Constrained Nonparametric Regression Analysis of Load Curves

In this paper, we analyze household load curves through the use of Constrained Smoothing Splines. These estimators are natural smoothing splines that allow to incorporate periodic shape constraints. Since the time pattern of electricity demand combines strong periodical regularities with abrupt changes along time, a nonparametric regression estimator that is able to incorporate regularity constrains appears to be very well suited to approach load curves. In the paper we also propose a method to compute the penalty parameters that appear in the constrained smoothing spline estimator, we show some statistical properties and finally we construct confidence intervals