Showing papers on "Harmonics published in 1985"

Power System Harmonics

Abstract: Preface Introduction Harmonic Analysis Harmonic Sources - The Static Convertor Other Harmonic Sources Harmonic Effects: Within the Power System Interference with Communications Power System Harmonic Measurements Transducers and Data Transmission Standards for the Limitation and Control of Power System Harmonics Harmonic Penetration in A.C. Systems Harmonic Elimination Index.

Relative dominance of individual partials in determining the pitch of complex tones

Abstract: These experiments were conducted to determine the dominance of each partial in determining the residue pitch of a complex tone. Subjects were required to make pitch matches to a complex tone which had one partial slightly mistuned from its ‘‘correct’’ harmonic value. The shift in residue pitch was measured as a function of the frequency shift of the harmonic, for each harmonic in turn. For mistunings up to ±2%–3% the shift in residue pitch was approximately a linear function of the shift in the harmonic, but for greater mistunings the shift in residue pitch was reduced. The degree to which a given harmonic can influence residue pitch gives a measure of the dominance of that harmonic. The dominant harmonics were always contained within the lowest six harmonics (for fundamental frequencies of 100, 200, and 400 Hz), but there were marked individual differences in the exact distribution of dominance across harmonics. The level of a harmonic relative to adjacent harmonics can have a significant effect on its dominance. The implications of the results for theories of pitch perception are discussed.

The Effects of Power System Harmonics on Power System Equipment and Loads

Abstract: This report is intended to present a summary of current knowledge regarding the effects of power system harmonics on system equipment and loads. The purpose of this summary is two-fold: first, to lay a groundwork for the study and control of system harmonics; and second, to promote a discussion with those closely involved with each of the various load types.

Thresholds for the detection of inharmonicity in complex tones

Abstract: Thresholds were measured for the detection of inharmonicity in complex tones. Subjects were required to distinguish a complex tone whose partials were all at exact harmonic frequencies from a similar complex tone with one of the partials slightly mistuned. The mistuning which allowed 71% correct identification in a two‐alternative forced‐choice task was estimated for each partial in turn. In experiment I the fundamental frequency was either 100, 200, or 400 Hz, and the complex tones contained the first 12 harmonics at equal levels of 60 dB SPL per component. The stimulus duration was 410 ms. For each fundamental the thresholds were roughly constant when expressed in Hz, having a mean value of about 4 Hz (range 2.4–7.3 Hz). In experiment II the fundamental frequency was fixed at 200 Hz, and thresholds for inharmonicity were measured for stimulus durations of 50, 110, 410, and 1610 ms. For harmonics above the fifth the thresholds increased from less than 1 Hz to about 40 Hz as duration was decreased from 1610–50 ms. For the lower harmonics (up to the fourth) threshold changed much less with duration, and for the three shorter durations thresholds for each duration were roughly a constant proportion of the harmonic frequency. The results suggest that inharmonicity is detected in different ways for high and low harmonics. For low harmonics the inharmonic partial appears to ‘‘stand out’’ from the complex tone as a whole. For high harmonics the mistuning is detected as a kind of ‘‘beat’’ or ‘‘roughness,’’ presumably reflecting a sensitivity to the changing relative phase of the mistuned harmonic relative to the other harmonics. The results are discussed in relation to theories of pitch perception.

A multifrequency phase fluorometer using the harmonic content of a mode-locked laser

Abstract: We describe the construction and operation of a cross-correlation phase and modulation fluorometer which uses the harmonic content of a high repetition rate mode-locked laser as the excitation source. A mode-locked argon ion laser is used to synchronously pump a dye laser. The pulse train output from the dye laser is amplitude modulated by an acousto-optic modulator and then frequency doubled with an angle tuned frequency doubler. With the particular dye utilized in these studies, the ultraviolet light obtained was continuously tunable over the range 280-310 nm. In the frequency domain the high repetition rate pulsed source gives a large series of equally spaced harmonic frequencies. The frequency spacing of the harmonics is determined by the repetition frequency of the laser. Amplitude modulation of the pulse train permits variation of the frequency quasi-continuously from a few hertz to gigahertz. Use of cross-correlation techniques permits precise isolation of individual frequencies. The cross...

Some Improved Forced Commutated Cycloconverter Structures

Abstract: Full automation in manufacturing processes has generated a considerable demand for ac motor drives and in particular static frequency changers (FC's). Forced commutated cycloconverters (FCC's) are frequency changers that can provide a wide output frequency range with minimum energy storage requirements. For this reason they can be manufactured in integrated form with significant savings in price, weight, and volume. These factors have generated considerable research activity toward the development of FCC structures that can compete with the typical rectifier-inverter structures. Some advanced FC cycloconverter structures with improved performance characteristics are considered. Areas of improvement include voltage utilization and generated harmonic distortion.

Radio frequency heating in the ion‐cyclotron range of frequencies

Abstract: Both the theory of the absorption process in the ion‐cyclotron range of frequencies and some of the experiments which slow the promise and problems with radio frequency plasma heating in this range are discussed. It is shown that mode conversion is invariably involved in the process and so an extensive review of mode conversion theory, expecially as it applies to problems with back‐to‐back cutoff‐resonance pairs, is included. This includes a discussion of the tunneling equation with and without absorption effects and with and without energy conservation. The general theory is applied to various ion‐cyclotron harmonics, the two‐ion hybrid resonance, and to a case where a wave converts to a Bernstein mode at the plasma edge. The results are given analytically for a variety of cases without absorption, and empirical formulas are given for the second and third harmonics of the ion‐cyclotron frequency, which include effects of absorption. Various problem areas in the theory are also discussed with some of the limitations caused by the approximations involved. A number of experiments are also discussed which show effective heating, and some show the features of the mode conversion process, indicating that the general processes of absorption are reasonably well understood. Areas where further work is necessary, both in fundamental theory and in comparing theory with experiment, are also discussed.

Surface studies by optical second harmonic generation: An overview

Abstract: Optical second harmonic generation for surface and interface studies is briefly reviewed, with numerous examples illustrating how powerful and versatile this new surface analytical technique can be.

Some properties of hyperspherical harmonics

Abstract: A general formula is given for the canonical decomposition of a homogeneous polynomial of order λ in m variables into a sum of harmonic polynomials. This formula, which involves successive applications of the generalized Laplace operator, is proved in the Appendix. It is shown that the group‐theoretical method for constructing irreducible Cartesian tensors follows from the general formula for canonical decomposition. The relationship between harmonic polynomials and hyperspherical harmonics is discussed, and an addition theorem for hyperspherical harmonics is derived. An expansion of a many‐dimensional plane wave in terms of Gegenbauer polynomials and Bessel functions is derived and used to construct bicenter expansions of arbitrary functions in many‐dimensional spaces. Finally, a formula is derived for the 3λ coefficients of hyperspherical harmonics. These coefficients give the values of integrals involving the products of three harmonics.

A Design Method of Bandpass Filters Using Dielectric-Filled Coaxial Resonators (Short Papers)

Abstract: Design formulas for capacitively coupled bandpass filters using dielectric-filled coaxial resonators are derived and experimentally verified. The most important advantage of this filter is its ability to provide wide stopband characteristics for harmonics suppression. Its features can be obtained from the configuration using both quarter-wavelength uniform impedance resonators (UIR's) and stepped impedance resonators (SIR's).

A probabilistic mechanism for small disturbance instabilities in electric power systems

Abstract: Unstable, oscillatory behavior has been observed on several occasions in electrical power systems operated in an unfaulted, normal state under moderate load. In some cases system failure has resulted from this behavior. In this paper, we report on some recent results in the mathematics of stochastic processes which suggest a mechanism leading to small disturbance instabilities of this type in power systems. Unstable oscillations in power angles may be produced in a system consisting of a synchronous machine with negligible damping weakly coupled through randomly fluctuating links to other machines each with positive damping. The assumptions necessary to structure the model to produce this behavior are simple, flexible and consistent with possible operating conditions in an electrical power system.

The Vector Harmonic Analysis of Laplace's Tidal Equations

Abstract: A modal analysis is presented of the linearized shallow-water equations on the sphere called Laplace's tidal equations, using the spherical vector harmonics. The present approach is more compact and conceptually simpler than past analyses in which the order of the differential equation was raised. The modes, called Hough harmonics, are expressed as a series in the spherical Vector harmonics whose coefficients are then computed as the eigenvectors of an infinite, banded, symmetric, linear system of equations. The frequencies of the modes are determined as the eigenvalues of the banded system. New zonal rotational modes for zonal wavenumber $m = 0$ are obtained as the limit of Hough vector harmonics as m tends to zero. Although the zonal rotational modes are not unique, this new set of functions shares many properties with the nonzonal rotational modes, including orthogonality of characteristic functions. Some limiting cases of the Hough harmonics are also discussed, including the Haurwitz modes, which are determined as the limit of solutions to the untransformed shallow-water equations as the equivalent height tends to infinity. Finally, a description of the software for computing the Hough harmonics as well as the Haurwitz modes is presented. This software package is available from the National Center for Atmospheric Research and consists of four user-entry FORTRAN subroutines. Subroutine SIGMA computes the frequencies of the normal modes. Subroutine ABCOEF computes the coefficients in the expansion of the normal modes in terms of the spherical vector harmonics. Subroutine UVH tabulates the components of the meridional structure of the Hough vector functions and subroutine UVHDER tabulates certain derivatives of the components.

The relationship between monopole harmonics and spin-weighted spherical harmonics

Abstract: We compare two independent generalizations of the usual spherical harmonics, namely monopole harmonics and spin‐weighted spherical harmonics, and make precise the sense in which they can be considered to be the same. By analogy with the spin‐gauge language, raising and lowering operators for the monopole index of the monopole harmonics can immediately be written down.

Harmonic Filters for Six-Phase and Other Multiphase Motors on Voltage Source Inverters

Abstract: Inverter-driven motors having five, six, or more phases have smaller torque pulsations and lower rotor I 2 R loss due to harmonics than do their three-phase counterparts. However, they generally have higher stator harmonic currents. For example, six-phase motors, supplied by a six step voltage source inverters have fifth and seventh harmonic currents which are from two to five times as large as in a comparable three-phase motor. If the motor has five or more phases, these currents can be substantially reduced by the harmonic filter described. The filter consists of transformer-like devices connected in the leads between the inverter and motor. The coils on these are interconnected in a prescribed way so that they add negligible impedance for fundamental currents, but they add considerable impedance for most harmonics. Since the filters do not affect fundamental current, they do not affect the speed-torque characteristic. These filters are described for any number of phases, and equations to determine their inductance values for the various harmonics are developed. Their effectiveness is demonstrated by experimental results.

Phase-locked loop for MFM data recording

Abstract: A phase-locked loop (PLL) for use in decoding MFM data recordings. The loop uses a counter to generate timing signals which divide bitcells into data and clock windows and which define times within these windows at which transitions in the MFM signal are expected to occur. Data and clock windows of differing relative size are readily accomodated. The PLL has two synchronization modes: one mode allows the PLL to take maximum advantage of both data and clock transitions which occur when reading actual data; a second mode is used during the synchronization period at the beginning of a data block and allows the PLL to lock quickly yet assure that it will lock to the bit frequency and not lock to harmonics or beat frequencies. A charge pump generates the PLL error signal by responding to pump-up and pump-down control signals which are set and cleared in response to the timing signals from the counter and in response to the detection of transitions in the input signal. While in data mode, a second counter is used to control the charge pump when a transition occurs after the time the transition is expected to occur. The charge storage circuit of the charge pump control over loop dynamics. The PLL includes a VCO with an automatic dynamic adjustment of the VCO's center frequency which is accomplished by adjusting the reverse bias voltage on a diode that functions as the timing capacitor for the VCO. This adjustment allows the PLL to make maximal use of the VCO's range.

Tutorial on classical free electron laser theory

Abstract: A simple theoretical approach to the free electron laser is reviewed. Extensions of the Lorentz-Maxwell theory are straight forward and can be solved analytically, or on a small computer. A brief discussion looks at high-gain collective effects, short pulse effects, harmonics, energy spread and emittance, transverse diffraction, and noise.

Harmonically graded airgap reluctance-type rotating electric resolver

Abstract: This invention relates to a harmonically graded airgap reluctance-type rotating electric resolver. The magnetic permeance of the airgap is made to vary sinusoidally. Therefore, only the fundamental wave exists, free of higher harmonics. The invention has application in numerous fields, including commutation of brushless motors and to precisely position machinery tools relative to work pieces in numerically controlled machines.

Low-frequency digital lock-in amplifier

Abstract: A digital lock‐in amplifier which simultaneously measures in phase and in quadrature components at a reference frequency and at twice this frequency is described. It is drift free, insensitive to harmonics, has a very high gain stability (25 ppm/K), and operates up to 1250 Hz with no limitations on the low‐frequency side.

Intermediate-scale magnetic anomalies of the Earth

Abstract: Four separate magnetic anomaly maps of the earth are derived from magnetometer satellite data acquired at dawn and at dusk using two different altitude ranges. The magnetic anomalies on the two dawn maps (or dusk maps) are well correlated for spherical harmonics of degree less than 51, suggesting that the time varying external magnetic field and leveling noise have negligible effects on these harmonics. Dawn and dusk maps have an appreciable asymmetric component for harmonics of degree n ⩽ 5 and n = 15 and 17, arising from the quasi‐stable external magnetic field. Dawn‐dusk covariant harmonics of degree 18⩽n⩽60 with signal‐to‐noise ratios greater than 1.5 correlate well. Correlation coefficients are higher than 0.75, implying that these harmonics can be repeatably derived. A global scalar magnetic anomaly map is derived based on these harmonics. The map is then converted to a magnetic susceptibility anomaly map by an inversion technique. The susceptibility anomalies delineate the ocean‐continent differenc...

Harmonic Analysis Of Induction Watthour Meter Performance

Abstract: A mathematical nonlinear model is developed to simulate the performance of an induction watthour meter for nonsinusoidal voltage and current waves. The computation results show that for the special case where the voltage is purely sinusoidal, the measurement error causedby the nonlinear magnetic circuits is generally small unless the current wave contains a relatively large third harmonic component. However, when the voltage and current waves are both nonsinusoidal, the registration error can be relatively large even for a small voltage distortion. This is attributed not only to the nonlinearity but also to the drooping frequency response curve of the meter. In both cases, the sign of the registration error depends largely on the phase angles of voltage and current harmonics with respect to their fundamentals. A comparison shows that the computation results are consistent with the experimental ones which are available in the literature.

The Effect of Harmonics on the Operating Points of Electromechanical Relays

Abstract: This paper is concerned with the effect of harmonics on the operating points of three types of relays. These are standard electromechanical relays of the instantaneous overcurrent, instantaneous voltage and time overcurrent types.

Power Line Considerations for Variable Frequency Drives

Abstract: More frequent use of variable frequency drives requires that the interaction between the drives and the power line be considered in order to avoid undesirable power line effects caused by the drive. In addition, the power line characteristics need to be defined by the drive manufacturer which assure proper operation of the variable frequency drive. The potential effects the drive has on the power line is discussed, including line harmonics, line notching, and line noise. General approaches for minimizing effects and installation guidelines are also reviewed.

Multiple scale analysis of the nonlinear surface acoustic wave propagation in anisotropic crystals

Abstract: A fundamental theory of nonlinear Rayleigh wave propagation is given here. Previously, the harmonic boundary value problem was solved by means of a direct iterative procedure. The nonlinear acoustic field could only be studied near the excitation transducer. The method could not explain the nonmonotonous behavior of curves giving the amplitude of various harmonics as a function of the propagation distance. In this paper, amplitude and phase relations of harmonics are calculated also in the far field. Anisotropy effect is demonstrated in the first numerical results obtained for various quartz crystal cuts.

Compensation of depolarizing effects in electron-positron storage rings

Abstract: It is shown that the depolarizing effects in the arc of an electron-positron storage ring can be minimized by minimizing certain Fourier harmonics of the particle trajectories. In more detail it is shown that the strength of the depolarizing resonance [(g - 2)/2] γ = n ± Qx is related to the harmonics of the closed orbit, the strength of the depolarizing resonance [(g - 2)/2] γ = m ± Qz to the harmonics of the vertical betatron oscillations, and the strength of the depolarizing resonance [(g - 2)/2] γ = i ± Qs to the harmonics of the closed orbit and the dispersion orbit. For all these depolarizing resonances compensation schemes are discussed.

Emission of light at half‐integer harmonics of the laser frequency

Abstract: Calculations have been made of the spectrum of light emitted at half‐integer harmonics of the laser light frequency ω0 The emitted light results from either the Raman scattering of laser light by Langmuir waves or by the direct conversion of Langmuir waves to light The Langmuir wave amplitude is calculated from convective instability theory for two‐plasmon decay in an inhomogeneous, plane‐stratified medium The Raman scattering process generates harmonics at (n/2) ω0 where n=1,3,5 ; however, only for n=1 and 3 is the emission level significant The conversion process produces (1/2) ω0 light with a comparable efficiency to the Raman scattering process near the two‐plasmon instability threshold Results of the calculation are in agreement with the general features of measured emission spectra

The Derivation of Gear Transmission Error from Pitch Error Records

Abstract: The effect of pitch errors on the transmission error of a gear pair has been much studied. In particular, it has been thought that, if pitch error alone is present, the frequency spectrum of the corresponding transmission error will have no components either at the tooth contact frequency or any of its harmonics. This result is here examined, and it is concluded that it is invalid. It is shown that, in general, tooth contact harmonics of significant amplitudes will exist.

A simple derivation of the addition theorems of the irregular solid harmonics, the Helmholtz harmonics, and the modified Helmholtz harmonics

Abstract: In this article a simple derivation of the addition theorems of the irregular solid harmonics, the Helmholtz harmonics, and the modified Helmholtz harmonics is presented. Our derivation is based upon properties of the differential operator Yml(∇), which is obtained from the regular solid harmonic Yml(r) by replacing the Cartesian components of r by the Cartesian components of ∇. With the help of this differential operator Yml(∇), which is an irreducible spherical tensor of rank l, the addition theorems of the anisotropic functions are obtained by differentiating the addition theorems of the isotropic functions. The performance of the necessary differentiations is greatly facilitated by a systematic exploitation of the tensorial nature of the differential operator Yml(∇).

Harmonic Resposnse Tests on Voltage Transducers for the New Zealand Power System

Abstract: This paper presents the results of harmonic response tests carried out on capacitive voltage transformers, as used on the New Zealand 220 kV a.c. network. It is shown that the harmonic response measured using low voltage test equipment is considerably different from that obtained at high voltage. The latter is highly non-linear and is affected by the specific magnetization characteristic of the CVT tested. It is concluded that for field measurement of harmonics at rated voltage, the transformer of a CVT unit should be disconnected and the CVT used as a purely capacitive or resistor-capacitor divider.