Recurrent Neuronal Networks for the Prediction of the Temperature of a Synchronous Machine During Its Operation

Response to Reviewer 1 Comments

1. Summary

First of all, we would like to thank you for your time and effort spent in the revision process of this manuscript. This review process has a great value for us in order to clarify better the ideas and results that we want to show in this paper. We have carefully read, analyzed and considered all the comments and suggestions you have provided. Please, find the detailed responses below in this document attached as well as the manuscript changes, which have been yellow highlighted. With these modifications, we think the paper is clearer and its quality has considerably improved.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Yes

Thank you for this positive evaluation about the manuscript.

Please, find the answers to your specific concerns in the “Point-by-point” section of this document, and if any of the points remain unclear or non-fulfilled, please do not hesitate to tell us.

Is the research design appropriate?

Yes

Are the methods adequately described?

Yes

Are the results clearly presented?

Yes

Are the conclusions supported by the results?

Yes

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1:

In Fugire 4, where is the no.8 temperature sensor? Is it missed?

Response 1:

Thank you for pointing this out.

The temperature sensors are named depending of the number of winding in which are allocated. The sensors (1, 2, 3, 4, 9, 10, 11, 12) are installed in the windings trying to observe the temperature variations in opposite sides of the stator, and the sensors (5,7,13,15) are installed in the iron-core. Thus, there are three numbers left between 1 and 15: 6, 8 and 14. So, we have decided to use 14 as the temperature sensor of the cooling air and 6 as the number of the temperature of the sensor of the hot air. The number 8 is not used.

Comments 2:

In some figures the physical meaning and the unit of X-axis are not clear, for instance, Figs.8-12.

Response 2:

Thanks for this comment.

In order to clarify better the X-axes unit, we have included in lines 186-187 (page 7 of the manuscript) the following sentence highlighted in yellow:

“””… The X-axis unit is the number of measurements (the time between measurements is 5 seconds) …”””

So, for example, in Figures 8 and 9, the maximum of the X-axis value is 700, that means that the duration of this heating test is the following:

Time of the test [h] = 700 measurements · 5 seconds/measurement· 1h / 3600s = 0.97 hours.

We hope this issue is clear in the reviewed version of the paper.

Comments 3:

In Figs.9-10, why the temperature of no.3 is pretty different from those of others? Could you please make an explanation?

Response 3:

Thank you for pointing this out.

The temperature that is almost different is not the temperature of sensor 3, is the temperature of the sensor 14, because it is the temperature of the cold air that entries to the refrigerant air system of the synchronous machines.

For clarification, we have included the following sentence in lines 196-199 (page 7) of the manuscript:

“”” … In both figures, one of the thermal variables has a much lower value than the others, that of temperature sensor 14, because it is the measured temperature of the cold air entering the cooling system …”””

We think it is clear in this new version of the manuscript.

Comments 4:

Is it possible for you to make a data comparison between the existing method and your proposed method so that the advantages of the proposed method can be more credible?

Response 4:

The temperatures in the machines normally have two thresholds, alarm and trip. This values, alarms and trips have a fix value regardless the load of the machine.

The proposed method cannot be compared to the existing method as it is completely different, as it is adaptative method.

In order to clarify this issue in the revised version of the manuscript the abstract has been modified as follows:

This work presents the development of an adaptive thermal protection system for synchronous machines (SM), taking into consideration the final cooling temperature and the operation point of the machine. This system aims to improve current thermal protections, which consist of a fixed alarm and trip thresholds regardless of the generator's operating point or ambient temperature.

4. Response to Comments on the Quality of English Language

Point 1:

The English is fine and does not require any improvement.

Response 1:

Thank you for this comment.

Response to Reviewer 2 Comments

1. Summary

Beforehand, we would like to thank you for your implication, your time, and your effort spent in the reviewing process of this manuscript. We deeply appreciate your evaluation about our manuscript. Also, we hope our modifications in the revised version of the paper will fulfil your inquiries. However, if there is any issue that remains unclear, please do not hesitate to contact us. Thank you again.

The authors.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

Thank you for this valuable and positive evaluation of the manuscript. We have used it to improve the revised version of the manuscript.

Please, find the corresponding answers to all your specific comments in the “Point-by-point” section of this document, and if any of the points remain unclear or non-fulfilled, please do not hesitate to tell us.

Is the research design appropriate?

Can be improved

Are the methods adequately described?

Can be improved

Are the results clearly presented?

Can be improved

Are the conclusions supported by the results?

Can be improved

3. Point-by-point response to Comments and Suggestions for Authors

Dear Authors,

the work in my opinion has a quite good scientific value. However, some improvements must be implemented:

First, thank for your comments, this review process has a great value for us in order to clarify better the ideas and results that we want to show in this paper. Also, we would like to thank you for your positive comments and suggestions.

Comments 1:

In paragraph 2.2. -> I found that Table 2 and Figure 7 don’t express the same information: test 1 at 0 W is not represented in Fig. 7. Moreover, some tests, e.g. the one at 500 W goes from -1500 var to 2000 var, the one at 1000 W goes from -1000 to 2500 var. I suggest adjusting the table with the real range of reactive power considered for each active power case.

Response 1:

Thank you for pointing out this issue.

We agree with this comment. Apologize for that mistake, the last table values were not updated to the correct values.

We have updated the range values as shown in the following table (updated also in the manuscript):

Table 2: Tests performed

Comments 2:

In paragraph 2.3. -> I think it is necessary to give more details about measurements. What is the sampling frequency? How long is the set of 700 measures (how many seconds/minutes/hours/etc. it lasts)?

Response 2:

Thank you for this comment. We apologize for the lack of clarity. We add a sentence in lines 186-187 (page 7) of the manuscript highlighted in yellow in order to clarify the sampling frequency:

“””… The X-axis unit is the number of measurements (the time between measurements is 5 seconds) …”””

For example, in Figures 8 and 9, the maximum of the X-axis value is 700, that means that the duration of this heating test is the following:

Time of the test [h] = 700 measurements · 5 seconds/measurement· 1h / 3600s = 0.97 hours

Comments 3:

In figure 9 -> temperatures seem to be very low. The machine reaches only about 40° C at a steady state. Why is the room temperature so low (sometimes also below 0° C)? Give more details about ambient temperature in this measurement, and why a class F machine reaches only 40° C at about 75% of its ratings.

Response 3:

Thank you for pointing this out.

The room where the tests were carried out is located within an industrial warehouse with very poor insulation, which means that the room temperature is highly influenced by the ambient temperature. In the case of the tests presented in the manuscript, it was carried out on winter, which explains the very low temperatures that were measured.

Although the insulation is class F (155°C), the heating is typically class B (130°C). Furthermore, this machine is not standard and it appears to be oversized.

Another point to keep in mind is that the temperature was measured with Pt-100 that we installed externally in the coil heads. As they were installed in the coil heads, not in the slot area, so the temperatures in the hottest parts of the machine are higher.

Finally, the design temperature of the cooling air is 40°C; however, since the tests were conducted at temperatures around 0°C, even though a heating of 40°C was achieved, if the tests had been conducted at 40°C ambient, the temperature would be 80°C, which would be more normal.

Comments 4:

Figure 12 -> caption in normal character, not bold. Why in this case the measure is 12000 (and in heating were only 700)? Does the total measurement time change or does the sampling frequency change?

Response 4:

Thank you for your comment

.

Apologize for this mistake. We have fixed the issue. The new figure caption stays in the revised version of the paper as follows:

The X-axis represents the number of measures (with a time of 5 seconds between measurements), so this means that the time to reach a steady state during the heating test shown in the figures 8, 9 is rounding the hour of testing and the time to reach a steady state during the cooling tests shows in figure 12 are rounding the 12-15 hours.

Comments 5:

Rows 210-212 -> you state that you have 30000 and 120000 measurements for heating and cooling respectively. Please explain how they are subdivided. A constant number of measures are taken for each operating point? How much are they?

Response 5:

Thank you for this comment.

We have performed 33 heating and cooling tests corresponding to the loads depicted in Fig. 7 of the manuscript.

The number of measurements in each load test is variable and ranges from 700 measurements to 1200 measurements depending on how long it takes for the test to reach steady state. With a mean of 932 measurements per heating test, the exact value of the measurements is the following:

932 measurements/test × 33 tests = 30.756 measurements, which is rounded to 30.000 in the manuscript to make the reader an idea of how much data it was collected to train the LSTMs.

The same happens with the cooling tests. The number of measurements in each test is variable and ranges from 3000 measurements to 12000 measurements depending on how long it takes for the test to reach steady state. With a mean of 3743 measurements per cooling test, the exact value of the measurements is the following:

3743 measurements/test × 33 tests = 123.519 measurements, which is rounded to 120.000 in the manuscript to make the reader an idea of how much data it was collected to train the LSTMs.

Comments 6:

Row 247 -> I suggest using “trials” instead of “tests” for clarity

Response 6:

We agree and we have used “trials” instead of “tests” in the manuscript (line 258 page 10):

“””… To train and test the LSTM neural network, the initial dataset of heating and cooling scenarios is divided into 80% of the trials to the training and 20% of the trials to the testing …”””

Thanks for this comment.

Comments 7:

Row 248-250 ->not clear. For the test phase or for the training phase the scenarios at medium active power have been used? To my logic should be in the training phase, but in the phrase in not clear.

Response 7:

Thanks for pointing this out.

We agree that it was not very clear, so in order to clarify it, we have rephrased the sentence, now in the manuscript stays as follows (lines 259-266 page 10):

“””… For the training phase we have tried to cover all active power levels, so that the LSTM networks are prepared to operate in the whole operating range of the machine. For the test phase, several scenarios with a medium active power level (2500-3500W) have been selected so that the network never tests with active power values outside the range in which it has been trained. That is to say, the tests at low and high power as well as several at medium power levels have been used for the training phase and for the LSTM network test, the remaining tests at medium power levels not used during the training phase have been used …”””

To resume, the idea is to not test the LSTM neural networks which values that are not in the range of the training values to obtain better results in the evaluation of the LSTM behavior.

Comments 8:

Row 250-252 -> so only high active power operating points are used in training and testing? This is in contrast with what is affirmed in row 61-63, where it is claimed that the system should work also at low load conditions. Please clarify this aspect.

Response 8:

Thanks for this comment.

We agree that it was not well explained in the previous version of the manuscript. We think that now with what is said in lines 259-266 (pages 9-10 of the manuscript) is clear that the LSTM is able to predict the correct value of the temperature in every operational point of the machine. But to achieve that, it is necessary to train the LSTM with the complete range of the electrical operation points of the SM.

“””… For the training phase we have tried to cover all active power levels, so that the LSTM networks are prepared to operate in the whole operating range of the machine. For the test phase, several scenarios with a medium active power level (2500-3500W) have been selected so that the network never tests with active power values outside the range in which it has been trained. That is to say, the tests at low and high power as well as several at medium power levels have been used for the training phase and for the LSTM network test, the remaining tests at medium power levels not used during the training phase have been used …”””

Comments 9:

Row 264-274 -> explain what optimization process did you use for finding 50 neurons in heating and 30 in cooling for each hidden layer. Why did you choose to put 3 hidden layers? Why did you choose to train with 30 epochs? The network output “Ti” is a temperature that can be assumed to be in which part of the motor? The hottest? The average? Why?

Response 9:

Thank you for this comment.

The followed process to select the best structure of the LSTM has been the following:

1. First, the number of layers was selected with a program with a for loop. This program evaluates the performance of the LSTM using 1, 2, 3, 4 and 5 hidden layers (for us is impossible to use more due to the computational cost), maintaining the number of neurons and the number of epochs constant. And the best results that were obtained was using three hidden layers.

1. After selecting the number of hidden layers, we have followed a similar process to select the best number of neurons in each layer. So, two programs were used in order to select which were the number of neurons that obtains better results in cooling and in heating scenarios. We have evaluated the following number of neurons: 10, 20, 30, 40, 50, 60 (for us is impossible to evaluate with a greater number of neurons because of the computational cost). The best results were obtained using 50 neurons and 30 neurons for the heating and cooling scenarios respectively.

1. Finally, using three hidden layers and the optimal number of neurons for each case, we have evaluated the following number of sequences: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100 (these values appeared in the tables 4 and 5 of the manuscript). As can be seen, the best results were obtained using 80 and 40 sequences for the heating and cooling scenarios respectively.

As for the number of epochs, in this case it is not a critical number because during training we have used an early stop value of 2 epochs. This means that in each interaction when the parameters of the LSTM network are recalculated, the behavior of the network is evaluated, and if it is seen that the RMSE has not improved for two consecutive epochs, the training is stopped and the last evaluation in which the behavior of the network improved is taken as good. In the case of these LSTMs, normally during training the average value of the epochs is 5 or 6, never reaching 30. We have selected 30 so that it would never be a limiting value, if a value of 3 for example had been set in this case, the best performance would not have been reached for many of the LSTMs trained.

Regarding the output of the LSTM models, Ti can represent any of the internal temperatures within the machine. The ultimate goal of this project is to develop a dedicated LSTM model for each internal temperature sensor. In Figures 16 and 17, we chose to present the results for only one specific temperature (corresponding to sensor 2) in order to provide a clearer and more focused illustration of the model’s performance.

However, it is important to note that an individual LSTM model is trained for each internal temperature. In a real-world implementation, monitoring each temperature separately is essential to ensure the safety and reliability of the system. Therefore, we do not use an average of the internal temperature measurements, as it would not provide the necessary resolution for effective thermal monitoring.

We appreciate the opportunity to clarify this aspect of our approach.

Comments 10:

Row 269 -> “hating and colling” -> heating and cooling

Response 10:

We apologize for that error. We have corrected these typos in the manuscript (line 283 page 11):

“””… The main data of the LSTMs neural networks used for the heating and cooling scenarios are summarized in Table 3 …”””

Comments 11:

Row 277 -> “LSTMs neural networks have been trained” what’s the meaning? All the network have the same architecture described above? What do you mean for “sequence”? a set of measures? This part in my opinion must be clarified.

Response 11:

Thank you for your comment.

We agree that maybe was not clear present the meaning of the sequence parameter in the previous version of the manuscript, so we have added the following sentences to make it clear (lines 310-311 page 13):

“””… The sequence parameter is a relevant in LSTMS neural networks, because is the number of previous data used to predict the following of the temperature. Multiple LSTMs neural networks have been trained with different sequence values. This has been done in order to be able to select which of the LSTM neural networks gives the best results …“””

So yes, we have trained multiple LSTM for each temperature sensor, to determine with is the best value of the sequences parameter. We have user the sequences values shows in tables 4 and 5 of the manuscript.

Comments 12:

16 -> all the prediction are for the temperature of sensor T2? So “Ti” correspond to the temperature T2? Or every sensor has its prediction values?

Response 12:

Thank you for pointing this out.

Yes, all sensors have their predicted values. In order to present the results more clearly, only the results obtained using the LSTM trained to predict the results for temperature sensor 2 are shown, but all sensors have each individual LSTM to predict their values.

Comments 13:

Row 338 -> what are “thermal flats”

Response 13:

We apologize for that error.

We have corrected this typo in the manuscript (line 373 page 15):

“””… Furthers works should aim to validate the thermal model obtained by applying thermal faults to the machine …”””

We wanted to say thermal faults.

Comments 14:

row 346 -> please provide a link to the patent if possible (not found on google patents)

Response 14:

Please find enclosed the link corresponding to the patent.

https://worldwide.espacenet.com/publicationDetails/biblio?CC=ES&NR=2876998B2&KC=B2&FT=D&ND=4&date=20230228&DB=EPODOC&locale=en_EP

4. Response to Comments on the Quality of English Language

Point 1:

The English is fine and does not require any improvement.

Response 1:

Thank you for this comment.

Response to Reviewer 3 Comments

1. Summary

First of all, we would like to thank you for your effort and time spent revising this manuscript. We have deeply read and analyzed all your comments, questions and suggestions and we have tried to fulfil all of them in detail. We think that the revised version of the manuscript is much clearer, incorporating the new changes that can be found yellow highlighted in the revised version of the paper. Moreover, if any of the inquiries remains unclear, please do not hesitate to tell us. Thank you very much again.

The authors.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

Thank you for these constructive comments. We have tried to improve each of the marks by introducing the upgrades you suggested in the following “Point-by-point” section. You will find a more extended answer to all of them in the following Section of this document. The modifications performed in the manuscript will also be attached at the end of each Point.

Is the research design appropriate?

Must be improved

Are the methods adequately described?

Must be improved

Are the results clearly presented?

Yes

Are the conclusions supported by the results?

Yes

3. Point-by-point response to Comments and Suggestions for Authors

The main contribution of the paper is the proposition of an adaptive thermal protection system for synchronous machines (SM) based on a recurrent neural network approach to predict SM temperatures during operation. The theme is relevant. For about 29 references are explored in the Introduction section to show the bottlenecks of the literature that justify the proposition.

Thank you for these positive comments. This revision process has a great value for us in order to clarify better the ideas and results that we want to show in this paper. Please, find attached below the answer to all your concerns.

Comments 1:

In reference [24] recently published by the same author are presented a brushless synchronous machine field winding interturn fault severity estimation using deep neural networks. Are the ANN applied here the same of this research? Please, clary the differences in the text and emphasize the new contribution.

Response 1:

Thank you for this comment.

The two articles only have in common the application of neural networks to predict a variable during a Synchronous Machine (SM) operation. The main differences are the following:

-          Reference [24] is a paper which main contribution is the development of an ANN model to predict the excitation current during a brushless machine operation to notice if the SM has an interturn fault. So, this method in that case was applied in a different laboratory setup (also a different SM) and the type of problem is different, because the excitation current could be predicted only using the electrical measurements (voltage, active and reactive power) measured in the same instant of time.

-          This article main contribution is the development using LSTM neural networks of a thermal protection for a SM, which actual thermal protection is based only in a fix threshold value which is not dependent of the point of operation. In the point of view of the authors, they humbly think that this idea is already presented in lines 11-14 of the abstract and in lines 93-103 of the manuscript (Section 2). It must be remark that the temperature predictions have the problem of the thermal inertia. For this reason, it is necessary to use LSTM neural networks, as they are specifically designed to consider the historical values of the input variables when predicting temperature. Using only the instantaneous measurements is insufficient; previous values are also essential to achieve accurate predictions. The neural networks used in research [24], are totally different of the neural networks used in this research (the type of the neural network, the machine to has been applied, the number of hidden layers, the number of inputs, the number of outputs, the target variable to predict…)

Comments 2:

Please, the authors should presents more details about the SM and the PT100 sensor used in the practicals experiments exposed in Figure 1.

Response 2:

The synchronous machine is a typical machine used in an emergency diesel generator. This machine is open air cooled. As the machine rated power is “small” it has not temperature sensors.

As the purpose of this paper is to test a new thermal protection, it was mandatory to install thermal sensors in the machine.

The Pt-100 sensors are standard. The installation of the sensors has been performed in the coil head area as shown in Figure 1 for the windings and Figure 2 for the iron core.

Comments 3:

The induction machiques is more applied in industrial process. Why the author's explores synchronous machine?

Response 3:

Thank you for your comment as it is a great idea to use this system for induction machines.

Currently induction machines are used for several industrial applications due to their simplicity and robustness, but the use of SM offer several key advantages that are essential for specific applications. These include the ability to operate at constant speed, adjust power factor, and provide reactive power support. Furthermore, recent developments have revitalized interest in synchronous machines, especially in their use as synchronous condensers for grid stabilization amidst increasing renewable energy penetration.

Therefore, our exploration of synchronous machines is motivated by their critical role in modern power systems and advanced industrial applications, which complements and, in some cases, surpasses the capabilities of induction machines.

It is also important to note that large electrical machines (ranging from 10 to 250/300 MVA) installed in hydroelectric, nuclear, and thermal power plants—which remain operational in most countries—are synchronous machines. These machines are among the most important generators in the power grid, as they typically serve as base-load generation units. In addition, they contribute significantly to grid inertia and have a direct impact on the short-circuit power capacity of the network.

Comments 4:

Figure 7 shows tested operational points in the PQ generator curve. How this curve was generated?

Response 4:

Thank you for this comment.

The PQ generator curve is generated using python (matplotlib library) and the data used is the reactive power capability of the SM and also the apparent power of the SM. This is not a detailed PQ generator curve, is only to present more clearly the operational points evaluated during the heating and cooling tests.

Comments 5:

Whats is the computacional environment used? Please, explain it in Appendix.   The reviewer suggests including an flowshart to show details about how the ANN was implemented in the context of the research. Wheres the ANN was implemented? The computacional routine must be showed.

Response 5:

Thank you for your comment.

The artificial neural network (ANN) was developed using Python 3.9 as the programming environment, with the TensorFlow library as the primary framework. TensorFlow provides a wide range of tools and functions specifically designed for building, training, and evaluating neural networks, making it well-suited for our research objectives.

Due to the complexity of the implementation and the size of the codebase—exceeding 3,000 lines—we believe that including the full computational routine in the main body of the paper or appendix would be impractical.

In order to clarify this issue we have included a new Figure displaying the computational routine..

4. Response to Comments on the Quality of English Language

Point 1:

The English is fine and does not require any improvement.

Response 1:

Thank you for this comment.

Response to Reviewer 4 Comments

1. Summary

Dear reviewer,

Beforehand, we would like to thank you for your implication, time, and effort in the reviewing process of this manuscript. We deeply appreciate your evaluation. We have worked thoroughly on all your comments and suggestions. We hope our modifications in the revised version of the paper will fulfil your inquiries. However, if there is any issue that persists, please do not hesitate to contact us. Thank you again.

The authors.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

Thank you for all these evaluations.

We have made modifications according to your comments, please find them detailed in the “Point-by-point” section below.

If any of the points shall be improved, please do not hesitate to tell us.

Is the research design appropriate?

Yes

Are the methods adequately described?

Can be improved

Are the results clearly presented?

Yes

Are the conclusions supported by the results?

Yes

3. Point-by-point response to Comments and Suggestions for Authors

Thank you for your submission.

The paper presents an interesting study on the application of LSTM-based RNN for adaptive thermal protection of synchronous machines. The experimental setup is thorough, and the methodology is well-structured. The idea of adjusting warning and trip threshold dynamically based on operating conditions can be quite useful, particularly for predictive maintenance applications.

Thank you very much for your comments and suggestions. This review process has a great value for us in order to clarify better the ideas and results that we want to show in this paper. Thank you also for considering interesting our research.

I have a few comments and suggestions for improvement:

Comments 1:

You mentioned "...because during the cooling tests the electrical variables are not relevant (because the machine is disconnected from the grid and the cooling system is off)." Can you clarify this further? Also, could residual electromagnetic behavior affect temperature decay?

Response 1:

Thank you for bringing this to our attention. We have reviewed the cited sentence and have made revisions to further clarify the non-influence of the electrical variables on the temperature prediction during the cooling tests. We have added the following in the manuscript (lines 293-303):

“””….During the training of the LSTMs, the overfitting has been considered and because of the overfitting the optimal structures of the LSTMs are using 30 neurons and 50 neurons for cooling and heating scenarios respectively. We have evaluated the number of neurons of each hidden layer from 10 to 100 and if the overfitting was not considered, the optimal number could be 100 neurons for both scenarios. Also, to remove the overfitting problem, we have added an early stopping parameter during the training process of the LSTMs. The early stop used is 2 epochs. This means that in each interaction when the parameters of the LSTM network are recalculated, the behavior of the network is evaluated, and if it is seen that the RMSE has not improved for two consecutive epochs, the training is stopped and the last evaluation in which the behavior of the network improved is taken as good.

Therefore, as the machine was stopped, the residual electromagnetic behavior has not influence in the cooling process.

Comments 2:

The use of a two-step Savitzky-Golay filter is noted, but no explanation is given for the choice of parameters or why a two-step process was necessary. 

Response 2:

Thank you for pointing this out.

We have used Savitzky-Golay filter to reduce the noise that appears because of the influence of the frequency variator operation. We have used a two-step filter because the results obtained have been better than if we used only a one step filter. To be clearer with the selection of the filter, we have added the parameters that defines the filter in the manuscript (lines 194-196):

“””… In order to not introduce noise into the neural network, a two-step Savitsky-Golay filter is used [32]. The parameters of the filter are the following: window_1 =5, poly_order_1=3, window_2 =11, poly_order_2=5. After the filter, the thermal variables measured are shown in Figure 10 …”””

Comments 3:

Regarding the optimization of sequence length: why does the optimal performance occur at 80 sequences for heating and 40 for cooling? Were factors such as overfitting, generalization, or computational cost considered? Also, the claim that all statistical metrics reach their minimum at 80 sequences is not entirely accurate. While MSE and RMSE are lowest at 80, MAE is actually better at 90 sequences.

Response 3:

Thank for you pointing this out.

The optimal performance depends on the following variables:

1.       Number of inputs: heating tests has 6, cooling tests only 2.

2.       Quality of the input data: during the heating tests the frequency variator has caused a lot of noise in the measurements.

These differences are the main reason obtaining differences LSTMs optimal structures for both scenarios.

The computational cost has been considered and because of that we were not able to train the LSTM using higher sequences values.

Also, the overfitting has been considered and because of the overfitting the optimal structures of the LSTMs are using 30 neurons and 50 neurons for cooling and heating scenarios respectively. We have evaluated the number of neurons of each hidden layer from 10 to 100 and if the overfitting was not considered, the optimal number would be 100 neurons for both scenarios. Also, to remove the overfitting problem, we have added an early stopping parameter during the training process of the LSTMs. The early stop used is 2 epochs. This means that in each interaction when the parameters of the LSTM network are recalculated, the behavior of the network is evaluated, and if it is seen that the RMSE has not improved for two consecutive epochs, the training is stopped and the last evaluation in which the behavior of the network improved is taken as good. In the case of these LSTMs, normally during training the average value of the epochs is 5 or 6, never reaching 30. We have selected 30 so that it would never be a limiting value, if a value of 3 for example had been set in this case, the best performance would not have been reached for many of thte LSTMs trained.

Finally, we have analyzed MAE, MSE and RMSE to evaluate the performance of the LSTM models, but to select the best LSTM, we have decided based on the RMSE, which is the most used statistical value to choose the best neuernal network model normally.

We have added the following in the manuscript (lines 293-303) to describe better the overfitting consideration during the LSTMs training process:

During the training of the LSTMs, the overfitting has been considered and because of the overfitting the optimal structures of the LSTMs are using 30 neurons and 50 neurons for cooling and heating scenarios respectively. We have evaluated the number of neurons of each hidden layer from 10 to 100 and if the overfitting was not considered, the optimal number could be 100 neurons for both scenarios. Also, to remove the over-fitting problem, we have added an early stopping parameter during the training process of the LSTMs. The early stop used is 2 epochs. This means that in each interaction when the parameters of the LSTM network are recalculated, the behavior of the network is evaluated, and if it is seen that the RMSE has not improved for two consecutive epochs, the training is stopped and the last evaluation in which the behavior of the network improved is taken as good.

Comments 4:

Including a comparison with a baseline approach (e.g., fixed-threshold or simple regression) would help quantify the actual performance improvement achieved by using LSTM.

Response 4:

The temperatures in the machines normally have two thresholds, an alarm and a trip. These values, alarms and trips have a fix value regardless the load of the machine.

The proposed method cannot be compared to the existing method as it is completely different, as it is adaptative method.

In order to clarify this issue in the revised version of the manuscript the abstract has been modified as follows:

This work presents the development of an adaptive thermal protection system for synchronous machines (SM), taking into consideration the final cooling temperature and the operation point of the machine. This system aims to improve current thermal protections, which consist of a fixed alarm and trip thresholds regardless of the generator's operating point or ambient temperature.

4. Response to Comments on the Quality of English Language

Point 1:

The English could be improved to more clearly express the research. A proofreading pass is recommended to correct language issues.

Response 1:

Thank you for your valuable comment. We have carefully reviewed the manuscript and made the necessary revisions to improve the clarity of the language. We hope that all typographical errors have been corrected.

Response to Reviewer 2 Comments

1. Summary

Beforehand, we would like to thank you for your implication, your time, and your effort spent in the reviewing process of this manuscript. We deeply appreciate your evaluation about our manuscript. Also, we hope our modifications in the revised version of the paper will fulfil your inquiries. However, if there is any issue that remains unclear, please do not hesitate to contact us. Thank you again.

The authors.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Yes

Thank you for this valuable and positive evaluation of the manuscript. We have used it to improve the revised version of the manuscript.

Please, find the corresponding answers to all your specific comments in the “Point-by-point” section of this document, and if any of the points remain unclear or non-fulfilled, please do not hesitate to tell us.

Is the research design appropriate?

Yes

Are the methods adequately described?

Can be improved

Are the results clearly presented?

Yes

Are the conclusions supported by the results?

Yes

3. Point-by-point response to Comments and Suggestions for Authors

Dear Authors,

thanks for the comments replies, that I think are satisfactory (all of them).

First, thank for your response, we appreciate that. This review process has a great value for us in order to clarify better the ideas and results that we want to show in this paper. Also, we would like to thank you for your positive comments and final suggestions.

Comments 1:

I just want to point out that many of the replies are not integrated in the paper text. For example, only a small phrase is inserted for comment 2 in the paper text and no additional text is added for comment 3, 4, 5, 9, 12 and 14. Though to me the concepts are now clear (because you had explained them in the responses) to a paper reader they can be not clear (because these explanations are not added to the paper). Consider adding them (fully or partially).

Response 1:

Thank you for pointing out.

We agree with this comment. After a revision of the manuscript, we have detected that it is true that some ideas could be presented in a clearer way as suggested in this comment. We have included the following modifications in the new version of the manuscript:

Lines 218-222:

The number of measurements varies slightly due to the time required to reach steady-state conditions: approximately 1 hour during the heating tests and approximately 12–15 hours during the cooling tests. On average, a heating test includes around 930 measurements, while a cooling test comprises approximately 3740 measurements.

Regarding comment 9, we believe that is explained in the lines 297-307 of the manuscript:

During the training of the LSTMs, the overfitting has been considered and because of the overfitting the optimal structures of the LSTMs are using 30 neurons and 50 neurons for cooling and heating scenarios respectively. We have evaluated the number of neurons of each hidden layer from 10 to 100 and if the overfitting was not considered, the optimal number could be 100 neurons for both scenarios. Also, to remove the overfitting problem, we have added an early stopping parameter during the training process of the LSTMs. The early stop used is 2 epochs. This means that in each interaction when the parameters of the LSTM network are recalculated, the behavior of the network is evaluated, and if it is seen that the RMSE has not improved for two consecutive epochs, the training is stopped and the last evaluation in which the behavior of the network improved is taken as good.

And in lines 276-283:

The LSTM neural network used is composed by 5 layers. Different architectures were tested, and the best results were obtained using 5 layers, with a reasonable computational effort. The output of the calculations is one of the internal temperatures, Ti where i= 1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 13, 15.                                                                       

The LSTM for the cooling scenarios has only T6 and T14 as inputs. Its architecture is slightly different from that of the heating scenarios due to the number of inputs and the number of neurons. Each hidden layer has now an optimal number of 30 neurons. The architecture is shown in Figure 15.

We have added the following to clarify the meaning of Ti between lines 318-320:

To present the results more clearly, only the results obtained using the LSTM trained to predict the results for temperature sensor 2 are shown, but all sensors have each individual LSTM to predict their values.

Finally, we have added the link of the patent in line 390 in the following hyperlink:

Link to the patent.

4. Response to Comments on the Quality of English Language

Point 1:

The English is fine and does not require any improvement.

Response 1:

Thank you for this comment.

Response to Reviewer 3 Comments

1. Summary

First of all, we would like to thank you for your effort and time spent revising this manuscript. We have deeply read and analyzed all your comments, questions and suggestions and we have tried to fulfil all of them in detail.

The authors.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Yes

Thank you for these constructive comments. We have tried to improve each of the marks by introducing the upgrades you suggested.

Is the research design appropriate?

Yes

Are the methods adequately described?

Yes

Are the results clearly presented?

Yes

Are the conclusions supported by the results?

Yes

3. Point-by-point response to Comments and Suggestions for Authors

Comments and Suggestions for Authors

Thanks for the improvements.

Thank you for these positive comments. We think that now the paper presents more clearly the ideas and results.

4. Response to Comments on the Quality of English Language

Point 1:

It is ok. 

Response 1:

Thank you for this comment.