Analysis and synthesis of the variability of irradiance and PV power time series with the wavelet transform

Abstract

The irradiance uctuations and the subsequent variability of the power output of a PV system are analysed with some mathematical tools based on the wavelet transform. It can be shown that the irradiance and power time series are nonstationary process whose behaviour resembles that of a long memory process. Besides, the long memory spectral exponent α is a useful indicator

Electrical power fluctuations in a network of DC/AC inverters in a large PV plant: Relationship between correlation, distance and time scale

“…The analysis of solar irradiance and electrical power time series with the wavelet transform can be found in a variety of research papers [8,9,13]. The wavelet transform is a filtering procedure which carries out a multiresolution analysis (MRA) of a time series, where each of the decompositions of the analysis is a representation of the original signal with a different temporal scale.…”

“…The wavelet transform is a filtering procedure which carries out a multiresolution analysis (MRA) of a time series, where each of the decompositions of the analysis is a representation of the original signal with a different temporal scale. This non-parametric analysis overcomes the restrictions imposed when using classical time series analysis: for example, AR, MA, ARMA models and spectral analysis, are based on the premises of stationarity and short memory process, conditions which are not fulfilled by solar irradiance time series [8]. Besides, this tool improves the examination of fluctuations in a time series: for example, it is common to find reports with fluctuations calculated as a simple substraction between two samples, with time intervals chosen arbitrarily, without relation with data.…”

“…These coefficients have mean zero for adequate wavelet filters, and therefore: Similarly the wavelet cross-correlation for scale λ j and lag τ can be defined with the wavelet cross-covariance and the wavelet variances for both processes 8 :…”

“…On the other hand, the wavelet transform (WT) is used in [8] to show that the irradiance and power time series are nonstationary processes whose behaviour resembles that of a long memory process. The combination of a wavelet variance analysis with the long memory spectral exponent shows again that a PV plant behaves as a low-pass filter.…”

Spatial and Temporal Day-Ahead Total Daily Solar Irradiation Forecasting: Ensemble Forecasting Based on the Empirical Biasing

“…Solar power that is generated on a solar farm can be easily calculated from the solar irradiation at the target location since the relationship between solar irradiation and solar power is nearly linear [24]. Furthermore, although hourly solar irradiation forecasting is much more useful for power system applications, it is beyond the scope of this paper, and, if necessary, hourly solar irradiation could be estimated from the total daily solar irradiation since solar irradiation follows a strong daily pattern even on cloudy days.…”