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Mathematical modeling and optimal control of carbon dioxide emissions from energy sector

Author

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  • Maitri Verma

    (Babasaheb Bhimrao Ambedkar University)

  • Alok Kumar Verma

    (Babasaheb Bhimrao Ambedkar University)

  • A. K. Misra

    (Banaras Hindu University)

Abstract

Energy demand is rising day by day and will continue to increase to meet the demand of the growing population. A major portion of global energy production comes from fossil fuel burning, resulting in the increase in the atmospheric burden of global warming gas carbon dioxide ( $$CO _{2}$$ C O 2 ). Cutting down $$CO _{2}$$ C O 2 emission from the energy sector is crucial to meet the climate change mitigation target. This paper is focused on fulfilling two objectives: The first objective is to present a mathematical model that captures the dynamical relationship between the human population, energy use, and atmospheric carbon dioxide, and the second aim is to derive a mathematical framework to effectively utilize the available mitigation options to curtail $$CO _{2}$$ C O 2 emission from energy use by proposing an optimal control problem. The mitigation options that reduce the $$CO _{2}$$ C O 2 emission rate from energy production, as well as the options that reduce the energy consumption rate, are considered in the modeling process. The proposed mathematical model is analyzed qualitatively to comprehend the system’s long-term behavior. The model parameters are fitted to real data of global energy use, population, and $$CO _{2}$$ C O 2 concentration. It is shown that the equilibrium level of $$CO _{2}$$ C O 2 reduces with the increase in the efficiencies of mitigation options to reduce the $$CO _{2}$$ C O 2 emission rate per unit energy use and energy consumption rate. The optimality system is derived analytically by taking the efficiencies of the mitigation options to reduce the $$CO _{2}$$ C O 2 emission rate and energy consumption rate as control variables. Numerical simulations are conducted to validate the theoretical findings and identify the optimal profiles of control variables under different settings of $$CO _{2}$$ C O 2 emission rate, energy consumption rate, and maximum efficiencies of available mitigation options to cut down $$CO _{2}$$ C O 2 emission rate and energy consumption rate. It is found that the development and implementation of more efficient mitigation options and switching to low carbon energy sources bring reduction in the mitigation cost.

Suggested Citation

  • Maitri Verma & Alok Kumar Verma & A. K. Misra, 2021. "Mathematical modeling and optimal control of carbon dioxide emissions from energy sector," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(9), pages 13919-13944, September.
  • Handle: RePEc:spr:endesu:v:23:y:2021:i:9:d:10.1007_s10668-021-01245-y
    DOI: 10.1007/s10668-021-01245-y
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    1. El-Fadel, M. & Chedid, R. & Zeinati, M. & Hmaidan, W., 2003. "Mitigating energy-related GHG emissions through renewable energy," Renewable Energy, Elsevier, vol. 28(8), pages 1257-1276.
    2. Zhang, Dongjie & Ma, Linwei & Liu, Pei & Zhang, Lili & Li, Zheng, 2012. "A multi-period superstructure optimisation model for the optimal planning of China's power sector considering carbon dioxide mitigation," Energy Policy, Elsevier, vol. 41(C), pages 173-183.
    3. Lonngren, Karl E. & Bai, Er-Wei, 2008. "On the global warming problem due to carbon dioxide," Energy Policy, Elsevier, vol. 36(4), pages 1567-1568, April.
    4. Feng, Y.Y. & Chen, S.Q. & Zhang, L.X., 2013. "System dynamics modeling for urban energy consumption and CO2 emissions: A case study of Beijing, China," Ecological Modelling, Elsevier, vol. 252(C), pages 44-52.
    5. Allen,Robert C., 2009. "The British Industrial Revolution in Global Perspective," Cambridge Books, Cambridge University Press, number 9780521868273, September.
    6. John P DeLong & Oskar Burger, 2015. "Socio-Economic Instability and the Scaling of Energy Use with Population Size," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-12, June.
    7. Gibbins, Jon & Chalmers, Hannah, 2008. "Carbon capture and storage," Energy Policy, Elsevier, vol. 36(12), pages 4317-4322, December.
    8. David I. Stern and Astrid Kander, 2012. "The Role of Energy in the Industrial Revolution and Modern Economic Growth," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    9. Wee, Jung-Ho, 2013. "A review on carbon dioxide capture and storage technology using coal fly ash," Applied Energy, Elsevier, vol. 106(C), pages 143-151.
    10. Pekala, Lukasz M. & Tan, Raymond R. & Foo, Dominic C.Y. & Jezowski, Jacek M., 2010. "Optimal energy planning models with carbon footprint constraints," Applied Energy, Elsevier, vol. 87(6), pages 1903-1910, June.
    11. Pao, Hsiao-Tien & Tsai, Chung-Ming, 2011. "Modeling and forecasting the CO2 emissions, energy consumption, and economic growth in Brazil," Energy, Elsevier, vol. 36(5), pages 2450-2458.
    12. Andrew K Jorgenson & Brett Clark, 2013. "The Relationship between National-Level Carbon Dioxide Emissions and Population Size: An Assessment of Regional and Temporal Variation, 1960–2005," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-8, February.
    13. AlFarra, Hasan Jamil & Abu-Hijleh, Bassam, 2012. "The potential role of nuclear energy in mitigating CO2 emissions in the United Arab Emirates," Energy Policy, Elsevier, vol. 42(C), pages 272-285.
    14. Phdungsilp, Aumnad, 2010. "Integrated energy and carbon modeling with a decision support system: Policy scenarios for low-carbon city development in Bangkok," Energy Policy, Elsevier, vol. 38(9), pages 4808-4817, September.
    15. Lu, Chuanyi & Zhang, Xiliang & He, Jiankun, 2010. "A CGE analysis to study the impacts of energy investment on economic growth and carbon dioxide emission: A case of Shaanxi Province in western China," Energy, Elsevier, vol. 35(11), pages 4319-4327.
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