Bayesian Time-Series Analysis to Predict Real-Time Smart Grid Energy Price Uncertainty

The prediction of the real-time (RT) electricity prices in the smart grids is one of the challenging problems for electricity producers as well as consumers. To participate in smart grids RT electricity market, it is essential to predict the uncertainty inherent in price values caused by data collection and analysis methods and conduct risk analysis. In this paper, using the Auto-regressive Integrated Moving-Average (ARIMA) formulation of time-series, first a deterministic model of RT price is developed. Then, using Bayesian theorem and considering stochastic behavior of the prices, a stochastic ARIMA model to predict price uncertainty is presented. To obtain RT price posterior distribution, two different Bayesian statistical approaches are used and compared against each other. The first approach is direct Bayesian modeling using Hamilton Monte Carlo Markov Chain (HMCMC) sampling and the second method is Variational Bayesian (VB) Inference. Both methods are implemented on the New England Independent System Operator (ISO) public price dataset. The results confirm the solidness of proposed method to obtain price uncertainty and optimal confidence intervals.