Optimal Distributed Generation Mix to Enhance Distribution Network Performance: A Deterministic Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The study presents a methodology for selecting the composition of distributed generation to ensure the efficiency of control networks. In connection with the active introduction of renewable energy sources into energy systems and the development of distribution networks, the problem considered by the authors is relevant. The article describes in detail the prerequisites for the study, provides a detailed review of the literature highlighting the features of existing methods, describes the optimization procedure that determines the composition of distributed generation and presents a numerical experiment. The study was performed at a high scientific level, corresponding to the Sustainability journal. To further improve the quality of the study, the following areas are highlighted:

- In the work, to select the composition of distributed generation, the objective function (1) was used, describing the total losses of active power. Did the authors consider the possibility of developing a more complex objective function describing the admissibility of the parameters of the post-emergency mode, the absence of current overloads of network elements, permissible voltages and AC frequency levels.
- To find the minimum of the objective function (1), the authors used the Jaya Optimization Algorithm. Was a comparison made with other optimization algorithms: gradient descent, metaheuristic algorithms?
- Was the possibility of conducting test experiments on more complex mathematical models of distribution power systems considered?
- The work must provide an analysis of the time costs for solving the optimization procedure, as well as the dependence of the time for solving the problem of selecting the composition of distributed generation depending on the dimension of the electrical network.
- Was the problem of using machine learning algorithms to optimize the placement of distributed generation in the electrical network considered? This problem can be solved by using the graph neural network algorithm.
- It is necessary to correct the design of the figures (Fig. 1: Classification criteria for defining DG [4] -> Figure 1. Classification criteria for defining DG [4]), Table 2.1: Summary of reviewed studies -> Table 1. Summary of reviewed studies)

Author Response

Manuscript ID: Sustainability-3648452

The authors offer heartfelt thanks to the anonymous reviewer for their thorough evaluation and for providing insightful and valuable comments that helped improve the manuscript to a higher standard. A detailed, point-by-point response to each comment is provided below.

Reviewer 1

Comment-1: In the work, to select the composition of distributed generation, the objective function (1) was used, describing the total losses of active power. Did the authors consider the possibility of developing a more complex objective function describing the admissibility of the parameters of the post-emergency mode, the absence of current overloads of network elements, permissible voltages and AC frequency levels.

Authors' Response: This study aims to determine the optimal combination of the proposed three distributed generation types and assess their effectiveness against the optimal mix of the four existing DG types in the literature. The existing and proposed DG types are presented in Fig. 3 and Fig. 4, respectively. To ensure a fair comparison, this analysis employs the widely used objective function of minimizing active power loss, as commonly used in the literature. Therefore, developing a more complex objective function that accounts for different parameters is avoided, and the scope of the study is limited to a single objective. Additionally, the reason for adopting minimizing total active power loss as the primary objective function is discussed in Section 7, point ii. The same paragraph also emphasizes that future studies can adopt a more complex, multiobjective optimization approach that considers techno-economic and environmental parameters.

Comment-2: To find the minimum of the objective function (1), the authors used the Jaya Optimization Algorithm. Was a comparison made with other optimization algorithms: gradient descent, metaheuristic algorithms?

Authors' Response: The optimal DG mix attained by the proposed Jaya algorithm is validated against several metaheuristic optimization algorithms. Please refer to Section 5.5, Table 10 of the manuscript. Since the Jaya algorithm is a metaheuristic technique, its performance is also compared against the metaheuristic approaches. 

Comment-3: Was the possibility of conducting test experiments on more complex mathematical models of distribution power systems considered?

Authors' Response: This study aims to determine the optimal combination of the proposed three distributed generation types and assess their effectiveness against the optimal mix of the four existing distributed generation types in the literature. Therefore, the scope of the study is limited to a single objective of minimizing total active power loss in the power distribution network. However, Section 7, point ii, recommended adopting more complex multiobjective models that consider techno-economic and environmental parameters. Additionally, the IEEE 33-bus distribution network is chosen specifically for this study because it is widely used in the literature due to its moderate structure. It makes the validation easier against the existing studies.   

Comment-4: The work must provide an analysis of the time costs for solving the optimization procedure, as well as the dependence of the time for solving the problem of selecting the composition of distributed generation depending on the dimension of the electrical network.

Authors' Response: The proposed study is typically a planning study that involves the optimal allocation of various distributed generation types. Keeping in view the essence of the study, the primary objective is to minimize active power losses only during the planning stage, not the operational stage. Since the allocation of DG is a planning problem and can be considered an offline optimization problem. Therefore, the primary aim of the planning studies is to enhance the network efficiency rather than analyze the time cost of the optimization technique. It is also evident from the existing studies reviewed for this study, against which the validation has been carried out, that most of the existing studies also avoided time cost analysis as a key parameter for optimal distributed generation allocation problems. Considering the presented facts, the time costs are not included in the scope of the proposed study.

Comment-5: Was the problem of using machine learning algorithms to optimize the placement of distributed generation in the electrical network considered? This problem can be solved by using the graph neural network algorithm.

Authors' Response: The proposed study addresses the optimal allocation of distributed generation (DG) units, indicating that the problem is a constrained optimization problem that requires a technique to select the optimal type, size, location, and combination of DGs in radial distribution networks. However, the suggested graph neural network or other machine learning algorithms are well-suited for prediction or classification-based problems. Therefore, considering the nature of the problem, this study proposes an efficient Jaya algorithm for the optimal allocation of a distributed generation (DG) mix.

Comment 6: It is necessary to correct the design of the figures (Fig. 1: Classification criteria for defining DG [4] -> Figure 1. Classification criteria for defining DG [4]), Table 2.1: Summary of reviewed studies -> Table 1. Summary of reviewed studies).

Authors' Response: Thank you for the suggestion regarding the design of the Fig. 1 and Table 1. The authors would like to share that the formatting styles for Fig. 1 and Table 1 are adopted from existing studies in the literature; therefore, these are retained for consistency and clarity. Moreover, since the reviewer did not specify the exact formatting issues or the preferred journal guidelines to be followed. However, the authors are open to revising the designs if more detailed formatting requirements are provided by the reviewer or editorial team.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This study proposes a multi-type distributed generation (DG) joint configuration method based on the parameter-free Jaya optimization algorithm. By simultaneously optimizing the site selection and capacity of type II, type III and type IV DG, the power loss of the distribution network can be significantly reduced. The effectiveness of this method in improving voltage levels and reducing losses is verified on the IEEE 33-bus system. The optimal configuration scheme reduces active power losses by 96.14%. This is a topic of interest to researchers in related fields, but some improvements are needed at this stage. My detailed opinions are as follows:

1 While the JO algorithm is described as parameter-free and simpler than traditional metaheuristics, the manuscript does not adequately discuss its computational efficiency or performance consistency in larger-scale networks beyond the IEEE 33-bus test system. The authors are encouraged to provide comparative analysis or runtime complexity evaluations, or at least comment on its feasibility in more complex distribution systems.

2 The manuscript categorizes distributed generation (DG) units into types II, III, and IV with specified power factor operating ranges. However, it does not provide a clear explanation regarding whether this classification is based on the inherent technical capabilities of the devices, the mode of grid integration, or the applied control strategies. It is recommended that the authors clearly state the rationale behind this classification and elaborate on its consistency with the operational characteristics of currently adopted mainstream DG technologies.

3 It is recommended that the authors consider incorporating Conditional Value-at-Risk (CVaR) into the distributed generation (DG) allocation framework to explicitly account for uncertainties arising from renewable energy intermittency and load forecasting errors. While the current model effectively minimizes power losses, the inclusion of a risk measure such as CVaR would enhance the robustness of the optimization results and mitigate the potential adverse impacts of overly optimistic assumptions in uncertain operating environments. For more comprehensive details, refer to the article at: DOI: 10.1016/j.apenergy.2025.125271.

4 The current study employs a deterministic optimization framework for DG allocation, which may overlook the impact of uncertainties such as renewable generation variability and load forecasting errors. It is suggested that a stochastic bi-level optimization approach be considered, incorporating scenario-based uncertainty modeling and clustering techniques. This would allow for a more robust evaluation of DG allocation strategies by jointly optimizing planning and operational decisions under uncertainty. For more comprehensive details, refer to the article at: DOI:10.1109/TCE.2024.3412803.

Author Response

Manuscript ID: Sustainability-3648452

The authors offer heartfelt thanks to the anonymous reviewer for their thorough evaluation and for providing insightful and valuable comments that helped improve the manuscript to a higher standard. A detailed, point-by-point response to each comment is provided below.

Reviewer 2

Comment 1: While the JO algorithm is described as parameter-free and simpler than traditional metaheuristics, the manuscript does not adequately discuss its computational efficiency or performance consistency in larger-scale networks beyond the IEEE 33-bus test system. The authors are encouraged to provide comparative analysis or runtime complexity evaluations, or at least comment on its feasibility in more complex distribution systems.

Authors' Response: Although several complex distribution networks are available, the IEEE 33-bus network is widely used in the literature. The paper examined a variety of cases that can be easily validated on the IEEE 33-bus radial distribution network, which serves as motivation to limit the scope to the IEEE 33-bus test system.

Furthermore, the proposed study is typically a planning study that involves the optimal allocation of various types of distributed generation units, primarily aiming to enhance network efficiency rather than analyze the computational efficiency (i.e., runtime) of an optimization algorithm. Most of the existing studies against which the validation was carried out also avoided computational time as a key parameter for analysis. Considering the presented facts, computational efficiency is not within the scope of the proposed study.

Comment 2: The manuscript categorizes distributed generation (DG) units into types II, III, and IV with specified power factor operating ranges. However, it does not provide a clear explanation regarding whether this classification is based on the inherent technical capabilities of the devices, the mode of grid integration, or the applied control strategies. It is recommended that the authors clearly state the rationale behind this classification and elaborate on its consistency with the operational characteristics of currently adopted mainstream DG technologies.

Authors' Response: Thank you for the insightful comment. The authors would like to clarify that the proposed classification is based on the inherent technical capabilities of DG units, specifically their active and reactive power-generating capacities. The classification reflects typical operational behavior of existing DG technologies, as outlined below:

Type II DGs are modeled as sources capable of supplying only reactive power, typically representing the capacitor banks.

Type III DGs are capable of supplying both active and reactive powers. This category commonly includes conventional synchronous generators or inverter-based PV systems configured with fixed or limited reactive power support capabilities.

Type IV DGs can supply active power while also dynamically adjusting reactive power (i.e., both supplying and absorbing reactive power as needed). This behavior is typical of advanced variable-speed wind turbines, such as those based on doubly fed induction generators (DFIGs), which can regulate reactive power according to grid requirements through advanced control strategies.

This discussion is also provided in the first paragraph on page 6 of 32, highlighted with yellow background. Fig. 4 also presents this classification.

Comment 3: It is recommended that the authors consider incorporating Conditional Value-at-Risk (CVaR) into the distributed generation (DG) allocation framework to explicitly account for uncertainties arising from renewable energy intermittency and load forecasting errors. While the current model effectively minimizes power losses, the inclusion of a risk measure such as CVaR would enhance the robustness of the optimization results and mitigate the potential adverse impacts of overly optimistic assumptions in uncertain operating environments. For more comprehensive details, refer to the article at: DOI: 10.1016/j.apenergy.2025.125271.

Authors' Response: The authors thank the reviewer for the insightful suggestion to incorporate Conditional Value-at-Risk (CVaR) into the DG allocation framework and acknowledge the importance of explicitly accounting for uncertainties associated with renewable energy intermittency and load demand. However, the scope of the present study is limited to a deterministic optimization approach, primarily aimed at minimizing power losses under simplified operating conditions. To support future research in this direction, the article recommended by the reviewer has been cited as a reference [31] in the revised manuscript, guiding readers interested in extending this work using risk-aware stochastic optimization techniques. Please refer to Section 7, page 30 of 32, highlighted with a green background.

Comment 4: The current study employs a deterministic optimization framework for DG allocation, which may overlook the impact of uncertainties such as renewable generation variability and load forecasting errors. It is suggested that a stochastic bi-level optimization approach be considered, incorporating scenario-based uncertainty modeling and clustering techniques. This would allow for a more robust evaluation of DG allocation strategies by jointly optimizing planning and operational decisions under uncertainty. For more comprehensive details, refer to the article at: DOI:10.1109/TCE.2024.3412803.

Authors' Response: The authors thank the reviewer for highlighting this limitation and fully acknowledge that the deterministic optimization framework adopted in this study simplifies the problem by assuming a static load demand and neglecting uncertainties associated with renewable energy generation and load demand. This limitation has been explicitly addressed in Section 7 (page 30 of 32) of the manuscript and is highlighted with a yellow background for clarity. The highlighted limitation of the study is as follows:

"A constant (static) load demand equal to 100% of the rated load capacity is assumed for the distribution network to simplify the analysis. The daily load demand profile is deterministic, i.e., time-dependent, and varies seasonally. Besides, the uncertain intermittent nature of DGs' output, such as type-III solar DGs with advanced converters and type-IV wind-based DFIGs, is also avoided. Thus, ignoring the dynamic loading and power generation capabilities may not fully capture the effectiveness of optimally allocating distributed generation units in real-world dynamic scenarios. However, this study provides a basis for executing real-time and dynamic scenarios, which has strong potential to extend to real-world applications, as it supports improving power system performance by optimally allocating distributed generation units."

We appreciate the reviewer's valuable suggestion to consider a stochastic bi-level optimization framework incorporating scenario-based uncertainty modeling and clustering techniques. The article recommended by the reviewer has been cited as a reference [32] in the revised manuscript to guide readers interested in extending this study toward a more robust and uncertainty-aware distributed generation allocation framework. Please refer to Section 7 (page 30 of 32) of the revised manuscript, highlighted with a green background.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The overall content of the paper is detailed and the workload is large, but there are still some minor issues that need to be improved:
(1) The difference between (b) and (c) in Figure 8 seems too small. The author should describe it appropriately here.
(2) The formula numbers are not aligned to the right.
(3) Tables 2 and 6 can be described directly as formulas without tables.
(4) In the introduction or outlook, the application of mainstream algorithms should be described, such as the mainstream algorithms in the paper "A Data-Driven Vehicle Speed ​​Prediction Transfer Learning Method With Improved Adaptability Across Working…….." and the paper "Short-Term Photovoltaic Power Probabilistic Forecasting Based on Temporal….."
(5) Figure 5 is too vague and can be removed.
(6) There are too few theoretical formulas in the paper as a whole, so it does not look like a research paper.
(7) The author should check the grammar of the paper and the format of tables and pictures.

Author Response

Manuscript ID: Sustainability-3648452

The authors offer heartfelt thanks to the anonymous reviewer for their thorough evaluation and for providing insightful and valuable comments that helped improve the manuscript to a higher standard. A detailed, point-by-point response to each comment is provided below.

Reviewer 3

Comment-1: The difference between (b) and (c) in Figure 8 seems too small. The author should describe it appropriately here.

Authors' Response: The discussion related to Figures 8b and 8c has been incorporated into the revised manuscript and is highlighted with a yellow background. Kindly refer to Section 5.1, point (iv), on pages 11-12 of 32 in the revised version.

Comment-2: The formula numbers are not aligned to the right.

Authors' Response: Thank you for the observation. The authors would like to confirm that, in the revised manuscript, the formula numbers are now aligned to the extreme right as per the journal's official template.

Comment-3: Tables 2 and 6 can be described directly as formulas without tables.

Authors' Response: Thank you for the suggestion. Tables 2, 4, and 6 have been replaced with equations (10), (11), and (12), respectively.

Comment-4: In the introduction or outlook, the application of mainstream algorithms should be described, such as the mainstream algorithms in the paper "A Data-Driven Vehicle Speed Prediction Transfer Learning Method With Improved Adaptability Across Working…….." and the paper "Short-Term Photovoltaic Power Probabilistic Forecasting Based on Temporal….."

Authors' Response: Thank you for the suggestion and for recommending additional papers to improve the introduction further. The introduction section has been carefully structured to provide a detailed description of the application of numerous mainstream metaheuristic optimization algorithms, specifically tailored to address the proposed problem of optimal distribution generation mix, thereby enhancing the performance of distribution networks. A summary of these mainstream metaheuristic optimization algorithms is also provided in Table 1 ( pages 4-5 of 32). The studies referenced in this section encompass a range of relevant optimization techniques within the context of distributed generation allocation. While the authors sincerely appreciate the reviewer's recommendations, the recommended papers pertain to different research domains, prediction and forecasting, which fall outside the research scope of the proposed study. Therefore, incorporating them directly into the introduction may not align with the thematic structure and focus of this manuscript.

Comment-5: Figure 5 is too vague and can be removed.

Authors' Response: Thank you for the valuable suggestion. As Fig. 5 outlines the key steps of the research methodology adopted in this study, its removal would compromise the clarity of the research framework. However, in response to the reviewer's concern, Fig. 5 has been updated in the revised manuscript to enhance its clarity and readability.

Comment-6: There are too few theoretical formulas in the paper as a whole, so it does not look like a research paper.

Authors' Response: Thank you for your insightful comment. The manuscript includes all the necessary formulas that support and explain the proposed methodology and analysis. These formulas are carefully selected to maintain focus and avoid redundancy, aligning with the proposed study's objectives and scope.

Comment-7: The author should check the grammar of the paper and the format of tables and pictures.

Authors' Response: Thank you for the suggestion. The authors have attempted to rectify the grammatical errors in the revised manuscript. Moreover, the manuscript has been thoroughly checked for language typos.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

This paper demonstrates the potential to improve the performance of power distribution networks by optimally allocating different types of distributed generation (DG) units simultaneously and optimally through parameter-free Jaya optimization techniques. This is a topic of interest to researchers in related fields, but some improvements are needed at this stage. My detailed comments are as follows:

1 In this paper, the parameter-free Jaya optimization algorithm is used for DG allocation optimization. Can you explain in more detail the features of Jaya's algorithm and how it compares to other meta-heuristic algorithms such as genetic algorithms, particle swarm optimization algorithms, etc.? Why choose the Jaya optimization algorithm over other common optimization methods?

2 In the actual power distribution system, the implementation of the optimal allocation of multiple types of DG may face some challenges, such as equipment compatibility, complexity of management and control, etc. Could you add a discussion of these practical challenges and how to overcome them?

3 In the future, it is suggested that the authors consider a risk-averse distributed energy management strategy when discussing the optimization of distributed generation unit configurations, especially in the face of renewable energy and electricity price fluctuations, in order to enhance the stability and reliability of distributed generation systems.

Author Response

The authors offer heartfelt thanks to the anonymous reviewer for their thorough evaluation and for providing insightful and valuable comments that helped improve the manuscript to a higher standard. A detailed, point-by-point response to each comment is provided below.

Reviewer 2, Round 2

Comment 1: In this paper, the parameter-free Jaya optimization algorithm is used for DG allocation optimization. Can you explain in more detail the features of Jaya's algorithm and how it compares to other meta-heuristic algorithms such as genetic algorithms, particle swarm optimization algorithms, etc.? Why choose the Jaya optimization algorithm over other common optimization methods?

Authors' Response: The explanation regarding the distinctive features of the Jaya optimization algorithm in comparison to the well-known meta-heuristic algorithms such as genetic algorithm, particle swarm optimization, etc., have already been included in the manuscript, as elaborated in the first two paragraphs of Section 4, page 9 of 32, highlighted with the yellow background.

The brief reiterate for clarity is as follows:

• The Jaya algorithm is parameter-free in the sense that it does not require algorithm-specific tuning parameters, such as mutation/crossover/selection operators in GA or inertia weight/social/cognitive parameters in PSO. The effectiveness of GA and PSO is highly dependent on the value of the mentioned parameters. However, the Jaya algorithm doesn’t involve any such algorithm-specific parameters.
• Its single-phase updating mechanism (i.e., moving toward the best and away from the worst solution, Eq. 9 in the manuscript) simplifies its implementation and reduces the computational cost.
• This simplifies convergence dynamics and improves robustness in achieving global optima, especially in complex, nonlinear search spaces such as the DG allocation problem.

Given these advantages, the Jaya algorithm was selected for this study to avoid the sensitivity and performance instability often observed with improperly tuned parameter-dependent algorithms.

Comment 2: In the actual power distribution system, the implementation of the optimal allocation of multiple types of DG may face some challenges, such as equipment compatibility, complexity of management and control, etc. Could you add a discussion of these practical challenges and how to overcome them?

Authors' Response: The authors sincerely appreciate the reviewer’s insightful observation regarding the practical implementation challenges associated with the optimal allocation of multiple types of distributed generation (DG) units in real distribution networks. The authors agree that integrating diverse DG types can introduce complexities related to equipment compatibility, management of protection, and control coordination. However, the current study is intended as a deterministic and initial-level analysis, with a primary focus on demonstrating the potential effectiveness of including a more diverse DG mix, particularly type-IV DG units with dynamic reactive power capability, which have not been adequately addressed in the existing literature. The goal is to highlight the performance gains in terms of minimizing power losses in distribution networks achievable through optimal allocation strategies involving different DG types. The encouraging results, especially the significant reduction in active power losses, validate the relevance and potential impact of such configurations, thereby providing a foundation for more detailed and comprehensive future investigations. These future studies can incorporate:

• Stochastic modeling of renewable energy sources (solar and wind) to address their intermittency.
• Dynamic simulations involving voltage regulation, harmonics, and power quality.
• Control strategies and communication frameworks to ensure the compatibility and manageability of mixed DG types.

To reflect the reviewer’s important concern, a discussion of these practical challenges has been included as a future direction in second and last paragraphs of Section 7, page 30 of 32, highlighted with a yellow background.

Comment 3: In the future, it is suggested that the authors consider a risk-averse distributed energy management strategy when discussing the optimization of distributed generation unit configurations, especially in the face of renewable energy and electricity price fluctuations, in order to enhance the stability and reliability of distributed generation systems.

Authors' Response: The authors appreciate and agree with this important suggestion from the reviewer, which has also been reflected as a future direction in the first paragraph of Section 7, page 30 of 32, highlighted with a yellow background.

Author Response File: Author Response.docx