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.

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.

7. Classification of harmonics :

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

13. MATHEMATICAL MODELLING :

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