Probabilistic Description of the State of Charge of Batteries Used for Primary Frequency Regulation

Elio Chiodo, Davide Lauria, Fabio Mottola, Daniela Proto, Domenico Villacci, Giorgio Maria Giannuzzi and Cosimo Pisani
Additional contact information
Elio Chiodo: Department of Industrial Engineering, University of Naples Federico II, 80125 Naples, Italy
Davide Lauria: Department of Industrial Engineering, University of Naples Federico II, 80125 Naples, Italy
Fabio Mottola: Department of Electrical Engineering and Information Technology, University of Naples Federico II, 80125 Naples, Italy
Daniela Proto: Department of Electrical Engineering and Information Technology, University of Naples Federico II, 80125 Naples, Italy
Domenico Villacci: Department of Industrial Engineering, University of Naples Federico II, 80125 Naples, Italy
Giorgio Maria Giannuzzi: Terna Italian Transmission System Operator, 00156 Rome, Italy
Cosimo Pisani: Terna Italian Transmission System Operator, 00156 Rome, Italy

Energies, 2022, vol. 15, issue 18, 1-24

Abstract: Battery participation in the service of power system frequency regulation is universally recognized as a viable means for counteracting the dramatic impact of the increasing utilization of renewable energy sources. One of the most complex aspects, in both the planning and operation stage, is the adequate characterization of the dynamic variation of the state of charge of the battery in view of lifetime preservation as well as the adequate participation in the regulation task. Since the power system frequency, which is the input of the battery regulation service, is inherently of a stochastic nature, it is easy to argue that the most proper methodology for addressing this complex issue is that of the theory of stochastic processes. In the first part of the paper, a preliminary characterization of the power system frequency is presented by showing that with an optimal degree of approximation it can be regarded as an Ornstein–Uhlenbeck process. Some considerations for guaranteeing desirable performances of the control strategy are performed by assuming that the battery-regulating power depending on the frequency can be described by means of a Wiener process. In the second part of the paper, more realistically, the regulating power due to power system changes is described as an Ornstein–Uhlenbeck or an exponential shot noise process driven by a homogeneous Poisson process depending on the frequency response features requested of the battery. Because of that, the battery state of charge is modeled as the output of a dynamic filter having this exponential shot noise process as input and its characterization constitutes the central role for the correct characterization of the battery life. Numerical simulations are carried out for demonstrating the goodness and the applicability of the proposed probabilistic approach.

Keywords: primary frequency regulation; battery energy storage system; Ornstein–Uhlenbeck stochastic process; compound poisson stochastic process (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2022
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