Stochastic Analysis of the LMS Algorithm for System Identification With Subspace Inputs

Bershad, N.J.; Bermudez, J.C.M.; Tourneret, Jean-Yves

doi:10.1109/tsp.2007.908967

Cited by 17 publications

(7 citation statements)

References 20 publications

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“…Generally, in order to design a PSS for stabilizing control, the supplementary signal at the AVR of generators are regarded as the input and the speed deviation responses are taken as the output. Though previous research has used SSI for power system identification [18], it is not applied for Multiple Input Multiple Output (MIMO) case; besides, the matrices B and C, were not identified. In the following cases shown, SSI is applied to (a) an input/output based model and (b) an output based model of the power system.…”

Section: Stochastic Subspace Identification (Ssi) Based Modal Analysismentioning

confidence: 99%

Damping inter-area oscillations using virtual generator based power system stabilizer

Tang

Venayagamoorthy

2015

Electric Power Systems Research

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In a power system, remote measurements are used by a controller to provide damping torque for inter-area oscillations. In this study, the operating conditions that give rise to inter-area oscillations are investigated using Stochastic Subspace Identification (SSI) based modal analysis. In a power system, generators can be grouped based on coherency and the groups can be represented by Virtual Generators (VGs). Damping inter-area oscillations using Virtual Generator based Power System Stabilizer (VG-PSS) that generates a supplementary control signal to the excitation system of one or more synchronous generators is presented. The generator choice for VG-PSS location is determined based on the generator that has maximum controllability on dominant weakly damped inter-area mode(s) in a power system. Modal analysis using SSI and real-time simulation results on the IEEE 68-bus power system are presented to illustrate the effectiveness of VG-PSSs in damping inter-area oscillations. In addition, the effect of time delays encountered as a result of wide area measurements and communications are considered in the studies presented.

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Section: Stochastic Subspace Identification (Ssi) Based Modal Analysismentioning

confidence: 99%

Damping inter-area oscillations using virtual generator based power system stabilizer

Tang

Venayagamoorthy

2015

Electric Power Systems Research

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“…Therefore, one approach to enforce the sparsity of the solution for the sparsity-aware LMS-type algorithms is to introduce the reweighted l 1 -norm penalty term in the cost function [24]. 3 Our reweighted l 1 -norm penalized LMS algorithm considers a penalty term proportional to the reweighted l 1 -norm of the coefficient vector. The corresponding cost function can be written as…”

Section: Standard Lmsmentioning

confidence: 99%

“…While RLS and Kalman filter need to know the covariance matrix of the input data sequence, the LMS algorithm only requires an approximate estimate of the largest eigenvalue of the covariance matrix for proper selection of the step size that guarantees the convergence. The LMS algorithm is being employed in a wide variety of applications in signal processing and communications including system identification [3], echo cancellation [4], channel estimation [5], adaptive communication line enhancement [6], etc. A particular application considered in this paper is that of estimating a finite impulse response (FIR) channel.…”

Section: Introductionmentioning

confidence: 99%

Reweighted l1-norm penalized LMS for sparse channel estimation and its analysis

Taheri

Vorobyov

2014

Signal Processing

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A new reweighted l 1 -norm penalized least mean square (LMS) algorithm for sparse channel estimation is proposed and studied in this paper. Since standard LMS algorithm does not take into account the sparsity information about the channel impulse response (CIR), sparsity-aware modifications of the LMS algorithm aim at outperforming the standard LMS by introducing a penalty term to the standard LMS cost function which forces the solution to be sparse. Our reweighted l 1 -norm penalized LMS algorithm introduces in addition a reweighting of the CIR coefficient estimates to promote a sparse solution even more and approximate l 0 -pseudo-norm closer. We provide in depth quantitative analysis of the reweighted l 1 -norm penalized LMS algorithm. An expression for the excess mean square error (MSE) of the algorithm is also derived which suggests that under the right conditions, the reweighted l 1 -norm penalized LMS algorithm outperforms the standard LMS, which is expected. However, our quantitative analysis also answers the question of what is the maximum sparsity level in the channel for which the reweighted l 1 -norm penalized LMS algorithm is better than the standard LMS. Simulation results showing the better performance of the reweighted l 1 -norm penalized LMS algorithm compared to other existing LMS-type algorithms are given.

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“…Therefore, little is known about the behavior of the LMS algorithm in such a situation and about its dependence on the rate of variation of the input power. To the best of our knowledge, an investigation of this issue is not available even in recent papers dealing with the algorithm [3][4][5][6][7][8][9][10][11]. Investigation of the dependence of the transient and steady-state performance of the algorithm on the rate of variation of the input power is the main concern of the present paper.…”

Section: Introductionmentioning

confidence: 97%

Behavior of the least mean square algorithm with a periodically time‐varying input power

Eweda

2012

Adaptive Control & Signal

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The paper analyzes the transient and steady-state performances of a least mean square algorithm in the rarely-studied situation of a time-varying input power. A scenario of periodic pulsed variation of the input power is considered. The analysis is carried out in the context of tracking a Markov plant with a white Gaussian input. It is shown that the mean square deviation (MSD) converges to a periodic sequence having the same period as that of the variation of the input power. Expressions are derived for the convergence time and the steady-state peak MSD. Surprisingly, it is found that neither the transient performance nor the steady-state performance degrades with rapid variation of the input power. On the other hand, slow input power variation causes degradation in both the transient and steady-state performances for given amplitude of variation of the input power. In the case of a time-invariant plant, neither rapid nor slow variation of the input power causes degradation in the steady-state performance. On the other hand, there is degradation in the transient performance for slow variation of the input power.

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Stochastic Analysis of the LMS Algorithm for System Identification With Subspace Inputs

Cited by 17 publications

References 20 publications

Damping inter-area oscillations using virtual generator based power system stabilizer

Damping inter-area oscillations using virtual generator based power system stabilizer

Reweighted l1-norm penalized LMS for sparse channel estimation and its analysis

Behavior of the least mean square algorithm with a periodically time‐varying input power

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