IEEE Transactions on Power Delivery, ISSN 0885-8977, 10/2006, Volume 21, Issue 4, pp. 2006 - 2016

Variable-speed wind turbines inject harmonic currents in the network, which may potentially create voltage distortion problems. In this paper, a case study is...

Harmonics modeling | Power system harmonics | Harmonic analysis | Power system modeling | Wind energy generation | Power system analysis computing | summation of harmonics | Voltage | Wind power generation | Wind farms | Harmonic distortion | wind turbines | Power generation | Wind turbines | Summation of harmonics | power system harmonics | TIME-VARYING HARMONICS | SUMMATION | PART II | harmonics modeling | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Air-turbines | Management | Harmonics (Electric waves) | Wind power | Analysis | Voltage distortion | Harmonics | Networks | Load-Flow | Fourier analysis | Mathematical models

Harmonics modeling | Power system harmonics | Harmonic analysis | Power system modeling | Wind energy generation | Power system analysis computing | summation of harmonics | Voltage | Wind power generation | Wind farms | Harmonic distortion | wind turbines | Power generation | Wind turbines | Summation of harmonics | power system harmonics | TIME-VARYING HARMONICS | SUMMATION | PART II | harmonics modeling | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Air-turbines | Management | Harmonics (Electric waves) | Wind power | Analysis | Voltage distortion | Harmonics | Networks | Load-Flow | Fourier analysis | Mathematical models

Journal Article

2.
Full Text
Assessing the Collective Harmonic Impact of Modern Residential Loads-Part I: Methodology

IEEE Transactions on Power Delivery, ISSN 0885-8977, 10/2012, Volume 27, Issue 4, pp. 1937 - 1946

The proliferation of power-electronic-based residential loads has resulted in significant harmonic distortion in the voltages and currents of residential...

residential loads | Current measurement | time-varying harmonics | Switches | Power system harmonics | Harmonic analysis | Probabilistic logic | Calibration | statistical analysis | Load modeling | SUMMATION | SYSTEMS | VOLTAGE DISTORTION | PROPAGATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Energy consumption | Usage | Electromagnetism | Energy use | Electric power | Research | Housing | Dwellings | Studies | Harmonics | Houses | Residential | Probability theory | Voltage | Transformers | Mathematical models | Probabilistic methods

residential loads | Current measurement | time-varying harmonics | Switches | Power system harmonics | Harmonic analysis | Probabilistic logic | Calibration | statistical analysis | Load modeling | SUMMATION | SYSTEMS | VOLTAGE DISTORTION | PROPAGATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Energy consumption | Usage | Electromagnetism | Energy use | Electric power | Research | Housing | Dwellings | Studies | Harmonics | Houses | Residential | Probability theory | Voltage | Transformers | Mathematical models | Probabilistic methods

Journal Article

IET Generation, Transmission & Distribution, ISSN 1751-8687, 12/2013, Volume 7, Issue 12, pp. 1391 - 1400

Estimation of total harmonic current generated by a group of sources is a difficult task, because of time variations of loads and background harmonic voltages...

power system harmonics | harmonic current summation analysis | total harmonic current estimation | industrial installations | harmonic magnitudes | background harmonic voltages | simulation technique | field measurements | load currents | probabilistic studies | ENGINEERING, ELECTRICAL & ELECTRONIC | phase angles | PHASE | load time variation | voltage distortion | current distortion | POWER-SYSTEM HARMONICS | LOADS

power system harmonics | harmonic current summation analysis | total harmonic current estimation | industrial installations | harmonic magnitudes | background harmonic voltages | simulation technique | field measurements | load currents | probabilistic studies | ENGINEERING, ELECTRICAL & ELECTRONIC | phase angles | PHASE | load time variation | voltage distortion | current distortion | POWER-SYSTEM HARMONICS | LOADS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 09/2015, Volume 154, pp. 144 - 159

We develop new closed form representations of sums of quadratic alternating harmonic numbers and reciprocal binomial coefficients.

Polylogarithm function | Combinatorial series identities | Partial fraction approach | Binomial coefficients | Alternating harmonic numbers | Summation formulas | MATHEMATICS | DIGAMMA | IDENTITIES

Polylogarithm function | Combinatorial series identities | Partial fraction approach | Binomial coefficients | Alternating harmonic numbers | Summation formulas | MATHEMATICS | DIGAMMA | IDENTITIES

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 08/2013, Volume 54, Issue 8, p. 82301

In recent three-loop calculations of massive Feynman integrals within Quantum Chromodynamics (QCD) and, e.g., in recent combinatorial problems the so-called...

MULTIPLE POLYLOGARITHMS | SYMBOLIC SUMMATION | TRANSCENDENTAL FUNCTIONS | DEEP-INELASTIC-SCATTERING | 3-LOOP SPLITTING FUNCTIONS | MELLIN TRANSFORMS | NUMERICAL EVALUATION | PHYSICS, MATHEMATICAL | EXPANDING HYPERGEOMETRIC-FUNCTIONS | WILSON COEFFICIENTS | NESTED SUMS | Harmonics | Algebra | Algorithms | Mathematical analysis | Mathematical models | Combinatorial analysis | Sums | Quantum chromodynamics | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | QUANTUM CHROMODYNAMICS | MELLIN TRANSFORM | ALGEBRA | SUM RULES | ALGORITHMS | ITERATIVE METHODS | COMPACTIFICATION | ASYMPTOTIC SOLUTIONS | FEYNMAN PATH INTEGRAL

MULTIPLE POLYLOGARITHMS | SYMBOLIC SUMMATION | TRANSCENDENTAL FUNCTIONS | DEEP-INELASTIC-SCATTERING | 3-LOOP SPLITTING FUNCTIONS | MELLIN TRANSFORMS | NUMERICAL EVALUATION | PHYSICS, MATHEMATICAL | EXPANDING HYPERGEOMETRIC-FUNCTIONS | WILSON COEFFICIENTS | NESTED SUMS | Harmonics | Algebra | Algorithms | Mathematical analysis | Mathematical models | Combinatorial analysis | Sums | Quantum chromodynamics | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | QUANTUM CHROMODYNAMICS | MELLIN TRANSFORM | ALGEBRA | SUM RULES | ALGORITHMS | ITERATIVE METHODS | COMPACTIFICATION | ASYMPTOTIC SOLUTIONS | FEYNMAN PATH INTEGRAL

Journal Article

Mathematical and Computer Modelling, ISSN 0895-7177, 2011, Volume 54, Issue 9, pp. 2220 - 2234

Harmonic numbers and generalized harmonic numbers have been studied since the distant past and are involved in a wide range of diverse fields such as analysis...

Stirling numbers of the first kind | Generalized hypergeometric function [formula omitted] | Harmonic numbers | Polygamma functions | Generalized harmonic numbers | Riemann Zeta function | Psi function | Hurwitz Zeta function | Summation formulas for [formula omitted] | Riemann zeta function | Summation formulas for pfq | Generalized hypergeometric function pfq | Hurwitz zeta function | INFINITE SERIES | MATHEMATICS, APPLIED | IDENTITIES | HYPERGEOMETRIC-SERIES | GENERATING-FUNCTIONS | RIEMANN ZETA | Generalized hypergeometric function F-p(q) | SUMS | INTEGRALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ZETA-FUNCTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SERIES REPRESENTATIONS | Summation formulas for F-p(q) | Statistics | Analysis | Algorithms

Stirling numbers of the first kind | Generalized hypergeometric function [formula omitted] | Harmonic numbers | Polygamma functions | Generalized harmonic numbers | Riemann Zeta function | Psi function | Hurwitz Zeta function | Summation formulas for [formula omitted] | Riemann zeta function | Summation formulas for pfq | Generalized hypergeometric function pfq | Hurwitz zeta function | INFINITE SERIES | MATHEMATICS, APPLIED | IDENTITIES | HYPERGEOMETRIC-SERIES | GENERATING-FUNCTIONS | RIEMANN ZETA | Generalized hypergeometric function F-p(q) | SUMS | INTEGRALS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ZETA-FUNCTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SERIES REPRESENTATIONS | Summation formulas for F-p(q) | Statistics | Analysis | Algorithms

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 218, Issue 3, pp. 734 - 740

Harmonic numbers and generalized harmonic numbers have been studied since the distant past and involved in a wide range of diverse fields such as analysis of...

Stirling numbers of the first kind | Harmonic numbers | Summation formulas for pFq | Polygamma functions | Generalized harmonic numbers | Psi-function | Riemann Zeta function | Generalized hypergeometric function pFq | Hurwitz Zeta function | Summation formulas for | Generalized hypergeometric function | GAMMA | MATHEMATICS, APPLIED | IDENTITIES | HYPERGEOMETRIC-SERIES | GENERATING-FUNCTIONS | Generalized hypergeometric function F-p(q) | SUMS | INTEGRALS | Riemann Zeta function, Hurwitz Zeta function | ZETA-FUNCTION | SERIES REPRESENTATIONS | Summation formulas for F-p(q) | EULER | Statistics | Analysis | Algorithms | Hypergeometric functions | Harmonics | Mathematical analysis | Infinite series | Elementary particles | Mathematical models | Number theory

Stirling numbers of the first kind | Harmonic numbers | Summation formulas for pFq | Polygamma functions | Generalized harmonic numbers | Psi-function | Riemann Zeta function | Generalized hypergeometric function pFq | Hurwitz Zeta function | Summation formulas for | Generalized hypergeometric function | GAMMA | MATHEMATICS, APPLIED | IDENTITIES | HYPERGEOMETRIC-SERIES | GENERATING-FUNCTIONS | Generalized hypergeometric function F-p(q) | SUMS | INTEGRALS | Riemann Zeta function, Hurwitz Zeta function | ZETA-FUNCTION | SERIES REPRESENTATIONS | Summation formulas for F-p(q) | EULER | Statistics | Analysis | Algorithms | Hypergeometric functions | Harmonics | Mathematical analysis | Infinite series | Elementary particles | Mathematical models | Number theory

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 08/2015, Volume 265, pp. 557 - 567

For and the th harmonic number of order is expressed in the form where are parameters controlling the magnitude of the error term. The function consists of...

Estimate | p-series | Approximation | Euler–Maclaurin summation | Generalized harmonic number | Zeta-generalized-Euler-constant function | Euler-Maclaurin summation | Zeta-generalized-Euler-Constant function | MATHEMATICS, APPLIED | Harmonics | Errors | Mathematical models | Computation | Mathematical analysis | Inequalities

Estimate | p-series | Approximation | Euler–Maclaurin summation | Generalized harmonic number | Zeta-generalized-Euler-constant function | Euler-Maclaurin summation | Zeta-generalized-Euler-Constant function | MATHEMATICS, APPLIED | Harmonics | Errors | Mathematical models | Computation | Mathematical analysis | Inequalities

Journal Article

IEEE Transactions on Power Delivery, ISSN 0885-8977, 04/2017, Volume 32, Issue 2, pp. 962 - 970

The total harmonic current emission in a public low-voltage (LV) network is mainly determined by the large number of electronic devices, which use different...

Circuit topology | Phase measurement | Current measurement | Instruments | Power system harmonics | prevailing harmonic phasor | Harmonic analysis | Harmonic phase angle | IEC Standards | public low-voltage network | power system harmonics | SUMMATION | ATTENUATION | DIVERSITY | ENGINEERING, ELECTRICAL & ELECTRONIC

Circuit topology | Phase measurement | Current measurement | Instruments | Power system harmonics | prevailing harmonic phasor | Harmonic analysis | Harmonic phase angle | IEC Standards | public low-voltage network | power system harmonics | SUMMATION | ATTENUATION | DIVERSITY | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Journal of Geodesy, ISSN 0949-7714, 7/2009, Volume 83, Issue 7, pp. 595 - 619

Four widely used algorithms for the computation of the Earth’s gravitational potential and its first-, second- and third-order gradients are examined: the...

Gravity tensors | Clenshaw summation | Earth Sciences | Mathematical Applications in Earth Sciences | Spherical harmonics | Geopotential | Geophysics/Geodesy | Gravitational gradients | Helmholtz polynomials | Associated Legendre functions | EARTH | REPRESENTATION | GRAVITY-FIELD | GOCE | MASS ELEMENTS | GEOCHEMISTRY & GEOPHYSICS | REMOTE SENSING | GRADIOMETRY | LEGENDRE FUNCTIONS | COMPUTATION | DERIVATIVES | Models | Algorithms | Analysis | Methods | Geodetics

Gravity tensors | Clenshaw summation | Earth Sciences | Mathematical Applications in Earth Sciences | Spherical harmonics | Geopotential | Geophysics/Geodesy | Gravitational gradients | Helmholtz polynomials | Associated Legendre functions | EARTH | REPRESENTATION | GRAVITY-FIELD | GOCE | MASS ELEMENTS | GEOCHEMISTRY & GEOPHYSICS | REMOTE SENSING | GRADIOMETRY | LEGENDRE FUNCTIONS | COMPUTATION | DERIVATIVES | Models | Algorithms | Analysis | Methods | Geodetics

Journal Article

Journal of Geodesy, ISSN 0949-7714, 4/2012, Volume 86, Issue 4, pp. 271 - 285

By extending the exponent of floating point numbers with an additional integer as the power index of a large radix, we compute fully normalized associated...

Floating point number | Earth Sciences | Spherical harmonics | Underflow problem | Earth Sciences, general | Geophysics/Geodesy | Exponent extension | Associated Legendre functions | GEOCHEMISTRY & GEOPHYSICS | NORMALIZED LEGENDRE POLYNOMIALS | REMOTE SENSING | SERIES | ALGORITHM | SUMMATION | GRADIENTS | Statistics | Analysis | Executions and executioners | Harmonic analysis | Numerical analysis

Floating point number | Earth Sciences | Spherical harmonics | Underflow problem | Earth Sciences, general | Geophysics/Geodesy | Exponent extension | Associated Legendre functions | GEOCHEMISTRY & GEOPHYSICS | NORMALIZED LEGENDRE POLYNOMIALS | REMOTE SENSING | SERIES | ALGORITHM | SUMMATION | GRADIENTS | Statistics | Analysis | Executions and executioners | Harmonic analysis | Numerical analysis

Journal Article

Integral Transforms and Special Functions, ISSN 1065-2469, 06/2016, Volume 27, Issue 6, pp. 430 - 442

Half integer values of harmonic numbers and reciprocal binomial coefficients sums are investigated in this paper. Closed-form representations and integral...

partial fraction approach | Secondary: 11B65 | binomial coefficients | 33C20 | combinatorial series identities | alternating harmonic numbers | integral representation | Half integer harmonic numbers | Primary: 05A10 | summation formulas | 11B83 | 05A19 | 11M06 | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | SUMS | Integers | Harmonics | Binomial coefficients | Integrals | Mathematical analysis | Transforms | Exact solutions | Representations

partial fraction approach | Secondary: 11B65 | binomial coefficients | 33C20 | combinatorial series identities | alternating harmonic numbers | integral representation | Half integer harmonic numbers | Primary: 05A10 | summation formulas | 11B83 | 05A19 | 11M06 | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | SUMS | Integers | Harmonics | Binomial coefficients | Integrals | Mathematical analysis | Transforms | Exact solutions | Representations

Journal Article

IEEE Transactions on Power Delivery, ISSN 0885-8977, 04/2012, Volume 27, Issue 2, pp. 1030 - 1032

At the point of common coupling, there are many cases where the phase-angle difference between harmonic vectors is unknown. In practice, for example, in...

probability and statistics | harmonic summation | Harmonic filter | IEC standards | harmonics | Power system harmonics | Harmonic analysis | Electromagnetic compatibility | power harmonics | Vectors | Probability distribution | ENGINEERING, ELECTRICAL & ELECTRONIC | Measurement | Learning models (Stochastic processes) | Usage | Harmonics (Electric waves)

probability and statistics | harmonic summation | Harmonic filter | IEC standards | harmonics | Power system harmonics | Harmonic analysis | Electromagnetic compatibility | power harmonics | Vectors | Probability distribution | ENGINEERING, ELECTRICAL & ELECTRONIC | Measurement | Learning models (Stochastic processes) | Usage | Harmonics (Electric waves)

Journal Article

Results in Mathematics, ISSN 1422-6383, 3/2018, Volume 73, Issue 1, pp. 1 - 14

Applying the modified Abel lemma on summation by parts, we examine infinite series containing generalized harmonic numbers of order 2 and 3. Several...

Secondary 40A25 | generalized harmonic numbers | Primary 05A19 | Mathematics, general | Abel’s lemma on summation by parts | partial fraction decomposition | Mathematics | harmonic numbers | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | Abel's lemma on summation by parts | SUMMATION

Secondary 40A25 | generalized harmonic numbers | Primary 05A19 | Mathematics, general | Abel’s lemma on summation by parts | partial fraction decomposition | Mathematics | harmonic numbers | MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | Abel's lemma on summation by parts | SUMMATION

Journal Article

International Association of Geodesy Symposia, ISSN 0939-9585, 2016, Volume 142, pp. 195 - 203

Conference Proceeding

Filomat, ISSN 0354-5180, 1/2016, Volume 30, Issue 13, pp. 3511 - 3524

We develop new closed form representations of sums of alternating harmonic numbers of order two and reciprocal binomial coefficients. Moreover we develop new...

Polylogarithm function | Combinatorial series identities | Binomial coefficients | Summation formulas | Partial fraction approach | Alternating harmonic numbers | Integral representation | MATHEMATICS | MATHEMATICS, APPLIED | DIGAMMA | IDENTITIES

Polylogarithm function | Combinatorial series identities | Binomial coefficients | Summation formulas | Partial fraction approach | Alternating harmonic numbers | Integral representation | MATHEMATICS | MATHEMATICS, APPLIED | DIGAMMA | IDENTITIES

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 11

A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range...

generalized hypergeometric function | generalized harmonic numbers | Mathematics | harmonic numbers | polygamma functions | Hurwitz zeta function | Stirling numbers of the first kind | summation formulas for | psi-function | Analysis | Riemann zeta function | Mathematics, general | Applications of Mathematics | F | Harmonic numbers | Polygamma functions | Generalized harmonic numbers | Psi-function | Summation formulas for | Generalized hypergeometric function | MATHEMATICS, APPLIED | generalized hypergeometric function F-p(q) | MATHEMATICS | ZETA | summation formulas for F-p(q) | SERIES REPRESENTATIONS | Harmonics | Operators | Algorithms | Binomial coefficients | Mathematical analysis | Elementary particles | Inequalities | Series (mathematics)

generalized hypergeometric function | generalized harmonic numbers | Mathematics | harmonic numbers | polygamma functions | Hurwitz zeta function | Stirling numbers of the first kind | summation formulas for | psi-function | Analysis | Riemann zeta function | Mathematics, general | Applications of Mathematics | F | Harmonic numbers | Polygamma functions | Generalized harmonic numbers | Psi-function | Summation formulas for | Generalized hypergeometric function | MATHEMATICS, APPLIED | generalized hypergeometric function F-p(q) | MATHEMATICS | ZETA | summation formulas for F-p(q) | SERIES REPRESENTATIONS | Harmonics | Operators | Algorithms | Binomial coefficients | Mathematical analysis | Elementary particles | Inequalities | Series (mathematics)

Journal Article

IEEE Latin America Transactions, ISSN 1548-0992, 05/2016, Volume 14, Issue 5, pp. 2291 - 2297

The increasing penetration of renewable energy sources with nonlinear characteristics, such as wind and photovoltaic power plants, demands a clear procedure...

Photovoltaic systems | Performance evaluation | Renewable energy sources | Photovoltaic Generation | Computational modeling | Summation Law | Harmonic analysis | Wind Generation | IEC Standards | Harmonic Distortion | Power Quality | Solar cells | Harmonics | Photovoltaic cells | Wind power generation | Wind turbines | Coupling | Parks

Photovoltaic systems | Performance evaluation | Renewable energy sources | Photovoltaic Generation | Computational modeling | Summation Law | Harmonic analysis | Wind Generation | IEC Standards | Harmonic Distortion | Power Quality | Solar cells | Harmonics | Photovoltaic cells | Wind power generation | Wind turbines | Coupling | Parks

Journal Article

Physics Letters B, ISSN 0370-2693, 10/2019, Volume 797, Issue C, p. 134815

We study systems of finite-number neutrons in a harmonic trap at the unitary limit. Two very different types of neutron-neutron interactions are applied,...

Unitary limit | Particle-particle hole-hole ring diagrams | Linear scaling | Tuned CD-Bonn potential | Fermi liquid at the unitary limit | SUMMATION | PHYSICS, NUCLEAR | NUCLEON-INTERACTION | PARTICLE-PARTICLE | THERMODYNAMICS | FERMI | ASTRONOMY & ASTROPHYSICS | RING DIAGRAMS | PHYSICS, PARTICLES & FIELDS | Physics - Nuclear Theory

Unitary limit | Particle-particle hole-hole ring diagrams | Linear scaling | Tuned CD-Bonn potential | Fermi liquid at the unitary limit | SUMMATION | PHYSICS, NUCLEAR | NUCLEON-INTERACTION | PARTICLE-PARTICLE | THERMODYNAMICS | FERMI | ASTRONOMY & ASTROPHYSICS | RING DIAGRAMS | PHYSICS, PARTICLES & FIELDS | Physics - Nuclear Theory

Journal Article

Journal of Chemical Theory and Computation, ISSN 1549-9618, 01/2019, Volume 15, Issue 1, pp. 68 - 77

We develop an algorithm for calculating the normal modes of vibration of mechanical systems with constraints, particularly of molecules with rigid bonds and...

TRANSITION | PHASES | FLUID | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | SYSTEMS | MONTE-CARLO METHOD | MODEL | EWALD SUMMATION | SIMULATION | MELTING-POINT | Chemical bonds | Vibration mode | Mathematical models | Anharmonicity | Mechanical systems | Free energy

TRANSITION | PHASES | FLUID | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | SYSTEMS | MONTE-CARLO METHOD | MODEL | EWALD SUMMATION | SIMULATION | MELTING-POINT | Chemical bonds | Vibration mode | Mathematical models | Anharmonicity | Mechanical systems | Free energy

Journal Article

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