Harmonic Regression Analysis of Time-Series Measurements

The growing influence of digitalization and the widespread availability of data from electrical systems have unlocked significant potential for data-driven analysis. This has led to substantial opportunities for enhancing power system performance, reliability, and overall operational efficiency. One concrete illustration of these data-driven analyses involves assessing and predicting harmonic distortion using statistical learning models, notably linear regression. The implementation of linear regression models may present various challenges, especially when dealing with time series data, which is the case of harmonic measurements too. One of the main issues is the presence of autocorrelation within error terms. In this situation, the conventional linear regression approach (ordinary least square) tends to lose its reliability due to the introduction of biased standard errors impacting the accuracy of the analysis. Experts in statistics have developed various methods to handle such situations, where the error terms show autocorrelation. Interestingly, these methods have been somehow ignored or perhaps sparsely discussed by power system engineers. The primary objective of this paper is to contribute to narrowing this gap. It does so by presenting the application of the Cochrane-Orcutt method in the harmonic data analysis context. The Cochrane-Orcutt method represents a well-known econometric technique used to consider serial correlations within the error terms of a linear model and can also be applied in the harmonic analysis domain. This paper is supported at first by an illustrative example based on simulated data, designed to provide a clear insight into the subject matter. Additionally, a case study with real-world measurement data is also presented, to further enhance the understanding.