Engineering, 2013, 5, 6-13

http://dx.doi.org/10.4236/eng.2013.59B002 Published Online September 2013 (http://www.scirp.org/journal/eng)

Copyright © 2013 SciRes. ENG

A Method for Assessing Customer Harmonic Emission

Level Based on th e Iterative Algorithm for

Least Square Estimation*

Runrong Fan, Tianyuan Tan, Hui Chang, Xiaoning Tong, Yunpeng Gao

School of Electrical Engineering, Wuhan University, Wuhan, China

Email: rrfran0426@whu.edu.cn, tty@whu.edu.cn

Received June 2013

ABSTRACT

With the power system harmonic pollution problems becoming more and more serious, how to distinguish the harmonic

responsibility accurately and solve the grid harmonics simply and effectively has become the main development direc-

tion in harmonic control subjects. This paper, based on linear regression analysis of basic equation and improvement

equation, deduced the least squ ares estimation (LSE) iterative algorithm and obtained the real -time estimates of regres-

sion coefficients, and then calculated the level of the harmonic impedance and emission estimates in real time. This

paper used power system simulation software Matlab/Simulink as analysis tool and analyzed the user side of the har-

monic amplitude and phase fluctuations PCC (point of common coupling) at the harmonic emission level, thus the re-

search has a certain theoretical significance. The development of this algorithm combined with the instrument can be

used in practical engineering.

Keywords: Harmonic Emission Levels; Harmonic Analysis; Least Square Estimation; Iterative Algor ithm

1. Introduction

In the modern power grid system, the traditional power

equipment has gradually been replaced by smart devices

which were based on power electronics and other non-

linear element. Meanwhile, nonlinear loads of the user

side were heavier and heavier. It made the harmonic pol-

lution problems more serious and harmful to the safe

operation of the power system. Besides, the users faced a

great power loss. With the public’s increasing emphasis

on harmonic problems, the user’s reasonable assessment

of harmonic emission levels in public connection point

became an important content of harmonic control [1].

The research of Emission level estimation of harmonic

source was focused on harmonic source qualitative anal-

ysis and quantitative estimates at home and abroad: ac-

tive power direction method [2] was widely used in en-

gineering harmonic source qualitative analysis method.

However, this method is affected deeply by the phase

difference between the harmonic sources. And there is a

big area of uncertainty, so it was not suitable for complex

power systems. Harmonic source in quantitative analysis,

also known as harmonic source emission level assess-

ment, can be divided into intervention type and non-in-

tervention type [3]. Intervention type need to inject into

the system disturbance artificially, which not only in-

creased the cost of harmonic analysis, also limited the

scope of its application. Non-intervention type was dif-

ferent; it could use harmonic source fluctuations of itself

to estimate the harmonic impedance in system without

interfering with its normal operation. This method was

simple to use, easy to the development of equipments. It

has made a great difference in practice [4]. At present,

the main non-invasive methods included fluctuations

method [5,6], the linear regression method [8,9] and the

reference impedance method [7]. Among them, fluctua-

tions method and linear regression method were based on

the condition that system harmonic impedance and

equivalent systems invariant harmonic voltage source

and the load harmonic impedance and equivalent load

harmonic current source change greatly (or vice versa), it

cannot be applied in a steady state harmonic source, and

cannot applied in the condition while the system and user

harmonic source volatility at the same [5-9]. The main

disadvantage of the reference impedance method is that it

needs to get more accurate prior reference impedance [7].

This paper proposed the iterative algorithm for least

square estimation is based on the linear regression analy-

sis of basic equation and the improvement equation. And

*Supported by “the Fundamental Research Funds for the Central Uni-

versities” (Grant No: 207-274592);

Supported by NSFC (Grant No:

51007066)