Reactive power sharing among distributed generators in a microgrid by using virtual current
This paper presents a new autonomous effective power distribution control strategy for three-phase parallel inverters. The proposal uses a controller that can provide the system with accurate power sharing among distributed generators installed in the microgrid once some load variations are presente...
- Autores:
-
Molina Vilora, Eder Alexander
Candelo Becerra, John Edwin
Hoyos Velasco, Fredy Edimer
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2021
- Institución:
- Tecnológico de Antioquia
- Repositorio:
- Repositorio Tdea
- Idioma:
- eng
- OAI Identifier:
- oai:dspace.tdea.edu.co:tdea/3053
- Acceso en línea:
- https://dspace.tdea.edu.co/handle/tdea/3053
- Palabra clave:
- Distributed generation
Generación distribuida
Microgrid
Microrred
Reactive power sharing
Reparto de potencia reactiva
Virtual current
Corriente virtual
Virtual impedance
Impedancia virtual
- Rights
- openAccess
- License
- https://creativecommons.org/licenses/by-sa/4.0/
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oai:dspace.tdea.edu.co:tdea/3053 |
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dc.title.none.fl_str_mv |
Reactive power sharing among distributed generators in a microgrid by using virtual current |
title |
Reactive power sharing among distributed generators in a microgrid by using virtual current |
spellingShingle |
Reactive power sharing among distributed generators in a microgrid by using virtual current Distributed generation Generación distribuida Microgrid Microrred Reactive power sharing Reparto de potencia reactiva Virtual current Corriente virtual Virtual impedance Impedancia virtual |
title_short |
Reactive power sharing among distributed generators in a microgrid by using virtual current |
title_full |
Reactive power sharing among distributed generators in a microgrid by using virtual current |
title_fullStr |
Reactive power sharing among distributed generators in a microgrid by using virtual current |
title_full_unstemmed |
Reactive power sharing among distributed generators in a microgrid by using virtual current |
title_sort |
Reactive power sharing among distributed generators in a microgrid by using virtual current |
dc.creator.fl_str_mv |
Molina Vilora, Eder Alexander Candelo Becerra, John Edwin Hoyos Velasco, Fredy Edimer |
dc.contributor.author.none.fl_str_mv |
Molina Vilora, Eder Alexander Candelo Becerra, John Edwin Hoyos Velasco, Fredy Edimer |
dc.subject.proposal.none.fl_str_mv |
Distributed generation Generación distribuida Microgrid Microrred Reactive power sharing Reparto de potencia reactiva Virtual current Corriente virtual Virtual impedance Impedancia virtual |
topic |
Distributed generation Generación distribuida Microgrid Microrred Reactive power sharing Reparto de potencia reactiva Virtual current Corriente virtual Virtual impedance Impedancia virtual |
description |
This paper presents a new autonomous effective power distribution control strategy for three-phase parallel inverters. The proposal uses a controller that can provide the system with accurate power sharing among distributed generators installed in the microgrid once some load variations are presented in the network. The methodology uses a virtual current loop introduced into the current controller of the inverter to optimize the output signal, which goes directly to the PWM. This virtual current is obtainedby using a virtual impedance loop. Furthermore, a small-signal model of the system is used to check stability of the proposed control strategy, which was developed for island mode operation of the microgrid. Simulations were performed for a microgrid withtwo generators and a load with five households and implemented in MATLAB/Simulinksoftware. The results show that the model provides a wide margin of stability and a rapid response when electrical loads change, thus fulfilling the reactive power sharing among generators. The proposed method shows a large margin of stability and a rapidtransient response of the system |
publishDate |
2021 |
dc.date.issued.none.fl_str_mv |
2021 |
dc.date.accessioned.none.fl_str_mv |
2023-05-26T04:07:43Z |
dc.date.available.none.fl_str_mv |
2023-05-26T04:07:43Z |
dc.type.spa.fl_str_mv |
Artículo de revista |
dc.type.coar.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
dc.type.content.spa.fl_str_mv |
Text |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/ART |
dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.coarversion.spa.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
format |
http://purl.org/coar/resource_type/c_2df8fbb1 |
status_str |
publishedVersion |
dc.identifier.issn.spa.fl_str_mv |
2088-8694 |
dc.identifier.uri.none.fl_str_mv |
https://dspace.tdea.edu.co/handle/tdea/3053 |
dc.identifier.eissn.spa.fl_str_mv |
2722-256X |
identifier_str_mv |
2088-8694 2722-256X |
url |
https://dspace.tdea.edu.co/handle/tdea/3053 |
dc.language.iso.spa.fl_str_mv |
eng |
language |
eng |
dc.relation.citationendpage.spa.fl_str_mv |
111 |
dc.relation.citationissue.spa.fl_str_mv |
1 |
dc.relation.citationstartpage.spa.fl_str_mv |
99 |
dc.relation.citationvolume.spa.fl_str_mv |
12 |
dc.relation.ispartofjournal.spa.fl_str_mv |
International Journal of Power Electronics and Drive Systems |
dc.relation.references.spa.fl_str_mv |
J. M. Guerrero, J. C. Vasquez, J. Matas, L. G. de Vicuna, and M. Castilla, “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 158–172, Jan. 2011, doi: 10.1109/TIE.2010.2066534. R. H. Lasseter, “MicroGrids,” in 2002 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.02CH37309), vol. 1, pp. 305–308, doi: 10.1109/PESW.2002.985003. N. Pogaku, M. Prodanovic, and T. C. Green, “Modeling, Analysis and Testing of Autonomous Operation of an Inverter-Based Microgrid,” IEEE Trans. Power Electron., vol. 22, no. 2, pp. 613–625, Mar. 2007, doi: 10.1109/TPEL.2006.890003 E. Molina, J.E. Candelo-Becerra, and F. E. Hoyos, “Control Strategy to Regulate Voltage and Share Reactive Power Using Variable Virtual Impedance for a Microgrid,” Appl. Sci., vol. 9, no. 22, p. 4876, Nov. 2019, doi: 10.3390/app9224876 A. W. N. Husna, M. A. Roslan, and M. H. Mat, “Droop control technique for equal power sharing in islanded microgrid,” International Journal of Power Electronics and Drive Systems (IJPEDS), vol. 10, no. 1, p. 530, 2019, doi: 10.11591/ijpeds.v10.i1.pp530-537. S. A. Pizarro, J. E. Candelo-Becerra, and F. E. H. Velasco, “Optimal parameters of inverter-based microgrid to improve transient response,” International Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 1, pp. 637–650, 2020, doi: 10.11591/ijece.v10i1.pp637-650 O. Feddaoui, R. Toufouti, and L. Djamel, “Active and reactive power sharing in micro grid using droop control,” International Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 3, pp. 2235–2244, 2019, doi: 10.11591/ijece.v10i3.pp2235-2244. J. M. Guerrero, L. GarciadeVicuna, J. Matas, M. Castilla, and J. Miret, “Output Impedance Design of Parallel-Connected UPS Inverters With Wireless Load-Sharing Control,” IEEE Trans. Ind. Electron., vol. 52, no. 4, pp. 1126–1135, Aug. 2005,doi: 10.1109/TIE.2005.851634. D. De and V. Ramanarayanan, “Decentralized Parallel Operation of Inverters Sharing Unbalanced and Nonlinear Loads,” IEEE Trans. Power Electron., vol. 25, no. 12, pp. 3015–3025, Dec. 2010, doi: 10.1109/TPEL.2010.2068313 E. A. A. Coelho, P. C. Cortizo, and P. F. D. Garcia, “Small signal stability for single phase inverter connected to stiff AC system,” pp. 2180–2187, 2003, doi: 10.1109/ias.1999.798756 J. He and Y. W. Li, “Analysis, design, and implementation of virtual impedance for power electronics interfaced distributed generation,” IEEE Trans. Ind. Appl., vol. 47, no. 6, pp. 2525–2538, Nov. 2011, doi: 10.1109/TIA.2011.2168592 Y. W. Li, “Control and resonance damping of voltage-source and current-source converters with LC filters,” IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1511–1521, 2009, doi: 10.1109/TIE.2008.2009562. T. L. Lee and P. T. Cheng, “Design of a new cooperative harmonic filtering strategy for distributed generation interface converters in an islanding network,” IEEE Trans. Power Electron., vol. 22, no. 5, pp. 1919–1927, Sep. 2007, doi: 10.1109/TPEL.2007.904200. M. A. Zamani, T. S. Sidhu, and A. Yazdani, “Investigations Into the Control and Protection of an Existing Distribution Network to Operate as a Microgrid: A Case Study,” IEEE Trans. Ind. Electron., vol. 61, no. 4, pp. 1904–1915, Apr. 2014, doi: 10.1109/TIE.2013.2267695 J. Rocabert, A. Luna, F. Blaabjerg, and P. Rodríguez, “Control of Power Converters in AC Microgrids,” IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4734–4749, Nov. 2012, doi: 10.1109/TPEL.2012.2199334 I. U. Nutkani, P. C. Loh, and F. Blaabjerg, “Droop Scheme With Consideration of Operating Costs,” IEEE Trans. Power Electron., vol. 29, no. 3, pp. 1047–1052, Mar. 2014, doi: 10.1109/TPEL.2013.2276251 C. K. Lee, B. Chaudhuri, and S. Y. Hui, “Hardware and Control Implementationof Electric Springs for Stabilizing Future Smart Grid With Intermittent Renewable Energy Sources,” IEEE J. Emerg. Sel. Top. Power Electron., vol. 1, no. 1, pp. 18–27, Mar. 2013, doi: 10.1109/JESTPE.2013.2264091 J. Kim, J. M. Guerrero, P. Rodriguez, R. Teodorescu, and K. Nam, “Mode Adaptive Droop Control With Virtual Output Impedances for an Inverter-Based Flexible AC Microgrid,” IEEE Trans. Power Electron., vol. 26, no. 3, pp. 689–701, Mar. 2011, doi: 10.1109/TPEL.2010.2091685. J. M. Guerrero, J. Matas, L. Garcia de Vicuna, M. Castilla, and J. Miret, “Decentralized Control for Parallel Operation of Distributed Generation Inverters Using Resistive Output Impedance,” IEEE Trans. Ind. Electron., vol. 54, no. 2, pp. 994–1004, Apr. 2007, doi: 10.1109/TIE.2007.892621. A. Tuladhar, Hua Jin, T. Unger, and K. Mauch, “Control of parallel inverters in distributed AC power systems with consideration of line impedance effect,” IEEE Trans. Ind. Appl., vol. 36, no. 1, pp. 131–138, 2000, doi: 10.1109/28.821807 Yun Wei Li and Ching-Nan Kao, “An Accurate Power Control Strategy for Power-Electronics-Interfaced Distributed Generation Units Operating in a Low-Voltage Multibus Microgrid,” IEEE Trans. Power Electron., vol. 24, no. 12, pp. 2977–2988, Dec. 2009, doi: 10.1109/TPEL.2009.2022828. Q.-C. Zhong, “Robust Droop Controller for Accurate Proportional Load Sharing Among Inverters Operated in Parallel,” IEEE Trans. Ind. Electron., vol. 60, no. 4, pp. 1281–1290, Apr. 2013, doi: 10.1109/TIE.2011.2146221. C.-T. Lee, C.-C. Chu, and P.-T. Cheng, “A New Droop Control Method for the Autonomous Operation of Distributed Energy Resource Interface Converters,” IEEE Trans. Power Electron., vol. 28, no. 4, pp. 1980–1993, Apr. 2013, doi: 10.1109/TPEL.2012.2205944. J. W. Simpson-Porco, Q. Shafiee, F. Dorfler, J. C. Vasquez, J. M. Guerrero, and F. Bullo, “Secondary Frequency and Voltage Control of Islanded Microgrids via Distributed Averaging,” IEEE Trans. Ind. Electron., vol. 62, no. 11, pp. 7025–7038, Nov. 2015, doi: 10.1109/TIE.2015.2436879 J. A. P. Lopes, C. L. Moreira, and A. G. Madureira, “Defining Control Strategies for MicroGrids Islanded Operation,” IEEE Trans. Power Syst., vol. 21, no. 2, pp. 916–924, May 2006, doi: 10.1109/TPWRS.2006.873018 V. Lavanya and N. S. Kumar, “Control strategies for seamless transfer between the grid-connected and islanded modes of a microgrid system,” International Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 5, pp. 4490–4506, 2020, doi: 10.11591/ijece.v10i5.pp4490-4506. A. Chaithanakulwat, “Development of DC voltage control from wind turbines using proportions and integrals for Three-phase grid-connected inverters,” International Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 2, pp. 1701–1711, 2020, doi: 10.11591/ijece.v10i2.pp1701-1711 Suroso, D. T. Nugroho, Amran, and T. Noguchi, “Parallel operation of current-source inverter for low-voltage high-current grid-connected photovoltaic system,” International Journal of Electrical and Computer Engineering (IJECE), vol. 9, no. 4, pp. 2220–2229, 2019, doi: 10.11591/ijece.v9i4.pp2220-2229 N. Chaitanya, P. Sujatha, and K. C. Sekhar, “Current Controller Based Power Management Strategy for Interfacing DG Units to Micro Grid,” International Journal of Electrical and Computer Engineering (IJECE), vol. 7, no. 5, p. 2300, 2017, doi: 10.11591/ijece.v7i5.pp2300-2308. |
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Molina Vilora, Eder Alexanderc53976f8-0ead-4aa5-a54c-48a6c2a11e23Candelo Becerra, John Edwinccbaea93-315c-4612-b0cf-31ddb6eeebcfHoyos Velasco, Fredy Edimer21861e8f-32e1-4f94-b084-37f88e45b5632023-05-26T04:07:43Z2023-05-26T04:07:43Z20212088-8694https://dspace.tdea.edu.co/handle/tdea/30532722-256XThis paper presents a new autonomous effective power distribution control strategy for three-phase parallel inverters. The proposal uses a controller that can provide the system with accurate power sharing among distributed generators installed in the microgrid once some load variations are presented in the network. The methodology uses a virtual current loop introduced into the current controller of the inverter to optimize the output signal, which goes directly to the PWM. This virtual current is obtainedby using a virtual impedance loop. Furthermore, a small-signal model of the system is used to check stability of the proposed control strategy, which was developed for island mode operation of the microgrid. Simulations were performed for a microgrid withtwo generators and a load with five households and implemented in MATLAB/Simulinksoftware. The results show that the model provides a wide margin of stability and a rapid response when electrical loads change, thus fulfilling the reactive power sharing among generators. The proposed method shows a large margin of stability and a rapidtransient response of the system13 páginasapplication/pdfengInstitute of Advanced Engineering and ScienceIndonesiahttps://creativecommons.org/licenses/by-sa/4.0/Atribución-CompartirIgual 4.0 Internacional (CC BY-SA 4.0)info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2https://ijpeds.iaescore.com/index.php/IJPEDS/article/view/20669/13329Reactive power sharing among distributed generators in a microgrid by using virtual currentArtículo de revistahttp://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a8511119912International Journal of Power Electronics and Drive SystemsJ. M. Guerrero, J. C. Vasquez, J. Matas, L. G. de Vicuna, and M. Castilla, “Hierarchical Control of Droop-Controlled AC and DC Microgrids—A General Approach Toward Standardization,” IEEE Trans. Ind. Electron., vol. 58, no. 1, pp. 158–172, Jan. 2011, doi: 10.1109/TIE.2010.2066534.R. H. Lasseter, “MicroGrids,” in 2002 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.02CH37309), vol. 1, pp. 305–308, doi: 10.1109/PESW.2002.985003.N. Pogaku, M. Prodanovic, and T. C. Green, “Modeling, Analysis and Testing of Autonomous Operation of an Inverter-Based Microgrid,” IEEE Trans. Power Electron., vol. 22, no. 2, pp. 613–625, Mar. 2007, doi: 10.1109/TPEL.2006.890003E. Molina, J.E. Candelo-Becerra, and F. E. Hoyos, “Control Strategy to Regulate Voltage and Share Reactive Power Using Variable Virtual Impedance for a Microgrid,” Appl. Sci., vol. 9, no. 22, p. 4876, Nov. 2019, doi: 10.3390/app9224876A. W. N. Husna, M. A. Roslan, and M. H. Mat, “Droop control technique for equal power sharing in islanded microgrid,” International Journal of Power Electronics and Drive Systems (IJPEDS), vol. 10, no. 1, p. 530, 2019, doi: 10.11591/ijpeds.v10.i1.pp530-537.S. A. Pizarro, J. E. Candelo-Becerra, and F. E. H. Velasco, “Optimal parameters of inverter-based microgrid to improve transient response,” International Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 1, pp. 637–650, 2020, doi: 10.11591/ijece.v10i1.pp637-650O. Feddaoui, R. Toufouti, and L. Djamel, “Active and reactive power sharing in micro grid using droop control,” International Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 3, pp. 2235–2244, 2019, doi: 10.11591/ijece.v10i3.pp2235-2244.J. M. Guerrero, L. GarciadeVicuna, J. Matas, M. Castilla, and J. Miret, “Output Impedance Design of Parallel-Connected UPS Inverters With Wireless Load-Sharing Control,” IEEE Trans. Ind. Electron., vol. 52, no. 4, pp. 1126–1135, Aug. 2005,doi: 10.1109/TIE.2005.851634.D. De and V. Ramanarayanan, “Decentralized Parallel Operation of Inverters Sharing Unbalanced and Nonlinear Loads,” IEEE Trans. Power Electron., vol. 25, no. 12, pp. 3015–3025, Dec. 2010, doi: 10.1109/TPEL.2010.2068313E. A. A. Coelho, P. C. Cortizo, and P. F. D. Garcia, “Small signal stability for single phase inverter connected to stiff AC system,” pp. 2180–2187, 2003, doi: 10.1109/ias.1999.798756J. He and Y. W. Li, “Analysis, design, and implementation of virtual impedance for power electronics interfaced distributed generation,” IEEE Trans. Ind. Appl., vol. 47, no. 6, pp. 2525–2538, Nov. 2011, doi: 10.1109/TIA.2011.2168592Y. W. Li, “Control and resonance damping of voltage-source and current-source converters with LC filters,” IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1511–1521, 2009, doi: 10.1109/TIE.2008.2009562.T. L. Lee and P. T. Cheng, “Design of a new cooperative harmonic filtering strategy for distributed generation interface converters in an islanding network,” IEEE Trans. Power Electron., vol. 22, no. 5, pp. 1919–1927, Sep. 2007, doi: 10.1109/TPEL.2007.904200.M. A. Zamani, T. S. Sidhu, and A. Yazdani, “Investigations Into the Control and Protection of an Existing Distribution Network to Operate as a Microgrid: A Case Study,” IEEE Trans. Ind. Electron., vol. 61, no. 4, pp. 1904–1915, Apr. 2014, doi: 10.1109/TIE.2013.2267695J. Rocabert, A. Luna, F. Blaabjerg, and P. Rodríguez, “Control of Power Converters in AC Microgrids,” IEEE Trans. Power Electron., vol. 27, no. 11, pp. 4734–4749, Nov. 2012, doi: 10.1109/TPEL.2012.2199334I. U. Nutkani, P. C. Loh, and F. Blaabjerg, “Droop Scheme With Consideration of Operating Costs,” IEEE Trans. Power Electron., vol. 29, no. 3, pp. 1047–1052, Mar. 2014, doi: 10.1109/TPEL.2013.2276251C. K. Lee, B. Chaudhuri, and S. Y. Hui, “Hardware and Control Implementationof Electric Springs for Stabilizing Future Smart Grid With Intermittent Renewable Energy Sources,” IEEE J. Emerg. Sel. Top. Power Electron., vol. 1, no. 1, pp. 18–27, Mar. 2013, doi: 10.1109/JESTPE.2013.2264091J. Kim, J. M. Guerrero, P. Rodriguez, R. Teodorescu, and K. Nam, “Mode Adaptive Droop Control With Virtual Output Impedances for an Inverter-Based Flexible AC Microgrid,” IEEE Trans. Power Electron., vol. 26, no. 3, pp. 689–701, Mar. 2011, doi: 10.1109/TPEL.2010.2091685.J. M. Guerrero, J. Matas, L. Garcia de Vicuna, M. Castilla, and J. Miret, “Decentralized Control for Parallel Operation of Distributed Generation Inverters Using Resistive Output Impedance,” IEEE Trans. Ind. Electron., vol. 54, no. 2, pp. 994–1004, Apr. 2007, doi: 10.1109/TIE.2007.892621.A. Tuladhar, Hua Jin, T. Unger, and K. Mauch, “Control of parallel inverters in distributed AC power systems with consideration of line impedance effect,” IEEE Trans. Ind. Appl., vol. 36, no. 1, pp. 131–138, 2000, doi: 10.1109/28.821807Yun Wei Li and Ching-Nan Kao, “An Accurate Power Control Strategy for Power-Electronics-Interfaced Distributed Generation Units Operating in a Low-Voltage Multibus Microgrid,” IEEE Trans. Power Electron., vol. 24, no. 12, pp. 2977–2988, Dec. 2009, doi: 10.1109/TPEL.2009.2022828.Q.-C. Zhong, “Robust Droop Controller for Accurate Proportional Load Sharing Among Inverters Operated in Parallel,” IEEE Trans. Ind. Electron., vol. 60, no. 4, pp. 1281–1290, Apr. 2013, doi: 10.1109/TIE.2011.2146221.C.-T. Lee, C.-C. Chu, and P.-T. Cheng, “A New Droop Control Method for the Autonomous Operation of Distributed Energy Resource Interface Converters,” IEEE Trans. Power Electron., vol. 28, no. 4, pp. 1980–1993, Apr. 2013, doi: 10.1109/TPEL.2012.2205944.J. W. Simpson-Porco, Q. Shafiee, F. Dorfler, J. C. Vasquez, J. M. Guerrero, and F. Bullo, “Secondary Frequency and Voltage Control of Islanded Microgrids via Distributed Averaging,” IEEE Trans. Ind. Electron., vol. 62, no. 11, pp. 7025–7038, Nov. 2015, doi: 10.1109/TIE.2015.2436879J. A. P. Lopes, C. L. Moreira, and A. G. Madureira, “Defining Control Strategies for MicroGrids Islanded Operation,” IEEE Trans. Power Syst., vol. 21, no. 2, pp. 916–924, May 2006, doi: 10.1109/TPWRS.2006.873018V. Lavanya and N. S. Kumar, “Control strategies for seamless transfer between the grid-connected and islanded modes of a microgrid system,” International Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 5, pp. 4490–4506, 2020, doi: 10.11591/ijece.v10i5.pp4490-4506.A. Chaithanakulwat, “Development of DC voltage control from wind turbines using proportions and integrals for Three-phase grid-connected inverters,” International Journal of Electrical and Computer Engineering (IJECE), vol. 10, no. 2, pp. 1701–1711, 2020, doi: 10.11591/ijece.v10i2.pp1701-1711Suroso, D. 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Sekhar, “Current Controller Based Power Management Strategy for Interfacing DG Units to Micro Grid,” International Journal of Electrical and Computer Engineering (IJECE), vol. 7, no. 5, p. 2300, 2017, doi: 10.11591/ijece.v7i5.pp2300-2308.Distributed generationGeneración distribuidaMicrogridMicrorredReactive power sharingReparto de potencia reactivaVirtual currentCorriente virtualVirtual impedanceImpedancia virtualTHUMBNAILReactive power sharing among distributed generators in a microgrid by using virtual current _ Molina-Viloria _ International Journal of Power Electronics and Drive Systems (IJPEDS).pdf.jpgReactive power sharing among distributed generators in a microgrid by using virtual current _ Molina-Viloria _ International Journal of Power Electronics and Drive Systems (IJPEDS).pdf.jpgGenerated 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 incorporada en las Obras Colectivas.

b.	Distribuir copias o fonogramas de las Obras, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública, incluyéndolas como incorporadas en Obras Colectivas, según corresponda.

c.	Distribuir copias de las Obras Derivadas que se generen, exhibirlas públicamente, ejecutarlas públicamente y/o ponerlas a disposición pública.
Los derechos mencionados anteriormente pueden ser ejercidos en todos los medios y formatos, actualmente conocidos o que se inventen en el futuro. Los derechos antes mencionados incluyen el derecho a realizar dichas modificaciones en la medida que sean técnicamente necesarias para ejercer los derechos en otro medio o formatos, pero de otra manera usted no está autorizado para realizar obras derivadas. Todos los derechos no otorgados expresamente por el Licenciante quedan por este medio reservados, incluyendo pero sin limitarse a aquellos que se mencionan en las secciones 4(d) y 4(e).

4. Restricciones.
La licencia otorgada en la anterior Sección 3 está expresamente sujeta y limitada por las siguientes restricciones:

a.	Usted puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra sólo bajo las condiciones de esta Licencia, y Usted debe incluir una copia de esta licencia o del Identificador Universal de Recursos de la misma con cada copia de la Obra que distribuya, exhiba públicamente, ejecute públicamente o ponga a disposición pública. No es posible ofrecer o imponer ninguna condición sobre la Obra que altere o limite las condiciones de esta Licencia o el ejercicio de los derechos de los destinatarios otorgados en este documento. No es posible sublicenciar la Obra. Usted debe mantener intactos todos los avisos que hagan referencia a esta Licencia y a la cláusula de limitación de garantías. Usted no puede distribuir, exhibir públicamente, ejecutar públicamente, o poner a disposición pública la Obra con alguna medida tecnológica que controle el acceso o la utilización de ella de una forma que sea inconsistente con las condiciones de esta Licencia. Lo anterior se aplica a la Obra incorporada a una Obra Colectiva, pero esto no exige que la Obra Colectiva aparte de la obra misma quede sujeta a las condiciones de esta Licencia. Si Usted crea una Obra Colectiva, previo aviso de cualquier Licenciante debe, en la medida de lo posible, eliminar de la Obra Colectiva cualquier referencia a dicho Licenciante o al Autor Original, según lo solicitado por el Licenciante y conforme lo exige la cláusula 4(c).

b.	Usted no puede ejercer ninguno de los derechos que le han sido otorgados en la Sección 3 precedente de modo que estén principalmente destinados o directamente dirigidos a conseguir un provecho comercial o una compensación monetaria privada. El intercambio de la Obra por otras obras protegidas por derechos de autor, ya sea a través de un sistema para compartir archivos digitales (digital file-sharing) o de cualquier otra manera no será considerado como estar destinado principalmente o dirigido directamente a conseguir un provecho comercial o una compensación monetaria privada, siempre que no se realice un pago mediante una compensación monetaria en relación con el intercambio de obras protegidas por el derecho de autor.

c.	Si usted distribuye, exhibe públicamente, ejecuta públicamente o ejecuta públicamente en forma digital la Obra o cualquier Obra Derivada u Obra Colectiva, Usted debe mantener intacta toda la información de derecho de autor de la Obra y proporcionar, de forma razonable según el medio o manera que Usted esté utilizando: (i) el nombre del Autor Original si está provisto (o seudónimo, si fuere aplicable), y/o (ii) el nombre de la parte o las partes que el Autor Original y/o el Licenciante hubieren designado para la atribución (v.g., un instituto patrocinador, editorial, publicación) en la información de los derechos de autor del Licenciante, términos de servicios o de otras formas razonables; el título de la Obra si está provisto; en la medida de lo razonablemente factible y, si está provisto, el Identificador Uniforme de Recursos (Uniform Resource Identifier) que el Licenciante especifica para ser asociado con la Obra, salvo que tal URI no se refiera a la nota sobre los derechos de autor o a la información sobre el licenciamiento de la Obra; y en el caso de una Obra Derivada, atribuir el crédito identificando el uso de la Obra en la Obra Derivada (v.g., "Traducción Francesa de la Obra del Autor Original," o "Guión Cinematográfico basado en la Obra original del Autor Original"). Tal crédito puede ser implementado de cualquier forma razonable; en el caso, sin embargo, de Obras Derivadas u Obras Colectivas, tal crédito aparecerá, como mínimo, donde aparece el crédito de cualquier otro autor comparable y de una manera, al menos, tan destacada como el crédito de otro autor comparable.

d.	Para evitar toda confusión, el Licenciante aclara que, cuando la obra es una composición musical:

i.	Regalías por interpretación y ejecución bajo licencias generales. El Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública o la ejecución pública digital de la obra y de recolectar, sea individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, SAYCO), las regalías por la ejecución pública o por la ejecución pública digital de la obra (por ejemplo Webcast) licenciada bajo licencias generales, si la interpretación o ejecución de la obra está primordialmente orientada por o dirigida a la obtención de una ventaja comercial o una compensación monetaria privada.

ii.	Regalías por Fonogramas. El Licenciante se reserva el derecho exclusivo de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, los consagrados por la SAYCO), una agencia de derechos musicales o algún agente designado, las regalías por cualquier fonograma que Usted cree a partir de la obra (“versión cover”) y distribuya, en los términos del régimen de derechos de autor, si la creación o distribución de esa versión cover está primordialmente destinada o dirigida a obtener una ventaja comercial o una compensación monetaria privada.

e.	Gestión de Derechos de Autor sobre Interpretaciones y Ejecuciones Digitales (WebCasting). Para evitar toda confusión, el Licenciante aclara que, cuando la obra sea un fonograma, el Licenciante se reserva el derecho exclusivo de autorizar la ejecución pública digital de la obra (por ejemplo, webcast) y de recolectar, individualmente o a través de una sociedad de gestión colectiva de derechos de autor y derechos conexos (por ejemplo, ACINPRO), las regalías por la ejecución pública digital de la obra (por ejemplo, webcast), sujeta a las disposiciones aplicables del régimen de Derecho de Autor, si esta ejecución pública digital está primordialmente dirigida a obtener una ventaja comercial o una compensación monetaria privada.

5. Representaciones, Garantías y Limitaciones de Responsabilidad.
A MENOS QUE LAS PARTES LO ACORDARAN DE OTRA FORMA POR ESCRITO, EL LICENCIANTE OFRECE LA OBRA (EN EL ESTADO EN EL QUE SE ENCUENTRA) “TAL CUAL”, SIN BRINDAR GARANTÍAS DE CLASE ALGUNA RESPECTO DE LA OBRA, YA SEA EXPRESA, IMPLÍCITA, LEGAL O CUALQUIERA OTRA, INCLUYENDO, SIN LIMITARSE A ELLAS, GARANTÍAS DE TITULARIDAD, COMERCIABILIDAD, ADAPTABILIDAD O ADECUACIÓN A PROPÓSITO DETERMINADO, AUSENCIA DE INFRACCIÓN, DE AUSENCIA DE DEFECTOS LATENTES O DE OTRO TIPO, O LA PRESENCIA O AUSENCIA DE ERRORES, SEAN O NO DESCUBRIBLES (PUEDAN O NO SER ESTOS DESCUBIERTOS). ALGUNAS JURISDICCIONES NO PERMITEN LA EXCLUSIÓN DE GARANTÍAS IMPLÍCITAS, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

6. Limitación de responsabilidad.
A MENOS QUE LO EXIJA EXPRESAMENTE LA LEY APLICABLE, EL LICENCIANTE NO SERÁ RESPONSABLE ANTE USTED POR DAÑO ALGUNO, SEA POR RESPONSABILIDAD EXTRACONTRACTUAL, PRECONTRACTUAL O CONTRACTUAL, OBJETIVA O SUBJETIVA, SE TRATE DE DAÑOS MORALES O PATRIMONIALES, DIRECTOS O INDIRECTOS, PREVISTOS O IMPREVISTOS PRODUCIDOS POR EL USO DE ESTA LICENCIA O DE LA OBRA, AUN CUANDO EL LICENCIANTE HAYA SIDO ADVERTIDO DE LA POSIBILIDAD DE DICHOS DAÑOS. ALGUNAS LEYES NO PERMITEN LA EXCLUSIÓN DE CIERTA RESPONSABILIDAD, EN CUYO CASO ESTA EXCLUSIÓN PUEDE NO APLICARSE A USTED.

7. Término.

a.	Esta Licencia y los derechos otorgados en virtud de ella terminarán automáticamente si Usted infringe alguna condición establecida en ella. Sin embargo, los individuos o entidades que han recibido Obras Derivadas o Colectivas de Usted de conformidad con esta Licencia, no verán terminadas sus licencias, siempre que estos individuos o entidades sigan cumpliendo íntegramente las condiciones de estas licencias. Las Secciones 1, 2, 5, 6, 7, y 8 subsistirán a cualquier terminación de esta Licencia.

b.	Sujeta a las condiciones y términos anteriores, la licencia otorgada aquí es perpetua (durante el período de vigencia de los derechos de autor de la obra). No obstante lo anterior, el Licenciante se reserva el derecho a publicar y/o estrenar la Obra bajo condiciones de licencia diferentes o a dejar de distribuirla en los términos de esta Licencia en cualquier momento; en el entendido, sin embargo, que esa elección no servirá para revocar esta licencia o que deba ser otorgada , bajo los términos de esta licencia), y esta licencia continuará en pleno vigor y efecto a menos que sea terminada como se expresa atrás. La Licencia revocada continuará siendo plenamente vigente y efectiva si no se le da término en las condiciones indicadas anteriormente.

8. Varios.

a.	Cada vez que Usted distribuya o ponga a disposición pública la Obra o una Obra Colectiva, el Licenciante ofrecerá al destinatario una licencia en los mismos términos y condiciones que la licencia otorgada a Usted bajo esta Licencia.

b.	Si alguna disposición de esta Licencia resulta invalidada o no exigible, según la legislación vigente, esto no afectará ni la validez ni la aplicabilidad del resto de condiciones de esta Licencia y, sin acción adicional por parte de los sujetos de este acuerdo, aquélla se entenderá reformada lo mínimo necesario para hacer que dicha disposición sea válida y exigible.

c.	Ningún término o disposición de esta Licencia se estimará renunciada y ninguna violación de ella será consentida a menos que esa renuncia o consentimiento sea otorgado por escrito y firmado por la parte que renuncie o consienta.

d.	Esta Licencia refleja el acuerdo pleno entre las partes respecto a la Obra aquí licenciada. No hay arreglos, acuerdos o declaraciones respecto a la Obra que no estén especificados en este documento. El Licenciante no se verá limitado por ninguna disposición adicional que pueda surgir en alguna comunicación emanada de Usted. Esta Licencia no puede ser modificada sin el consentimiento mutuo por escrito del Licenciante y Usted.
 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