Harmonics in the Squirrel Cage Induction Motor Analytic Calculation Part III: Influence on the Torque-speed Characteristic

The harmonics that appear in the squirrel cage asynchronous machine have been discussed in great detail in the literature for a long time. However, the systematization of the phenomenon is still pending, so we made an attempt to fill this gap in the previous parts of our study by elaborating formulas for calculation of parasitic torques. It was a general demand among those who work in this field towards the author to verify his formulas with measurements. In the literature, it seems,only one detailed, purposeful series of measurements has been published so far, the purpose of which was to investigate the effect of the number of rotor slots on the torque-speed characteristic curve of the machine. The main goal of this study is to verify the correctness of the formulas by comparing them with the referred series of measurements. Relying on this, the expected synchronous parasitic torques were developed for the frequently used rotor slot numbers-as a design guide for the engineer.Thus, together with our complete table for radial magnetic pull published in our previous work, the designer has all the principles, data and formulas available for the right number of rotor slots for his given machine and for the drive system. This brings this series of papers to an end.

Harmonic Bergman Metric

We have constructed the positive definite metric matrixes for the bounded domains of R^n and proved an inequality which is about the Jacobi matrix of a harmonic mapping on a bounded domain of R^n and the metric matrix of the same bounded domain.

Harmonic State Space Based Impedance Modeling and Virtual Impedance Based Stability Enhancement Control for LCC-HVDC Systems

Line commutated converter based high-voltage direct-current(LCC-HVDC)transmissions are prone to harmonic oscillation under weak grids.Impedance modeling is an effective method for assessing interaction stability.Firstly,this paper proposes an improved calculation method for the DC voltage and AC currents of commutation stations to address the complex linearization of the commutation process and constructs an overall harmonic state-space(HSS)model of an LCC-HVDC.Based on the HSS model,the closed-loop AC impedances on the LCC-HVDC sending and receiving ends are then derived and verified.The impedance characteristics of the LCC-HVDC are then analyzed to provide a physical explanation for the harmonic oscillation of the system.The effects of the grid strength and control parameters on system stability are also analyzed.To improve the impedance characteristics and operating stability of the LCC-HVDC system,a virtual impedance based stability enhancement control is proposed,and a parameter design method is considered to ensure satisfactory phase margins at both the sending and receiving ends.Finally,simulation results are presented to verify the validity of the impedance model and virtual impedance based stability enhancement control.

Harmonic Impedance Modeling and Oscillation Analysis of Modular Multilevel Converter

To facilitate rapid analysis of the oscillation stability mechanism in modular multilevel converter-based high voltage direct current(MMC-HVDC)systems and streamline the simulation process for determining MMC impedance characteristics,a simplified mathematical simulation model for MMC closed-loop impedance is developed using the harmonic state space method.This model considers various control strategies and includes both AC-side and DC-side impedance models.By applying a Nyquist criterion-based impedance analysis method,the stability mechanisms on the AC and DC sides of the MMC are examined.In addition,a data-driven oscillation stability analysis method is also proposed,leveraging a global sensitivity algorithm based on fast model results to identify key parameters influencing MMC oscillation stability.Based on sensitivity analysis results,a parameter adjustment strategy for oscillation suppression is proposed.The simulation results from the MATLAB/Simulinkbased MMC model validate the effectiveness of the proposed method.

Commuting dual Toeplitz operators on the harmonic Bergman space

We completely characterize commuting dual Toeplitz operators with bounded harmonic symbols on the harmonic Bergman space of the unit disk. We show that for harmonic ■ and ψ, S■Sψ= SψS■ on(L2h)⊥if and only if ■ and ψ satisfy one of the following conditions:(1) Both ■ and ψ are analytic on D.(2) Both ■ and ψ are anti-analytic on D.(3) There exist complex constants α and β, not both 0, such that ■ = αψ + β.Furthermore, we give the necessary and sufficient conditions for S■Sψ= S■ψ.

Commuting Dual Toeplitz Operators on the Harmonic Dirichlet Space

In this paper, we characterize the symbols for （semi-）commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space. We show that for φ ,ψ ∈ W1, ∞, SφSψ = SψSφ on （Dh）⊥ if and only if φ and ψ satisfy one of the following conditions： （1） Both φ and ψ are harmonic functions; （2） There exist complex constants α and β, not both O, such that φ = αφ＋β.

Algebraic Properties of Toeplitz and Small Hankel Operators on the Harmonic Bergman Space

In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.

Positivity of Toeplitz Operators on Harmonic Bergman Space

In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator.

Product of Toeplitz Operators on the Harmonic Dirichlet Space

In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product of two Toeplitz operators is another Toeplitz operator only if one factor is constant.

Dual Toeplitz Operators on the Orthogonal Complement of the Harmonic Bergman Space

In this paper,we characterize that the boundedness,compactness and spectral structure of dual Toeplitz operators acting on the orthogonal complement of the harmonic Bergman space.This generalizes the corresponding results for dual Toeplitz operators on the orthogonal complement of the Bergman space due to Stroethoff and Zheng’s paper[Trans.Amer.Math.Soc.,354,2495–2520(2002)].

Hyponormal Dual Toeplitz Operators on the Orthogonal Complement of the Harmonic Bergman Space

In this paper,we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space.First we show that the dual Toeplitz operator with the bounded symbol is hyponormal if and only if it is normal.Then we obtain a necessary and sufficient condition for the dual Toeplitz operator S_(φ) with the symbol φ(z)=az^(n1zm1)+bz^(n2zm2)(n1,n2,m1,m2∈N and a,b∈C)to be hyponormal.Finally,we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a finite rank.

Carleson Type Measures for Harmonic Mixed Norm Spaces with Application to Toeplitz Operators

Let Ω be a bounded domain in Rnwith a smooth boundary, and let h p,q be the space of all harmonic functions with a finite mixed norm. The authors first obtain an equivalent norm on h p,q, with which the definition of Carleson type measures for h p,q is obtained. And also, the authors obtain the boundedness of the Bergman projection on h p,q which turns out the dual space of h p,q. As an application, the authors characterize the boundedness(and compactness) of Toeplitz operators T μ on h p,q for those positive finite Borel measures μ.

The Role of Forced Oscillators of Coupled Circuits in Radiation Physics: New Linear Accelerator Design Improving Tomo-Scanning Technology (Radiotherapy and CT), Heisenberg-Euler Scatter, and Extension to Bremsstrahlung with GeV Electrons

The quantization of circuits has received to be rather attractive in domains of solid state—molecular—and biophysics, since the quanta referred to as Q-bits play a significant role in the design of the quantum computer and entangled structures. Quantized circuits cannot be applied without modifications, since the energy differences are not equidistant and the polarization of the excited states has to be accounted for having particular importance for the creation of virtual states. Applications of the presented theory are scanning methods in radiotherapy without multi-leaf collimators, which may be realized in tomo-scanning radiotherapy and in the keV domain, which provides a new design of CT. The problem of lateral scatter in the target and energy storage by heat production is significantly reduced by a multilayer system with focusing the impinging electrons at the walls and by a magnetic field. The verification of the Heisenberg-Euler scatter of crossing beams of 9 MV is a central problem of photon physics and can be solved by the new bremsstrahlung technique. A comparison with GEANT 4 Monte-Carlo data indicates that the presented method also works in the GeV domain, and a multi-target can improve the bremsstrahlung yield. GEANT 4 provides the spatial distribution, whereas the virtual oscillator states only show the created energy spectrum. In every case, the exploitation yield can be drastically improved by the superiority of the focused multitarget system compared to a single standard target, and the door to new technologies is opened.

The spectrum of Bergman Toeplitz operators with some harmonic symbols

In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .

Hyponormality of Toeplitz Operators on the Dirichlet Space

In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.

A Note on the Maximal Functions on Weighted Harmonic AN Groups

In this paper, the authors point out that the methods used by Li(2004, 2005,2007) can be applied to study maximal functions on weighted harmonic AN groups.

A SEMI-ANALYTICAL METHOD FOR THE VIBRATION OF AND SOUND RADIATION FROM A TWO-DIMENTIONAL BEAM-STIFFENED PLATE

A semi-analytical method based on space harmonics to investigate the vibration of and sound radiation from an infinite, fluid-loaded plate is presented. The plate is reinforced with two sets of orthogonally and equally spaced beam stiffeners, which are assumed to be line forces. The response of the stiffened plate to a convected harmonic pressure in the wave-number space is obtained by adopting the Green＇s function and Fourier transform methods. Using the boundary conditions and space harmonic method, we establish the relationship between the stiffener forces and the vibration displacement of the plate. In this paper, the stiffener forces are expressed in terms of harmonic amplitudes of the plate displacement, which are calculated by using a numerical reduction technique. Finally, the Fourier inverse transform is employed to find expressions of the vibration and sound radiation in physical space. Agreements with existing results prove the validity of this approach and more numerical results are presented to show that this method converges rapidly.

Reproducing Kernel for D^2(Ω,ρ) and Metric Induced by Reproducing Kernel

An important property of the reproducing kernel of D2(Ω,ρ) is obtained and the reproducing kernels for D2(Ω,ρ) are calculated when Ω = Bn × Bn and ρ are some special functions.A reproducing kernel is used to construct a semi-positive definite matrix and a distance function defined on Ω×Ω.An inequality is obtained about the distance function and the pseudo-distance induced by the matrix.