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Application of genetic algorithm for optimal placement of wind generators in the MV power grid

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The paper presents a modelling method of optimal connection of wind generators to a medium voltage (MV) power grid taking into account minimum active power losses. A genetic algorithm was applied to optimize active power losses in the power grid. Streszczenie. W Pracy przedstawiono metodę modelowania optymalnego podłączenia elektrowni wiatrowych do sieci elektroenergetycznych średniego napięcia. Minimalizowano straty mocy czynnej w sieci stosując w tym celu algorytm genetyczny. (Zastosowanie algorytmu genetycznego do optymalnego rozmieszczenia turbozespołów wiatrowych w elektroenergetycznej sieci średniego napięcia) Keywords: genetic algorithm, wind generators, power grid. Słowa kluczowe: algorytmy genetyczne, elektrownie wiatrowe, sieci elektroenergetyczne. Introduction Due to a great interest in connecting wind generators into medium voltage power grids, a current problem arises of using the existing power grid infrastructure in an optimal way. In this case it is reasonable to consider two optimization aspects: - operating optimization of the existing power generating units (or their possible reconstruction), - or, optimal placement of power generating units to be installed at specific places. The former problem was presented in paper [1], the latter is considered below. The paper presents an example of an optimal solution of placing wind generators over a specific area using a method based on a genetic algorithm. The area analyzed encompasses a surface of 81 square kilometers including the existing medium voltage infrastructure. Figure 1 presents a topological segment of a medium voltage power grid where a connection of wind generators is planned. The aim of the optimization procedure is to determine the connection nodes for wind generators characterized by specific rate powers in such a way as to obtain minimum power losses in the analyzed segment. The planned objective should be reached considering the following limitati[...]

Criterion for transient behaviour in a nonlinear Duffing oscillator DOI:10.15199/48.2019.04.36

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From a practical point of view, to determine the duration of transient behavior in nonlinear physical systems constitutes both an important and interesting problem. Transient behaviour occurs both in mechanical systems as well as electrical and electronic ones. In stable linear systems, it is assumed that the transient process fades after a time equal to five time constants. For an autonomous system analysis a more exact assessment of the duration of transients was presented in [1]. It used a Lyapunov function to define time ttr, in which the trajectory of an autonomous system, starting from the initial state, reaches a specific area including the origin of the coordinate system. In that case, ttr≤-ϑlnV[x(ttr)]/V[x(0)], where V[x] is a Lyapunov function, while ϑ is the largest eigenvalue of a matrix determined from dependency . max( ( ) / ( )) x   V x V x . The analysis of transient behaviour in nonlinear systems is more complicated as the superposition principle cannot be used here and, as a result, transient and steady components cannot be separated. In harmonic enforcement, nonlinear systems are characterized by the occurrence of a non-sinusoidal response. In many cases, they are systems with chaotic dynamics in which transient chaos are distinguished [2, 11]. The duration of the transient behaviour depends, among others, on the choice of initial conditions and the values of the system parameters. A great number of physical phenomena are modeled by basic differential equations. For example, vibrations in electrical, electronic and mechanical systems can be analyzed using the Duffing equation [3, 4]. The system of three Lorenz equations has been used to characterize the convective movement occurring, for instance, in the Earth's atmosphere [5, 6]. Electronic oscillators with non-linear damping are described by Van der Pol's equation [7, 8]. Below, we present a brief overview of [...]

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