A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models

This paper addresses the problems of power flow and optimal power flow analysis considering voltage-dependent load models from the convex point of view. First, Taylor series expansion method is employed for linearizing the power flow equations generating a set of affine h yperplanes. S econd, the se...

Full description

Autores:
Gil-González, Walter
Garcés, A.
Casilimas-Peña, A.
Garrido Arévalo, Víctor Manuel
Montoya, Oscar
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:20.500.12585/9941
Acceso en línea:
https://hdl.handle.net/20.500.12585/9941
https://ieeexplore.ieee.org/document/9272042
Palabra clave:
Direct–current networks
Optimal power flow analysis
Sequential quadratic programming
Taylor’s based series expansion method
Rights
closedAccess
License
http://purl.org/coar/access_right/c_14cb
id UTB2_68a7240df27bac91dd7e1d3b4ee76929
oai_identifier_str oai:repositorio.utb.edu.co:20.500.12585/9941
network_acronym_str UTB2
network_name_str Repositorio Institucional UTB
repository_id_str
dc.title.spa.fl_str_mv A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models
title A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models
spellingShingle A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models
Direct–current networks
Optimal power flow analysis
Sequential quadratic programming
Taylor’s based series expansion method
title_short A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models
title_full A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models
title_fullStr A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models
title_full_unstemmed A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models
title_sort A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models
dc.creator.fl_str_mv Gil-González, Walter
Garcés, A.
Casilimas-Peña, A.
Garrido Arévalo, Víctor Manuel
Montoya, Oscar
dc.contributor.author.none.fl_str_mv Gil-González, Walter
Garcés, A.
Casilimas-Peña, A.
Garrido Arévalo, Víctor Manuel
Montoya, Oscar
dc.subject.keywords.spa.fl_str_mv Direct–current networks
Optimal power flow analysis
Sequential quadratic programming
Taylor’s based series expansion method
topic Direct–current networks
Optimal power flow analysis
Sequential quadratic programming
Taylor’s based series expansion method
description This paper addresses the problems of power flow and optimal power flow analysis considering voltage-dependent load models from the convex point of view. First, Taylor series expansion method is employed for linearizing the power flow equations generating a set of affine h yperplanes. S econd, the sequential quadratic programming (SQP) approach is employed for adjusting the linearization point to eliminate the voltage estimation error between the exact and proposed convex models recursively. Two voltage-dependent load models are considered in our power flow a nd o ptimal p ower fl ow pr oposals wh ich based on the exponential and polynomial models. General algebraic modeling system (GAMS) and its nonlinear optimization packages are employed for comparison purposes. Two DC-test systems with 6 and 21 nodes are used to validate the performance of the SQP proposed. The proposed SQP approach is implemented in MATLAB software with quadprog toolbox.
publishDate 2020
dc.date.issued.none.fl_str_mv 2020-12-01
dc.date.accessioned.none.fl_str_mv 2021-02-08T14:58:48Z
dc.date.available.none.fl_str_mv 2021-02-08T14:58:48Z
dc.date.submitted.none.fl_str_mv 2021-02-03
dc.type.coarversion.fl_str_mv http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/lecture
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_8544
status_str publishedVersion
dc.identifier.citation.spa.fl_str_mv W. Gil-González, A. Garces, A. Casilimas-Peña, V. M. Garrido and O. Montoya, "A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models," 2020 IEEE ANDESCON, Quito, Ecuador, 2020, pp. 1-6, doi: 10.1109/ANDESCON50619.2020.9272042.
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12585/9941
dc.identifier.url.none.fl_str_mv https://ieeexplore.ieee.org/document/9272042
dc.identifier.doi.none.fl_str_mv 10.1109/ANDESCON50619.2020.9272042.
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 W. Gil-González, A. Garces, A. Casilimas-Peña, V. M. Garrido and O. Montoya, "A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models," 2020 IEEE ANDESCON, Quito, Ecuador, 2020, pp. 1-6, doi: 10.1109/ANDESCON50619.2020.9272042.
10.1109/ANDESCON50619.2020.9272042.
Universidad Tecnológica de Bolívar
Repositorio Universidad Tecnológica de Bolívar
url https://hdl.handle.net/20.500.12585/9941
https://ieeexplore.ieee.org/document/9272042
dc.language.iso.spa.fl_str_mv eng
language eng
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_14cb
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/closedAccess
eu_rights_str_mv closedAccess
rights_invalid_str_mv http://purl.org/coar/access_right/c_14cb
dc.format.extent.none.fl_str_mv 6 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 2020 IEEE ANDESCON
institution Universidad Tecnológica de Bolívar
bitstream.url.fl_str_mv https://repositorio.utb.edu.co/bitstream/20.500.12585/9941/1/108.pdf
https://repositorio.utb.edu.co/bitstream/20.500.12585/9941/2/license.txt
https://repositorio.utb.edu.co/bitstream/20.500.12585/9941/3/108.pdf.txt
https://repositorio.utb.edu.co/bitstream/20.500.12585/9941/4/108.pdf.jpg
bitstream.checksum.fl_str_mv e210f0f2ffb4cf45f15c42cb32f9d3e2
e20ad307a1c5f3f25af9304a7a7c86b6
4f428fda458112798614bcfcc7894dc0
94d0f516599079cd101a70352b42ebbb
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Institucional UTB
repository.mail.fl_str_mv repositorioutb@utb.edu.co
_version_ 1814021663217418240
spelling Gil-González, Walterce1f5078-74c6-4b5c-b56a-784f85e52a08Garcés, A.a200514e-3b0c-4824-8d29-f80875fadd0aCasilimas-Peña, A.f04d5d6b-2f3b-472c-9f92-5f86a6b75d69Garrido Arévalo, Víctor Manuel5c72390f-bbbf-414d-bd59-09c2e872bf1dMontoya, Oscar008c220c-d50f-41c7-8294-a0fd23bfd9f22021-02-08T14:58:48Z2021-02-08T14:58:48Z2020-12-012021-02-03W. Gil-González, A. Garces, A. Casilimas-Peña, V. M. Garrido and O. Montoya, "A Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Models," 2020 IEEE ANDESCON, Quito, Ecuador, 2020, pp. 1-6, doi: 10.1109/ANDESCON50619.2020.9272042.https://hdl.handle.net/20.500.12585/9941https://ieeexplore.ieee.org/document/927204210.1109/ANDESCON50619.2020.9272042.Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis paper addresses the problems of power flow and optimal power flow analysis considering voltage-dependent load models from the convex point of view. First, Taylor series expansion method is employed for linearizing the power flow equations generating a set of affine h yperplanes. S econd, the sequential quadratic programming (SQP) approach is employed for adjusting the linearization point to eliminate the voltage estimation error between the exact and proposed convex models recursively. Two voltage-dependent load models are considered in our power flow a nd o ptimal p ower fl ow pr oposals wh ich based on the exponential and polynomial models. General algebraic modeling system (GAMS) and its nonlinear optimization packages are employed for comparison purposes. Two DC-test systems with 6 and 21 nodes are used to validate the performance of the SQP proposed. The proposed SQP approach is implemented in MATLAB software with quadprog toolbox.6 páginasapplication/pdfeng2020 IEEE ANDESCONA Convex OPF Approximation for DC Networks Considering Voltage-Dependent Load Modelsinfo:eu-repo/semantics/lectureinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_8544http://purl.org/coar/version/c_970fb48d4fbd8a85Direct–current networksOptimal power flow analysisSequential quadratic programmingTaylor’s based series expansion methodinfo:eu-repo/semantics/closedAccesshttp://purl.org/coar/access_right/c_14cbCartagena de IndiasInvestigadoresW Simpson-Porco, F. Dorfler y F. Bullo, "Sobre redes resistivas de dispositivos de potencia constante", IEEE Trans. Circuitos Syst. II Express Briefs , vol. 62, no. 8, págs.811-815, agosto de 2015.S. Parhizi, H. Lotfi, A. Khodaei and S. Bahramirad, "State of the art in research on microgrids: A review", IEEE Access, vol. 3, pp. 890-925, 2015.O. D. Montoya, L. F. Grisales-Noreña, D. González-Montoya, C. Ramos-Paja and A. Garces, "Linear power flow formulation for low-voltage DC power grids", Electr. Power Syst. Res, vol. 163, pp. 375-381, 2018.A. Garces, "Uniqueness of the power flow solutions in low voltage direct current grids", Electr. Power Syst. Res, vol. 151, no. Supplement C, pp. 149-153, 2017.N. Barabanov, R. Ortega and R. G. B. Polyak, "On existence and stability of equilibria of linear time-invariant systems with constant power loads", IEEE Trans. Circuits Syst. I Regul. Pap, vol. 63, no. 1, pp. 114-121, Jan 2016.D. Karimipour and F. R. Salmasi, "Stability Analysis of AC Microgrids With Constant Power Loads Based on Popov’s Absolute Stability Criterion", IEEE Trans. Circuits Syst. II Express Briefs, vol. 62, no. 7, pp. 696-700, July 2015.M. Su, Z. Liu, Y. Sun, H. Han and X. Hou, "Stability analysis and stabilization methods of dc microgrid with multiple parallel-connected dc–dc converters loaded by cpls", IEEE Transactions on Smart Grid, vol. 9, no. 1, pp. 132-142, Jan 2018.Y. Gu, W. Li and X. He, "Passivity-based control of dc microgrid for self-disciplined stabilization", IEEE Transactions on Power Systems, vol. 30, no. 5, pp. 2623-2632, Sep. 2015.O. D. Montoya, W. Gil-González and A. Garces, "Sequential quadratic programming models for solving the OPF problem in DC grids", Electr. Power Syst. Res, vol. 169, pp. 18-23, 2019.A. Garces, "On Convergence of Newtons Method in Power Flow Study for DC Microgrids", IEEE Trans. Power Syst, pp. 1-1, 2018.O. D. Montoya, V. M. Garrido, W. Gil-González and L. Grisales-Noreãa, "Power Flow Analysis in DC Grids: Two Alternative Numerical Methods", IEEE Trans. Circuits Syst. II, pp. 1-1, 2019.O. D. Montoya, "On Linear Analysis of the Power Flow Equations for DC and AC Grids with CPLs", IEEE Trans. Circuits Syst. II, pp. 1-1, 2019.J. Li, F. Liu, Z. Wang, S. Low and S. Mei, "Optimal Power Flow in Stand-alone DC Microgrids", IEEE Trans. Power Syst, pp. 1-1, 2018.W. Gil-González, O. D. Montoya, E. Holguín, A. Garces and L. F. Grisales-Noreña, "Economic dispatch of energy storage systems in dc microgrids employing a semidefinite programming model", Journal of Energy Storage, vol. 21, pp. 1-8, 2019O. D. Montoya, "Numerical Approximation of the Maximum Power Consumption in DC-MGs with CPLs via an SDP Model", IEEE Trans. Circuits Syst. II, pp. 1-1, 2018.S. Bahrami, F. Therrien, V. W. S. Wong and J. Jatskevich, "Semidefinite Relaxation of Optimal Power Flow for AC–DC Grids", IEEE Trans. Power Syst, vol. 32, no. 1, pp. 289-304, Jan 2017.M. Baradar, M. R. Hesamzadeh and M. Ghandhari, "Second-Order Cone Programming for Optimal Power Flow in VSC-Type AC-DC Grids", IEEE Trans. Power Syst, vol. 28, no. 4, pp. 4282-4291, Nov 2013.O. D. Montoya, W. Gil-González and A. Garces, "Optimal Power Flow on DC Microgrids: A Quadratic Convex Approximation", IEEE Trans. Circuits Syst. II, pp. 1-1, 2018.H. Yuan, F. Li, H. Cui, X. Lu, D. Shi and Z. Wang, "A measurement-based VSI for voltage dependent loads using angle difference between tangent lines of load and PV curves", Electr. Power Syst. Res, vol. 160, pp. 13-16, 2018.J. R. Martí, H. Ahmadi and L. Bashualdo, "Linear Power-Flow Formulation Based on a Voltage-Dependent Load Model", IEEE Trans. Power Del, vol. 28, no. 3, pp. 1682-1690, July 2013.Z. Li, J. Yu and Q. H. Wu, "Approximate Linear Power Flow Using Logarithmic Transform of Voltage Magnitudes With Reactive Power and Transmission Loss Consideration", IEEE Trans. Power Syst, vol. 33, no. 4, pp. 4593-4603, July 2018.C. Gavriluta, I. Candela, C. Citro, A. Luna and P. Rodriguez, "Design considerations for primary control in multi-terminal VSC-HVDC grids", Electr. Power Syst. Res, vol. 122, pp. 33-41, 2015.http://purl.org/coar/resource_type/c_c94fORIGINAL108.pdf108.pdfAbstractapplication/pdf61254https://repositorio.utb.edu.co/bitstream/20.500.12585/9941/1/108.pdfe210f0f2ffb4cf45f15c42cb32f9d3e2MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/9941/2/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD52TEXT108.pdf.txt108.pdf.txtExtracted texttext/plain1069https://repositorio.utb.edu.co/bitstream/20.500.12585/9941/3/108.pdf.txt4f428fda458112798614bcfcc7894dc0MD53THUMBNAIL108.pdf.jpg108.pdf.jpgGenerated Thumbnailimage/jpeg49230https://repositorio.utb.edu.co/bitstream/20.500.12585/9941/4/108.pdf.jpg94d0f516599079cd101a70352b42ebbbMD5420.500.12585/9941oai:repositorio.utb.edu.co:20.500.12585/99412023-05-26 10:06:03.798Repositorio Institucional UTBrepositorioutb@utb.edu.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