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

The irradiance fluctuations 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 of the fluctuation level of a irradiance time series. On the other side, a time series of global irradiance on the horizontal plane can be simulated by means of the wavestrapping technique on the clearness index and the fluctuation behaviour of this simulated time series correctly resembles the original series. Moreover, a time series of global irradiance on the inclined plane can be simulated with the wavestrapping procedure applied over a signal previously detrended by a partial reconstruction with a wavelet multiresolution analysis, and, once again, the fluctuation behaviour of this simulated time series is correct. This procedure is a suitable tool for the simulation of irradiance incident over a group of distant PV plants. Finally, a wavelet variance analysis and the long memory spectral exponent show that a PV plant behaves as a low-pass filter.