**Wavelet Packet Decomposition for IEC Compliant Assessment of Harmonics under Stationary and Fluctuating Conditions**

#### **Stefano Lodetti, Jorge Bruna, Julio J. Melero \* and José F. Sanz**

Instituto Universitario de Investigación CIRCE (Fundación CIRCE—Universidad de Zaragoza), C/Mariano Esquillor 15, 50018 Zaragoza, Spain; slodetti@fcirce.es (S.L.); jbruna@fcirce.es (J.B.); jfsanz@unizar.es (J.F.S.)

**\*** Correspondence: melero@unizar.es; Tel.: +349-7676-2402

Received: 10 October 2019; Accepted: 15 November 2019; Published: 19 November 2019

**Abstract:** This paper presents the validation and characterization of a wavelet based decomposition method for the assessment of harmonic distortion in power systems, under stationary and non-stationary conditions. It uses Wavelet Packet Decomposition with Butterworth Infinite Impulse Response filters and a decomposition structure, which allows the measurement of both odd and even harmonics, up to the 63rd order, fully compliant with the requirements of the IEC 61000-4-7 standard. The method is shown to fulfil the IEC accuracy requirements for stationary harmonics, obtaining the same accuracy even under fluctuating conditions. Then, it is validated using simulated signals with real harmonic content. The proposed method is proven to be fully equivalent to Fourier analysis under stationary conditions, being often more accurate. Under non-stationary conditions, instead, it provides significantly higher accuracy, while the IEC strategy produces large errors. Lastly, the method is tested with real current and voltage signals, measured in conditions of high harmonic distortion. The proposed strategy provides a method with superior performance for fluctuating harmonics, but at the same time IEC compliant under stationary conditions.

**Keywords:** harmonic analysis; power quality; wavelet transform; wavelet packet; measurement techniques
