Rudy Calif

By Rudy Calif, François G. Schmitt and O. Durán Medina

The massive integration of sustainable energies into electrical grids (non-interconnected or connected) is a major problem due to their stochastic character revealed by strong fluctuations at all scales. In this paper, the scaling behaviour or power law correlations and the nature of scaling behaviour of sustainable resource data such as flow velocity, atmospheric wind speed, solar global solar radiation and sustainable energy such as, wind power output, are highlighted. For the first time, Fourier power spectral densities are estimated for each dataset. We show that the power spectrum densities obtained are close to the 5/3 Kolmogorov spectrum. Furthermore, the multifractal and intermittent properties of sustainable resource and energy data have been revealed by the concavity of the scaling exponent function. The proposed analysis frame allows a full description of fluctuations of processes considered. A good knowledge of the dynamic of fluctuations is crucial to management of the integration of sustainable energies into a grid.

Part of the book: Sustainable Energy

By Thomas Plocoste and Rudy Calif

During the last 20 years, many megacities have experienced air pollution leading to negative impacts on human health. In the Caribbean region, air quality is widely affected by African dust which causes several diseases, particularly, respiratory diseases. This is why it is crucial to improve the understanding of PM10 fluctuations in order to elaborate strategies and construct tools to predict dust events. A first step consists to characterize the dynamical properties of PM10 fluctuations, for instance, to highlight possible scaling in PM10 density power spectrum. For that, the scale-invariant properties of PM10 daily time series during 6 years are investigated through the theoretical Hilbert frame. Thereafter, the Hilbert spectrum in time-frequency domain is considered. The choice of theoretical frame must be relevant. A comparative analysis is also provided between the results achieved in the Hilbert and Fourier spaces.

Part of the book: Functional Calculus

By Maina André and Rudy Calif

The characterization of irradiance variability needs tools to describe and quantify variability at different time scales in order to optimally integrate PV onto electrical grids. Recently in the literature, a metric called nominal variability defines the intradaily variability by the ramp rate’s variance. Here we will concentrate on the quantification of this parameter at different short time scales for tropical measurement sites which particularly exhibit high irradiance variability due to complex microclimatic context. By analogy with Taylor law performed on several complex processes, an analysis of temporal fluctuations scaling properties is proposed. The results showed that the process of intradaily variability obeys Taylor’s power law for every short time scales and several insolation conditions. The Taylor power law for simulated PV power output has been verified for very short time scale (30s sampled data) and short time scale (10 min sampled data). The exponent λ presents values between 0.5 and 0.8. Consequently, the results showed a consistency of Taylor power law for simulated PV power output. These results are a statistical perspective in solar energy area and introduce intradaily variability PV power output which are key properties of this characterization, enabling its high penetration.

Part of the book: Solar Radiation