HARMONIC ESTIMATION BY SW-LMS ALGORITHM

Presented by-Arunima Dutta

T14EE009

Satabdy Jena

T14EE003

Mtech(Power and energy systems)

Contents :

Introduction

Power quality

Harmonics

LMS algorithm and sliding window LMS algorithm

Comparison of results

Conclusion

IntroductionPower system harmonics is an area that is receiving a great deal of attention recently. This is primarily due to the fact that non-linear (or harmonic producing) loads are comprising an ever-increasing portion of the total load for a typical industrial plant. Incidence of harmonic related problems is low, but awareness of harmonic issues can help to increase plant power system reliability.

There are various methods for analysis of harmonics like FFT,LMS,RLS,etc.

Power Quality

The power quality of a system expresses to which degree practical supply system resembles the ideal supply system.

The best electrical supply would be a constant magnitude and frequency sinusoidal voltage waveform.

Due to transients, outages, voltage spikes etc. reality is different.

Causes of poor power quality:

Reactive power

Harmonic pollution

Load imbalance

Fast voltage variation

Effects of poor power quality :Power failureEquipment malfunctioning, failure, overheating,etc.EMI Increase in lossesOversizing of installationsPenalties imposed by utilitiesConnection refusal

Harmonics

Harmonics is a mathematical way of describing distortion to a current or voltage waveform.

Integer multiple of fundamental frequency.

Classification of harmonics :

 

Terminologies Related to Harmonics

 

Effect of HarmonicsOverheating of distribution transformersPoor system efficiency InstabilityDisturbance of the other consumersMalfunctioning of medical facilities

Drawbacks with FFT :

Spectral leakage.Aliasing.“Picket –fence” effect.

LMS ALGORITHM :

Features :SimplicityLow computational complexityRobustnessNo matrix inversion is required

Drawbacks :Slow convergenceData dependent behaviorSensitivity to noise

SLIDING WINDOW LMS ALGORITHM :

Easy to work with noisy system.Good estimation in different SNR.No oscillations in results obtained.To increase the convergence speed.

Circuit configurations :Single phase diode

bridge rectifierThree phase diode

bridge rectifier

MATHEMATICAL MODELLING :

Let the current waveform of frequency be represented as :

n= order of harmonicsn=2fo=fundamental frequency

Thus the equation reduces to the form given below :

Where the weight and the constants are updated as folows :

USING SLIDING WINDOW :

SW training algorithms also known as high order training algorithms use a sliding window of system input/output observations to perform instantaneous learning.It can be applied when the data is highly noisy.Typically the model weights are updated using information obtained from store of [L ]previous training vectors.

Given [L] vector data store and current data point ,this algorithm computes a moving average search direction for LMS as follows :

The weighting factor controls the contribution of the current vector to the search direction. The weights are updated as follows :

The store S for harmonic estimation includes only input given as :S=[ x1 x2 … xL]

BLOCK DIAGRAM :

Analysis of Simulation ResultsThe assumed signal is:

Waveforms:

Conclusion :Thus we see that the LMS algorithm employed with

sliding window gives better results,excludes oscillations and is effective even in high noise signals.

Harmonic mitigation equipment includes : Line reactors Isolation transformers Filters 12 and 18 pulse rectifiers

References :

“Power system harmonic estimation using sliding window based LMS”, Hussam,Nursyarizal,M.F.Abdullah,Vijanth S. Asirvadam.(IEEE 2013 International Conference on signal and image processing).

“A review of harmonic mitigation techniques” ,Gonzalo Sandoval & John Houdek.

Power system harmonics by Allen Bradley.

Thank You