A Model for the State of Charge of a Battery Connected to a Wind Power Plant Under a Ramp Rate Limitation Regime

  • Guglielmo D’Amico Department of Economics, University G. D’Annunzio, Pescara 65122, Italy
  • Fulvio Gismondi Department of Economic and Business Science, University G. Marconi, Roma 00193, Italy
  • Salvatore Vergine Department of Neurosciences, Imaging and Clinical Sciences, University G. D’Annunzio, Chieti 66100, Italy
Keywords: integral equation, Markov model, battery, wind power

Abstract

In this paper, the expected value of the first hitting time of a threshold of the state of charge of a battery is investigated. The model considers a battery storage system connected to a wind power plant under a ramp rate limitation scheme. The level of charge in the battery is the result of operations that are modelled by a Markov chain model with random rewards. The Markov chain and reward characteristics do depend on the considered ramp rate limitation scheme that the wind power producer has to respect in order to guarantee a quasi-stable output power to the grid. In this paper, we derive a system of integral equations for the hitting time of the state of charge of the battery and the application to real data validates the analytical results.

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Author Biographies

Guglielmo D’Amico, Department of Economics, University G. D’Annunzio, Pescara 65122, Italy

Guglielmo D’Amico is a Full Professor in Mathematical Methods in Economics, Finance and Insurance at the Department of Economics of the “G. D’Annunzio” University of Chieti-Pescara. He received his PhD in Mathematics for applications in Economics, Finance and Insurance from the University “La Sapienza” of Rome in May 2005. His research interests include the theory of stochastic processes and their applications in finance, insurance, economics, reliability and wind energy. He is interested also in nonparametric statistical inference for stochastic processes. His research has appeared in several refereed journals: European Journal of Operational Research, Applied Mathematical Finance, Scandinavian Actuarial Journal, Applied Mathematical Modelling, IMA Journal of Management Mathematics, Journal of the Operational Research Society, Reliability Engineering and System Safety, Stochastics, Insurance: Mathematics and Economics.

Fulvio Gismondi, Department of Economic and Business Science, University G. Marconi, Roma 00193, Italy

Fulvio Gismondi is a Full Professor in Mathematical Methods in Economics, Finance and Insurance at the Department of Economic and Business Science at the “G. Marconi” University of Rome. He received his PhD in Actuarial Sciences from the University “La Sapienza” of Rome. His research interests include the theory of stochastic processes and their applications in finance and insurance. His research has appeared in several refereed journals: Methodology and Computing in Applied Probability, Mathematics, Physica a: Statistical Mechanics and its Applications, Theory of Probability and Mathematical Statistics, Annals of Actuarial Science.

Salvatore Vergine, Department of Neurosciences, Imaging and Clinical Sciences, University G. D’Annunzio, Chieti 66100, Italy

Salvatore Vergine is a PhD student at the Department of Neurosciences, Imaging and Clinical Sciences of the “G. D’Annunzio” University of Chieti-Pescara. Before starting the university studies, he worked as a bank employee for two years. He gained his first Master’s degree in Civil Engineering at University of Salento in Apulia in April 2017. Afterwards, he got the Master’s degree in Environmental Engineering at Imperial College London in November 2020. His research interests focus on financial mathematics, stochastic processes, renewable energies and specifically wind energy. His first research has appeared in the journal Energies.

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Published
2022-07-27
Section
Reliability and Stochastic Processes