Evidence of crossover phenomena in wind speed data

In this report, a systematic analysis of hourly wind speed data obtained from three potential wind generation sites (in North Dakota) is analyzed. The power spectra of the data exhibited a power-law decay characteristic of $1/f^{\alpha}$ processes with possible long-range correlations. Conventional analysis using Hurst exponent estimators proved to be inconclusive. Subsequent analysis using detrended fluctuation analysis (DFA) revealed a crossover in the scaling exponent ($\alpha$). At short time scales, a scaling exponent of $\alpha \sim 1.4$ indicated that the data resembled Brownian noise, whereas for larger time scales the data exhibited long range correlations ($\alpha \sim 0.7$). The scaling exponents obtained were similar across the three locations. Our findings suggest the possibility of multiple scaling exponents characteristic of multifractal signals

A Multifractal Description of Wind Speed Records

In this paper, a systematic analysis of hourly wind speed data obtained from four potential wind generation sites in North Dakota is conducted. The power spectra of the data exhibited a power law decay characteristic of $1/f^{\alpha}$ processes with possible long range correlations. The temporal scaling properties of the records were studied using multifractal detrended fluctuation analysis {\em MFDFA}. It is seen that the records at all four locations exhibit similar scaling behavior which is also reflected in the multifractal spectrum determined under the assumption of a binomial multiplicative cascade model

Minimizing the effect of sinusoidal trends in detrended fluctuation analysis

The detrended fluctuation analysis (DFA) [Peng et al., 1994] and its extensions (MF-DFA) [Kantelhardt et al., 2002] have been used extensively to determine possible long-range correlations in self-affine signals. While the DFA has been claimed to be a superior technique, recent reports have indicated its susceptibility to trends in the data. In this report, a smoothing filter is proposed to minimize the effect of sinusoidal trends and distortion in the log-log plots obtained by DFA and MF-DFA techniques

Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise

Detrended fluctuation analysis (DFA) has been proposed as a robust technique to determine possible long-range correlations in power-law processes [1]. However, recent studies have reported the susceptibility of DFA to trends [2] which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. Inspired by these reports, we propose a technique based on singular value-decomposition (SVD) of the trajectory matrix to minimize the effect of linear, power-law, periodic and also quasi-periodic trends superimposed on long-range correlated power-law noise. The effectiveness of the technique is demonstrated on publicly available data sets [2].Comment: 15 pages, 13 Figure

Analysis of Bifurcations in a Power System Model with Excitation

This paper studies bifurcations in a three node power system when excitation limits are considered. This is done by approximating the limiter by a smooth function to facilitate bifurcation analysis. Spectacular qualitative changes in the system behavior induced by the limiter are illustrated by two case studies. Period doubling bifurcations and multiple attractors are shown to result due to the limiter. Detailed numerical simulations are presented to verify the results and illustrate the nature of the attractors and solutions involved

Steady State Analysis of an induction generator infinite bus system

This paper conducts a fundamental analysis on the induction generator infinite bus system which is a useful representation for a wind energy converter interfaced to a utility through a transmission line. A third order dynamic model is used to represent the induction generator and the resultant nonlinear system equations are analyzed to derive a condition that guarantees the existence of equilibrium points (or steady state solutions) to the dynamic system. This condition is used to derive three other auxiliary conditions which compute (i) the minimum value of capacitance, (ii) the maximum deliverable power and (iii) the maximum external reactance that can be connected to the machine. It is also shown that terminal voltage regulation has a strong restrictive influence on each the issues above. The analysis presented could be a useful tool for preliminary planning studies involving wind energy converters

Analytical Prediction of Subharmonic Oscillations in a Ferroresonant Circuit

Ferroresonance is a nonlinear oscillatory phenomenon that occurs in capacitively coupled transformers or reactors under certain conditions. In this paper, an averaging method is utilized to compute the domain in 2-D parameter space where subharmonic (period-3) ferroresonant oscillations could persist. The accuracy of the analytical results is verified using numerical simulations and the power spectral density. It is shown that the proposed method yields a quick means to determine (i) the proximity to initiation of subharmonic resonance and (ii) the effect of core loss on the domains of subharmonic oscillations