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

Authors

  • 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

DOI:

https://doi.org/10.13052/jrss0974-8024.1522

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.

References

G. F. Frate, L. Ferrari, and U. Desideri. Impact of Forecast Uncertainty on Wind Farm Profitability. Journal of Engineering for Gas Turbines and Power, 142(4), 2020.

H. Dehghani, B. Vahidi, and S. H. Hosseinian. Wind farms participation in electricity markets considering uncertainties. Renewable Energy, 101:907–918, 2017.

E. Hittinger, J. Apt, and J. F. Whitacre. The effect of variability-mitigating market rules on the operation of wind power plants. Energy Systems, 5(4):737–766, 2014.

D. Lee, J. Kim, and R. Baldick. Ramp rates control of wind power output using a storage system and gaussian processes. University of Texas at Austin, Electrical and Computer Engineering, 2012.

D. Lee and R. Baldick. Limiting ramp rate of wind power output using a battery based on the variance gamma process. In Conf. Renew. Energies Power, 1–6, 2012.

E. Hittinger, J. F. Whitacre, and J. Apt. Compensating for wind variability using co-located natural gas generation and energy storage. Energy Systems, 1(4):417–439, 2010.

S. Teleke, M. E. Baran, A. Q. Huang, S. Bhattacharya, and L. Anderson. Control strategies for battery energy storage for wind farm dispatching. IEEE Transactions on Energy Conversion, 24(3):725–732, 2009.

Y. Uchida, G. Koshimizu, T. Nanahara, and K. Yoshimoto. New control method for regulating state-of-charge of a battery in hybrid wind power/battery energy storage system. In 2006 IEEE PES Power Systems Conference and Exposition, 1244–1251, 2006.

F. Luo, K. Meng, Z. Y. Dong, Y. Zheng, Y. Chen, and K. P. Wong. Coordinated operational planning for wind farm with battery energy storage system. IEEE Transactions on Sustainable Energy, 6(1):253–262, 2015.

D. L. Yao, S. S. Choi, K. J. Tseng, and T. T. Lie. Determination of short-term power dispatch schedule for a wind farm incorporated with dual-battery energy storage scheme. IEEE Transactions on Sustainable Energy, 3(1):74–84, 2011.

A. Gautam, and S. Dharmaraja. An analytical model driven by fluid queue for battery life time of a user equipment in LTE-A networks. Physical Communication, 30:213–219, 2018.

S. Kapoor, and S. Dharmaraja. Applications of Fluid Queues in Rechargeable Batteries. In Applied Probability and Stochastic Processes, 91–101, Springer, Singapore, 2020.

G. D’Amico. Measuring the quality of life through Markov reward processes: analysis and inference. Environmetrics: The official journal of the International Environmetrics Society, 21(2):208–220, 2010.

G. D’Amico, F. Gismondi, J. Janssen, and R. Manca. Discrete time homogeneous Markov processes for the study of the basic risk processes. Methodology and Computing in Applied Probability, 17(4):983–998, 2015.

G. D’Amico, F. Petroni, and S. Vergine. An Analysis of a Storage System for a Wind Farm with Ramp-Rate Limitation. Energies, 14(13):4066, 2021.

C. Venu, Y. Riffonneau, S. Bacha, and Y. Baghzouz. Battery storage system sizing in distribution feeders with distributed photovoltaic systems. In2009 IEEE Bucharest PowerTech, 1–5, 2009.

Global Modeling and Assimilation Office (GMAO) (2015) Modern-Era Retrospective analysis for Research and Applications, Version 2. [https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/data_access/]. Accessed: [2021-07-15].

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Published

2022-07-27

How to Cite

D’Amico, G. ., Gismondi, F. ., & Vergine, S. . (2022). A Model for the State of Charge of a Battery Connected to a Wind Power Plant Under a Ramp Rate Limitation Regime. Journal of Reliability and Statistical Studies, 15(02), 431–458. https://doi.org/10.13052/jrss0974-8024.1522

Issue

2022: Vol 15 Iss 2

Section

Reliability and Stochastic Processes