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Analysis of three-phase systems with neutral under distorted and unbalanced conditions in the symmetrical component-based framework
Triplen harmonics: myths and reality
In a symmetrical and balanced three-phase system with distorted waveforms, a well-known rule states that each harmonic order corresponds to a specified sequence (positive, negative or zero). In this ideal case, the current in the neutral conductor (or more generally in the return path) contains only triplen harmonics. However, this rule is no longer valid in practical distribution systems subject to unbalance and waveform distortion, in which phase and neutral currents at any sequence generally contain components of any harmonic order. Possible improper extension of the ideal case concepts to general situations may create a sort of myth, to be removed by providing tutorial and practical examples. This paper provides a direct quantification of the extent to which non-triplen harmonics are present in the zero-sequence current components and triplen harmonics are present in the positive and negative sequence current components. An original set of indicators, built on the basis of the theoretical symmetrical component-based framework developed by the authors, is introduced for assessing the specific impact of the triplen harmonics at the different sequences. Some classical myths based on the ideal case are illustrated and discussed on specific examples including theoretical cases and experimental analyses, quantifying the actual role played by the triplen harmonics in these applications
Energy release rate and stress intensity factor in antiplane elasticity
In the setting of antiplane linearized elasticity, we show the existence of the stress intensity factor and its relation with the energy release rate when the crack path is a C(1.1) curve. Finally, we show that the energy release rate is continuous with respect to the Hausdorff convergence in a class of admissible cracks
Experimental evaluation and interpretation of the harmonic distortion in unbalanced systems
Limits of Dirichlet problems in perforated domains: a new formulation
Sia A un operatore ellittico lineare del secondo ordine con coefficienti
misurabili e limitati su un aperto limitato di
, sia
e sia un'arbitraria successione di sottoinsiemi aperti
di . Dimostriamo il seguente risultato di compattezza: esistono
una sottosuccessione, che indichiamo ancora con ed una
funzione w{*} K{*} tali che, per ogni f
, le soluzioni u delle
equazioni Au = f in , estese a zero su ,
convergano debolmente in all'unica
soluzione u del problema.
Studiamo inoltre in maniera sistematica le proprietà delle soluzioni
di tale equazione. Dimostriamo infine il seguente risultato di densità:
per ogni w{*}K{*} esiste una successione
di sottoinsiemi aperti di tali che per ogni f
le soluzioni u dell'equazione
Au=f in , estese a zero convergano
debolmente in alla soluzione di ({*}).Let A be a linear elliptic operator of the second order with bounded
measurable coefficients on a bounded open set of
, let
and let be an arbitrary sequence of open subsets of
. We prove the following compactness result: there exist
a subsequence, still denoted by and a function w{*}
K{*} such that, for every f
, the solutions u
of the equation Au = f in , extended by zero
on , converge weakly in
to the unique solution u of the problem.
We provide a self-contained study of the properties of the solutions
of ({*}). We prove also the following density result: for any w{*}K{*}
there exists a sequence of open subsets of
such that for every f the
solutions u of the
equation Au=f in , extended by zero on
converge weakly in to the solution
of ({*})
Operational and computational aspects of the neutral conductor interruption in low-voltage distribution systems
Proc. 4th Symposium CEE 200
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