An impedance matrix constrained‐based method for harmonic emission level estimation

Abstract

Summary The harmonic impedances are important for both utility companies and their customers. The data have many uses, such as estimating harmonic emission levels, designing filters. Complex independent component analysis is a well‐accepted method for harmonic impedance estimation. However, a lack of data points for each calculation leads to wrong results. To increase the feasibility of this method, we proposed a constrained complex independent component analysis‐based method by adding the essential feature of the harmonic impedance matrix. Thus, the recovered source signals, which are highly consistent with the original source signals can be found when the data quantity for each calculation is little. The method has been verified using simulation studies and extensive field data. The results show that the proposed method can serve as a useful tool to support the harmonic impedance calculation task of utility companies and their customers.

Blind source separation methods applied to evaluate harmonic contribution

“…However, these methods adopt simplifying assumptions, such as that the utility's impedance is much larger than the consumer's and are sensitive to background voltage harmonics and to the changes of frequency. 9 , 10 …”

“…Consequentially, different BSS techniques have been proposed and are well‐established in academic fields, such as telecommunications, audio signal separation, feature extraction, biomedical signal processing, pattern recognition, and financial time series analysis. 11 , 12 , 13 In EPS, more specifically in power quality issues, the BSS methods have been used for harmonic load identification, 14 , 15 , 16 in the separation of harmonic components 17 , 18 and to estimate the utility 9 , 19 , 20 , 21 and consumer 10 , 22 , 23 harmonic impedance at PCC.…”

“…Thus, different noninvasive methods have been proposed to estimate the harmonic equivalent impedance of the system, and consequently the harmonic contribution, for example, the method based on covariance characteristic of random vectors, the fluctuation method, the linear regression method, the method based on data selection, among others. However, these methods adopt simplifying assumptions, such as that the utility's impedance is much larger than the consumer's and are sensitive to background voltage harmonics and to the changes of frequency 9,10 …”

“…Although a methodology for determining the harmonic contribution through the BSS method already exists in the literature, by using the ICA approach, 10,22,23 the application of this technique is not consolidated yet due to the complexity characteristic of BSS methods and the absence of more comprehensive analyses considering the nature of the EPS. For example, several articles make computational evaluations using hypothetical current sources with the same mean and variance for both utility and the consumer 19,22,23 .…”

“…However, these methods adopt simplifying assumptions, such as that the utility's impedance is much larger than the consumer's and are sensitive to background voltage harmonics and to the changes of frequency. 9,10 Given the above, the use of blind source separation (BSS) techniques to identify harmonic contributions at the PCC is a promising alternative, as it does not require the installation of any specific equipment and that does not require the impedance of the supplying system to be much higher than that of the consumer.…”