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The Bulletin of Irkutsk State University. Series Mathematics, 2019, Volume 30, Pages 59–72 (Mi iigum395)  

Dynamic systems and optimal control

Control of accuracy on Taylor-collocation method for load leveling problem

S. Noeiaghdamab, D. N. Sidorovbcd, I. R. Muftahovce, A. V. Zhukovcf

a 2South Ural State University, Chelyabinsk, Russian Federation
b Irkutsk National Research Technical University, Irkutsk, Russian Federation
c Melentiev Energy Systems Institute SB RAS, Irkutsk, Russian Federation
d Irkutsk State University, Irkutsk, Russian Federation
e Irkutsk Division of Main Computer Centre, JSC Russian Railways, Irkutsk, Russian Federation
f Institute of Solar-Terrestrial Physics SB RAS, Irkutsk, Russian Federation

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.

Keywords: load leveling problem, Taylor-collocation method, stochastic arithmetic, CESTAC method.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-31-00206
This research was supported by RFBR Grant No. 18-31-00206.


DOI: https://doi.org/10.26516/1997-7670.2019.30.59

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UDC: 51-74
MSC: 45D05, 65D30
Received: 31.10.2019
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Citation: S. Noeiaghdam, D. N. Sidorov, I. R. Muftahov, A. V. Zhukov, “Control of accuracy on Taylor-collocation method for load leveling problem”, The Bulletin of Irkutsk State University. Series Mathematics, 30 (2019), 59–72

Citation in format AMSBIB
\Bibitem{NoeSidMuf19}
\by S.~Noeiaghdam, D.~N.~Sidorov, I.~R.~Muftahov, A.~V.~Zhukov
\paper Control of accuracy on Taylor-collocation method for load leveling problem
\jour The Bulletin of Irkutsk State University. Series Mathematics
\yr 2019
\vol 30
\pages 59--72
\mathnet{http://mi.mathnet.ru/iigum395}
\crossref{https://doi.org/10.26516/1997-7670.2019.30.59}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000504646800005}


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