Correlated Synthetic Time Series Generation using Fourier and ARMA
As the contribution of renewable energy grows in electricity markets, the complexity nuclear’s place within the energy mix increases, and likewise the need for robust simulation techniques. While decades of wind, solar, and demand pro- files can sometimes be obtained, this is too few samples to provide a statistically meaningful analysis of a system with baseload, peaker, and renewable generation. Synthetic time series generation presents itself as a suitable methodology to meet this need. One approach for synthetic series generation is training a model using Fourier series decomposition for seasonal patterns and Auto-Regressive Moving Average models (ARMA) to describe time-correlated statistical noise about the seasonal patterns. When combined, the Fourier plus ARMA (FARMA) model has been shown to provide an infinite set of independent, identically-distributed sample time series with the same statistical properties as the original data [1]. When considering an energy mix with renewable electricity production, several time series of energy, grid, and weather measurements are needed for each synthetic year modeled to statistically comprehend the efficiency of any given energy mix. These cannot be considered independent series in a given synthetic year. To capture and reproduce the correlations that might exist in the measured histories, the ARMA can further be extended as a Vector ARMA (VARMA). In the VARMA algorithm, covariance in statistical noise is captured both within a history as part of the autoregressive moving average, and with respect to the other variables in the time series. In this work the implementation of the Fourier VARMA in the RAVEN uncertainty quantification and risk analysis software framework [2] is presented, along with examples of correlated synthetic history generation.