Magnetic core saturation of transformers and rotating machines generate harmonics. Harmonics are integer multiples of the fundamental frequency. Harmonics is caused by nonlinear devices in the power system. Due to the non-linear loads, power frequency harmonics exist mainly in distribution systems. The current harmonics cause voltage harmonics, hence resulting in nonsinusoidal supply voltage in...

At least two modes of pitch perception exist: in one, the fundamental frequency (F0) of harmonic complex tones is estimated using the temporal fine structure (TFS) of individual low-order resolved harmonics; in the other, F0 is derived from the temporal envelope of high-order unresolved harmonics that interact in the auditory periphery. Pitch is typically more accurate in the former than in the...

In these notes I will describe the separation of variable technique for solving Laplace’s equation, using spherical polar coordinates. The solutions will involve Legendre polynomials for cases with azimuthal symmetry, and more generally they will involve spherical harmonics. I will construct these solutions using traceless symmetric tensors, but in Lecture Notes 8 I describe how the solutions i...

In this paper, for bus voltage control and to reduce power system harmonics, the active filtering technique is used in the mechanism of wind turbine control. Here a grid-connected doubly fed induction generator (DFIG) is considered in a wind turbine. In addition to harmonics that are related to the DFIG, a nonlinear load is also added to the system to simulate loads that produce more harmonics....

We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this paper, we suggest two possible reasons for the paucity relative to...

The objective of the electric utility is to deliver sinusoidal voltage at fairly constant magnitude throughout their system. This objective is complicated by the fact that there are loads on the system that produce harmonics currents. These currents result in distorted voltages and currents that can adversely impact the system performance in different ways. When harmonic currents flow through t...

We solved one dimensional Schrodinger equation in a H2+ molecular environment by using 3 femtosecond homogeneous and nonhomogeneous laser fields. In homogeneous case, we found out that larger inter nuclear distances result in earlier ionization and also more instability in the wave packet. We deducted that the more the instability is, the more modulated the power spectrum will be. So, by choosi...

introduction:  the  use  of  mobile  communication  systems  has  dramatically  increased  over  the  past  decade. although many studies have been performed to determine the effect of radio frequency (rf) but  less attention has been paid to the possible biological impact of exposure to extremely low frequency  (elf) components.   the objective of this study is two folds. one is to design the ...

We introduce the reader to the mathematics behind projection of n-dimensional vectors into a basis on n-dimensional space, where n can be anything upto and including infinity. We show how ideally one wants to project into the duals of a basis if this basis is not orthonormal, and provide the mathematics to formulate this operation in matrix form. The second part of the article discusses spheric...

In this paper we present the first practical method for importance sampling functions represented as spherical harmonics (SH). Given a spherical probability density function (PDF) represented as a vector of SH coefficients, our method warps an input point set to match the target PDF using hierarchical sample warping. Our approach is efficient and produces high quality sample distributions. As a...