Data-Driven Trajectory Prediction of Grid Power Frequency Based on Neural Models

Round 1

Reviewer 1 Report

The current paper proposes to analyse the system frequency response following disturbances and proposes a data-driven approach for predicting it by using machine learning techniques like Nonlinear Auto-regressive (NAR) Neural Networks (NN) and Long Short Term Memory (LSTM) networks from simulated and measured Phasor Measurement Unit (PMU) data. The algorithm is validated through simulation results.

Comments to authors:

- The authors can add the steps of implementing the algorithms. The theoretical part can be better detailed. The steps will be in the benefit of the readers, maybe they’ll help the readers to implement the proposed algorithm.

- Please add more details of how the theory from the first sections is applied in the results section.

- Please add the units of measurement both abscissa and orderly in all figures.

- Please add more details regarding the obtained results.

- The state of the art it is very poor regarding representative papers on data-driven control and it should be improved, maybe the author could add the following publications:

o Hybrid Data-Driven Fuzzy Active Disturbance Rejection Control for Tower Crane Systems, European Journal of Control, doi https://doi.org/10.1016/j.ejcon.2020.08.001, pp. 1-11, 2020.

o Event-Triggered Adaptive Fuzzy Control for Stochastic Nonlinear Systems with Unmeasured States and Unknown Backlash-Like Hysteresis, IEEE Transactions on Fuzzy Systems, doi 10.1109/TFUZZ.2020.2973950, pp. 1–19, 2020.

- Please add more details regarding the obtained results.

- The authors could add a paragraph with the disadvantages of the proposed method. In the proposed manuscript only the advantages are presented.

- Please add more details regarding paper’s novelty.

Author Response

- The authors can add the steps of implementing the algorithms. The theoretical part can be better detailed. The steps will be in the benefit of the readers, maybe they’ll help the readers to implement the proposed algorithm.

Thanks for this comment and making the paper publishable. Section 5 was renamed as “Methodology” in order to include a comprehensive introductory text (in red) and then a suitable brief explanation of the steps of the proposal, also a new figure 5 is added, the new figure will support the explanation of the methodology making the reader easy to follow and understand it—subsections 5.1, 5.2 and 5.3 present model details of the steps of the methodology.

- Please add more details of how the theory from the first sections is applied in the results section.

Thanks for this essential suggestion to improve the quality of the paper. Following your advice, we have included a more extensive explanation about how the theory is applied to our specific data sets.

- Please add the units of measurement both abscissa and orderly in all figures.

We sincerely regret these issues and thanks again for making the paper more attractive and publishable. We have ordered the figures accordingly, and also the figures have the proper labels and units.

- Please add more details regarding the obtained results.

The authors made a sacrifice to include more explanation, taking into account the limited time. Aspects as the performance of the predictions, differences between the neural networks’ models, noise addition and application scenarios were detailed. This information was described along with figures to explain what was observed—the discussion section deals with more specific comments about the results in terms of our analysis. The authors agree with the reviewer, there is room for more details, but the authors have already submitted another paper with the more profound and broader discussion on this topic.

- The state of the art it is very poor regarding representative papers on data-driven control and it should be improved, maybe the author could add the following publications:

o Hybrid Data-Driven Fuzzy Active Disturbance Rejection Control for Tower Crane Systems, European Journal of Control, doi https://doi.org/10.1016/j.ejcon.2020.08.001, pp. 1-11, 2020.

o Event-Triggered Adaptive Fuzzy Control for Stochastic Nonlinear Systems with Unmeasured States and Unknown Backlash-Like Hysteresis, IEEE Transactions on Fuzzy Systems, doi 10.1109/TFUZZ.2020.2973950, pp. 1–19, 2020.

Thanks for the comment and providing an insightful information for our paper and making publishable. Authors have added the suggested references and few of others relevant in the discussion.

- The authors could add a paragraph with the disadvantages of the proposed method. In the proposed manuscript only the advantages are presented.

Thanks for the comment. It is a very important comment; consequently, the authors have added more details at the end of the discussion section, the reviewer can identify a couple of paragraphs including some limitations of the study.

- Please add more details regarding paper’s novelty.

Thanks very much to this review for asking to enlighten the novelty of our paper. We have highlighted the main contribution of the paper in the introduction. However, it was previously stated that this time-series grid power frequency forecasting had not been seen by the authors in the literature. Frequency deviations time series has few studies related to its forecasting. The present work holds the first application of machine learning methods through the employment of artificial neural networks. Basic models were used as the first sight of this methodology, also, to observe the forecasting is when nonlinear association from data points from the same time series are employed to obtain the behavior of series. Further analyses allow improving the quality of forecasting when more complex models and the inclusion of more exogenous data can contribute. Indeed, it is necessary to propose the inclusions, create the models, validate and analyze the results to consolidate those new aspects to evaluate.

Reviewer 2 Report

This paper introduces two prediction models of a power system frequency response following disturbances: the Nonlinear Auto-regressive (NAR) Neural Networks (NN) and Long Short Term Memory (LSTM) networks using simulated and measured Phasor Measurement Unit (PMU) data. 

Some questions are the following:

1) Present the rationale for the choice of the two methods NAR-NN and LSTM because many more methods for time series prediction exist.

2) Describe better the Generator Replacement Cases in table 1 (how the generators are replaced, and relevant power circuits) and the reasons for frequency deviations.

3) Provide a thorough comparison of results in Fig. 5 and 6 and explain why LSTM achieve apparently better results than NAR-NN. In Fig. 11 and 12 it appears that NAR-NN is performing better than LSTM. What are the reasons for such differences?

4) Explain the Time series proportion used in the models training 5%, 6.25%, 7.5%, their definition and how the actual values were chosen. Can NAR-NN predictions be improved by choosing a number greater than 7.5% ?

5)  This study is limited by the unidimensional analysis of time-series. The inclusion of more variables to do the forecasting could be explore in future work. The authors should also consider Vector Auto-Regressive methods and inclusion of exogenous inputs in their models.

Author Response

1) Present the rationale for the choice of the two methods NAR-NN and LSTM because many more methods for time series prediction exist.

A1. Thanks to this reviewer for this very important comment. This point was strengthened in lines 50 to 57, searching to explain the justification of the employment of the NN models as a first approximation for time series forecasting for frequency deviations in power systems. In general, these two models’ objective was to observe the forecasting performance, employing basic neural networks models, which include nonlinear association from previous data points in time series.

2) Describe better the Generator Replacement Cases in table 1 (how the generators are replaced, and relevant power circuits) and the reasons for frequency deviations.

A2 Thanks for the comment. The authors have included a brief description of the system and the single line diagram for illustration.

3) Provide a thorough comparison of results in Fig. 5 and 6 and explain why LSTM achieve apparently better results than NAR-NN. In Fig. 11 and 12 it appears that NAR-NN is performing better than LSTM. What are the reasons for such differences?

Thanks to this reviewer for the very important comment, the authors have emphasized the reasons for the differences in the results section. Also, LSTM models hold an architecture-specific for data with dependencies in time. It means that the recurrent mode of this network has different aspects of developing the forecasting. However, each application is different, and it means that we hope that LSTM was better than NAR models, but for the specific case, data had better forecasting employing the NAR models. From the results, it is possible to see that it is not necessary a LSTM model make the predictions for the studied time series.

4) Explain the Time series proportion used in the models training 5%, 6.25%, 7.5%, their definition and how the actual values were chosen. Can NAR-NN predictions be improved by choosing a number greater than 7.5% ?

Thanks for the comment. Authors wanted to compare both methods with the same training percentages as the figure of merit. Effectively, choosing higher percentages will improve forecasting data, the authors recognize this as a critical research point as a consequence, it is a topic of a future work.

Also, the objective was to observe how the forecasting was with data before the nadir point. Then, the used proportions happened to consider this aspect. For that time series, a more significant proportion means that we need information beyond the nadir point.

5)  This study is limited by the unidimensional analysis of time-series. The inclusion of more variables to do the forecasting could be explore in future work. The authors should also consider Vector Auto-Regressive methods and inclusion of exogenous inputs in their models.

Thanks to this reviewer for this critical comment. Indeed, VAR is a fascinating method. Authors consider this a very important topic that requires a separate discussion, and it will be included in future works. This was included in the discussion when the limitations were described and the conclusions as future work.

Round 2

Reviewer 1 Report

In this revision the paper has been seriously improved. The authors answered to all my concerns and from my point of view the paper can be published in Electronics journal.

Reviewer 2 Report

Overall, the revised version of the paper addresses in a very satisfactory manner my comments given to the first submission.