A New Model Making the Transition From Oil to Solar Energy

Authors

  • Séverine Bernard Department of Mathematics and Computer Sciences, University of Antilles, LAMIA (EA 4540), BP 250, 97159, Pointe-à-Pitre, Guadeloupe, France
  • Alain Pietrus Department of Mathematics and Computer Sciences, University of Antilles, LAMIA (EA 4540), BP 250, 97159, Pointe-à-Pitre, Guadeloupe, France
  • Watson Sainvil Department of Mathematics and Computer Sciences, University of Antilles, LAMIA (EA 4540), BP 250, 97159, Pointe-à-Pitre, Guadeloupe, France

DOI:

https://doi.org/10.37256/cm.5220244027

Keywords:

solar energy, oil energy, deterministic and stochastic models, Brownian motion, maximum Pontryagin’s principle, limit cycles

Abstract

Today, the use of renewable energy sources such as sun, wind and hot water to generate electricity is increasingly becoming a global priority. In this paper, we propose a deterministic dynamical system reporting the transition from oil to solar energy, in which we then add the randomness of this phenomenon. First, we study the positivity of the deterministic oil-solar model and show that there is a maximum solution of the deterministic model and that the system is controllable at any time T > 0 from an initial point. We also prove the existence of an equilibrium state, study its nature and prove that there is no limit cycle between the quantity of oil available and the solar production capacity installed. Secondly, we formulate the stochastic solar energy model from the deterministic model, for which we proved the existence of a unique solution. Finally, using a model extracted from the model performed and examining the transition from the amount of available oil to the installed solar generation capacity, we associate a linear optimal control problem, from which we prove that the optimal control components are of bang-bang type, and we characterize them.

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Published

2024-04-25

How to Cite

1.
Bernard S, Pietrus A, Sainvil W. A New Model Making the Transition From Oil to Solar Energy. Contemp. Math. [Internet]. 2024 Apr. 25 [cited 2024 May 27];5(2):1311-30. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/4027