, the number of cells and control algorithms is shown. The result of mathematical modeling of the phase voltage at the output of a cascade frequency converter synthesized using three two-level cells with differentiated supply voltage and control algorithms with summation and difference of cell voltages in phase is presented. Practical relevance: the proposed schemes and methods for improving the quality of the synthesized voltage at the output of the cascade frequency converter and the results of the studies can be used in the design and development of electric power converters with high quality output voltage. This allows you to increase energy efficiency and significantly improve the harmonic composition of the synthesized voltage.

Keywords: cascade frequency converter, quality of synthesized voltage, electromagnetic compatibility, cell, voltage level, voltage inverter, positional number system, differentiated cell power, pulse-width modulation.

Gelver Fedor Andreevich (Saint Petersburg, Russian Federation) is a Ph.D. in Technical Sciences, Associate Professor, Head of the laboratory of the branch “TsNII SET” Krylov State Research Center (196128, Saint Petersburg, 6, Blagodatnaya str.), Associate Professor “Electric drive and electrical equipment of shore installations” GUMRF named after Admiral S.O. Makarov (198035, Saint Petersburg, 5/7, Dvinskaya str., e-mail: gelver@bk.ru).

Belousov Igor Vladimirovich (Saint Petersburg, Russian Federation) is a Associate Professor of the Department “Electric Drive and Electrical Equipment of Coastal Installations” FSBEI HE “GUMRF named after Admiral S.O. Maka­rov (196128, Saint Petersburg, 1980, 5/7, Dvinskaya str.), leading engineer of the branch “TsNII SET” FGUP “Krylovskiy gosudarstvennyy nauchnyy tsentr” (196128, Saint Petersburg, 6, Blagodatnaya str., e-mail: ibel@bk.ru).

Samoseiko Veniamin Frantsevich (Saint Petersburg, Russian Federation) is a Doctor of Technical Sciences, Professor Department of the electric drive and electrical equipment onshore installations Admiral
S.O. Makarov State University of Maritime and Inland Shipping (198035, Saint Petersburg, 5/7, Dvinskaya str., e-mail: samoseyko@mail.ru).

1. Moskalenko V.V. Energoeffektivnost' kak vazhneishaia kharakteristika elektroprivoda i obsluzhivaemykh im tekhnologicheskikh protsessov [Energy efficiency as the most important characteristic of an electric drive and its technological processes]. Energosberezhenie sredstvami elektroprivoda. Doklady nauchno-metodicheskogo seminara. Moscow: Moskovskii energeticheskii institut, 2011, pp. 4-15.

2. Il'inskii N.F. Elektroprivod v sovremennom mire [Electric drive in the modern world]. Trudy 5-i Mezhdunarodnoi konferentsii po avtomatizi­rovannomu elektroprivodu (AEP–2007). Saint Petersburg, 2007, pp. 17-19.

3. GOST R 54130-2010. Natsional'nyi standart Rossiiskoi Federatsii. Kachestvo elektricheskoi energii. Terminy i opredeleniia [GOST R 54130-2010. National standard of the Russian Federation. The quality of electrical energy. Terms and Definitions]. Dostup iz spravochno-pravovoi sistemy Konsul'tantPlius.

4. Kartashev I.I., Tul'skii V.N., Shamonov R.G. et al. Upravlenie kachestvom elektroenergii [Power quality management]. Ed. Iu.V. Sharova. Moscow: Izdatel'skii dom Moskovskogo energeticheskogo instituta,
2006. 320 p.

5. Agunov A.V. Upravlenie kachestvom elektroenergii pri nesinu­soidal'nykh rezhimakh [Power quality management in non-sinusoidal modes]. Saint Petersburg: Sankt-Peterburgskii gosudarstvennyi morskoi tekhnicheskii universitet, 2009. 134 p.

6. Pronin M.V., Vorontsov A.G. Silovye polnost'iu upravliaemye poluprovodnikovye preobrazovateli (modelirovanie i raschet) [Power fully controlled semiconductor converters (modeling and calculation)]. Ed.
E.A. Krutiakova. Saint Petersburg: Elektrosila, 2003. 172 p.

7. Belousov I.V., Gel'ver F.A., Samoseiko V.F., Khomiak V.A. Shirotno-impul'snye preobrazovateli elektricheskoi energii [Pulse-width converters of electrical energy]. Saint Petersburg: Krylovskii gosudarstvennyi nauchnyi tsentr, 2019. 228 p.

8. Donskoi N., Ivanov A., Matison V., Ushakov I. Mnogourovnevye avtonomnye invertory dlia elektroprivoda i energetiki [Multilevel autonomous inverters for electric drives and energy]. Silovaia elektronika, 2008, no. 1, pp. 43-46.

9. Burdasov B.K., Nesterov S.A., Fedotov Iu.B. Mnogourovnevye i kaskadnye preobrazovateli chastoty dlia vysokovol'tnykh elektroprivodov peremennogo toka [Multilevel and cascade frequency converters for high-voltage electric drives of alternating current]. Apriori. Estestvennye i tekhnicheskie nauki, 2015, no. 5.

10. Lazarev G.B. Vysokovol'tnye preobrazovateli dlia chastotno-reguliruemogo elektroprivoda. Postroenie razlichnykh skhem [High voltage converters for variable frequency drive. The construction of various schemes] Novosti elektrotekhniki, 2005, no. 2(32), pp. 30-36.

11. Mikheev K.E., Tomasov V.S. Analiz energeticheskikh pokazatelei mnogourovnevykh poluprovodnikovykh preobrazovatelei sistem elektroprivoda [Analysis of energy indicators of multilevel semiconductor converters of electric drive systems]. Nauchno-tekhnicheskii vestnik informatsionnykh tekhnologii, mekhaniki i optiki, 2012, no. 1(77), pp. 46-52.

12. Shavelkin A.A. Kaskadnye mnogourovnevye preobrazovateli chastoty s uluchshennymi energeticheskimi kharakteristikami [Cascade multilevel frequency converters with improved energy characteristics]. Tekhnіchna elektrodinamіka: naukovo-prikladnii zhurnal. Tem. vipusk. Silova elektronіka і energoefektivnіst'. Kiev, 2010. part 1, pp. 65-70.

13. Khakim'ianov M.I., Shabanov V.A. Mnogourovnevyi preobrazovatel' chastoty s differentsirovannymi napriazheniiami urovnei i baipasnymi poluprovodnikovymi kliuchami [Multilevel frequency converter with differentiated voltage levels and bypass semiconductor switches]. Patent Rossiiskaia Federatsiia RU2510769 (2012).

14. Shreiner R.T., Krivoviaz V.K., Kalygin A.I. Razvitie vysokovol'tnykh kaskadnykh preobrazovatelei chastoty dlia elektroprivoda [Development of high-voltage cascade frequency converters for electric drive]. Trudy V Mezhdunarodnoi (16-i Vserossiiskoi) konferentsii po avtomatizirirovannomu elektroprivodu Sankt-Peterburgskogo gosudarstven­nogo politekhnicheskogo universiteta, 18-21 September 2007. Saint Petersburg, 2007, pp. 186-189.

15. Irusapparajan G., Periyaazhagar D. Asymmetric three-phase cascading trinary-DC source multilevel inverter topologies for variable frequency PWM. Circuits and Systems, 2016, 7, pp. 506-519, http://dx.doi.org/10.4236/cs.2016.74043

http://dx.doi.org/10.1109/TPEL.2004.826495

17. Mauricio Rotella, Gonzalo Peñailillo, Javier Pereda, Juan Dixon. PWM Method to Eliminate Power Sources in a Nonredundant 27-Level Inverter for Machine Drive Applications. IEEE transactions on industrial electronics. January 2009, vol. 56, no. 1, pp. 194-201.

18. Ramani K., Krishnan A. New hybrid 27 level multilevel inverter fed induction motor drive. International Journal of Recent Trends in Engineering, 2009, 2, pp. 38-42.

19. Mahato B., Mittal S., Nayak P. N-Level Cascade Multilevel Converter with optimum number of switches. International Conference on Recent Trends in Electrical, Control and Communication (RTECC), 2018, pp. 228-233.

20. Filatov V. Dvukh- i trekhurovnevye invertory na IGBT. Perspektivnye resheniia [Two- and three-level inverters on IGBT. Promising solutions]. Silovaia elektronika, 2012, no. 4, pp. 38-41.

21. Chekhet E.M., Mordach V.V., Sobolev V.N. Neposredstvennye preobrazovateli chastoty dlia elektroprivoda [Direct frequency converters for electric drive]. Kiev: Naukova dumka, 1988. 222 p.

22. Efimov A.A., Shreiner R.T. Aktivnye preobrazovateli v reguliruemykh privodakh peremennogo toka [Active Converters in AC Drives]. Novoural'sk: Novosibirskii gosudarstvennyi tekhnicheskii universitet, 2001. 250 p.

23. Gel'ver F.A. Aktivnyi preobrazovatel' kak sredstvo povysheniia energeticheskoi effektivnosti sistem elektroprivoda [Active converter as a means of increasing the energy efficiency of electric drive systems]. Trudy nauchno-tekhnicheskoi konferentsii molodykh uchenykh sotrudnikov Sankt-Peterburgskogo gosudarstvennogo universiteta vodnykh kommunikatsii,
1-7 June 2005. Saint Petersburg, 2005, vol. 1, pp. 100-104.

24. Efimov A.A., Bazarnov A.A., Glukhov V.A., Zinov'ev G.S. Matematicheskoe modelirovanie i ispytaniia opytnogo obraztsa aktivnogo vypriamitelia napriazheniia [Mathematical modeling and testing a prototype of an active voltage rectifier]. Krasnoiarsk: Sibirskii federal'nyi universitet, IKIT, 2013, pp. 128-134.

25. Gel'ver F.A., Belousov I.V., Samoseiko V.F. Grebnye elektricheskie ustanovki sudov bol'shoi moshchnosti [Rowing electrical installations of high power vessels]. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Elektrotekhnika, informatsionnye tekhnologii, sistemy upravleniia, 2019, no. 2(30), pp. 7-27.

26. Gel'ver F.A. Struktura elektrodvizhitel'noi ustanovki sudna bol'shoi moshchnosti [The structure of the electromotive installation of a ship of high power]. Rechnoi transport (XXI vek), 2018, no. 4(88), pp. 44-49.

This article is sanctified to the problem to technical diagnostics on a public electric transport and electrical equipment. By reason of absence of methodologies of timely control of the state of brush-collector knot (BCK) and acceptance of measures on renewal of the capable of working state, about 50-60 % comes in uselessness, not working to the complete term of exploitation. Perfection of construction of BCK, development of new and improvement of existent methods of increase of reliability of exploitation of BCK, is the actual task sent to the increase of longevity and faultlessness of work of electric motors on the whole. Purpose is to develop the improved brush-collector knot of electric motors of direct-current with enhances able reliability. Methods used for creation of mathematical model and development of methodology for estimation the electric motors refuses intensity and hardware takes into account all lacks of the considered analogues and allows to carry out monitoring on refuses and disrepairs of BCK of electric motors during work on a rolling stock. Results basic reliability indexes of BCK were expected. A mathematical model is worked out for the exposure of types of refuses of brush-collector knot taking into account his technical descriptions (size of pressure, beating, amplitude of vibration) influencing on reliability indexes in the process of exploitation. The scrutinous of efficiency of functioning of improved BCK electric motors program is worked out with enhance able reliability in the process of exploitation for the extension of his time of service. Practical relevance: the offered model on the basis of research of types of refuses of brush-collector knot of electric motors is worked out the improved construction of a brush knot, that allows to increase the resource of brush and bring down expenses on technical maintenance of electric motors in the process of exploitation. Recommendations offer for passing to repair of electric motors on the actual state for a rolling stock.

Keywords: reliability improvement, spectral method, component, conversion process, method, operating time, fault, possible states.

Filina Olga Alekseevna (Kazan, Russian Federation) is a Senior Lecturer Department of Electrotechnical Complexes and Systems Kazan State Energy University (420066, Kazan, 51, Krasnoselskaya str., e-mail: olga_yuminova83@mail.ru).

Tsvetkov Alexey Nikolaevich (Kazan, Russia) is a Ph.D. in Technical Sciences, Associate Professor Department of Electrotechnical Complexes and Systems Kazan State Energy University (420066, Kazan, 51, Krasnoselskaya str., e-mail: tsvetkov9@mail.ru)

Khusnutdinov Azat Nazipovich (Kazan, Russian Federation) is a Senior Lecturer Department of Electrotechnical Complexes and Systems Kazan State Energy University (420066, Kazan, 51, Krasnoselskaya str.,
e-mail: khusnutdinov.an.kgeu@mail.ru).

Logacheva Alla Grigoryevna (Kazan, Russian Federation) is a Ph.D. in Technical Sciences, Associate Professor Department of Electrotechnical Complexes and Systems Kazan State Energy University (420066, Kazan, 51, Krasnoselskaya str., e-mail: logacheva.alla@kgeu.ru).

1. Rylov Iu.A., Stepanov E.L., Filina O.A. Issledovanie resursa elektroshchetok tiagovykh elektricheskikh mashin [Research of a resource of the electric brushes of the traction electric machines]. Nauchnye problemy transporta Sibiri i Dal'nego Vostoka, 2010, no. 1, pp. 320-323.
2. Khusnutdinov A.N., Idiiatullin R.G., Aukhadeev A.E., Filina O.A. Opyt ekspluatatsii elektroshchetok s povyshennym resursom v real'nykh tekhnologicheskikh usloviiakh [Operating experience of the electric brushes with the increased resource under the real technological conditions]. Elektrotekhnicheskie sistemy i kompleksy, 2017, no. 1(34), pp. 56-59.
3. Litvinenko R.S., Aukhadeev A.E., Filina O.A. Issledovanie tekhnicheskoi nadezhnosti gorodskoi elektrotransportnoi sistemy [Investigation of the city electrical transport system technical reliability]. Transport: nauka, tekhnika, upravlenie, 2017, no. 8, pp. 60-71.
4. Filina O.A. Issledovanie ekspluatatsionnogo resursa elektro­shchetok elektrodvigatelia postoiannogo toka podvizhnogo sostava [Research of an operating resource of the DC electric motor electric brushes of a rolling stock]. Izvestiia vysshikh uchebnykh zavedenii. Problemy energetiki, 2017, vol. 19, no. 9-10, pp. 133-139.
5. Filina O.A., Tsvetkov A.N. Evaluation of the operational life of direct current motors. IOP Conference Series: Materials Science and Engineering, 2019, p. 012016.
6. Filina O.A., Tsvetkov A.N., Pavlov P.P., Radu D., Butakov V.M. Vibration model as a system of coupled oscillators in a direct current electric motor. Smart Energy Systems 2019 (SES-2019), E3S Web Conf., 2019, vol. 124, 02002. DOI: https://doi.org/10.1051/e3sconf/201912402002
7. Lifshits P.S., Bodrov I.I., Kubarev V.E. O nekotorykh itogakh rabot po povysheniiu nadezhnosti shchetok [On some of the results of brush reliability improvement works]. Promyshlennaia energetika, 1985, no. 2, pp. 42-45.
8. Khusnutdinov A.N., Butakov B.M., Khusnutdinova E.M. Operation of brushes with increased service life on traction machines of electric vehicles. IOP Conf. Series: Materials Science and Engineering, 2019, vol. 570, p. 012053. DOI:10.1088/1757-899X/570/1/012053
9. Khusnutdinov A.N., Idiiatullin R.G., Vdovin A.M., Popov A.V. Issledovanie vliianiia ekspluatatsionnykh faktorov na temperaturnoe pole obmotki iakoria generatora GP-311B [Investigation of the effect of operational factors on the temperature field of the GP-311B generator armature winding]. Nauchnye problemy transporta Sibiri i Dal'nego Vostoka. Novosibirsk, 2012, no. 1, pp. 437-438.
10. Khusnutdinov A.N., Idiiatullin R.G., Vdovin A.M., Popov A.V., Kisneeva L.N. Otsenka ekspluatatsionnoi nadezhnosti tiagovykh generatorov [Estimation of the traction generator operational reliability]. Problemy energetiki. Izvestiia vysshikh uchebnykh zavedenii. Kazan': Kazanskii gosudarstvennyi energeticheskii universitet, 2012, no. 11-12.
11. Shchurov N.I., Vil'berger M.E., Malozemov B.V., Stepanov E.L. Analiz iznosa elektroshchetok lokomotiva [Electric brush wear analysis of the locomotive]. Sbornik nauchnykh trudov Novosibirskogo gosudarstvennogo tekhnicheskogo universiteta, 2010, no. 3(61).
12. Korshunov G.M., Derbenev V.A., Stepanov V.P. K voprosu obespecheniia nadezhnoi raboty uzla tokos"ema elektricheskikh mashin [To the issue of ensuring reliable operation of the electric machine slip-ring unit]. Elektrotekhnika, 2001, no. 8, pp. 31-32.
13. Kotelenets N.F., Kuznetsov N.L. Ispytaniia i nadezhnost' elektricheskikh mashin [Testing and reliability of electrical machines]. Moscow: Vysshaia shkola, 1988. 232 p.
14. Galkin V.G., Paramzin V.P., Chetvergov V.A. Nadezhnost' tiagovogo podvizhnogo sostava [Reliability of traction rolling stock]. Moscow: Transport, 1981. 184 p.
15. Ermolin N.P., Zherikhin I.P. Nadezhnost' elektricheskikh mashin [Reliability of electrical machines]. Leningrad: Energiia, 1976. 248 p.
16. Idiiatullin R.G. Nadezhnost' tiagovykh elektricheskikh mashin [Reliability of traction electric machines]. Moscow: Mekhnat, 1987. 152 p.
17. Kuznetsov N.L. Nadezhnost' elektricheskikh mashin [Reliability of electrical machines]. Moscow: Moskovskii energeticheskii institut, 2006. 432 p.
18. Ismailov Sh.K., Bublik V.V. et al. Statisticheskoe issledovanie zavisimosti chastoty otkazov ot kachestva kommutatsii tiagovykh elektrodvigatelei [Statistical study of frequency dependence of failures on switching quality of traction motors]. Nauchnye problemy transporta Sibiri i Dal'nego Vostoka, 2009, no. 1, pp. 402-404.
19. Barkov A.V., Barkova N.A., Azovtsev A.Iu. Monitoring i diagnostika rotornykh mashin po vibratsii [Monitoring and diagnosis of rotary machines by vibration]. Saint Petersburg, 1997. 286 p.
20. Gioev Z.G. Osnovy vibroakusticheskoi diagnostiki elektro­mekhanicheskikh sistem lokomotivov [Basics of Vibroacoustic Diagnostics of Electromechanical Systems of Locomotives]. Moscow: Marshrut, 2006. 273 p.

Currently, research is actively ongoing in the field of quantum computing, quantum computers. Most likely, quantum computers, as it was already in the history of science many times, is not a panacea, but will occupy its niche on a par with conventional calculators. Moreover, in this area there are some features that can be used in binary logic. We are talking about the so-called reversible calculations and special elements, for example, Fredkin’s elements.

Purpose: development of a methodology for studying billiard logic circuits in practical classes, development of thedevelopment of a decoder and a memory element, Fredkin element for use in laboratory classes.

Methods: The analysis of the billiard full adder, the synthesis of thedecoder and a memory element, Fredkin element based on the LUT FPGA.

Results: The study tested in detail the steps of an example of such calculations and offers an element for their implementation in binary logic.Thecircuit operation of the “forward” and “backward” using the symbols of “billiard” balls is analyzed.Decoder and memory element developed,Fredkin element based on the LUT FPGA. Running simulation in NI Multisim, the system of the company National Instruments Electronics Workbench Group circuit simulation, confirming the workability of the proposed gate.

Practical relevance:a technique for studying billiard logic circuits is useful in practical exercises; the developed Fredkin element can be used in laboratory classes.

Keywords: Billiard-Ball Computing, Full Adder, Fredkin Gate.

Tyurin Sergey Feofentovich (Perm, Russian Federation) is a Honored Inventor of the Russian Federation, Doctor of Technical Sciences, Professor at the Department of Automation and Telemechanics Perm National Research Polytechnic University (614990, Perm, 29, Komsomolsky pr.,
e-mail: tyurinsergfeo@yandex.ru), Professor at the Department of Software Computing Systems Perm State National Research University (614990, Perm 15, Bukireva str.).

1. Pal'chenkov Iu.D. Struktura kvantovogo komp'iutera [Quantum computer structure]. Voprosy oboronnoi tekhniki. Tekhnicheskie sredstva protivodeistviia terrorizmu, 2012, no. 7-8, pp. 131-136.
2. Sigov A.S., Andrianova E.G., Zhukov D.O., Zykov S.V., Tarasov I.E. Kvantovaia informatika: obzor osnovnykh dostizhenii [Quantum computer science: a review of key achievements]. Rossiiskii tekhnologicheskii zhurnal, 2019, vol. 7, no. 1(27), pp. 5-37.
3. Stefanova T.S. Otbor soderzhaniia obucheniia kvantovym vychisleniiam bakalavrov fiziko-matematicheskogo obrazovaniia [Selection of the content of teaching quantum computing bachelors in physical and mathematical education]. Izvestiia Rossiiskogo gosudarstvennogo pedagogicheskogo universiteta im. A.I. Gertsena, 2008, no. 61, pp. 467-469.
4. Chivilikhin S.A. Kvantovaia informatika [Quantum informatics], available at: https://books.ifmo.ru/file/pdf/626.pdf (accessed 14 December 2019).
5. Pronin Ts.B., Ostroukh A.V. Kvantovye logicheskie elementy, rezul'taty i analiz ikh vliianiia na kvantovye tsepi [Quantum logic elements, results and analysis of their influence on quantum circuits]. Luchshaia studencheskaia stat'ia 2017. Sbornik statei XI Mezhdunarodnogo nauchno-prakticheskogo konkursa. Penza, 2017, part 1, pp. 73-78.
6. Gurov S.I., Zhukov A.E. Obratimye vychisleniia: elementy teorii i primery primeneniia [Reversible Computing: Elements of Theory and Application Examples]. XXX Krymskaia osenniaia matematicheskaia shkola-simpozium po spektral'nym i evoliutsionnym zadacham. Sbornik materialov mezhdunarodnoi konferentsii KROMSh-2019. Krym, poselok Batiliman, 2019, рр. 293-295.
7. Gavrilov S.V., Matiushkin I.V., Stempkovskii A.L. Vychislimost' v kletochnykh avtomatakh [Computability in cellular automata]. Iskusstvennyi intellekt i priniatie reshenii, 2016, no. 1, pp. 18-36.
8. Pravil'shchikov P.A. Novaia kvantovaia logika: novye odnorodnye i neodnorodnye logicheskie elementy [New quantum logic: new homogeneous and heterogeneous logic elements]. Informatsionnye tekhnologii v proektirovanii i proizvodstve, 2019, no. 1(173), pp. 42-51.
9. Zakablukov D.V. Sintez skhem iz obratimykh elementov [Synthesis of circuits from reversible elements]. Bezopasnost' informatsionnykh tekhnologii, 2013, vol. 20, no. 1, pp. 100-101.
10. Frantseva A.S. Algoritm minimizatsii funktsii algebry logiki v klasse obratimykh skhem Toffoli [Algorithm for minimizing the functions of the algebra of logic in the class of invertible Toffoli circuits]. Izvestiia Irkutskogo gosudarstvennogo universiteta. Matematika, 2018, vol. 25, pp. 144-158.
11. Quantum Gates, available at: https://www.sciencedirect.com/topics/engineering/quantum-gate (accessed 07 December 2019).
12. Fredkin E., Toffoli T. Conservative logic. International Journal of Theoretical. Physics, 1982, vol. 21, no. 3-4, pp. 219-253.
13. Raj B. Patel1, Joseph Ho, Franck Ferreyrol1, Timothy C. Ralph, Geoff J. Pryde. A quantum Fredkin gate, available at: https://advances.sciencemag.org/content/2/3/e1501531 (accessed 12 December 2019).
14. Prasanna M., Amudha S. Implementation of testable reversible sequential circuit on FPGA. 2015 International Conference on Innovations in Information, Embedded and Communication Systems, ICIIECS-2015, 19-20 March 2015: proceedings. Coimbatore, India: IEEE, 2015, pp. 145-150. DOI: 10.1109/ICIIECS.2015.7192888
15. Himanshu Thapliyal, Vinod A.P. Design of Reversible Sequential Elements With Feasibility of Transistor Implementation. 2007 IEEE International Symposium on Circuits and Systems, 27-30 May 2007: proceedings. New Orleans, LA, USA: IEEE, 2007, pp. 121-126. DOI: 10.1109/ISCAS.2007.378815
16. Prashant R. Yelekar, Sujata S. Chiwande. Design of sequential circuit using reversible logic. IEEE-International Conference On Advances In Engineering, Science And Management, ICAESM-2012, 30-31 March 2012: proceedings. Nagapattinam, Tamil Nadu, India: IEEE, 2012, pp. 321-326.
17. Kiran J., Binu K.M. Implementation of a FIR filter model using reversible Fredkin Gate. 2014 International Conference on Control, Instrumentation, Communication and Computational Technologies, ICCICCT-2014, 10-11 July 2014: proceedings. Kanyakumari, India: IEEE, 2014, pp. 125-132. DOI: 10.1109/ICCICCT.2014.6993048
18. Dueck G.W., Maslov D., Miller D.M. Transformation-based synthesis of networks of Toffoli/Fredkin gates. Canadian Conference on Electrical and Computer Engineering. Toward a Caring and Humane Technology, CCECE-2003, 4-7 May 2003: proceedings. Montreal, Quebec, Canada: IEEE, 2003, pp. 211-214. DOI: 10.1109/CCECE.2003.1226380
19. Himanshu Thapliyal, Nagarajan Ranganathan, Saurabh Kotiyal. Design of Testable Reversible Sequential Circuits. IEEE Transactions on Very Large Scale Integration (VLSI) Systems. July 2013, vol. 21, no. 7, pp. 1201-1209. DOI: 10.1109/TVLSI.2012.2209688
20. Tiurin S.F., Chudinov M.A. FPGALUT s dvumia vykhodami dekompozitsii po Shennonu [FPGA¢s LUT with two Shannon decomposition outputs]. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Elektrotekhnika, informatsionnye tekhnologii, sistemy upravleniia, 2019, no. 29, pp. 136-147.
21. Sait razrabotchika National Instruments [National Instruments Developer Website], available at: http://www.ni.com/multisim/ (accessed 11 December 2019).

The use of a double-fed electric machine as the main power generator is one of the main areas of development of wind energy. This class of electric machines has been known for a long time, but their use for wind power plants (wind turbines) is a new technical solution. To be able to optimally design this type of generator, it is necessary to develop new methodologies. The article shows one of the approaches to the optimal design of a double-fed generator as applied to wind turbines. Purpose: development of a mathematical model of an asynchronized synchronous wind generator for the task of optimizing the basic geometric dimensions based on generalized variables. Methods: creating a mathematical model of the generator, in which the geometric dimensions of all the elements of the cross section of the magnetic circuit will be described using generalized variables. These variables provide a dependence and an accurate description of the dimensions of the elements of the magnetic circuit from each other. Results: On the basis of the proposed mathematical model, a methodology for synthesizing options for solving the problem of optimizing the basic geometric dimensions of a double-fed machine is built. This technique allows, with a limited amount of input data for designing, to calculate all elements of the magnetic circuit and then make a complete calculation of the electric machine, with geometry optimization using the Gauss-Seidel coordinate descent method when moving towards the optimum in combination with the Fibonacci method when choosing a step. Practical relevance: This technique is implemented in the Delphi software environment and used to design double-fed generators. It allows the developer to significantly reduce time and labor for the synthesis of optimal design options for the active parts of the double-fed machine, while ensuring sufficient accuracy of calculations.

Keywords: doubly-fed induction machine, asynchronoussynchronous generator, wind generator, generalized variables, optimality criteria, optimal design, mathematical model.

Kotov Anton Andreevich (Chelyabinsk, Russian Federation) is a Graduate Student of the Department of Theoretical Foundations of Electrical Engineering of the South Ural State University (454080, Chelyabinsk, 76, Lenin pr., e-mail: aakot@mail.ru).

Neystroev Nikolai Igorevich (Chelyabinsk, Russian Federation) is a Graduate Student of the Department of Theoretical Foundations of Electrical Engineering of the South Ural State University (454080, Chelyabinsk, 76, Lenin pr., e-mail: neustroev.nikolai@mail.ru).

Chyidyk Ivan Aleksandrovich (Chelyabinsk, Russian Federation) is a Graduate Student of the Department of Theoretical Foundations of Electrical Engineering of the South Ural State University (454080, Chelyabinsk, 76, Lenin pr., e-mail: ivan957495@bk.ru).

1. Botvinnik M.M. Asinkhronizirovannaia sinkhronnaia mashina [Asynchronous Synchronous Machine]. Moscow, Leningrad: Gosenergoizdat, 1960. 70 p.

2. Kotov A.A., Neustroev N.I. Primenenie generatora dvoinogo pitaniia dlia vetroenergeticheskikh ustanovok maloi, srednei i bol'shoi moshchnosti [The use of dual power generator for wind power plants of low, medium and high power]. Vestnik Iuzhno-Ural'skogo gosudarstvennogo universiteta. Energetika, 2017, vol. 17, no. 4, pp. 80-89. DOI: 10.14529/power170409

3. Gandzha S.A., Kiessh I.E. Varible speed power.

4. Gandzha S., Kiesh I. A proposal of doubly-fed alternator for windmill application. 2nd International Conference on Industrial Engineering. IEEE Conferences. Applications and Manufacturing (ICIEAM). Year, 2016, pp. 1-3.

5. Gandzha S.A. The application of synchronous induction generator for windmill. ELMASH-2009. Trudi simposiuma. Moskow, 2009, vol. 1,
pp. 168-170.

6. Gandzha S.A., Kiessh I.E. Application brushless machines with combine excitation for a small and medium power windmills.

7. Obozov A.Dzh., Botpaev R.M. Vozobnovliaemye istochniki energii [Renewable energy sources]. Bishkek: Kyrgyzskii gosudarstvennyi tekhnicheskii universitet, 2010. 218 p.

8. Stumpf P., Berei J., Nagy I., Vajk I. Dynamics of DFIG controlled by rotor side converter in wind energy. IEEE, 5th International Youth Conference on Energy, 2015, pp. 446-454. DOI: 10.1109/IYCE.2015.7180797

9. Lebsir A. Electric Generators Fitted to Wind Turbine Systems: An Up-to-Date Comparative Study, available at: https://hal.archives-ouvertes.fr/hal-01213120 (accessed 10 August 2018).

10. Md. Rejwanur Rashid Mojumdar, Mohammad Sakhawat Hossain Himel, Md. Salman Rahman, Sheikh Jakir Hossain. Electric Machines and their comparative study for wind energy conversion systems (WECSs). Journal of Clean Energy Technologies, 2016, vol. 4, no. 4, pp. 290-294. DOI: 10.7763/JOCET.2016.V4.299

11. Fujin Deng, Dong Liu, Zhe Chen, Peng Su. Control Strategy of Wind Turbine Based on Permanent Magnet Synchronous Generator and Energy Storage for Stand-Alone Systems. Chinese Journal of Electrical Engineering, 2017, vol. 3, no. 1, pp. 51-62.

12. Parker M.A., Soraghan C., Giles A. Comparison of power electronics lifetime between vertical- and horizontal-axis wind turbines. IET Renewable Power Generation, 2016, vol. 10, pp. 679-686. DOI: 10.1049/iet-rpg.2015.0352

13. Kurochka A.L. Sintez optimal'nykh mashin postoiannogo i pul'siruiushchego toka na osnove agregirovannykh peremennykh [Synthesis of optimal DC and pulsating current machines based on aggregated variables]. Izvestiia vysshikh uchebnykh zavedenii. Elektromekhanika, 1976, no. 6,
pp. 608-617.

14. Mehmet Cunkas. Design optimization of electric motors by multiobjective fuzzy genetic algorithms. Mathematical and Computational Applications, 2008, vol. 13, no. 3, pp. 153-163.

15. Gemintern V.I., Kagan B.M. Metody optimal'nogo proektirovaniia [Optimal Design Methods]. Moscow: Energiia, 1980.

16. Gandzha S.A. Optimization of parameters of brushless electric machines of a direct current with an axial air gap. State and prospects of development of Electrotechnology (XII Benardos readings): TEZ. Doc. International. scientific.-tech. conf., 1-3 June 2005. Ivan. State Energy. Univ. of Illinois. Ivanovo, 2005, vol. 2, 82 p.

17. Gang Lei, Jianguo Zhu, Youguang Guo, Chengcheng Liu, Bo Ma. A Review of Design Optimization Methods for Electrical Machines. Energies, 2017, vol. 10, pp. 1-31. DOI: 10.3390/en10121962

18. Gandzha S, Kotov A. Application of an Asynchronous Synchronous Alternator for Wind Power Plant of Low, Medium and High Power. Chapter in open access book Winding Engineering. Intech Open, available at: https://www.intechopen.com/online-first/application-of-an-asynchronous-synchronous-alternator-for-wind-power-plant-of-low-medium-and-high-po. DOI: 10.5772/intechopen.89255

19. Gandzha S.A., Kotov A.A., Neystroev N.I. Geometry Optimization of Asynchronous Synchronous Alternator with Using Generalized Variables. 2019 International Ural Conference on Electrical Power Engineerings (UralCon), 2019, pp. 373-377. DOI: 10.1109/URALCON.2019.8877634

20. Kopylov I.P. Proektirovanie elektricheskikh mashin [Electrical Machine Design]. Moscow: Vysshaia shkola, 2005. 767 p.

21. Lifanov, V.A., Pomogaev G.V., Ermolin N.P. Raschet elektricheskikh mashin maloi moshchnosti [Calculation of low-power electric machines]. Cheliabinsk: Iuzhno-Ural'skii gosudarstvennyi universitet, 2008. 127 p.

22. Martyanov A.S., Neustroyev N.I. ANSYS Maxwell Software for Electromagnetic Field Calculations. Eastern European Scientific Journal, 2014, no. 5, pp. 206-210. DOI: 10.12851/EESJ201410C05ART03

23. Neustroev N.I., Kotov A.A., Kiessh I.E. Primenenie sistemy avtomaticheskogo proektirovaniia AnsysMaxwell dlia kolichestvennoi otsenki vliianiia effekta vytesneniia toka v elektricheskikh mashinakh peremennogo toka [Application of AnsysMaxwell automated design system to quantify the effect of current displacement effect in AC electric machines]. Vestnik Iuzhno-Ural'skogo gosudarstvennogo universiteta. Energetika, 2018, vol. 18, no. 1, pp. 112-121.

24. Gandzha S.A. Modelling of Permanent Magnet Direct Current Motor with Electromagnetic Reduction. Collection of papers of Software Users Sixth Conference CAD_FEMGmbH, 20-21 April 2006. Moscow, 2006, pp. 358-360.

25. Gandzha S.A., Erlisheva A.V. Starter-generator for autonomous source of energy supply. Vestnik Iuzhno-Ural'skogo gosudarstvennogo universiteta. Energetika, 2005, iss. 6, no. 9, pp. 84-86.

26. Gandzha S.A., Sogrin A.I., Kiessh I.E. The Comparative Analysis of Permanent Magnet Electric Machines with Integer and Fractional Number of Slots per Pole and Phase. Engineering. December 2015,
vol. 129, p. 408-414.

Thearticle substantiates the necessity of developing mathematical models of heat exchangers. A review of the methods of parametric and non-parametric identification of heat exchangers based on experimental data, as well as on material and heat balances is given. The author discusses advantages and disadvantages of these methods. The input, output, and intermediate parameters are selected as the main parameters of the object of study (shell-and-tube evaporator of the oil stabilization unit). The statement of the control problem is given. A mathematical model of the evaporator is developed in the form of a heat balance in a differential form. The coefficients in the heat balance equations are expressed through technological and design parameters. A transition was made from the obtained system of ordinary differential equations to expressions in the form of a system of transfer functions over various channels. The possibility of constructing a mathematical model of the studied object with the adjustment of the coefficients in the model using the experimental data of the current unit was suggested. The initial data were obtained from the trends of the process parameters. The resulting automatic control system is implemented using the tools of the software package Simulink. The search for coefficients in the model according to the selected criterion was performed using the fminsearch optimization function. As the initial search conditions, pre-calculated values of the coefficients of the model, presented in the form of heat balance, are accepted. The quality of the model was estimated by the average relative error of approximation. The proposed method for identifying the parameters of a dynamic shell-and-tube evaporator model improves the accuracy of the models. Research results were obtained using the Matlab software package. The proposed model of the object can be applied in the development of simulators, the study of the operating modes of the system, and in process control using mathematical models.

Keywords: identification, heat exchanger, rectification, model, heat balance, experiment.

Zatonskiy Andrei Vladimirovich (Berezniki, Russian Federation) is a Doctor of Technical Sciences, Professor, Head of department of automation of technological processes, Perm National Polytechnic Research University Berezniki Branch (618404, Berezniki, Tel’man str., 7, e-mail: zxenon@narod.ru).

Tugashova Larisa Gennadievna (Almetyevsk, Russian Federation) is a Ph.D. in Technical Sciences, Senior Lecturer of department of automation and information technology Almetyevsk State Oil Institute (423450, Almetyevsk, 2, Lenin str., e-mail: tugashowa.agni@yandex.ru).

1. Gartman T.N., Klushin D.V. Osnovy komp'iuternogo modelirovaniia khimiko-tekhnologicheskikh protsessov [Fundamentals of computer modeling of chemical and technological processes]. Moscow: Akademkniga, 2008. 416 p.
2. Dudnikov E.G., Kazakov A.V., Sofieva Iu.N., Sofiev A.E., Tsirlin A.M. Avtomaticheskoe upravlenie v khimicheskoi promyshlennosti [Automatic control in the chemical industry]. Moscow: Khimiia, 1987. 368 p.
3. Shteinberg Sh.E. Identifikatsiia v sistemakh upravleniia [Identification in control systems]. Moscow: Energoatomizdat, 1987. 80 p.
4. Rubanov V.G., Porkhalo V.A. Poluchenie matematicheskoi modeli obzhiga klinkera s primeneniem statisticheskikh metodov [Obtaining a mathematical model of the clinker burning with the application of statistical methods]. Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Ekonomika. Informatika, 2010, no. 7(78), pp. 80-87.
5. Usachev M.V., Baranov S.B., Salikhov M.Z., Baranov M.S., Klochkov O.S. Nelineinaia avtoregressionnaia neirosetevaia model' dinamiki nagreva pri posledovatel'no-nepreryvnoi zakalke prokatnykh valkov [Nonlinear autoregressive neural network model of heating dynamics in series-continuous hardening of rolling rolls]. Avtomatizatsiia v promyshlennosti, 2013, no. 12, pp. 32-34.
6. Shumikhin A.G., Aleksandrova A.S., Mustafin A.I. Parametricheskaia identifikatsiia tekhnologicheskogo ob"ekta v rezhime ego ekspluatatsii s primeneniem tekhnologii neironnykh setei [Parametric identification of a technological object in its operation mode using neural network technology]. Vestnik Permskogo natsional'nogo issledovatel'skogo poli­tekhnicheskogo universiteta. Elektrotekhnika, informatsionnye tekhnologii, sistemy upravleniia, 2018, no. 26, pp. 29-41.
7. Sahoo А., Radhakrishnan T.K., Sankar Rao C. Modeling and control of a real time shell and tube heat exchanger. Resource-Efficient Technologies. Technoscape 2016: International Conference on Separation Technologies in Chemical, Biochemical, Petroleum and Environmental Engineering, 2017, vol. 3, iss. 1, pp. 124-132.
8. Tugashova L.G. Virtual'nye analizatory pokazatelei kachestva protsessa rektifikatsii [Virtual analyzers of rectification process quality indicators]. Elektrotekhnicheskie i informatsionnye kompleksy i sistemy, 2013, vol. 9, no. 3, pp. 97-103.
9. Slastenov I.V. Identifikatsiia trenazhernykh modelei po dannym real'nogo tekhnologicheskogo protsessa [Identification of simulator models according to the real technological process]. Avtomatizatsiia v promyshlennosti, 2013, no. 7, pp. 29-36.
10. Shpak O.S., Faizov A.R., Churakova S.K., Kantor E.A. Matematicheskoe modelirovanie tekhnologicheskogo protsessa v srede Unisim Design i ASPEN PIMS [Mathematical modeling of technological process in unisim Design and ASPEN PIMS environment]. Ufa: Ufimskii gosudarstvennyi neftianoi tekhnicheskii universitet, 2006, available at: http://www.rusoil.net (accessed 10 Oktober 2018).
11. Nizamov E.S., Kiriushin O.V. Identifikatsiia pechi podogreva nefti dlia trenazhera-imitatora dobychi i podgotovki nefti [Identification of oil heating furnace for oil production and preparation simulator]. Problemy avtomatizatsii tekhnologicheskikh protsessov dobychi, transporta i pererabotki nefti i gaza. Sbornik trudov. V Vserossiiskoi zaochnoi nauchno-prakticheskoi konferentsii. Ufa: Ufimskii gosudarstvennyi neftianoi tekhnicheskii universitet, 2017, pp. 77-81.
12. Val'shin I.R. Novye metody intensifikatsii massoobmennykh protsessov pri obessolivanii nefti [New methods of intensification of mass transfer processes in oil desalination]. Neft'. Gaz. Novatsii, 2018, no. 5, pp. 24-29.
13. Verevkin A.P. Sistemotekhnika “prodvinutogo” upravleniia v neftepererabotke [System engineering of “advanced” control in oil refining]. Problemy avtomatizatsii tekhnologicheskikh protsessov dobychi, transporta i pererabotki nefti i gaza. Sbornik trudov II Vserossiiskoi nauchno-prakticheskoi internet-konferentsii. Ufa: Ufimskii gosudarstvennyi neftianoi tekhnicheskii universitet, 2014. 125 p.
14. Dmitrievskii B.S., Zatonskii A.V., Tugashova L.G. Zadacha upravleniia protsessom rektifikatsii nefti i metod ee resheniia [The task of controlling the process of oil rectification and the method of its solution]. Izvestiia Tomskogo politekhnicheskogo universiteta. Inzhiniring geore­sursov, 2018, vol. 329, no. 2, pp. 136-145.
15. Zatonskiy A.V., Tugashova L.G., Alaeva N.N., Gorshkova K.L. Controlling the Oil Rectification Processina Primary Oil Refining Unit Using a Dynamic Model. Petroleum Chemistry, 2017, vol. 57, no. 12, pp. 1121-1131.
16. Soboleva E.G. Modelirovanie i algoritmizatsiia sistemy upravleniia protsessom polucheniia stirol-akrilovoi dispersii [Modeling and algorithmization of the control system of the process of obtaining a styrene-acrylic dispersion]. Abstract of Ph.D. thesis: 05.13.06. Dzerzhinsk, 2013. 21 p.
17. Prokhorenkov A.M. Modelirovanie protsessov teploobme­na,protekaiushchikh v plastinchatykh teploobmennykh aparatakh [Modeling of heat exchange processes in plate heat exchangers]. Vestnik Moskovskogo gosudarstvennogo tekhnicheskogo uuniversiteta imeni N.E. Baumana. Mashinostroenie, 2014, no. 1, pp. 92-101.
18. Attarakih M., Abu-Khaderb M., Bartc H.-J. Dynamic analysis and control of sieve tray gas absorption column using MatLab and Simulink. Applied Soft Computing 13, 2013, pp. 1152-1169.
19. Pavlov K.F., Romankov P.G., Noskov A.A. Primery i zadachi po kursu protsessov i apparatov khimicheskoi tekhnologi [Examples and tasks in the course of processes and devices of chemical technology]. Мoscow, 2005. 572 p.
20. Zatonskii A.V., Tugashova L.G. Modelirovanie ob"ektov upravleniia v MatLab [Modelling of control objects in MatLab]. Saint Petersburg: Lan', 2019. 144 p.

In modern control systems, there is an upward trend to increase its algorithmic (software) part and, accordingly, to decrease the hardware part. With this approach, an object model is used, the accuracy of which significantly affects the quality of processes in the system. Therefore, the development of methods for finding the parameters of control object is very promising. Thus, in the absence of direct feedbacks in the drive control system, the determination of the required state variables can be carried out indirectly by the object model. Accuracy of the rotor circuit model of DC motor to a large extent depends on the accuracy of the rotor circuit time constant determination. Purpose: development of methods for identifying the time constant of the motor rotor circuit and, therefore, clarifying parameters of its model in the control system. Methods: creating an identification system based on replacing the motor rotor circuit with an RL-circuit; simulation of an identification system in a graphical environment of Simulink simulation modeling and optimization of parameters. Results: refinement of parameters of DC motor model used in the indirect assessment of its parameters. The methodology for identifying the rotor time constantinDC motor based on the approximate replacement of this circuit with an RL-circuit.The time constant determination carried out by finding the tangent to the graph of current in this circuit and based on the values of the current measured at a certain time and the steady-state current value. The resulting system allows you to specify the motor parameters necessary for the proper functioning of the control system. The ability to indirect measurement of the electric motor speed with a small error allows you to abandon the use of devices for direct measurement, e.g. encoders. Practical relevance: this identification system improves the control quality of sensorless systems and entire drive reliability.The proposed method can also work to determine the parameters of AC motors (stator circuit). However, in order to simplify the object model we consider DC machine.

Keywords: electric motor, electric drive, measurement, identification, time constant, control system, DC motor, modeling

Popov Sergey Anatolevich (Krasnodar, Russian Federation) is a Ph.D. in Technical Sciences, Associate Professor Department of Electrical Engineering and Electric Machines Kuban State Technological University (350072, Krasnodar, 2, Moskovskaya str., e-mail: sa_popov@inbox.ru).

Krivchenkov Vladimir Igorevich (Krasnodar, Russian Federation) is a Graduate Student Department of Electrical Engineering and Electric Machines, Kuban State Technological University (350072, Krasnodar,
2, Moskovskaya str., e-mail: vldmrkr5@ya.ru).

1. Kopylov I.P. Elektricheskie mashiny [Electrical machines]. 2nd ed. Moscow: Vysshaia shkola: Logos, 2000. 607 p.
2. Vol'dek A.I., Popov V.V. Elektricheskie mashiny. Vvedenie v elektromekhaniku. Mashiny postoiannogo toka i transformatory [Electrical machines. Introduction to Electromechanics. DC machines and transformers]. Saint Petersburg: Piter, 2008. 320 p.
3. James Kirtley Jr. 6.685 Electric Machines.Fall 2013. Massachusetts Institute of Technology: MIT OpenCourseWare, available at: https://ocw.mit.edu (accessed 24 September 2019).
4. Moskalenko V.V. Avtomatizirovannyi elektroprivod [Automated electric drive]. Moscow: Energoatomizdat, 1986. 416 p.
5. Anuchin A.S. Sistemy upravleniia elektroprivodov [Electric drive control systems]. Moscow: Moskovskii energeticheskii institut, 2015. 373 p.
6. Krivchenkov V.I., Popov S.A. Issledovanie vidov nabliudatelei dlia bezdatchikovykh sistem upravleniia elektroprivodom postoiannogo toka [Study of types of observers for sensorless control systems for DC electric drives]. Razvitie sovremennoi nauki: teoreticheskie prikladnye aspekty. Ed. T.M. Sigitov. Perm': IP Sigitov T.M., 2017, pp. 23-26.
7. Kalachev Iu.N. Nabliudateli sostoianiia v vektornom elektroprivode [Vector drive status observers], available at: http://privod.news/files/nabludateli_10.16_1.pdf (accessed 24 September 2019).
8. Gargaev A.N., Kashirskikh V.G. Identifikatsiia parametrov dvigatelei postoiannogo toka s pomoshch'iu poiskovykh metodov [Identification of DC motor parameters using search methods]. Vestnik Kuzbasskogo gosudarstvennogo tekhnicheskogo universiteta, 2013, no. 1(95), pp. 131-134.
9. Gargaev A.N., Kashirskikh V.G. Identifikatsiia parametrov dvigatelei postoiannogo toka s pomoshch'iu metoda roia chastits [Identification of parameters of DC motors using the particle swarm method]. Vestnik Kuzbasskogo gosudarstvennogo tekhnicheskogo universiteta, 2015, no. 4(110), pp. 71-75.
10. Pankratov V.V., Kucher E.S. Analiz metodov predvaritel'noi identifikatsii postoiannoi vremeni rotora asinkhronnogo dvigatelia v sistemakh elektroprivoda [Analysis of methods for preliminary identification of the time constant of the rotor of an induction motor in electric drive systems]. Nauchnyi vestnik Novosibirskogo gosudarstvennogo tekhnicheskogo universiteta, 2012, no. 1(46), pp. 127-134.
11. Radimov I.N., Gulyi M.V., Rymsha V.V., Chan Tkhi Tkhu Khyong. Parametry ventil'nogo dvigatelia s postoiannymi magnitami [Permanent Magnet Valve Parameters]. Elektrotekhnika i elektromekhanika. Khar'kov: Natsional'nyi tekhnicheskii universitet “Khar'kovskii politekhnicheskii institute”, 2008, no. 6, pp. 40-43.
12. Ovcharenko V.N. Adaptivnaia identifikatsiia parametrov v dinamicheskikh i staticheskikh sistemakh [Adaptive parameter identification in dynamical and static systems]. Avtomatika i telemekhanika, 2011, no. 3, pp. 113-123.
13. Solodkii E.M., Dadenkov D.A., Kostygov A.M. Paramet­richeskaia identifikatsiia asinkhronnogo dvigatelia na osnove algoritma fazovoi avtopodstroiki chastoty [Parametric identification of an induction motor based on a phase-locked-loop frequency control algorithm]. Elektrotekhnika, 2018, no. 11, pp. 53-57.
14. Odnol'ko D.S. Sovmestnaia identifikatsiia aktivnogo soprotivleniia statora i rotora asinkhronnogo dvigatelia na intervale shirotno-impul'snoi moduliatsii [Identifying the active stator and rotor impedances of an induction motor over the pulse-width modulation interval]. Elektrotekhnika, 2013, no. 5, pp. 16-20.
15. Volkov A.V., Skal'ko Iu.S. Identifikatsiia potokostsepleniia rotora i skorosti asinkhronnogo dvigatelia s uchetom izmeneniia ego aktivnykh soprotivlenii [Identification of rotor flow connection and asynchronous motor speed taking into account variation of its active resistances]. Elektrotekhnika, 2009, no. 11, pp. 2-12.
16. Besekerskii V.A., Popov E.P. Teoriia sistem avtomaticheskogo upravleniia [Theory of automatic control systems]. 4nd ed. Saint Petersburg: Professiia, 2003. 752 p.
17. Tutunji Tarek. DC Motor Identification using Impulse Response Data. Eurocon 2005. Serbia and Montenegro, Belgrade, 2005, pp. 1734-1736.
18. Rotach V.Ia. Teoriia avtomaticheskogo upravleniia [Automatic сontrol theory]. Moscow: Moskovskii energeticheskii institut, 2005. 400 p.
19. Shreiner R.T. Sistemy podchinennogo regulirovaniia elektroprivodov [Systems of subordinate regulation of electric drives]. Ekaterinburg: Rossiiskii gosudarstvennyi professional'no-pedagogicheskii universitet, 2008. 279 p.
20. Chernykh I.V. SIMULINK: sreda sozdaniia inzhenernykh prilozhenii [SIMULINK: engineering application creation environment]. Ed. V.G. Potemkin. Moscow: Dialog-MIFI, 2003. 496 p.
21. Meleshin V.I., Ovchinnikov D.A. Upravlenie tranzistornymi preobrazovateliami elektroenergii [Transistor power converters]. Moscow: Tekhnosfera, 2011. 576 p.
22. Oppengeim A., Shafer R. Tsifrovaia obrabotka signalov [Discrete-time signal processing]. Moscow: Tekhnosfera, 2006. 856 p.

The relevance of the task considered in the paper is connected with the use of empirical models and classification methods for the preprocessing and preparation of data, and on their basis, increasing of accuracy and objectivity of decisions made as well as with the consideration of observed systems and tasks, and the use of statistical data. The paper is aimed at considering the identification method selection task to increase its efficiency performance on the base of a specific applied task under continuous data include. For the set task to be handled, the paper investigates the application of machine learning methods on the base of real time-collected statistical data about customer actions in self-service retail shops with a special device for scanning bar codes of goods. The obtained results allow classifying data into two categories (i.e. to identify target states. In the paper, this is the identification of frauds on the base of customer actions. The selected models and the ways to improve their efficiency can be used directly in the areas where staff and clients’ supervision and control in real-time (i.e. based on their e-actions) are of importance. The significance of the study is greatly connected with the outcome according to which classification methods used to consider various tasks show different efficiency levels. In the conducted study is given the method which determines how to build and select the most efficient models for solving binary classification and identification tasks. This process is limited to the series of formal operations, which can be performed by solving any classification task. Efficiency was evaluated with help of ROC curves, and the efficiency of machine learning methods’ performance was measured with help of building models’ ensembles, using cross-validation, special metrics by training models, and resembling. 

Keywords: retail, identification, binary classification, machine learning, frauds, model selection, efficiency increase, models’ ensemble, decision making support.

Mylnikov Leonid Aleksandrovich (Perm, Russian Federation) is a Ph.D. in Technical Science, Associated Professor of Microprocessor Automation Means Department Perm National Research Polytechnic University (614990, Perm, 29, Komsomolskypr., e-mail: leonid.mylnikov@pstu.ru).

Morozov Aleksey Sergeevich (Perm, Russian Federation) is a Master Student at Microprocessor Automation Means Department Perm National Research Polytechnic University (614990, Perm, 29, Komsomolskypr.,
e-mail: morozov.leha@mail.ru).

Pukhareva Daria Vadimovna (Perm, Russian Federation) is a Master Student atInformation Technology and Automation Systems Department Perm National Research Polytechnic University (614990, Perm, 29, Komsomolskypr., e-mail: dasha.pukhareva@yandex.ru).

1.  Aivazian S.A. et al. Prikladnaia statistika: Klassifikatsiia i snizhenie razmernosti [Applied statistics: classification and reduction of dimensions]. Мoscow, 1989. 607 p.

2.  Vapnik V.N., Chervonenkis A.Ia. Teoriia raspoznavaniia obrazov [Pattern Recognition Theory]. Moscow: Nauka, 1974. 487 p.

3.  L. Breiman et al. Classification and Regression Trees. Belmont (CA): Wadsworth Int. Group, 1984. 368 p.

4.  Breiman L. Random forests. Mach. Learn, 2001, vol. 45,
no. 1, pp. 5-32.

5.  Zhang L., Wang Z. A multi-view camera-based anti-fraud system and its applications. J. Vis. Commun. Image Represent, 2018, vol. 55, pp. 263-269.

6.  Gabbur P. et al. A pattern discovery approach to retail fraud detection. Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD ’11. New York, USA: ACM Press, 2011, P. 307.

7.  Carcillo F. et al. Combining unsupervised and supervised learning in credit card fraud detection.  Inf. Sci. (Ny), 2019, vol. S002002551.

8.  Kim E. Champion-challenger analysis for credit card fraud detection: Hybrid ensemble and deep learning. Expert Syst. Appl, 2019, vol. 128, pp. 214-224.

9.  Chouiekh A., EL Haj E.H.I. ConvNets for Fraud Detection analysis. Procedia Comput. Sci, 2018, vol. 127, pp. 133-138.

10.  Sridhar S., Karthigayani P. A novel approach for decision tree occlusion on detection (DTOD) classifier for face verification and estimation of age using back propagation Neural Network (BPNN).
J. Computer Sci. Inf. Technol. Res, 2013, vol. 3, no. 1, pp. 1-10.

11.  Ahmed I., Pariente A., Tubert-Bitter P. Class-imbalanced subsampling lasso algorithm for discovering adverse drug reactions. Stat. Methods Med. Res, 2018, vol. 27, no. 3, pp. 785-797.

12.  Demirci Orel F., Kara A. Supermarket self-checkout service quality, customer satisfaction, and loyalty: Empirical evidence from an emerging market. J. Retail. Consum. Serv, 2014, vol. 21, no. 2, pp. 118-129.

13.  Myl'nikov L.A., Kolchanov S.A. Metodika vyiavleniia kliuchevykh parametrov innovatsionnykh proektov na osnove statisticheskikh dannykh [Methodology for identifying key parameters of innovative projects based on statistical data]. Ekonomicheskii analiz teoriia i praktika, 2012, no. 5(260), pp. 22-28.

14.  Shahrokh Esfahani M., Dougherty E.R. Effect of separate sampling on classification accuracy. Bioinformatics, 2013, vol. 30, no. 2,
pp. 242-250.

15.  James G. et al. An Introduction to Statistical Learning: with Applications in R. Springer New York, 2014.

16.  Myl'nikov L.A. Statisticheskie metody intellektual'nogo analiza dannykh [Statistical methods of intelligent data analysis]. Perm': Permskii natsional'nyi issledovatel'skii politekhnicheskii universitet, 2018. 168 p.

17.  Kohavi R. A Study of Cross-validation and Bootstrap for Accuracy Estimation and Model Selection. Proceedings of the 14th International Joint Conference on Artificial Intelligence. San Francisco, CA, USA: Morgan Kaufmann Publishers Inc., 1995, vol. 2, pp. 1137-1143.

18.  Shitikov V.K., Rozenberg G.S. Randomizatsiia i butstrep: statisticheskii analiz v biologii i ekologii s ispol'zovaniem R [Randomization and bootstrap: statistical analysis in biology and ecology using R]. Tol'iatti: Kassandra, 2013. 314 p.

19.  Myl'nikov L.A. et al. Intellektual'nyi analiz dannykh v upravlenii proizvodstvennymi sistemami: podkhody i metody [Intelligent data analysis in the management of production systems (approaches and methods)]. Moscow: Biblio-globus, 2017. 332 p.

20.  Wolpert D.H. Stacked generalization. Neural Networks, 1992,
vol. 5, no. 2, pp. 241-259.

21.       Mylnikov L.A., Kulikov M.V., Krause B. The selection of optimal control of the operation modes of heterogeneous duplicating equipment based on statistical models with learning. Int. J. Mech. Eng. Technol, 2018, vol. 9, no. 9.

At present, in the production of high-voltage cables with cross-linked polyethylene (XLPE) insulation on the surface of screens, as a rule, fiber-optic temperature sensors are mounted that are used to monitor cable lines in real time during their operation. In this case, the determination of the thermal state of the cable line by the temperature of the optical fiber is possible only using a mathematical model of non-stationary thermal conduction under conditions of changing current load. Research objective: to create a mathematical model for calculating and predicting the temperature of cable strand veins based on data on the environmental parameters, cable line design, and also the temperature in the screens obtained by measurement. Results: research is carried out on the example of a three-phase high-voltage cable line laid in the ground and consisting of three single-core cables with copper conductive conductors with XLPE insulation. Three ways of laying the cable line are considered: in the horizontal plane at a distance in the light equal to the diameter of the cable; in the horizontal plane close; triangle. A two-dimensional mathematical model of non-stationary thermal conductivity is proposed, the numerical implementation of which is carried out in the Ansys Fluent software package. Initially, as a result of solving the problem of stationary thermal conductivity, the nominal current load is determined by the value of the long-term allowable temperature for insulation from cross-linked polyethylene. As an initial condition for solving the problem of non-stationary thermal conduction, the temperature field obtained at a current of 70 % of the nominal value is used. Further, the current in the cable line changes stepwise in the range from 150 % of the nominal to 70 % and vice versa. In the process of numerical studies, the time to reach the maximum temperature to the specified levels is estimated and the change in the temperature difference between the conductive core and the screen is determined. Practical relevance: this mathematical model can be used to assess the temperature conditions of high-voltage cable lines with fiber-optic temperature sensors.

Keywords: mathematical model, high voltage power cable, thermal field, cable lines, non-stationary problem, methods of heat conduction.

Naumov Mikhail Dmitrievich (Perm, Russian Federation) is a Student Perm National Research Polytechnic University (614990, Perm, 29, Komsomolsky pr., e-mail: naumoff.mikh@yandex.ru).

Shcherbinin Alexey Grigoryevich (Perm, Russian Federation) is a Doctor of Technical Sciences, Professor of the Department of Design and Technology in Electrical Perm National Research Polytechnic University (614990, Perm, 29, Komsomolsky pr., e-mail: agshch@mail.ru).

1. Iakunin A.V. Monitoring teplovogo rezhima ekspluatatsii kabel'nykh linii 110-500 kV [Monitoring of the thermal regime of exploitation of cable lines 110-500 kV]. Linii elektroperedachi 2010: proektirovanie, stroitel'stvo opyt ekspluatatsii i nauchno-tekhnicheskii progress. Materialy IV Rossiiskoi nauchno-prakticheskoi konferentsii s mezhdunarodnym uchastiem. Novosibirsk, 2010, pp. 306-310.
2. Mokanski V. Silovoi kabel' vysokogo napriazheniia so vstroennym volokonno-opticheskim modulem [Power cable high voltage with integrated fiber optic module]. Kabeli i provoda, 2009, no. 2, pp. 14-17.
3. Larin Iu.T., Smirnov Iu.V., Grinshtein M.L. Primenenie sistemy temperaturnogo monitoringa s pomoshch'iu opticheskogo kabelia dlia kontrolia raspredeleniia temperatury vdol' elektricheskogo silovogo kabelia [Application of the temperature monitoring system using an optical cable to control the temperature distribution along the electric power cable]. Kabel'-news, 2009, no. 8, pp. 48-53.
4. Beliakov V.V., Malyshev A.V., Krivosheev N.V., Marshner V.K. Monitoring silovykh kabel'nykh linii s adaptatsiei k usloviiam okruzhaiushchei sredy v rezhime real'nogo vremeni [Monitoring of power cable lines with adaptation to environmental conditions in real time]. Elektro, 2008, no. 5, pp. 38-40.
5. Greshniakov G.V., Kovalev G.G. Chislennyi metod analiza nagruzochnoi sposobnosti vysokovol'tnoi kabel'noi sistemy [Numerical method for analysis of load carrying capacity of HV cable systems]. Kabel'-news, 2013, no. 3, pp. 32-37.
6. Anders G.J., Braun J.-M., John A. Downes, Fujimoto N., Luton M-H., Rizzetto S. Real Time Monitoring of Power Cables by Fibre Optic Technologies. Tests, Applications and Outlook. 6th International Conference on Insulated Power Cables (JiCable'03). Paris, 2003.
7. Lavrov Iu.A. Kabeli vysokogo napriazheniia s izoliatsiei iz sshitogo polietilena. Trebovaniia ekonomichnosti, nadezhnosti, ekologichnosti [High voltage Cables with XLPE insulation. Requirements of efficiency, reliability, environmental friendliness]. Novosti elektrotekhniki, 2008, no. 2.
8. Lavrov Iu.A. Sistemnyi podkhod k proektirovaniiu vozdushnykh i kabel'nykh linii elektroperedachi srednego i vysokogo napriazheniia [System approach to the design of overhead and cable power lines of medium and high voltage]. Linii elektroperedachi 2008: proektirovanie, stroitel'stvo opyt ekspluatatsii i nauchno-tekhnicheskii progress. Materialy III Rossiiskoi nauchno-prakticheskoi konferentsii s mezhdunarodnym uchastiem. Novosibirsk, 2008, pp. 17-27.
9. Shcherbinin A.G., Trufanova N.M., Savchenko V.G. Opredelenie tokovykh nagruzok kabelei [Determination of current loads of cables]. Elektrotekhnika, 2010, no. 6, pp. 61-64.
10. Shcherbinin A.G., Trufanova N.M., Navalikhina E.Iu., Savchenko V.G. Opredelenie ekspluatatsionnykh kharakteristik kabelei, prolozhennykh v kabel'nom kanale [Determination of operational characteristics of cables laid in the cable channel]. Elektrotekhnika, 2011, no. 11, pp. 16-19.
11. Titkov V.V. K otsenke teplovogo rezhima trekhfaznoi linii iz SPE-kabelia [To the assessment of the thermal regime of three-phase lines from the EIT-cable]. Kabel'-news, 2009, no. 10, pp. 47-51.
12. Kholodnyi S.D. Nagrevanie i okhlazhdenie kabelia, prolo­zhennogo v zemle [Heating and cooling of the cable laid in the ground]. Elektrichestvo, 1964, no. 6, pp. 35-40.
13. Kozhevnikov A.G. Sistemy kabel'nykh linii s izoliatsiei iz sshitogo polietilena - optimal'noe reshenie nadezhnogo elektrosnabzheniia promyshlennykh i sotsial'nykh ob"ektov sovremennogo goroda [Systems of cable lines with insulation of cross-linked polyethylene - the optimal solution for reliable power supply of industrial and social facilities of the modern city]. Kabel' info, 2006, no. 9, pp. 25-27.
14. Shneerson E.M. Tsifrovaia releinaia zashchita [Digital relay protection]. Moscow: Energoatomizdat, 2007, pp. 221-225.
15. Buller F.H. Thermal Transient on Buried Cables. AIEE Transactions, 1951, vol. 70, pp. 45-55.
16. Lavrov Iu.A. Kabeli 6-35 kV s plastmassovoi izoliatsiei. Faktory ekspluatatsionnoi nadezhnosti [Cables 6-35 kV with plastic insulation. Factors of operational reliability]. Novosti elektrotekhniki, 2006, no. 6.
17. Osika L.K. Sposoby ucheta izmereniia temperatury po trassam linii elektroperedachi dlia utochneniia ikh matematicheskikh modelei [Methods of accounting for temperature measurement along the routes of power lines to clarify their mathematical model]. Elektro, 2006, no. 6, pp. 27-29.
18. Udovichenko O.V. Temperaturnyi monitoring kabel'nykh linii vysokogo napriazheniia na osnove kabelei s izoliatsiei iz sshitogo polietilena [Temperature monitoring of high-voltage cable lines based on cables with cross-linked polyethylene insulation]. Linii elektroperedachi 2008: proektirovanie, stroitel'stvo opyt ekspluatatsii i nauchno-tekhnicheskii progress. Materialy III Rossiiskoi nauchno-prakticheskoi konferentsii s mezhdunarodnym uchastiem. Novosibirsk, 2008, pp. 301-304.
19. Neher J.H., McGrath M.H. Calculation of the Temperature Rise and Load Capability of Cable Systems. AIEE Transactions, 1957, vol. 76, part 3, pp. 755-772.
20. Mikheev M.A., Mikheeva I.M. Osnovy teploperedachi [Fundamentals of heat transfer]. Moscow: Energiia, 2010. 343 p.
21. Isachenko V.P., Osipova V.A., Sukomel A.S. Teploperedacha [Heat Transfer]. Moscow: Energoizdat, 1981. 416 p.

The most common method of controlling asynchronous motors is vector control with the installation of sensors directly on the motor. The presence of sensors in the control system increases the risk of equipment failure. The most effective way to improve the quality characteristics of the electric drive,in particular, with vector control, is to approach sensorless methods of controlling an induction motor. Purpose: to develop a method for calculating the speed and position of the rotor of an induction motor with a sensorless vector control with fast programmed calculation time and with a simple implementation of regulation, taking advantage of complex calculations. Methods: the article considers a computer with sensorless control of an induction motor, obtained by solving the system of Park-Gorev equations in complex form. Conducting a simultaneous calculation for two projections of variables using recording in complex form allows you to speed up the calculation speed. Verification of the results was carried out using computer simulation. For these purposes, an asynchronous motor model was built in the MatLab software. Results: a computer assembled on the basis of the solution proposed in this article, with high accuracy (0,5 %) determines the value of the engine speed, has a simple and flexible structure. The solution can be scaled and applied in other versions of the electric drive due to its versatility. Practical relevance: a solution of the Park-Gorev system of equations in a complex form is proposed. A base has been obtained for creating an asynchronous motor control system with an integrated computer. The application of the method considered in the article allows the use of a microprocessor of lower performance and power, which significantly reduces the cost of the hardware of the control system.

Keywords: observer, Park-Gorev equations, motor model, sensorless control, asynchronous motor.

Klyuchnikov Anatoly Terent'evich (Perm, Russian Federation) is a Ph.D. in Technical Sciences, Associate Professor of Department of Electrical Engineering and Electromechanics Perm National Research Polytechnic University (614990, Perm, 29, Komsomolsky pr., e-mail: aklu2011@pstu.ru).

Turpak Alexander Mikhailovich (Perm, Russian Federation) is a Graduate Student of Department of Electrical Engineering and Electromechanics Perm National Research Polytechnic University (614990, Perm, 29, Komsomolsky pr., e-mail: Turpak.Alexander@gmail.com

1. Zhou Q. et al. A Method for Permanent Magnet Synchronous Motor Control Based on Single-Loop SVPWM. Adv. Technol. Teach, 2012, no. 9, pp. 333-342.
2. Vorob'ev V.E. Osnovy elektromekhaniki: Pis'mennye lektsii [Fundamentals of Electromechanics: Written Lectures]. Saint Petersburg: SZTU, 2003. 79 p.
3. Blaschke F. Method for Controlling Asynchronous Machines: US Patent 3 824 437. July 16, 1974.
4. Kozlova L.E., Timoshkin V.V., Glazyrin A.S. Razrabotka nabliudatelia skorosti dlia sistemy upravleniia asinkhronnogo elektroprivoda s tiristornym reguliatorom napriazheniia [Development of a speed observer for an asynchronous electric drive control system with a thyristor voltage regulator]. Fundamental'nye issledovaniia, 2012, no. 9-3, pp. 656-661, available at: http://fundamental-research.ru/ru/article/view?id=30328 (accessed 17 May 2019).
5. Vishnevskii V.I., Lazarev S.A., Mitiukov P.V. Adaptivnyi skol'ziashchii nabliudatel' skorosti dlia bezdatchikovogo asinkhronnogo elektroprivoda [Adaptive sliding speed observer for a sensorless asynchronous electric drive]. Vestnik ChGU, 2010, no. 3, available at: https://cyber­leninka.ru/article/n/adaptivnyy-skolzyaschiy-nablyudatel-skorosti-dlya-bez­datchikovogo-asinhronnogo-elektroprivoda (accessed 17 May 2019).
6. Glazyrin A.S. Bezdatchikovoe upravlenie asinkhronnym elektro­privodom s sinergeticheskim reguliatorom [Sensorless control of an asynchronous electric drive with a synergistic controller]. Izvestiia Tomskogo politekhnicheskogo universiteta, 2012, no. 4, available at: https://cyber­leninka.ru/article/n/bezdatchikovoe-upravlenie-asinhronnym-elektroprivo-dom-s-sinergeticheskim-regulyatorom (accessed 17 May 2019).
7. Yan Z., Jin C., Utkin V.I. Sensorless sliding-mode control of induction motors. IEEE Trans. Ind. Electron, 2000, vol. 47, pp. 1286-1297.
8. Brammer K., Zifling G. Fil'tr Kalmana-B'iusi [Kalman-Bucy Filter]. Ed. I.E. Kazakova. Moscow: Nauka, 1982. 199 p.
9. Grigoryev M.A., Gorozhankin A.N., Kinas S.I., Belousov E.V. Dynamic parameters of active rectifiers. Russian Electrical Engineering, 2014, vol. 85, no. 10, pp. 638-640.
10. Funk T.A., Saprunova N.M., Belousov E.V., Zhuravlev A.M. Kosvennoe opredelenie sostavliaiushchikh peremeshcheniia v elektro­privode [Indirect determination of the components of the displacement in the electric drive]. Elektrotekhnika, 2015, no. 12.
11. Sinergeticheskie metody upravleniia slozhnymi sistemami: mekhanicheskie i elektromekhanicheskie sistemy [Synergistic methods of control of complex systems: mechanical and electromechanical systems]. Ed. A.A. Kolesnikov. Moscow: Editorial URSS, 2006. 279 p.
12. Veselov G.E. Prikladnaia teoriia i metody sinergeticheskogo sinteza ierarkhicheskikh sistem upravleniia [Applied theory and methods of synergistic synthesis of hierarchical control systems]. Ph. D. thesis. Taganrog, 2006. 332 p.
13. Tsytovich L.I., Brylina O.G., Dudkin M.M., Rakhmatulin R.M. Adaptive intervalcode integrating synchronization of control systems for power converters. Russian Electrical Engineering, 2013, vol. 84, no. 3, pp. 122-128.
14. Kalachev Iu.N. Nabliudateli sostoianiia v vektornom elektroprivode (zapiski diletanta) [State monitors in the vector drive (notes amateur)]. Moscow, 2015. 60 p.
15. Romanov I.V., Chudakov P.L. et al. Sposob upravleniia asinkhronnym tiagovym dvigatelem [Method of controlling an asynchronous traction motor]. Patent Rossiiskaia Federatsiia no. 2451389 (2012).
16. Balkovoi A.P., Tsatsenkin V.K. Pretsizionnyi elektroprivod s ventil'nymi dvigateliami [Precision electric drive with valve engines]. Moscow: Moskovskii energeticheskii institut, 2010.
17. Kopylov I.P. Matematicheskoe modelirovanie elektricheskikh mashin [Mathematical modeling of electrical machines]. Moscow: Vysshaia shkola, 2001.
18. Mukha V.S. Vychislitel'nye metody i komp'iuternaia algebra [Computational Methods and Computer Algebra.]. 2nd ed. Минск: Belorusskii gosudarstvennyi universitet informatiki i radioelektroniki, 2010. 148 p.
19. Kliuchnikov A.T. Tarirovka uravnenii asinkhronnykh mashin pri modelirovanii v otnositel'nykh edinitsakh [Calibration of the equations of asynchronous machines when modeling in relative units]. Elektrotekhnika, 2012, no. 3.
20. Kliuchnikov A.T. Uravneniia nesimmetrichnoi mnogofaznoi mashiny v prostranstvenno-vremennykh koordinatakh [The equations of an asymmetric multiphase machine in space-time coordinates]. Elektrichestvo, 1998, no. 7, pp. 36-39.

The electric power systems (EPS) of various industrial enterprises for a number of reasons are characterized by low quality of electric energy, in particular, the presence of higher harmonics in the grids, as a result of which conductive low-frequency electromagnetic interference (EMI) occurs, which has a negative effect on electrical equipment. This leads to the problem of the quality of electric energy in the EPS, which negatively affects the electrical equipment. The question of determining the conductive low-frequency EMI by the coefficient of the n-th harmonic component of the voltage within the framework of this problem remains unresolved. Purpose: development of an algorithm for determining the conductive low-frequency EMI by the coefficient of the n-th harmonic component of the voltage, which allows scientifically sound estimation of the electromagnetic environment in electric grids. Methods: the formation of a sequence of actions to determine the quality criterion for the functioning of electric power systems by the coefficient of the n-th harmonic component of the voltage. Results: based on the theory of probability and mathematical statistics, an algorithm has been developed for determining the conductive low-frequency electromagnetic field by the coefficient of the nth harmonic component of the voltage, based on the requirements of the standard GOST 32144-2013.

Based on the algorithm, a computer program that allows automated calculation of the parameters of the electromagnetic environment, including the distribution parameters of the coefficient of the n-th harmonic component of the voltage, such as the mean and standard deviation, the probability of the coefficients of the n-th harmonic component of the voltage exceeding the normalized values and the probability of the conductive low-frequency EMI by the coefficient of the n-th harmonic component of the voltage was developed. The program allows you to visualize the data arrays that were obtained during various experimental studies using waveforms and histograms. Practical relevance: the proposed algorithm allows you to generate reliable information about electromagnetic environment in EES and can be used to develop a concept for improving the quality of electric energy, taking into account the analytical and numerical aspects of computer research.

Keywords: Algorithm, power quality, conductive noise, harmonics, coefficient of the nth harmonic component of voltage.

Rudi Dmitry Yuryevich (Novosibirsk, Russian Federation) is a Graduate Student of the Department of Electric Power Systems and Electrical Engineering of the Siberian State University of Water Transport (630099, Novosibirsk, 33, Schetinkina str., e-mail: dima_rudi@mail.ru).

Gorelov Sergey Valeryevich (Novosibirsk, Russian Federation) is a Doctor of Technical Sciences, Professor, Professor of the Department of Electric Power Systems and Electrical Engineering of the Siberian State University of Water Transport (630099, Novosibirsk, 33, Schetinkina str.,
e-mail: nsawt_ese@mail.ru).

Vishnyagov Mikhail Gennadievich (Omsk, Russian Federation) is a Ph.D. in Technical Sciences, Associate Professor, Associate Professor of the Department of Electrical Engineering and Electrical Equipment of the Omsk Institute of Water Transport – Branch of the Siberian State University of Water Transport (644099, Omsk, 4, Ivan Alekseev str., e-mail: vishnyagov @ mail.ru).

Zubanov Dmitry Alexandrovich (Omsk, Russian Federation) is a Senior Lecturer, Department of Electrical Engineering and Electrical Equipment, Omsk Institute of Water Transport - Branch of the Siberian State University of Water Transport (644099, Omsk, 4, Ivan Alekseev str., e-mail: serdimitri@mail.ru).

Zubanova Natalia Valeryevna (Novosibirsk, Russian Federation) is a Graduate Student of the Department of Electric Power Systems and Electrical Engineering of the Siberian State University of Water Transport (630099, Novosibirsk, 33 Schetinkina str., e-mail: nsawt_ese@mail.ru).

Ivanov Dmitry Mikhailovich (Novosibirsk, Russian Federation) is a Student Novosibirsk State Technical University (630073, Novosibirsk, 20,
K. Marx ave., e-mail: nsawt_ese@mail.ru).

Ruppel Aleksandr Alexandrovich (Omsk, Russian Federation) is a Ph.D. in Technical Sciences, Associate Professor, Professor of the Department of Electrical Engineering and Electrical Equipment of the Omsk Institute of Water Transport – Branch of the Siberian State University of Water Transport (644099, Omsk, 4, Ivan Alekseev str., e-mail: ruppelsan@mail.ru).

1. GOST 32144–2013. Mezhgosudarstvennyi standart. Elektricheskaia energiia. Sovmestimost' tekhnicheskikh sredstv elektromagnitnaia. Normy kachestva elektricheskoi energii v sistemakh elektrosnabzheniia obshchego naznacheniia. (Vzamen GOST 13109-9, vved. 2014-07-01) [GOST 32144-2013. Interstate standard. Electric Energy. Electromagnetic compatibility. Quality standards for electric energy in general-purpose power supply systems. Instead of GOST 13109-97, enter 2014-07-01]. Moscow: Standartinform, 2014. 20 с.
2. Danilov G.A., Denchik Iu.M., Ivanov M.N., Sitnikov G.V. Povyshenie kachestva funktsionirovaniia linii elektroperedachi [Improving the quality of the functioning of power lines]. Eds. V.P. Gorelova, V.G. Sal'nikova. Novosibirsk: Novosibirskaia gosudarstvennaia akademiia vodnogo transporta, 2013. 559 p.
3. Rudi D.Iu., Antonov A.I., Vishniagov M.G. et al. Issledovanie vysshikh garmonik v elektricheskikh setiakh nizkogo napriazheniia [The study of higher harmonics in low voltage electrical networks]. Omskii nauchnyi vestnik, 2018, no. 6(162), pp. 119-125.
4. Khatsevskii K.V., Denchik Iu.M., Kleutin V.I. et al. Problemy kachestva elektroenergii v sistemakh elektrosnabzheniia [Problems of power quality in power supply systems]. Omskii nauchnyi vestnik, 2012, no. 2(110), pp. 212-214.
5. Ivanova E.V., Ruppel' A.A. Konduktivnye elektromagnitnye pomekhi v elektricheskikh setiakh 6-10 kV [Conducted electromagnetic interference in electric networks 6-10 kV]. Ed. V.P. Gorelova. Omsk: Novosibirskaia gosudarstvennaia akademiia vodnogo transporta, Omskii filial, 2004. 284 p.
6. Grigor'ev O. Vysshie garmoniki v setiakh elektrosnabzheniia 0,4 kV [Higher harmonics in 0.4 kV power supply networks]. Novosti elektrotekhniki, 2003, no. 1, pp. 54-56.
7. Stepanov V.M., Bazyl' I.M. Vliianie vysshikh garmonik v sistemakh elektrosnabzheniia predpriiatiia na poteri elektricheskoi energii [The influence of higher harmonics in the power supply systems of the enterprise on the loss of electric energy]. Izvestiia Tul'skogo gosudarstvennogo universiteta. Tekhnicheskie nauki, 2013, no. 12-2, pp. 27-31.
8. Glotov A.A., Denchik Iu.M. Obespechenie elektromagnitnoi sovmestimosti elektricheskikh setei po dopustimym urovniam konduktivnykh nizkochastotnykh elektromagnitnykh pomekh [Ensuring the electromagnetic compatibility of electrical networks at acceptable levels of conductive low-frequency electromagnetic interference]. Energetika: effektivnost', nadezhnost', bezopasnost'. Materialy XXI Vserossiiskoi nauchno-tekhnicheskoi konferentsii, 2015, pp. 12-15.
9. Ivanova E.V. Konduktivnye elektromagnitnye pomekhi v elektroenergeticheskikh sistemakh [Conducted electromagnetic interference in electric power systems]. Eds. V.P. Gorelov, N.N. Lizalek. Novosibirsk: Novosibirskaia gosudarstvennaia akademiia vodnogo transporta, 2006. 432 p.
10. Olhovskiy V.Ya., Myateg S.V., Myateg T.V. Analyzes of high harmonics generation and power losses of low power consumers within 1000 V networks. 2016 2nd International Conference on Industrial Engineering, Applications and Manufacturing, ICIEAM 2016 - Proceedings 2, 2016. P. 7911026.
11. Ded A.V., Maltsev V.N., Sikorski S.P. Comparative analysis of the specifications on the power quality of the european union and the Russian Federation. Journal of Physics: Conference Series Theory and Practice. Ser. Metrology, Standardization, Quality: Theory and Practice, MSQ 2017, 2018. P. 012007.
12. Denchik Iu.M. Metodika opredeleniia konduktivnoi nizkochastotnoi elektromagnitnoi pomekhi v elektricheskoi seti pri garmonicheskom vozdeistvii [Method for determining the conductive low-frequency electromagnetic interference in the electric network under harmonic influence]. Nauchnye problemy transporta Sibiri i Dal'nego Vostoka, 2013, no. 2, pp. 218-221.
13. Antonov A.I., Vishniagov M.G., Denchik Iu.M. et al. Analiz opredeleniia konduktivnoi nizkochastotnoi pomekhi po koeffitsientu nesinusoidal'nosti krivoi napriazheniia [Analysis of the definition of conductive low-frequency noise by the coefficient of non-sinusoidality of the voltage curve]. Omskii nauchnyi vestnik, 2015, no. 3(143), pp. 244-247.
14. Denchik Iu.M. Opredelenie parametrov polia sobytii v elektricheskikh setiakh pri slozhnoi elektromagnitnoi obstanovki [Determination of the parameters of the field of events in electrical networks in a complex electromagnetic environment]. Nauchnye problemy transporta Sibiri i Dal'nego Vostoka, 2010, no. 2, pp. 418-424.
15. Kovalev A.Iu., Kovaleva N.A., Ivanova E.V. et al. Matema­ticheskoe opisanie protsessa formirovaniia v elektricheskoi seti konduk­tivnykh nizkochastotnykh elektromagnitnykh pomekh [A mathematical description of the process of formation of conductive low-frequency electromagnetic interference in the electric network]. Kul'tura, nauka, obrazo­vanie: problemy i perspektivy. Materialy VI Mezhdunarodnoi nauchno-prakticheskoi konferentsii, 2017, pp. 143-145.
16. Antonov A.I., Vishniagov M.G., Kleutin V.I., Ruppel' A.A. Veroiatnost' i protsess vozniknoveniia konduktivnoi elektromagnitnoi pomekhi v elektroenergeticheskikh sistemakh [The probability and process of the occurrence of conductive electromagnetic interference in electric power systems]. Sbornik nauchnykh trudov Omskogo instituta vodnogo transporta (filial) - SGUVT. Omsk, 2015, pp. 4-8.
17. Ivanova Iu.M. Metodologiia issledovaniia konduktivnykh elektro­magnitnykh pomekh, rasprostraniaiushchikhsia po setiam [Methodology for the study of conducted electromagnetic interference propagating through networks]. Konduktivnye elektromagnitnye pomekhi v elektroenergeticheskikh sistemakh. Eds. V.P. Gorelov, N.N. Lizalek. Novosibirsk: Novosibirskaia gosudarstvennaia akademiia vodnogo transporta, 2006. 432 p, pp. 52-56.
18. Denchik Iu.M. Metodika opredeleniia konduktivnoi nizkochastotnoi elektromagnitnoi pomekhi v elektricheskoi seti pri garmonicheskom vozdeistvii [Method for determining the conductive low-frequency electromagnetic interference in an electric network under harmonic influence]. Nauchnye problemy transporta Sibiri i Dal'nego Vostoka, 2013, no. 2, pp. 218-221.
19. Ivanova E.V., Kulikov S.G. Opredelenie konduktivnoi elektromagnitnoi pomekhi po koeffitsientu iskazheniia sinusoidal'nosti krivoi napriazheniia v seti obshchego naznacheniia [Determination of conducted electromagnetic interference by the distortion coefficient of the sinusoidality of the voltage curve in a general-purpose network]. Transportnoe delo Rossii, 2006, no. 11-1, pp. 42-44.
20. Gorelov, S.V., Glotov A.A., Denchik Iu.M. Dopustimye urovni elektromagnitnoi sovmestimosti dlia konduktivnykh nizkochastotnykh elektromagnitnykh pomekh v elektroenergeticheskoi sisteme [Permissible levels of electromagnetic compatibility for conductive low-frequency electromagnetic interference in an electric power system]. Nauchnye problemy transporta Sibiri i Dal'nego Vostoka, 2015, no. 3, pp. 194-197.
21. Antonov A.I., Denchik Iu.M., Zubanov D.A. et al. Algoritm opredeleniia konduktivnoi nizkochastotnoi elektromagnitnoi pomekhi po koeffitsientu n-i garmonicheskoi sostavliaiushchei napriazheniia [The algorithm for determining the conductive low-frequency electromagnetic interference by the coefficient of the nth harmonic component of the voltage]. Nauka i obrazovanie. Avgust 2019, no. 8(123). 28 p.
22. Rudi D.Iu., Gorelov S.V., Ruppel' A.A. Issledovanie vysshikh garmonik v rabochei elektricheskoi seti nizkogo napriazheniia [The study of higher harmonics in a working low voltage electrical network]. Aktual'nye voprosy professional'nogo obrazovaniia i puti ikh resheniia. Materialy mezhdunarodnoi nauchno-prakticheskoi konferentsii. Iakutsk, 2019, pp. 27-32.
23. Rudi D.Iu. Issledovanie summarnogo koeffitsienta garmonicheskikh sostavliaiushchikh v elektricheskikh setiakh nizkogo napriazheniia [Investigation of the total coefficient of harmonic components in low voltage electrical networks]. Nauchnoe soobshchestvo studentov XXI stoletiia. Tekhnicheskie nauki. Materialy LXXVII Studencheskoi mezhdunarodnoi nauchno-prakti­cheskoi konferentsii. Novosibirsk, 2019, pp. 231-238.
24. Rudi D.Iu. Issledovanie pokazatelei kachestva elektroenergii v rabochei elektricheskoi seti tsekha metalloizdelii [Study of indicators of the quality of electricity in the working electric network of the metalware workshop]. Teoreticheskie i prakticheskie problemy razvitiia sovremennoi nauki: sb. materialov XVIII Mezhdunarodnoi nauchno-prakticheskoi konferentsii, 2019, pp. 7-14.

When the distance between electric charges tends to zero, the potential energy of the electrostatic field tends to infinity, which is not good. Possible attempts to save the situation by reasoning about the impossibility of achieving a zero distance due to the finite size of charged objects are unproductive, since it is believed that, for example, electrons and positrons have no sizes. The purpose of the study is to exclude the possibility of developing infinitely large electrostatic energy. The relevance of the work is due to a significant increase in the role of electrostatic energy in connection with the start of mass production of electric vehicles and the need for the development of theoretical support in this regard. Definitions are given. Definition 1. The total stored energy is the energy of a system or an object equal to the maximum work that a system or object can do if it or he is given such an opportunity. Definition 2. The conditional realized stored energy is a part of the total stored energy of a system or object equal to the work that the system or object can do, limited by the condition that excludes the possibility of the system or object performing the maximum work that the system or object can hypothetically perform. Definition 3. Conditional unrealizable stored energy is a part of the total stored energy of a system or object equal to the work that the system or object cannot perform, limited by the condition that excludes the possibility of the system or object performing the maximum work that the system or object can hypothetically perform. A number of theorems are proved, including Theorem 1 - the stored energy is always positive; Theorem 6 - the field energy of a system of two charged spheres, one of which is completely inside the other, is a constant, i.e. independent of the location of the inner sphere.

Keywords: full, conditional realized, unrealized, stored, electrostatic energy, homonymous, unlike charges.

Popov Igor Pavlovich (Kurgan, Russian Federation) is a Senior Lecturer of the Department “Technology of mechanical engineering, machine tools and instruments” Kurgan State University (640020, Kurgan, 63/4, Sovetskaya str., e-mail: ip.popow@yandex.ru).

1. Popov I.P. The size of the electron with spin. Engineering physics, 2016, no. 9, pp. 45-46.
2. Karaian G.S., Gandilian S.V. Tendentsii razvitiia sovmeshchennykh magnito-elektroinduktsionnykh elektromekhanicheskikh preobrazovatelei energii [Development trends of combined magneto-electric induction electromechanical energy converters]. Vestnik Moskovskogo energeticheskogo instituta, 2018, no 2, pp. 65-71. DOI: 10.24160/1993-6982-2018-2-65-71
3. Kuznetsova T.A. Algoritmy analiza elektricheskikh polei kabelei postoiannogo toka v sostave SAU GTD [Algorithms for the analysis of the electric fields of DC cables as part of the ACS GTE]. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Elektrotekhnika, informatsionnye tekhnologii, sistemy upravleniia, 2018, no. 25, pp. 23-35.
4. Trufanova N.M., Borodulina K.V., Diatlov I.Ia. Matematicheskoe modelirovanie zavisimosti napriazhennosti elektricheskogo polia na provodakh vozdushnoi linii ot parametrov rasshchepleniia [Mathematical modeling of the dependence of the electric field on the wires of the overhead line on the splitting parameters]. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Elektrotekhnika, informatsionnye tekhnologii, sistemy upravleniia. 2018, no. 27, pp. 128-138.
5. Kovrigin L.A., Sitchikhin N.A. Issledovanie ekraniruiushchikh svoistv pletenok v statsionarnom elektricheskom pole [The study of the shielding properties of braids in a stationary electric field]. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo univer­siteta. Elektrotekhnika, informatsionnye tekhnologii, sistemy upravleniia, 2012, no. 6, pp. 93-97.
6. Butlitskii M.A., Zelener B.B., Zelener B.V., Manykin E.A. Dvukhchastichnaia matritsa plotnosti i psevdopotentsial elektron-protonnogo vzaimodeistviia dlia ul'tranizkikh temperatur [Two-particle density matrix and pseudopotential of electron-proton interaction for ultra-low temperatures]. Zhurnal vychislitel'noi matematiki i matematicheskoi fiziki, 2008, vol. 48, no. 1, pp. 154-158.
7. Teber S., Kotikov A.V. Effekty elektron-elektronnogo vzaimo­deistviia v planarnykh zhidkostiakh Diraka [Effects of electron-electron interaction in Dirac planar fluids]. Teoreticheskaia i matematicheskaia fizika, 2019, vol. 200, no. 2, pp. 343-360, available at: https://doi.org/10.4213/tmf9678
8. Neznamov V.P., Safronov I.I. Statsionarnye resheniia uravneniia vtorogo poriadka dlia fermionov vo vneshnem kulonovskom pole [Stationary solutions of the second order equation for fermions in an external Coulomb field]. Zhurnal eksperimental'noi i teoreticheskoi fiziki, 2019, vol. 155, no. 5, pp. 792-805. DOI: 10.1134/S0044451019050031
9. Keikimanova M.T., Muratova G.I., Nametkulova R.Zh., Sarybekov M.N., Tkachenko I.M. Dinamicheskie svoistva dvumernogo plotnogo elektronnogo gaza [Dynamic properties of a two-dimensional dense electron gas]. Zhurnal eksperimental'noi i teoreticheskoi fiziki, 2019, vol. 155, no. 6, pp. 1098-1106. DOI: 10.1134/S0044451019060142
10. Popov I.P. Dielektricheskoe soprotivlenie i analog zakona Oma dlia tsepi potoka elektricheskogo smeshcheniia [Dielectric resistance and an analogue of Ohm's law for an electric bias flow circuit]. Sbornik nauchnykh trudov aspirantov i soiskatelei Kurganskogo gosudarstvennogo universiteta, 2010, iss. XII, pp. 19-20.
11. Popov I.P. Combined vectors and magnetic charge. Applied Physics and Mathematics, 2018, no. 6, pp. 12-20. DOI: 10.25791/pfim.06.2018.329
12. Popov I.P. Mathematical modeling of the formal analogy of electromagnetic field. Applied mathematics and control sciences, 2016, no. 4, pp. 36-60.
13. Shcherbakov A.V. Impul'snyi vysokovol'tnyi moduliator s chastichnym razriadom emkostnogo nakopitelia [Pulse high-voltage modulator with partial discharge of a capacitive storage]. Vestnik Moskovskogo energeticheskogo instituta, 2017, no. 1, pp. 50-57.
14. Popov I.P., Sarapulov F.N., Sarapulov S.F. Emkostno-emkostnaia kolebatel'naia sistema [Capacitive-capacitive oscillatory system]. Vestnik Kurganskogo gosudarstvennogo universiteta. Tekhnicheskie nauki, 2014, iss. 9, no. 2(33), pp. 21-23.
15. Smirnov D.S. Udel'naia moshchnost' silovykh induktivnostei i emkostei [Power density inductance and capacitance]. Vestnik Moskovskogo energeticheskogo instituta, 2017, no. 2, pp. 82-87.
16. Popov I.P. Calculated reference systems for relative motion of space objects. Engineering physics, 2019, no. 3, pp. 40-43. DOI: 10.25791/infizik.03.2019.564
17. Popov I.P. Reference Systems in the Navigation of Moving Objects. Mechatronics, Automation, Control, 2019, vol. 20, no. 3, pp. 189-192, available at: https://doi.org/10.17587/mau.20.189-192
18. Popov I.P. “Unikal'nye” sistemy otscheta [“Unique” reference systems]. Vestnik Kaluzhskogo universiteta, 2019, no. 1, pp. 67-69.
19. Popov I.P. Modeling of objects in the form of superposition of states. Applied mathematics and control sciences, 2015, no. 2, pp. 18-27.
20. Popov I.P. Superpozitsiia granichnykh sostoianii makroob"ektov [Superposition of the boundary states of macro-objects]. Vesti vysshikh uchebnykh zavedenii Chernozem'ia, 2015, no. 2, pp. 43-47.