A Method for Judging the Accuracy of Harmonic Impedance

Calculation Results

Ping Li

, Xuke Cheng

, Guanfeng Zhang

, Jiayu Li

, Shenghui Li

, Xue Bai

, Cijian Xie

and Jinshuai Zhao

2,*

State Grid Liaoning Electric Power Research Institute, Shengyang, China

Sichuan University, Chengdu, China

Keywords: Nonlinear Users, Harmonic Impedance, Criteria Selection, Superposition Principle.

Abstract: The issue of harmonic pollution in the power grid has received widespread attention. The harm of

harmonics includes causing equipment overheating, shortening equipment life, increasing additional line

losses, and reducing operational efficiency. Accurately calculating harmonic impedance is one of the keys

to studying harmonic problems. Based on harmonic measurement data at common connection points,

existing scholars have proposed several non-invasive harmonic impedance estimation methods. After

calculating the harmonic impedance, it is necessary to verify the correctness of the calculation results.

Accurately solving the harmonic impedance of the system and user sides is of great significance for

accurately quantifying harmonic responsibility, guiding the development of filter design related work,

guiding harmonic suppression and resonance mitigation, and other aspects. However, there is currently no

unified method to verify the correctness of obtaining harmonic impedance. Therefore, this article proposes a

method for determining the accuracy of harmonic impedance calculation results.

INTRODUCTION

Electric energy, as a clean and convenient secondary

energy source, permeates every aspect of people's

daily life and industrial and agricultural production,

and is the main foundation for the development and

progress of modern society. Among the loads

connected to the distribution network, in addition to

those with good conventional symmetry and no

harmonic pollution to the power grid, there are also

impulsive, large capacity, and nonlinear load

equipment, such as electric arc furnaces, electric

locomotives, etc. At the same time, in the context of

the construction of smart distribution networks, new

elements such as source load network storage and

charging are developing on a large scale in 10kV

distribution networks and 400V low-voltage

distribution stations, and the "power electronics"

characteristics of distribution networks are becoming

increasingly evident. A large number of power

electronic devices are distributed or centrally

connected in the distribution network, resulting in

disorderly transmission and superposition of

broadband harmonic disturbances in the distribution

network. This exacerbates harmonic pollution in the

distribution network, deteriorates the power quality

environment of the distribution network, and affects

the reliable and economic operation of power

equipment on both sides of the power supply and

consumption. It has become an important challenge

for power quality management.

In summary, in order to ensure the safe and

economical operation of the power grid, the normal

use of conventional electrical equipment, and the

provision of continuous and reliable electricity to

users, it is necessary to control the harmonic content

of the distribution network within the allowable limit

range. Many countries and relevant authoritative

institutions have formulated, promulgated, and

implemented relevant standards and regulations to

limit the harmonic distortion value of the

distribution network. Power engineers from various

countries have also proposed various methods for

harmonic analysis based on corresponding standards

and regulations, including frequency domain

analysis, time domain analysis, Fourier transform

analysis, etc.

This article proposes a method for determining

the correctness of harmonic impedance calculation

(Yao Xiao, Jin Hui). The main idea of existing

methods is to compare the calculated harmonic

voltage of the utility side with the harmonic voltage

204

Li, P., Cheng, X., Zhang, G., Li, J., Li, S., Bai, X., Xie, C. and Zhao, J.

A Method for Judging the Accuracy of Harmonic Impedance Calculation Results.

DOI: 10.5220/0012277600003807

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 2nd International Seminar on Artiﬁcial Intelligence, Networking and Information Technology (ANIT 2023), pages 204-207

ISBN: 978-989-758-677-4

measured at the PCC point after the user exits the

operation (Jin Hui - Xi Zhao). If the difference

between the calculated harmonic voltages of the

utility side and the measured voltage at the point of

common coupling is not significant, it indicates that

the harmonic impedance has been calculated

accurately(Farzad Karimzadeh - V.G. Reju); On the

contrary, it indicates that there is a significant error

in obtaining the harmonic impedance. The harmonic

voltages of the utility side can be calculated

according to IEC61000-3-6 or the superposition

principle method (Bofill Pau, Zhang Jie). However,

when verifying the accuracy of the harmonic

impedance obtained, the existing research has

neglected one point, that is, because the basic

principles of IEC method and Superposition

principle method are different, they need to be

selected according to the actual working conditions,

and cannot be selected arbitrarily, otherwise there

may be a risk of miscalculation of the accuracy of

harmonic impedance (Yuanqing Li, Fasong Wang).

This article divides nonlinear users into two

categories based on their cessation of operation: 1)

only cutting off the harmonic source while retaining

their user side impedance to connect to the power

grid (such as photovoltaic stations), and 2) cutting

off the harmonic source and user side impedance

(such as electric arc furnaces) . Then, this paper

studies the difference between IEC method and

Superposition principle method and their respective

application scope in the process of verifying the

accuracy of harmonic impedance. Finally, according

to the characteristics of these 2 methods and the

category of nonlinear users, a method that can

accurately verify the correctness of obtaining

harmonic impedance is proposed.

CALCULATE HARMONIC

VOLTAGE PRODUCED BY

THE UTILITY SIDE BASED ON

THE IEC METHOD

The corresponding modal is shown in Figure 1, Zu,

Zc,



、



, are the harmonic impedances and

harmonic current sources on the system side and

user side, respectively. The harmonic voltage

measured at the PCC point and the harmonic current

measured on the public line, respectively.

Utility side Customer Side

pcc

PCC

pcc

Figure 1: Circuit for analyzing the utility and customer sides.

When the switch is closed, we have

cc-post u u pcc u

ZZV=I+I



(1)

When the switch is disconnected, the user side

stops running, we have

cc-pre u u

ZV=I



(2)

Based on the definition of harmonic emission

level in IEC61000-3-6 standard, we have

IEC

c-pcc pcc u



(3)

IEC

u - p c c u u

=ZVI



(4)

CALCULATE THE HARMONIC

VOLTAGE OF UTILITY SIDE

ACCORDING TO THE

SUPERPOSITION PRINCIPLE

Figure 2 shows the corresponding modal of the

Superposition principle method. When the system

side harmonic source and the user side harmonic

source operate separately, and when the nonlinear

user side harmonic source operates separately, the

harmonic voltages generated by them at the common

connection point, that is, the emission levels of the

system side and user side harmonic voltages, can be

expressed as

sup

u-pcc u



(5)

sup

c-pcc c

V= I



(6)

Utility

side

Customer

side

PCC

Utility

side

Customer

side

PCC

(a) (b)

Figure 2: Equivalent circuit corresponding to

Superposition principle method

A Method for Judging the Accuracy of Harmonic Impedance Calculation Results

205

METHOD FOR VERIFYING

THE ACCURACY OF

OBTAINING HARMONIC

IMPEDANCE

When nonlinear users are connected in, if the

harmonic impedance of the system and user sides

can be accurately calculated, then the obtained

harmonic voltage of the utility side is also accurate.

By comparing the calculated harmonic voltage of the

utility side with the reference voltage, the

correctness of the obtaining harmonic impedances

on the system side and the user side can be verified.

The present invention divides nonlinear users

into the following two categories based on their way

of exiting operation.

4.1 Model A

For non-linear users such as electric arc furnaces,

when the user is not working, after accurately

obtaining Zu,

IEC

u-pcc



will be equal to

u-pcc



. It is

worth noting that since equation (4) does not contain

Zc, this modal cannot verify the correctness of

obtaining harmonic impedance of customer side.

4.2 Model B

When Zc and Zu are accurately determined,

u-pcc



and

u-pcc



are equal. It is worth noting that since

equation (5) contains both Zc and Zu, this method

can simultaneously verify the correctness of

obtaining Zc and Zu.

After determining the user class, the accuracy of

harmonic impedance can be verified according to the

magnitude relationship between the system side and

the user side harmonic impedance. The specific

process is as follows.

(1) The amplitude of Zc is not much greater than

that of Zu

When | Zc | is not much greater than | Zu |,

according to equations (4) and (5), the background

harmonic voltages

IEC

u-pcc



and

sup

u-pcc



obtained are

not equal to each other. Therefore,

IEC

u-pcc



will not be

equal to

u-pcc



, and

sup

u-pcc



will not be equal to

u-pcc



In order to avoid the above misjudgment, it is

necessary to use the correct method (IEC method or

Superposition principle method) to match the user

model.

(2) The amplitude of Zc is far greater than that of

Under this situation, the error in obtaining Zc is

usually large, so only the accuracy of obtaining Zu

needs to be verified. Due to | Zc |>>| Zu |,

ZZ 0≈

holds, and equation (5) can be

changed into equation (7). Therefore, when the

harmonic impedance of the user side is unknown,

the superposition principle can be used.

sup

u-pcc u u u

1Z Z

.≈



V= I I

(7)

It is worth noting that equation (7) is equivalent

to equation (5), and the obtained

IEC

u-pcc



and

sup

u-pcc



are approximately equal to each other. Therefore,

both Class A and Class B nonlinear users can verify

the accuracy of Zu based on IEC method or

Superposition principle.

(3) Method for determining the size relationship

between Zc and Zu

When | Zc |>>| Zu |,

ZZ 0≈

is established,

resulting in

cc c u c

cu cu

Z+Z Z+Z

.−≈



IIII

(8)

Thus, by quantifying the similarity between



and



, we can indirectly evaluate whether |

Zc |>>| Zu | is valid. In this evaluation process, the

independent component analysis (ICA) can be used

to reconstruct the source signal



Based on the Norton modal shonw in Figure 1 or

Figure 2, when a nonlinear user is connected to the

system, there is



cu cu

pcc

cucu

pcc

cucu

ZZ ZZ

ZZZZ

Z+Z Z+Z









=⋅







−











(9)

In the formula, matrix X is composed of

observation signals



and



, matrix I is

composed of harmonic current sources



and



and the impedance matrix

Z is composed of

harmonic impedances on both sides of PCC points.

Before using the ICA algorithm, it is necessary to

extract the rapidly changing components of the

signal through median filtering technology to ensure

ANIT 2023 - The International Seminar on Artiﬁcial Intelligence, Networking and Information Technology

206

the independence between the source signals. The

harmonic source signal

𝐼



= 𝐼







𝐼











can be

reconstructed using the ICA algorithm. The

similarity between signal

𝐼





pcc

and

fast



quantified through correlation coefficients. The

greater the correlation coefficient, the more similar

the two signals are.

CONCLUSION

Harmonic pollution has a significant impact on the

safe, stable, and economic operation of the power

grid. In order to accurately carry out harmonic

control work, this article conducts research on

solving harmonic impedance and evaluating

harmonic emission levels. In practical engineering

applications, by comparing the background

harmonic voltage obtained with the voltage

measured at the common connection point when the

user is not working, the accuracy of the harmonic

impedance obtained on the system side and the user

side can be indirectly verified. Generally speaking,

there are 2 ways for calculating harmonics produced

by the utility sides harmonic sources. This paper

discusses the applicability of these two methods.

Based on the research results of this article, the

correctness of the results of quantifiable harmonic

impedance calculation, harmonic responsibility

quantification, and harmonic emission level

evaluation has guiding significance for precise

harmonic control.

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