The Experts below are selected from a list of 30294 Experts worldwide ranked by ideXlab platform
D G Holmes - One of the best experts on this subject based on the ideXlab platform.
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natural capacitor voltage balancing for a flying capacitor converter induction motor drive
IEEE Transactions on Power Electronics, 2009Co-Authors: B P Mcgrath, D G HolmesAbstract:This paper presents an analysis of the natural voltage balancing dynamics of a three-phase flying capacitor converter when supplying an induction motor. The approach substitutes double Fourier Harmonic Series for the pulsewidth modulation switching waveforms and the frequency response of the motor, to create a linear state-space model of this type of load. The model requires the mid-frequency response (500 Hz-20 kHz) of the induction motor impedance to be identified, and takes skin and proximity effects into account by adding parallel R-L networks to a standard motor model. Model parameters were measured by applying FFT analysis to variable frequency square waves injected into the motor terminals, and fitting parameter values to these measurements using a least squares minimization method. From the analysis, it was found that the converter voltage balancing behavior degrades substantially at low motor speeds, and that a balance booster filter, as previously proposed, considerably improves the dynamic response. Experimental verification results using a scaled-down flying capacitor converter drive are included in the paper.
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natural capacitor voltage balancing for a flying capacitor converter induction motor drive
Power Electronics Specialists Conference, 2008Co-Authors: B P Mcgrath, D G HolmesAbstract:This paper presents an analysis of the natural voltage balancing dynamics of a three phase flying capacitor converter when supplying an induction motor. The approach substitutes Double Fourier Harmonic Series for the PWM switching waveforms and the frequency response of the motor, to create a linear state space model of this type of load. The model requires the mid-frequency response (500 Hz - 20 kHz) of the induction motor impedance to be identified, and takes skin and proximity effects into account by adding parallel R-L networks to a standard motor model. Model parameters were measured by applying FFT analysis to variable frequency square waves injected into the motor terminals, and fitting parameter values to these measurements using a least squares minimisation method. From the analysis, it was found that the converter voltage balancing behavior degrades substantially at low motor speeds, and that a balance booster filter, as previously proposed, considerably improves the dynamic response. Experimental verification results using a scaled-down flying capacitor converter drive are included in the paper.
B P Mcgrath - One of the best experts on this subject based on the ideXlab platform.
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natural capacitor voltage balancing for a flying capacitor converter induction motor drive
IEEE Transactions on Power Electronics, 2009Co-Authors: B P Mcgrath, D G HolmesAbstract:This paper presents an analysis of the natural voltage balancing dynamics of a three-phase flying capacitor converter when supplying an induction motor. The approach substitutes double Fourier Harmonic Series for the pulsewidth modulation switching waveforms and the frequency response of the motor, to create a linear state-space model of this type of load. The model requires the mid-frequency response (500 Hz-20 kHz) of the induction motor impedance to be identified, and takes skin and proximity effects into account by adding parallel R-L networks to a standard motor model. Model parameters were measured by applying FFT analysis to variable frequency square waves injected into the motor terminals, and fitting parameter values to these measurements using a least squares minimization method. From the analysis, it was found that the converter voltage balancing behavior degrades substantially at low motor speeds, and that a balance booster filter, as previously proposed, considerably improves the dynamic response. Experimental verification results using a scaled-down flying capacitor converter drive are included in the paper.
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natural capacitor voltage balancing for a flying capacitor converter induction motor drive
Power Electronics Specialists Conference, 2008Co-Authors: B P Mcgrath, D G HolmesAbstract:This paper presents an analysis of the natural voltage balancing dynamics of a three phase flying capacitor converter when supplying an induction motor. The approach substitutes Double Fourier Harmonic Series for the PWM switching waveforms and the frequency response of the motor, to create a linear state space model of this type of load. The model requires the mid-frequency response (500 Hz - 20 kHz) of the induction motor impedance to be identified, and takes skin and proximity effects into account by adding parallel R-L networks to a standard motor model. Model parameters were measured by applying FFT analysis to variable frequency square waves injected into the motor terminals, and fitting parameter values to these measurements using a least squares minimisation method. From the analysis, it was found that the converter voltage balancing behavior degrades substantially at low motor speeds, and that a balance booster filter, as previously proposed, considerably improves the dynamic response. Experimental verification results using a scaled-down flying capacitor converter drive are included in the paper.
Michael Kuhn - One of the best experts on this subject based on the ideXlab platform.
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A numerical study on the integration radius separating convergent and divergent spherical Harmonic Series of topography-implied gravity
Journal of Geodesy, 2020Co-Authors: Blažej Bucha, Michael KuhnAbstract:We show that far-zone topography-implied gravitational effects may be accurately computed via external spherical Harmonics not only above the limit sphere encompassing all the masses, but also inside it on planetary topographies. Although a rigorous mathematical proof is still missing, our numerical experiments indicate that this is possible, provided that near-zone masses within a certain spherical cap centred at the evaluation point are omitted from gravity forward modelling. We formulate and numerically examine a hypothesis, saying that in order to achieve convergence, the cap size needs to be larger than the highest topographical height. The hypothesis relies on the spherical arrangement of field-generating topographic masses and strictly positive topographic heights. To put our hypothesis to a test, we gravity forward model lunar degree-2160 topography using a constant mass density and expand the far-zone gravitational effects up to degree 10,800. The results are compared with respect to divergence-free reference values from spatial-domain gravity forward modelling. By systematically increasing the cap radius from 2.5 km up to 100.0 km (the maximum topographic height is $${\sim }\,20\,\mathrm {km}$$ ∼ 20 km ), we obtained results that appear to be in line with our hypothesis. Nonetheless, a rigorous mathematical proof still needs to be found to prove whether the hypothesis is true or false. The outcomes of the paper could be beneficial for the study of convergence/divergence of spherical Harmonics on planetary surfaces and for geoid computations based on spherical Harmonic expansion of far-zone gravitational effects.
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divergence free spherical Harmonic gravity field modelling based on the runge krarup theorem a case study for the moon
Journal of Geodesy, 2019Co-Authors: Blažej Bucha, Christian Hirt, Michael KuhnAbstract:Recent numerical studies on external gravity field modelling show that external spherical Harmonic Series may diverge near or on planetary surfaces. This paper investigates an alternative solution that is still based on external spherical Harmonic Series, but capable of avoiding the divergence effect. The approach relies on the Runge–Krarup theorem and the iterative downward continuation. In theory, Runge–Krarup-type solutions are able to approximate the true potential within the entire space external to the masses with an arbitrary $$\varepsilon $$ -accuracy, $$\varepsilon >0$$ . Using gravity implied by the lunar topography, we show numerically that this technique avoids indeed the divergence effect, at least at the studied 5 arc-min resolution. In the context of the iterative scheme, we show that a function expressed as a truncated solid spherical Harmonic expansion on a general star-shaped surface possesses an infinite surface spherical Harmonic spectrum after it is mapped onto a sphere. We also study the convergence of the gradient approach, which is a technique for efficient grid-wise synthesis on irregular surfaces. We show that the resulting Taylor Series may converge slowly when analytically upward continuing from points inside the masses. The continuation from the mass-free space should therefore be preferred. As an underlying topic of the paper, spherical Harmonic coefficients from spectral gravity forward modelling and their Runge–Krarup counterpart are numerically studied. Regarding their different nature, we formulate some research topics that might contribute to a deeper understanding of the current methodologies used to develop combined high-degree spherical Harmonic gravity models.
Christopher Jekeli - One of the best experts on this subject based on the ideXlab platform.
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a numerical comparison of spherical spheroidal and ellipsoidal Harmonic gravitational field models for small non spherical bodies examples for the martian moons
Journal of Geodesy, 2015Co-Authors: Christopher JekeliAbstract:We present a comprehensive numerical analysis of spherical, spheroidal, and ellipsoidal Harmonic Series for gravitational field modeling near small moderately irregular bodies, such as the Martian moons. The comparison of model performances for these bodies is less intuitive and distinct than for a highly irregular object, such as Eros. The Harmonic Series models are each associated with a distinct surface, i.e., the Brillouin sphere, spheroid, or ellipsoid, which separates the regions of convergence and possible divergence for the parent infinite Series. In their convergence regions, the models are subject only to omission errors representing the residual field variations not accounted for by the finite degree expansions. In the regions inside their respective Brillouin surfaces, the models are susceptible to amplification of omission errors and possible divergence effects, where the latter can be discerned if the error increases with an increase in the maximum degree of the model. We test the Harmonic Series models on the Martian moons, Phobos and Deimos, with moderate oblateness of $$<$$ 0.4. The possible divergence effects and amplified omission errors of the models are illustrated and quantified. The three models yield consistent results on a bounding sphere of Phobos in their common convergence region, with relative errors in potential of $$\sim $$ 0.01 and $$\sim $$ 0.001 % for expansions up to degree 10 and degree 20 respectively. On the surface of Phobos, the spherical and spheroidal models up to degree 10 both have maximum relative errors of $$\sim $$ 1 % in potential and $$\sim $$ 100 % in acceleration due ostensibly to divergence effect. Their performances deteriorate more severely on the more irregular Deimos. The ellipsoidal model exhibits much less distinct divergence behavior and proves more reliable in modeling both potential and acceleration, with respective maximum relative errors of $$\sim $$ 1 and $$\sim $$ 10 %, on both bodies. Our results show that for the Martian moons and other such moderately irregular bodies, the ellipsoidal Harmonic Series should be considered preferentially for gravitational field modeling.
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on the computation and approximation of ultra high degree spherical Harmonic Series
Journal of Geodesy, 2007Co-Authors: Christopher Jekeli, Jong Ki Lee, Jay H KwonAbstract:Spherical Harmonic Series, commonly used to represent the Earth’s gravitational field, are now routinely expanded to ultra-high degree (> 2,000), where the computations of the associated Legendre functions exhibit extremely large ranges (thousands of orders) of magnitudes with varying latitude. We show that in the degree-and-order domain, (l,m), of these functions (with full ortho-normalization), their rather stable oscillatory behavior is distinctly separated from a region of very strong attenuation by a simple linear relationship: \(m = \ell \sin \theta\), where θ is the polar angle. Derivatives and integrals of associated Legendre functions have these same characteristics. This leads to an operational approach to the computation of spherical Harmonic Series, including derivatives and integrals of such Series, that neglects the numerically insignificant functions on the basis of the above empirical relationship and obviates any concern about their broad range of magnitudes in the recursion formulas that are used to compute them. Tests with a simulated gravitational field show that the errors in so doing can be made less than the data noise at all latitudes and up to expansion degree of at least 10,800. Neglecting numerically insignificant terms in the spherical Harmonic Series also offers a computational savings of at least one third.
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an analysis of vertical deflections derived from high degree spherical Harmonic models
Journal of Geodesy, 1999Co-Authors: Christopher JekeliAbstract:The theoretical differences between the Helmert deflection of the vertical and that computed from a truncated spherical Harmonic Series of the gravity field, aside from the limited spectral content in the latter, include the curvature of the normal plumb line, the permanent tidal effect, and datum origin and orientation offsets. A numerical comparison between deflections derived from spherical Harmonic model EGM96 and astronomic deflections in the conterminous United States (CONUS) shows that correcting these systematic effects reduces the mean differences in some areas. Overall, the mean difference in CONUS is reduced from −0.219 arcsec to −0.058 arcsec for the south–north deflection, and from +0.016 arcsec to +0.004 arcsec for the west–east deflection. Further analysis of the root-mean-square differences indicates that the high-degree spectrum of the EGM96 model has significantly less power than implied by the deflection data.
Blažej Bucha - One of the best experts on this subject based on the ideXlab platform.
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A numerical study on the integration radius separating convergent and divergent spherical Harmonic Series of topography-implied gravity
Journal of Geodesy, 2020Co-Authors: Blažej Bucha, Michael KuhnAbstract:We show that far-zone topography-implied gravitational effects may be accurately computed via external spherical Harmonics not only above the limit sphere encompassing all the masses, but also inside it on planetary topographies. Although a rigorous mathematical proof is still missing, our numerical experiments indicate that this is possible, provided that near-zone masses within a certain spherical cap centred at the evaluation point are omitted from gravity forward modelling. We formulate and numerically examine a hypothesis, saying that in order to achieve convergence, the cap size needs to be larger than the highest topographical height. The hypothesis relies on the spherical arrangement of field-generating topographic masses and strictly positive topographic heights. To put our hypothesis to a test, we gravity forward model lunar degree-2160 topography using a constant mass density and expand the far-zone gravitational effects up to degree 10,800. The results are compared with respect to divergence-free reference values from spatial-domain gravity forward modelling. By systematically increasing the cap radius from 2.5 km up to 100.0 km (the maximum topographic height is $${\sim }\,20\,\mathrm {km}$$ ∼ 20 km ), we obtained results that appear to be in line with our hypothesis. Nonetheless, a rigorous mathematical proof still needs to be found to prove whether the hypothesis is true or false. The outcomes of the paper could be beneficial for the study of convergence/divergence of spherical Harmonics on planetary surfaces and for geoid computations based on spherical Harmonic expansion of far-zone gravitational effects.
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divergence free spherical Harmonic gravity field modelling based on the runge krarup theorem a case study for the moon
Journal of Geodesy, 2019Co-Authors: Blažej Bucha, Christian Hirt, Michael KuhnAbstract:Recent numerical studies on external gravity field modelling show that external spherical Harmonic Series may diverge near or on planetary surfaces. This paper investigates an alternative solution that is still based on external spherical Harmonic Series, but capable of avoiding the divergence effect. The approach relies on the Runge–Krarup theorem and the iterative downward continuation. In theory, Runge–Krarup-type solutions are able to approximate the true potential within the entire space external to the masses with an arbitrary $$\varepsilon $$ -accuracy, $$\varepsilon >0$$ . Using gravity implied by the lunar topography, we show numerically that this technique avoids indeed the divergence effect, at least at the studied 5 arc-min resolution. In the context of the iterative scheme, we show that a function expressed as a truncated solid spherical Harmonic expansion on a general star-shaped surface possesses an infinite surface spherical Harmonic spectrum after it is mapped onto a sphere. We also study the convergence of the gradient approach, which is a technique for efficient grid-wise synthesis on irregular surfaces. We show that the resulting Taylor Series may converge slowly when analytically upward continuing from points inside the masses. The continuation from the mass-free space should therefore be preferred. As an underlying topic of the paper, spherical Harmonic coefficients from spectral gravity forward modelling and their Runge–Krarup counterpart are numerically studied. Regarding their different nature, we formulate some research topics that might contribute to a deeper understanding of the current methodologies used to develop combined high-degree spherical Harmonic gravity models.
