Multi-Energy Static Modeling Approaches: A Critical Overview

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

Dear Author, 

Please find the review report. Thank you and good luck!

Comments for author File: Comments.pdf

Author Response

The analysis and review of this paper proved to be a valuable scholarly endeavour. The author has meticulously delineated and systematically presented a series of technical arguments and substantiating evidence concerning the prevailing modelling techniques for the various components of the most significant energy carriers. The paper provides further elucidation on the most prevalent techniques employed to integrate these components with the goal of formulating MES simulation models.

I thank the reviewer for the positive evaluation of the paper.

However, the following recommendations are proposed:

Comment 1: Rows 13-14: The explanation provided in brackets could be reworded to enhance clarity.

Response: As requested by the Editor, the whole Abstract has been shortened and simplified. Taking also into account this comment, the sentence has been simplified as follows: “As RES generation is characterized by a variable generation pattern and as the electric carrier is characterized by scarce intrinsic flexibility, since storage capabilities through electrochemical batteries as well as demand-side flexibility contributions stay rather limited, it is quite natural to think of other energy carriers as possible service providers towards the electricity system”. I hope in this way the concept is clearer.

Comment 2: Rows 20-23: The sentence can be restructured and reformulated to enhance comprehension.

Response: the sentence was too long and complex. It was streamlined as follows: “Gas and heat networks and, in the future, also hydrogen networks could provide storage services for the electricity system. This could allow to increase the amount of RES penetration to be managed safely by the electric system without incurring in blackouts and to avoid non-economically-motivated grid reinforcements to prevent curtailment of RES generation peaks”. I hope in this way the concept is clearer.

Comment 3: Row 26: Prior to the energy carriers in brackets, the phrase “i.e.” can be employed.

Response: Done.

Comment 4: Rows 36-38: The sentence could be improved by providing a more thorough elaboration of the concrete practical implications of the analysis.

Response: As said, taking on board the request by the Editor, the abstract section was shrunken and made more compact. Regarding the sentence “The style of this paper is that of a tutorial aimed at providing some guidance and a few biblio-graphic references to those who are interested to approach this theme in the next years”, the aim was to explain that rather than being the classic review paper, with a lot of bibliographic references, I tried to keep a “tutorial” style, by introducing formulas, explaining them, comparing approaches and the like. Practical implications are described elsewhere, e.g. in the conclusions, where it is written: “ME models can be very useful for the system operators of the different grids to analyse the efficacy of flexibility measures across the energy carriers and for the national regulatory authorities to assess the possible technical-economic impact of new regulatory provisions. In this framework, the main contribution of the present paper is to provide a synthetic and complete review of the current modelling techniques for the different components of the most important energy carriers and of the most typical techniques to join them to create MES simulation models”.

Comment 5: Rows 53-62: The paragraph can be divided and structured into several sentences to support the main argument.

Response: True that the sentence is long, but the concepts are also complex and articulated. I don’t see how to express the same concepts in a more compact way. If the paragraph is divided in several sentences we just obtain a text more cumbersome to read (I have tried it!).

Comment 6: Rows 90-91: Please remove the unnecessary space.

Response: Done

Comment 7: Rows 116-122: Sentences may be reformulated to achieve optimal clarity and precision.

Response: Also in this case, I don’t see where the sentence is unclear: it is just a list of different applications of multi-energy models (either to calculate load flows, or for optimization of the dispatch or of the planning). True that the necessary explanation of the acronyms OPEX, CAPEX and TOTEX makes reading a bit more complicated, but the meaning stays quite clear and explained in a concise way.

Comment 8: Rows185-186: The sentence is not entirely clear; therefore, it would be preferable to rephrase it.

Response: The sentence “More detail on components behavior implies a more complex mathematical description” means that the more a component is described in detail, the more the mathematical model becomes complex. It seems clear to me.

Comment 9: As posited on rows 356-357, the presented equation (in this case, Weymouth equation) can be developed from a theoretical point of view.

Response: This remark is not clear. The Weymouth equation was indeed theoretically derived from the steady equations of a gas pipeline, and it is just highlighted that this formulation is valid only if the gravitational term is disregarded (in any case, this hypothesis is quite common when analyzing big gas transmission grids).

Comment 10: Row 406: Check for spelling and punctuation errors.

Response: The sentence “Linearized formulations for the solving problem of the gas flow equations (9)(10) do exist.” doesn’t include punctuation errors. Here, the “do” is used in an emphatic way, just as “indeed” or other affirmative particles.

Comment 11: Rows 418-419: Please remove the unnecessary space.

Response: A different spacing was needed to highlight we are passing from the long section dedicated to the pipelines to the one dedicated to the other components.

Comment 12: Row 437: An explanatory note is required for Figure 4.

Response: I agree: the following description has been added: “the blue curves represent compressor characteristics for different speeds; “surge” and “stonewall” limits define the operative region”

Comment 13: Rows 545-546: Please remove the unnecessary space.

Response: The extra space delimits the separation between the end of the text describing figure (31) and the summary of what the following section will present.

Comment 14: Rows 834-835: Please remove the unnecessary space.

Response: The extra space separates the end of the section dedicated to the PlaMES model from the beginning of that dedicated to the MAGNITUDE project.

Comment 15: Rows 927-939: Please restructure the paragraph to make the argument clearer. The paragraph is too long. The same applies to the following paragraphs (see rows 944-971 and rows 977-990).

Response: I don’t find this section is unclear. These sentences are not long and there is, in my opinion, a good compromise between conciseness and clarity (please also consider that the paragraph on numerical issues has been added as a short introduction to the topic, but this is not the “core” of the paper, which remains devoted to modelling issues).

Comment 16: Rows 995-996: Please remove the unnecessary space.

Response: Done.

Comment 17: Rows 1017-1018: Please remove the unnecessary space.

Response: Done (also between 1030-1031).

Comment 18: The conclusions section is well formulated. Nevertheless, further elaboration is necessary to provide a more comprehensive and precise set of arguments that can be used to achieve the decarbonization target. Similarly, the author could improve the explanation of the study's specific limitations.

Response: The following sentences was added “As highlighted in the introduction of the present paper, the decarbonization pathway goes also through an evaluation of the support that other carriers can provide to enhance the typically very limited flexibility of the electric system. ME models can help providing the relevant techno-economic assessments and, thus, promise to become a key ingredient for all future scenario analyses. ME models can be very useful for the system operators of the different grids to analyse the efficacy of flexibility measures across the energy carriers and for the national regulatory authorities to assess the possible technical-economic impact of new regulatory provisions.”. Regarding the limitation of this study, as remarked several times in thew text, this paper deals mainly with modelling issues. Additionally, it provides some hints on the numerical issues, which, however, stay very complex for such large mathematical models, as clarified in the sentences: “However, it must be admitted that, as already clarified in section 3.6, matching a numerically tractable technique to the solution of very large MES (like the most general one de-scribed by (31)) is still a daunting task and an important field of research: numerical techniques are gradually adapted to the steadily increasing performances of computer hard-ware and software. However, on this regard, recently, the introduction of cloud computing ([66]) has brought new possible horizons”. Overcoming such limitations, by means of decomposition techniques and parallelization will be the aim of all future R&D on multi-energy models. I think this is adequately stressed in the text.

Author Response File: Author Response.docx

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

The manuscript provides a comprehensive overview of static multi-energy system (MES) modeling approaches, emphasizing their relevance in achieving decarbonization targets. The topic is timely and aligns well with the journal's scope. The technical depth is commendable, particularly in modeling gas and electricity networks, and the inclusion of European projects (e.g., PlaMES, MAGNITUDE) adds practical insights. However, the paper could be significantly improved by the following suggestions: 

1. The abstract could be shorter and should explicitly mention the gap this review addresses, the methodological approach and findings/contributions of the research. 

2. The manuscript lacks a synthesized comparison of approaches (e.g., energy hubs vs. graph models). Add a table summarizing pros/cons, computational demands, and use cases for each method (e.g., scalability, suitability for planning vs. dispatch).

3. There is an overemphasis on European case studies. Broaden the discussion to include non-EU examples (e.g., U.S. hydrogen initiatives, Asian smart grid projects) to enhance universality.

4. The authors should check that all in-text references are properly cited.

 

Author Response

The manuscript provides a comprehensive overview of static multi-energy system (MES) modeling approaches, emphasizing their relevance in achieving decarbonization targets. The topic is timely and aligns well with the journal's scope. The technical depth is commendable, particularly in modeling gas and electricity networks, and the inclusion of European projects (e.g., PlaMES, MAGNITUDE) adds practical insights.

I really thank the reviewer for this positive appreciation.

However, the paper could be significantly improved by the following suggestions: 

Comment 1: The abstract could be shorter and should explicitly mention the gap this review addresses, the methodological approach and findings/contributions of the research. 

Response: The abstract was considerably shortened as requested by the Editor. The gap this review addresses is already well synthetized by the sentences “The present paper aims at describing the most important approaches to static ME modelling by comparing pros and cons of all of them with a holistic approach. The style of this paper is that of a tutorial aimed at providing some guidance and a few bibliographic references to those who are interested to approach this theme in the next years.”. Actually, I don’t know anything similar in the scientific literature. In the introduction chapter, more details are provided, as it deserves.

Comment 2: The manuscript lacks a synthesized comparison of approaches (e.g., energy hubs vs. graph models). Add a table summarizing pros/cons, computational demands, and use cases for each method (e.g., scalability, suitability for planning vs. dispatch).

Response: The two approaches  (energy hubs vs. graph models) are actually not in mutual contrast but in synergy. The energy hubs approach helps to describe all conversion processes occurring in a complex energy hub in a tidy and coherent way and to collect the outcome in matrix format. The graph-based representation helps to tackle all carriers in the same way as the electric carrier, for which node and mesh balance equations are written to describe the system layout in a mathematical way. For MES, adopting a graph representation extends this approach and allows to write all balances for all carriers in a coherent way.

A table summarizing different aspects regarding a comparison of numerical complexity of different problems under several aspects (computation complexity, scalability and, consequently, suitability of the different methods) has been included. This should complete the remarks done in section 3.6. More detailed remarks would be possible only with reference to a specific problem structure, not in in the generic context of the paper.

Comment 3: There is an overemphasis on European case studies. Broaden the discussion to include non-EU examples (e.g., U.S. hydrogen initiatives, Asian smart grid projects) to enhance universality.

Response: True that the brief regulation introduction is euro-centric, and this is due to my know-how, which is more focused on the European context. However, this part (which could be by far much further extended also with reference to the European context) is just included in order to clarify to the reader that speaking about static MES is not just an academic exercise but is a hot topic present regulation is dealing with as well. Who is interested to know more on regulation (and on a more extended world overlook) can have a view to article [2] of the bibliography, published by my and some other colleagues some months ago for ENERGIES. Here the focus is on hydrogen potentials instead on MES modelling, and the international regulation is extensively treated, as it deserves.

Comment 4: The authors should check that all in-text references are properly cited.

Response: All references in bibliography are also cited in the text: this was checked again.

Author Response File: Author Response.docx

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

Here are some suggestions.

1. The introduction and title focus on static modelling approaches, however, several dynamic models, and optimization, planning problems are also mentioned in the context. The main focus should be more explicit.
2. The authors are suggested to restructure the contents to clearly outline the gaps in existing literature that this review addresses, particularly regarding the critical comparison of static models.
3. ​While the paper references key policy documents (e.g., EU strategies, ENTSO-E/ENTSOG scenarios), it lacks a thorough discussion of recent academic advancements in multi-energy static modelling. Incorporating recent studies would strengthen the review’s relevance. For example, the authors used power flow model for electric system, dynamic model for gas system, why do the authors simply introduce the static heating system model? Actually, dynamic heating system model is also a hot topic in MES, such as [1] doi: 10.1109/TSG.2024.3493818; [2] doi: 10.1109/ACCESS.2022.3161961. Please also discuss about these models.
4. The linearization approaches for gas networks (Section 2.2) should be further discussed. Besides the approaches mentioned in this paper, there also other linear models of gas system, such as [3] https://doi.org/10.1016/j.apenergy.2024.124052 and [4] https://doi.org/10.1016/j.apenergy.2019.114029. A dedicated subsection discussing these linearization methods is suggested.
5. ​A consolidated table summarizing the computational complexity, scalability, and suitability of different models for specific use cases are suggested.
6. ​Please discuss about open challenges (e.g., data interoperability between gas/electricity/hydrogen TSOs) or emerging tools (e.g., digital twins for multi-carrier systems) for MES. Expanding the conclusion to address these aspects would enhance impact.

Author Response

Comment 1: The introduction and title focus on static modelling approaches, however, several dynamic models, and optimization, planning problems are also mentioned in the context. The main focus should be more explicit.

Response: The focus of the paper is indeed only on static modelling. As explained in the paper, the concrete applications I have in mind for these models are: (1) load flow models aiming at calculating intensive nodal quantities (voltages, pressures…) once the input extensive variable are known; (2) optimization models aiming at minimizing operative costs (OPEX), typically in terms of hourly dispatch of the ME system. Market solution optimizations, e.g., have to be thought in this context; (3) optimization models aiming at optimizing total costs (TOTEX), defined as sum of dispatch and investment costs. This is the typical layout of planning problems.

In this framework, the only non-static model which has been dealt with in the paper is the method of the characteristics, introduced for compressible fluid pipelines (gas, hydrogen…). The reasons for this exception are essentially two: (1) the derivation of the method of the characteristics is an excellent way to introduce the Weymouth equation, which is the typical static modelling tool for gas pipeline. By means of the full description of the derivation process, it is possible to understand which are the assumptions and limitations that define the perimeter in which it can be used; (2) the Weymouth equation doesn’t model the transport time that a pressure wave caused by a step change of mass flow rate at the pipeline inlet takes to go through the entire pipeline. This can be important if we want to model a very extensive network of pipeline ducts (e. a European one). Of course, to model this aspect, it is necessary to abandon the static model domain. This is paid in terms of a much heavier model, which is definitely too complicated for allowing to simulate a multi-energy context in which a true gas network and a true electricity network are both modelled (some thousands of nodes each). By contrast, there is no use to introduce dynamic model for district heating systems, because they are significantly reduced in terms of geographic extension, so a static model should fit perfectly.

To clarify why the method of the characteristic has been described yet in a static context, I have added the following sentence: “The method of the characteristics is the only non-static model described in the present paper. It might seem a contradiction to employ a non-static methodology in a static context. However, this is the only way to model time delays in the propagation of a pres-sure wave generated by a step change either in the gas injected at the pipeline inlet or in the consumption at the pipeline outlet. As gas networks are characterized by important spatial extensions (e.g. embracing entire Europe), the effects of a decoupling between injec-tion and availability for the consumer is particularly evident (this is, by contrast, not the case for district heating networks, significantly reduced in their geographical extension)”.

Comment 2: The authors are suggested to restructure the contents to clearly outline the gaps in existing literature that this review addresses, particularly regarding the critical comparison of static models.

Response: As written in the paper several times, the advantage of the present paper is that it presents the modelling of the single carrier and puts in highlight pros and cons of this in a context in which the carriers are simulated together. I don’t know any other contribution of this kind. The reference point to compare the approaches has been to ensure convexity and linearity, because only in this way it is possible to assemble models of considerable dimension, representing real networks (e.g. for planning purposes) and still preserve numerical tractability. Then, chapter 3.6 introduces the concepts of computational complexity, convergence, scalability and robustness and provides a few guidelines on how to ensure that the have the best characteristics to be solved. So, the holistic vision is what motivates the present work, and I think this vision has been reasonably enforced throughout the paper.

Comment 3: ​While the paper references key policy documents (e.g., EU strategies, ENTSO-E/ENTSOG scenarios), it lacks a thorough discussion of recent academic advancements in multi-energy static modelling. Incorporating recent studies would strengthen the review’s relevance. For example, the authors used power flow model for electric system, dynamic model for gas system, why do the authors simply introduce the static heating system model? Actually, dynamic heating system model is also a hot topic in MES, such as [1] doi: 10.1109/TSG.2024.3493818; [2] doi: 10.1109/ACCESS.2022.3161961. Please also discuss about these models.

Response: As above mentioned, the focus of the paper is only on static models (being the method of characteristics the only exception, mentioned for already explained reasons. I am sure that dynamic models of district heating, useful in other contexts, are presently a hot topic. Nonetheless, the already more than 30 pages long contribution has its focus on static models: a new paper could be explicitly dedicated to dynamic models. Additionally, the typical timesteps for the above-mentioned static models (e.g. 1 hour) see typically all district heating transients concluded, so there is no interest to include the relevant dynamics.

Comment 4: The linearization approaches for gas networks (Section 2.2) should be further discussed. Besides the approaches mentioned in this paper, there also other linear models of gas system, such as [3] https://doi.org/10.1016/j.apenergy.2024.124052 and [4] https://doi.org/10.1016/j.apenergy.2019.114029. A dedicated subsection discussing these linearization methods is suggested.

Response: Two reference papers are already quoted on linearization ([] and []). With pleasure, I add one of the papers suggested by the reviewer: the one where a static model of gas ducts is introduced, and the Weymouth equation is linearized by means of a Taylor expansion. However, I don’t think adding a section dedicated to linearization is really necessary (it is a detail topic, and complicated analytic approaches are often adopted: interested readers can for sure make reference to the quoted papers, which is also in the spirit of a review paper).

​Comment 5: A consolidated table summarizing the computational complexity, scalability, and suitability of different models for specific use cases are suggested.

Response: This is an interesting suggestion: I agree this can constitute an important plus for the paper. Such table has been added at the end of section 3.6.

​Comment 6: Please discuss about open challenges (e.g., data interoperability between gas/electricity/hydrogen TSOs) or emerging tools (e.g., digital twins for multi-carrier systems) for MES. Expanding the conclusion to address these aspects would enhance impact.

Response: In the conclusions, one list of emerging challenges/tools is already present (e.g. digital twins are already mentioned there). By contrast, a detailed description is outside the scope of the present work.

Regarding, instead, data interoperability between gas/electricity/hydrogen TSOs, this is a very interesting issue, with important numeric and modelling implications. On this topic, I added the following sentences in the conclusions chapter: “Data interoperability between Transmission System Operators (TSOs) is a further important point with modelling and numerical implications. Usually, each carrier is managed by a distinct national TSO (one for electricity, one for gas and, in the future, one for hydrogen). Up to now, each TSO was requested to elaborate a separate planning document. Presently, as highlighted when illustrating the evolution of the European regulation, the TSOs have been requested to elaborate joint scenarios. In the future, it will be re-quested to elaborate a joined planning strategy, so that the global minimum cost strategy is implemented. However, an important problem lies in the availability of data for setting up an overall planning model: every TSO has responsibility for the privacy of its own data and exchange of information is not so easy to program. On this regard, it can be profitable to set up algorithms allowing to coordinate different planning models (one per carrier) by a supervisor process allowing an exchange of data at the border between the different carriers. Such kind of algorithm has already been experimented at the border between electric transmission and distribution networks (see [72]) and could be profitably extended to MES. Furthermore, this approach would allow to decouple the solution of the optimization problems for the different carriers yet retaining a coordination between them. This would possibly result in a reasonable sub-optimum but, by contrast, would help to retain numerical tractability for bigger MES problems”.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

Comments have been addressed by the authors

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

Dear Authors, 

Please find my review report! Thank you and good luck!

Comments for author File: Comments.pdf

Author Response

I find that the article entitled “Multi energy static modelling approaches: a critical overview“ provides a detailed overview of how energy transportation and energy carriers are being planned and improved, with a strong emphasis on the increasing role and contribution of renewable energy sources. Also, the novelty of this research paper is noticed from the very beginning of the article, where it focuses on the discussion of these static multi-energy models of energy transmission performance, especially in these current conditions characterized by increasing unpredictability and volatility.

At the same time, I consider that this paper represents a valuable contribution to the energy field, promoting the impact of renewable energy resources, which may generate interest for researchers, readers and policy makers.

I really thank the reviewer for this very positive introduction to the contents of the paper.

However, this paper can be improved in some directions to increase its scientific relevance, and my specific recommendations are outlined below in this review report.

Comment 1: I would suggest that the abstract be more focused and better structured. In this respect, my recommendation is that the abstract should more clearly state the central objective and the intended purpose of this study. Also in the abstract, the main practical implications of this study should be better and more detailed.

Response: I thank the reviewer for this suggestion. By reading again the abstract, I realized that I had forgotten to add the focus on static ME models and to add which stakeholders could take profit of such models (and why). Thus, I added the following sentences: “In particular, the focus is on static multi-energy models, useful either for calculating the network flows once the injected and withdrawn powers are known (load flow analysis) or for optimizing the system dispatch or the planning of new grid infrastructure. The resulting multi energy models can be very useful for the system operators of the different grids to analyze the efficacy of flexibility measures across the energy carriers and for the national regulatory authorities to assess the possible technical-economic impact of new regulatory provisions.”.

Comment 2: Although the introduction part is well organized and provides a well-detailed background to the topic, it would be recommended that the authors specify the specific objectives of this study and how they can be achieved. Thus, the methodological approach that has been followed and structured in this paper can be presented.

Response: The introduction has been restructured to highlight the fact that the focus is on static ME models and not on generic ME models (“The above considerations clarify the importance to adopt a Multi Energy (ME) ap-proach. In particular, in this paper the focus is on static multi-energy models, useful either for calculating the network flows once the injected and withdrawn powers are known (load flow analysis) or for optimizing the system dispatch or the planning of new grid in-frastructure. All such models in common the static description of the different carriers (as opposed to the one oriented to study transient phenomena) and the fact that very often they imply either the solution of a system of equations…”). Additionally, it is better clarified who are the stakeholders that should prove mostly interested in this kind of models. Regarding the objectives of the study, it is better clarified that “This paper aims at highlighting which modelling issues have to be taken into account in order to build up a ME static model. By contrast, it does not treat algorithms and techniques fit to solve the very large mathematical models generated in this way”. The fact that the paper first (chapter 2) considers the modelling of the single components of each carrier as the building blocks of the model, and then (chapter 3) analyses techniques to put them together in a large ME model, was already well explained. So, it was not deemed useful to change this part.

Comment 3: It would be necessary to include a paragraph in the introduction on the importance of static multi-energy models for energy decision makers and practitioners. Also, practical implications of the paper could be better integrated in the introduction.

Response: This has been done: see previous point.

Comment 4: In Section 2, I would suggest that each heading be numbered for a better organization and structure. For example, 2.1. would be the overview of electricity network models; 2.2. would be the sub-section presenting natural gas/compressible fluids network models; and 2.3. would be the sub-section presenting heat network models.

Response: I agree: the suggestion has been implemented in the paper.

Comment 5: For Figure 2 and Figure 3, the source should be indicated.

Response: Figure 2 and Figure 3 are not taken from external sources: Figure 2 represents the pi-equivalent of an electric line and can be found in many texts. Figure 3 is a graphic representation of the Method of the Characteristics: also for this there is no specific external reference. However, as a similar figure was also included in [31] and [32], I will add these references to the figure.

Comment 6: In section 3, the conceptual presentation of the financial indicators used for CAPEX and OPEX would be required.

Response: CAPEX and OPEX don’t represent “financial indicators” but, as already explained in the introduction chapter of the paper, the two tags stand respectively for OPerative EXpenditures (i.e. operative costs, e,g. dispatching cost) and CAPital EXpenditures (= investment cost in new assets). In any case, I see that the definition of CAPEX was not provided. I fixed this.

Comment 7: I would suggest that each heading in section 3 be numbered (3.1., 3..2 and so on) for better organization of this part of the paper.

Response: I agree: the suggestion has been implemented in the paper.

Comment 8: At the end of Section 3, a few paragraphs can be introduced to explain the link between the use of multi-energy static models, decarbonisation and the performance of energy carriers. The conclusion part can be expanded and improved by providing the practical implications of the research and suggesting possible future directions of this study. Also in the conclusion part, the specific limitations of this research can be mentioned.

Response: A sentence was added in the conclusions to state that decarbonization of electricity generation and moving towards a 100% RES-based generation mix passes through assessing the flexibility contribution that other carriers can provide to the electric system, through the analysis and simulation of MES. Regarding limitations and possible directions for future research, the already existing text stressing the need of new numerical research in order to improve the number of equations and/or optimization constraints that can be considered as numerically tractable seems sufficient to clarify the point.

Comment 9: The reference list would need to be checked again by the authors (some links cannot be opened).

Response: I checked all links in the reference list, and I was able to open all of them.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents a general overview of multi-energy static modeling approaches. It covers the modeling of electricity, gas, hydrogen, and heat networks, including their coupling strategies and optimization methods.

The document is interesting and well written; it covers a broad spectrum of approaches. However, some areas lack depth in critical comparison and real-world applications.

• The document lacks a concise statement of the paper's contributions. It is more like a book introduction chapter rather than a Review paper.
• There is no clear methodological approach to write this document, what sources were selected, and under what criterias?
• Why PRISMA was not used?
• The document covers energy carrier modeling but lacks detailed discussions on emerging technologies, such as hybrid energy storage systems or advanced power-to-gas solutions.
• The paper does not critically assess the trade-offs between model simplification and accuracy.
• Numerical information regarding computational efficiency, accuracy, or scalability for large-scale systems, in all fields (electricity, gas, hydrogen, and heat networks) is missing.
• Also, there is no information regarding the robustness and sensibility of the ME models.

Some topics should be included in this review but did not:

• Hybrid energy storage systems.
• Digital Twins and AI integration for modelling.
• How demand-side management programs can interact with multi-energy models
• The paper does not explore how multi-energy modeling applies to specific sectors like industrial complexes, smart cities, or microgrids.
• It has not addressed the challenge of integrating models across platforms and ensuring interoperability between tools like MATPOWER, PowerModels, and GasPowerModels.
• The paper briefly mentions European policies.

The manuscript includes 57 references, which is short for a review article of this length (as the author recognizes). Given the scope of the paper and the rapid advancement in MES modeling, the number of references must be expanded to include more recent contributions and comprehensive studies.

Some references are to general websites (like Wikipedia for convexity and optimization techniques!) and conference papers. They do not carry the same academic weight as peer-reviewed journal articles.

Please carefully check the necessity of self-citations like [2], [32], [43].

Only 12 references are from the last three years (2022–2024); the references must be more up-to-date, especially for a Review type manuscript.

Author Response

The manuscript presents a general overview of multi-energy static modeling approaches. It covers the modeling of electricity, gas, hydrogen, and heat networks, including their coupling strategies and optimization methods.

The document is interesting and well written; it covers a broad spectrum of approaches.

I thank the reviewer for this positive comment.

However, some areas lack depth in critical comparison and real-world applications.

Comment 1: The document lacks a concise statement of the paper's contributions.

Response: The introduction has been expanded in order to better delimit the object of the present paper (in particular: to underline that static ME models are specifically reviewed) and a specific sentence has been added to the conclusions chapter (“The main contribution of the present paper is to provide a synthetic and complete review of the current modelling techniques for the different components of the most important energy carriers and of the most typical techniques to join them to create MES simulation models.”).

Comment 2: It is more like a book introduction chapter rather than a Review paper.

Response: As clarified in both the abstract and the introduction “the present paper aims at describing the most important of these approaches and comparing pros and cons of all of them. The style is that of a tutorial aimed at providing some guidance and a few bibliographic references to those who are interested to approach this issue in the next years”. This makes it a bit atypical with respect to a customary review paper. Here, the attention is more on introducing the most typical approaches providing references for the references that provided a “track opening” on that very technique rather than on chasing any kind of recent publication providing variations on them. This explains also the reason why the number of bibliographic references is not huge and why the references have not necessarily been published in the last year(s): the significance of the shown approach was the preferred selection criterion.

Comment 3: There is no clear methodological approach to write this document, what sources were selected, and under what criterias?

Response: The criterion adopted to select the resources was based on highlighting the most important approaches both for modelling the single components of each carrier and the typical ways to put them together to create MES systems. From this point of view, “path opening” contributions (often doctorate dissertations) which set for the first time a given methodology were preferred to more recent approaches which prove less didactic to explain.

Comment 4: Why PRISMA was not used?

Response: I don’t understand this remark. What is PRISMA?

Comment 5: The paper does not critically assess the trade-offs between model simplification and accuracy.

Response: Actually, this very important point has been stressed several times in the paper. E.g. when the Weymouth equation for gases was introduced and then criticized so that the Method of Characteristics was then introduced. However, then it was clarified that in this way a wide system of non-linear equations should be solved, what makes the more detailed approach non-practically usable for big planning models. So, everything depends on the kind and extension of the model to solve. This is clearly stressed at the beginning of chapter 2, where it is said: “More detail on components behavior implies a more complex mathematical description. So, it is of paramount importance to understand which is the best compromise between completeness of the mathematical representation of the system and complexity of the resulting problem (which implies the kind of solver which can be used and the time of resolution or, in many cases, just whether the problem is numerical tractable with the present hardware and software or not).”. This concept is underlined several times throughout the document.

Comment 6: Numerical information regarding computational efficiency, accuracy, or scalability for large-scale systems, in all fields (electricity, gas, hydrogen, and heat networks) is missing.

Response: The paper concentrates on the modelling approaches for the single components of a ME system (chapter 2) and on how these single components can be put together in order to create a full model, be it for planning, operational dispatch or, simply for a load flow analysis. This is clearly stated in the introduction (“This paper concentrates only on modelling issues and does not treat algorithms and techniques fit to solve the very large mathematical models generated in this way”). Treating the solution techniques could be an interesting subject for another paper (maybe a follow up of this one: so, I take it as a suggestion). Nonetheless, the fact that the (typically) huge resulting optimization system requires special decoupling techniques is said several times in the paper and the most typical decoupling technique (Benders’s decomposition) is quoted in the paper, along with an interesting bibliographic source providing a good tutorial for applying it to a grid planning optimization problem.

Comment 7: Also, there is no information regarding the robustness and sensibility of the ME models.

Response: Again, as said at the previous point, the paper is on pure modelling, not on solution techniques, hence no consideration is paid on the robustness of the solution techniques.

Comment 8: The document covers energy carrier modeling but lacks detailed discussions on emerging technologies, such as hybrid energy storage systems or advanced power-to-gas solutions. Some topics should be included in this review but did not: hybrid energy storage systems, Digital Twins and AI integration for modelling, how demand-side management programs can interact with multi-energy models. The paper does not explore how multi-energy modeling applies to specific sectors like industrial complexes, smart cities, or microgrids.

Response: All these sectors constitute potential fields of investigation for ME models. Thus, I thought of adding a small paragraph to the conclusions in order to mention these fields of analysis, yet not entering into details because this would go beyond the goals of the paper.

Comment 9: It has not addressed the challenge of integrating models across platforms and ensuring interoperability between tools like MATPOWER, PowerModels, and GasPowerModels.

Response: MATPOWER and PowerModels are both useful for modeling exclusively electric power systems (so, not ME systems). They are optimized to be used, respectively, within MATLAB or Julia codes. Therefore, they are in alternative: no interoperability issue subsists in this case. GasPowerModel is a library capable to model both gas grids and electric grids in one ME model written in Julia. So, only this platform must be used, and there is no interoperability issue either.

Comment 10: The paper briefly mentions European policies.

Response: Performing a complete review of European policies is not in the scope of this paper. For this reason, only some important milestones stressing the importance of running multi-energy models was included. Here, the mentioned document from the European Commission unfortunately still stays quite isolated: unlike the needs to decarbonize the system and the potential importance of hydrogen (see reference [2] for details). By contrast, the existence of specific recommendation from the Agency of the Regulators (ACER) as well as the publication of joint scenarios from ENTSO-E and ENTSOG, both duly quoted in the paper, are important milestones.

Comment 11: The manuscript includes 57 references, which is short for a review article of this length (as the author recognizes). Given the scope of the paper and the rapid advancement in MES modeling, the number of references must be expanded to include more recent contributions and comprehensive studies.

Response: As already explained, the paper aims at explaining the most significant modelling approaches, both on modelling single carrier components and on joining together several carriers in one simulation model. The style is the one of a tutorial aimed at introduce with clarity the key approaches that are still actual nowadays rather than chasing all the most recent publications.

Comment 12: Some references are to general websites (like Wikipedia for convexity and optimization techniques!) and conference papers. They do not carry the same academic weight as peer-reviewed journal articles.

Response: I agree with the reviewer that Wikipedia does not carry the same weight as peer-reviewed journal articles, however the reason why I included a few of Wikipedia links is due to the fact that the paper, as a review paper, is very wide and touches a series of concepts, e.g. convexity or optimization techniques, each of which should be duly introduced. However, should the paper do it, it would be much bulkier and the thread of the speech would be easily lost. So, I decided to make reference to Wikipedia as a publicly accessible source of definitions for some important concepts.

Comment 13: Please carefully check the necessity of self-citations like [2], [32], [43].

Response: I agree that self-citations should be included with care. However, in this case there are strong reasons suggesting the inclusion. [2] is a very wide and in-depth open access paper on prospects regarding hydrogen as a new carrier in the energy system: its location is fully justified by the issues covered in the introduction, where the motivations for considering the multi-energy perspective are provided. [32] was my thesis work, I which (in my opinion for the first time) the topic of non-isothermal gas pipelines was tackled (this reference is provided for those who would like to see how modelling is in that case, which is the most general one). [43] is an open access paper providing a comprehensive introduction to the FlexPlan EU project approach, which is quoted several times in this paper (in any case this is definitely not a paper of myself as it includes 13 authors of several companies).

Comment 14: Only 12 references are from the last three years (2022–2024); the references must be more up-to-date, especially for a Review type manuscript.

Response: As already commented, the main interest was to provide the “track opening” works showing the approaches that are still nowadays used, not to chase the most recent publications. This is coherent with the tutorial style of the work.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The author has presented interesting arguments for my comments. The work is well written but lacks a scientific style and methodological approach for a Review paper.

The methodology for selecting the source and references is unclear; choosing fundamental work is valid, and there are no clear criteria for including or excluding documents beyond the author's perspective. PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) is a standard framework ensuring transparency in literature selection. The author should consider incorporating at least a simplified PRISMA approach and revise the Journal guidelines for authors.

The author argues that the paper focuses on modeling, not solving techniques; however, this is a significant limitation from my perspective. Even if the focus is on modeling, the paper should still provide numerical insights into computational complexity, convergence issues, and scalability.

The author states that robustness is a solution-related issue, not a modeling concern. This is not entirely correct. The paper should acknowledge that some modeling approaches are inherently more robust to parameter variations and discuss model sensitivity to input variations.

The author justifies the limited number of references by prioritizing foundational works.

I agree that foundational works are important. However, review papers should also include recent advancements.

The number of references is too low for a review of this scope.

The use of Wikipedia as a reference is inappropriate for an academic paper. Instead, textbooks, authoritative review papers, or research articles should be cited.

Author Response

Comment 1: The author has presented interesting arguments for my comments. The work is well written but lacks a scientific style and methodological approach for a Review paper.

Response: As already said, this is not a standard “review” paper but configures itself rather as a tutorial for those who would like to enter the world of multi-energy modeling and analyze the most significant approaches with their pros and cons. That is what brought to the methodological approach I applied, which is not to chase every single literature contribution, but to select the most significant ones because they act as a “path-opener” for a well-defined approach, both in modelling the single components and in putting them together to model a complex multi-energy system.

Comment 2: The methodology for selecting the source and references is unclear; choosing fundamental work is valid, and there are no clear criteria for including or excluding documents beyond the author's perspective. PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) is a standard framework ensuring transparency in literature selection. The author should consider incorporating at least a simplified PRISMA approach and revise the Journal guidelines for authors.

Response: Now, I see what PRISMA means. It is a methodology able to analyze large databases and to screen a subset of selected choices on the basis of some criteria of exclusion. So, implicitly, it is a bottom-up approach that one should use when he/she doesn’t know initially what to include and wants to have an idea by screening a large number of items. By contrast, here I do have a clear idea of what to include, because, on the basis of a long experience in modelling, I know the subject and I know what are the most important approaches to tackle it. So, I performed an orthogonal top-down analysis: first, I singled out the topics to treat, then I matched them with the most significant papers by means of an extensive research on the web. I have prepared a graph that should give an idea of my methodological approach (see attached file).

This was the approach I adopted, and the paper has been built in this way. Another approach (based on data mining techniques, like the systematic use of PRISMA implies – often matched with the use of Artificial Intelligence techniques) could bring to a completely different paper, with different aims with respect to mine. I repeat: the paper was not meant as the classic “review” paper but rather as a tutorial to introduce the most significant approaches.

Comment 3: The author argues that the paper focuses on modeling, not solving techniques; however, this is a significant limitation from my perspective. Even if the focus is on modeling, the paper should still provide numerical insights into computational complexity, convergence issues, and scalability. The author states that robustness is a solution-related issue, not a modeling concern. This is not entirely correct. The paper should acknowledge that some modeling approaches are inherently more robust to parameter variations and discuss model sensitivity to input variations.

Response: Yet insisting that the main target of this paper is not on entering into details on solving techniques, I recognize the topic is important. So, I have added a new section (3.6) dedicated to computational complexity, convergence, scalability and robustness. Here the concepts are defined an a few considerations are brought with respect to the modelling approaches illustrated in the paper.

Comment 4: The author justifies the limited number of references by prioritizing foundational works. I agree that foundational works are important. However, review papers should also include recent advancements. The number of references is too low for a review of this scope.

Response: Yet, stating again that my target was not to provide a high number of references but to highlight the most important approaches, I added further literature contributions: as a whole 9 new bibliographic references related to works of the last years.

Comment 5: The use of Wikipedia as a reference is inappropriate for an academic paper. Instead, textbooks, authoritative review papers, or research articles should be cited.

Response: Wikipedia is not supposed to be considered to the same extent as academic papers. As already stated, it is used to avoid defining in the paper some general concepts (like convergence, convexity, etc). Instead of Wikipedia I could, of course, quote texts for academic courses (typically not open access) where the reader should go through hundreds of pages to find the concept to be defined. Wikipedia gives this shortly and, in general, efficiently, as I checked for all quotations included in the paper.

Author Response File: Author Response.docx

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

The author has made his point; however, I recommend avoiding using Wikipedia as a scientific source for this work. 

It is a captivating manuscript that differs from a standard review paper. 

Author Response

All Wikipedia references have been replaced with other publications.