Robust Harmonic Estimation Using Forgetting Factor Rls

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  • Topic: Digital signal processing, Acoustics, White noise
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  • Published : March 1, 2013
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ROBUST HARMONIC ESTIMATION USING
FORGETTING FACTOR RLS
H.K.SAHOO

POOJA SHARMA

Dept. of Electronics and Telecommunication
IIIT, Bhubaneswar
India
Email: harish@iiit-bh.ac.in

Dept. of Electronics and Telecommunication
BIT, Mesra, India
Email: haipoo29@gmail.com

N.P.RATH
Dept. of Electronics and Telecommunication
VSSUT, Burla, India
Email: n_p_rath@hotmail.com
Abstract— The prime reasons for power quality
degradation include voltage sag, swell and momentary
interruptions and also the presence of harmonics. Thus
accurate computation of harmonics is really a challenging
problem in power system. Many algorithms have been
proposed for harmonic estimation to improve the power
quality. In this paper the Forgetting Factor RLS (FFRLS)
approach has been considered to estimate not only voltage
sag,swell,momentary interruption but also the amplitudes and phases of harmonics in case of time varying power signals in presence of White Gaussian Noise. Also comparison results
with LMS and NLMS algorithms are presented to show the
effectiveness of the proposed RLS algorithm.
Keywords- RLS, LMS, NLMS, Harmonic Estimation, White
Gaussian Noise
I.

INTRODUCTION

The wide spread applications of electronically controlled loads have increased the harmonic distortion in power system
voltage and current waveforms. As power semiconductors are
switched on and off at different points on the voltage
waveform, damped high frequency transients are generated. If switching occurs at the same points on each cycle, the
transient becomes periodic. This transient whose frequency is not a multiple of fundamental frequency is non-stationary.
Consequently voltage and current waveforms of a distribution or transmission system are not pure sinusoids, but may consist of a combination of fundamental frequency, harmonics and
high frequency transients. Also many of power system loads,
especially industrial loads are dynamic in nature, which
implies time varying amplitude of the current waveform.

In order to provide the quality of the delivered power, it is imperative to know the harmonics parameters such as
amplitude and phase. This is essential for designing filter for eliminating or reducing the effects of harmonics in a power
system. Different algorithms are proposed to estimate the
harmonics{1,2] in a power system.LMS[3,4,5] and NLMS[6]
approaches are also quite popular for estimating frequency of distorted sinusoidal signals under noisy conditions
In this paper, Fogetting Factor RLS has been
proposed for estimating sag, swell, momentary interruption as well as amplitudes and phases of different harmonics [7] of
distorted power signals in presence of white noise.
II. SIGNAL MODELS FOR POWER QUALITY
DISTURBANCES AND HARMONIC ESTIMATION
Two types of signal models are proposed to estimate power
quality disturbances like voltage sag and swell, notch,
momentary interruption as well as amplitudes and phases of
different harmonics like fundamental, third and fifth
harmonics.
A. Signal Model for Power Quality Disturbances

d k at time k is a sinusoid yk in the presence
of white Gaussian noise vk .
Consider a signal

d k = yk + vk

(1)

yk = a1 sin(kω1Ts + φ1 )

(2)

Where

ω1

B. SIGNAL MODELING FOR HARMONIC ESTIMATION

= fundamental of angular frequency;

A static signal and a dynamic power system signal have been
considered for estimation, which contains higher harmonics of the 3rd and 5th order.

φ1 = fundamental of phase angle;
a1 = fundamental amplitude of the signal;

The static power system signal is given by

Ts = sampling time
The noise

yk = 1.2sin(kωTs + π / 6) + 0.5sin(3kωTs + π / 3)

vk is a white Gaussian noise with a zero mean and

a variance σ v .

+0.2sin(5kωTs + π / 4)

(8)

2

The dynamic power system signal is given by

So the signal can be modeled as:

yk = (1.5 + a1 (t )) sin( kωTs + π / 6)
+ (0.5 + a3 (t )) sin(3kωTs + π / 3)

T
yk =...
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