534 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 2, APRIL 2010 Processing of Harmonics and Interharmonics Using an Adaptive Notch Filter Mohsen Mojiri, Masoud Karimi-Ghartemani, Senior Member, IEEE, and Alireza Bakhshai, Senior Member, IEEE Abstract—A method for real-time detection and extraction of individual harmonic and interharmonic components in a power signal with potentially time-varying characteristics is presented. The proposed method, which is based on the concept of adaptive notch filter (ANF), adaptively decomposes the measured power signal into its constituting components independent of where their frequencies are located. The algorithm provides instantaneous values of the various estimated frequency components in addition to the values of their frequencies, amplitudes, and phase angles. The structure and mathematical formulation of the proposed technique, including guidelines for its parameter tuning, are presented and its performance is studied in a variety of scenarios where the power signal attributes, such as fundamental frequency and amplitude, undergo variations over time. This study confirms the desirable transient and steady-state performances of the pro- posed method. Compared with its recently proposed counterpart, the proposed method of this paper obviates the need for using a phase-locked loop (PLL), and hence, offers a more simplified structure which makes it more attractive from an implementation point of view. Index Terms—Adaptive notch filter, harmonics detection and ex- traction, harmonics measurement, interharmonics, power signal analysis. I. INTRODUCTION P OWER system signals are often polluted and distorted by undesired components as a result of nonlinear loads, mainly power-electronic devices. Widespread use of sensitive loads, such as computers and microprocessor-based industrial controllers, signify the ever-increasing need for efficient har- monic measurement and compensating systems [1]. Moreover, power systems protection, control, and performance efficiency and power-quality (PQ) improvements have been achieved through increased efforts in devising signal detection and extraction algorithms and devices over the last decade. A signal detection algorithm requires means for accurate and real-time measurement of individual harmonics and inter- harmonics within a signal, and their signal attributes, such as magnitudes, phase angles, and frequencies. Mutual erroneous Manuscript received January 01, 2008; revised March 10, 2009, June 19, 2009, and September 22, 2009. First published March 08, 2010; current ver- sion published March 24, 2010. Paper no. TPWRD-00001-2008. M. Mojiri is with the Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran (e-mail: mohsen. mojiri@cc.iut.ac.ir). M. Karimi-Ghartemani and A. Bakhshai are with the Department of Elec- trical and Computer Engineering, Queen’s University, Kingston, ON K7L 3N6, Canada (e-mail: karimig@queensu.ca; alireza.bakhshai@queensu.ca). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRD.2009.2036624 impacts of harmonic/interharmonic components on each other, their dynamic nature, and the noise pollution are factors which make the problem challenging, thereby rendering it an active field of research. A variety of techniques exist and are used to analyze har- monics. Those are discrete Fourier transform (DFT) [2]–[4]; artificial neural networks (ANNs) [5], [6]; least-squares tech- niques [7], [8]; Kalman filtering [9]; Parseval’s relation and en- ergy concept [10]; adaptive infinite impulse-response line en- hancer [11]; and the phase-locked-loop-based technique [12]. The desirable objectives are adaptability to frequency-varying situations, having a simple and robust structure suitable for prac- tical applications and desirable noise immunity [12]. Recently, a set of adaptive signal-processing techniques for the estimation of the attributes of a signal composed of sinusoids has been proposed in [13] and [14]. Those techniques, which are based on the adaptive notch filtering concept, have been pro- posed for the analysis of a harmonically constructed signal [13] and, in general, a signal composed of sinusoids [14]. These tech- niques are capable of completely removing the mutual impacts of the constituting components on each other. This is due to the inherent structure of these techniques which is based on a full decomposition of the signal. General evaluation of those tech- niques has been carried out in [13] and [14]. The method of [13] makes a fundamental assumption that the existing frequency components in the signal are in the form of harmonics. The method of [14] demands further calculations to arrive at a full decomposition of the signal. The presented work of this paper, on the other hand, relaxes that assumption and presents a major improvement into the algorithms of [13] and [14] which enables direct detection and extraction of arbitrary frequency components, including unknown interharmonics. Guidelines on tuning the controlling parameters of the system are provided as well. Moreover, a comprehensive evaluation of the improved algorithm in the context of various scenarios related to power system signals is presented. The adaptive na- ture of the proposed technique enables tracking of variations in all characteristics of the power signal, such as variations in the frequency and amplitude of the fundamental, harmonic, and/or interharmonic components. The desired tracking performance of the proposed algorithm as well as its noise immunity feature are verified by computer simulations. The main advantage of the proposed algorithm, compared with a recently presented technique which is based on the concept of the phase-locked loop (PLL) [12], is in terms of the building components: the proposed structure obviates the need for a voltage-controlled oscillator (VCO) which makes it computationally more effi- cient. The proposed system exhibits a longer transient time than some fast digital algorithms, such as those based on fast 0885-8977/$26.00 © 2010 IEEE