General analytical solutions for DC/AC circuit-network analysis
In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm’s law is valid at every edge and that charge at every node is conserved (w...
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| Médium: | article |
| Jazyk: | angličtina |
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2017
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| On-line přístup: | https://hdl.handle.net/20.500.12008/22102 |
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| _version_ | 1868890109231759360 |
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| author | Rubido, Nicolás |
| author2 | Grebogi, C. Baptista, M. S. |
| author2_role | author author |
| author_browse | Baptista, M. S. Grebogi, C. Rubido, Nicolás |
| author_facet | Rubido, Nicolás Grebogi, C. Baptista, M. S. |
| author_role | author |
| collection | COLIBRI |
| dc.contributor.none.fl_str_mv | Rubido, Nicolás. Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física |
| dc.creator.none.fl_str_mv | Rubido, Nicolás Grebogi, C. Baptista, M. S. |
| dc.date.none.fl_str_mv | 2017 2019-10-02T22:14:54Z 2019-10-02T22:14:54Z 20191001 |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Rubido, N.,Grebogi, C., Baptista, M.S.General analytical solutions for DC/AC circuit-network analysis. European Physical Journal: Special Topics, 2017, 226 (9): 1829-1844. doi: 10.1140/epjst/e2017-70074-2. 1951-6355 https://hdl.handle.net/20.500.12008/22102 10.1140/epjst/e2017-70074-2 |
| dc.language.none.fl_str_mv | en eng |
| dc.publisher.none.fl_str_mv | Springer Verlag |
| dc.relation.none.fl_str_mv | European Physical Journal: Special Topics, 2017, 226 (9): 1829-1844 |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess Licencia Creative Commons Atribución (CC –BY 4.0) |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.none.fl_str_mv | Electric power transmission Física |
| dc.title.none.fl_str_mv | General analytical solutions for DC/AC circuit-network analysis |
| dc.type.none.fl_str_mv | Artículo info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| description | In this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm’s law is valid at every edge and that charge at every node is conserved (with the exception of the source/sink nodes). The resistive, capacitive, and/or inductive properties of the lines in the circuit define a complex network structure with given impedances for each edge. Our solution for the currents at each edge is derived in terms of the eigenvalues and eigenvectors of the Laplacian matrix of the network defined from the impedances. This derivation also allows us to compute the equivalent impedance between any two nodes of the circuit and relate it to currents in a closed circuit which has a single voltage generator instead of many input/output source/sink nodes. This simplifies the treatment that could be done via Thévenin’s theorem. Contrary to solving Kirchhoff’s equations, our derivation allows to easily calculate the redistribution of currents that occurs when the location of sources and sinks changes within the network. Finally, we show that our solutions are identical to the ones found from Circuit Theory nodal analysis. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | anni_7ee71bd734849b30fd0f4b77fcb88814 |
| identifier_str_mv | Rubido, N.,Grebogi, C., Baptista, M.S.General analytical solutions for DC/AC circuit-network analysis. European Physical Journal: Special Topics, 2017, 226 (9): 1829-1844. doi: 10.1140/epjst/e2017-70074-2. 1951-6355 10.1140/epjst/e2017-70074-2 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | anni |
| network_name_str | oai-lr-anni |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/22102 |
| publishDate | 2017 |
| publishDateSort | 2017 |
| publisher.none.fl_str_mv | Springer Verlag |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | Licencia Creative Commons Atribución (CC –BY 4.0) |
| spelling | General analytical solutions for DC/AC circuit-network analysisRubido, NicolásGrebogi, C.Baptista, M. S.Electric power transmissionFísicaIn this work, we present novel general analytical solutions for the currents that are developed in the edges of network-like circuits when some nodes of the network act as sources/sinks of DC or AC current. We assume that Ohm’s law is valid at every edge and that charge at every node is conserved (with the exception of the source/sink nodes). The resistive, capacitive, and/or inductive properties of the lines in the circuit define a complex network structure with given impedances for each edge. Our solution for the currents at each edge is derived in terms of the eigenvalues and eigenvectors of the Laplacian matrix of the network defined from the impedances. This derivation also allows us to compute the equivalent impedance between any two nodes of the circuit and relate it to currents in a closed circuit which has a single voltage generator instead of many input/output source/sink nodes. This simplifies the treatment that could be done via Thévenin’s theorem. Contrary to solving Kirchhoff’s equations, our derivation allows to easily calculate the redistribution of currents that occurs when the location of sources and sinks changes within the network. Finally, we show that our solutions are identical to the ones found from Circuit Theory nodal analysis.Springer VerlagRubido, Nicolás. Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física2019-10-02T22:14:54Z2019-10-02T22:14:54Z201720191001Artículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfRubido, N.,Grebogi, C., Baptista, M.S.General analytical solutions for DC/AC circuit-network analysis. European Physical Journal: Special Topics, 2017, 226 (9): 1829-1844. doi: 10.1140/epjst/e2017-70074-2. 1951-6355https://hdl.handle.net/20.500.12008/2210210.1140/epjst/e2017-70074-2 reponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaenengEuropean Physical Journal: Special Topics, 2017, 226 (9): 1829-1844Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad De La República. (Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución (CC –BY 4.0)oai:colibri.udelar.edu.uy:20.500.12008/221022026-04-14T10:09:21Z |
| spellingShingle | General analytical solutions for DC/AC circuit-network analysis Rubido, Nicolás Electric power transmission Física |
| status_str | publishedVersion |
| title | General analytical solutions for DC/AC circuit-network analysis |
| title_full | General analytical solutions for DC/AC circuit-network analysis |
| title_fullStr | General analytical solutions for DC/AC circuit-network analysis |
| title_full_unstemmed | General analytical solutions for DC/AC circuit-network analysis |
| title_short | General analytical solutions for DC/AC circuit-network analysis |
| title_sort | General analytical solutions for DC/AC circuit-network analysis |
| topic | Electric power transmission Física |
| url | https://hdl.handle.net/20.500.12008/22102 |