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Online monitoring of the power system stability based on the critical clearing time

Eleschová Žaneta, Beláň Anton, Cenký Matej, Bendík Jozef, Cintula Boris, Janiga Peter

Przegląd Elektrotechniczny

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2021

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R. 97, nr 6

122--127

EN

This work refers to the concept of online monitoring of generators' dynamic stability based on the critical clearing time (hereinafter referred to as "CCT"). The CCT may be considered a basic criterion of the dynamic stability of a synchronous generator. The work presents an analysis of factors (operating condition of a generator, short-circuit power of the system, increase of the proportion of distributed production in the distribution system (hereinafter referred to as "DS ") influencing the CCT and analysis of possibilities to increase the value of the CCT. In this work, we present a relatively simple concept built on the calculation of the CCT using a swing equation, which may be implemented into the dispatch control of power systems (hereinafter referred to as "PS").

PL

Praca odnosi się do koncepcji monitorowania online dynamicznej stabilności generatorów w oparciu o krytyczny czas rozliczeniowy (zwany dalej „CCT”). CCT można uznać za podstawowe kryterium stabilności dynamicznej generatora synchronicznego. W pracy dokonano analizy czynników (stan pracy generatora, moc zwarciowa systemu, zwiększenie udziału produkcji rozproszonej w systemie dystrybucyjnym (dalej „DS”) wpływających na CCT oraz analizę możliwości zwiększyć wartość CCT W pracy przedstawiamy stosunkowo prostą koncepcję opartą na obliczeniu CCT za pomocą równania wahadłowego, która może zostać zaimplementowana w sterowaniu dyspozycją systemów elektroenergetycznych (dalej „PS”).

2

The basis property of eigenfunctions in the problem of a nonhomogeneous damped string

Rzepnicki Ł.

Opuscula Mathematica

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2017

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Vol. 37, no. 1

141--165

EN

The equation which describes the small vibrations of a nonhomogeneous damped string can be rewritten as an abstract Cauchy problem for the densely defined closed operator iA. We prove that the set of root vectors of the operator A forms a basis of subspaces in a certain Hilbert space H. Furthermore, we give the rate of convergence for the decomposition with respect to this basis. In the second main result we show that with additional assumptions the set of root vectors of the operator A is a Riesz basis for H.

3

Zastosowanie równań różniczkowych cząstkowych drugiego stopnia w zagadnieniach technicznych

Biały J., Gołębiowski J.

Zeszyty Naukowe / Wyższa Szkoła Oficerska Sił Powietrznych

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2013

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Nr 1

9--21

PL

Niniejszy artykuł ma za zadanie przybliżyć zagadnienie dotyczące rozwiązania równania struny i membrany metodą Fouriera, pokazać sposób jej wykorzystania w różnych dziedzinach.

EN

The following article is intended to focus on the problem pertaining to the solution of string and membrane equation with Fourier’s method as well as to show its applications in various fields.

4

Exact controllability for the semilinear string equation in non cylindrical domains

Araruna F. D., Antunes G. O., Medeiros L. A.

Control and Cybernetics

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2004

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Vol. 33, no 2

237-257

EN

In this paper, we investigate the exact controllability for a mixed problem for the equation u^n - [...] + f(u) = 0 in a non cylindrical domain. This model, without the resistance represented for f(u), is a linearization of Kirchhoff's equation for small vibrations of a stretched elastic string when the ends are variables, see Medeiros, Limaco, Menezes (2002). We employ a variant, due to Zuazua (1990b), of the Hilbert Uniqueness Method (HUM), idealized by Lions (1988a, b).

5

Ingham-Type Inequalities and Riesz Bases of Divided Differences

Avdonin S., Moran W.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 4

803-820

EN

We study linear combinations of exponentials e^{i lambda_n t}, lambda_n in Lambda in the case where the distance between some points lambda_n tends to zero. We suppose that the sequence Lambda is a finite union of uniformly discrete sequences. In (Avdonin and Ivanov, 2001), necessary and sufficient conditions were given for the family of divided differences of exponentials to form a Riesz basis in space L^2 (0,T). Here we prove that if the upper uniform density of Lambda is less than T/(2 pi), the family of divided differences can be extended to a Riesz basis in L^2 (0,T) by adjoining to {e^{i lambda_n t} } a suitable collection of exponentials. Likewise, if the lower uniform density is greater than T/(2 pi), the family of divided differences can be made into a Riesz basis by removing from {e^{i lambda_n t} } a suitable collection of functions e^{i lambda_n t}. Applications of these results to problems of simultaneous control of elastic strings and beams are given.