Solving the Real Power Limitations in the Dynamic Economic Dispatch of Large-Scale Thermal Power Units under the Effects of Valve-Point Loading and Ramp-Rate Limitations

Round 1

Reviewer 1 Report

This manuscript provides a novel optimization technique applied to solve the dynamic economic dispatch of large power system considering valve point loading and ramp rate limitations. It is interesting study and shows both methods and results and it is well structured. Although this work stands in terms of the optimization technique and findings, I would like to see the contribution to the methodological approach in the Conclusions.

Author Response

Thanks for your comments 

Author Response File: Author Response.docx

Reviewer 2 Report

The article concerns the problem of the optimal distribution of the real (active) power generation in the power system. This is a well-known problem, called economic dispatch (ED). In the classic approach, it involves the control of the real power generation to achieve the minimal value of the total operating fuel costs. The obtained dispatch has to meet the system load, subject to operational constraints of generators. Typically, the operating costs of individual generating units are modeled with a piecewise linear function or a quadratic function. The authors refine this approach considering the valve-point loading effects on the shape of cost characteristics (they use a quadratic function with an additional sinusoidal component).

The ED method can be used for daily planning of the operation of centrally dispatched generating units (e.g. thermal power units). In the simplest approach, a day is divided into several periods (e.g. hours or shorter periods) for which the optimal generation distribution is calculated separately. However, the operating conditions of the power system (total load and generation of renewable sources) may change significantly in subsequent periods. It means that the change of generation from the dispatch obtained for period t to the dispatch obtained for a period t + 1 can’t always be possible. To solve this problem, it is necessary to take into account the ramp rate limits of individual generating units, which leads to the so-called dynamic economic dispatch (DED). This approach is used by the authors in their research. However, considering the valve-point loading effects and the ramp rate limits makes the DED problem much more difficult to solve than the ED problem, especially for large power systems with hundreds of generating units.

The literature describes many methods that can be used to solve the DED problem. These methods can be divided into traditional and non-traditional optimization techniques. In this article, the authors used the particle swarm optimization (PSO) algorithm for this purpose, which belongs to the class of metaheuristic algorithms, i.e. it is the non-traditional optimization technique. The authors also proposed a modification of the PSO algorithm, that lead to improving its efficiency, comparing to other PSO formulation and other non-traditional optimization techniques. The developed method was illustrated with several calculation examples of various complexity.

Conclusions: I find the chosen research problem interesting. I also assess that the method of its solution is appropriate. However, the article has many drawbacks and errors that must be cleared up or corrected before publication. General and detailed comments on the article are listed below.

General comments on the article:

1. The subject of this article was also the subject of the research described by the authors in articles [62] and [63]. In the Introduction section, the authors should refer to these works and describe exactly what in this article has been done more in relation to [62] and [63] (the differences between this article and the articles [62] and [63] should be highlighted).
2. In the Introduction section, the authors should summarize in one or two paragraphs the main contributions of the paper (what is the advantage of the proposed method comparing to the reviewed method in the literature).
3. In section 2 the mathematical formation of DED of real power is presented. The authors extend the classic formulation of the DED problem to include transmission losses. There are also other extensions of the DED problem in the literature, e.g. including power reserves constraints, emission limits, etc. I think that a brief literature review of the various formulations of the DED problem would be interesting for the readers.
4. Table 3 contains the values of ramp limits of individual generators that were used in all analyses described in section 5. For real generating units, the ramp limits are usually in the range from 2% to 6% of P_max. In their research, the authors assume the range of ramp limits from 0.28 to 0.91% of P_max. This discrepancy should be explained. Its influence on the obtained results should also be discussed.
5. Sections 5.2 and 5.3 present the case studies for 10 thermal power units. Power generating system with and without including the transmission losses are considered. In both cases, the description of the analysis is quite long and very similar. I suggest that the authors could combine the descriptions of both problems into one section. Graphs for both problems can be presented side by side (in two columns). Tables with results can be combined (tables 5 and 9 can be moved to the appendix). The proposed way of presenting the results will allow the reader to easily compare the results for the problems with and without losses.

Detailed comments on the article:

1. Line 164: there should be a ??,?−1 in the parentheses.
2. Line 187: there should be a ?j,? in the formula (9).
3. Figure 1: sections of pseudocode have wrong numbers (1, 2, 4…8 instead of 1, 2, 3…).
4. Figure 1, section 4: there is “positionvector” instead of “position vector”.
5. Line 269: formula (19) and the following formulas on this page: “xplore” or “explore”, “xploit” or “exploit”?
6. Line 271: “γ is a positive and real number in the range of [0, 1].” – in what way the value of γ was selected?
7. Line 277: there is “w_ini,k and w_ini,k “; should be “w_ini,k and w_fin,k “.
8. Line 278: “The two values are positive and real numbers in the range of [0, 1].” – in what way these numbers were selected?
9. Figure 2: formulas (26) and (35): in the third component of the formulas there should be c₂ instead of c₁₂ or c₁.
10. Figure 2: formula (36) should be below the formula (35) (not in the same line).
11. Line 313: there are too many spaces at the end of this line (“for TPUs”).
12. Lines 316 and 317: “They are two synchronous generators (SGs) with several valves.” – the synchronous generator has no valves. This sentence should be changed.
13. Lines 338 – 340: “The economic dispatch of real power and optimum feasible area of the generation of the TPU1 and TPU2 are [200, 455] MW and [300, 460] MW, respectively” - How these results were obtained? What do these numbers mean?
14. Figure 3 – units for TPU₁ and TPU₂ are missed.
15. Table 2 – the total system load in hour 20 is equal to 2076 MW, while in tables 7 and 9 is equal to 2072 MW. Which value is correct?
16. Line 428 – “The capacity of this power system is 40198 MW”. I don’t think that it is the capacity. The capacity of the analyzed power system is equal to the sum of the maximum powers of the generators, which is equal to 2358 MW (table 3). In what way the number 40198 was obtained and what does it really mean?
17. Figure 4 (A) – units are missed.
18. Table 6, No. 12 – the value of σ should be written in a single line.
19. Table 7 – the value of P_i,t for t = 20 is equal to 2071.76 MW. The value of P_i,t for t = 20 calculated based on the data presented in Table 5 is equal to 2041 MW. Which value is correct? What is the reason for this discrepancy?
20. Lines 459 and 460 – “The parameters utilized in MG-PSO algorithm (Case Study #2) are shown in Table 4.” – The title of table 4 says that these parameters are for Case Study #1 (“Table 4. Parameters utilized in MG-PSO algorithm for 10 TPU PGS (Case Study #1).”).
21. Line 475 – “at each t period Δ?_? = 0.0” – It is not true for all hours. Based on the data provided in table 9, Δ?_? for t = 12 is equal to 2.7 MW.
22. Line 477 – “?_?,? = 799.92 MW” – Based on the data provided in table 9, the number 799.92 is equal to the sum of ?_i,? in a 24-hour period. But this number does not indicate the power losses (in MW) but it indicates energy losses (in MWh).
23. Line 481 – “t = 230” – should be t = 230 s.
24. Lines 494 and 495 – “Total load demand during the day is 40108 MW.” – This is no power (in MW) but energy (in MWh)!
25. Line 496 – “?_?,? = 40910.68 MW” – This is no power (in MW) but energy (in MWh)!
26. Line 497 – “?_?,? = 802.68 MW” – This is no power (in MW) but energy (in MWh)! Data from which table do I need to use to calculate this value? Based on the data provided in table 9 the value of energy losses is equal to 799.92 MWh.
27. Figure 7 (A) – units for t are missed.
28. Figure 9 – units for Y-axis are missed.
29. Line 530 – “D = ” – should be d =. See line 390.
30. Figure 10 (A) – units for t are missed.
31. References – check references 16 and 61 (Mohammadi-ivatloo – lowercase i?), 23 (for sustainabledynamic – space is missed), 62 (AL-Bahrani, while in 63 and 64 is Al-Bahrani), 68 (Particle swarm optimization. in neural networks – the point after “optimization”).

Comments for author File: Comments.pdf

Author Response

Thank you for your comments.

Author Response File: Author Response.pdf

Reviewer 3 Report

In this paper, the real power constraints on the dynamic economic dispatch of large-scale thermal power units under the influence of valve point loading and ramp rate constraints are investigated. Athough the manuscript is too lang, but it is inovative and worth publishing.

Author Response

Thank you for your comments. 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

My comments were taken into account. Thanks for the answers. I have no additional comments. Please check the text of the article and remove minor editorial flaws.