Gaussian modeling of harmonic vectors in power systems

Cavallini, A.; Langella, R.; Testa, A.; Ruggiero, F.

doi:10.1109/ichqp.1998.760179

Cited by 20 publications

(27 citation statements)

References 7 publications

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“…Traditional Rayleigh distribution, Bessel function, and Rician distribution are all derived from Equation (4), in the hypothesis that the pdfs of X h and Y h can be approximated by Gaussian distributions [32]. The hypothesis is important to study the harmonic propagation and summation [33].…”

Section: Low Order Non-characteristic Harmonicsmentioning

confidence: 99%

Harmonic Propagation and Interaction Evaluation between Small-Scale Wind Farms and Nonlinear Loads

Guo-dong

Zhang

et al. 2013

Energies

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Distributed generation is a flexible and effective way to utilize renewable energy. The dispersed generators are quite close to the load, and pose some power quality problems such as harmonic current emissions. This paper focuses on the harmonic propagation and interaction between a small-scale wind farm and nonlinear loads in the distribution grid. Firstly, by setting the wind turbines as P -Q(V) nodes, the paper discusses the expanding Newton-Raphson power flow method for the wind farm. Then the generalized gamma mixture models are proposed to study the non-characteristic harmonic propagation of the wind farm, which are based on Gaussian mixture models, improved phasor clustering and generalized Gamma models. After the integration of the small-scale wind farm, harmonic emissions of nonlinear loads will become random and fluctuating due to the non-stationary wind power. Furthermore, in this paper the harmonic coupled admittance matrix model of nonlinear loads combined with a wind farm is deduced by rigorous formulas. Then the harmonic propagation and interaction between a real wind farm and nonlinear loads are analyzed by the harmonic coupled admittance matrix and generalized gamma mixture models. Finally, the proposed models and methods are verified through the corresponding simulation models in MATLAB/SIMULINK and PSCAD/EMTDC.

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Section: Low Order Non-characteristic Harmonicsmentioning

confidence: 99%

Harmonic Propagation and Interaction Evaluation between Small-Scale Wind Farms and Nonlinear Loads

Guo-dong

Zhang

et al. 2013

Energies

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“…For this reason, several studies have been conducted to obtain analytical pdf expressions. If no fully analytical solution can be reached, sometimes there exist empirical solutions, which allow the determination of closed-forms equaling some statistical moments of actual and approximate distributions [12], [14]. In this section, the third, fifth, and seventh harmonic distributions obtained from wind farm experimental measurements are discussed and compared with some of the analytical and empirical distributions in the literature.…”

Section: Stochastic Assessment Of Wind Farm Harmonic Currentsmentioning

confidence: 99%

“…) regardless of the individual variable distributions if the number of WTs is sufficiently large [11], [12], and [14]. The mean value and the standard deviation of the aforementioned variables are given by the following:…”

Section: Stochastic Assessment Of Wind Farm Harmonic Currentsmentioning

confidence: 99%

“…According to that and considering ρ X h Y h the correlation coefficient of the variables, the joint pdf of X h and Y h in (1) is a bivariate normal distribution [11], [12], [14], i.e.,…”

Section: Stochastic Assessment Of Wind Farm Harmonic Currentsmentioning

confidence: 99%

“…It is a measure of linear dependence between the variables, and ρ X h Y h = ±1 implies variables perfectly correlated on a straight line with positive/negative slope [11], [12], [14].…”

Section: Stochastic Assessment Of Wind Farm Harmonic Currentsmentioning

confidence: 99%

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Deterministic and Stochastic Study of Wind Farm Harmonic Currents

Sainz

Mesas

Teodorescu

et al. 2010

IEEE Trans. Energy Convers.

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Abstract-Wind farm harmonic emissions are a well-known power quality problem, but little data based on actual wind farm measurements are available in literature. In this paper, harmonic emissions of an 18 MW wind farm are investigated using extensive measurements, and the deterministic and stochastic characterization of wind farm harmonic currents is analyzed. Specific issues addressed in the paper include the harmonic variation with the wind farm operating point and the random characteristics of their magnitude and phase angle.

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Summation of Random Harmonic Currents

Ribeiro

2009

Time‐Varying Waveform Distortions in Power Systems

Self Cite

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This chapter deals with the probabilistic modeling of harmonic currents. After some definitions about single current injection models, the vectorial summation of random harmonic currents characterized by distributions independent of time is considered. The basic methods presented in literature for harmonic current summation modeling are discribed: the convolution method, the joint density method and Monte Carlo simulations. Applications of the methods to different case studies give an idea of the accuracy of the models considered.One aspect of assessing the harmonics tolerated by a power system is the estimation of the statistic figures of harmonics arising from the various time-varying/probabilistic sources. The assessment of harmonics is not exact or uniform, since there will be unpredictable variations in either the nonlinear sources and/or parameters of the system which affect the summation.The combination of a number of harmonic time-varying sources will generally lead to less than the arithmetic sum of the maximum values due to uncertainty of magnitude and phase angle. Hence the resulting summation is extremely difficult to estimate accurately.Before introducing the methods that can be adopted to solve the summation problem, it is necessary to introduce and discuss some basic concepts: random harmonic and interharmonic vectors, the harmonic summation principle and essential nomenclature. Time-Varying Waveform Distortions in Power Systems Edited by Paulo F. Ribeiro

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Gaussian modeling of harmonic vectors in power systems

Cited by 20 publications

References 7 publications

Harmonic Propagation and Interaction Evaluation between Small-Scale Wind Farms and Nonlinear Loads

Harmonic Propagation and Interaction Evaluation between Small-Scale Wind Farms and Nonlinear Loads

Deterministic and Stochastic Study of Wind Farm Harmonic Currents

Summation of Random Harmonic Currents

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