Stochastic Flexible Power System Expansion Planning, Based on the Demand Response Considering Consumption and Generation Uncertainties
and Tomonobu Senjyu 5,*
Round 1
Reviewer 1 Report
The comments of this reviewer are listed as below:
1) The definition of equations need to mention after each equation to make it easier to follow the paper.
2) In literature review, the papers are not considered well and the limitations of published paper are not consider to show the limitation in this field.
3) In this paper, the hybrid evolutionary algorithm based on the combination of crow search algorithm and grey wolf optimizer is used to determine the optimal point with approximate unique solution but the method is not considered. Add a section in the paper and consider the method with details.
4) Add the flowchart of the proposed method.
5) Did the authors implement all method in table 1 or does it need references?
6) The comparison section is missing, add a comparison section to the results and compared the method in details with published works.
7) In page 5, lines 183, 184, The authors said "in this case, index h is selected from the 183 set [1-34].", are authors used all these references for index h?
8) The references are mentioned twice in Reference section, Edit this part and mention references once.
Author Response
Reviewer #1:
The comments of this reviewer are listed as below:
Firstly, the authors would like to appreciate the respectable reviewer for their appropriate comments. The responses to your comments are provided below.
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Comment 01: The definition of equations need to mention after each equation to make it easier to follow the paper.
Response and Action: Thanks for your valuable comment. In accordance with this comment, section 2.1 is modified as follows:
In this section, the dynamic GTEP formulation is expressed by considering the location model of SCBs and the operation model of DRP. This problem minimizes the total planning cost of GUs, TLs, and SCBs by considering AC-PF constraints; the planning-operating model of GUs, SCBs, and TLs; DRP operation model; and operation and flexibility limits of the network. Therefore, the optimization formulation of this scheme can be written as follows:
Objective function: The objective function of this formulation is presented in Eq. (1), which has four terms. In the terms 1-3 in this equation, the investment costs in the construction of TLs, SCBs, and GUs are presented, respectively. Note that the transmission line between buses b and l and buses l and b is the same, so in the first term of Eq. (1), the term 1/2 appears. In the last term of the equation, the expected operating cost of the GUs is formulated. This function includes the fuel cost of GUs, which has a parabolic function [14].
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(1) |
Planning constraints: The planning model of SCBs, GUs, and TLs is described in constraints (2) to (11) [14, 17]. Constraints (2)-(4) refer to the investment budget for GUs, SCBs, and TLs, respectively, where the investment budget represents the maximum capital available for the construction of these elements. In the proposed design, dynamic planning is considered for the mentioned elements. In other words, if the planning horizon is 6 years, planning is performed for smaller intervals such as 2 years. In this case, index h is selected from the set {1, 2, 3}. The elements of this set refer to the first to third planning period, where the planning step is 2 years. Now, Eqs. (5)-(7) represent a logical constraint stating that the referred power elements can be installed only in one planning period. In other words, each element can be constructed only in one of the first to third periods. Constraints (8) to (10) also determine the presence of GUs, SCBs, and TLs in the planning periods, respectively. For example, if an element is constructed at h = 2, then that binary variable corresponding to its presence at h = 1 is zero, and for other values, ​​u has a value of unity. Finally, in Eq (11) a logical constraint is used which indicates that the TL between buses b and l is the same as the TL between buses l and b.
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Power flow constraints: The AC-PF constraints of the system are presented in the Eqs. (12) to (15) [45-47], which expresses the power balance (active and reactive) for a bus, (12)-(13), and the power (active and reactive) passing from TL, (14)-(15) [48-50]. Note, however, that Eqs. (14)-(15) represent a combined operation and planning model of TL so that if the binary variable uL is equal to unity, TL is exploited based on Eqs. (14) and (15). However, if uL = 0, TL is not present in the network, then there is no operating model for it.
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Model of GUs and SCBs: In the following, the combined planning-operation model of GUs and SCBs is formulated in (16) - (18) and (19)-(20), respectively. Constraints (16) and (17) refer to the GU capability curve [51], which expresses the controllable range of power (active and reactive) in the GU. Constraint (18) is used only for renewable GUs such as WF [6]. This relationship points to the fact that renewable GUs inject active power into the transmission system, where it equal to their upper capacity in proportion to the weather term ( ) [6]. This is because the operating cost of these types of GUs is very low [52]. In constraints (19)-(20), the injected reactive power of SCBs into the transmission network is calculated by Eq. (19), and its step performance limit is formulated in Eq. (20). In these constraints, the operation model of GU (SCB) is applicable only if uG = 1 (uSCB = 1).
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Formulation of DRP: Next, the operating formulation of DRP is given in (21)-(22) [53]. Equation (21) indicates the controllable range of power of consumers participating in DRP. Constraints (22) also guarantee that the reduced energy of these consumers in a certain operating period will be provided by the grid during other operation hours. In this DRP, consumers are expected to participate in the plan to shift their energy consumption at peak load period to off-peak time. This is because it is commensurate with minimizing the fuel cost of GUs in the last part of Eq. (1). So that if the load decreases during peak hours, GUs with low fuel costs will feed the consumers. Also, because energy demand is low during off-peak hours, increased consumption during this period may be met by inexpensive GUs. This corresponds to minimizing the operating costs of GUs.
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Network limits: Transmission network operation and flexibility constraints are formulated in (23)-(24) [54] and (25) [7], respectively. Operation limitations of the network include the limit of apparent power passing through the TL, (23), and the limit of the voltage magnitude of the buses, (24). High voltage limits are used to prevent insulation damage to network equipment due to overvoltage. Its lower limit is also used to prevent mains shut down due to severe voltage drop in the network [54]. In this section, in order to establish the desired flexibility in the transmission network, a flexibility constraint such as constraint (25) is used for non-renewable GUs. Note that it is expected that the results of real-time and day-ahead operation of a system will not be the same in the presence of renewable GUs, which is due to a forecasting error in the output active power of these types of GUs. This is known as low system flexibility, which can lead to damage to the network due to an imbalance between demand and supply at the real-time scheduling. To compensate for this, flexibility sources such as DRP [7] or storage systems [55-59] must be able to reduce the power fluctuations of renewable GUs in real-time scheduling. In this condition, the desired flexibility is established in the network [7]. However, considering this requires a mathematical formulation of flexibility in the proposed framework, this section presents the constraint (25). In this case, the deviation of the generated active power for non-renewable GUs in scenario s from the scenario related to the deterministic problem (with the forecasted values ​​of the uncertainty parameters assumed equal to the first scenario) should be less than DF, which DF represents flexibility tolerance. If DF = 0, then 100% flexibility for the network can be evaluated. Therefore, it is expected that with this flexibility model, the results of the real-time scheduling will be close to the results in day-ahead operation.
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Comment 02: In literature review, the papers are not considered well and the limitations of published paper are not consider to show the limitation in this field.
Response and Action: Thanks for your valuable comment. Note that section 1.2 reports different research works, and their limitations are presented as research aps in section 1.3:
- In most researches focusing on PSEP such as [10-19], the economic planning and technical (operation) indices of the network have been considered. However, it should be noted that WFs thanks to their low pollution and low operating costs can be an important factor in improving the economic, environmental, and power network operation. However, their presence will reduce the flexibility of the network. To compensate for this, FSs such as storage and DRP are suitable approaches [9]. Although this has been stated in various studies, less research has focused on the mathematical model of flexibility, noting that to assess an index its status should be measured and this can be derived by providing a mathematical model of flexibility in the problem.
- Reactive power devices are generally able to improve the voltage profile and voltage security index in the network by controlling reactive power [17, 18], among which the capacitor bank is economically viable and cost-effective. Note, however, that if the optimal location and size are achieved for these devices, it is expected that optimal conditions will be obtained for the mentioned indices. This is achieved in the case of the capacitor bank placement problem. However, in less research such as [17], the location of reactive power devices in the PSEP problem has been considered.
- The PSEP problem includes AC-OPF equations, so it has a MINLP framework. To solve this problem, some research such as [10, 18, 19] use iterative numerical solutions or evolutionary algorithms to solve this problem. These algorithms suffer from long computational time. They also have different optimal solutions, in other words, they are not unique. Therefore, the obtained solution has a low confidence factor. Moreover, some studies, such as [11, 13, 15, and 16], have proposed a PSEP model based on DC optimal power flow (DC-OPF). Although this model has a linear formulation and following it the computational time will be low and a unique optimal solution will be obtained, variables such as voltage drop, reactive power, and power loss are eliminated in this model. Consequently, the numerical results obtained from this model will not be accurate and will have a significant computational error. To compensate for the limitations of these two approaches, some studies such as [12, 14, 17] present the PSEP model based on linearized AC-OPF. Nonetheless, there is also a significant computational error in this technique regarding some variables such as power loss.
However, to address this comment, Table 1 is added to section 1.2 in the revised version of the manuscript:
Table 1. Taxonomy of recent research works.
|
Solver |
Planning of switched capacitor bunk |
Flexibility modeling |
Ref. |
|
NHEA |
No |
No |
[10] |
|
Solvers for linear model |
No |
No |
[11] |
|
Solvers for linear model |
No |
No |
[12] |
|
Solvers for linear model |
No |
No |
[13] |
|
Solvers for linear model |
No |
No |
[14] |
|
Solvers for linear model |
No |
No |
[15] |
|
Solvers for linear model |
No |
No |
[16] |
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Solvers for linear model |
Yes |
No |
[17] |
|
NHEA |
No |
No |
[18] |
|
NHEA |
No |
No |
[19] |
|
HEA |
Yes |
Yes |
Current paper |
HEA: Hybrid evolutionary algorithm, NHEA: non-HEA
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Comment 03: In this paper, the hybrid evolutionary algorithm based on the combination of crow search algorithm and grey wolf optimizer is used to determine the optimal point with approximate unique solution but the method is not considered. Add a section in the paper and consider the method with details.
Response and Action: Thanks for your valuable comment. Details of CSA and GWO algorithms are referenced in this paper so that prevent repetition. Then, the steps of problem solution using the CSA+GWO is reported in Section 3. Note that, in this solver, the CSA accounts for updating decision variables in each iteration and GWO performs this process. Finally, to clarify more, the flowchart of the problem solution is added to Section 3 in the form of following figure:
Figure 2. Flowchart of the CSA+GWO for solving of the proposed scheme.
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Comment 04: Add the flowchart of the proposed method.
Response and Action: Thanks for your valuable comment. Please refer to Comment 03.
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Comment 05: Did the authors implement all method in table 2 or does it need references?
Response: Thanks for your valuable comment. All of the algorithms reported in Table 2 were applied to the problem proposed in this paper. Hence, only the general procedure of each algorithm is referenced in section 4.1.B. However, note that the solution procedure of each algorithm is provided in Fig. 2, but the NHEAs like CSA, GWO, PSO, and GA, rectangles 6 and 7 are removed and rectangles 4 and 5 of the corresponding algorithm are substituted.
Figure 2. Flowchart of the CSA+GWO for solving of the proposed scheme.
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Comment 06: The comparison section is missing, add a comparison section to the results and compared the method in details with published works.
Response and Action: Thanks for your valuable comment. To make a comparison between the proposed scheme with those presented in the Literature review section, Table 1 is added as follows to section 1.2. This table states the limitations of the previous studies and benefits and contributions of the suggested scheme.
Table 1. Taxonomy of recent research works.
|
Solver |
Planning of switched capacitor bunk |
Flexibility modeling |
Ref. |
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NHEA |
No |
No |
[10] |
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Solvers for linear model |
No |
No |
[11] |
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Solvers for linear model |
No |
No |
[12] |
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Solvers for linear model |
No |
No |
[13] |
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Solvers for linear model |
No |
No |
[14] |
|
Solvers for linear model |
No |
No |
[15] |
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Solvers for linear model |
No |
No |
[16] |
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Solvers for linear model |
Yes |
No |
[17] |
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NHEA |
No |
No |
[18] |
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NHEA |
No |
No |
[19] |
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HEA |
Yes |
Yes |
Current paper |
HEA: Hybrid evolutionary algorithm, NHEA: non-HEA
Table 2 presents a comparison of problem solution with different algorithms and this is used in section 1.3 and the last contribution in section 1.4 to highlight the research gaps. Also, Table 4 presents the status of economic and technical indices for the following case studies:
- Case I: Considering only AC-PF studies
- Case II: Implementation of the proposed GTEP framework without DRP and SCB
- Case III: coupling GTEP and SCB placement problems
- Case IV: Implementation of GTEP in a network with DRP without considering SCB
- Case V: GTEP implementation and SCB location in a network with DRP
In these cases, Case V concerns the proposed scheme, but cases II to IV are related to previous research works. For instance, Case III is almost similar to the study of [17], or Case II is similar to those of [10-16, 18-19].
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Comment 07: In page 5, lines 183, 184, The authors said "in this case, index h is selected from the 183 set [1-34].", are authors used all these references for index h?
Response and Action: Thanks for your valuable comment. “In this case, index h is selected from the set {1, 2, 3}.” is correct. This is modified.
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Comment 08: The references are mentioned twice in the Reference section, Edit this part and mention the reference once.
Response and Action: Thanks for your valuable comment. This is addressed and the changes are made.
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Author Response File: 
Author Response.doc
Reviewer 2 Report
This paper focuses on Stochastic Flexible Power System Expansion Planning based on Demand Response Considering Consumption and Generation Uncertainties. The generation and transmission expansion planning with considering switched capacitive banks allocation in the power system including demand response program was proposed. However, there are also several problems that the authors haven’t clearly addressed. Please find the detailed comments below.
1 Contributions is too long, suggest to cut the content and move the existing research gaps to Literature review.
2 The second point of the Contributions, Considering optimal economic, operational, and flexibility conditions, is not innovative or does not adequately reflect the special features of the work.
3 The number of uncommon abbreviations used in this paper is slightly high, which creates some obstacles for the reader.
4 The third section, Problem solution, suggests additional algorithm flow diagrams to enhance the readability of the article.
5 The proposed algorithm is described in detail, but it is not mentioned adequately in the abstract, so it is suggested to add a description of the performance of the algorithm at the abstract.
6 Table 4 and some figures in this paper can be further optimized, e.g., Figure 4 can use bar graph to make the relationship of each component more clear.
7 The structure and syntax of this paper should be further improved, and the English grammar, formatting issues and the layout of formulas need to be carefully reviewed.
Author Response
Reviewer #2:
This paper focuses on Stochastic Flexible Power System Expansion Planning based on Demand Response Considering Consumption and Generation Uncertainties. The generation and transmission expansion planning with considering switched capacitive banks allocation in the power system including demand response program was proposed. However, there are also several problems that the authors haven’t clearly addressed. Please find the detailed comments below.
Firstly, the authors would like to appreciate the respectable reviewer for their appropriate comments. The responses to your comments are provided below.
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Comment 01: Contributions is too long, suggest to cut the content and move the existing research gaps to Literature review.
Response and Action: Thanks for your valuable comment. To respond to this comment, research gaps are provided in section 1.3 under the title: Research gaps. Then, details of the proposed scheme together with the contributions are presented in section 1.4 under the title: Contributions. The changes are given as follows:
1.3. Research gaps
Based on the literature and Table 1, there are the following major research gaps in the field of PSEP:
- In most researches focusing on PSEP such as [10-19], the economic planning and technical (operation) indices of the network have been considered. However, it should be noted that WFs thanks to their low pollution and low operating costs can be an important factor in improving the economic, environmental, and power network operation. However, their presence will reduce the flexibility of the network. To compensate for this, flexibility sources such as storage and DRP are suitable approaches [9]. Although this has been stated in various studies, less research has focused on the mathematical model of flexibility, noting that to assess an index its status should be measured and this can be derived by providing a mathematical model of flexibility in the problem.
- Reactive power devices are generally able to improve the voltage profile and voltage security index in the network by controlling reactive power [17, 18], among which the capacitor bank is economically viable and cost-effective. Note, however, that if the optimal location and size are achieved for these devices, it is expected that optimal conditions will be obtained for the mentioned indices. This is achieved in the case of the capacitor bank placement problem. However, in less research such as [17], the location of reactive power devices in the PSEP problem has been considered.
- The PSEP problem includes AC-OPF equations, so it has a MINLP framework. To solve this problem, some research such as [10, 18, 19] use iterative numerical solutions or evolutionary algorithms to solve this problem. These algorithms suffer from long computational time. They also have different optimal solutions, in other words, they are not unique. Therefore, the obtained solution has a low confidence factor. Moreover, some studies, such as [11, 13, 15, and 16], have proposed a PSEP model based on DC optimal power flow (DC-OPF). Although this model has a linear formulation and following it the computational time will be low and a unique optimal solution will be obtained, variables such as voltage drop, reactive power, and power loss are eliminated in this model. Consequently, the numerical results obtained from this model will not be accurate and will have a significant computational error. To compensate for the limitations of these two approaches, some studies such as [12, 14, 17] present the PSEP model based on linearized AC-OPF. Nonetheless, there is also a significant computational error in this technique regarding some variables such as power loss.
1.4. Contributions
In this paper, to compensate for the first and second research gaps, the dynamic GTEP problem is considered by taking into account the optimal location of switched capacitor banks (SCBs) in a transmission network with DRP, as shown in Fig. 1. The scheme aims to minimize the total construction cost of power sources, lines, and SCBs plus the expected operation cost of sources, which is subject to AC-OPF, network flexibility constraints, and models of sources, DRPs, and SCBs. In this case, the network load and generation power of WFs are uncertainties. Therefore, in this paper, scenario-based stochastic programming (SBSP) is used to model them. This technique is also compatible with the combination of Monte Carlo simulation (MCS) and the Kantorovich method, which are used to generate and reduce scenarios, respectively. The hybrid evolutionary algorithm (HEA) based on the combination of crow search optimization (CSA) and grey wolf optimizer (GWO) is employed to solve the problem and cover the third research gap. Note that in this algorithm, updating decision variables is performed in two different processes. Therefore, the optimal solution obtained is expected to have a low standard deviation in the final response. Of course, to prove this, we can refer to solving an optimization problem using a genetic algorithm (GA) without/with mutation process [20]. According to [20], if a mutation is used in GA, a more optimal solution can be obtained because decision variables have been updated in two different processes [20]. In the end, the contributions of this paper are:
- Formulation of dynamic power system planning with the optimal location of switched capacitor bank in the power network with demand response program,
- Obtaining the optimal placement and time of installation of GUs, TLs, and SCBs while considering optimal economic, operation, and flexibility conditions, and
- Using the combined CSA and GWO solver to obtain the optimal point with low standard deviation in the final solution for the PSEP problem.
Figure 1. The proposed PSEP framework.
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Comment 02: The second point of the Contributions, Considering optimal economic, operational, and flexibility conditions, is not innovative or does not adequately reflect the special features of the work.
Response and Action: Thanks for your valuable comment. The second contribution reported in section 1.4 is modified as follows:
“Obtaining the optimal placement and time of installation of GUs, TLs, and SCBs based on the network flexibility model”
According to Table 1 and research gaps given in section 1.3, the flexibility model is less concerned in research works related to power system planning.
Table 1. Taxonomy of recent research works.
|
Solver |
Planning of switched capacitor bunk |
Flexibility modeling |
Ref. |
|
NHEA |
No |
No |
[10] |
|
Solvers for linear model |
No |
No |
[11] |
|
Solvers for linear model |
No |
No |
[12] |
|
Solvers for linear model |
No |
No |
[13] |
|
Solvers for linear model |
No |
No |
[14] |
|
Solvers for linear model |
No |
No |
[15] |
|
Solvers for linear model |
No |
No |
[16] |
|
Solvers for linear model |
Yes |
No |
[17] |
|
NHEA |
No |
No |
[18] |
|
NHEA |
No |
No |
[19] |
|
HEA |
Yes |
Yes |
Current paper |
HEA: Hybrid evolutionary algorithm, NHEA: non-HEA
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Comment 03: The number of uncommon abbreviations used in this paper is slightly high, which creates some obstacles for the reader.
Response and Action: Thanks for your valuable comment. This is addressed and necessary corrections are applied. So, most abbreviations like DA, RT, LOLE, VaR, CVaR, etc. are deleted.
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Comment 04: The third section, Problem solution, suggests additional algorithm flow diagrams to enhance the readability of the article.
Response and Action: Thanks for your valuable comment. In accordance to this comment, Fig. 2 is added to Section 3:
Figure 2. Flowchart of the CSA+GWO for solving of the proposed scheme.
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Comment 05: The proposed algorithm is described in detail, but it is not mentioned adequately in the abstract, so it is suggested to add a description of the performance of the algorithm at the abstract.
Response and Action: Thanks for your valuable comment. Note that, in this paper, similar to most of the popular papers, the general statements of the proposed scheme are provided in the Abstract. Their comprehensive details are provided in the next sections of the paper. However, in accordance with this comment, the capabilities of the algorithm and proposed scheme are added to Abstract in the revised version of the paper. The Abstract is modified as follows:
Abstract: This paper presents the generation and transmission expansion planning (GTEP) with considering switched capacitive banks (SCBs) allocation in the power system including demand response program (DRP). This scheme is based on of system flexibility. The objective function of scheme minimizes the expected planning cost that is equaled to summation of the total construction cost of SCBs, generation units (GUs) and transmission lines (TLs), and operating cost of GUs. It is consternated to AC power flow constraints, the planning-operation model of the mentioned elements, the DRP operation formulation, and the operating and flexibility limits of network. In the following, scenario-based stochastic programming is used to modeling of the uncertainty parameters such as load and renewable power of wind farms. Then, the hybrid evolutionary algorithm based on the combination of crow search algorithm and grey wolf optimizer is used to determine the optimal point with approximate unique solution. Finally, the scheme is applied on the transmission networks, the numerical results confirm the capabilities of the proposed scheme in simultaneously improving the flexibility, operation, and economic situation of the transmission network so that the hybrid algorithm achieves the optimal solution in lower computation time compared with non-hybrid algorithms. This algorithm has a low standard deviation of about 92% in the final response. The proposed scheme with optimal planning of lines, sources, and capacitor banks together with the optimal operation of the DRP succeeded to improve energy loss and voltage deviation by about 30-36% and 25-30% compared with those of power flow studies.
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Comment 06: Table 5 and some figures in this paper can be further optimized, e.g., Table 5 can use bar graph to make the relationship of each component more clear.
Response: Thanks for your valuable comment. Note that some tables such as tables 2, 4, and 5 provide different information, whose presentation requires several figures. This will lead to increased volume of the paper. Also, figures are not as capable as tables in providing readable numbers. So, some of the reports are stated in the form of tables. The authors hope that these reasons satisfy the respectable reviewer’s expectations.
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Comment 07: The structure and syntax of this paper should be further improved, and the English grammar, formatting issues and the layout of formulas need to be carefully reviewed.
Response and Action: Thanks for your valuable comment. The paper tried to observe the proposed structure of the journal. Also, to improve the quality of the paper, research gaps and contributions are provided in separate sections in Section 1. The report of this issue is given in Comment 01. Moreover, section 1.2 is modified as follows:
In this section, the dynamic GTEP formulation is expressed by considering the location model of SCBs and the operation model of DRP. This problem minimizes the total planning cost of GUs, TLs, and SCBs by considering AC-PF constraints; the planning-operating model of GUs, SCBs, and TLs; DRP operation model; and operation and flexibility limits of the network. Therefore, the optimization formulation of this scheme can be written as follows:
Objective function: The objective function of this formulation is presented in Eq. (1), which has four terms. In the terms 1-3 in this equation, the investment costs in the construction of TLs, SCBs, and GUs are presented, respectively. Note that the transmission line between buses b and l and buses l and b is the same, so in the first term of Eq. (1), the term 1/2 appears. In the last term of the equation, the expected operating cost of the GUs is formulated. This function includes the fuel cost of GUs, which has a parabolic function [14].
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(1) |
Planning constraints: The planning model of SCBs, GUs, and TLs is described in constraints (2) to (11) [14, 17]. Constraints (2)-(4) refer to the investment budget for GUs, SCBs, and TLs, respectively, where the investment budget represents the maximum capital available for the construction of these elements. In the proposed design, dynamic planning is considered for the mentioned elements. In other words, if the planning horizon is 6 years, planning is performed for smaller intervals such as 2 years. In this case, index h is selected from the set {1, 2, 3}. The elements of this set refer to the first to third planning period, where the planning step is 2 years. Now, Eqs. (5)-(7) represent a logical constraint stating that the referred power elements can be installed only in one planning period. In other words, each element can be constructed only in one of the first to third periods. Constraints (8) to (10) also determine the presence of GUs, SCBs, and TLs in the planning periods, respectively. For example, if an element is constructed at h = 2, then that binary variable corresponding to its presence at h = 1 is zero, and for other values, ​​u has a value of unity. Finally, in Eq (11) a logical constraint is used which indicates that the TL between buses b and l is the same as the TL between buses l and b.
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Power flow constraints: The AC-PF constraints of the system are presented in the Eqs. (12) to (15) [45-47], which expresses the power balance (active and reactive) for a bus, (12)-(13), and the power (active and reactive) passing from TL, (14)-(15) [48-50]. Note, however, that Eqs. (14)-(15) represent a combined operation and planning model of TL so that if the binary variable uL is equal to unity, TL is exploited based on Eqs. (14) and (15). However, if uL = 0, TL is not present in the network, then there is no operating model for it.
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(14) |
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(15) |
Model of GUs and SCBs: In the following, the combined planning-operation model of GUs and SCBs is formulated in (16) - (18) and (19)-(20), respectively. Constraints (16) and (17) refer to the GU capability curve [51], which expresses the controllable range of power (active and reactive) in the GU. Constraint (18) is used only for renewable GUs such as WF [6]. This relationship points to the fact that renewable GUs inject active power into the transmission system, where it equal to their upper capacity in proportion to the weather term ( ) [6]. This is because the operating cost of these types of GUs is very low [52]. In constraints (19)-(20), the injected reactive power of SCBs into the transmission network is calculated by Eq. (19), and its step performance limit is formulated in Eq. (20). In these constraints, the operation model of GU (SCB) is applicable only if uG = 1 (uSCB = 1).
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(16) |
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(17) |
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(18) |
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(19) |
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(20) |
Formulation of DRP: Next, the operating formulation of DRP is given in (21)-(22) [53]. Equation (21) indicates the controllable range of power of consumers participating in DRP. Constraints (22) also guarantee that the reduced energy of these consumers in a certain operating period will be provided by the grid during other operation hours. In this DRP, consumers are expected to participate in the plan to shift their energy consumption at peak load period to off-peak time. This is because it is commensurate with minimizing the fuel cost of GUs in the last part of Eq. (1). So that if the load decreases during peak hours, GUs with low fuel costs will feed the consumers. Also, because energy demand is low during off-peak hours, increased consumption during this period may be met by inexpensive GUs. This corresponds to minimizing the operating costs of GUs.
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(21) |
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(22) |
Network limits: Transmission network operation and flexibility constraints are formulated in (23)-(24) [54] and (25) [7], respectively. Operation limitations of the network include the limit of apparent power passing through the TL, (23), and the limit of the voltage magnitude of the buses, (24). High voltage limits are used to prevent insulation damage to network equipment due to overvoltage. Its lower limit is also used to prevent mains shut down due to severe voltage drop in the network [54]. In this section, in order to establish the desired flexibility in the transmission network, a flexibility constraint such as constraint (25) is used for non-renewable GUs. Note that it is expected that the results of real-time and day-ahead operation of a system will not be the same in the presence of renewable GUs, which is due to a forecasting error in the output active power of these types of GUs. This is known as low system flexibility, which can lead to damage to the network due to an imbalance between demand and supply at the real-time scheduling. To compensate for this, flexibility sources such as DRP [7] or storage systems [55-59] must be able to reduce the power fluctuations of renewable GUs in real-time scheduling. In this condition, the desired flexibility is established in the network [7]. However, considering this requires a mathematical formulation of flexibility in the proposed framework, this section presents the constraint (25). In this case, the deviation of the generated active power for non-renewable GUs in scenario s from the scenario related to the deterministic problem (with the forecasted values ​​of the uncertainty parameters assumed equal to the first scenario) should be less than DF, which DF represents flexibility tolerance. If DF = 0, then 100% flexibility for the network can be evaluated. Therefore, it is expected that with this flexibility model, the results of the real-time scheduling will be close to the results in day-ahead operation.
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(23) |
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(24) |
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(25) |
Regarding this part of the comment: “English grammar, formatting issues and the layout of formulas”, modifications are made as much as possible.
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Author Response File: Author Response.doc
Round 2
Reviewer 1 Report
The author revised the paper well and it can be accepted.
