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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2019. Vol. 30

Control of Accuracy on Taylor-Collocation Method for Load Leveling Problem

Author(s)
S. Noeiaghdam, D. N. Sidorov, I. R. Muftahov, A. V. Zhukov
Abstract

High penetration of renewable energy sources coupled with decentralization of transport and heating loads in future power systems will result even more complex unit commitment problem solution using energy storage system scheduling for efficient load leveling. This paper employees an adaptive approach to load leveling problem using the Volterra integral dynamical models. The problem is formulated as solution of the Volterra integral equation of the first kind which is attacked using Taylor-collocation numerical method which has the second-order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. Also the CESTAC method is applied to find the optimal approximation, optimal error and optimal step of collocation method. This adaptive approach is suitable for energy storage optimization in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of the Island of Ireland.

About the Authors

Samad Noeiaghdam, PhD, Assoc. Prof., Baikal School of BRICS, Irkutsk National Research Technical University, 83, Lermontov st., Irkutsk, 664074, Russian Federation; South Ural State University, 76, Lenin prospect, Chelyabinsk, 454080, Russian Federation, e-mail: samadnoeiaghdam@gmail.com

Denis Sidorov, Dr. Sci. (Phys.–Math.), Prof., Melentiev Energy Systems Institute SB RAS, 130, Lermontov st., Irkutsk, 664033, Russian Federation, tel.: (3952) 500-646 ext. 258; Irkutsk National Research Technical University, 83, Lermontov st., Irkutsk, 664074, Russian Federation; Irkutsk State University, 1, K. Marx st., Irkutsk, 664003, Russian Federation, e-mail: dsidorov@isem.irk.ru

Ildar Muftahov, Programmer, Irkutsk Computing Center of Joint Stock Company Russian Railways, 25, Mayakovaskii st., Irkutsk, 664005, Russian Federation; Melentiev Energy Systems Institute SB RAS, 130, Lermontov st., Irkutsk, 664033, Russian Federation, e-mail: ildar sm@mail.ru

Aleksei Zhukov, Junior Research Fellow, Institute of Solar-Terrestrial Physics SB RAS, 126a, Lermontov st., Irkutsk, 664033, Russian Federation; Melentiev Energy Systems Institute SB RAS, 130, Lermontov st., Irkutsk, 664033, Russian Federation, e-mail: zhukovalex13@gmail.com

For citation

Noeiaghdam S., Sidorov D.N., Muftahov I.R., Zhukov A.V. Control of Accuracy on Taylor-Collocation Method for Load Leveling Problem. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 30, pp. 59-72. https://doi.org/10.26516/1997-7670.2019.30.59

Keywords
load leveling problem, Taylor-collocation method, stochastic arithmetic, CESTAC method
UDC
51-74
MSC
45D05, 65D30
DOI
https://doi.org/10.26516/1997-7670.2019.30.59
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