Review Reports - Research on Synchronous Transfer Control Technology for Distribution Network Load Based on Imprecise Probability

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I thank the authors for presenting the work on title, “Research on Distribution Network Load Synchronous Transfer Control Technology Based on Imprecise Probability”.

I request the authors to modify the manuscript as per following suggestion for better understanding of readers: -

On page 4, line 133, whether it should be m_n in place of m_i? please clarify.
On page 6, Fig. 1 and related discussion, alphabets used in description are small, while figure represents capital alphabets. Which one is correct?
On page 8, figure 4, please increase the font size for E₁, E₂ for better readability.
On page 8, line 283, ‘ E_1,1, 282 E_1,2, and E_1,3are good, good, and attention states of phase A current status”, whether it is correct or good, alert and attention are the states?
On page 11, the microgrid system details are given. It is better if a diagram of system is added with the details given therein for better understanding of the system.
On page 13, line 379 and on page 14, line 393, the chapter word is used, is it correct?
6 is unreadable for English readers. Please modify it.
In literature review, where more than 2 authors are there, it is necessary to use word et al. after first author, which was not done in your literature review section.

additional comments：

Authors have written the paper on Load Synchronous Transfer Control Technology Based on Imprecise Probability. This paper addresses the issue of shifting of load from one network to other because of either fault on the system or non-availability of sufficient power in the grid.

The topic is relevant in today’s era of increase of penetration of renewable energy into the grid. Authors in their paper addressed the issue of isolation and connection of load from one network to other using the probability analysis. For the stability of power system it is very much necessary to isolate the faulty part from the system and from reliability point of view availability of un-interrupted power supply to the consumer is essential. Authors contribution added the imprecise probability-based synchronous load transfer control method for distribution networks. The major contribution of the authors is to avoid the circulating current during the disconnection and reconnection of supply within a time span less than one cycle. Authors in their concluding remarks specifically mentioned about the effective identification and mitigation and avoid the misclassification risks in uncertain scenarios by outputting ‘similarity sets’. I appreciate the authors work towards the meeting of stringent requirements of time-synchronized control in the distribution network. As I requested if authors provide the single line diagram of the case study they have done then more critical comments may be possible. The authors have appropriately used the references and done the literature review.

Author Response

Comments 1: On page 4, line 133, whether it should be m_n in place of m_i? please clarify.

Response 1: Thank you for pointing this out. As you mentioned, the “mi” should be changed to “mn” in this instance. We have made the necessary correction on page 4, line 136.

Comments 2: On page 6, Fig. 1 and related discussion, alphabets used in description are small, while figure represents capital alphabets. Which one is correct?

Response 2: Thank you for pointing this out. Therefore, we have made the necessary modifications to the issue you raised.The capital letters in the diagram are correct. I have made the necessary modifications on page 6, lines 232 and 233.

Comments 3: On page 8, figure 4, please increase the font size for E₁, E₂ for better readability.

Response 3: Thank you for pointing this out. Accordingly, we have made the necessary revisions to address your concerns. Based on suggestions from other reviewers, we have renamed Figure 4 to Figure 5. We have revised Figure 5 on page 10, enlarging the dimensions of E1 to E6.

Comments 4:On page 8, line 283, ‘ E_1,1, 282 E_1,2, and E_1,3are good, good, and attention states of phase A current status”, whether it is correct or good, alert and attention are the states?

Response 4: Thank you for pointing this out.E1,1, 282 E1,2, and E1,3 are good, decent, and attention states of phase A current status. I have made the necessary modifications on page 10, lines 316. Additionally, we identified an identical issue on page 11, line 340, which has also been corrected.

Comments 5:On page 11, the microgrid system details are given. It is better if a diagram of system is added with the details given therein for better understanding of the system.

Response 5: Thank you for pointing this out.Based on your feedback and that of other reviewers, we have added this system diagram on page 8, titled Figure 4.

Comments 6:On page 13, line 379 and on page 14, line 393, the chapter word is used, is it correct?

Response 6: Thank you for pointing this out. Based on your feedback, we have revised the relevant issues. Regarding the issue on page 13, line 379, we have optimized the wording on page 15, lines 413 to 426. We have also refined the presentation of Case 2's results. On page 16, lines 436 to 452. Regarding the issue on page 14, line 393, we have similarly refined the wording， On page 15, lines 432 to 433.

Comments 7:6 is unreadable for English readers. Please modify it.

Response 7: Thank you for pointing this out. Based on your feedback and that of other reviewers, Figure 6 has been renamed to Figure 7. We have optimized this figure to present its content more clearly.

Comments 8:In literature review, where more than 2 authors are there, it is necessary to use word et al. after first author, which was not done in your literature review section.

Response 8: Thank you for pointing this out. We have revised the references for more than two authors on pages 20 and 21.

Reviewer 2 Report

Comments and Suggestions for Authors

The analysis of imprecise probability theory is sufficiently addressed up to Section 4.

All mathematical equations and figures must be explicitly referenced within the text flow. Ensure proper citation for the origin of all mathematical equations (i.e., whether derived in the paper or sourced from literature).

Section 5: Case Study Integration and Detail

The article must explicitly and systematically link the methodologies developed in previous sections (e.g., imprecise probability techniques) to the double-fed distribution network case study. This integration is currently obscure.

Provide a thorough and precise description of the probabilistic analysis used for both the Distributed Generators (DGs) and the load profiles. Insufficient detail is currently provided on how uncertainty for these elements is defined and applied.

Author Response

Comments 1: The analysis of imprecise probability theory is sufficiently addressed up to Section 4.

Response 1: In section 3, this paper systematically elaborates on the foundational imprecise probability theory employed and its specific application form within the controller. Firstly, the core principles of the Imprecise Dirichlet Model (IDM) are detailed. The IDM estimates probability intervals for multi-state random variables under small-sample conditions by utilizing a set of Dirichlet prior distributions instead of a single prior. The mathematical expressions for its prior and posterior probability density functions are provided, and the calculation method for its posterior expectation is clarified; this expectation constitutes the upper and lower bounds of the probability interval. In this way, the IDM effectively avoids the negative impact of a single unreasonable prior on probability estimation when data is insufficient, thereby enhancing the model's robustness. Secondly, the Naive Credal Classifier (NCC) is introduced as the core of classification decision-making in this study. Unlike the Naive Bayes classifier, which outputs a single posterior probability, the NCC describes the imprecise probabilistic characteristics of node random variables using a "credal set," meaning the occurrence probability of each category is represented by an interval value. The mechanism of NCC reasoning based on the credal set is expounded, including the calculation formulas for its upper and lower probability bounds. More importantly, the classification output criteria of the NCC are defined: when the lower bound of the posterior probability for one category is higher than the upper bounds of the posterior probabilities for all other categories, a unique category is output; when the maximum a posteriori imprecise probability intervals overlap, a "set of similar classes" containing multiple possible categories is output, thereby proactively reducing the risk of misjudgment under uncertain conditions.

Section 4 primarily elaborates on the construction method of the switching action time prediction model based on the IDM and the Naive Credal Classifier. This model uses the three-phase voltage and current peaks at the PCC as evidence variables to construct the credal network structure and utilizes the IDM to estimate conditional probability intervals. By introducing credal sets and interval probabilities, the model's robustness under small-sample conditions is enhanced, and the model's learning algorithm and classification output process are detailed.

Section 5 validates the effectiveness of the proposed method through two typical cases. Case 1 demonstrates that the imprecise probability method yields consistent results with the Bayesian classifier when a unique category is output. Case 2 illustrates that when probability intervals overlap, the credal classifier can output a "set of similar categories," effectively avoiding misjudgment and enhancing the accuracy and reliability of predictions.

Section 6 proposes a time-constrained whole-process control model for load synchronous transfer, defining the objective of controlling the time difference between "open-then-close" operations within 20ms. By designing a dynamic delay strategy and combining it with physical experimental validation, the results show that all operational time differences are controlled within the range of 2–12ms, meeting the engineering requirements and verifying the effectiveness and practicality of the control strategy.

Comments 2: All mathematical equations and figures must be explicitly referenced within the text flow. Ensure proper citation for the origin of all mathematical equations (i.e., whether derived in the paper or sourced from literature).

Response 2: We expresses gratitude for the feedback and confirms that the manuscript has undergone a thorough review in accordance with the suggestions, ensuring that every mathematical formula and figure is explicitly referenced in the main text with clear sources provided. Regarding the citation and sourcing of mathematical formulas, the following approach has been adopted: for well-established fundamental formulas in the field, references are explicitly cited. For instance, the Dirichlet prior probability density function in Equation (1) is sourced from Reference [11], the posterior probability density function in Equation (2) from Reference [12], and the posterior expectation estimation method in Equation (3) from Reference [13]. Concerning the series of formulas constituting the core methodology of this research, while drawing upon existing theoretical frameworks, their specific presentation and derivation were completed to address the specific problems of this study. For example, the IDM-NCC fusion model described in Equations (11) to (14) was specifically derived and presented within the context of this paper. Figures 1, 2, and 3 are introduced in Section 3.3 to intuitively illustrate the fundamental differences in decision-making principles between Bayesian classifiers and credal classifiers; these three schematic diagrams were self-drawn to explain the methodology of this paper. Figure 4 is a newly added diagram showcasing the typical structure of the double-feeder distribution network containing distributed photovoltaics used in the case study of this paper. Figure 5, referenced in the main text, depicts the specific network structure of the switching action time prediction classifier constructed based on the credal network; this figure was self-drawn to visually represent the model built in this research. Figure 6, referenced in the main text, clearly outlines the complete process for estimating switching action time based on imprecise probability proposed in this paper in a flowchart format; this flowchart was self-drawn to summarize and present the core methodology. Figure 7, referenced in the main text, presents the physical experimental environment set up to verify the control time accuracy. Figures 8 and 9 are newly added diagrams displaying the typical daily load profile and the typical daily photovoltaic power output curve used for uncertainty analysis, respectively. Tables 1 and 2, referenced in the main text, collectively define the input and output of the prediction model. Table 1 details the switching action time intervals corresponding to 34 fault types and locations, while Table 2 specifies the six electrical quantity features serving as evidential inputs to the model; the structure and content of these two tables were self-defined and constructed based on the diagnostic requirements and engineering practices of this study. Table 3, referenced in the main text, displays portions of the normalized training and testing data samples; the data in this table are entirely derived from the simulation results of this research. Tables 4 and 5 are cited together in the analysis of Case 1, presenting the calculation results for the same test sample based on the imprecise probability method and the traditional Bayesian classifier, respectively. Tables 6 and 7 are cited together in the analysis of Case 2, respectively showing the calculation results of the imprecise probability method and the Bayesian classifier under another test scenario. Table 8, referenced in the experimental verification section, records the raw time data from 10 physical experiments; the data in this table were actually measured using a time synchronization tester on the experimental platform built for this study, providing direct experimental evidence for the effectiveness of the proposed control strategy.

Comments 3:Section 5: Case Study Integration and Detail

Response 3:For Section 5, this paper has supplemented the specific parameters of the model and optimized the description of the simulation results.

The system base voltage is set to 10.5 kV, with all lines being overhead lines having a unit length resistance and reactance of 0.26 Ω/km and 0.355 Ω/km, respectively. In the network, the lengths of feeder segments AB and BC are both 3 km, while feeder AD is 10 km long. Both feeder ends are connected to loads with a capacity of 6 MVA and a power factor of 0.85. The output power of the distributed photovoltaic source is adjustable within the range of 0 to 10 MW. Fault points are set at locations f₁, f₂, and f₃, with a unified fault initiation time of 0.5 seconds. A switch is installed at the Point of Common Coupling (PCC) to monitor its action sequence. By simulating 310 different operating conditions, the three-phase voltage and current peak data at the PCC are collected, forming a 310×6-dimensional feature matrix. To eliminate dimensional influences, the min-max normalization method is used to preprocess the data into the [0,1] interval. The data is then randomly split into a training set (248 instances) and a test set (62 instances) in a certain ratio, laying the data foundation for subsequent model training and validation.

Case 1 demonstrates a scenario where the credal network classifier can output a single, definitive diagnostic result. When the evidence variable state is the vector S₁, the imprecise probability method and the traditional Bayesian classifier are respectively applied to predict the switching action time. The calculation results of the imprecise probability method show that the posterior probability interval for category F₃₀ is [1.24×10⁻², 4.28×10⁻²], and its lower probability bound is significantly higher than the upper probability bounds of all other categories, thus clearly identifying F₃₀ as the only credible diagnostic result. Simultaneously, the Bayesian classifier also concludes that F₃₀ has the maximum posterior probability (2.12×10⁻²). The diagnostic results of the two methods are completely consistent, both pointing to category F₃₀ , which corresponds to a switching action time range of [38, 39) ms. This case proves that when the mapping relationship between data and state is clear, the imprecise probability prediction control method proposed in this paper performs comparably to the traditional Bayesian classifier, both achieving accurate and unique judgments.

Case 2 focuses on verifying the unique advantage of the proposed method in handling samples with high uncertainty. When the evidence variable state is another specific vector, the calculation results of the imprecise probability method show overlapping probability intervals: the probability intervals for categories F₂₂ and F₂₃ are [3.70×10⁻², 5.35×10⁻²] and [3.54×10⁻², 5.53×10⁻²], respectively. According to the decision criterion of the credal classifier, the system cannot determine a single most probable category and therefore outputs a set of similar classes containing both {F₂₂ , F₂₃ }, corresponding to a predicted switching action time range of [30, 32) ms. In contrast, the Bayesian classifier, based on precise probability calculation, gives a definite diagnostic result F₂₃, corresponding to a time range of [31, 32) ms. However, the actual detected switching action time is 30ms, which falls precisely within the time range output by the credal classifier's similar set but lies outside the range of the Bayesian classifier's single result. This outcome strongly demonstrates that the imprecise probability method, by outputting a "set of similar classes," can effectively express the uncertainty in decision-making, thereby avoiding forcing a potentially incorrect single judgment when information is insufficient.

Comments 4: The article must explicitly and systematically link the methodologies developed in previous sections (e.g., imprecise probability techniques) to the double-fed distribution network case study. This integration is currently obscure.

Response 4:Thank you for pointing this out. Specifically, at the beginning of Section 4.1, "Naive Credal Model for Distribution Network Switching Time Prediction," this paper adds a core paragraph to systematically build a bridge from the general methodology to the specific case. The paper first clarifies the application scenario and physical foundation of the model, pointing out that in power systems, the Point of Common Coupling (PCC) is a key node for monitoring system operational status. It explains the rationale for selecting three-phase voltage and current peaks as evidence variables, namely that these electrical quantities are easy to measure and can effectively reflect system stability. In Chapter 5, the double-feeder experimental case is introduced in detail. The added content states that this study uses a typical double-feeder distribution network structure containing distributed photovoltaics as the modeling basis, whose topology is shown in Figure 4, and it elaborately defines the 12 typical operational states serving as the parent nodes of the credal classifier. This clearly demonstrates how to apply the imprecise probability theory to a specific distribution network structure. Finally, the paper details that the dataset used for model training and testing is derived from simulations of this specific case. The added paragraph describes how, by simulating different operating conditions of this distribution network and collecting the three-phase voltage and current peaks at the PCC, a database containing 310 sets of operational condition data was constructed, and the division of the training set and test set is specified. Through these additions, this paper systematically explains the physical basis for selecting input features, the way the theoretical model is integrated with the specific system structure, and the data source for model instantiation, thereby tightly coupling the IDM-NCC methodology with the subsequent case simulations.

Comments 5: Provide a thorough and precise description of the probabilistic analysis used for both the Distributed Generators (DGs) and the load profiles. Insufficient detail is currently provided on how uncertainty for these elements is defined and applied.

Response 5:Thank you for pointing this out.Regarding the suggestion for a more detailed probabilistic analysis of distributed generation and load profiles, this paper has specifically addressed this by adding a new Section 6.3. In this newly added section, the paper clearly elaborates on the sources of uncertainty and their impact on system operation. For load profiles, it points out that their uncertainty primarily stems from factors such as user behavior patterns, seasonal variations, and meteorological conditions. It explains that while typical daily loads exhibit periodic variations, the magnitude of their fluctuations is relatively limited, and they change gradually over millisecond to second timescales. For distributed photovoltaic (PV) generation, the section describes its distinct diurnal periodicity and weather dependence, emphasizing its characteristic hysteresis and intermittency in output power, and notes that the overall process shows a smooth transition trend rather than abrupt change characteristics. Crucially, the added section states that the time interval between the disconnection and reconnection operations for the imprecise probability-based distribution network load synchronous transfer is controlled within 20ms. This duration is deemed fully adequate to accommodate the inherent uncertainty range of the described load fluctuations and distributed generation output variations. This supplement systematically links the discussion of uncertainty inherent in the system's stochastic elements with the robust control capability of the proposed method, demonstrating that the proposed approach can effectively handle the variability present in real-world distribution networks.