Análisis y simulación de convertidores para microrredes eléctricas DC domiciliarias

Autores/as

César Leonardo Trujillo Rodríguez
Universidad Distrital Francisco José de Caldas
https://orcid.org/0000-0002-0985-1472
Rafael Antonio Peña Suesca
Universidad Distrital Francisco José de Caldas
https://orcid.org/0000-0003-0795-7764

Sinopsis

En el presente libro se aborda una metodología de diseño de los convertidores electrónicos que hacen parte de una microrred DC domiciliaria y se valida su funcionamiento a través de la operación de cada uno de ellos en la microrred a través de simulación. En la primera parte, se identifican las topologías convertidoras más comunes que pueden hacer parte de una microrred DC domiciliaria, teniendo en cuenta la fuente de generación o almacenamiento y la carga a alimentar. Posteriormente, se diseñan los convertidores que mejor se ajustan a los requerimientos de una microrred prototipo y se establecen los objetivos de control en función de la operación de los convertidores en la microrred. Finalmente, se valida su diseño y operación mediante la inserción de estos convertidores en la microrred, validando así, la metodología de diseño planteada.

Capítulos

  • Introducción
  • Capítulo 1
    Microrredes DC
  • Capítulo 2
    Convertidores para microrredes DC domiciliarias
  • Capítulo 3
    Microrred DC domiciliaria-estudio de caso
  • Conclusiones

Descargas

Los datos de descarga aún no están disponibles.

Biografía del autor/a

César Leonardo Trujillo Rodríguez, Universidad Distrital Francisco José de Caldas

Ingeniero electrónico de la Universidad Distrital Francisco José de Caldas, Bogotá, Colombia. Magister en Ingeniería Eléctrica de la Universidad Nacional de Colombia, Bogotá, Colombia. PhD en Ingeniería Electrónica de la Universidad Politécnica de Valencia, Valencia, España. Actualmente es Profesor Titular en el programa de Ingeniería Eléctrica de la Universidad Distrital Francisco José de Caldas, donde imparte cursos de circuitos analógicos y electrónica de potencia. Sus principales intereses en investigación incluyen: modelado y control de convertidores electrónicos de potencia aplicados a generación distribuida y microrredes eléctricas.

Rafael Antonio Peña Suesca, Universidad Distrital Francisco José de Caldas

Ingeniero Electrónico y Especialista en Ingeniería de software de la Universidad Distrital Francisco José de Caldas, Bogotá, Colombia. Magister en Ingeniería Eléctrica de la Universidad Nacional de Colombia, Bogotá, Colombia. Actualmente es profesor titular en el programa de Ingeniería Electrónica de la Universidad Distrital Francisco José de Caldas, donde imparte cursos de circuitos analógicos y electrónica de potencia. Sus principales intereses en investigación incluyen: análisis y diseño de topologías de convertidores electrónicos conmutados y generación distribuida.

Referencias

ETP SmartGrids, Smart Grids: strategic deployment document for Europe’s electricity networks of the future, 2010.

D. W. Gao, Ed., “Foreword,” en Energy Storage for Sustainable Microgrid, Oxford: Academic Press, 2015, pp. vii-ix.

H. Bevrani, B. Francois y T. Ise, Microgrid Dynamics and Control. 2017.

R. H. Lasseter, “MicroGrids,” 2002 IEEE Power Eng. Soc. Winter Meet. Conf. Proc. (Cat. No. 02CH37309), vol. 1, pp. 305-308, enero 2002, doi: https://doi.org/10.1109/PESW.2002.985003.

S. Hajiaghasi, A. Salemnia y M. Hamzeh, “Hybrid energy storage system for microgrids applications: A review”, Journal of Energy Storage, vol. 21, pp. 543-570, 2019, doi: https://doi.org/10.1016/j.est.2018.12.017.

J. Rocabert, A. Luna, F. Blaabjerg y P. Rodríguez, “Control of power converters in AC microgrids”, IEEE Trans. Power Electron., 2012, doi: https://doi.org/10.1109/TPEL.2012.2199334.

C. L. Trujillo, F. Santamaría, J. Hernández, M. Jaramillo y E. E. Gaona-García, Microrredes Eléctricas. Universidad Distrital Francisco José de Caldas, 2015.

L. Fusheng, L. Ruisheng y Z. Fengquan, Microgrid technology and engineering application. 2015.

Y. Zhou y C. Ngai-Man Ho, “A review on Microgrid architectures and control methods”, 2016, doi: https://doi.org/10.1109/IPEMC.2016.7512799.

A. Banerji et al., “Microgrid: A review,” 2013, doi: https://doi.org/10.1109/GHTC-SAS.2013.6629883.

Y. Lv, P. Yang, Z. Liu, Y. Chen y J. Chen, “Real-time model predictive control for the regional autonomy multi-microgrids with three-phase/single-phase architecture”, en 2019 IEEE Innovative Smart Grid Technologies-Asia (ISGT Asia), mayo 2019, pp. 2693-2697, doi: https://doi.org/10.1109/ISGT-Asia.2019.8881566.

M. Barnes et al., “Real-world MicroGrids-An overview”, 2007, doi: https://doi.org/10.1109/SYSOSE.2007.4304255.

I. Patrao, E. Figueres, G. Garcerá y R. González-Medina, “Microgrid architectures for low voltage distributed generation”, Renewable and Sustainable Energy Reviews. 2015, doi: https://doi.org/10.1016/j.rser.2014.11.054.

E. Unamuno y J. A. Barrena, “Hybrid ac/dc microgrids-Part I: Review and classification of topologies”, Renewable and Sustainable Energy Reviews. 2015, doi: https://doi.org/10.1016/j.rser.2015.07.194.

J. M. Guerrero, J. C. Vásquez, J. Matas, L. G. De Vicuña y 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, 2011, doi: https://doi.org/10.1109/TIE.2010.2066534.

I. Batarseh, K. Siri y H. Lee, “Investigation of the output droop characteristics of parallel-connected DC-DC converters”, 1994, doi: https://doi.org/10.1109/pesc.1994.373859.

B. Subudhi y R. Pradhan, “A comparative study on maximum power point tracking techniques for photovoltaic power systems”, IEEE Trans. Sustain. Energy, 2013, doi: https://doi.org/10.1109/TSTE.2012.2202294.

J. M. Guerrero, L. G. de Vicuña y J. Uceda, “Uninterruptible power supply systems provide protection”, IEEE Ind. Electron. Mag., 2007, doi: https://doi.org/10.1109/MIE.2007.357184.

T. Dragičević, X. Lu, J. C. Vásquez y J. M. Guerrero, “DC Microgrids-Part II: A review of power architectures, applications, and standardization issues”, IEEE Trans. Power Electron., vol. 31, no. 5, pp. 3528-3549, 2016, doi: https://doi.org/10.1109/TPEL.2015.2464277.

H. A. Gabbar, Smart energy grid engineering. 2016.

M. Ahmed, L. Meegahapola, A. Vahidnia y M. Datta, “Stability and control aspects of microgrid architectures-a comprehensive review”, IEEE Access. 2020, doi: https://doi.org/10.1109/ACCESS.2020.3014977.

H. Abdelgawad y V. K. Sood, “A comprehensive review on microgrid architectures for distributed generation”, en 2019 IEEE Electrical Power and Energy Conference (EPEC), oct. 2019, pp. 1-8, doi: https://doi.org/10.1109/EPEC47565.2019.9074800.

E. Planas, J. Andreu, J. I. Gárate, I. Martínez De Alegría y E. Ibarra, “AC and DC technology in microgrids: A review”, Renewable and Sustainable Energy Reviews. 2015, doi: https://doi.org/10.1016/j.rser.2014.11.067.

F. Zhang, C. Meng, Y. Yang, C. Sun, C. Ji, Y. Chen, W. Wei, H. Qiu y G. Yang, Advantages and challenges of DC microgrid for commercial building: A case study from Xiamen university DC microgrid, 2015, doi: https://doi.org/10.1109/ICDCM.2015.7152068.

J. Umuhoza, Y. Zhang, S. Zhao y H. A. Mantooth, An adaptive control strategy for power balance and the intermittency mitigation in battery-PV energy system at residential DC microgrid level, 2017, doi: https://doi.org/10.1109/APEC.2017.7930870.

E. Rodríguez-Díaz, M. Savaghebi, J. C. Vásquez y J. M. Guerrero, An overview of low voltage DC distribution systems for residential applications, 2016, doi: https://doi.org/10.1109/ICCE-Berlin.2015.7391268.

H. Kakigano, Y. Miura y T. Ise, “Low-voltage bipolar-type DC microgrid for super high quality distribution”, IEEE Trans. Power Electron., 2010, doi: https://doi.org/10.1109/TPEL.2010.2077682.

A. T. Elsayed, A. A. Mohamed y O. A. Mohammed, “DC microgrids and distribution systems: An overview”, Electric Power Systems Research. 2015, doi: https://doi.org/10.1016/j.epsr.2014.10.017.

A. Emadi, Y. J. Lee y K. Rajashekara, “Power electronics and motor drives in electric, hybrid electric, and plug-in hybrid electric vehicles”, IEEE Transactions on Industrial Electronics. 2008, doi: https://doi.org/10.1109/TIE.2008.922768.

T. M. Gruzs y J. Hall, “AC, DC or hybrid power solutions for today’s telecommunications facilities”, INTELEC, Int. Telecommun. Energy Conf., 2000, doi: https://doi.org/10.1109/intlec.2000.884275.

F. Bodi, ‘DC-grade’ reliability for UPS in telecommunications data centers, 2007, doi: https://doi.org/10.1109/INTLEC.2007.4448849.

A. Pratt, P. Kumar y T. V. Aldridge, Evaluation of 400V DC distribution in telco and data centers to improve energy efficiency, 2007, doi: https://doi.org/10.1109/INTLEC.2007.4448733.

D. J. Becker y B. J. Sonnenberg, DC microgrids in buildings and data centers, 2011, doi: https://doi.org/10.1109/INTLEC.2011.6099725.

D. Wang, X. Ma, P. Su, B. Liu, W. Du y L. Wu, Household microgrid interaction technology based on power router, 2019, doi: https://doi.org/10.1016/j.egypro.2019.01.135.

X. Chen, T. Wei y S. Hu, “Uncertainty-aware household appliance scheduling considering dynamic electricity pricing in smart home”, IEEE Trans. Smart Grid, 2013, doi: https://doi.org/10.1109/TSG.2012.2226065.

P. Du y N. Lu, “Appliance commitment for household load scheduling”, IEEE Trans. Smart Grid, 2011, doi: https://doi.org/10.1109/TSG.2011.2140344.

E. Rodríguez-Díaz, J. C. Vásquez y J. M. Guerrero, “Intelligent DC homes in future sustainable energy systems: When efficiency and intelligence work together”, IEEE Consumer Electronics Magazine, vol. 5, no. 1. pp. 74-80, 2016, doi:10.1109/MCE.2015.2484699

M. H. Ryu, H. S. Kim, J. H. Kim, J. W. Baek y J. H. Jung, Test bed implementation of 380V DC distribution system using isolated bidirectional power converters, 2013, doi: https://doi.org/10.1109/ECCE.2013.6647085.

D. Dong, F. Luo, X. Zhang, D. Boroyevich, y P. Mattavelli, “Grid-interface bidirectional converter for residential DC distribution systems-Part 2: AC and DC interface design with passive components minimization”, IEEE Trans. Power Electron., 2013, doi: https://doi.org/10.1109/TPEL.2012.2213614.

C. A. Ramos-Paja, R. Giral, E. I. Arango-Zuluaga, “Distributed maximum power point tracking in photovoltaic applications: Active bypass DC/DC converter”, Rev. Fac. Ing. Antioquia, pp. 32-44, 2012, https://doi.org/10.17533/udea.redin.13112

R. F. Coelho, F. Concer y D. C. Martins, A study of the basic DC-DC converters applied in maximum power point tracking, 2009, doi: https://doi.org/10.1109/COBEP.2009.5347723.

M. A. Farahat, H. M. B. Metwally y A. Abd-Elfatah Mohamed, “Optimal choice and design of different topologies of DC-DC converter used in PV systems, at different climatic conditions in Egypt”, Renew. Energy, 2012, doi: https://doi.org/10.1016/j.renene.2011.10.021.

I. Glasner y J. Appelbaum, Advantage of boost vs. buck topology for maximum power point tracker in photovoltaic systems, 1996, doi: https://doi.org/10.1109/eeis.1996.566988.

F. Blaabjerg, M. Liserre y K. Ma, Power electronics converters for wind turbine systems, 2012, doi: https://doi.org/10.1109/TIA.2011.2181290.

T. Ackermann, Wind Power in Power Systems. 2005.

H. Li y Z. Chen, “Overview of different wind generator systems and their comparisons”, IET Renew. Power Gener., 2008, doi: https://doi.org/10.1049/iet-rpg:20070044.

M. Arifujjaman, M. T. Iqbal y J. E. Quaicoe, “Energy capture by a small wind-energy conversion system”, Appl. Energy, 2008, doi: https://doi.org/10.1016/j.apenergy.2007.06.002.

K. Amei, Y. Takayasu, T. Ohji y M. Sakui, A maximum power control of wind generator system using a permanent magnet synchronous generator and a boost chopper circuit, 2002, doi: https://doi.org/10.1109/PCC.2002.998186.

S. M. Muyeen, R. Takahashi, T. Murata y J. Tamura, Transient stability enhancement of variable speed wind turbine driven PMSG with rectifier-boost converter-inverter, 2008, doi: https://doi.org/10.1109/ICELMACH.2008.4799893.

T. Tafticht, K. Agbossou y A. Chériti, DC bus control of variable speed wind turbine using a buck-boost converter, 2006, doi: https://doi.org/10.1109/pes.2006.1709469.

S. M. Muyeen, R. Takahashi, T. Murata y J. Tamura, “Integration of an energy capacitor system with a variable-speed wind generator”, IEEE Trans. Energy Convers., 2009, doi: https://doi.org/10.1109/TEC.2009.2025323.

R. Peña, A. Santos y C. L. Trujillo, “Análisis de los sistemas de almacenamiento basados en baterías para microrredes eléctricas,” Rev. Ing., vol. 3, n°. 25, pp. 1-17, 2020, doi: https://doi.org/10.14483/23448393.15613.

F. Nejabatkhah y Y. W. Li, “Overview of power management strategies of hybrid AC/DC microgrid”, IEEE Transactions on Power Electronics. 2015, doi: https://doi.org/10.1109/TPEL.2014.2384999.

O. López-Santos, Y. A. Aldana-Rodríguez, G. García y L. Martínez-Salamero, “A unified multimode control of a DC-DC interlinking converter integrated into a hybrid microgrid”, Electron., 2019, doi: https://doi.org/10.3390/electronics8111314.

B. Zhao, Q. Yu y W. Sun, “Extended-phase-shift control of isolated bidirectional DC-DC converter for power distribution in microgrid”, IEEE Trans. Power Electron., 2012, doi: https://doi.org/10.1109/TPEL.2011.2180928.

D. C. Erb, O. C. Onar y A. Khaligh, Bi-directional charging topologies for plug-in hybrid electric vehicles, 2010, doi: https://doi.org/10.1109/APEC.2010.5433520.

B. L. Narasimharaju, V. V. Prahlad, U. R. Reddy, K. Vijay Babu y P. Srinivasan, Optimized dual active bridge Bi-directional DC-DC converter for UPS application, 2014, doi: https://doi.org/10.1109/PEDES.2014.7042117.

Y. Shan, J. Hu, K. W. Chan, Q. Fu y J. M. Guerrero, “Model predictive control of bidirectional DC-DC converters and AC/DC interlinking converters-a new control method for pv-wind-battery microgrids”, IEEE Trans. Sustain. Energy, 2019, doi: https://doi.org/10.1109/TSTE.2018.2873390.

J. Zhang, J. S. Lai, R. Y. Kim y W. Yu, “High-power density design of a soft-switching high-power bidirectional DC-DC converter”, IEEE Trans. Power Electron., 2007, doi: https://doi.org/10.1109/TPEL.2007.900462.

S. Moussa, M. J. Ben Ghorbal y I. Slama-Belkhodja, DC voltage level choice in residential remote area, 2018, doi: https://doi.org/10.1109/IREC.2018.8362444.

P. Biczel, Power electronic converters in DC microgrid, 2007, doi: https://doi.org/10.1109/CPE.2007.4296505.

S. Dahale, A. Das, N. M. Pindoriya y S. Rajendran, An overview of DC-DC converter topologies and controls in DC microgrid, 2018, doi: https://doi.org/10.1109/ICPES.2017.8387329.

R. W. Erickson y D. Maksimovic, Fundamentals of power electronics, 2004, [Online]. Recuperado de http://www.books24x7.com/marc.asp?bookid=16231.

R. Teodorescu, M. Liserre y P. Rodríguez, Grid converters for photovoltaic and wind power systems. 2007.

S. M. Sharkh, M. A. Abu- Sara, G. I. Orfanoudakis and B. Hussain, Power electronic converters for microgrids. IEEE Press, 2014.

D. M. Baker, V. G. Agelidis and C. V. Nayar, A comparison of tri-level and bi-level current controlled grid-connected single-phase full-bridge inverters 1997, doi: https://doi.org/10.1109/isie.1997.648992.

W. Li, Y. Gu, H. Luo, W. Cui, X. He y C. Xia, “Topology review and derivation methodology of single-phase transformerless photovoltaic inverters for leakage current suppression”, IEEE Trans. Ind. Electron., 2015, doi: https://doi.org/10.1109/TIE.2015.2399278.

M. Islam, N. Afrin y S. Mekhilef, “Efficient single phase transformerless inverter for grid-tied PVG system with reactive power control”, IEEE Trans. Sustain. Energy, 2016, doi: https://doi.org/10.1109/TSTE.2016.2537365.

I. Patrao, E. Figueres, F. González-Espín y G. Garcerá, “Transformerless topologies for grid-connected single-phase photovoltaic inverters”, Renewable and Sustainable Energy Reviews, 2011, doi: https://doi.org/10.1016/j.rser.2011.03.034.

X. Guo, “A novel CH5 inverter for single-phase transformerless photovoltaic system applications”, IEEE Trans. Circuits Syst. II Express Briefs, 2017, doi: https://doi.org/10.1109/TCSII.2017.2672779.

P. S. Gotekar, S. P. Muley, D. P. Kothari y B. S. Umre, Comparison of full bridge bipolar, H5, H6 and HERIC inverter for single phase photovoltaic systems-A review, 2016, doi: https://doi.org/10.1109/INDICON.2015.7443837.

J. A. Ziani, M. J. Ben Ghorbal y S. Moussa, Comparative study of boost and zeta converters in DC microgrid applications, 2020, doi: https://doi.org/10.1109/ENERGYCon48941.2020.9236476.

C. Bali, P. Choudekar, D. Asija y R. Ruchira, Power converters for DC microgrids modelling and simulation, 2021, doi: https://doi.org/10.1109/RDCAPE52977.2021.9633383.

M. Alshareef, Z. Lin, F. Li y F. Wang, “A grid interface current control strategy for DC microgrids”, CES Trans. Electr. Mach. Syst., 2021, doi: https://doi.org/10.30941/cestems.2021.00028.

N. Kim, C. Roy y B. Parkhideh, A single-stage capacitor-bridge boost converter topology for PV-battery series integration in regulated DC microgrids, 2021, doi: https://doi.org/10.1109/APEC42165.2021.9487440.

B. Jyothi, P. Bhavana, B. Thirumala Rao y M. Sai Krishna Reddy, “A review on various DC-DC converters for photo voltaic based DC micro grids”, 2021, doi: https://doi.org/10.1109/ETI4.051663.2021.9619280.

Y. Kishor y R. N. Patel, “Solar pv fed two-stage DC/DC converter for low-voltage dc-microgrid, 2021, doi: https://doi.org/10.1109/MASCON51689.2021.9563259.

S. Sharma, V. M. Iyer, S. Bhattacharya, J. Kikuchi y K. Zou, Tertiary control method for droop controlled DC-DC converters in DC microgrids, 2021, doi: https://doi.org/10.1109/ECCE47101.2021.9595384.

J. D. Garzón-Hidalgo y A. J. Saavedra-Montes, “Una metodología de diseño de micro redes para zonas no interconectadas de Colombia”, TecnoLógicas, 2017, doi: https://doi.org/10.22430/22565337.687.

S. Anand y B. G. Fernandes, Optimal voltage level for DC microgrids, 2010, doi: https://doi.org/10.1109/IECON.2010.5674947.

N. Mohan, T. M. Undeland y W. P. Robbins, Power electronics. Converters, applications and design, Third. John Wiley and Sons, Inc, 2003.

V. Vorpérian, “Simplified analysis of PWM converters using model of pwm switch part I: Continuous conduction mode”, IEEE Trans. Aerosp. Electron. Syst., 1990, doi: https://doi.org/10.1109/7.106127.

G. Garcerá, E. Figueres y A. Abellán, Conversores conmutados: Circuitos de potencia y control. Valencia: Universidad Politécnica de Valencia, 1998.

D. M. Sable, R. B. Ridley and B. H. Cho, “Comparison of performance of single-loop and current-injection control for PWM converters that operate in both continuous and discontinuous modes of operation”, IEEE Trans. Power Electron., 1992, doi: https://doi.org/10.1109/63.124586.

V. Vorpérian, “Simplified analysis of pwm converters using model of PWM switch part I: continuous conduction mode”, IEEE Trans. Aerosp. Electron. Syst., 1990, doi: https://doi.org/10.1109/7.106126.

Y. Liu, M. Li, X. Ji, X. Luo, M. Wang y Y. Zhang, “A comparative study of the maximum power point tracking methods for PV systems”, Energy Convers. Manag., 2014, doi: https://doi.org/10.1016/j.enconman.2014.01.049.

D. W. Hart, Power electronics, The 1st Ed. McGraw-Hill Science/Engineering/Math, 2010.

W. Tang, F. C. Lee y R. B. Ridley, “Small-signal modeling of average current-mode control”, IEEE Trans. Power Electron., 1993, doi: https://doi.org/10.1109/63.223961.

T. Esram y P. L. Chapman, “Comparison of photovoltaic array maximum power point tracking techniques”, IEEE Trans. Energy Convers., 2007, doi: https://doi.org/10.1109/TEC.2006.874230.

A. Mirecki, X. Roboam y F. Richardeau, “Architecture complexity and energy efficiency of small wind turbines”, IEEE Trans. Ind. Electron., 2007, doi: https://doi.org/10.1109/TIE.2006.885456.

O. Carranza, E. Figueres, G. Garcerá y R. Gonzalez-Medina, “Analysis of the control structure of wind energy generation systems based on a permanent magnet synchronous generator”, Appl. Energy, 2013, doi: https://doi.org/10.1016/j.apenergy.2012.10.015.

E. Koutroulis y K. Kalaitzakis, “Design of a maximum power tracking system for wind-energy-conversion applications”, IEEE Trans. Ind. Electron., 2006, doi: https://doi.org/10.1109/TIE.2006.870658.

Q. Wang y L. Chang, “An intelligent maximum power extraction algorithm for inverter-based variable speed wind turbine systems”, IEEE Trans. Power Electron., 2004, doi: https://doi.org/10.1109/TPEL.2004.833459.

P. A. Dahono, A. Purwadi y A. Qamaruzzaman, An LC filter design method for single-phase PWM inverters, 1995, doi: https://doi.org/10.1109/peds.1995.405006.

K. H. Ahmed, S. J. Finney y B. W. Williams, Passive filter design for three-phase inverter interfacing in distributed generation, 2007, doi: https://doi.org/10.1109/CPE.2007.4296511.

S. B. Kjaer, J. K. Pedersen y F. Blaabjerg, “A review of single-phase grid-connected inverters for photovoltaic modules”, IEEE Transactions on Industry Applications. 2005, doi: https://doi.org/10.1109/TIA.2005.853371.

D. N. Zmood y D. G. Holmes, “Stationary frame current regulation of PWM inverters with zero steady-state error”, IEEE Trans. Power Electron., 2003, doi: https://doi.org/10.1109/TPEL.2003.810852.

V. Kaura y V. Blasko, “Operation of a phase locked loop system under distorted utility conditions”, IEEE Trans. Ind. Appl., 1997, doi: https://doi.org/10.1109/28.567077.

S. M. Silva, B. M. Lopes, B. J. C. Filho, R. P. Campana y W. C. Boaventura, Performance evaluation of PLL algorithms for single-phase grid-connected systems, 2004, doi: https://doi.org/10.1109/ias.2004.1348790.

Descargas

Publicado

April 22, 2024

Licencia

Creative Commons License

Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.

Detalles sobre el formato de publicación disponible: Formato físico

Formato físico

ISBN-13 (15)

978-958-787-663-5

Dimensiones físicas

Detalles sobre el formato de publicación disponible: PDF

PDF

ISBN-13 (15)

978-958-787-664-2
Loading...