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 =...