A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors
This study analyzes the numerical convergence and processing time required by several classical and new solution methods proposed in the literature to solve the power-flow problem (PF) in direct-current (DC) networks considering radial and mesh topologies. Three classical numerical methods were stud...
- Autores:
-
Grisales-Noreña, Luis Fernando
Montoya, Oscar Danilo
Gil-González, Walter
Perea-Moreno, Alberto-Jesus
Perea-Moreno, Miguel-Angel
- 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:20.500.12585/9940
- Palabra clave:
- Direct-current network
Power-flow analysi
Distribution networks
Numerical methods
Literature review
Processing time
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
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A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors |
| title |
A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors |
| spellingShingle |
A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors Direct-current network Power-flow analysi Distribution networks Numerical methods Literature review Processing time LEMB |
| title_short |
A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors |
| title_full |
A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors |
| title_fullStr |
A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors |
| title_full_unstemmed |
A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors |
| title_sort |
A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors |
| dc.creator.fl_str_mv |
Grisales-Noreña, Luis Fernando Montoya, Oscar Danilo Gil-González, Walter Perea-Moreno, Alberto-Jesus Perea-Moreno, Miguel-Angel |
| dc.contributor.author.none.fl_str_mv |
Grisales-Noreña, Luis Fernando Montoya, Oscar Danilo Gil-González, Walter Perea-Moreno, Alberto-Jesus Perea-Moreno, Miguel-Angel |
| dc.subject.keywords.spa.fl_str_mv |
Direct-current network Power-flow analysi Distribution networks Numerical methods Literature review Processing time |
| topic |
Direct-current network Power-flow analysi Distribution networks Numerical methods Literature review Processing time LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
This study analyzes the numerical convergence and processing time required by several classical and new solution methods proposed in the literature to solve the power-flow problem (PF) in direct-current (DC) networks considering radial and mesh topologies. Three classical numerical methods were studied: Gauss–Jacobi, Gauss–Seidel, and Newton–Raphson. In addition, two unconventional methods were selected. They are iterative and allow solving the DC PF in radial and mesh configurations. The first method uses a Taylor series expansion and a set of decoupling equations to linearize around the desired operating point. The second method manipulates the set of non-linear equations of the DC PF to transform it into a conventional fixed-point form. Moreover, this method is used to develop a successive approximation methodology. For the particular case of radial topology, three methods based on triangular matrix formulation, graph theory, and scanning algorithms were analyzed. The main objective of this study was to identify the methods with the best performance in terms of quality of solution (i.e., numerical convergence) and processing time to solve the DC power flow in mesh and radial distribution networks. We aimed at offering to the reader a set of PF methodologies to analyze electrical DC grids. The PF performance of the analyzed solution methods was evaluated through six test feeders; all of them were employed in prior studies for the same application. The simulation results show the adequate performance of the power-flow methods reviewed in this study, and they permit the selection of the best solution method for radial and mesh structures. |
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2020 |
| dc.date.issued.none.fl_str_mv |
2020-12-03 |
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2021-02-08T14:53:17Z |
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2021-02-08T14:53:17Z |
| dc.date.submitted.none.fl_str_mv |
2021-02-05 |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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info:eu-repo/semantics/article |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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publishedVersion |
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Grisales-Noreña, L.F.; Montoya, O.D.; Gil-González, W.J.; Perea-Moreno, A.-J.; Perea-Moreno, M.-A. A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors. Electronics 2020, 9, 2062. https://doi.org/10.3390/electronics9122062 |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/9940 |
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https://www.mdpi.com/2079-9292/9/12/2062 |
| dc.identifier.doi.none.fl_str_mv |
10.3390/electronics9122062 |
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Universidad Tecnológica de Bolívar |
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Repositorio Universidad Tecnológica de Bolívar |
| identifier_str_mv |
Grisales-Noreña, L.F.; Montoya, O.D.; Gil-González, W.J.; Perea-Moreno, A.-J.; Perea-Moreno, M.-A. A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors. Electronics 2020, 9, 2062. https://doi.org/10.3390/electronics9122062 10.3390/electronics9122062 Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
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https://hdl.handle.net/20.500.12585/9940 https://www.mdpi.com/2079-9292/9/12/2062 |
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eng |
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eng |
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Attribution-NonCommercial-NoDerivatives 4.0 Internacional |
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openAccess |
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20 páginas |
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Cartagena de Indias |
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Electronics 2020, 9(12), 2062 |
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Universidad Tecnológica de Bolívar |
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Grisales-Noreña, Luis Fernando7c27cda4-5fe4-4686-8f72-b0442c58a5d1Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Gil-González, Walter1747fed9-7818-4c10-a283-efb3c73ebb27Perea-Moreno, Alberto-Jesuse78da438-8ed5-40ab-a12c-74e84e6d691bPerea-Moreno, Miguel-Angeld9531a58-ba07-42c6-9379-79326fc504222021-02-08T14:53:17Z2021-02-08T14:53:17Z2020-12-032021-02-05Grisales-Noreña, L.F.; Montoya, O.D.; Gil-González, W.J.; Perea-Moreno, A.-J.; Perea-Moreno, M.-A. A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors. Electronics 2020, 9, 2062. https://doi.org/10.3390/electronics9122062https://hdl.handle.net/20.500.12585/9940https://www.mdpi.com/2079-9292/9/12/206210.3390/electronics9122062Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis study analyzes the numerical convergence and processing time required by several classical and new solution methods proposed in the literature to solve the power-flow problem (PF) in direct-current (DC) networks considering radial and mesh topologies. Three classical numerical methods were studied: Gauss–Jacobi, Gauss–Seidel, and Newton–Raphson. In addition, two unconventional methods were selected. They are iterative and allow solving the DC PF in radial and mesh configurations. The first method uses a Taylor series expansion and a set of decoupling equations to linearize around the desired operating point. The second method manipulates the set of non-linear equations of the DC PF to transform it into a conventional fixed-point form. Moreover, this method is used to develop a successive approximation methodology. For the particular case of radial topology, three methods based on triangular matrix formulation, graph theory, and scanning algorithms were analyzed. The main objective of this study was to identify the methods with the best performance in terms of quality of solution (i.e., numerical convergence) and processing time to solve the DC power flow in mesh and radial distribution networks. We aimed at offering to the reader a set of PF methodologies to analyze electrical DC grids. The PF performance of the analyzed solution methods was evaluated through six test feeders; all of them were employed in prior studies for the same application. The simulation results show the adequate performance of the power-flow methods reviewed in this study, and they permit the selection of the best solution method for radial and mesh structures.20 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 2020, 9(12), 2062A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errorsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Direct-current networkPower-flow analysiDistribution networksNumerical methodsLiterature reviewProcessing timeLEMBCartagena de IndiasPúblico generalMontoya, O.D. On Linear Analysis of the Power Flow Equations for DC and AC Grids with CPLs. IEEE Trans. Circuits Syst. II Express Briefs 2019.Rouzbehi, K.; Heidary Yazdi, S.S.; Shariati Moghadam, N. Power Flow Control in Multi-Terminal HVDC Grids Using a Serial-Parallel DC Power Flow Controller. IEEE Access 2018, 6, 56934–56944.Gil-González, W.; Montoya, O.D.; Grisales-Noreña, L.F.; Cruz-Peragón, F.; Alcalá, G. Economic Dispatch of Renewable Generators and BESS in DC Microgrids Using Second-Order Cone Optimization. Energies 2020, 13, 1703.Molzahn, D.K. Identifying and Characterizing Non-Convexities in Feasible Spaces of Optimal Power Flow Problems. IEEE Trans. Circuits Syst. II Express Briefs 2018, 65, 672–676.Li, H.; Zhang, L.; Shen, X. A loop-analysis theory based power flow method and its linear formulation for low-voltage DC grid. Electr. Power Syst. Res. 2020, 187, 106473.Simpson-Porco, J.W.; Dörfler, F.; Bullo, F. On Resistive Networks of Constant-Power Devices. IEEE Trans. Circuits Syst. II Express Briefs 2015, 62, 811–815.Montoya, O.D.; Grisales-Noreña, L.F.; Gil-González, W.; Alcalá, G.; Hernandez-Escobedo, Q. Optimal Location and Sizing of PV Sources in DC Networks for Minimizing Greenhouse Emissions in Diesel Generators. Symmetry 2020, 12, 322.Grainger, J.; Stevenson, W. Power System Analysis; Mcgraw-Hill Series in Electrical and Computer Engineering: Power and Energy; McGraw-Hill: New York, NY, USA, 1994.Krebs, V.; Schewe, L.; Schmidt, M. Uniqueness and multiplicity of market equilibria on DC power flow networks. Eur. J. Oper. Res. 2018, 271, 165–178.Milano, F. Analogy and Convergence of Levenberg’s and Lyapunov-Based Methods for Power Flow Analysis. IEEE Trans. Power Syst. 2016, 31, 1663–1664.Papadimitriou, C.; Zountouridou, E.; Hatziargyriou, N. Review of hierarchical control in DC microgrids. Electr. Power Syst. Res. 2015, 122, 159–167.Parhizi, S.; Lotfi, H.; Khodaei, A.; Bahramirad, S. State of the Art in Research on Microgrids: A Review. IEEE Access 2015, 3, 890–925.Barelli, L.; Bidini, G.; Pelosi, D.; Ciupageanu, D.; Cardelli, E.; Castellini, S.; Lăzăroiu, G. Comparative analysis of AC and DC bus configurations for flywheel-battery HESS integration in residential micro-grids. Energy 2020, 204, 117939.Montoya, O.D.; Gil-González, W.; Rivas-Trujillo, E. Optimal Location-Reallocation of Battery Energy Storage Systems in DC Microgrids. Energies 2020, 13, 2289.Siraj, K.; Khan, H.A. DC distribution for residential power networks A framework to analyze the impact of voltage levels on energy efficiency. Energy Rep. 2020, 6, 944–951.Duan, J.; Li, Z.; Zhou, Y.; Wei, Z. Study on the voltage level sequence of future urban DC distribution network in China: A Review. Int. J. Electr. Power Energy Syst. 2020, 117, 105640.Lotfi, H.; Khodaei, A. AC Versus DC Microgrid Planning. IEEE Trans. Smart Grid 2017, 8, 296–304.Grisales-Noreña, L.F.; Garzon-Rivera, O.D.; Ramírez-Vanegas, C.A.; Montoya, O.D.; Ramos-Paja, C.A. Application of the backward/forward sweep method for solving the power flow problem in DC networks with radial structure. J. Phys. Conf. Ser. 2020, 1448, 012012.Gonzalez-longatt, F.; Roldan, J.; Charalambous, C. Solution of ac/dc power flow on a multiterminal HVDC system: Illustrative case supergrid phase I. In Proceedings of the 2012 47th Universities Power Engineering Conference (UPEC), London, UK, 4–7 September 2012.Beerten, J.; Cole, S.; Belmans, R. Generalized steady-state VSC MTDC model for sequential AC/DC power flow algorithms. IEEE Trans. Power Syst. 2012, 27, 821–829.Hartani, M.; Hamouda, M.; Abdelkhalek, O.; Benabdelkader, A.; Meftouhi, A. Static-Dynamic Analysis of an LVDC Smart Microgrid for a Saharian-Isolated Areas Using ETAP/MATLAB Software. In Smart Energy Empowerment in Smart and Resilient Cities; Springer: Berlin/Heidelberg, Germany, 2019; pp. 496–505.Garces, A. Uniqueness of the power flow solutions in low voltage direct current grids. Electr. Power Syst. Res. 2017, 151, 149–153.Garcés, A. On the Convergence of Newton’s Method in Power Flow Studies for DC Microgrids. IEEE Trans. Power Syst. 2018, 33, 5770–5777.Garces, A.; Montoya, D.; Torres, R. Optimal power flow in multiterminal HVDC systems considering DC/DC converters. In Proceedings of the 2016 IEEE 25th International Symposium on Industrial Electronics (ISIE), Santa Clara, CA, USA, 8–10 June 2016; pp. 1212–1217.Li, J.; Liu, F.; Wang, Z.; Low, S.H.; Mei, S. Optimal Power Flow in Stand-Alone DC Microgrids. IEEE Trans. Power Syst. 2018, 33, 5496–5506.Montoya, O.D. Numerical Approximation of the Maximum Power Consumption in DC-MGs With CPLs via an SDP Model. IEEE Trans. Circuits Syst. II Express Briefs 2019, 66, 642–646.Capitanescu, F. Critical review of recent advances and further developments needed in AC optimal power flow. Electr. Power Syst. Res. 2016, 136, 57–68.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.Montoya, O.D.; Grisales-Noreña, L.F.; González-Montoya, D.; Ramos-Paja, C.; Garces, A. Linear power flow formulation for low-voltage DC power grids. Electr. Power Syst. Res. 2018, 163, 375–381.Montoya, O.D.; Garrido, V.M.; Gil-González, W.; Grisales-Noreña, L.F. Power Flow Analysis in DC Grids: Two Alternative Numerical Methods. IEEE Trans. Circuits Syst. II Express Briefs 2019, 66, 1865–1869.Montoya, O.D.; Grisales-Noreña, L.F.; Gil-González, W. Triangular Matrix Formulation for Power Flow Analysis in Radial DC Resistive Grids with CPLs. IEEE Trans. Circuits Syst. II Express Briefs 2019.Montoya, 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 Express Briefs 2019.Garcés, A.; Herrera, J.; Gil-González, W.; Montoya, O. Small-Signal Stability in Low-Voltage DC-Grids. In Proceedings of the 2018 IEEE ANDESCON, Santiago de Cali, Colombia, 22–24 August 2018; pp. 1–5.Montoya, 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.Machado, J.E.; Griñó, R.; Barabanov, N.; Ortega, R.; Polyak, B. On Existence of Equilibria of Multi-Port Linear AC Networks With Constant-Power Loads. IEEE Trans. Circuits Syst. I Regul. Pap. 2017, 64, 2772–2782.Sanchez, S.; Ortega, R.; Griño, R.; Bergna, G.; Molinas, M. Conditions for Existence of Equilibria of Systems With Constant Power Loads. IEEE Trans. Circuits Syst. I Regul. Pap. 2014, 61, 2204–2211.Benedito, E.; del Puerto-Flores, D.; Dòria-Cerezo, A.; Scherpen, J.M. Port-Hamiltonian based Optimal Power Flow algorithm for multi-terminal DC networks. Control Eng. Pract. 2019, 83, 141–150.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; pp. 1–6.Montoya, O.D.; Gil-González, W.; Garces, A. Optimal Power Flow on DC Microgrids: A Quadratic Convex Approximation. IEEE Trans. Circuits Syst. II Express Briefs 2018.Garces, A. A Linear Three-Phase Load Flow for Power Distribution Systems. IEEE Trans. Power Syst. 2016, 31, 827–828.Montoya, O.D.; Escobar, A.F.; Garrido, V.M. Power flow solution in direct current grids using the linear conjugate gradient approach. J. Phys. Conf. Ser. 2020, 1448, 012016.Wang, W.; Barnes, M. Power Flow Algorithms for Multi-Terminal VSC-HVDC With Droop Control. IEEE Trans. Power Syst. 2014, 29, 1721–1730.Huang, G.; Ongsakul, W. Managing the bottlenecks in parallel Gauss-Seidel type algorithms for power flow analysis. IEEE Trans. Power Syst. 1994, 9, 677–684.Zhang, H.; Vittal, V.; Heydt, G.T.; Quintero, J. A relaxed AC optimal power flow model based on a Taylor series. In Proceedings of the 2013 IEEE Innovative Smart Grid Technologies-Asia (ISGT Asia), Bangalore, India, 10–13 November 2013; pp. 1–5.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.Moradi, M.; Abedini, M. A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution systems. Int. J. Electr. Power Energy Syst. 2012, 34, 66–74.Grisales-Noreña, L.F.; Montoya, O.D.; Grajales, A.; Hincapie, R.A.; Granada, M. Optimal Planning and Operation of Distribution Systems Considering Distributed Energy Resources and Automatic Reclosers. IEEE Lat. Am. Trans. 2018, 16, 126–134.Grisales-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, 1018.Baran, M.E.; Wu, F.F. Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans. Power Deliv. 1989, 4, 1401–1407.Baran, M.E.; Wu, F.F. Optimal capacitor placement on radial distribution systems. IEEE Trans. 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