A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks
This paper proposes a quadratic convex model for optimal operation of battery energy storage systems in a direct current (DC) network that approximates the original nonlinear non-convex one. The proposed quadratic convex model uses Taylor’s series expansion to transform the product between voltage v...
- Autores:
-
Montoya, Oscar Danilo
Arias‑Londoño, Andrés
Garrido Arévalo, Víctor Manuel
Gil-González, Walter
Grisales-Noreña, Luis Fernando
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Tecnológica de Bolívar
- Repositorio:
- Repositorio Institucional UTB
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.utb.edu.co:20.500.12585/10430
- Acceso en línea:
- https://hdl.handle.net/20.500.12585/10430
- Palabra clave:
- Battery energy storage systems
Quadratic convex approximation
Economic dispatch
Taylor’s series expansion
Direct current distribution networks
Artifcial neural networks
LEMB
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-nd/4.0/
| id |
UTB2_da8d8067d1b217169a8119793a1e9f1e |
|---|---|
| oai_identifier_str |
oai:repositorio.utb.edu.co:20.500.12585/10430 |
| network_acronym_str |
UTB2 |
| network_name_str |
Repositorio Institucional UTB |
| repository_id_str |
|
| dc.title.spa.fl_str_mv |
A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks |
| title |
A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks |
| spellingShingle |
A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks Battery energy storage systems Quadratic convex approximation Economic dispatch Taylor’s series expansion Direct current distribution networks Artifcial neural networks LEMB |
| title_short |
A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks |
| title_full |
A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks |
| title_fullStr |
A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks |
| title_full_unstemmed |
A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks |
| title_sort |
A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks |
| dc.creator.fl_str_mv |
Montoya, Oscar Danilo Arias‑Londoño, Andrés Garrido Arévalo, Víctor Manuel Gil-González, Walter Grisales-Noreña, Luis Fernando |
| dc.contributor.author.none.fl_str_mv |
Montoya, Oscar Danilo Arias‑Londoño, Andrés Garrido Arévalo, Víctor Manuel Gil-González, Walter Grisales-Noreña, Luis Fernando |
| dc.subject.keywords.spa.fl_str_mv |
Battery energy storage systems Quadratic convex approximation Economic dispatch Taylor’s series expansion Direct current distribution networks Artifcial neural networks |
| topic |
Battery energy storage systems Quadratic convex approximation Economic dispatch Taylor’s series expansion Direct current distribution networks Artifcial neural networks LEMB |
| dc.subject.armarc.none.fl_str_mv |
LEMB |
| description |
This paper proposes a quadratic convex model for optimal operation of battery energy storage systems in a direct current (DC) network that approximates the original nonlinear non-convex one. The proposed quadratic convex model uses Taylor’s series expansion to transform the product between voltage variables in the power balance equations into a linear combination of them. Numerical simulations in the general algebraic modeling system (GAMS) for both models show small diferences in the daily energy losses, which are lower than 3.00%. The main advantage of the proposed quadratic model is that its optimal solution is achievable with interior point methods guaranteeing its uniqueness (convexity properties of the solution space and objective function), which is not possible to guarantee with the exact nonlinear non-convex model. The 30-bus DC test feeder with four distributed generators (with power generation forecast via artifcial neural networks with errors lower than 1% between real and predicted generation curves) and three batteries is used to validate the proposed convex and exact models. Numerical results obtained by GAMS show the efectiveness of the proposed quadratic convex model for diferent simulation scenarios tested, which was confrmed by the CVX tool for convex optimization in MATLAB |
| publishDate |
2021 |
| dc.date.issued.none.fl_str_mv |
2021-11-07 |
| dc.date.accessioned.none.fl_str_mv |
2022-01-28T20:41:17Z |
| dc.date.available.none.fl_str_mv |
2022-01-28T20:41:17Z |
| dc.date.submitted.none.fl_str_mv |
2022-01-28 |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.hasversion.spa.fl_str_mv |
info:eu-repo/semantics/restrictedAccess |
| dc.type.spa.spa.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.identifier.citation.spa.fl_str_mv |
Montoya Giraldo, Oscar & Arias-Londoño, Andrés & Garrido, Victor & Gil González, Walter & Grisales-Noreña, Luis. (2021). A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks. Energy Systems. 10.1007/s12667-021-00495-z. |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/20.500.12585/10430 |
| dc.identifier.doi.none.fl_str_mv |
10.1007/s12667-021-00495-z |
| 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 Giraldo, Oscar & Arias-Londoño, Andrés & Garrido, Victor & Gil González, Walter & Grisales-Noreña, Luis. (2021). A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks. Energy Systems. 10.1007/s12667-021-00495-z. 10.1007/s12667-021-00495-z Universidad Tecnológica de Bolívar Repositorio Universidad Tecnológica de Bolívar |
| url |
https://hdl.handle.net/20.500.12585/10430 |
| 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 |
22 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 |
Energy Systems |
| institution |
Universidad Tecnológica de Bolívar |
| bitstream.url.fl_str_mv |
https://repositorio.utb.edu.co/bitstream/20.500.12585/10430/1/AquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdf https://repositorio.utb.edu.co/bitstream/20.500.12585/10430/2/license_rdf https://repositorio.utb.edu.co/bitstream/20.500.12585/10430/3/license.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/10430/4/AquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdf.txt https://repositorio.utb.edu.co/bitstream/20.500.12585/10430/5/AquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdf.jpg |
| bitstream.checksum.fl_str_mv |
9c89e771266bd2b3abba63829577a58e 4460e5956bc1d1639be9ae6146a50347 e20ad307a1c5f3f25af9304a7a7c86b6 872f658ad3c260c5215b9e6b59153722 8cc191ab221acf06169a3445831231fc |
| 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_ |
1814021739394367488 |
| spelling |
Montoya, Oscar Danilo8a59ede1-6a4a-4d2e-abdc-d0afb14d4480Arias‑Londoño, Andrés89909de0-da09-49a3-8e61-83197925ba34Garrido Arévalo, Víctor Manuelf53136bc-ecc5-45ad-a5a6-d1b2c1455a92Gil-González, Walterce1f5078-74c6-4b5c-b56a-784f85e52a08Grisales-Noreña, Luis Fernando7c27cda4-5fe4-4686-8f72-b0442c58a5d12022-01-28T20:41:17Z2022-01-28T20:41:17Z2021-11-072022-01-28Montoya Giraldo, Oscar & Arias-Londoño, Andrés & Garrido, Victor & Gil González, Walter & Grisales-Noreña, Luis. (2021). A quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networks. Energy Systems. 10.1007/s12667-021-00495-z.https://hdl.handle.net/20.500.12585/1043010.1007/s12667-021-00495-zUniversidad Tecnológica de BolívarRepositorio Universidad Tecnológica de BolívarThis paper proposes a quadratic convex model for optimal operation of battery energy storage systems in a direct current (DC) network that approximates the original nonlinear non-convex one. The proposed quadratic convex model uses Taylor’s series expansion to transform the product between voltage variables in the power balance equations into a linear combination of them. Numerical simulations in the general algebraic modeling system (GAMS) for both models show small diferences in the daily energy losses, which are lower than 3.00%. The main advantage of the proposed quadratic model is that its optimal solution is achievable with interior point methods guaranteeing its uniqueness (convexity properties of the solution space and objective function), which is not possible to guarantee with the exact nonlinear non-convex model. The 30-bus DC test feeder with four distributed generators (with power generation forecast via artifcial neural networks with errors lower than 1% between real and predicted generation curves) and three batteries is used to validate the proposed convex and exact models. Numerical results obtained by GAMS show the efectiveness of the proposed quadratic convex model for diferent simulation scenarios tested, which was confrmed by the CVX tool for convex optimization in MATLAB22 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_abf2Energy SystemsA quadratic convex approximation for optimal operation of battery energy storage systems in DC distribution networksinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/restrictedAccesshttp://purl.org/coar/resource_type/c_2df8fbb1Battery energy storage systemsQuadratic convex approximationEconomic dispatchTaylor’s series expansionDirect current distribution networksArtifcial neural networksLEMBCartagena de IndiasAlharbi, T., Bhattacharya, K.: Optimal scheduling of energy resources and management of loads in isolated/islanded microgrids. Can. J. Electr. Comput. Eng. 40(4), 284–294 (2017)Schoendienst, T., Vokkarane, V.M.: Reducing greenhouse gas emissions with power source-aware multidomain multilayer networks. IEEE Syst. J. 11(2), 673–683 (2017). Bogaerts, M., Cirhigiri, L., Robinson, I., Rodkin, M., Hajjar, R., Junior, C.C., Newton, P.: Climate change mitigation through intensifed pasture management: estimating greenhouse gas emissions on cattle farms in the Brazilian Amazon. J. Clean. Prod. 162, 1539–1550 (2017)Crosson, P., Shalloo, L., O’Brien, D., Lanigan, G., Foley, P., Boland, T., and Kenny, D.: A review of whole farm systems models of greenhouse gas emissions from beef and dairy cattle production systems, Anim. Feed Sci. Technol. 166–167, 29–45 (2011). Special Issue: Greenhouse Gases in Animal Agriculture—Finding a Balance between Food and EmissionsThaker, S., Oni, A.O., Gemechu, E., Kumar, A.: Evaluating energy and greenhouse gas emission footprints of thermal energy storage systems for concentrated solar power applications. J. Energy Storage 26, 100992 (2019). Karmaker, A.K., Rahman, M.M., Hossain, M.A., Ahmed, M.R.: Exploration and corrective measures of greenhouse gas emission from fossil fuel power stations for Bangladesh. J. Clean. Prod. 244, 118645 (2020). Bauer, A., Menrad, K.: Standing up for the Paris Agreement: do global climate targets infuence individuals’ greenhouse gas emissions? Environ. Sci. Policy 99, 72–79 (2019)Ferreira, A., Pinheiro, M.D., de Brito, J., Mateus, R.: Decarbonizing strategies of the retail sector following the Paris Agreement. Energy Policy 135, 110999 (2019)Montoya, O.D., Gil-González, W., Grisales-Norena, L., Orozco-Henao, C., Serra, F.: Economic dispatch of BESS and renewable generators in DC microgrids using voltage-dependent load models. Energies 12(23), 4494 (2019)Yan, Q., Zhang, B., Kezunovic, M.: Optimized operational cost reduction for an EV charging station integrated with battery energy storage and PV generation. IEEE Trans. Smart Grid 10(2), 2096– 2106 (2019)Adefarati, T., Bansal, R.C., John Justo, J.: Techno-economic analysis of a PV-wind-battery-diesel standalone power system in a remote area. J. Eng. 2017(13), 740–744 (2017)Naumann, M., Karl, R.C., Truong, C.N., Jossen, A., Hesse, H.C.: Lithium-ion battery cost analysis in PV-household application. Energy Procedia 73, 37–47 (2015). 9th International Renewable Energy Storage Conference, IRES 2015Wentker, M., Greenwood, M., Leker, J.: A bottom-up approach to lithium-ion battery cost modeling with a focus on cathode active materials. Energies 12(3), 504 (2019)Montoya, O.D., Grajales, A., Garces, A., Castro, C.A.: Distribution systems operation considering energy storage devices and distributed generation. IEEE Lat. Am. Trans. 15(5), 890–900 (2017)Wang, Z., Du, J., Zhang, M., Yu, J., Liu, H., Chai, X., Yang, B., Zhu, C., Xu, J.: Continuous preparation of high performance fexible asymmetric supercapacitor with a very fast, low-cost, simple and scalable electrochemical co-deposition method. J. Power Sources 437, 226827 (2019)Krishan, O., Suhag, S.: Grid-independent PV system hybridization with fuel cell-battery/supercapacitor: optimum sizing and comparative techno-economic analysis. Sustain. Energy Technol. Assess. 37, 100625 (2020)Teyber, R., Rowe, A.: Superconducting magnet design for magnetic liquefers using total cost minimization. Cryogenics 99, 114–122 (2019)Gil-González, W., Montoya, O.D., Garces, A.: Control of a SMES for mitigating subsynchronous oscillations in power systems: a PBC-PI approach. J. Energy Storage 20, 163–172 (2018)Kale, V., Secanell, M.: A comparative study between optimal metal and composite rotors for fywheel energy storage systems. Energy Rep. 4, 576–585 (2018)Ramli, M.A., Hiendro, A., Twaha, S.: Economic analysis of PV/diesel hybrid system with fywheel energy storage. Renew. Energy 78, 398–405 (2015)Gil-González, W., Montoya, O.D., Holguín, E., Garces, A., Grisales-Norena, L.F.: Economic dispatch of energy storage systems in dc microgrids employing a semidefnite programming model. J. Energy Storage 21, 1–8 (2019)Vazquez, L., Majanne, Y., Castro, M., Luukkanen, J., Hohmeyer, O., Vilaragut, M., Diaz, D.: Energy system planning towards renewable power system: energy matrix change in Cuba by 2030 IFAC-PapersOnLine 51(28), 522–527 (2018). 10th IFAC Symposium on Control of Power and Energy Systems CPES 2018Cepeda, C., Orozco-Henao, C., Percybrooks, W., Pulgarín-Rivera, J.D., Montoya, O.D., GilGonzález, W., Vélez, J.C.: Intelligent fault detection system for microgrids. Energies 13(5), 1223 (2020)Jiang, Q., Xue, M., Geng, G.: Energy management of microgrid in grid-connected and stand-alone modes. IEEE Trans. Power Syst. 28(3), 3380–3389 (2013)Montoya, O.D., Grisales-Norena, 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 12(2), 322 (2020)Messo, T., Luhtala, R., Roinila, T., de Jong, E., Scharrenberg, R., Caldognetto, T., Mattavelli, P., Sun, Y., Fabian, A.: Using high-bandwidth voltage amplifer to emulate grid-following inverter for AC microgrid dynamics studies. Energies 12(3), 379 (2019)Grisales-Norena, L.F., Ramos-Paja, C.A., Gonzalez-Montoya, D., Alcalá, G., Hernandez-Escobedo, Q.: Energy management in PV based microgrids designed for the Universidad Nacional de Colombia. Sustainability 12(3), 1219 (2020). Xia, Y., Wei, W., Yu, M., Wang, X., Peng, Y.: Power management for a hybrid AC/DC microgrid with multiple subgrids. IEEE Trans. Power Electron. 33(4), 3520–3533 (2018)Montoya, O.D.: A convex OPF approximation for selecting the best candidate nodes for optimal location of power sources on DC resistive networks. Eng. Sci. Technol. Int. J. 23(3), 527–533 (2020)Li, J., Liu, F., Wang, Z., Low, S.H., Mei, S.: Optimal power fow in stand-alone DC microgrids. IEEE Trans. Power Syst. 33(5), 5496–5506 (2018). Iskender, I., Genc, N.: Power electronic converters in DC microgrid. In: Power Systems, pp. 115– 137. Springer International Publishing (2019). Biczel, P.: Power electronic converters in DC microgrid. In: Compatibility in Power Electronics, May 2007, pp. 1–6 (2007)Murillo-Yarce, D., Garcés-Ruiz, A., Escobar-Mejía, A.: Passivity-based control for DC-microgrids with constant power terminals in island mode operation. Revista Facultad de Ingeniería Universidad de Antioquia 86, 32–39 (2018)Mahmoodi, M., Shamsi, P., Fahimi, B.: Economic dispatch of a hybrid microgrid with distributed energy storage. IEEE Trans. Smart Grid 6(6), 2607–2614 (2015)Dominguez-Jimenez, J., Montoya, O., Campillo, J., Gil-González, W.: Economic dispatch in dc microgrids considering diferent battery technologies: a benchmark study. In: 2020 IEEE International Autumn Meeting on Power, Electronics and Computing (ROPEC), vol. 4, pp. 1–6. IEEE (2020)Grisales-Norena, L.F., Montoya, O.D., Ramos-Paja, C.A.: An energy management system for optimal operation of bss in dc distributed generation environments based on a parallel PSO algorithm. J. Energy Storage 29, 101488 (2020)Montoya, O.D., Gil-González, W., Garces, A.: Optimal power fow on DC microgrids: a quadratic convex approximation. IEEE Trans. Circuits Syst. II 66(6), 1018–1022 (2018)Molina-Martin, F., Montoya, O.D., Grisales-Norena, L.F., Hernández, J.C., Ramírez-Vanegas, C.A.: Simultaneous minimization of energy losses and greenhouse gas emissions in AC distribution networks using BESS. Electronics 10(9), 1002 (2021)Garcés, A., Montoya, O.-D.: A potential function for the power fow in DC microgrids: an analysis of the uniqueness and existence of the solution and convergence of the algorithms. J. Control Autom. Electr. Syst. 30(5), 794–801 (2019)Montoya, O.D., Grisales-na, L., González-Montoya, D., Ramos-Paja, C., Garces, A.: Linear power fow formulation for low-voltage DC power grids. Electr. Power Syst. Res. 163, 375–381 (2018)Garces, A.: Uniqueness of the power fow solutions in low voltage direct current grids. Electr. Power Syst. Res. 151, 149–153 (2017)liliana and Napitupulu, T.A.: Artifcial neural network application in gross domestic product forecasting: an Indonesia case. In: 2010 Second International Conference on Advances in Computing, Control, and Telecommunication Technologies. IEEE (2010)Tümer, A.E., Akkuş, A.: Forecasting gross domestic product per capita using artifcial neural networks with non-economical parameters. Phys. A Stat. Mech. Appl. 512, 468–473 (2018)Jung, D.-H., Kim, H.-J., Kim, J.Y., Lee, T.S., Park, S.H.: Model predictive control via output feedback neural network for improved multi-window greenhouse ventilation control. Sensors 20(6), 1756 (2020)Fente, D.N., Singh, D.K.: Weather forecasting using artifcial neural network. In: 2018 Second International Conference on Inventive Communication and Computational Technologies (ICICCT). IEEE (2018)Antanasijević, D.Z., Ristić, M., Perić-Grujić, A.A., Pocajt, V.V.: Forecasting GHG emissions using an optimized artifcial neural network model based on correlation and principal component analysis. Int. J. Greenh. Gas Control 20, 244–253 (2014)Yu, L., Wang, S., Lai, K.K.: Foreign-Exchange-Rate Forecasting With Artifcial Neural Networks. Springer US, New York (2007)Montoya, 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. 85, 106710 (2020)Kocer, M.C., Cengiz, C., Gezer, M., Gunes, D., Cinar, M.A., Alboyaci, B., Onen, A.: Assessment of battery storage technologies for a Turkish power network. Sustainability 11(13), 3669 (2019)Wang, P., Ang, W., Xu, D.: Optimal sizing of distributed generations in DC microgrids with comprehensive consideration of system operation modes and operation targets. IEEE Access 6, 31129– 31140 (2018)Data, s.s.r. time series of solar radiation data. Available online http://www.soda-pro.com/. Accessed 5 July 2019Montoya, O.D., Grajales, A., Garces, A., Castro, C.A.: Distribution systems operation considering energy storage devices and distributed generation. IEEE Lat. Am. Trans. 15(5), 890–900 (2017Giraldo, O.D.M.: Solving a classical optimization problem using gams optimizer package: economic dispatch problem implementation. Ingeniería y Ciencia 13(26), 39–63 (2017)Montoya, O.D., Gil-González, W., Grisales-Norena, L.: An exact MINLP model for optimal location and sizing of DGs in distribution networks: a general algebraic modeling system approach. Ain Shams Eng. J. 11(2), 409–418 (2020)Tartibu, L., Sun, B., Kaunda, M.: Multi-objective optimization of the stack of a thermoacoustic engine using GAMS. Appl. Soft Comput. 28, 30–43 (2015)Skworcow, P., Paluszczyszyn, D., Ulanicki, B., Rudek, R., Belrain, T.: Optimisation of pump and valve schedules in complex large-scale water distribution systems using GAMS modelling language. Procedia Eng. 70, 1566–1574. 12th International Conference on Computing and Control for the Water Industry, CCWI2013 (2014)Pintér, J.D.: Nonlinear optimization with GAMS /LGO. J. Glob. Optim. 38(1), 79–101 (2006)http://purl.org/coar/resource_type/c_2df8fbb1ORIGINALAquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdfAquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdfapplication/pdf3188352https://repositorio.utb.edu.co/bitstream/20.500.12585/10430/1/AquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdf9c89e771266bd2b3abba63829577a58eMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.utb.edu.co/bitstream/20.500.12585/10430/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-83182https://repositorio.utb.edu.co/bitstream/20.500.12585/10430/3/license.txte20ad307a1c5f3f25af9304a7a7c86b6MD53TEXTAquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdf.txtAquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdf.txtExtracted texttext/plain54235https://repositorio.utb.edu.co/bitstream/20.500.12585/10430/4/AquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdf.txt872f658ad3c260c5215b9e6b59153722MD54THUMBNAILAquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdf.jpgAquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdf.jpgGenerated Thumbnailimage/jpeg26280https://repositorio.utb.edu.co/bitstream/20.500.12585/10430/5/AquadraticconvexapproximationforoptimaloperationofbatteryenergystoragesystemsinDCdistributionnetworks.pdf.jpg8cc191ab221acf06169a3445831231fcMD5520.500.12585/10430oai:repositorio.utb.edu.co:20.500.12585/104302023-05-26 11:15:36.992Repositorio Institucional UTBrepositorioutb@utb.edu.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 |