Hexagonal Circuit Research Articles

Study of Partial-Phase Steady-State Operation Modes of Phase-Shift Transformer with Hexagonal Circuit and Regulating Autotransformer

The scope of the work was the study of the phase failure operating for the new FACT’s type phase-shifting device, intended for the flexible connection of AC power systems. The mathamatical model has been developed for conducting this study. The device contains the main phase-shifting transformer based on hexagon circuit with additional regulating autotransformer, this creates the possibility of circular regulation of phase shift angle between connected systems. The model includes two 6-winding three-legs transformers, for which two sets of parameters can be independently set based on the data for the short circuit and no-load modes. The data for the direct sequence parameters is usually provided by the transformer manufacturers, and the data for the zero sequence parameters could be obtained upon additional request. As a result of modeling, the vectors of the voltages and currents were obtained in all windings in the investigated modes with supply source phase failure. This makes it possible to analyze the admissibility of such modes and estimate the need for taking special measures of protection against them. It is shown that the voltages on the windings of the main transformer insignificantly depend on the connection mode of the regulating autotransformer, while the pattern of currents distribution in the windings of the main and regulating transformers to a large extent is determined by said connection mode of the autotransformer. The presence of perceptible zero-sequence current flowing through the grounded neutrals of the power supply source and load is noticed. This fact is connected with the release of insignificant magnetic flux from the magnetic circuit in the surrounding space

Derivation and reduction of the singular Fornasini–Marchesini state‐space model for a class of multidimensional systems

This study is devoted to derive the singular Fornasini–Machesini (F-M) state-space model for a class of MIMO multidimensional (n -D) systems represented by non-causal multivariate transfer function matrices. It is shown, first, that the singular n -D F-M realisation can be generated by using the realisation methods of the standard n -D F-M models. Since the resulted realisations are usually non-minimal and deriving a minimal realisation is an extremely difficult problem, a model-order reduction method is developed. In particular, the common eigenvector approach is proposed, which significantly reveals the relationship among the reducibility, the eigenvalues and the eigenvectors associated with a given singular F-M state-space model. An example of spatially interconnected, hexagonal circuit is also given to illustrate some details and confirm the effectiveness of the proposed method.

Very Fast Electron Migrations within p-Doped Aromatic Cofacial Arrays Leading to Three-Dimensional (Toroidal) π-Delocalization

The charge-resonance phenomenon originally identified by Badger and Brocklehurst lies at the core of the basic understanding of electron movement and delocalization that is possible within p-doped aromatic (face-to-face) arrays. To this end, we now utilize a series of different aryl-donor groups (Ar) around a central platform to precisely evaluate the intramolecular electron movement among these tethered redox centers. As such, the unique charge-resonance (intervalence) absorption bands observed upon the one-electron oxidation or p-doping of various hexaarylbenzenoid arrays (Ar6C6) provide quantitative measures of the reorganization energy (lambda) and the electronic coupling element (H(ab)) that are required for the evaluation of the activation barrier (deltaG(ET)) for electron-transfer self-exchange according to Marcus-Hush theory. The extensive search for viable redox centers is considerably aided by the application of a voltammetric criterion that has led in this study to Ar = N,N-dialkyl-p-anilinyl, in which exceptionally low barriers are shown to lie in the range deltaG(ET) = 0.3-0.7 kcal mol(-1) for very fast electron hopping or peregrination around the hexagonal circuit among six equivalent Ar sites. Therefore, at transition temperatures T(t) > 0.5/R or roughly -20 degrees C, the electron-transfer dynamics become essentially barrierless since the whizzing occurs beyond the continuum of states and effectively achieves complete pi-delocalization.