Harmonic estimation by lms algorithm
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This document discusses harmonic estimation using the sliding window least mean square (SW-LMS) algorithm. It introduces harmonics and their effects, as well as traditional Fourier transform and LMS algorithms for analysis. The SW-LMS algorithm is presented as improving on LMS by using a sliding window to exclude oscillations and work better in noisy signals. Simulation results show the SW-LMS algorithm can effectively estimate harmonics even at high noise levels. In conclusion, SW-LMS provides an effective technique for harmonic estimation.
![ 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.](https://image.slidesharecdn.com/harmonicestimationbylmsalgorithm-141011000910-conversion-gate01/85/Harmonic-estimation-by-lms-algorithm-16-320.jpg)
![ Given [L] vector data store and current data point 푥푡,this
algorithm computes a moving average search direction
for LMS as follows :
The weighting factor 훼 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]](https://image.slidesharecdn.com/harmonicestimationbylmsalgorithm-141011000910-conversion-gate01/85/Harmonic-estimation-by-lms-algorithm-17-320.jpg)
Harmonic estimation by lms algorithm
- 1. HARMONIC ESTIMATION BY SW-LMS ALGORITHM Presented by- Arunima Dutta T14EE009 Satabdy Jena T14EE003 Mtech(Power and energy systems)
- 2. Contents : Introduction Power quality Harmonics LMS algorithm and sliding window LMS algorithm Comparison of results Conclusion
- 3. Introduction Power 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.
- 4. 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
- 5. Effects of poor power quality : Power failure Equipment malfunctioning, failure, overheating,etc. EMI Increase in losses Oversizing of installations Penalties imposed by utilities Connection refusal
- 6. Harmonics Harmonics is a mathematical way of describing distortion to a current or voltage waveform. Integer multiple of fundamental frequency.
- 9. Effect of Harmonics Overheating of distribution transformers Poor system efficiency Instability Disturbance of the other consumers Malfunctioning of medical facilities
- 10. Drawbacks with FFT : Spectral leakage. Aliasing. “Picket –fence” effect. LMS ALGORITHM : Features : Simplicity Low computational complexity Robustness No matrix inversion is required
- 11. Drawbacks : Slow convergence Data dependent behavior Sensitivity 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.
- 12. Circuit configurations : Single phase diode bridge rectifier Three phase diode bridge rectifier
- 14. Let the current waveform of frequency 휔 be represented as : n= order of harmonics 휔n=2휋푛푓표 fo=fundamental frequency
- 15. Thus the equation reduces to the form given below :
- 16. 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.
- 17. Given [L] vector data store and current data point 푥푡,this algorithm computes a moving average search direction for LMS as follows : The weighting factor 훼 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]
- 18. BLOCK DIAGRAM :
- 19. Analysis of Simulation Results The assumed signal is:
- 20. Waveforms:
- 24. 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
- 25. 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.
- 26. Thank You