Non-parametric Regression Model for Continuous-time Day Ahead Load Forecasting with Bernstein Polynomial

Growing perception of diverse generation resources and demand response operation of power system with high uncertainty has increased the attention to a more dynamic and accurate day-ahead load prediction. In this paper, we develop an stochastic model for short term load forecasting based on the Gaussian process, in which the non parametric estimator of the regression functions are obtained by using Bernstein polynomials. One of the major features of this model is its ability to predict a continuous load at any time of the day with a regression function. We use the historical data for training and the constrained marginal likelihood problem is optimized for finding the hyperparameters of the model. Real data sets from California ISO were used for training and testing the model. The results are compared to the day ahead piecewise constant load and the real time load. The common error measures are employed to infer the deviation of the load forecast from the real data.