| 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.
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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
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.