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The present study proposes a novel method of tracking the time varying frequency and amplitude of a distorted power frequency signal using an unscented Kalman filter (UKF). The UKF is a derivative free estimator which does not compute Jacobian matrices and therefore offers significant computational advantages over the extended Kalman filter (EKF)....
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This paper proposes the application of a non-linear Extended Kalman Filter (EKF) for accurate instantaneous dynamic phasor estimation. An EKF-based algorithm is proposed to better adapt to the dynamic measurement requirements and to provide real-time tracking of the fundamental harmonic components and power system frequencies. This method is evalua...
With the power system harmonic pollution problems becoming more and more serious, how to distinguish the harmonic responsibility accurately and solve the grid harmonics simply and effectively has become the main development direction in harmonic control subjects. This paper, based on linear regression analysis of basic equation and improvement equa...
Citations
... To determine the noise covariance matrices, we first construct the measured signal using the calculated harmonic components and equation (15), including the direct current (constant) term. Then we calculate the covariance matrix of the error between the constructed signal and the measured one. ...
This paper introduces a new model for estimation of the fundamental frequency as well as power harmonics components using extended and linear Kalman filters. It also compares the proposed method with existing techniques including a commercial power harmonic measuring device compatible to IEC 61000-4-7 standard in an experimental setting. The proposed method is shown to result in significantly enhanced estimation of the fundamental frequency and slightly improved harmonic estimation.
... for k ∈ Z + , where T is the interval between samples and n(kT ) ∼ N (0, R) is zero-mean, Gaussian, white noise with variance R ∈ R, the aim is to generateŝ(T ) the estimate of the underlying signal at each of the sampling points, together with estimates of α(kT ) and ω(kT ). This problem was motivated by the need to track sinusoidal signals in Coriolis flow metering [1], but is also encountered in applications such as power systems, speech recognition and communications [2], [3], [4], [5], [6], [7], [8], [9]. ...
... Identification and management of PQ events is a major research concern for the successful and efficient operation of the existing and future smart grids. Perhaps for this reason, the identification and remedy of PQ events have attracted the attention of many researchers [1][2][3][4][5]. ...
The present study comprehensively investigates Power Quality (PQ) identification problem and proposes the optimum combination of base wavelet and Machine Learning Algorithm (MLA) which would yield highest classification accuracy. Although this problem has been studied by various researchers in the recent past, the selection of appropriate base wavelet and MLA, which would give better classification accuracy, have received comparatively less attention. This study bridges this gap by investigating the classification performance of 110 wavelets and 7 well-known MLAs across various noise levels using over 3500 PQ events generated as per IEEE Standard 1159. The results of this investigation demonstrate that the choice of base wavelet does significantly affect the classification performance. Further, it was observed that a single base wavelet does not provide optimum performance across all MLAs at various noise levels. In contrast, each MLA gives the maximum accuracy with a distinct base wavelet. The robustness of MLA against noise is studied which establishes that the simple MLAs, such as Decision Tree (DT) and Naive-Bayes (NB), are more robust against noise compared to the other intricate MLAs. Finally, several recommendations are drawn for the selection of base wavelet and MLA which yields the best possible accuracy.
... The parameter β is used to incorporate prior knowledge of the distribution of sigma points x and it is usually set to 2 for a Gaussian distribution [23]. ...
We present a dynamic frequency and amplitude estimation algorithm for unbalanced three-phase power systems with harmonics. To develop the algorithm, we first construct a nonlinear dynamic model of the complex representation of the three-phase voltage with harmonic content and then apply an unscented Kalman filter to estimate magnitudes and frequencies of the fundamental component and its harmonics. Performance evaluation of the algorithm via Monte Carlo simulation shows the accurate tracking and fast convergence time when the frequency and amplitude of the grid voltage waveform change continuously or abruptly. Specifically, we benchmark the proposed algorithm with two types of input amplitudes and two types of frequency changes.
... The core idea of this approach is to integrate the information about the cardinality (i.e., the number of features) into the search process. This learning approach has been applied to address the power quality problems [10] and has been shown to perform better than some of the existing approaches [11]- [13]. In this study, it has been shown that this learning approach can easily be applied to address the model structure selection problem, as in essence, the main objective of both the feature selection and the structure detection are similar, i.e., detect a parsimonious model or remove redundant features/terms. ...
The present study applies a novel two-dimensional learning framework (2D-UPSO) based on particle swarms for structure selection of polynomial nonlinear auto-regressive with exogenous inputs (NARX) models. This learning approach explicitly incorporates the information about the cardinality (i.e., the number of terms) into the structure selection process. Initially, the effectiveness of the proposed approach was compared against the classical genetic algorithm (GA) based approach and it was demonstrated that the 2D-UPSO is superior. Further, since the performance of any meta-heuristic search algorithm is critically dependent on the choice of the fitness function, the efficacy of the proposed approach was investigated using two distinct information theoretic criteria such as Akaike and Bayesian information criterion. The robustness of this approach against various levels of measurement noise is also studied. Simulation results on various nonlinear systems demonstrate that the proposed algorithm could accurately determine the structure of the polynomial NARX model even under the influence of measurement noise.
... Bayesian dynamic estimation of frequency has been recently applied using the Kalman filter and its variants [25][26][27][28][29]. In [25] the authors present a linear Kalman filter to detect fast modal changes in power systems, including frequency estimation. ...
The frequency of the grid voltage is a time-varying parameter caused by mismatches between power generation and power consumption. In fact, the fundamental frequency decreases when large loads are connected to the system or when a large generation source goes offline. The opposite holds true for an increase in the fundamental frequency, e.g. when generation exceeds consumption. Hence, in order to protect a power system against loss of synchronism, under-frequency relaying, and power system stabilisation, accurate frequency estimation is necessary. This study proposes an adaptive algorithm based on a master-slave unscented Kalman filter (UKF) configuration to estimate both the voltage frequency and the measurement noise. Specifically, the master UKF uses the strong tracking filter condition to improve tracking accuracy, speed of convergence, and to desensitise the filter from initial conditions. The slave UKF uses the master UKF innovation to estimate the measurement noise covariance. The proposed approach addresses the tracking weaknesses of other frequency estimation algorithms when the frequency of the grid voltage waveform changes abruptly. Algorithm performance is measured through computer simulation.
... Over the years, several signal processing techniques have been employed for the purpose of feature extraction which includes but not limited to Fourier Transform, Hilbert Transform, Short-Time Fourier Transform, Stockwell Transform and Wavelet Transform [2]- [8]. Especially, Stockwell Transform (ST) and Wavelet Transform (WT) can extract information in temporal and frequency domain which is crucial for the accurate event identification. ...
The present study focuses on the selection of appropriate wavelet basis which would result in better classification of Power Quality (PQ) events. The accuracy of the classification is often critically dependent on the nature of wavelet basis and the induction algorithm. This study, therefore, comprehensively investigates the performance of several wavelet families including Daubechies, Coiflets, Symlets, Fejer-Korovkin, Bi-orthogonal and Reverse Bi-orthogonal from the prospective of PQ event identification. The performance of these wavelets was evaluated through fourteen distinct single and simultaneous PQ events which were generated following IEEE Std. 1159. Further, to investigate the interaction between induction algorithm and wavelet basis, two induction algorithms were included: k-Nearest Neighbor (k-NN) and Naive Bayes (NB). The results of the investigation convincingly demonstrate that `db18' from the Daubechies family provides the best overall performance among 110 wavelet bases included in this study.
... These issues have lead to various Power Quality (PQ) problems which has been a major concern for the utilities. Perhaps, for this reason PQ has attracted many researchers over the past few years [1]- [3]. This study essentially focus on identification of PQ events. ...
This study investigates the performance of a filter based feature selection approach for PQ event identification. The filter based approach is independent of the nature of induction algorithms used for the classification purposes and therefore offers several advantages over other approaches such as wrappers. This property of filter approach has been exploited in this study to obtain a generic feature subset that can be used with any induction algorithm. For this purpose, fourteen distinct single and simultaneous PQ events were simulated following IEEE Std. 1159. The feature selection of these events is accomplished through a combination of meta-heuristic search method and correlation based feature evaluation. Two meta-heuristic search methods based on Genetic Algorithm (GA) and Binary Particle Swarm Optimization (BPSO) have been included for the comparison of search performance. The efficacy of reduced feature subsets is evaluated through induction algorithm based on Naive-Bayes. The results convincingly demonstrated that it is possible to obtain significant reduction in the features (approx. 50% with GA, 86% with BPSO) without any compromise in the classification performance.
... The remedial actions for PQ improvement can only be initiated, if the nature the PQ disturbances, their impact on overall PQ and the frequency of their occurrence is correctly monitored [2]. Hence, the identification of PQ disturbance through classification is essential before taking any remedial action [3]- [5]. For this purpose, the IEEE 1159-2009 standard broadly defines the different PQ disturbances [6] such as voltage sag, voltage swell, interruptions, harmonics, oscillatory and impulsive transients on the basis of their magnitude, duration and spectral content. ...
... C6(2,3), C11 (3,4) the hidden layer (hidden neurons) to beÑ ), the output of ELM for the j th training sample (o j ) can be given by the following equation [21], [22], ...
A novel method of classifying Power quality (PQ) events using Wavelet Packet Transform (WPT) and Extreme Learning Machines (ELM) has been proposed. In recent times, the power quality has been a major research concern due to changing regulations, liberalized distribution market and increased use of power electronic based equipment. The first step of any remedial action requires proper identification of PQ events. One of the major challenge of this event identification is to extract significant features from the limited measurements, which can subsequently be used for the classification. Therefore, in the present study Wavelet Packet Transform (WPT) has been used to obtain several mathematical features. These features can segregate both single and simultaneous PQ event occurrences. Further to improve the classification performance, the ELM based classifier has been used. This classifier significantly reduces the training time by many-fold. The performance of the proposed approach has been compared with ANN based classifier considering over 1000 PQ signals from various PQ events. The results of the simulation demonstrate that the proposed approach can achieve over 99% classification accuracy.
... The process of constructing mathematical models from the observed input and output data is called system identification. Methods Commonly used for system identification are Neural Network methods[1,2,3], least square method[4] , Kalman Filter [5], Extended Kalman Filter [6,7], Unscented Kalman Filter [8,9] etc. Paper [1], proposed ARMA model utilizes two hidden units for first order polynomial function. Similarly non linear ARMA is analysed. ...
... The most popular adaptive filter is Kalman filter. The popular suboptimal nonlinear filters are extended Kalman filter (EKF) [6,7], Unscented Kalman filter [8,9]. KF is formulated in a predictor corrector manner. ...
... In this section, the paper compares the performance of different adaptive filter approaches like EKF [7], UKF [9] with the SVSF [13] with the proposed method on popular system identification problem. The purpose of this experiment is to demonstrate the improved robustness, stability and accuracy of different variants of SVSF algorithm over conventional algorithms like EKF, UKF. ...
This paper proposes a model based approach for nonlinear dynamic system identification, which utilizes Smooth variable structure filter (SVSF) having multi fold advantages over other adaptive filters. The SVSF is based on sliding mode control concept and can be applied to both linear and nonlinear system. Further to increase the accuracy of nonlinear chaotic system identification the 'memory element' γ is tuned iteratively in the measurement matrix of SVSF. So, a self tuning approach for updating memory element is proposed, which is inversely proportional to the sample number. Further SVSF is modified by introducing a nonlinear term with square innovation error in measurement matrix to achieve higher order sliding mode control. The effect and the improvement of this modification has been verified under different test conditions. Various simulations have been carried out to show the stability and improved robustness of the proposed algorithm over other conventional methods. The mean square error obtained using this approach is found to be significantly less than other conventional methods.
