Calculation of Magnetic Flux Density Harmonics in the Vicinity of Overhead Lines

Round 1

Reviewer 1 Report

In this manuscript, the authors study a procedure for the computation of magnetic fluxes in the vicinity of overhead distribution lines. This method takes into account higher current harmonics by using the Biot-Savart law and complex image method.   I have carefully read the manuscript and I think it needs important improvements before being considered for a possible publication:   1.- First, in the manuscript I have read, the references are missed. When the text cites a reference or a figure, question marks are shown.   2.- Second, in Figure 1(b) the fits look very robust. However, I think it is necessary to provide a chi-square or a different likelihood analysis in order to quantify their quality.   3.- Finally, as the authors comment, Figure 2(b) and 5(b) show an important mismatch among calculated magnetic flux density harmonics and the prescribed limit values for general and occupational exposure. In this case, a more detailed discussion is needed in order to explain such results.  

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper is devoted to computation of electromagnetic quantities (harmonics of flux density) near an overhead distribution line. The subject lies within the scope of MDPI Electronics, which covers industrial electronics, thus EMC-related issues.

The authors develop a computation method based on Biot-Savart law and the method of images in order to determine how individual harmonics of distorted currents flowing in the overhead line contribute to the outcome magnetic flux density computed in an arbitrarily chosen point of interest (lying right below the central phase conductor 1 meter above the earth level, as can be inferred from the text). The computation results are provided both for monoharmonic and distorted excitation signals and compared against recommendations of International Commission on Non-Ionizing Radiation Protection (ICNIRP) reference values for time-varying magnetic field.

Three first authors of the present contribution published recently a paper on similar subject in IEEE Access (10.1109/ACCESS.2021.3099760), however there are different points of focus in both contributions. The aforementioned paper introduced the readers into the issue how to compute electromagnetic quantities for the considered three phase system using the method of images and Biot-Savart law, discussed in an insightful way how to simplify computations by introducing equivalent radii of several conductors in a bundle as well as provided information on the capabilities of ANNs to predict the profiles of electric field strength intensity. In the present paper the authors focused rather on the issue that phase currents may be distorted thus on the effect of harmonics.  Thus the choice of the subject is original.

There are some weaker points about the manuscript:

1. It is a pity that this paper is focused only on computation and there is no comparison to real-life measurements made with some portable instrument. There is only one case of validation using the data available in [15]. Some measurements would greatly enhance the value of the paper.
2. The authors apply the Fortescue method to phase angles for individual harmonics (4)-(6). However the presentation at this point is rather obscure. Is it possible to split the phase currents into harmonics first, carry out the computations for every single harmonic, and finally to sum up the total output induction? Is this what the authors meant here?
3. Did the authors take into account how the results may be affected by Earth magnetic field at the considered location (Sarajevo)? The reviewer means that maybe not all digits after the decimal point as shown e.g. in lines 155 and 156 are significant.
4. The authors provide a computation example for a rich input spectrum, up to 31st harmonic (odd ones), Table 1. The reviewer understands this is an example from literature, but did the authors compare that rich spectrum to a more limited one, the reviewer means here, whether such a signal differs much to a more limited one, say up to the 13^th or 19^th (taking “above 5% in magnitude” as criterion) harmonic?   

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have partially addressed the criticisms raised in my previous review. I appreciate the effort of the authors to improve the manuscript. So, I recommend the acceptance of the paper in the present form.  

Reviewer 2 Report

The authors have addressed the issues raised in my previous review in sufficient manner. There are some slight language mistakes e.g. lines 73 or 74 "criteria" is plural, in singular it is "criterion", the relationship (12) should be rewritten (the modulus sign should be the same size for the both components). But these minor deficiencies may be removed during the proof stage.

I recommend the acceptance of the paper in the present form.