Methodology and Application of Statistical Techniques to Evaluate the Reliability of Electrical Systems Based on the Use of High Variability Generation Sources

Round 1

Reviewer 1 Report

In this paper is presented a new methodology based on Monte-Carlo techniques that evaluates the reliability of a carbon-free power generation system based on renewable energy sources. The variation of the power demand and the power supplied by renewable energy sources is considered, so a certain supply reliability level is determined.
My comments regarding the paper are:
- use for e.g. [4-7] when you cite multiple references;
- present more detailed the other researchers work;
- present in what environment are the simulations performed;
- present more information about the reliability level considering the cases with conventional power plants, such as nuclear;
- rephrase the sentences where you use figures in a not so appropriate way, such as in the Abstract ("This huge figures decrease substantially if contributions from nuclear and storage technologies are included").

Author Response

Point 1: use for e.g. [4-7] when you cite multiple references

Response 1: When multiple references are cited, the notation has been changed to the form suggested by the reviewer.

Point 2: present more detailed the other researchers work

Response 2: As suggested by the reviewer, the part of the introduction that discusses the work of other researchers has been expanded. Specifically, an additional half page has been written, text in which the main types of existing energy models are briefly described. Around 20 additional references have been added, so those who wish to look for more detailed information have the information available to search for it directly (this increase in the number of references has also been suggested by the second reviewer).

Point 3: present in what environment are the simulations performed

Response 3: On the one hand, as can be seen in Figure 6, data on the evolution of electricity demand in Spain between 1990 and 2016 (IEA data, reference 55) have been used to estimate the demand in the year 2040. From these data a linear extrapolation has been considered (BAU scenario), as commented at the end of page 9. While on the other hand, the data of February 2017 has been used to estimate the PDFs followed by each generation source and by the demand curve. Then, the simulations have been carried from a random sampling of these PDFs (59 combinations of random values of the PDFs followed by the variables). Thus, from these data, the PDFs of both demand and generation sources have been obtained and it has been assumed that the shape (not the values) of these PDFs is maintained in the year 2040.

Point 4: present more information about the reliability level considering the cases with conventional power plants, such as nuclear

Response 4: As conventional energy source, only nuclear has been considered, so that given its extreme stability, a capacity factor of about 90% has been considered for the simulations (typical value that appears in the literature for this type of technology and also extracted from REE generation data, reference 43), this aspect is also mentioned at the end of page 16.

Point 5: rephrase the sentences where you use figures in a not so appropriate way, such as in the Abstract ("This huge figures decrease substantially if contributions from nuclear and storage technologies are included")

Response 5: Since the word figure (understood as value) could lead to confusion, as pointed out by the reviewer, it has been changed throughout the text by the word value itself.

Reviewer 2 Report

1. Currently, the following methods are widely used to analyze the reliability of power systems with RES: analytical; the method of state space (Markov processes) and the method of statistical modeling (Monte Carlo method), but all these methods have disadvantages in terms of evaluating the reliability of renewable energy production systems. So, the Monte Carlo method in most cases, can be used as a model, required special software; its using connected with the fact, that:

- the accuracy of solutions depends on the number of simulations performed (this limitation becomes less significant with increasing computer speed);
- based on the ability to represent the uncertainty of parameters using a reliable distribution;
- voluminous and complex models can present difficulties for modeling specialists and make it difficult for stakeholders to participate;
- the methodology may not adequately take into account unlikely events with serious consequences and, therefore, does not allow taking into account the organization's propensity to risk in the analysis.
In this regard, I would like to know how the authors of the methodology propose to reduce the negative impact of these factors, especially for analysis of reliability of large scale power systems.                                         2. The list of references should be expanded.        

Author Response

Point 1: Currently, the following methods are widely used to analyze the reliability of power systems with RES: analytical; the method of state space (Markov processes) and the method of statistical modeling (Monte Carlo method), but all these methods have disadvantages in terms of evaluating the reliability of renewable energy production systems. So, the Monte Carlo method in most cases, can be used as a model, required special software; its using connected with the fact, that:

- the accuracy of solutions depends on the number of simulations performed (this limitation becomes less significant with increasing computer speed);

- based on the ability to represent the uncertainty of parameters using a reliable distribution;

- voluminous and complex models can present difficulties for modeling specialists and make it difficult for stakeholders to participate;

- the methodology may not adequately take into account unlikely events with serious consequences and, therefore, does not allow taking into account the organization's propensity to risk in the analysis.

In this regard, I would like to know how the authors of the methodology propose to reduce the negative impact of these factors, especially for analysis of reliability of large scale power systems.

Response 1: In next lines, the impact in the power systems reliability of each factor mentioned by the reviewer is analyzed:

The way to reduce the negative impact of the first factor is shown in the second factor proposed by the reviewer (when “reliable” PDFs are determined from the available data for each variable the accuracy of the methodology is almost independent of the number of simulations).

The second factor, the ability to represent parameter uncertainty, which is improved by the use of a large database for each variable, in order to have reliable and detailed data for each one of them, from which the PDF followed by that variable is accurately estimated.

Third factor, the basis of the model is not so complex, once the PDF of each variable is obtained and the demand forecast is estimated, then, only the generation has to be higher than the demand with the desired coverage degree for all the cases of random sampling carried out in modeling. While it is true that a large amount of data can be used if a large data history is used to determine PDFs and/or demand forecasting. But currently the most difficult thing is the implementation of the model, since the current computational power allows that the handling of a large amount of data is not a major problem.

The next factor, the negative effect of unlikely events on generation and/or demand, this aspect is difficult to take into account unless these events occurred when the measurements collected in the database used were taken. The only way would be to try to be conservative (increase of the confidence level) and increase the variability in the PDFs used to perform the simulations (in normal PDFs by increasing the standard deviation, uniform PDFs by increasing the minimum and/or maximum allowed values, etc.). This conservatism implies an additional oversizing of the generation system.

In summary, the accuracy of the results will depend largely on the “quality of the data” used, so that it is possible to capture the behavior of the different variables (covering the range of variation and their frequency within these), i.e. accuracy depends on the capacity to estimate the PDFs adequately for the generation sources and for the demand.

Point 2: The list of references should be expanded

Response 2: As suggested by the reviewer, the number of references has been increased (22 new references have been introduced, mainly to provide some references where documentation of the most commonly used energy system models can be found).