Active Harmonic Elimination in Multilevel Converters

The modulation technique for multilevel converters is a key issue for multilevel converter control. The traditional pulse width modulation (PWM), space vector PWM, and space vector control methods do not completely eliminate specified harmonics. In addition, space vector PWM and space vector control method cannot be applied to multilevel converters with unequal DC voltages. The carrier phase shifting method for traditional PWM method also requires equal DC voltages. The number of harmonics that can be eliminated by the selective harmonic elimination method is restricted by the number of unknowns in the harmonic equations and available solutions. For these reasons, this thesis develops a new modulation control method which is referred to as the active harmonic elimination method to conquer some disadvantages for the existing methods. The active harmonic elimination method contributes to the existing methods because it not only generates the desired fundamental frequency voltage, but also completely eliminates any number of harmonics without the restriction of the number of unknowns in the harmonic equations and available solutions for the harmonic equations. Also the active harmonic elimination method can be applied to both equal DC voltage cases and unequal DC voltage cases. Another contribution of the active harmonic elimination method is that it simplifies the optimal system performance searching by making a tradeoff between switching frequency and harmonic distortion. Experiments on an 11-level multilevel converter validate the active harmonic elimination method for multilevel converters

Rotationally symmetric harmonic diffeomorphisms between surfaces

In this paper, we show that the nonexistence of rotationally symmetric harmonic diffeomorphism between the unit disk without the origin and a punctured disc with hyperbolic metric on the target.Comment: Minor typos correcte

Elastic-Plastic Fracture Mechanics Analysis of a Tubular T-Joint in Offshore Structures

A tubular welded T-joint containing a series of semi-elliptical cracks of increasing depth located near the chord-brace intersection under both elastic and elastic-plastic conditions, has been analysed using shell elements with the cracks modelled by line springs. The same problem has also been modelled with 20 noded bricks allowing the stress intensity factor and J integral to be determined by virtual crack extension. The direction of crack growth has been determined both using off-axis virtual crack extension, and solutions for kinked cracks, to determine the orientation which maximise either the strain energy release rate or the mode I stress intensity factor. The calculated crack path agrees with reported experiments. The stress intensity factors for straight and curved cracks in simple welded joints have been compared in terms of their effective depth. Finally, the stress field in single edge bars under mixed mode elastic-plastic loading condition relevant to tubular joints has been analysed, and the size requirement for J dominance is discussed

Non-quadratic Euclidean complete affine maximal type hypersurfaces for θ∈(0,(N−1)/N]\theta\in(0,(N-1)/N]

Bernstein problem for affine maximal type equation \begin{equation}\label{e0.1} u^{ij}D_{ij}w=0, \ \ w\equiv[\det D^2u]^{-\theta},\ \ \forall x\in\Omega\subset{\mathbb{R}}^N \end{equation} has been a core problem in affine geometry. A conjecture proposed firstly by Chern (Proc. Japan-United States Sem., Tokyo, 1977, 17-30) for entire graph and then extended by Trudinger-Wang (Invent. Math., {\bf140}, 2000, 399-422) to its full generality asserts that any Euclidean complete, affine maximal type, locally uniformly convex $C^4$-hypersurface in ${\mathbb{R}}^{N+1}$ must be an elliptic paraboloid. At the same time, this conjecture was solved completely by Trudinger-Wang for dimension $N=2$ and $\theta=3/4$, and later extended by Jia-Li (Results Math., {\bf56} 2009, 109-139) to $N=2, \theta\in(3/4,1]$ (see also Zhou (Calc. Var. PDEs., {\bf43} 2012, 25-44) for a different proof). On the past twenty years, much efforts were done toward higher dimensional issues but not really successful yet, even for the case of dimension $N=3$. Recently, counter examples were found in \cite{Du2} (J. Differential Equations, {\bf269} (2020), 7429-7469) for $N\geq3$ and $\theta\in(1/2,(N-1)/N)$ using a much more complicated argument. In this paper, we will construct explicitly various new Euclidean complete affine maximal type hypersurfaces which are not elliptic paraboloid for the improved range $$N\geq2, \ \ \theta\in(0,(N-1)/N].$$Comment: arXiv admin note: text overlap with arXiv:2103.0892