Analysis and Prediction of Electric Power System’s Stability Based on Virtual State Estimators

Bakhtadze, Natalia; Yadikin, Igor B.

doi:10.3390/math9243194

Cited by 4 publications

(4 citation statements)

References 28 publications

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“…The use of canonical forms of controllability allow to propose a pioneering approach to computation of Gramians based on the use of Routh tables and Xiao matrices. This paper proposes to improve this approach by using spectral decompositions of the Gramians and the representation of the resolvent of the dynamics matrix by extending the scope to multivariable linear and bilinear control systems [11,[26][27][28][29].…”

Section: Main Contributionmentioning

confidence: 99%

“…In Section 3, we propose to use the representation of the dynamics matrix resolvent of continuous linear stationary systems with many inputs and one output (MISO LTI) in the form of a Faddeev-Levereux series segment for Gramian decomposition [27,30]. Conversion of the state equations to the canonical form of controllability allowed us to exclude the right part of the Lyapunov equations and the Fadeev matrix from the spectral expansions of the Gramians.…”

Section: Main Contributionmentioning

confidence: 99%

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Spectral Decompositions of Gramians of Continuous Stationary Systems Given by Equations of State in Canonical Forms

Yadykin

2022

Mathematics

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The application of transformations of the state equations of continuous linear and bilinear systems to the canonical form of controllability allows one to simplify the computation of Gramians of these systems. In this paper, we develop the method and obtain algorithms for computation of the controllability and observability Gramians of continuous linear and bilinear stationary systems with many inputs and one output, based on the method of spectral expansion of the Gramians and the iterative method for computing the bilinear systems Gramians. An important feature of the concept is the idea of separability of the Gramians expansion: separate computation of the scalar and matrix parts of the spectral Gramian expansion reduces the sub-Gramian matrices computation to calculation of numerical sequences of their elements. For the continuous linear systems with one output the method and the algorithm of the spectral decomposition of the controllability Gramian are developed in the form of Xiao matrices. Analytical expressions for the diagonal elements of the Gramian matrices are obtained, and by making use of which the rest of the elements can be calculated. For continuous linear systems with many outputs the spectral decompositions of the Gramians in the form of generalized Xiao matrices are obtained, which allows us to significantly reduce the number of calculations. The obtained results are generalized for continuous bilinear systems with one output. Iterative spectral algorithms for computation of elements of Gramians of these systems are proposed. Examples are given that illustrate theoretical results.

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Section: Main Contributionmentioning

confidence: 99%

Section: Main Contributionmentioning

confidence: 99%

Spectral Decompositions of Gramians of Continuous Stationary Systems Given by Equations of State in Canonical Forms

Yadykin

2022

Mathematics

View full text Add to dashboard Cite

show abstract

“…The paper proposes to improve this approach by using spectral decompositions of the Gramians and the representation of the resolvent of the dynamics matrix by extending the scope to multivariable linear and bilinear control systems. [11,[26][27][28] In Section 3, we propose to use for Gramian decomposition the representation of the dynamics matrix resolvent of continuous linear stationary systems with many inputs and one output (MISO LTI) in the form of a Fadeev-Levereux series segment [29]. Conversion of the state equations to the canonical form of controllability allowed us to exclude the right part of the Lyapunov equations and the Fadeev matrix from the spectral expansions of the Gramians, This allowed us to further simplify the scalar part of the spectral expansions and to link the localization of the Gramian elements with the residues of the scalar transfer function of the linear system.…”

Section: Main Contributionmentioning

confidence: 99%

Spectral Decompositions of Gramians of Continuous Stationary Systems Given by Equations of State in Canonical Forms

Yadykin¹

2022

Preprint

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The application of transformations of the state equations of continuous linear and bilinear systems to the canonical form of controllability allows one to simplify the computation of Gramians of these systems. In the paper we developed the method and obtain algorithms for computation of the controllability and observability Gramians of continuous linear and bilinear stationary systems with many inputs and one output, based on the method of spectral expansion of the Gramians and the iterative method for computing the bilinear systems Gramians. An important feature of the concept is the idea of separability of the Gramians expansion: sep333arate computation of the scalar and matrix parts of the spectral Gramian expansion reduces the sub-Gramian matrices computation to calculation of numerical sequences of their elements. For the continuous linear systems with one output the method and the algorithm of the spectral decomposition of the controllability Gramian are developed in the form of Xiao matrices. Analytical expressions for the diagonal elements of the Gramian matrices are obtained, making use of which the rest elements can be calculated. For continuous linear systems with many outputs the spectral decompositions of the Gramians in the form of generalized Xiao matrices are obtained, which allows to significantly reduce the number of calculations. The obtained results are generalized for continuous bilinear systems with one output. Iterative spectral algorithms for computation of elements of Gramians of these systems are proposed. Examples are given that illustrate theoretical results.

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“…Therefore, the comprehensive, timely and accurate monitoring of the power system equipment health status ensures the stable operation of equipment, reduces the accidental shutdown rate and has a high investment-income ratio. To this end, researchers carried out systematic research on temperature, vibration, image and other aspects of various power system equipment, and obtained effective information characteristics [1][2][3]. In addition, artificial intelligence [4], deep learning [5] and neural network [6] have been used to realize fault monitoring of equipment.…”

Section: Introductionmentioning

confidence: 99%

HOG-SVM-Based Image Feature Classification Method for Sound Recognition of Power Equipments

Bai

Zhou²,

Cui

et al. 2022

Energies

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In this paper, a method of power system equipment recognition based on image processing is proposed. Firstly, we carry out wavelet transform on the sound signal of power system equipment collected from the site, and obtain the wavelet coefficient–time diagram. Then, the similarity of wavelet coefficients–time images of different equipment and the same equipment in different periods is calculated, which is used as the basis of the feasibility of image recognition. Finally, we select the HOG features of the image, and classify the selected features using SVM classifier. The method proposed in this paper can accurately identify and classify power system equipment through sound signals, and is different from the traditional method of classifying sound signals directly. The advantages of image processing can be effectively utilized through image processing to avoid the limitations of sound signal processing.

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Analysis and Prediction of Electric Power System’s Stability Based on Virtual State Estimators

Cited by 4 publications

References 28 publications

Spectral Decompositions of Gramians of Continuous Stationary Systems Given by Equations of State in Canonical Forms

Spectral Decompositions of Gramians of Continuous Stationary Systems Given by Equations of State in Canonical Forms

Spectral Decompositions of Gramians of Continuous Stationary Systems Given by Equations of State in Canonical Forms

HOG-SVM-Based Image Feature Classification Method for Sound Recognition of Power Equipments

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