Several variants of Kalman Filter algorithm for power system harmonic estimation Santosh Kumar Singh ⇑ , Nilotpal Sinha, Arup Kumar Goswami, Nidul Sinha Electrical Engineering Department, National Institute of Technology Silchar, Silchar, Assam, India article info Article history: Received 20 December 2014 Received in revised form 23 November 2015 Accepted 17 December 2015 Available online 4 January 2016 Keywords: Signal processing Local Ensemble Transform based Kalman Filter Harmonics Power quality abstract This paper presents the maiden application of a variant of Kalman Filter algorithm known as Local Ensemble Transform based Kalman Filter (LET-KF) for power system harmonic estimation. The proposed algorithm is applied for estimating the harmonic parameters of a power signal containing harmonics, sub-harmonics, inter-harmonics in presence of white Gaussian noise. These algorithms are applied and tested for both stationary as well as dynamic signals containing harmonics. The LET-KF algorithm reported in this paper is compared with the earlier reported Kalman Filter based algorithms like Kalman Filter (KF) and Ensemble Kalman Filter (EnKF) algorithms for harmonic estimation. The proposed algorithm is found superior than the reported algorithm for its improved efficiency and accuracy in terms of simplicity and computational features, since there are less multiplicative operations, which reduces the rounding errors. It is also less expensive as it reduces the requirement of storing large matrices, such as the Kalman gain matrix used in other KF based methods. Practical validation is carried out with exper- imentation of the algorithms with the real time data obtained from a large paper industry. Comparison of the results obtained with KF, EnKF and LET-KF algorithms reveals that the proposed LET-KF algorithm is the best in terms of accuracy and computational efficiency for harmonic estimation. Ó 2015 Elsevier Ltd. All rights reserved. Introduction For the development of effective Power Quality (PQ) monitoring techniques, greater efforts are made by the researchers towards the development of less-complex and more efficient techniques for detection, classification, identification of power quality disturbances. Another key and challenging problem reported recently by the researchers related to power quality is the estimation of harmonic parameters for fundamental, harmonics, inter-harmonics and sub-harmonics components of voltage and currents signals. Accurate and efficient estimation of harmonics from the distorted voltage signals is an important issue for monitoring and analysis of power quality problems [1,2]. Harmonics are components of a distorted periodic waveform, whose frequencies are integer multiples of the fundamental fre- quency. In electrical power networks, the increasing use of nonlin- ear loads and power electronic based load devices has caused much more harmonic pollution, which significantly deteriorates the power quality [1]. In order to reduce the harmonic pollution, it is necessary to estimate the parameters of the harmonics. With the estimated parameters, such as amplitudes and phases, appropriate compensation system can be designed for improving the poor power quality performances [1,2]. For past few decades, various approaches have been proposed to estimate the parameters of these harmonics [1]. The Fast Fourier Transform (FFT) is a suitable approach for stationary signal, but it loses accuracy under time varying frequency conditions and also posses picket and fence problems [3–5]. The International Electro- Technical Commission (IEC) standard drafts have specified signal processing recommendations and definitions for harmonic, sub- harmonic and inter-harmonic measurement [4]. These standards recommend using Discrete Fourier Transform (DFT) for harmonic estimation with some windowing based issues but the DFT-based algorithms do not perform stably for systems with time varying frequency [5–7]. Many recursive algorithms are also proposed to solve harmonic estimation problem but each of them have several limitations in terms of accuracy, convergence and computational time. The Least Mean Square (LMS) based algorithms have the drawbacks for their poor convergence in addition to being failure in case of signal drifting and changing conditions. However, Recursive Least Square (RLS) group is the successful algorithms to some extent but the ini- tialization for these algorithm parameters still remains a challenge in case of time varying dynamic signals. The accuracy is also limited for this class of algorithms [5–7]. http://dx.doi.org/10.1016/j.ijepes.2015.12.028 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +91 9678845384; fax: +91 0091 3842 224797. E-mail address: santoshkrsingh.nits@gmail.com (S.K. Singh). Electrical Power and Energy Systems 78 (2016) 793–800 Contents lists available at ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes