Problems in Modeling Three-Phase Three-Wire Circuits in the Case of Non-Sinusoidal Periodic Waveforms and Unbalanced Load

Round 1

Reviewer 1 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

I have carefully reviewed the revised version of the manuscript entitled "Problems in modeling three-phase three-wire circuits in the case of non-sinusoidal periodic waveforms and unbalanced load." As the reviewer of the original submission, I recognize the substantial effort the authors have made to address all previously raised comments and concerns in a thorough and technically sound manner. The revised manuscript demonstrates clear improvements in structure, clarity, and technical depth. The authors have responded adequately to each point raised in the initial review, providing detailed explanations and implementing necessary modifications. I am of the opinion that the manuscript, in its current form, meets the standards for publication in journal and recommend its acceptance without the need for further revision.

Author Response

Thank You very much for Your time for our article. In the current version of the article, we have made some minor changes that are in response to comments from one of the reviewers.

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

This article addresses mathematical modeling challenges in three-phase three-wire power systems under conditions of non-sinusoidal periodic waveforms and unbalanced loads.

1. Despite the in-depth theoretical derivations, the manuscript does not present any experimental or real-system validation to support the revised CPC formulations.
2. Most of the presented analyses assume linear time-invariant (LTI) loads. However, many real-world unbalanced and harmonic-rich systems involve nonlinearities. This oversimplification undermines the generalizability of the results.
3. While the CPC theory is emphasized throughout, the paper misses an opportunity to quantitatively compare its results with other established power theories (e.g., IEEE 1459, Instantaneous Power Theory) under the same conditions.
4. Some numerical examples use arbitrary values without clear justification or unit consistency.
5. Although mathematical formulations are presented in detail, their physical meaning or engineering relevance—such as how the revised CPC model influences compensator design or energy measurement in smart grids—is not discussed thoroughly.
6. The introduction lacks a concise problem statement and clear research questions.
7. The manuscript does not define any quantifiable performance metric (e.g., power loss reduction, modeling accuracy, error in parameter estimation) to validate the advantages of the proposed methods.
8. While the references are numerous, many are self-citations or dated theoretical sources. There is insufficient engagement with recent developments in measurement-based power decomposition and signal-processing-based power theories.

Author Response

Thank You very much for Your time for our article. We are aware that a good article must have a reliable review. We are very fortunate that this article has good reviewers.

This paper was presented at an international conference in late 2024. It made a positive impression on the listeners. That's why we believe it will have a major impact on the scientific community.

We have included responses to Your comments in the attached file. We have made some changes in the current version of the manuscript.

Author Response File: Author Response.doc

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

Article review: "Problems in modeling three-phase three-wire circuits in the case of non-sinusoidal periodic waveforms and unbalanced load" Authors: Konrad Zajkowski, Stanislaw Duer The article is devoted to the actual problem of modeling three-phase three-wire circuits with non-sinusoidal periodic signals and an unbalanced load. The method of decomposition of current components considered by the authors using the theory of physical components of currents is devoted to the ambiguities that arise in calculations. The research is devoted to improving the quality of electrical energy and the efficiency of power supply systems. Non-sinusoidal and asymmetric operating modes are common in modern electrical networks, and lead to increased power losses and disruption of the normal operation of electrical appliances. The problems of providing high-quality electricity are an acute problem now and will be an important problem in the future, due to the widespread use of modern devices that lead to a deterioration in the quality of electricity. A detailed analysis of the methods of current decomposition presented in the paper and its comparison with other approaches, such as the IEEE 1459 standard, allows the reader to familiarize himself with the advantages and limitations of each method. The material makes it clear and useful due to the numerical examples provided. The paper offers refinements in methods for determining symmetric components for non-sinusoidal modes, which has a positive effect on the development of the theory. The authors' work represents a contribution to the field of modeling three-phase circuits in non-sinusoidal and asymmetric modes of operation, of interest to specialists in the field of providing high-quality electricity, increasing energy efficiency and reducing losses in electrical distribution networks. The article is structured, written in clear and understandable language, the conclusions are logical, the literature corresponds to the stated topic. The scientific article by Konrad Zajkowski, Stanislaw Duer "Problems in modeling three-phase three-wire circuits in the case of non-sinusoidal periodic waveforms and unbalanced load" has a certain scientific significance, the results of the work will be of interest to design and operational organizations, teachers, graduate students and undergraduates of universities dealing with problems of improving the quality of electricity, energy efficiency and reduction of electricity losses in electric distribution networks. Conclusion: the reviewed article meets the requirements for scientific publications and can be recommended for publication.

Author Response

Thank You very much for Your time for our article. In the current version of the article, we have made some minor changes that are in response to comments from one of the reviewers.

Round 2

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

The new version of the paper does not show any obvious signs of revision, and the authors did not actually make revisions based on the comments from the previous round of review.

Author Response

Thank You very much for Your valuable time. We have marked the changes in the manuscript in red. All our responses - as before - are attached in a separate file in the attachment.

Author Response File: Author Response.doc

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper aims to highlight the challenges in defining powers in non-sinusoidal, balanced, and unbalanced three-phase three-wire systems. The authors examine irregularities in using the Currents' Physical Component (CPC) theory and propose ways to avoid them when calculating powers in single-phase and three-phase three-wire systems. They have carefully studied CPC theory and provided examples to support their recommendations and corrections.

I have some comments on the revision of the CPC power theory in the paper:

1. The authors stated that when calculating RMS voltage, voltage components that do not contribute to current flow should not be included. In single-phase systems, this statement contradicts the definition of RMS voltage and current used in circuit theory, which includes all harmonic components. Therefore, one should be cautious when eliminating voltage components. In well-known power theories that deal with three-phase power systems, active currents are proportional to the voltages relative to the virtual star point, provided that the voltages do not contain zero-sequence components. These voltages can be determined from the measurable line-to-line voltages, as specified in the DIN 40110 Standard. However, omitting a voltage (or a voltage component) that does not generate current may lead to incorrect power and power factor calculations. For example, in a three-phase three-wire system, if a load is connected only between phases R and S, then the voltage of phase T does not generate current. Calculating the equivalent RMS voltage for a three-phase three-wire system without including the voltage of phase T results in incorrect values of powers and power factor. Additionally, the most common definition of apparent power states that it is equal to the maximum active power that may be transmitted to the load for a given RMS voltage and a given RMS current. If a voltage (or a voltage component) does not generate current, energy transmission efficiency to the load decreases, which should be reflected in powers and power factor. I advise the authors to consult the relevant literature, and, to define powers, to reconsider the use of voltage components that do not contribute to energy transmission to the load.

2. When determining the symmetrical components using the Fortescue transformation in the presence of multiple harmonics, the rise of the turnover factor α to the power of the harmonic order is natural. In a three-phase three-wire system, zero-sequence voltage components are prevented by the choice of a reference point for voltages, and zero-sequence current components are prevented by Kirchhoff's first law. Therefore, the proposed revision of the CPC power definition in Chapter 5 of the paper is justified, as only the positive and negative sequence voltage and current components contribute to the powers in a three-phase three-wire system.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper tires to propose point out some problems in computation. However, the logic in the paper is weak and it lacks examinations of the proposed problems.
The manuscript exhibits  conceptual misunderstandings and lacks alignment with established power system theories.

1. The phase shift is not a problem, it is common in power system that sometimes people use cos to transform and sometimes people use sin function. 
Since the current and voltage must follow the same transformation, the phase difference between current and voltage remain the same. People are doing this all the time 
in DQ transformation. Otherwise, the authors should explicitly provide the example that such problem really generates wrong measurements.

2. The authors try to redefine V RMS in example 1, a RC circuit, which is confusing. Normally, RMS essentially calculates the equivalent direct current (dc) value of an ac waveform. U0 is not a AC waveform so such problem doesn't exist in real world. If a DC component is appeared in RMS, it doesn't mean it cannot generate energy effect because the energy effects are formed by currents and voltages together. In fact the DC energy effect is happening there and it is the very basic knowledge of power electronic. 

If using a RC circuit and apply a DC voltage on it, it is not going to be the same to the "no effect". The DC current component is 0 because the capacitor must be charged to V_dc so that the voltage drop over R is 0. In this case we can easily find that the RMS must include the DC component because the current, although it is 0 at the steady-state, the transient current is allowed to have a DC component. 
 
 Usually, people use frequency domain analysis for AC systems so it is wrong to mix multiple frequency domain together. In addition, the real-world true RMS meter won't distinguish the frequency components in a waveform, and it only performs high-frequency sampling and direct compute the RMS with a numerical method. 

3. the "Three-phase Current Components in Time-domain" is confusing. I cannot find any time-domain element in this section. "the voltages in the remaining phases are equal" is an obvious mistake. I see nothing related to time-domain in the whole paper actually. It is a complete mistake to draw multiple frequencies in the same complex plane in figure 3. Also, the figure 3 only contains RST and three U_z is appeared. It is totally illogic.

In all, the paper contains too many ambiguous symbols and mistakes and the logic chain is very weak.

 

Comments on the Quality of English Language

"the voltages in the remaining phases are equal" is an obvious mistake.  Many symbols are ambiguous.

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript analyzes the method of mathematical decomposition of current components in the case of a three-phase power supply of linear time-invariant systems from an asymmetric source. The manuscript is interesting, however, it needs certain improvements. First of all, it is necessary to explain in more detail the motivation for solving the problem that the authors are addressing in the manuscript under consideration. Also, it is required to provide a more detailed background description of the problem and to accompany it with an adequate literature review that would show the achievements of other authors in this area. Through the literature review, it is necessary to precisely define the research gap that the author solves with the proposed method, as well as to list the contributions of this manuscript in the introductory part. Also, the contributions should be noted in the abstract of the manuscript. At the end of the introductory section, it is necessary to provide an overview of the structure of the manuscript by sections. It is necessary to add explanations of the symbols used in all equations, immediately after the equations themselves. In the way it is written now, the mathematical model is confusing and in certain parts it is difficult to determine whether the equations are physically correct. It is necessary to add more general explanations and introductions to the issues at the beginning of each section. To improve the quality of the overall manuscript, it would be a significant contribution to considering one or more case studies, preferably with real problems in which the proposed method finds its application.