Power Curve Estimation: Functional Estimation Imposing the Regular Ultra Passum Law

Abstract

Imposing economic relationships such as the Regular Ultra Passum (RUP) law improves the statistical efficiency of nonparametric estimators in finite samples. RUP law bears relevance in engineering applications such as power curve estimation in the wind energy industry. Unfortunately, the few estimators known to satisfy the RUP law are based on deterministic assumptions that do not allow noise in the modeling. In most engineering applications, however, data are inevitably noisy, due to equipment calibration, natural variations, or other issues. Thus, we propose an estimator that satisfies the RUP law while also capable of handling noisy data. We use Monte Carlo simulations to show that the proposed estimator outperforms existing deterministic estimators, particularly when the scale of noise is large. We use the proposed method to estimate a power curve considering approximately 13,000 observations of a wind turbine. The results demonstrate that the proposed estimator is well suited for engineering applications with a high degree of noise.

Keywords: convex nonparametric least squares, curve fitting with shape constraints, nonparametric statistics, production economics analysis, wind energy application