On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence
This paper presents a general formulation of the classical iterative-sweep power flow, which is widely known as the backward–forward method. This formulation is performed by a branch-to-node incidence matrix with the main advantage that this approach can be used with radial and meshed configurations...
- Autores:
-
Montoya, Oscar Danilo
Gil-González, Walter
Giral-Ramírez, Diego Armando
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/9557
- Palabra clave:
- Backward–forward power flow
Branch-to-node incidence matrix
Banach fixed-point theorem
Convergence test
Numerical methods
Radial distribution networks
Mesh distribution networks
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| id |
UTB2_a6b6b9512d0df53c1dcd00011913390e |
|---|---|
| oai_identifier_str |
oai:repositorio.utb.edu.co:20.500.12585/9557 |
| network_acronym_str |
UTB2 |
| network_name_str |
Repositorio Institucional UTB |
| repository_id_str |
|
| dc.title.spa.fl_str_mv |
On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence |
| title |
On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence |
| spellingShingle |
On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence Backward–forward power flow Branch-to-node incidence matrix Banach fixed-point theorem Convergence test Numerical methods Radial distribution networks Mesh distribution networks |
| title_short |
On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence |
| title_full |
On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence |
| title_fullStr |
On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence |
| title_full_unstemmed |
On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence |
| title_sort |
On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergence |
| dc.creator.fl_str_mv |
Montoya, Oscar Danilo Gil-González, Walter Giral-Ramírez, Diego Armando |
| dc.contributor.author.none.fl_str_mv |
Montoya, Oscar Danilo Gil-González, Walter Giral-Ramírez, Diego Armando |
| dc.subject.keywords.spa.fl_str_mv |
Backward–forward power flow Branch-to-node incidence matrix Banach fixed-point theorem Convergence test Numerical methods Radial distribution networks Mesh distribution networks |
| topic |
Backward–forward power flow Branch-to-node incidence matrix Banach fixed-point theorem Convergence test Numerical methods Radial distribution networks Mesh distribution networks |
| description |
This paper presents a general formulation of the classical iterative-sweep power flow, which is widely known as the backward–forward method. This formulation is performed by a branch-to-node incidence matrix with the main advantage that this approach can be used with radial and meshed configurations. The convergence test is performed using the Banach fixed-point theorem while considering the dominant diagonal structure of the demand-to-demand admittance matrix. A numerical example is presented in tutorial form using the MATLAB interface, which aids beginners in understanding the basic concepts of power-flow programming in distribution system analysis. Two classical test feeders comprising 33 and 69 nodes are used to validate the proposed formulation in comparison with conventional methods such as the Gauss–Seidel and Newton–Raphson power-flow formulations. |
| publishDate |
2020 |
| dc.date.accessioned.none.fl_str_mv |
2020-11-05T21:03:40Z |
| dc.date.available.none.fl_str_mv |
2020-11-05T21:03:40Z |
| dc.date.issued.none.fl_str_mv |
2020-08-21 |
| dc.date.submitted.none.fl_str_mv |
2020-11-03 |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.hasversion.spa.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| dc.type.spa.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
| status_str |
publishedVersion |
| dc.identifier.citation.spa.fl_str_mv |
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. |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/9557 |
| dc.identifier.url.none.fl_str_mv |
https://www.mdpi.com/2076-3417/10/17/5802 |
| dc.identifier.doi.none.fl_str_mv |
10.3390/app10175802 |
| 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.; 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. 10.3390/app10175802 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/9557 https://www.mdpi.com/2076-3417/10/17/5802 |
| 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 |
21 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 |
Appl. Sci. 2020, 10(17), 5802 |
| institution |
Universidad Tecnológica de Bolívar |
| bitstream.url.fl_str_mv |
https://repositorio.utb.edu.co/bitstream/20.500.12585/9557/1/82.pdf https://repositorio.utb.edu.co/bitstream/20.500.12585/9557/2/license_rdf https://repositorio.utb.edu.co/bitstream/20.500.12585/9557/3/license.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/9557/4/82.pdf.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/9557/5/82.pdf.jpg |
| bitstream.checksum.fl_str_mv |
81a2204e08110b3bac3a5e105ea97049 4460e5956bc1d1639be9ae6146a50347 e20ad307a1c5f3f25af9304a7a7c86b6 b76c5cdc999fa3b85aec584c2cfd15f6 2b7b53fba649565b617660029ce6f699 |
| 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_ |
1814021617197514752 |
| spelling |
Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Gil-González, Walterce1f5078-74c6-4b5c-b56a-784f85e52a08Giral-Ramírez, Diego Armando04c23b18-18fe-4cbb-a925-7b44d9849c1e2020-11-05T21:03:40Z2020-11-05T21:03:40Z2020-08-212020-11-03Montoya, 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.https://hdl.handle.net/20.500.12585/9557https://www.mdpi.com/2076-3417/10/17/580210.3390/app10175802Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis paper presents a general formulation of the classical iterative-sweep power flow, which is widely known as the backward–forward method. This formulation is performed by a branch-to-node incidence matrix with the main advantage that this approach can be used with radial and meshed configurations. The convergence test is performed using the Banach fixed-point theorem while considering the dominant diagonal structure of the demand-to-demand admittance matrix. A numerical example is presented in tutorial form using the MATLAB interface, which aids beginners in understanding the basic concepts of power-flow programming in distribution system analysis. Two classical test feeders comprising 33 and 69 nodes are used to validate the proposed formulation in comparison with conventional methods such as the Gauss–Seidel and Newton–Raphson power-flow formulations.21 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_abf2Appl. Sci. 2020, 10(17), 5802On the Matricial Formulation of Iterative Sweep Power Flow for Radial and Meshed Distribution Networks with Guarantee of Convergenceinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Backward–forward power flowBranch-to-node incidence matrixBanach fixed-point theoremConvergence testNumerical methodsRadial distribution networksMesh distribution networksCartagena de IndiasPúblico generalWillis, L. Introduction to transmission and distribution (T&D) networks: T&D infrastructure, reliability and engineering, regulation and planning. In Electricity Transmission, Distribution and Storage Systems; Melhem, Z., Ed.; Woodhead Publishing Series in Energy; Woodhead Publishing: Cambridge, UK, 2013; pp. 3–38.Bernstein, A.; Wang, C.; Dall’Anese, E.; Le Boudec, J.; Zhao, C. Load Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity and Linear Models. IEEE Trans. Power Syst. 2018, 33, 5832–5843Zidan, A.; Gabbar, H. Chapter 4 - Scheduling interconnected micro energy grids with multiple fuel options. In Smart Energy Grid Engineering; Gabbar, H.A., Ed.; Academic Press: New York, NY, USA, 2017; pp. 83–99.Hayes, B. Chapter 9-Distribution Generation Optimization and Energy Management. In Distributed Generation Systems; Gharehpetian, G., Agah, S.M.M., Eds.; Butterworth-Heinemann: Oxford, UK, 2017; pp. 415–451Grisales-Noreña, L.F.; Gonzalez-Montoya, D.; Ramos-Paja, C.A. Optimal Sizing and Location of Distributed Generators Based on PBIL and PSO Techniques. Energies 2018, 11, 1018Lavorato, M.; Franco, J.F.; Rider, M.J.; Romero, R. Imposing Radiality Constraints in Distribution System Optimization Problems. IEEE Trans. Power Syst. 2012, 27, 172–180Garces, A. A Linear Three-Phase Load Flow for Power Distribution Systems. IEEE Trans. Power Syst. 2016, 31, 827–828.Baradar, M.; Hesamzadeh, M.R. AC Power Flow Representation in Conic Format. IEEE Trans. Power Syst. 2015, 30, 546–547Simpson-Porco, J.W.; Dorfler, F.; Bullo, F. On Resistive Networks of Constant–Power Devices. IEEE Trans. Circuits Syst. II Express Briefs 2015, 62, 811–815Montoya, O.D. On Linear Analysis of the Power Flow Equations for DC and AC Grids With CPLs. IEEE Trans. Circuits Syst. II 2019, 66, 2032–2036.Montoya-Giraldo, O.D.; Gil-González, W.J.; Garcés-Ruíz, A. Flujo de potencia óptimo para redes radiales y enmalladas empleando programación semidefinida. TecnoLógicas 2017, 20, 29–42.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.Shen, T.; Li, Y.; Xiang, J. A Graph-Based Power Flow Method for Balanced Distribution Systems. Energies 2018, 11, 511.Grainger, J.J.; Stevenson, W.D. Power System Analysis; McGraw-Hill Series in Electrical and Computer Engineering: Power and Energy; McGraw-Hill: New York, NY, USA, 2003. Celli, G.; Pilo, F.; Pisano, G.; Allegranza, V.; Cicoria, R.; Iaria, A. Meshed vs. radial MV distribution network in presence of large amount of DG. IEEE PES Power Syst. Conf. Expo. 2004, 2, 709–714Adebiyi, A.A.; Akindeji, K.T. Investigating the effect of Static Synchronous Compensator (STATCOM) for voltage enhancement and transmission line losses mitigation. In Prcoceedings of the 2017 IEEE PES PowerAfrica, Accra, Ghana, 27–30 June 2017; pp. 462–467.Gönen, T. Modern Power System Analysis; CRC Press: Boca Raton, FL, USA, 2016Montoya, O.D. On the Existence of the Power Flow Solution in DC Grids with CPLs Through a Graph-Based Method. IEEE Trans. Circuits Syst. II 2020, 67, 1434–1438Milano, F. Analogy and Convergence of Levenberg’s and Lyapunov-Based Methods for Power Flow Analysis. IEEE Trans. Power Syst. 2016, 31, 1663–1664Jesus, 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, 148–159Suchite-Remolino, A.; Ruiz-Paredes, H.F.; Torres-García, V. A New Approach for PV Nodes Using an Efficient Backward/Forward Sweep Power Flow Technique. IEEE Lat. Am. Trans. 2020, 18, 992–999.Garces, A. Uniqueness of the power flow solutions in low voltage direct current grids. Electr. Power Syst. Res. 2017, 151, 149–153Nguyen, H.L. Newton-Raphson method in complex form [power system load flow analysis]. IEEE Trans. Power Syst. 1997, 12, 1355–1359Lagace, P.J.; Vuong, M.H.; Kamwa, I. Improving power flow convergence by Newton Raphson with a Levenberg-Marquardt method. In Prcoceedings 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; pp. 1–6Manrique, M.L.; Montoya, O.D.; Garrido, V.M.; Grisales-Noreña, L.F.; Gil-González, W. Sine-Cosine Algorithm for OPF Analysis in Distribution Systems to Size Distributed Generators. In Communications in Computer and Information Science; Springer International Publishing: Cham, Switzerland, 2019; pp. 28–39.Hernandez, J.; Ruiz-Rodriguez, F.; Jurado, F.; Sanchez-Sutil, F. Tracing harmonic distortion and voltage unbalance in secondary radial distribution networks with photovoltaic uncertainties by an iterative multiphase harmonic load flow. Electr. Power Syst. Res. 2020, 185, 106342.Ruiz-Rodriguez, F.; Hernandez, J.; Jurado, F. Iterative harmonic load flow by using the point-estimate method and complex affine arithmetic for radial distribution systems with photovoltaic uncertainties. Int. J. Electr. Power Energy Syst. 2020, 118, 105765Gil-González, W.; Montoya, O.D.; Holguín, E.; Garces, A.; Grisales-Noreña, L.F. Economic dispatch of energy storage systems in dc microgrids employing a semidefinite programming model. J. Energy Storage 2019, 21, 1–8.Li, Z.; Yu, J.; Wu, Q.H. Approximate Linear Power Flow Using Logarithmic Transform of Voltage Magnitudes With Reactive Power and Transmission Loss Consideration. IEEE Trans. Power Syst. 2018, 33, 4593–4603.Chang, G.W.; Chu, S.Y.; Wang, H.L. An Improved Backward/Forward Sweep Load Flow Algorithm for Radial Distribution Systems. IEEE Trans. Power Syst. 2007, 22, 882–884.Verma, H.K.; Singh, P. Optimal reconfiguration of distribution network using modified culture algorithm. J. Inst. Eng. India Ser. B 2018, 99, 613–622Montoya, O.D.; Garrido, V.M.; Grisales, L.F. Optimal Location and Sizing of Capacitors in Radial Distribution Networks Using an Exact MINLP Model for Operating Costs Minimization. Wseas Trans. Bus. Econ. 2017, 14, 244–252Nojavan, S.; Jalali, M.; Zare, K. Optimal allocation of capacitors in radial/mesh distribution systems using mixed integer nonlinear programming approach. Electr. Power Syst. Res. 2014, 107, 119–124Shuaib, Y.M.; Kalavathi, M.S.; Rajan, C.C.A. Optimal capacitor placement in radial distribution system using Gravitational Search Algorithm. Int. J. Electr. Power Energy Syst. 2015, 64, 384–397Montoya, O.D.; Gil-González, W. Dynamic active and reactive power compensation in distribution networks with batteries: A day-ahead economic dispatch approach. Comput. Electr. Eng. 2020, 85, 106710http://purl.org/coar/resource_type/c_2df8fbb1ORIGINAL82.pdf82.pdfArtículo principalapplication/pdf415051https://repositorio.utb.edu.co/bitstream/20.500.12585/9557/1/82.pdf81a2204e08110b3bac3a5e105ea97049MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.utb.edu.co/bitstream/20.500.12585/9557/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/9557/3/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD53TEXT82.pdf.txt82.pdf.txtExtracted texttext/plain56449https://repositorio.utb.edu.co/bitstream/20.500.12585/9557/4/82.pdf.txtb76c5cdc999fa3b85aec584c2cfd15f6MD54THUMBNAIL82.pdf.jpg82.pdf.jpgGenerated Thumbnailimage/jpeg93302https://repositorio.utb.edu.co/bitstream/20.500.12585/9557/5/82.pdf.jpg2b7b53fba649565b617660029ce6f699MD5520.500.12585/9557oai:repositorio.utb.edu.co:20.500.12585/95572023-05-26 10:24:43.898Repositorio Institucional UTBrepositorioutb@utb.edu.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 |