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

Abstract

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 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. 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.

Integrated Energy Systems: 2020 Roadmap

“…Most of the work in this respect is focused on reduction of the necessary number of samples to ensure a reliable convergence of the stochastic optimization under probabilistic constraints. For further details on the simulation framework see references (Rabiti et al 2017;Epiney et al 2018;Talbot et al 2018).…”

Evaluation of Hybrid FPOG Applications in Regulated and Deregulated Markets Using HERON

“…Each synthetic history generation represents a multiyear scenario with the same statistical characteristics as the data on which it is trained, but with distinct signals [23]. This enables a set of components with fixed capacities to be tested under a variety of realistic circumstances and determine the system's statistical economic viability.…”

HERON as a Tool for LWR Market Interaction in a Deregulated Market

“…] to construct an analysis framework using RAVEN for systems of energy producers and consumers in a method that allows statistically-meaningful decisions to be made with regards to the economic viability of energy grid portfolios and configurations. The results of this effort have shown value both in a theoretical sense [1,2,4,5,7,[9][10][11][12] as well as for specific applications when paired with industrial partners in the energy space [3,16]. However, the development and maintenance of these RAVEN workflows has been burdensome, and often involves complicated copy-and-modify operations that significantly slow the user experience.…”

“…The price of electricity sold at the Grid is given by a synthetic history [9,10,11] and changes for each time step. For this example, we consider on the resolution of the first time step as an example.…”