## Power System Harmonics Analysis Using Frequency-Domain Impedance Model of Network and Methods of Disposal

##### Abstract

Power grids can be described as low power quality if they contain distorted currents which are known as harmonics. Harmonics mean that the alternating current (AC) wave contains multiple integers of the fundamental frequency.
In the past, this distortion was caused by the elements of the network itself, such as transformers, when they enter the saturation area in periods of high demand for energy. The generators themselves produce waves with a slight degree of distortion because the distribution of the magnetic flux is not optimal. But nowadays, the main reason for the problem is the spread of nonlinear loads, especially power electronic devices, for domestic and commercial use. Several small devices spread through the whole network are participating in the distortion.
Distortion due to harmonics has become very important in the field of power quality studies because of the negative effects of the distortion on equipment and what is accompanied by negative effects such as resonance.
In order to understand the problem of harmonics, an accurate analysis of the network must be carried out in the presence of the sources of harmonics. The main goal of this analysis is to find different values of the distortion and to compare them with the standards set to the normal level. Also, such studies enable us to study the effectiveness of different procedures followed in eliminating harmonics and controlling their flow.
In this thesis, a frequency-domain model of a distribution network was developed and an analysis was carried out to enable us to calculate the required values of distortion. All this was accompanied by a software simulation of the same network in order to compare the accuracy of the results.
Problem statement
The spread of nonlinear loads in the electric power systems will result in distortions in the current wave and thus distortion on the voltage, which is called the harmonics. These distorted currents will be injected back into the power supply to cause a negative effect on the power quality that is to increase the losses and reduce the power factor. The network equipment itself will also be subject to damage and downtime due to harmonics. This has necessitated worldwide interest in harmonics studies, including harmonics estimation, elimination and a variety of related areas.
Objectives
To learn how to form a frequency-dependent model for network elements depending on the nature of each element and how it behaves with harmonics frequencies.
To develop a methodology for harmonics analysis of networks so that this method can be adopted by network operators as a guide to execute of various calculations related to harmonics.
To study procedures used in harmonics mitigation and to ensure their effectiveness by simulation.
To present all issues associated with harmonics such as general characteristics, sources, effects, harmonics indices and standards.
Methodology
A mathematical model for the whole electric network is developed in order to carry out harmonics power flow analysis by hand calculation. Later, the analysis is carried out to evaluate the developing method proposed by using a computer program ETAP12.6.
Thesis layout
The thesis is organized as follows: Chapter 1 provides a basic theory about harmonics and related topics such as distortion measurements, harmonics sequences and calculation of electrical quantities of distorted waves. Chapter 2 deals with the undesirable effects of harmonics as they pass through the various network equipment. It also looks at the effects on the entire network such as resonance. Chapter 3 covers the sources of harmonics in the electric network with a description of the nature of the harmonics injected during the operation of the device. Chapter 4 covers a brief discussion on standards for distortion limits. Chapter 5 models the network elements based on the nature of the interaction of the element with the passage of harmonics in it. Each element will be dealt with separately to get a frequency dependent impedance. Chapter 6 represents building a complete harmonics model for a distribution network and conduct an accurate analysis of harmonics frequencies, thus calculate the bus voltages and then calculate the distortion measurements. This is accompanied by simulations of the same network to determine the accuracy of the model and manual analysis. Chapter 7 covers several procedures that can be used for the mitigation of harmonics. A simulation was done to make sure that they are correct. Chapter 8 includes appropriate conclusions and suggestions for future work. Appendix A: includes MATLAB coding for harmonics voltages calculation. Appendix B: includes proof of phase shift (∆ to ∆/Y connection) method which is used for harmonics cancelation. Appendix C: includes filter harmonics currents calculation. Appendix D: includes selected examples of harmonics analyzer.