Continuous-Time Stochastic Modeling and Estimation of Electricity Load

The current discrete-time (e.g., hourly) modeling and prediction methods fall short in capturing and anticipating the sub-interval variations of electricity load. This leads to inability of power system operators to appropriately utilize the available resources to follow and compensate the load variations. This paper takes a novel and different approach on modeling electricity load, and proposes a continuous-time model for characterizing the uncertainty and variability of load. More specifically, the electricity load is modeled as a continuous-time stochastic process that is projected on a reduced-order function space spanned by Bernstein polynomials, which ensures the continuity of the process over the estimation and forecasting horizons. We assume a Gaussian process (GP) prior on the load process and design a covariance function that reflects the periodicity and smoothness of electricity load. We develop a computationally efficient method for estimating the hyperparameters of the model using the solution of a maximum likelihood estimation problem and form the posterior GP process. The proposed method is utilized to model and predict the load of California Independent System Operator (CAISO). The proposed model uniquely predicts the continuous-time mean value and uncertainty envelopes of future CAISO load, which inherently embeds information on the continuous-time variations and the associated ramping requirements of the load.