Dependence structure learning and joint probabilistic forecasting of stochastic power grid variables

Stochastic optimization is a promising approach to support a reliable and cost-efficient transition to a renewable generation-dominated power grid. However, utilization of this approach requires accurate and computationally affordable probabilistic forecasts that rigorously quantify the uncertainty in and the correlation between stochastic grid variables (wind/solar generation and load demand). We investigate and compare two types of probabilistic forecasting model architectures for jointly predicting stochastic variables in a power grid: sequence-to-sequence models and recursive one step ahead prediction models. A long short-term memory (LSTM) neural network model is chosen to represent sequence-to-sequence deep learning models and a periodic vector autoregressive (PVAR) model is chosen to represent the one step ahead recursive models. For each model architecture, we consider three forecasting approaches: predicting each time series variable separately, jointly predicting all time series variables of a given type (e.g., wind generation or load), or jointly predicting all time series variables. We quantify the predictive capability of these forecasting models with respect to accuracy degradation with increasing prediction horizon, ability to characterize uncertainty, and ability to capture cross-variable dependence structure. We train and test the forecasting models using publicly available zonal power supply and demand time series data for the French power grid. We find that different modeling architectures/approaches show superior forecasting capability for different prediction horizons. Our results show that in general, one step-ahead recursive (PVAR) models have high prediction accuracy for short forecast horizons, and sequence-to-sequence (LSTM) models have slower performance degradation for longer forecast horizons.