the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 Jun 2025
Adaptive economic wind turbine control
Abstract. Model predictive control (MPC) for wind turbines offers several interesting advantages over simpler techniques, as for example the direct optimization of a goal function, the inclusion of constraints, non-linear coupled dynamics, and wind preview (when available). To enable real-time execution, MPC uses a reduced order model (ROM) that approximates the dynamics of the controlled system using only a limited number of degrees of freedom. As a result, the accuracy of the ROM is often the main limit to the performance of MPC. To address this problem, an adaptive controller-internal model can reduce plant-model mismatches, potentially leading to improved performance.
This work proposes an adaptive economic nonlinear MPC (ENMPC) for wind turbines. The controller maximizes profit by optimally balancing fatigue damage cost with revenue due to power generation. The cyclic fatigue cost is formulated directly within the controller using the novel parametric online rainflow counting (PORFC) approach. PORFC provides a rigorous continuous expression of the discontinuous cyclic fatigue cost using time-varying parameters. Adaptivity is obtained by a controller-internal grey-box model that combines reduced order physical dynamics with data-driven correction terms. These are implemented via a neural network that is trained offline. Additionally, system state and disturbance estimators are included in the closed-loop controller.
The improvement in state predictions due to model adaptation is first assessed and compared with respect to the non-adapted baseline ROM in open loop. The performance of the adaptive ENMPC and the impact of a reduced plant-model mismatch is then assessed in closed loop for a reference multi-MW onshore wind turbine in a realistic simulation environment. Results show that the adaptive ENMPC yields higher economic profits at significantly lower pitch and torque travels, compared to the baseline non-adaptive ENMPC. While the enhanced closed-loop performance and economic gains of the proposed model adaptation are significant, they come at the cost of a slight increase in the computational burden of the controller.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Wind Energy Science.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.- Preprint
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Status: open (until 15 Aug 2025)
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RC1: 'Comment on wes-2025-101', Anonymous Referee #1, 30 Jul 2025
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Review of WES-2025_101
The paper investigates the use of an adaptive economic nonlinear MPC , known as ENMPC for wind turbines. The aim is to optimize turbine profit by optimising power generation while reducing fatigue damage cost. The profit-based approach is interesting to those of us who have worked on control methods to reduce turbine fatigue loads. Typically, control performance is measured by reducing DELS. The current paper seeks to take this further by replacing DELS with measurements of tower damage costs, extending earlier work by this group of authors on economic MPC. The novelty of the current contribution is enhance the ROM dynamics used for the MPC control scheme by adding a corrective term to compensate for the mismatch between the ROM and the actual wind behaviour. Studies show a 9% increase in the cumulative profit relative to an economic MPC scheme that did not include the adaptive model correction term. As such the paper contains sufficient novelty and worthwhile results to be potentially publishable.
Nonetheless there are significant limitations and issues with the proposed method that need to be further addressed
- Given the power generation term in (17), how does MPC avoid exceeding rated power in Region 3? The simulation scenario shown is Figure 6 is for a 11 m/s wind speed which is in Region 2 for the 5 MW turbine.
- The proposed method is conceptually complicated, and requires considerable computational resources to train the NN. In the given study, the FAST turbine simulator was used. There needs to be some discussion of the feasibility of training the NN on a physical turbine.
- Its not clear if the adaptive MPC controller could be implemented sufficiently rapidly for real time implementation, even with the computational resources available for simulation.
- A comparative study of profit generation should provided against a well-designed baseline controller, such as ROSCO (see Abbas et al, A reference open-source controller for fixed and floating offshore wind turbines, Wind Energy Science, 2022 ) to see if the extra computational efforts yield some meaningful performance improvement. The widely used NREL baseline controller of Wright and Fingersh, Tech. Rep. NREL/TP500-42437, 2008 should preferably be avoided as it has been convincingly superseded by ROSCO.
- Another significant limitations is that in an operational setting, profit will depend upon the prevailing power prices, but the authors have assumed a constant power to revenue factor, equivalent to assuming constant power prices. The simulation results would be a lot more convincing if real-world power prices were employed in the case study.
In some places found the paper hard to read, the following comments relate to improving clarity:
Page 5: V_w is introduced in line 122 but not defined until Line 135. There is no discussion of how wind speed is to be interpreted, is REWS intended?
In line 122, It is also interesting that the authors include the adjusted wind speed V_w - \dot(d)_{T_{FA}} in their aerodynamic torque and force component terms; given that wind speeds will be above 8 m/s in typical operating conditions, is the tower bending velocity \dot(d)_{T_{FA}} generally large enough to warrant inclusion?
In (9), why is V_w given in brackets?
In (12) its not really clear how the inputs and outputs of the NN in (10) relate to the wind turbine model. What is an activation function?
Line 165: ‘data is obtained using a high-fidelity simulation model’ but there is no discussion of which high-fidelity simulation model is used. Also the wind profiles and control inputs to compute the states of both the ROM and hi-fidelity model have not been discussed. Are the NN parameters p in (12) independent of the wind profile used?
In (14a) the functions J^{FA} and J^{SS} are not defined until (18a)-(18c), which makes this section hard to read.
Also the constraints (14c) to (14f) need more justification, since these quantities are all vectors, how can they satisfy an inequality?
Line 208: the statement ‘aims to maximize the generated profit by balancing the revenue accrued from wind power generation and cost incurred due to fatigue damage’ seems a little strange, since if the revenue and costs are balanced, the profit will be zero.
In line 218, referring to (17), we are told that ‘in this work the aerodynamic power is maximized.’ I understand this to mean w_P, used to covert to power to revenue, is assumed constant at all times. While the turnpike effect needs to be avoided ( short term power maximisation by extracting energy from the blades), such a simplifying assumption would seem to render the present study unsuitable for implementation in realistic operating scenarios where the power prices fluctuate considerably in short time intervals and are known only a short time in advance.
In Line 223, the values of c have not been defined. In (18a) we see that c can equal 1 or 2, but the physical meaning remains obscure.
In (18a), its not clear how the J^{FA} function ( and J^{SS} yields costs in revenue units (e.g dollars, euros) that can be compared with the revenue units used J^{power generation} to compute profit. In particular if t_0 is the time of commissioning a new turbine and t_end is 20 years, the expected life span of the turbine, is it true that J^{FA} + J^{SS} = a_m, the capital cost of the turbine?
Line 255: Should blade pitch rate also be subject to an inequality constraint?
In Line 288, why are \beta_g and T_g described as disturbance inputs? Are they not control inputs? Also in (20) \nu(t) is undefined.
Citation: https://doi.org/10.5194/wes-2025-101-RC1 -
RC2: 'Comment on wes-2025-101', Anonymous Referee #2, 05 Aug 2025
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This paper proposed an adaptive economic nonlinear MPC for wind turbines, which aims at reducing plant-model mismatch, and improving control performance with adaptivity. Similar with other EMPC design, the controller maximizes profits by balancing (fatigue damage) cost with revenue of power production. Adaptivity comes from the internal gray box model which is a combined physics and data-driven correction terms trained offline. This paper also showcases the improvement in state predictions compared to the regular non-adapted baseline method. The results show that the adaptive EMPC has higher economic profit with lower pitch and torque travels, compared to the baseline one. The computational cost is discussed in this paper.
In general, this paper is well organized, technically sound and presents some original contributions in adaptive EMPC of wind turbines, mainly the integration of PORFC and combined ROM and offline-trained neural network corrections to minimize the plant-model mismatch. This paper is recommended to accept after minor revisions. Below are some specific comments that can be considered in revision:
Page 1-2 Introduction: The introduction is clear, but it does not sufficiently indicate the difference of this work from existing adaptive MPC studies. The authors need to explicitly state how this work (integration of PORFC with NN-offline adaptation) advances beyond prior work on adaptive MPCs.
Page 4 equation (1): Need more clarity about the free parameter p. How is it obtained by data and how is it related to the NN’s input/output?
Page 6 equation (10): How do you choose activation function here? The author should brief explain, e.g. why a radial basis activation was chosen, and how it affects the numerical stability.
Page 6 equation (11): Does it normalize across the entire dataset or per feature per batch?
Page 7 equation (14): The objective terms (profit, fatigue cost) are introduced without scaling discussion. How these terms are weighted or normalized? What’s the rationale for chosen weights?
Page 9 equation (18): Parameters, Rm and m are introduced and used later without references or values. Add a table summarizing all parameters, their sources used for the case study.
page 16 Figure 5: The dataset size sensitivity analysis is interesting but lacks explanation of why performance plateaus at 85%. Discuss whether this is due to model saturation or just dataset redundancy.
Page 22 Figure 22: It is great to see the computational feasibility, but the absolute CPU times per control iteration are missing.
Page 24 Conclusion: while future research direction is briefly mentioned, this paper can give a more explicit discussion on potential extension, e.g. extending PORFC to other fatigue-critical components of wind turbines.
Citation: https://doi.org/10.5194/wes-2025-101-RC2
Data sets
Adaptive economic wind turbine control - Software and data Abhinav Anand and Carlo L. Bottasso https://doi.org/10.5281/zenodo.15530467
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