Correlated synthetic time series generation for energy system simulations using Fourier and ARMA signal processing

As the contribution of renewable energy grows in electricity markets, the complexity of the energy mix required to meet demand grows, likewise the need for robust simulation techniques. While decades of wind, solar, and demand profiles can sometimes be obtained, this is too few samples to provide a statistically meaningful analysis of a system with baseload, peaker, and renewable generation. To demonstrate the viability of an energy mix, many thousands of samples are needed. Synthetic time series generation presents itself as a suitable methodology to meet this need. For a synthetic time series to be statistically viable, several conditions must be met. The series generator must produce independent, identically distributed samples, each having the same fundamental properties as the original signal without duplicating it exactly. One approach for such a generator is training a surrogate model using Fourier series decomposition for seasonal patterns and autoregressive moving average (ARMA) models 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. This includes measurements of solar exposure, air temperature, wind velocity, and electricity demand. These cannot be considered independent series in a given synthetic year; for example, in summer months demand may be higher when solar exposure and air temperature are high and wind velocity is low. 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. Finally, methods to extend synthetic signals to multiyear samples are presented and discussed.