Abstract
Problem Statement (Relevance): This paper describes one of the possible variants of the quantitative relationship between the coefficients of the B-form equations and the equations of other forms that evaluate the state of a passive six-terminal network with two input and four output terminals. Such six-terminal network can replace devices, elements or parts of electrical circuits or electric power systems. The coefficients of the B-form equations, as well as the coefficients of the A-form equations, can be determined experimentally. In principle, the coefficients of equations of other forms can also be determined experimentally. However, such experiments are usually difficult to set up and conduct. Thus, it seems to be more reasonable to determine these coefficients from the established quantitative relationship with the previously determined coefficients of the B-form. Objectives: To establish a quantitative relationship between the coefficients of the B-form equations describing the state of the six-terminal network with two input and four output terminals and the coefficients of the G-, H-, Y- and Z-form equations describing the state of the same six-terminal network. Methods Applied: Mathematical modelling and some elements of the theory of multi-terminal networks. Originality: The originality of this research lies in the proposed method of establishing a quantitative relationship between the coefficients of the A-form equations and the equations of other forms describing the state of the passive six-terminal network with two input and four output terminals. Findings: This paper examines one of the possible variants of the quantitative relationship between the coefficients of the B-form equations and the coefficients of the G-, H-, Y- and Z-form equations describing the state of the passive six-terminal network with two input and four output terminals. Some mathematical statements are presented which can help establish such relationship. Practical Relevance: If one knows the values of the B-form equation coefficients, the proposed quantitative relationship between the coefficients of various forms of equations will help build equations of other forms and establish various types of dependencies between the input and output characteristics of an electric power unit, which can be replaced with a six-terminal network with two input and four output terminals. This technique can be used to establish a quantitative relationship between the coefficients of the G-, H-, Y- or Z-form equations and the coefficients of equations of other forms describing the state of different modifications of passive six-terminal networks.
Keywords
Equations, coefficients, stresses, currents, A-form, B-form, G-form, H-form, Y-form, Z-form.
1. Voronov R.A. Obshchaya teoriya chetyrekhpolyusnikov i mnogopolyusnikov [The general theory of four- and multi-terminal networks]. Moscow; Leningrad: Gosenergoizdat, 1951, 192 p. (In Russ.)
2. Zeveke G.V. Mnogopolyusniki [Multipoles]. Moscow: MEI, 1971, 23 p. (In Russ.)
3. Popov N.M., Olin D.M., Kirilin A.A. Signal transmission over 0.38 kV rural distribution networks. Vestnik KrasGAU [Bulletin of KrasGAU], 2017, no. 2, pp. 88-97. (In Russ.)
4. Barabanov E.A., Maltseva I.S., Barabanov I.O. Algorithm of parallel data processing in optical networks. Nauchnyy vestnik NGTU [Science bulletin of NSTU], 2004, vol. 56, no. 3, pp. 88–95. (In Russ.)
5. Hansen R.C. Fazirovannye antennye reshetki [Phased array antennas]. Moscow: Tekhnosfera, 2012, 560 p. (In Russ.)
6. Skobelev S.P. Fazirovannye antennye reshetki s sektornymi diagrammami napravlennosti [Phased array antennas with sector-shaped patterns]. Moscow: Fizmatlit, 2016, 320 p. (In Russ.)
7. Fanyaev I.A., Kudin V.P. Distribution power matrix for an eight-element antenna array. Vestnik Gomelskogo gosudarstvennogo tekhnicheskogo universiteta im. P.O. Sukhogo [Bulletin of Sukhoi State Technical University of Gomel], 2012, no. 4, pp. 52–57. (In Russ.)
8. Shauerman A.A. Understanding how the uncertainty of measuring the complex reflection coefficient of terminal devices depends on the parameters of the measuring transducer. Vestnik SibGUTI [Bulletin of SibSUTIS], 2013, no. 3, pp. 20–28. (In Russ.)
9. Salimonenko D.A. Application of linear programming methods for determining the parameters of electrical circuits Part 1. Vestnik Bashkirskogo universiteta [Bulletin of Bashkir University], 2015, vol. 20, no. 4, pp. 1155–1163.
10. Selivanov V.N. Exploring the programmes for calculating the ATR-EMTR electromagnetic processes in the educational process. Vestnik MGTU [Vestnik of MSTU], 2009, vol. 12, no. 1, pp. 107–112. (In Russ.)
11. Kulikov A.L., Lukicheva I.A. Location of faults in power transmission lines based on the instantaneous values of the alarm oscillograms. Vestnik IGEU [Vestnik of Ivanovo State Power Engineering University], 2016, Issue 5, pp. 16–21. (In Russ.)
12. Kitaev A.V., Agbomassu V.L., Glukhova V.I. Equivalent circuits for AC motors. Elektrotekhnicheskie i kompyuternye sistemy [Electrical and computer systems], 2013, no. 11 (87), pp. 59–65. (In Russ.)
13. Belyakov Yu.S. Mnogopolyusnik kak model elektricheskikh sistem [Multipole network as a model electrical system]. Part 2. Moscow: NTF Energoprogress, 2013, 92 p. (In Russ.)
14. Sarapulov F.N., Sarapulov S.F., Radionov I.E. Modelling of temperature regimes of a traction linear induction motor. Elektroprivody peremennogo toka [Alternating current drives], 2015, pp. 141–144. (In Russ.)
15. Belyakov Yu.S. Raschet rezhimov elektricheskikh sistem, predstavlennykh mnogopolyusnikami [Calculation of themodes of electrical systems represented by multipoles]. Moscow: Sputnik, 2008, 124 p. (In Russ.)
16. Fedotov Yu.B., Nesterov S.A., Mustafa G.M. Optimized programs for modelling power electronics devices. Apriori. Seriya: estestvennye i tekhnicheskie nauki [Apriori. Series: Natural and technical sciences], 2015, no. 6, pp. 1–14. (In Russ.)
17. Tlustenko S.F., Koptev A.N. Developing and understanding the ways to ensure information support of aircraft assembly line systems. Izvestiya Samarskogo nauchnogo tsentra RAN [Izvestia of Samara Scientific Center of the Russian Academy of Sciences], 2015, vol. 17, no. 6 (2), pp. 491–497. (In Russ.)
18. Musaeva U.A. Computer-aided design of microwave phase shifter. Molodoy uchenyy [Young scientist], 2013, no. 3, pp. 83–88. (In Russ.)
19. Lvov A.A., Lvov P.A. Application of an integrated multipole reflectometer for measuring the distance to a flat surface. XII Vserossiyskoe soveshchanie po problemam upravleniya [12th National Conference on Control Problems], 2014. Moscow, 2014, pp. 7044–7055. (In Russ.)
20. Kryukov A.N., Shakhmatov E.V., Samsonov V.N., Druzhin A.N. Design methodology and advanced design of noise reduction means for ship pipelines. Fundamentalnaya i prikladnaya gidrofizika [Fundamental and applied hydrophysics], 2014, vol. 7, no. 3, pp. 67–79. (In Russ.)
21. Levitskiy Zhorzh G., Imanov Zhenis Zh., Nurgaliyeva Assel D. Quasianalog transformation of the Compound Ventilating Network. European Researcher, 2013, vol (40), no. 2–1, pp. 259–267.
22. Poplavskiy V.B. Cramer's formula for systems of linear equations and inequalities over Boolean algebra. Izvestiya Saratovskogo universiteta. Seriya: Matematika. Informatika [Bulletin of Saratov University. Series: Mathematics. Informatics], 2011, iss. 5, part 2, pp. 43–46. (In Russ.)
23. Akopjanyan G.D., Safaryan V.S. Synthesizing a passive linear multi-terminal network from one pair of terminals. Izvestiya NAN RA i GIUA. Seriya: Tekhnicheskie nauki [Bulletin of the National Academy of Sciences of the Republic of Armenia and the State Engineering University of Armenia. Series: Engineering], 2002, Т.LV., no. 2, pp. 258–262. (In Russ.)
24. Popov S.A., Korchagin A.F. Evaluating the parameters of the equivalent circuit of multipoles with the help of multiresponse models. Vestnik Novgorodskogo gosudarstvennogo universiteta [Bulletin of Novgorod State University], 2004, no. 28, pp. 150–155. (In Russ.)
25. Bessonov A.V., Luzin S.Yu., Lyachek Yu.T. Definition of the multi-terminal network neighborhood. Izvestiya SPbGETU [Proceedings of Saint Petersburg Electrotechnical University], 2015, no. 5, pp. 20–23. (In Russ.)
26. Bolshanin G.A. Mnogopolyusniki [Multipoles]. Bratsk: Publishing House of Bratsk State University, 2017, 337 p. (In Russ.)