This paper proposes the use of a least mean fourth (LMF)-based algorithm for single-stage three-phase grid-integrated solar photovoltaic (SPV) system. It consists of an SPV array, voltage source converter (VSC), three-phase grid, and linear/nonlinear loads. This system has an SPV array coupled with a VSC to provide three-phase active power and also acts as a static compensator for the reactive power compensation. It also conforms to an IEEE-519 standard on harmonics by improving the quality of power in the three-phase distribution network. Therefore, this system serves to provide harmonics alleviation, load balancing, power factor correction and regulating the terminal voltage at the point of common coupling. In order to increase the efficiency and maximum power to be extracted from the SPV array at varying environmental conditions, a single-stage system is used along with perturb and observe method of maximum power point tracking (MPPT) integrated with the LMF-based control technique. The proposed system is modeled and simulated using MATLAB/Simulink with available simpower system toolbox and the behaviour of the system under different loads and environmental conditions are verified experimentally on a developed system in the laboratory.

LMF-Based Control Algorithm for Single Stage Three-Phase Grid Integrated Solar PV System

Cyclostationarity: New trends and applications

We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost inspired by the “competitive methods” from the online learning literature. The competitive or regret based approaches stabilize or improve the convergence performance of adaptive algorithms through relative cost functions. The new family elegantly and gradually adjusts the conventional cost functions in its optimization based on the error amount. We introduce important members of this family of algorithms such as the least mean logarithmic square (LMLS) and least logarithmic absolute difference (LLAD) algorithms. However, our approach and analysis are generic such that they cover other well-known cost functions as described in the paper. The LMLS algorithm achieves comparable convergence performance with the least mean fourth (LMF) algorithm and enhances the stability performance significantly. The LLAD and least mean square (LMS) algorithms demonstrate similar convergence performance in impulse-free noise environments while the LLAD algorithm is robust against impulsive interferences and outperforms the sign algorithm (SA). We analyze the transient, steady-state and tracking performance of the introduced algorithms and demonstrate the match of the theoretical analyses and simulation results. We show the enhanced stability performance of the LMLS algorithm and analyze the robustness of the LLAD algorithm against impulsive interferences. Finally, we demonstrate the performance of our algorithms in different scenarios through numerical examples.

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A Novel Family of Adaptive Filtering Algorithms Based on the Logarithmic Cost

This paper deals with the combined least mean square–least mean fourth (LMS–LMF)-based control algorithm for distribution static compensator (DSTATCOM) in three-phase distribution system to alleviate the power quality problems caused by solid-state equipments and devices. The combined LMS–LMF-based algorithm is simulated using Sim Power System (SPS) toolbox in MATLAB for obtaining the corresponding active and reactive weights and supply reference currents. The proposed control algorithm has advantages of both LMF- and LMS-based control algorithms, which helps in fast and accurate response with a robust design. Depending on the value of error signal obtained in any of the phases either of LMS- or LMF-based control is used to minimize the error. The developed combined LMS–LMF-based algorithm is implemented on the prototype of the proposed system and responses obtained are found satisfactory with harmonic spectra of the supply currents meeting the power quality standards.

Combined LMS–LMF-Based Control Algorithm of DSTATCOM for Power Quality Enhancement in Distribution System

Rapid industrialization and its automation on the globe demands increased generation of electrical energy with more reliability and quality. Renewable energy (RE) sources are considered as a green form of energy and extensively used as an alternative source of energy for conventional energy sources to meet the increased demand for electrical power. However, these sources, when integrated to the utility grid, pose challenges in maintaining the power quality (PQ) and stability of the power system network. This is due to the unpredictable and variable nature of generation by these sources. The distributed flexible AC transmission system (DFACTS) devices such as distributed static compensator (DSTATCOM) and dynamic voltage restorer (DVR) play an active role in mitigating PQ issues associated with RE penetration. The performance of DFACTS devices is mostly dependent on the type of control algorithms employed for switching of these devices. This paper presents a comprehensive review of various conventional and adaptive algorithms used to control DFACTS devices for improvement of power quality in utility grids with RE penetration. This review intends to provide a summary of the design, experimental hardware, performance and feasibility aspects of these algorithms reported in the literature. More than 170 research publications are critically reviewed, classified, and listed for quick reference for the advantage of engineers and academician working in this area.

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Comprehensive Review of Distributed FACTS Control Algorithms for Power Quality Enhancement in Utility Grid With Renewable Energy Penetration

The least mean fourth algorithm has several stability problems. Its stability depends on the variance and distribution type of the adaptive filter input, the noise variance, and the initialization of the filter weights. The present correspondence provides a global solution to all these stability problems. This is achieved by normalizing the weight vector update term by a term that is fourth order in the regressor and second order in the estimation error. The former property stabilizes the algorithm against the variance and distribution type of the filter input, while the latter stabilizes the algorithm against the noise variance and the weight initialization. The obtained algorithm is stable for all values of the step-size between 0 and 2. The stability of the algorithm is supported by simulations.

Global Stabilization of the Least Mean Fourth Algorithm

The least mean fourth (LMF) algorithm has several stability problems. Its stability depends on the variance and distribution type of the adaptive filter input, the noise variance, and the initialization of the filter weights. A global solution to these stability problems was presented recently for a normalized LMF (NLMF) algorithm. Here, a stochastic analysis of the mean-square deviation (MSD) of the globally stable NLMF algorithm is provided. The analysis is done in the context of adaptive noise canceling with a white Gaussian reference input and Gaussian, binary, and uniform desired signals. The analytical model is shown to accurately predict the results of Monte Carlo simulations. Comparisons of the NLMF and NLMS algorithms are then made for various parameter selections. It is then shown under what conditions the NLMF algorithm is superior to NLMS algorithm for adaptive noise canceling.

Stochastic Analysis of a Stable Normalized Least Mean Fourth Algorithm for Adaptive Noise Canceling With a White Gaussian Reference

This paper studies the stochastic behavior of the LMS and NLMS algorithms for a system identification framework when the input signal is a cyclostationary white Gaussian process. The input cyclostationary signal is modeled by a white Gaussian random process with periodically time-varying power. Mathematical models are derived for the mean and mean-square-deviation (MSD) behavior of the adaptive weights with the input cyclostationarity. These models are also applied to the non-stationary system with a random walk variation of the optimal weights. Monte Carlo simulations of the two algorithms provide strong support for the theory. Finally, the performance of the two algorithms is compared for a variety of scenarios.

Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian Inputs

The available normalization of the least mean fourth algorithm is investigated. It is shown that that normalization does not protect the algorithm from divergence when the input power of the adaptive filter increases. The reason of this drawback is that the normalization is done by dividing the weight vector update term by the squared norm of the regressor, while the update term is a fourth order polynomial in the regressor. The paper presents a normalized LMF algorithm that is based on dividing the weight vector update term by the fourth power of the norm of the regressor. This normalization protects the algorithm from divergence when the input power increases. An approximate stability step-size bound of the proposed algorithm is derived. The step-size bound depends on the weight initialization, while it does not depend on the input power of the adaptive filter for non-small signal-to-noise ratio. Simulation results support the analytical results of the paper.

New insights into the normalization of the least mean fourth algorithm

The paper investigates a new stability problem of the least mean fourth (LMF) algorithm, which is the dependence of the algorithm stability on the time-variation of the target weights of the adaptive filter. The analysis is done in the context of tracking a Markov plant with a stationary white Gaussian input. It is found that the algorithm diverges if the mean square increment of the plant parameter vector exceeds a threshold value that depends on the step-size, input variance, and noise moments. The paper also derives a closed form of the steady-state mean square deviation without the usual assumption of a strong noise. Comparison of the tracking capabilities of the LMF and LMS algorithms is provided. The comparison is done in terms of the minimum mean square deviation attained by each algorithm over the stability range of its step-size. Gaussian, uniform, and binary distributions of the noise are considered. Conditions that make one algorithm outperform the other are determined. Analytical results are supported by simulations.

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Papers

Global Stabilization of the Least Mean Fourth Algorithm

Stochastic Analysis of a Stable Normalized Least Mean Fourth Algorithm for Adaptive Noise Canceling With a White Gaussian Reference

Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian Inputs

New insights into the normalization of the least mean fourth algorithm

Dependence of the Stability of the Least Mean Fourth Algorithm on Target Weights Non-Stationarity