the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 May 2023
Turbine scaling for offshore wind farms
Michiel Bastiaan Zaaijer
Dominic von Terzi
Abstract. Large-scale exploitation of offshore wind energy is deemed essential to provide its expected share to electricity needs of the future. To achieve the same, turbine and farm-level optimizations play a significant role. Over the past few years, the growth in the size of turbines has massively contributed to the reduction in costs. However, growing turbine sizes come with challenges in rotor design, turbine installation, supply chain, etc. It is, therefore, important to understand how to size wind turbines when minimizing the Levelized Cost of Electricity (LCoE) of an offshore wind farm. Hence, this study looks at how the rated power and rotor diameter of a turbine affect various turbine and farm-level metrics and uses this information in order to identify the key design drivers and how their impact changes with setup. A Multi-disciplinary Design Optimization and Analysis (MDAO) framework is used to capture the trade-offs between various disciplines of the offshore wind farm. A baseline case, for a typical setup in the North Sea, is defined where LCoE is minimized for a given farm power and area constraint with the IEA 15 MW reference turbine as a starting point. It is found that the global optimum design, for this baseline case, is a turbine with a rated power of 15 MW and a rotor diameter of 222 m. This is already close to the state-of-the-art designs observed in the industry and close enough to the starting design to justify the applied scaling. A sensitivity study is also performed that identifies the design drivers and quantifies the impact of model uncertainties, technology/cost developments, varying farm design conditions, and different farm constraints on the optimum turbine design. To give an example, certain scenarios, like a change in the wind regime or the removal of farm power constraint, result in a significant shift in the scale of the optimum design and/or the specific power of the optimum design. Redesigning the turbine for these scenarios is found to result in an LCoE benefit of the order of 1–2 % over the already optimized baseline. The work presented here gives insights to designers, project developers, and policy makers as to how their decision may impact the optimum turbine scale.
- Preprint
(9788 KB) - Metadata XML
- BibTeX
- EndNote
Mihir Kishore Mehta et al.
Status: closed
- RC1: 'Comment on wes-2023-39', Anonymous Referee #1, 05 Jul 2023
-
RC2: 'Comment on wes-2023-39', Anonymous Referee #2, 05 Sep 2023
This manuscript examines contributions and interactions of two simple design varaibles, namely turbine rated power and rotor diameter, concerning various metrics at both the turbine and farm levels in the offshore wind farm scaling problem. The aim is to recognize the pivotal design drivers and comprehend their influence based on the configuration, their performance metrices, and their sensitivities. An MDAO framework was employed to assess trade-offs within different disciplines. The study focused on determining the LCoE regarding the optimum turbine size, uncertainty and model behaviors, and farm-level constraints.
The reviewer recommend a major revision to this manuscript, considering the following comments and items to improve:
The title of the paper does not convey the core contribution of this paper. Please be specific to include what authors' contributions to the research community are, besides what field authors' are working in.
The scientific implications of this study include the use of MDAO framework in the system-wide perspective of the wind farm design problem. Findings suggest that optimum specific power has different sensitivities to conditions and scale of the farm. Some findings may inform policy-makers and wind farm developers useful insights. However, the study itself is highly simplified and the design variables are highly limited. Thus, the reviewer think that this study is an exploratory work that provides the potential possibilities of application of MDAO in the large-scale wind farm design problems. The authors are suggested to clearly express this limitation in the context of paper scope.
In general, the reviewer views this manuscript missing many important information about modeling side. Please provide modeling details. All models used in this work are expressed in some function f, without any detail. Important models need to be articulated in the main content of the manuscript. If model is too large to be included, Appendix may be used. Without model details, the paper has little meanings to the research community.
RNA is a nested sub-optimization problem, as given in Fig. 1. However, in the XDSM, objective function for this optimization sub-problem is unclear. Also, which analysis model reurns objective function value (or quantities used for calculating that) is unclear.
It is obvious that the overall system-level design variables are P and D. However, for the RNA optimization sub-problem, what are the design variables, and how that connects to the system-level problem?
Farm-level analysis model is not shown clearly. What factors drive difference in the objective function, when farm area, number of turbines, and each turbine scale changes? Within the XDSM given in Fig. 1, information regarding this aspect is largely missing.
The XDSM given in Fig. 1 does not provide enough detail about models, how models interact with each other, and what information is exchanged between models. Please refer to the original XDSM paper (Lambe and Martins, 2012) and follow the widely-accepted XDSM conventions.
Regarding Fig. 2(b), is there an identifiable point with minimum LCoE on the response surface? Also, please explain meaningful observations from this plot. The reviewer thinks that important interpretation on the observations here is largely missing.
In Eq. (6), N_T is discrete variable. How this discrete variable is incorporated in the optimization problem? Did the authors used mixed integer programming method to incorporate the discrete variables, used relaxation method to solve discrete problem in the continuous variable framework, or completely enumerated all possible discrete value options?
In the AEP calculation, can you provide details on how the wake superposition and deficit are calculated with which wake models? Please also provide model parameters used in the farm-level wake calculations.
The case studies involve an hypothetical site location with assumed environmental conditions in a stochastic manner. Please provide how these hypothetical site conditions are assumed or derived. If there is a reference for the probabilistic data, please provide a reference. Please also provide how much these hypothetical conditions represent the actual North Sea conditions in the real world, as the authors claimed the condition to be the hypothetical site in the North Sea.
Regarding Eq. (15), (17), (18), the reviewer cannot understand the meanings of these equations. First of all, the equations are wrong. \partial C / \partial D \partial P is mathematically not correct way for the second order partial derivatives. Please revisit these equations, and provide correct equations. Also, the reviewer cannot understand the physical meaning of the second-order partial derivatives in the context of gradient. They can be vector quantities with first-order partial derivatives to represent gradient. Or, they can represent Hessian in the context of positive definitiveness of the response surface. Eq. (15), (17), (18) do not represent either of them, and the reviewer cannot understand their meanings.
Please use the same mathematical style throughout the entire manuscript. Check styles of Eq. (15)-(18), in comparison to Eq. (7). E.g., AEP, LCoE should not be italicized as they are not mathematical symbols, but abbreviated word representing quantities. Follow the style used in Eq. (7) for the entire manuscript.
Check subscript styles of Eq. (17)-(18). "turbine", "other", "support", "wake", ..., they also need to be non-italized as they are not symbols. Follow the same style used in earlier equations, e.g., Eq. (7)-(14).
Regarding Fig. 10(b), why markers represent values in certain design directions only? They can have values in the entire D and P plane. Also, why the directions are different for each quantitie of interest? Please provide details of the authors' reasoning for the decisions.
Citation: https://doi.org/10.5194/wes-2023-39-RC2 - AC1: 'Comment on wes-2023-39', Mihir Mehta, 25 Sep 2023
Status: closed
- RC1: 'Comment on wes-2023-39', Anonymous Referee #1, 05 Jul 2023
-
RC2: 'Comment on wes-2023-39', Anonymous Referee #2, 05 Sep 2023
This manuscript examines contributions and interactions of two simple design varaibles, namely turbine rated power and rotor diameter, concerning various metrics at both the turbine and farm levels in the offshore wind farm scaling problem. The aim is to recognize the pivotal design drivers and comprehend their influence based on the configuration, their performance metrices, and their sensitivities. An MDAO framework was employed to assess trade-offs within different disciplines. The study focused on determining the LCoE regarding the optimum turbine size, uncertainty and model behaviors, and farm-level constraints.
The reviewer recommend a major revision to this manuscript, considering the following comments and items to improve:
The title of the paper does not convey the core contribution of this paper. Please be specific to include what authors' contributions to the research community are, besides what field authors' are working in.
The scientific implications of this study include the use of MDAO framework in the system-wide perspective of the wind farm design problem. Findings suggest that optimum specific power has different sensitivities to conditions and scale of the farm. Some findings may inform policy-makers and wind farm developers useful insights. However, the study itself is highly simplified and the design variables are highly limited. Thus, the reviewer think that this study is an exploratory work that provides the potential possibilities of application of MDAO in the large-scale wind farm design problems. The authors are suggested to clearly express this limitation in the context of paper scope.
In general, the reviewer views this manuscript missing many important information about modeling side. Please provide modeling details. All models used in this work are expressed in some function f, without any detail. Important models need to be articulated in the main content of the manuscript. If model is too large to be included, Appendix may be used. Without model details, the paper has little meanings to the research community.
RNA is a nested sub-optimization problem, as given in Fig. 1. However, in the XDSM, objective function for this optimization sub-problem is unclear. Also, which analysis model reurns objective function value (or quantities used for calculating that) is unclear.
It is obvious that the overall system-level design variables are P and D. However, for the RNA optimization sub-problem, what are the design variables, and how that connects to the system-level problem?
Farm-level analysis model is not shown clearly. What factors drive difference in the objective function, when farm area, number of turbines, and each turbine scale changes? Within the XDSM given in Fig. 1, information regarding this aspect is largely missing.
The XDSM given in Fig. 1 does not provide enough detail about models, how models interact with each other, and what information is exchanged between models. Please refer to the original XDSM paper (Lambe and Martins, 2012) and follow the widely-accepted XDSM conventions.
Regarding Fig. 2(b), is there an identifiable point with minimum LCoE on the response surface? Also, please explain meaningful observations from this plot. The reviewer thinks that important interpretation on the observations here is largely missing.
In Eq. (6), N_T is discrete variable. How this discrete variable is incorporated in the optimization problem? Did the authors used mixed integer programming method to incorporate the discrete variables, used relaxation method to solve discrete problem in the continuous variable framework, or completely enumerated all possible discrete value options?
In the AEP calculation, can you provide details on how the wake superposition and deficit are calculated with which wake models? Please also provide model parameters used in the farm-level wake calculations.
The case studies involve an hypothetical site location with assumed environmental conditions in a stochastic manner. Please provide how these hypothetical site conditions are assumed or derived. If there is a reference for the probabilistic data, please provide a reference. Please also provide how much these hypothetical conditions represent the actual North Sea conditions in the real world, as the authors claimed the condition to be the hypothetical site in the North Sea.
Regarding Eq. (15), (17), (18), the reviewer cannot understand the meanings of these equations. First of all, the equations are wrong. \partial C / \partial D \partial P is mathematically not correct way for the second order partial derivatives. Please revisit these equations, and provide correct equations. Also, the reviewer cannot understand the physical meaning of the second-order partial derivatives in the context of gradient. They can be vector quantities with first-order partial derivatives to represent gradient. Or, they can represent Hessian in the context of positive definitiveness of the response surface. Eq. (15), (17), (18) do not represent either of them, and the reviewer cannot understand their meanings.
Please use the same mathematical style throughout the entire manuscript. Check styles of Eq. (15)-(18), in comparison to Eq. (7). E.g., AEP, LCoE should not be italicized as they are not mathematical symbols, but abbreviated word representing quantities. Follow the style used in Eq. (7) for the entire manuscript.
Check subscript styles of Eq. (17)-(18). "turbine", "other", "support", "wake", ..., they also need to be non-italized as they are not symbols. Follow the same style used in earlier equations, e.g., Eq. (7)-(14).
Regarding Fig. 10(b), why markers represent values in certain design directions only? They can have values in the entire D and P plane. Also, why the directions are different for each quantitie of interest? Please provide details of the authors' reasoning for the decisions.
Citation: https://doi.org/10.5194/wes-2023-39-RC2 - AC1: 'Comment on wes-2023-39', Mihir Mehta, 25 Sep 2023
Mihir Kishore Mehta et al.
Mihir Kishore Mehta et al.
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 769 | 392 | 16 | 1,177 | 13 | 6 |
- HTML: 769
- PDF: 392
- XML: 16
- Total: 1,177
- BibTeX: 13
- EndNote: 6
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1