RESEARCH ARTICLE A dynamic harmonic domain–based framework to detect 3‐phase balanced systems under dynamic transients: the test case of inrush current in transformers Ehsan Karami 1 * | Manuel Madrigal 2 | Shahram Montaser Kouhsari 1 | Seyed Mahdi Mazhari 1 1 Amirkabir University of Technology, Tehran, Iran 2 Instituto Tecnológico de Morelia, Morelia, Mexico Correspondence Ehsan Karami, Amirkabir University of Technology, Tehran 15875‐4413, Iran. Email: ehsankarami@aut.ac.ir Abstract It is well known that energizing a transformer can cause significant transients and harmonic pollution especially in the first few cycles. The waveforms of the 3‐phase inrush currents are different even if the transformer is operating in a balanced con- dition; but analyzing the harmonics of 3‐phase inrush currents shows that they are completely balanced if the transformer is under a balanced condition. This observation is possible only if the transformer is analyzed by using the dynamic har- monic domain. The dynamic harmonic domain provides dynamic analysis of the harmonics in the transformer from transient period to steady state. In this paper, physical meaning of harmonics during the transient period is also included. More- over, a concept of 3‐phase balanced systems under dynamic nonsinusoidal condi- tions is presented and explained with the inrush current in a 3‐phase transformer. KEYWORDS balanced system, DHD, inrush current, transformer, transient harmonics, WFT 1 | INTRODUCTION Owing to the daily increasing of power electronic devices and equipment behaving as nonlinear loads, modeling and analy- sis of harmonic sources play vital roles for power quality assessment. 1 Generally speaking, harmonic sources are cate- gorized into nonlinear and time‐periodic systems where saturable elements such as transformer magnetizing circuits fall into the first group and switching‐based power electronic converters are set into the last category. 2 The problem of how to quantify harmonic impacts of some prevalent harmonic producing loads on a particular location of a power grid is investigated by Wang et al 3 in which a multiple linear regression analysis–based technique is introduced to solve the issue. Harmonic impacts of photovoltaic inverters on the distribution systems are assessed by Shi et al 4 ; the proposed analytical model illus- trates that the photovoltaic inverter blurt characteristics asso- ciated to both a harmonic source and a harmonic impedance. Transformers are crucial elements of power systems, which are treated as harmonic sources while saturation takes place in their magnetic cores. It is shown in the specialized literature that saturation characteristic affects the magnetiza- tion current in both steady state and transient state. Although the transformer steady‐state magnetization current is about 1% to 2% of the rated current value, it may increase up to 10 to 20 times of the rated value in case of energization owing to inrush currents. 5–7 Inrush currents are a transient phenomenon that increases sharply to peak value and injects significant harmonic contents to the grid, resulting in adverse operation conditions. It is known that they can cause unnecessary tripping of differential protection relays. 8 It should be noted that as the transformer core is designed to operate close to the knee point, a small overexcitation raises the harmonic generation. Moreover, inrush currents may last for several seconds; thus, they may cause long‐term overvolt- ages in the system when large power factor capacitors are located at the secondary side. In this case, a combination of capacitor and inductive system impedance may lead to a parallel resonance circuit of high impedance. 9 Therefore, an appropriate approach for both harmonic and transient studies is important. Received: 25 August 2015 Revised: 1 June 2016 Accepted: 7 July 2016 DOI 10.1002/etep.2252 Int. Trans. Electr. Energ. Syst. 2016; 1–13 Copyright © 2016 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/etep 1