Analysis of installed photovoltaic capacity in Mexico: A systems dynamics and conformable fractional calculus approach

Jorge Manuel Barrios-Sánchez; Roberto Baeza-Serrato; Leonardo Martínez-Jiménez; Jorge Manuel Barrios-Sánchez; Roberto Baeza-Serrato; Leonardo Martínez-Jiménez

doi:10.3934/energy.2025015

AIMS Energy

2025, Volume 13, Issue 2: 402-427. doi: 10.3934/energy.2025015

Previous Article Next Article

Research article Topical Sections

Analysis of installed photovoltaic capacity in Mexico: A systems dynamics and conformable fractional calculus approach

1.
Universidad de Guanajuato, Campus Irapuato-Salamanca, Departamento de Estudios Multidisciplinarios, Guanajuato, México
2.
Corporación Universitaria Rafael Núñez, Colombia

Received: 03 January 2025 Revised: 02 March 2025 Accepted: 24 March 2025 Published: 31 March 2025

This study develops a new estimation method within the system dynamics (SD) framework, incorporating fractional calculus (FC) to conduct a sensitivity analysis on photovoltaic capacity growth in Mexico. The primary goal is to address the need to model energy transitions accurately and realistically, considering Mexico's advantages in renewable energy, particularly solar power. The study explores the use of FC to improve the precision of simulations and provide valuable insights into the growth of photovoltaic installations under different market conditions and policies.
The methodology is structured in three phases. Initially, an exponential growth model is developed to simulate the early stage of photovoltaic capacity expansion, incorporating key variables such as public investment, subsidies, and the effects of rural loss on the adoption of renewable technologies. In the second phase, a sigmoidal growth model is applied to represent more realistic capacity limits, considering market saturation and structural limitations. The differential equations governing the growth were solved using the conformable derivative, which captures the complexity of the system's dynamics, including memory effects.
The sensitivity analysis performed on both the exponential and sigmoidal models reveals that the fractional parameter $ \alpha = 0.8652 $ provides the best fit to the actual data from 2015 to 2023, reducing the average error to 16.52%. Projections for the period from 2023 to 2030 suggest that Mexico's installed photovoltaic capacity could range between 23,000 and 25,000 MW, with $ \alpha $ values varying between 0.8 and 1, aligning with the expected market dynamics and national energy goals.
This study emphasizes the importance of using system dynamics combined with FC as an innovative tool for energy planning in Mexico. The ability to simulate multiple scenarios and perform sensitivity analyses is crucial for optimizing energy resources, designing policies that promote renewable technologies, and ensuring a successful transition to a sustainable energy future.
- renewable technologies,
- solar irradiance,
- sensitivity analysis,
- system dynamics,
- fractional conformable derivative,
- installed photovoltaic capacity
Citation: Jorge Manuel Barrios-Sánchez, Roberto Baeza-Serrato, Leonardo Martínez-Jiménez. Analysis of installed photovoltaic capacity in Mexico: A systems dynamics and conformable fractional calculus approach[J]. AIMS Energy, 2025, 13(2): 402-427. doi: 10.3934/energy.2025015

Related Papers:

Abstract

This study develops a new estimation method within the system dynamics (SD) framework, incorporating fractional calculus (FC) to conduct a sensitivity analysis on photovoltaic capacity growth in Mexico. The primary goal is to address the need to model energy transitions accurately and realistically, considering Mexico's advantages in renewable energy, particularly solar power. The study explores the use of FC to improve the precision of simulations and provide valuable insights into the growth of photovoltaic installations under different market conditions and policies.

The methodology is structured in three phases. Initially, an exponential growth model is developed to simulate the early stage of photovoltaic capacity expansion, incorporating key variables such as public investment, subsidies, and the effects of rural loss on the adoption of renewable technologies. In the second phase, a sigmoidal growth model is applied to represent more realistic capacity limits, considering market saturation and structural limitations. The differential equations governing the growth were solved using the conformable derivative, which captures the complexity of the system's dynamics, including memory effects.

The sensitivity analysis performed on both the exponential and sigmoidal models reveals that the fractional parameter $ \alpha = 0.8652 $ provides the best fit to the actual data from 2015 to 2023, reducing the average error to 16.52%. Projections for the period from 2023 to 2030 suggest that Mexico's installed photovoltaic capacity could range between 23,000 and 25,000 MW, with $ \alpha $ values varying between 0.8 and 1, aligning with the expected market dynamics and national energy goals.

This study emphasizes the importance of using system dynamics combined with FC as an innovative tool for energy planning in Mexico. The ability to simulate multiple scenarios and perform sensitivity analyses is crucial for optimizing energy resources, designing policies that promote renewable technologies, and ensuring a successful transition to a sustainable energy future.

References

[1]	Zhang T, Ma Y, Li A (2021) Scenario analysis and assessment of China's nuclear power policy based on the Paris Agreement: A dynamic CGE model. Energy 228: 120541. https://doi.org/10.1016/j.energy.2021.120541 doi: 10.1016/j.energy.2021.120541
[2]	Li N, Chen W (2019) Energy-water nexus in China's energy bases: From the Paris Agreement to the well below 2 degrees target. Energy 166: 277–286. https://doi.org/10.1016/j.energy.2018.10.039 doi: 10.1016/j.energy.2018.10.039
[3]	Kat B, Paltsev S, Yuan M (2018) Turkish energy sector development and the Paris Agreement goals: A Cge model assessment. Energy Policy 122: 84–96. https://doi.org/10.1016/j.enpol.2018.07.030 doi: 10.1016/j.enpol.2018.07.030
[4]	Nong D, Siriwardana M (2018) Effects on the US economy of its proposed withdrawal from the Paris Agreement: A quantitative assessment. Energy 159: 621–629. https://doi.org/10.1016/j.energy.2018.06.178 doi: 10.1016/j.energy.2018.06.178
[5]	Secretaría de Energía (SENER) (2021) Balance Nacional de Energía 2020. México: SENER. Available from: https://www.gob.mx/cms/uploads/attachment/file/707654/BALANCE_NACIONAL_ENERGIA_0403.pdf.
[6]	Secretaría de Energía (SENER) (2018) Prospectivas del Sector Energético. México: SENER. Available from: https://www.gob.mx/sener/documentos/prospectivas-del-sector-energetico.
[7]	Secretaría de Energía (SENER) (2019) Balance Nacional de Energía 2018. México: SENER. Available from: https://www.gob.mx/cms/uploads/attachment/file/528054/Balance_Nacional_de_Energ_a_2018.pdf.
[8]	Palacios A, Koon RK, Castro-Olivera PM, et al. (2024) Paths towards hydrogen production through variable renewable energy capacity: A study of Mexico and Jamaica. Energy Convers Manage 311: 118483. https://doi.org/10.1016/j.enconman.2024.118483 doi: 10.1016/j.enconman.2024.118483
[9]	Silva JA, Andrade MA (2020) Solar energy analysis in use and implementation in Mexico: A review. Int J Energy Sect Manage 14: 1333–1349. https://doi.org/10.1108/IJESM-01-2020-0010 doi: 10.1108/IJESM-01-2020-0010
[10]	Pérez AJG, Hansen T (2020) Technology characteristics and catching-up policies: Solar energy technologies in Mexico. Energy Sustainable Dev 56: 51–66. https://doi.org/10.1016/j.esd.2020.03.003 doi: 10.1016/j.esd.2020.03.003
[11]	Paleta R, Pina A, Silva CA (2012) Remote autonomous energy systems project: towards sustainability in developing countries. Energy 48: 431–439. https://doi.org/10.1016/j.energy.2012.06.004 doi: 10.1016/j.energy.2012.06.004
[12]	Mishra AK, Sudarsan JS, Suribabu CR, et al. (2024). Cost-benefit analysis of implementing a solar powered water pumping system–-A case study. Energy Nexus 16: 100323. https://doi.org/10.1016/j.nexus.2024.100323 doi: 10.1016/j.nexus.2024.100323
[13]	Nabil MH, Barua J, Eiva URJ, et al. (2024) Techno-economic analysis of commercial-scale 15 MW on-grid ground solar PV systems in Bakalia: A feasibility study proposed for BPDB. Energy Nexus 14: 100286. https://doi.org/10.1016/j.nexus.2024.100286 doi: 10.1016/j.nexus.2024.100286
[14]	Koot M, Wijnhoven F (2021) Usage impact on data center electricity needs: A system dynamic forecasting model. Appl Energy 291: 116798. https://doi.org/10.1016/j.apenergy.2021.116798 doi: 10.1016/j.apenergy.2021.116798
[15]	Dnekeshev A, Kushnikov V, Tsvirkun A (2024) System-Dynamic model for analysis and forecasting emergency situations of oil refinery enterprises. 2024 17th International Conference on Management of Large-Scale System Development (MLSD), IEEE, 1–4. https://doi.org/10.1109/MLSD61779.2024.10739602
[16]	Pásková M, Štekerová K, Zanker M, et al. (2024) Water pollution generated by tourism: Review of system dynamics models. Heliyon 10. https://doi.org/10.1016/j.heliyon.2023.e23824 doi: 10.1016/j.heliyon.2023.e23824
[17]	Awah LS, Belle JA, Nyam YS, et al. (2024) A participatory systems dynamic modelling approach to understanding flood systems in a coastal community in Cameroon. Int J Disast Risk Re 101: 104236. https://doi.org/10.1016/j.ijdrr.2023.104236 doi: 10.1016/j.ijdrr.2023.104236
[18]	Du Q, Yang M, Wang Y, et al. (2024) Dynamic simulation for carbon emission reduction effects of the prefabricated building supply chain under environmental policies. Sustain Cities and Soc 100: 105027. https://doi.org/10.1016/j.scs.2023.105027 doi: 10.1016/j.scs.2023.105027
[19]	Capellán-Pérez I, de Blas I, Nieto J, et al. (2020) MEDEAS: A new modeling framework integrating global biophysical and socioeconomic constraints. Energy Environ Sci 133: 986–1017. https://doi.org/10.1039/C9EE02627D doi: 10.1039/C9EE02627D
[20]	Capellán-Pérez I, Mediavilla M, de Castro C, et al. (2014) Fossil fuel depletion and socio-economic scenarios: An integrated approach. Energy 77: 641–666. https://doi.org/10.1016/j.energy.2014.09.063 doi: 10.1016/j.energy.2014.09.063
[21]	Yu X, Wu Z, Wang Q, et al. (2020) Exploring the investment strategy of power enterprises under the nationwide carbon emissions trading mechanism: A scenario-based system dynamics approach. Energy Policy 140: 111409. https://doi.org/10.1016/j.enpol.2020.111409 doi: 10.1016/j.enpol.2020.111409
[22]	Mariano-Hernández D, Hernández-Callejo L, Zorita-Lamadrid A, et al. (2021) A review of strategies for building energy management system: Model predictive control, demand side management, optimization, and fault detect & diagnosis. J Build Eng 33: 101692. https://doi.org/10.1016/j.jobe.2020.101692 doi: 10.1016/j.jobe.2020.101692
[23]	López-Cruz IL, Ramírez-Arias A, Rojano-Aguilar A (2004) Análisis de sensibilidad de un modelo dinámico de crecimiento para lechugas (Lactuca sativa L.) cultivadas en invernadero. Agrociencia 38: 613–624. Available from: https://agrociencia-colpos.org/index.php/agrociencia/article/view/355.
[24]	Aguilar C, Polo MJ (2005) Análisis de sensibilidad de AnnAGNPS en la dinámica de herbicidas en cuencas de olivar. In: Samper CJ, Paz GA (Eds.), Estudios en la Zona no Saturada del Suelo 7: 337–343. Available from: Availabel from: https://abe.ufl.edu/Faculty/carpena/files/pdf/zona_no_saturada/estudios_de_la_zona_v7/c337-343.pdf.
[25]	Barrios-Sánchez JM, Baeza-Serrato R, Martínez-Jiménez L (2024) FC to analyze efficiency behavior in a balancing loop in a system dynamics environment. Fractal Fract 8: 212. https://doi.org/10.3390/fractalfract8040212 doi: 10.3390/fractalfract8040212
[26]	Khalil R, Al Horani M, Yousef A, et al. (2014) A new definition of fractional derivative. J Comput Appl Math 264: 65–70. https://doi.org/10.1016/j.cam.2014.01.002 doi: 10.1016/j.cam.2014.01.002
[27]	Yu Y, Yin Y (2022) Fractal operators and convergence analysis in fractional viscoelastic theory. Fractal Fract 8: 200. https://doi.org/10.3390/fractalfract8040200 doi: 10.3390/fractalfract8040200
[28]	Rosales JJ, Toledo-Sesma L (2023) Anisotropic fractional cosmology: K-essence theory. Fractal Fract 7: 814. https://doi.org/10.3390/fractalfract7110814 doi: 10.3390/fractalfract7110814
[29]	Adervani A, Saadati SR, O'Regan D, et al. (2022) Uncertain asymptotic stability analysis of a fractional-order system with numerical aspects. Mathematics 12: 904. https://doi.org/10.3390/math12060904 doi: 10.3390/math12060904
[30]	Abdeljawad T (2015) On conformable FC. J Comput Appl Math 279: 57–66. https://doi.org/10.1016/j.cam.2014.10.016 doi: 10.1016/j.cam.2014.10.016
[31]	Martinez L, Rosales JJ, Carreño J, et al. (2018) Electrical circuits described by fractional conformable derivative. Int J Circuit Theory Appl 46: 1091–1100. https://doi.org/10.1002/cta.2475 doi: 10.1002/cta.2475
[32]	Rahman MU, Karaca Y, Sun M (2024) Complex behaviors and various soliton profiles of (2 + 1)—dimensional complex modified Korteweg-de Vries equation. Opt Quant Electron 56: 878. https://doi.org/10.1007/s11082-024-06514-4 doi: 10.1007/s11082-024-06514-4
[33]	Statista (2024) Capacidad instalada de energía solar en México desde 2013 hasta 2023. Statista. Available from: https://es.statista.com/estadisticas/1238183/capacidad-instalada-energia-solar-mexico/.
[34]	INEGI (2024). Estadísticas de energía. INEGI. Available from: https://www.inegi.org.mx/.
[35]	Sterman J (2002) System Dynamics: Systems Thinking and Modeling for a Complex World. McGraw-Hill. Available from: http://hdl.handle.net/1721.1/102741.
[36]	Roberts MJ (1973) The Limits of "The Limits to Growth". Harvard University. Available from: https://doi.org/10.3138/9781487595029-020
[37]	Forrester JW (2012) Dinámica industrial: un gran avance para los tomadores de decisiones. In: Las raíces de la logística, Springer, Berlín, Heidelberg, 141–172. https://doi.org/10.1007/978-3-642-27922-5_13
[38]	Sterman J (2002) Dinámica de sistemas: pensamiento y modelado sistémico para un mundo complejo. Availabel from: http://hdl.handle.net/1721.1/102741.
[39]	Zhao D, Luo M (2017) General conformable fractional derivative and its physical interpretation. Calcolo 54: 903–917. https://doi.org/10.1007/s10092-017-0213-8 doi: 10.1007/s10092-017-0213-8
[40]	Kajouni A, Chafiki A, Hilal K, et al. (2021) A new conformable fractional derivative and applications. Int Differ Equations, 2021. https://doi.org/10.1155/2021/6245435 doi: 10.1155/2021/6245435
[41]	Abdeljawad T (2015) On conformable fractional calculus. J Comput Appl Math 279: 57-66. https://doi.org/10.1016/j.cam.2014.10.016 doi: 10.1016/j.cam.2014.10.016

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)