A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation
This paper presents a comparative analysis of six different iterative power flow methods applied to AC distribution networks, which have been recently reported in the scientific literature. These power flow methods are (i) successive approximations, (ii) matricial backward/forward method, (iii) tria...
- Autores:
-
Montoya, Oscar Danilo
Molina-Cabrera, Alexander
Hernández, Jesus C.
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/10382
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/10382
https://doi.org/10.3390/electronics10212573
- Palabra clave:
- Power flow methods
Electric distribution grids
Single-phase representation
Numerical methods for distribution networks
Linear and quadratic convergence
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| id |
UTB2_25f68f5f10f1e6fe51c0edd3a16b87e6 |
|---|---|
| oai_identifier_str |
oai:repositorio.utb.edu.co:20.500.12585/10382 |
| network_acronym_str |
UTB2 |
| network_name_str |
Repositorio Institucional UTB |
| repository_id_str |
|
| dc.title.spa.fl_str_mv |
A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation |
| title |
A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation |
| spellingShingle |
A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation Power flow methods Electric distribution grids Single-phase representation Numerical methods for distribution networks Linear and quadratic convergence LEMB |
| title_short |
A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation |
| title_full |
A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation |
| title_fullStr |
A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation |
| title_full_unstemmed |
A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation |
| title_sort |
A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation |
| dc.creator.fl_str_mv |
Montoya, Oscar Danilo Molina-Cabrera, Alexander Hernández, Jesus C. |
| dc.contributor.author.none.fl_str_mv |
Montoya, Oscar Danilo Molina-Cabrera, Alexander Hernández, Jesus C. |
| dc.subject.keywords.spa.fl_str_mv |
Power flow methods Electric distribution grids Single-phase representation Numerical methods for distribution networks Linear and quadratic convergence |
| topic |
Power flow methods Electric distribution grids Single-phase representation Numerical methods for distribution networks Linear and quadratic convergence LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
This paper presents a comparative analysis of six different iterative power flow methods applied to AC distribution networks, which have been recently reported in the scientific literature. These power flow methods are (i) successive approximations, (ii) matricial backward/forward method, (iii) triangular-based approach, (iv) product linearization method, (v) hyperbolic linearization method, and (vi) diagonal approximation method. The first three methods and the last one are formulated without recurring derivatives, and they can be directly formulated in the complex domain; the fourth and fifth methods are based on the linear approximation of the power balance equations that are also formulated in the complex domain. The numerical comparison involves three main aspects: the convergence rate, processing time, and the number of iterations calculated using the classical Newton–Raphson method as the reference case. Numerical results from two test feeders composed of 34 and 85 nodes demonstrate that the derivative-free methods have linear convergence, and the methods that use derivatives in their formulation have quadratic convergence |
| publishDate |
2021 |
| dc.date.issued.none.fl_str_mv |
2021-10-21 |
| dc.date.accessioned.none.fl_str_mv |
2022-01-17T20:39:58Z |
| dc.date.available.none.fl_str_mv |
2022-01-17T20:39:58Z |
| dc.date.submitted.none.fl_str_mv |
2022-01-07 |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.hasversion.spa.fl_str_mv |
info:eu-repo/semantics/restrictedAccess |
| dc.type.spa.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.identifier.citation.spa.fl_str_mv |
Montoya, O.D.; Molina-Cabrera, A.; Hernández, J.C. A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation. Electronics 2021, 10, 2573. https://doi.org/10.3390/ electronics10212573 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/10382 |
| dc.identifier.doi.none.fl_str_mv |
https://doi.org/10.3390/electronics10212573 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Tecnológica de Bolívar |
| dc.identifier.reponame.spa.fl_str_mv |
Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Montoya, O.D.; Molina-Cabrera, A.; Hernández, J.C. A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation. Electronics 2021, 10, 2573. https://doi.org/10.3390/ electronics10212573 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/10382 https://doi.org/10.3390/electronics10212573 |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.uri.*.fl_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
| dc.rights.cc.*.fl_str_mv |
Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
| rights_invalid_str_mv |
http://creativecommons.org/licenses/by-nc-nd/4.0/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.extent.none.fl_str_mv |
17 páginas |
| dc.format.mimetype.spa.fl_str_mv |
application/pdf |
| dc.publisher.place.spa.fl_str_mv |
Cartagena de Indias |
| dc.source.spa.fl_str_mv |
Electronics - vol. 10 n° 21 |
| institution |
Universidad Tecnológica de Bolívar |
| bitstream.url.fl_str_mv |
https://repositorio.utb.edu.co/bitstream/20.500.12585/10382/1/%5bArt.%2044%5d%20A%20Comparative%20Study%20on%20Power%20Flow%20M_Oscar%20Danilo%20Montoya.pdf https://repositorio.utb.edu.co/bitstream/20.500.12585/10382/2/license_rdf https://repositorio.utb.edu.co/bitstream/20.500.12585/10382/3/license.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/10382/4/%5bArt.%2044%5d%20A%20Comparative%20Study%20on%20Power%20Flow%20M_Oscar%20Danilo%20Montoya.pdf.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/10382/5/%5bArt.%2044%5d%20A%20Comparative%20Study%20on%20Power%20Flow%20M_Oscar%20Danilo%20Montoya.pdf.jpg |
| bitstream.checksum.fl_str_mv |
d7296c9e1e41a83c058d2ac882a1f123 4460e5956bc1d1639be9ae6146a50347 e20ad307a1c5f3f25af9304a7a7c86b6 0888932445b964358fe87ad1224c6332 3ec452cb239bf19c547fa67647781621 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional UTB |
| repository.mail.fl_str_mv |
repositorioutb@utb.edu.co |
| _version_ |
1814021646523039744 |
| spelling |
Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Molina-Cabrera, Alexander01b29f76-a1f3-4151-a070-ce883ba39849Hernández, Jesus C.349b3120-388b-42be-8bea-32156f0dc09d2022-01-17T20:39:58Z2022-01-17T20:39:58Z2021-10-212022-01-07Montoya, O.D.; Molina-Cabrera, A.; Hernández, J.C. A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representation. Electronics 2021, 10, 2573. https://doi.org/10.3390/ electronics10212573https://hdl.handle.net/20.500.12585/10382https://doi.org/10.3390/electronics10212573Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis paper presents a comparative analysis of six different iterative power flow methods applied to AC distribution networks, which have been recently reported in the scientific literature. These power flow methods are (i) successive approximations, (ii) matricial backward/forward method, (iii) triangular-based approach, (iv) product linearization method, (v) hyperbolic linearization method, and (vi) diagonal approximation method. The first three methods and the last one are formulated without recurring derivatives, and they can be directly formulated in the complex domain; the fourth and fifth methods are based on the linear approximation of the power balance equations that are also formulated in the complex domain. The numerical comparison involves three main aspects: the convergence rate, processing time, and the number of iterations calculated using the classical Newton–Raphson method as the reference case. Numerical results from two test feeders composed of 34 and 85 nodes demonstrate that the derivative-free methods have linear convergence, and the methods that use derivatives in their formulation have quadratic convergence17 páginasapplication/pdfenghttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://purl.org/coar/access_right/c_abf2Electronics - vol. 10 n° 21A Comparative Study on Power Flow Methods Applied to AC Distribution Networks with Single-Phase Representationinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/resource_type/c_2df8fbb1Power flow methodsElectric distribution gridsSingle-phase representationNumerical methods for distribution networksLinear and quadratic convergenceLEMBCartagena de IndiasMurty, P. Load Flow Analysis. In Electrical Power Systems; Elsevier: Amsterdam, The Netherlands, 2017; pp. 527–587. doi:10.1016/b978-0-08-101124-9.00019-x.Albadi, M. Power Flow Analysis. In Computational Models in Engineering; IntechOpen: London, UK, 2020. doi:10.5772/intechopen.83374.Tyagi, A.; Kumar, K.; Ansari, M.A.; Kumar, B. An efficient load flow solution for distribution system with addition of distributed generation using improved harmony search algorithms. J. Electr. Syst. Inf. Technol. 2020, 7, 1–16. doi:10.1186/s43067-020-00014-7Milano, F. Analogy and Convergence of Levenberg’s and Lyapunov-Based Methods for Power Flow Analysis. IEEE Trans. Power Syst. 2016, 31, 1663–1664. doi:10.1109/tpwrs.2015.2415455.Acosta, C.; Hincapié, R.A.; Granada, M.; Escobar, A.H.; Gallego, R.A. An Efficient Three Phase Four Wire Radial Power Flow Including Neutral-Earth Effect. J. Control Autom. Electr. Syst. 2013, 24, 690–701. doi:10.1007/s40313-013-0049-7Herrera-Briñez, M.C.; Montoya, O.D.; Alvarado-Barrios, L.; Chamorro, H.R. The Equivalence between Successive Approximations and Matricial Load Flow Formulations. Appl. Sci. 2021, 11, 2905. doi:10.3390/app11072905Shirmohammadi, D.; Hong, H.; Semlyen, A.; Luo, G. A compensation-based power flow method for weakly meshed distribution and transmission networks. IEEE Trans. Power Syst. 1988, 3, 753–762. doi:10.1109/59.192932.Cheng, C.; Shirmohammadi, D. A three-phase power flow method for real-time distribution system analysis. IEEE Trans. Power Syst. 1995, 10, 671–679. doi:10.1109/59.387902.Haque, M. Efficient load flow method for distribution systems with radial or mesh configuration. IEE Proc. Gener. Transm. Distrib. 1996, 143, 33. doi:10.1049/ip-gtd:19960045.Teng, J.H. A modified Gauss–Seidel algorithm of three-phase power flow analysis in distribution networks. Int. J. Electr. Power Energy Syst. 2002, 24, 97–102. doi:10.1016/s0142-0615(01)00022-9.Teng, J.H. A direct approach for distribution system load flow solutions. IEEE Trans. Power Deliv. 2003, 18, 882–887. doi:10.1109/tpwrd.2003.813818.Yang, H.; Wen, F.; Wang, L. Newton-Raphson on power flow algorithm and Broyden Method in the distribution system. In Proceedings of the 2008 IEEE 2nd International Power and Energy Conference, Johor Bahru, Malaysia , 1–3 December 2008. doi:10.1109/pecon.2008.4762737.Lagace, P.J.; Vuong, M.H.; Kamwa, I. Improving power flow convergence by Newton Raphson with a Levenberg-Marquardt method. In Proceedings of the 2008 IEEE Power and Energy Society General Meeting—Conversion and Delivery of Electrical Energy in the 21st Century, Pittsburgh, PA, USA, 20–24 July 2008. doi:10.1109/pes.2008.4596138Augugliaro, A.; Dusonchet, L.; Favuzza, S.; Ippolito, M.; Sanseverino, E.R. A backward sweep method for power flow solution in distribution networks. Int. J. Electr. Power Energy Syst. 2010, 32, 271–280. doi:10.1016/j.ijepes.2009.09.007Lourenco, E.M.; Loddi, T.; Tortelli, O.L. Unified load flow analysis for emerging distribution systems. In Proceedings of the 2010 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT Europe), Gothenburg, Sweden, 11–13 October 2010. doi:10.1109/isgteurope.2010.5638877.Jesus, P.D.O.D.; Alvarez, M.; Yusta, J. Distribution power flow method based on a real quasi-symmetric matrix. Electr. Power Syst. Res. 2013, 95, 148–159. doi:10.1016/j.epsr.2012.08.011Tortelli, O.L.; Lourenco, E.M.; Garcia, A.V.; Pal, B.C. Fast Decoupled Power Flow to Emerging Distribution Systems via Complex pu Normalization. IEEE Trans. Power Syst. 2015, 30, 1351–1358. doi:10.1109/tpwrs.2014.2343193.Sianipar, G.H.M.; Setia, G.A.; Santosa, M.F. Implementation of Axis Rotation Fast Decoupled Load Flow on distribution systems. In Proceedings of the 2016 3rd Conference on Power Engineering and Renewable Energy (ICPERE), Yogyakarta, Indonesia, 29–30 November 2016. doi:10.1109/icpere.2016.7904872.Garces, A. A Linear Three-Phase Load Flow for Power Distribution Systems. IEEE Trans. Power Syst. 2016, 31, 827–828. doi:10.1109/tpwrs.2015.2394296.Bolognani, S.; Zampieri, S. On the Existence and Linear Approximation of the Power Flow Solution in Power Distribution Networks. IEEE Trans. Power Syst. 2016, 31, 163–172. doi:10.1109/tpwrs.2015.2395452Shen, T.; Li, Y.; Xiang, J. A Graph-Based Power Flow Method for Balanced Distribution Systems. Energies 2018, 11, 511. doi:10.3390/en11030511.Marini, A.; Mortazavi, S.; Piegari, L.; Ghazizadeh, M.S. An efficient graph-based power flow algorithm for electrical distribution systems with a comprehensive modeling of distributed generations. Electr. Power Syst. Res. 2019, 170, 229–243. doi:10.1016/j.epsr.2018.12.026Montoya, O.D.; Gil-González, W. On the numerical analysis based on successive approximations for power flow problems in AC distribution systems. Electr. Power Syst. Res. 2020, 187, 106454. doi:10.1016/j.epsr.2020.106454Bocanegra, S.Y.; Gil-Gonzalez, W.; Montoya, O.D. A New Iterative Power Flow Method for AC Distribution Grids with Radial and Mesh Topologies. In Proceedings of the 2020 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC), Ixtapa, Mexico, 4–6 November 2020. doi:10.1109/ropec50909.2020.9258750.Montoya, O.D.; Gil-González, W.; Giral, D.A. On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence. Appl. Sci. 2020, 10, 5802. doi:10.3390/app10175802Herrera-Briñez, M.C.; Montoya, O.D.; Molina-Cabrera, A.; Grisales-Noreña, L.F.; Giral-Ramirez, D.A. Convergence analysis of the triangular-based power flow method for AC distribution grids. Int. J. Electr. Comput. Eng. (IJECE) 2021, 12. doi:10.11591/ijece.v12i1.pp\%25pMontoya, O.D.; Giraldo, J.S.; Grisales-Noreña, L.F.; Chamorro, H.R.; Alvarado-Barrios, L. Accurate and Efficient Derivative-Free Three-Phase Power Flow Method for Unbalanced Distribution Networks. Computation 2021, 9, 61. doi:10.3390/computation9060061.Montoya, O.D.; Rueda, L.E.; Gil-Gonzalez, W.; Molina-Cabrera, A.; Chamorro, H.R.; Soleimani, M. On the Power Flow Solution in AC Distribution Networks Using the Laurent’s Series Expansion. In Proceedings of the 2021 IEEE Texas Power and Energy Conference (TPEC), College Station, TX, USA, 2–5 February 2021. doi:10.1109/tpec51183.2021.9384936.Sereeter, B.; Markensteijn, A.; Kootte, M.; Vuik, C. A novel linearized power flow approach for transmission and distribution networks. J. Comput. Appl. Math. 2021, 394, 113572. doi:10.1016/j.cam.2021.113572.Kawambwa, S.; Mwifunyi, R.; Mnyanghwalo, D.; Hamisi, N.; Kalinga, E.; Mvungi, N. An improved backward/forward sweep power flow method based on network tree depth for radial distribution systems. J. Electr. Syst. Inf. Technol. 2021, 8, 1–18. doi:10.1186/s43067-021-00031-0Deng, J.J.; Chiang, H.D. Convergence Region of Newton Iterative Power Flow Method: Numerical Studies. J. Appl. Math. 2013, 2013, 1–12. doi:10.1155/2013/509496.Kulworawanichpong, T. Simplified Newton–Raphson power-flow solution method. Int. J. Electr. Power Energy Syst. 2010, 32, 551–558. doi:10.1016/j.ijepes.2009.11.011.Prakash, D.; Lakshminarayana, C. Optimal siting of capacitors in radial distribution network using Whale Optimization Algorithm. Alex. Eng. J. 2017, 56, 499–509. doi:10.1016/j.aej.2016.10.002Molzahn, D.K.; Hiskens, I.A. Convex Relaxations of Optimal Power Flow Problems: An Illustrative Example. IEEE Trans. Circuits Syst. I Regul. Pap. 2016, 63, 650–660. doi:10.1109/tcsi.2016.2529281.Garces, A. A quadratic approximation for the optimal power flow in power distribution systems. Electr. Power Syst. Res. 2016, 130, 222–229. doi:10.1016/j.epsr.2015.09.006Bahrami, S.; Therrien, F.; Wong, V.W.; Jatskevich, J. Semidefinite Relaxation of Optimal Power Flow for AC–DC Grids. IEEE Trans. Power Syst. 2017, 32, 289–304. doi:10.1109/tpwrs.2016.2543726Molzahn, D.K.; Holzer, J.T.; Lesieutre, B.C.; DeMarco, C.L. Implementation of a Large-Scale Optimal Power Flow Solver Based on Semidefinite Programming. IEEE Trans. Power Syst. 2013, 28, 3987–3998. doi:10.1109/tpwrs.2013.2258044Yuan, Z.; Hesamzadeh, M.R. Second-order cone AC optimal power flow: Convex relaxations and feasible solutions. J. Mod. Power Syst. Clean Energy 2018, 7, 268–280. doi:10.1007/s40565-018-0456-7.Chowdhury, T.; Kamalasadan, S. A New Second-Order Cone Programming Model for Voltage Control of Power Distribution System with Inverter Based Distributed Generation. IEEE Trans. Ind. Appl. 2021, in press. doi:10.1109/tia.2021.3107825Ferreira, L. Tellegen’s theorem and power systems-new load flow equations, new solution methods. IEEE Trans. Circuits Syst. 1990, 37, 519–526. doi:10.1109/31.52753.Issicaba, D.; Coelho, J. Evaluation of the Forward-Backward Sweep Load Flow Method using the Contraction Mapping Principle. Int. J. Electr. Comput. Eng. (IJECE) 2016, 6, 3229. doi:10.11591/ijece.v6i6.pp3229-3237Wang, X.F.; Song, Y.; Irving, M. Modern Power Systems Analysis; Springer: New York, NY, USA, 2008. doi:10.1007/978-0-387- 72853-7.Zhang, D.; Fu, Z.; Zhang, L. An improved TS algorithm for loss-minimum reconfiguration in large-scale distribution systems. Electr. Power Syst. Res. 2007, 77, 685–694. doi:10.1016/j.epsr.2006.06.005.http://purl.org/coar/resource_type/c_2df8fbb1ORIGINAL[Art. 44] A Comparative Study on Power Flow M_Oscar Danilo Montoya.pdf[Art. 44] A Comparative Study on Power Flow M_Oscar Danilo Montoya.pdfapplication/pdf694166https://repositorio.utb.edu.co/bitstream/20.500.12585/10382/1/%5bArt.%2044%5d%20A%20Comparative%20Study%20on%20Power%20Flow%20M_Oscar%20Danilo%20Montoya.pdfd7296c9e1e41a83c058d2ac882a1f123MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.utb.edu.co/bitstream/20.500.12585/10382/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/10382/3/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD53TEXT[Art. 44] A Comparative Study on Power Flow M_Oscar Danilo Montoya.pdf.txt[Art. 44] A Comparative Study on Power Flow M_Oscar Danilo Montoya.pdf.txtExtracted texttext/plain57842https://repositorio.utb.edu.co/bitstream/20.500.12585/10382/4/%5bArt.%2044%5d%20A%20Comparative%20Study%20on%20Power%20Flow%20M_Oscar%20Danilo%20Montoya.pdf.txt0888932445b964358fe87ad1224c6332MD54THUMBNAIL[Art. 44] A Comparative Study on Power Flow M_Oscar Danilo Montoya.pdf.jpg[Art. 44] A Comparative Study on Power Flow M_Oscar Danilo Montoya.pdf.jpgGenerated Thumbnailimage/jpeg96351https://repositorio.utb.edu.co/bitstream/20.500.12585/10382/5/%5bArt.%2044%5d%20A%20Comparative%20Study%20on%20Power%20Flow%20M_Oscar%20Danilo%20Montoya.pdf.jpg3ec452cb239bf19c547fa67647781621MD5520.500.12585/10382oai:repositorio.utb.edu.co:20.500.12585/103822023-05-26 13:14:58.001Repositorio Institucional UTBrepositorioutb@utb.edu.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 |