Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design

A bilinear PI control based on passivity theory for the adequate integration of distributed energy resources (DERs) in ac microgrids is presented in this paper. DERs are integrated into the grid by voltage source converters (VSC), the most common and suitable technology for this type of application....

Full description

Autores:
Gil-González, Walter
Montoya, Oscar D.
Garcés, Alejandro
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:20.500.12585/9504
Acceso en línea:
https://hdl.handle.net/20.500.12585/9504
https://www.tandfonline.com/doi/abs/10.1080/15325008.2020.1793831
Palabra clave:
Bilinear PI control
Lyapunov’s stability
Photovoltaic generator
AC microgrids
Supercapacitor energy storage system
Rights
closedAccess
License
http://purl.org/coar/access_right/c_14cb
id UTB2_103aab167a7ba86b7a4460ae71b9cbd9
oai_identifier_str oai:repositorio.utb.edu.co:20.500.12585/9504
network_acronym_str UTB2
network_name_str Repositorio Institucional UTB
repository_id_str
dc.title.spa.fl_str_mv Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design
title Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design
spellingShingle Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design
Bilinear PI control
Lyapunov’s stability
Photovoltaic generator
AC microgrids
Supercapacitor energy storage system
title_short Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design
title_full Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design
title_fullStr Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design
title_full_unstemmed Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design
title_sort Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design
dc.creator.fl_str_mv Gil-González, Walter
Montoya, Oscar D.
Garcés, Alejandro
dc.contributor.author.none.fl_str_mv Gil-González, Walter
Montoya, Oscar D.
Garcés, Alejandro
dc.subject.keywords.spa.fl_str_mv Bilinear PI control
Lyapunov’s stability
Photovoltaic generator
AC microgrids
Supercapacitor energy storage system
topic Bilinear PI control
Lyapunov’s stability
Photovoltaic generator
AC microgrids
Supercapacitor energy storage system
description A bilinear PI control based on passivity theory for the adequate integration of distributed energy resources (DERs) in ac microgrids is presented in this paper. DERs are integrated into the grid by voltage source converters (VSC), the most common and suitable technology for this type of application. The proposed control guarantees asymptotically stable operation for the dynamical system under closed-loop operating scenarios via Hamiltonian and Lyapunov formulations. ZP load models and π-model of the transmission lines are considered in the stability analysis of the microgrid. Conventional PI control is also implemented for comparative purposes. Simulation results in Matlab/Simulink demonstrate the effectiveness and stability of the proposed control’s performance in a radial microgrid composed of a photovoltaic generator, a supercapacitor energy storage (SCES) system and unbalanced loads.
publishDate 2020
dc.date.accessioned.none.fl_str_mv 2020-10-30T14:49:11Z
dc.date.available.none.fl_str_mv 2020-10-30T14:49:11Z
dc.date.issued.none.fl_str_mv 2020-07-30
dc.date.submitted.none.fl_str_mv 2020-10-28
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 Artículo
status_str publishedVersion
dc.identifier.citation.spa.fl_str_mv Walter Gil-González, Oscar D. Montoya & Alejandro Garces (2020) Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design, Electric Power Components and Systems, 48:4-5, 447-458, DOI: 10.1080/15325008.2020.1793831
dc.identifier.issn.none.fl_str_mv 1532-5008
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12585/9504
dc.identifier.url.none.fl_str_mv https://www.tandfonline.com/doi/abs/10.1080/15325008.2020.1793831
dc.identifier.doi.none.fl_str_mv 10.1080/15325008.2020.1793831
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 Walter Gil-González, Oscar D. Montoya & Alejandro Garces (2020) Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design, Electric Power Components and Systems, 48:4-5, 447-458, DOI: 10.1080/15325008.2020.1793831
1532-5008
10.1080/15325008.2020.1793831
Universidad Tecnológica de Bolívar
Repositorio Universidad Tecnológica de Bolívar
url https://hdl.handle.net/20.500.12585/9504
https://www.tandfonline.com/doi/abs/10.1080/15325008.2020.1793831
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 11 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.place.spa.fl_str_mv Cartagena de Indias
dc.publisher.sede.spa.fl_str_mv Campus Tecnológico
dc.source.spa.fl_str_mv Electric Power Components and Systems Volume 48, 2020 - Issue 4-5
institution Universidad Tecnológica de Bolívar
bitstream.url.fl_str_mv https://repositorio.utb.edu.co/bitstream/20.500.12585/9504/1/41.pdf
https://repositorio.utb.edu.co/bitstream/20.500.12585/9504/2/license.txt
https://repositorio.utb.edu.co/bitstream/20.500.12585/9504/3/41.pdf.txt
https://repositorio.utb.edu.co/bitstream/20.500.12585/9504/4/41.pdf.jpg
bitstream.checksum.fl_str_mv fdfd2a2062f885cd1928cf81dea3ab08
e20ad307a1c5f3f25af9304a7a7c86b6
168fa521099b315bb6c7ae56280420c5
f1b6dd39e3f89ced35ee88eedcccd0a7
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_ 1814021758617911296
spelling Gil-González, Walterce1f5078-74c6-4b5c-b56a-784f85e52a08Montoya, Oscar D.d48a6b1c-a97a-4bbd-8303-dca6fbe71386Garcés, Alejandro1f6fb709-fba4-4fc8-9381-be1f0ca81b822020-10-30T14:49:11Z2020-10-30T14:49:11Z2020-07-302020-10-28Walter Gil-González, Oscar D. Montoya & Alejandro Garces (2020) Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Design, Electric Power Components and Systems, 48:4-5, 447-458, DOI: 10.1080/15325008.2020.17938311532-5008https://hdl.handle.net/20.500.12585/9504https://www.tandfonline.com/doi/abs/10.1080/15325008.2020.179383110.1080/15325008.2020.1793831Universidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarA bilinear PI control based on passivity theory for the adequate integration of distributed energy resources (DERs) in ac microgrids is presented in this paper. DERs are integrated into the grid by voltage source converters (VSC), the most common and suitable technology for this type of application. The proposed control guarantees asymptotically stable operation for the dynamical system under closed-loop operating scenarios via Hamiltonian and Lyapunov formulations. ZP load models and π-model of the transmission lines are considered in the stability analysis of the microgrid. Conventional PI control is also implemented for comparative purposes. Simulation results in Matlab/Simulink demonstrate the effectiveness and stability of the proposed control’s performance in a radial microgrid composed of a photovoltaic generator, a supercapacitor energy storage (SCES) system and unbalanced loads.Ministerio de Ciencia11 páginasapplication/pdfengElectric Power Components and Systems Volume 48, 2020 - Issue 4-5Bilinear Control for Three-Phase Microgrids: A Proportional-Integral Passivity-Based Designinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_2df8fbb1Bilinear PI controlLyapunov’s stabilityPhotovoltaic generatorAC microgridsSupercapacitor energy storage systeminfo:eu-repo/semantics/closedAccesshttp://purl.org/coar/access_right/c_14cbCartagena de IndiasCampus TecnológicoO.Ellabban, H.Abu-Rub and F.Blaabjerg , “Renewable energy resources: Current status, future prospects and their enabling technology,” Renew. Sustain. Energy Rev. , vol. 39, pp. 748–764, 2014. DOI: 10.1016/j.rser.2014.07.113.F.Katiraei, R.Iravani, N.Hatziargyriou and A.Dimeas , “Microgrids management,” IEEE Power Energy Mag. , vol. 6, no. 3, pp. 54–65, 2008. DOI: 10.1109/MPE.2008.918702.A.Keyhani , Design of Smart Power Grid Renewable Energy Systems . United States of America: John Wiley & Sons, 2016.E.Planas, J.Andreu, J. I.Gárate, I. M.de Alegría and E.Ibarra , “AC and DC technology in microgrids: A review, Renew,” Sustain. Energy Rev. , vol. 43, pp. 726–749, 2015. DOI: 10.1016/j.rser.2014.11.067.S. M.Kaviri, M.Pahlevani, P.Jain and A.Bakhshai , “A review of AC microgrid control methods,” in 2017 IEEE 8th International Symposium on Power Electronics for Distributed Generation Systems (PEDG), IEEE, 2017, pp. 1–8. DOI: 10.1109/PEDG.2017.7972498.O. D. M.Giraldo, W. J. G.González, A. G.Ruiz, A. E.Mejía and L. F. G.Noreña , “Nonlinear control for battery energy storage systems in power grids,” in 2018 IEEE Green Technologies Conference (GreenTech), IEEE, 2018, pp. 65–70.X.Luo, J.Wang, M.Dooner and J.Clarke , “Overview of current development in electrical energy storage technologies and the application potential in power system operation,” Appl. Energy , vol. 137, pp. 511–536, 2015. DOI: 10.1016/j.apenergy.2014.09.081.H.Han, X.Hou, J.Yang, J.Wu, M.Su and J. M.Guerrero , “Review of power sharing control strategies for islanding operation of AC microgrids,” IEEE Trans. Smart Grid , vol. 7, no. 1, pp. 200–215, 2016. DOI: 10.1109/TSG.2015.2434849.J. M.Guerrero, P. C.Loh, T.-L.Lee and M.Chandorkar , “Advanced control architectures for intelligent microgrids–Part II: Power quality, energy storage, and AC/DC microgrids,” IEEE Trans. Ind. Electron. , vol. 60, no. 4, pp. 1263–1270, 2013. DOI: 10.1109/TIE.2012.2196889.X.Wang, J. M.Guerrero and Z.Chen , “Control of grid interactive AC microgrids,” in 2010 IEEE International Symposium on Industrial Electronics, IEEE, 2010, pp. 2211–2216.V.Nasirian, Q.Shafiee, J. M.Guerrero, F. L.Lewis and A.Davoudi , “Droop-free distributed control for AC microgrids,” IEEE Trans. Power Electron. , vol. 31, no. 2, pp. 1600–1617, 2016. DOI: 10.1109/TPEL.2015.2414457.O. D.Montoya, A.Garcés and F. M.Serra , “DERs integration in microgrids using VSCs via proportional feedback linearization control: Supercapacitors and distributed generators,” J. Energy Storage , vol. 16, pp. 250–258, 2018. DOI: 10.1016/j.est.2018.01.014.F. M.Serra, C. H. D.Angelo and D. G.Forchetti , “Interconnection and damping assignment control of a three-phase front end converter,” Int. J. Elec. Power , vol. 60, pp. 317–324, 2014. DOI: 10.1016/j.ijepes.2014.03.033.F. M.Serra and C. H. D.Angelo , “IDA-PBC controller design for grid connected Front End Converters under non-ideal grid conditions,” Electr. Power Syst. Res. , vol. 142, pp. 12–19, 2017. DOI: 10.1016/j.epsr.2016.08.041.O. D.Montoya, W.Gil-González and A.Garces , “Control for EESS in Three–Phase Microgrids Under Time–Domain Reference Frame via PBC Theory,” IEEE Trans. Circuits Syst. II , vol. 66, no. 12, pp. 2007–2011, 2019. DOI: 10.1109/TCSII.2019.2893842.S.Vazquez, J.Rodriguez, M.Rivera, L. G.Franquelo and M.Norambuena , “Model predictive control for power converters and drives: Advances and trends,” IEEE Trans. Ind. Electron. , vol. 64, no. 2, pp. 935–947, 2017. DOI: 10.1109/TIE.2016.2625238.A.Parisio, E.Rikos and L.Glielmo , “A model predictive control approach to microgrid operation optimization,” IEEE Trans. Contr. Syst. Technol. , vol. 22, no. 5, pp. 1813–1827, 2014. DOI: 10.1109/TCST.2013.2295737.R.Aghatehrani and R.Kavasseri , “Sensitivity-analysis-based sliding mode control for voltage regulation in microgrids,” IEEE Trans. Sustain. Energy , vol. 4, no. 1, pp. 50–57, 2013. DOI: 10.1109/TSTE.2012.2197870.M.Cucuzzella, G. P.Incremona and A.Ferrara , “Design of robust higher order sliding mode control for microgrids,” IEEE J. Emerg. Sel. Topics Circuits Syst. , vol. 5, no. 3, pp. 393–401, 2015. DOI: 10.1109/JETCAS.2015.2450411.G.Kyriakarakos, A. I.Dounis, K. G.Arvanitis and G.Papadakis , “A fuzzy logic energy management system for polygeneration microgrids,” Ren. Energy , vol. 41, pp. 315–327, 2012. DOI: 10.1016/j.renene.2011.11.019.R.Cisneros, M.Pirro, G.Bergna, R.Ortega, G.Ippoliti and M.Molinas , “Global tracking passivity-based pi control of bilinear systems: Application to the interleaved boost and modular multilevel converters,” Control Eng. Pract. , vol. 43, pp. 109–119, 2015. DOI: 10.1016/j.conengprac.2015.07.002.R.Teodorescu, M.Liserre and P.Rodriguez , Grid Converters for Photovoltaic and Wind Power Systems . United Kingdom: Wiley-IEEE, Wiley, 2011.S.Golestan, J. M.Guerrero and J. C.Vasquez , “Three-phase PLLs: A review of recent advances,” IEEE Trans. Power Electron. , vol. 32, no. 3, pp. 1894–1907, 2017. DOI: 10.1109/TPEL.2016.2565642.J.Machowski, J. W.Bialek and J. R.Bumby , Power System Dynamics: Stability and Control , 2nd ed. United Kingdom: John Wily & Sons, 2008.O. D.Montoya, A.Garces, S.Avila-Becerril, G.Espinosa-Pérez and F. M.Serra , “Stability analysis of single-phase low-voltage AC microgrids with constant power terminals,” IEEE Trans. Circuits Syst. II , vol. 66, no. 7, pp. 1212–1216, 2019. DOI: 10.1109/TCSII.2018.2878188.IEEE Standard for Interconnecting Distributed Resources with Electric Power Systems—Amendment 1, IEEE Std 1547a-2014 (Amendment to IEEE Std 1547-2003), 2014, pp. 1–16.W.Gil-González, O. D.Montoya and A.Garces , “Direct power control for VSC-HVDC systems: An application of the global tracking passivity-based PI approach,” Int. J. Elec. Power , vol. 110, pp. 588–597, 2019. DOI: 10.1016/j.ijepes.2019.03.042.http://purl.org/coar/resource_type/c_2df8fbb1ORIGINAL41.pdf41.pdfapplication/pdf122897https://repositorio.utb.edu.co/bitstream/20.500.12585/9504/1/41.pdffdfd2a2062f885cd1928cf81dea3ab08MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/9504/2/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD52TEXT41.pdf.txt41.pdf.txtExtracted texttext/plain929https://repositorio.utb.edu.co/bitstream/20.500.12585/9504/3/41.pdf.txt168fa521099b315bb6c7ae56280420c5MD53THUMBNAIL41.pdf.jpg41.pdf.jpgGenerated Thumbnailimage/jpeg52755https://repositorio.utb.edu.co/bitstream/20.500.12585/9504/4/41.pdf.jpgf1b6dd39e3f89ced35ee88eedcccd0a7MD5420.500.12585/9504oai:repositorio.utb.edu.co:20.500.12585/95042020-11-02 00:52:40.947Repositorio Institucional UTBrepositorioutb@utb.edu.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