A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System

With the rapid development of power-electronics-enabled power systems, the new converter-based generators are deteriorating the small-signal stability of the power system. Although the numerical differentiation method has been widely used for approximately calculating the eigenvalue sensitivities, i...

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Autores principales:	Peijie Li, Yucheng Wei, Junjian Qi, Xiaoqing Bai, Hua Wei
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	Closed-form formulation converter-based devices eigenvalue sensitivity matrix calculus small-signal stability Production of electric energy or power. Powerplants. Central stations TK1001-1841 Renewable energy sources TJ807-830
Acceso en línea:	https://doaj.org/article/a711cff589024004ad3b031bdddd3f9f
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id	oai:doaj.org-article:a711cff589024004ad3b031bdddd3f9f
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spelling	oai:doaj.org-article:a711cff589024004ad3b031bdddd3f9f2021-11-27T00:01:17ZA Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System2196-542010.35833/MPCE.2019.000225https://doaj.org/article/a711cff589024004ad3b031bdddd3f9f2021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9282059/https://doaj.org/toc/2196-5420With the rapid development of power-electronics-enabled power systems, the new converter-based generators are deteriorating the small-signal stability of the power system. Although the numerical differentiation method has been widely used for approximately calculating the eigenvalue sensitivities, its accuracy has not been carefully investigated. Besides, the ele-ment-based formulation for computing closed-form eigenvalue sensitivities has not been used in any commercial software due to the average efficiency, complicated formulation, and error-prone characteristics. Based on the matrix calculus, this paper proposes an easily manipulated formulation of the closed-form eigenvalue sensitivities with respect to the power generation. The distinguishing feature of the formulation is that all the formulas consist of vector and matrix operations, which can be performed by developed numerical algorithms to take full advantages of architectural features of the modern computer. The tests on WSCC 3-machine 9-bus system, New England to-ma-chine 39-bus system, and IEEE 54-machine 118-bus system show that the accuracy of the proposed formulation is superior to the numerical differentiation method and the efficiency is also greatly improved compared to the element-based closed-form formulation. The proposed formulation will be helpful to perform a more accurate and faster stability analysis of a power grid with converter-based devices.Peijie LiYucheng WeiJunjian QiXiaoqing BaiHua WeiIEEEarticleClosed-form formulationconverter-based deviceseigenvalue sensitivitymatrix calculussmall-signal stabilityProduction of electric energy or power. Powerplants. Central stationsTK1001-1841Renewable energy sourcesTJ807-830ENJournal of Modern Power Systems and Clean Energy, Vol 9, Iss 6, Pp 1436-1445 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Closed-form formulation converter-based devices eigenvalue sensitivity matrix calculus small-signal stability Production of electric energy or power. Powerplants. Central stations TK1001-1841 Renewable energy sources TJ807-830
spellingShingle	Closed-form formulation converter-based devices eigenvalue sensitivity matrix calculus small-signal stability Production of electric energy or power. Powerplants. Central stations TK1001-1841 Renewable energy sources TJ807-830 Peijie Li Yucheng Wei Junjian Qi Xiaoqing Bai Hua Wei A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System
description	With the rapid development of power-electronics-enabled power systems, the new converter-based generators are deteriorating the small-signal stability of the power system. Although the numerical differentiation method has been widely used for approximately calculating the eigenvalue sensitivities, its accuracy has not been carefully investigated. Besides, the ele-ment-based formulation for computing closed-form eigenvalue sensitivities has not been used in any commercial software due to the average efficiency, complicated formulation, and error-prone characteristics. Based on the matrix calculus, this paper proposes an easily manipulated formulation of the closed-form eigenvalue sensitivities with respect to the power generation. The distinguishing feature of the formulation is that all the formulas consist of vector and matrix operations, which can be performed by developed numerical algorithms to take full advantages of architectural features of the modern computer. The tests on WSCC 3-machine 9-bus system, New England to-ma-chine 39-bus system, and IEEE 54-machine 118-bus system show that the accuracy of the proposed formulation is superior to the numerical differentiation method and the efficiency is also greatly improved compared to the element-based closed-form formulation. The proposed formulation will be helpful to perform a more accurate and faster stability analysis of a power grid with converter-based devices.
format	article
author	Peijie Li Yucheng Wei Junjian Qi Xiaoqing Bai Hua Wei
author_facet	Peijie Li Yucheng Wei Junjian Qi Xiaoqing Bai Hua Wei
author_sort	Peijie Li
title	A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System
title_short	A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System
title_full	A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System
title_fullStr	A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System
title_full_unstemmed	A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System
title_sort	closed-form formulation of eigenvalue sensitivity based on matrix calculus for small-signal stability analysis in power system
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/a711cff589024004ad3b031bdddd3f9f
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A Closed-form Formulation of Eigenvalue Sensitivity Based on Matrix Calculus for Small-signal Stability Analysis in Power System

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