**MatLab Simulink Modeling for Network-Harmonic Impedance Assessment: Useful Tool to Estimate Harmonics Amplification**

Alexandru Băloi and Adrian Pană

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76461

### Abstract

The importance of the subject is given by the fact that harmonics are making their presence felt in electrical distribution networks, and the cheapest and most widespread solution for power factor correction is the capacitor banks. This chapter proves that the harmonic impedance is an efficient tool for assessing the state of distribution networks containing harmonics. The unfavorable operating conditions are anticipated based on the network harmonic impedance values, and the means of intervention are selected. Harmonic impedance monitoring and using it in expert systems for operating condition optimization will increase in the future. Power factor correction by shunt capacitor switching in electrical networks containing harmonics can lead to harmonics amplifications by harmonic voltage increasing and capacitors thermal overstressing by great values of the currents flowing through them. This chapter proposes a method for practical determination of harmonic impedance. Based on its values, a quick method is developed to anticipate the harmonic voltages and current amplifications that can occur when a shunt capacitor is installed for power factor correction. Amplification factors are calculated depending on the equivalent harmonic impedance of the network seen in the compensation bus. A distribution network containing harmonics is modeled using MatLab Simulink, and harmonic impedance is determined by simulation in different operating conditions. Using the values of the harmonic impedance and the capacitive reactance of the capacitor bank that is connected for power factor correction, the amplification of the harmonic voltages and currents is estimated by calculus. The results obtained by calculus are then compared with the values obtained by simulation after the connection of the capacitor bank to the network. In conclusion, the chapter proves that the network harmonic impedance is a useful tool to estimate the harmonics amplification caused by power factor correction using shunt capacitor banks.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Keywords: distribution electrical networks, reactive power compensation, capacitor banks, harmonic impedance, harmonics amplification

1. Introduction

Harmonics are making their presence felt in electrical distribution networks due to both the use of nonlinear devices in the consumers' area and the high development of distributed generation [1, 2].

The harmonics of the electrical networks have negative effects like increasing active power losses, resonance over voltages, increasing the potential of the transformers' neutral point, over currents in three-phase networks which can lead to difficulties regarding the protection relay selectivity, and capacitor banks overstressing. The effects of some types of loads like office equipment, air conditioning units, lighting devices, motor drives, and household equipment are presented in [3]. This study discusses the influence of capacitor banks on the network harmonics conditions.

Connecting a capacitor bank to the electrical network leads to the resonance phenomena, which, superimposed over the harmonic current flow on frequencies close to the resonance frequency, result in high harmonic voltage values at the capacitor terminals and high harmonic currents flowing through the capacitor bank. Over voltages lead to insulation overstressing, and high currents produce a capacitor bank heating that is also reflected in insulation damage [4, 5].

There are many methods for network harmonic impedance determination, which are presented in many literature works [6–12]. Even the operation of switching the capacitor bank can be used for harmonic impedance measuring [13], and online determination of the harmonic impedance is the subject of many works [14, 15]. One problem that is less noticed in these works is how to determine the phase of the complex harmonic impedance.

This chapter presents a method, which uses the network harmonic impedance like a tool to anticipate the harmonic condition amplifications in the case of reactive power compensation by capacitor banks.

In order to reach this objective, Section 2 presents a method to determinate the complex harmonic impedance. In order to find the phase of the impedance, the series–parallel circuit transformation is used. A mathematical model to anticipate the harmonic currents and voltage amplification, based on the harmonic impedance values, when a capacitor bank is connected to the network, is also described in Section 2. The mathematical model is validated, in Section 3, by a MatLab Simulink simulation for an electrical distribution network that comprises a bus with a capacitor bank installed for power factor correction. The results obtained by simulation are compared with those obtained by calculus from the mathematical model. Section 4 presents, step by step, how the distribution network is implemented on a Matlab Simulink model. Section 5 comprises the conclusions of the chapter.
