A Special Ordered Set of Type 2 Modeling for a Monthly Hydropower Scheduling of Cascaded Reservoirs with Spillage Controllable

Round 1

Reviewer 1 Report

The reviewed article concerns the modeling of the operation of hydropower plants created on cascade reservoirs with the possibility of controlling the outflow of water. It is an interesting contribution to issues related to rational and sustainable water management, focusing on maximizing the work efficiency of this type of hydrotechnical structures while minimizing environmental impacts and maximizing profits. I think that the presented research can be applied to a wider group of recipients - both for designers and owners of hydroelectric power plants, offices related to water management or scientists involved in research on the optimization of the operation of this type of systems. The manuscript itself requires clarification on issues related to the goals of the research, defining its innovativeness, research methodology, discussion of results, conclusions and editorial issues, which I have listed below. The manuscript requires major revisions and will be suitable for publication in the journal Water.

 

- Title: please expand the abbreviation "SOS2"; we do not use abbreviations in the title (unless they are generally known). Alternatively, I would ask you to change the wording of the entire title to be unambiguous.

- Missing keywords, please complete them.

- Please standardize the text: font size and typeface, use of single spaces, citations in the text adjusted to citations in the bibliography (e.g. in line 48 you write that the research was done by Ahmed, and Ma & Teng, 2018 are quoted).

- How innovative is the research and what gap in knowledge does it fill? Please specify these issues as they are not explicitly stated in the manuscript.

- The specific objectives of the article should be defined.

- The manuscript has an unusual text layout - usually Introduction, Materials and Methods, Results, Discussion of Results, Conclusion/Summary, Bibliography.

- Line 104-112: please add sources in the text.

- Please check if the text refers to the sources correctly - in some places "Error! Reference source not found” (e.g. line 160, 173, 202).

- Add a map with the location of the reservoirs along with their catchments and marked hydropower plants.

- Line 192-204: no source reference.

- On what basis were hydropower plants selected in the case studies? What criteria have been adopted? Were some variants used?

- Please check that all tables, figures and formulas are referenced in the text.

- Please explain "Zmin", "Zmax" and "Z" in Figure 2.

- What does "Obj" mean in table 3?

- Why was the SQP model selected for comparison? Have others been considered?

- Please specify how the presented modeling results from chapter 4.4 compare to the actual results.

- Please insert tables and figures after the paragraph in which they are mentioned.

- Please point out the issues in lines 291-304.

- Conclusions: What future directions can be taken? What are the limitations of the presented analytical methods?

- Bibliography: please standardize fonts and citation style (e.g. add DOI).

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

A review of “SOS2 Modeling for a Monthly Hydropower Scheduling of Cascaded Reservoirs With Spillage Controllable”

 

The problem is well defined, but the presentation of the results could be improved.  The paper has number of unresolved references in the text that should be corrected (i.e. the message “Error! Reference source not found” is found several times throughout the manuscript).

 

The term “hydraulic coupling” used in this paper (starting from the abstract) typically refers to the cascade of hydro power plants where the head water levels of the downstream dam determine the tail water levels of the upstream dam. This is not the case here, since the tail water levels were read from the rating curve at a downstream cross section immediately below the hydro power plant.

 

One of the stated goals is to minimize spills.  However, this goal cannot be properly tested using the mean monthly flows.  Observe a comparison between monthly, weekly and daily flows for the same natural flow time series shown below.  It is obvious that peak flow events which cause inevitable spills disappear from the monthly hydrograph due to monthly averaging.  Modeling studies conducted in Canada in the late 1990s compared the spills from the same system as a function of the time step length, and found that spills in weekly simulation were 28% higher than the spills in monthly simulations, caused only by the different shape of the hydrograph.  This leads to an obvious conclusion that monthly time step is not the best for minimizing reservoir spills, due to the flat shape of monthly inflow hydrographs.  The authors should comment on the limitations of using the monthly time steps, and the need to include hydrological channel routing in between the reservoirs for using daily time steps on a system of this size, for which there are appropriate references among reservoir optimization models (Ilich, 2021).

 

 

The system seems to be solved for four reservoirs and for 12 months, which gives de facto 48 master decision variables (reservoir releases through hydro power plant), and just as many decisions related to spills.  Together, those 96 decision variables determine the final solution, since all other variables (storage change for each reservoir) are constrained by the local inflows (which are given as constant monthly inflows) and the mass balance constraint.  While piece-wise linearization of the non-linear constraints increases the number of variables, it is not completely clear why such a high resolution is required to move from 96 decision variables to as mana as 32464 variables! Also, there is no mention of the need to include net evaporation in the reservoir mass balance equation, which seems to have been left out of the equation (2) that addressed the reservoir mass balance calculation.  It is also not clear why the spills are happening at Xiaowan and Monwan reservoirs between June and September when the storage is not full.  I would expect to see the spills only when the storage is full and the flows through the HP are maximized.

 

In spite of the above limitations, this paper could still provide a useful benchmark test problem for other researchers, especially since it uses a dynamic function related to the maximum flow through the turbine as a function of the net head, as shown by expression (8), since most other publications ignore the dynamic nature of this constraint and model the upper limit on turbine flows as a fixed constant.  I therefore propose that the researchers summarize the model results in a different fashion and present it in such a way that other researchers can use their data to test other similar models and compare their solutions to the benchmark obtained from this paper. In particular:

 

§  Start by showing the modeling schematic (location of each reservoir and each hydro power plant in simplified form, as shown below, such that the readers can see the sequence of the reservoirs and their hydro power plants from upstream to downstream.  The schematic should also show the locations where local inflows are input into the system.  I propose something like this although it does not have to be to scale:

 

§  Summarize the results in the following table (assuming no net evaporation was accounted for):

 The above table should also be accompanied by the elevation-area-volume tables for the four reservoirs, as well as by the head-flow-efficiency functions for the hydro power plants associated with the four reservoirs (those could be added in the appendix of the paper or posted on a downloadable link listed in the paper).  This approach would fully define the problem and enable other researchers to use the same problem in their research.  In that sense, it would be a valuable contribution to the scientific community.  If possible, function (8) could be defined using a polynomial fit (assumed a good fit is possible).

Reference

Ilich, N. 2021.  WEB.BM – a Web Based River Basin Management Model with Multiple Time Step Optimization and the SSARR Channel Routing Options. Hydrological Sciences Journal, Vol. 6 (2) p. 175-190.

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Thank you for the corrections made by the authors. All of them have been properly addressed in the text and in its current form it is suitable for publication. I would only improve the map by adding a scale, a north arrow and a map illustrating the location in China or this part of Asia. I wish you success in the further editorial process and keep my fingers crossed for the successful publication of the manuscript in Water journal.