Delegates are invited to meet and discuss with the poster presenters in this topic directly after the session 'Advanced control concepts' taking place on Wednesday, 12 March 2014 at 11:15-12:45. The meet-the-authors will take place in the poster area.

**Marc Guadayol**ALSTOM EnergÃas Renovables EspaÃ±a S.L., Spain

Co-authors:

Marc Guadayol (1)

^{F}

^{P}Pep Prats (5) Manfred Morari (4)

(1) ALSTOM EnergÃas Renovables, Barcelona, Spain (2) ETH, ZÃ¼rich, Switzerland (3) Automatic Control Laboratory ETH, ZÃ¼rich, Switzerland (4) Automatic Control Laboratory, Department of Information Technology and Electrical Engineering, ETH , ZÃ¼rich, Switzerland (5) ALSTOM EnergÃas Renovables EspaÃ±a S.L., Barcelona, Spain

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## Presenter's biography

*Biographies are supplied directly by presenters at EWEA 2014 and are published here unedited*

NMarc Guadayol has been working in the wind industry for more than 10 years. He graduated in Physics from Universitat AutÃ²noma de Barcelona. He works in ALSTOM EnergÃas Renovables EspaÃ±a S.L. He is now a PhD candidate at ETH ZÃ¼rich. His redsearch interests include Model Predictive Control and Wind Turbine Control.

## Abstract

**Thrust constraints using model predictive control
****Introduction**

This work addresses the problem of reducing low-frequency blade and tower loads using the natural ability of MPC to enforce constraints. The proposed approach uses blade root load measurements, combines them and applies a linear MPC controller to limit the thrust force applied to the rotor. A useful variation imposes a constraint on the thrust rate. The simulation results show that the proposed methods can be very effective to reduce blade and tower loads, which can lead to significant cost reduction in wind turbines.

**Approach**

Model Predictive Control (MPC) is a control formalism that uses an explicit model of the plant and optimizes future behavior in real-time. Recently, MPC for wind turbine control has attracted the attention of several authors, either in linear [1], [2] or nonlinear form [3], [4] , and usually combined with LIDAR [5], [6], trailing edge flaps [7], [8], floating wind turbines [9] or load reduction [10], [11]. This paper focuses on the ability of MPC to enforce constraints, which can be very effective to reduce structural loads.

The first objective of the present work has been the design of a MPC controller with a similar performance to that of a conventional controller. The inputs of this basic setup are collective pitch demand and generator torque demand, u=[Î¸ T_g ], while the measurements are generator speed and tower fore-aft acceleration, y=[Ï‰g acc] . As not all the states can be measured, a standard Kalman Filter (KF) is used to estimate them.

To track the steady-state curve in all operating conditions, the plant has been augmented with a constant disturbance model, following the offset-free tracking formalism that is quite common in the linear MPC framework [12], [13], [14].

This work uses linear models, derived as a linearization of the equations of motion of a high-fidelity aeroelastic code. The model has been simplified and only the following degrees of freedom have been retained: flexible drive train, tower 1st fore-aft motion, pitch actuator model, and 1st collective flapwise bending mode.

A common formulation of MPC using linear models results in a Quadratic Program (QP)

where x is the state of the turbine, d is an external disturbance, eis a slack variable, xt and ut are the state and input of the target.

To achieve a desired frequency response it may be necessary to augment the basic model with additional states. This has been described for LQR controllers in [15], [16]. As an example, Figure 1 shows the result of an aeroelastic simulation with and without drive train damping by the MPC controller, and the method effectively reduces drive train oscillations.

Figure 1 Effect of Drive Train Damping using MPC controller

**Main body of abstract**

Once the basic algorithm has been defined, the main challenge is to benefit from those features of MPC which are difficult to implement using a conventional controller. One of these features could be a LIDAR measurement, which has already been discussed by several authors and will not be considered in this paper. By contrast, our main goal will be the reduction of the maximum thrust force. The motivation is that a significant reduction in the maximum thrust is expected to give a corresponding decrease in tower and blade loads.

Blade load measurements, using strain gauges for example, are common in algorithms that use Individual Pitch Control [17]. Only collective pitch is considered in this study, while individual pitch could be a further development of the method. The controller receives the blade root load measurements and pre-processes them if necessary. Then computes the three out-of-plane blade root loads and adds them. The model output is then extended with this signal and a maximum constraint is enforced by the MPC controller. Although the sum of the out-of-plane blade root loads is not the thrust force, it is closely related to it, so with some abuse of notation we will sometimes refer to this scheme as a thrust constraint.

As is common in MPC literature, constraints on outputs or states are implemented as soft constraints. The reason for that is that a big disturbance can easily push the wind turbine out of the feasible region, causing a solver failure. For this reason, such constraints are usually relaxed by some amount Ïµ, which is then heavily weighted in the objective function.

To assess the performance of the algorithm, realistic simulations with a commercial high fidelity aeroelastic code have been run. The simulations used a model of an ALSTOM Eco100 3MW wind turbine, according to the standard IEC 61400-1 Edition 2. Figure 2 shows the turbulent wind speed that is used in the rest of figures of this paper. Figures 3, 4, 5, 6 compare the performance of an MPC controller with thrust constraints (in red) to that of a conventional controller (in blue). First of all, note that the MPC controller has a smoother power and a tighter speed regulation. This is essentially due to a slightly different basic design, not to the new constraint. As a result of the thrust constraint, the tower base load is bounded, and the MPC controller is forced to increase the pitch demand. Note how the thrust force is limited, justifying the name of thrust constraint. The negative effect is an energy reduction, especially with low values of the constraint. Table 1 shows a summary of the energy and main loads affected by the algorithm. A reduction of 7% in tower base My Damage Equivalent Loads (DEL) is achieved at the expense of a 0.5% reduction in Annual Energy Production (AEP).

Table 1. Simulation results of energy and loads affected by the maximum thrust constraint algorithm (complete DLC 1.2 cases)

Low levels of maximum thrust can lead to a decrease in energy production and a careful design requires a good tradeoff between load reduction and power loss. To improve such tradeoff, alternative configurations have been considered. The first one includes a minimum thrust constraint, which is not as straightforward, but can also reduce fatigue loads. However, minimum constraints need to be handled with care because they can cause undesired behaviors, like a rotor speed increase. A more promising variation employs thrust rate constraints, which prevents structural damage due to sudden wind gusts but with a limited power loss in low turbulence winds. Figure 8 shows the tower base bending moment for such algorithm, where it is clearly seen how the rate of the load is limited. Figure 7 illustrate how tight thrust rate constraints also result in a relaxed generator speed control.

The MPC controller solves a quadratic program (QP) online, using a sampling time of 50ms. The simulations were run using FORCES [18], achieving computing times around 10ms.

Figure 2. Wind speed

Figure 3. Generator Speed response with Max Thrust constraint

Figure 4. Electrical Power responsewith Max Thrust constraint

Figure5. Tower Base My response with Max Thrust constraint

Figure 6. Thrust force response Max Thrust constraint

Figure 7. Generator Speed response with Thrust Rate constraints

Figure 8. Tower Base My response with Thrust Rate constraints

**Conclusion**

A linear MPC controller has been designed, implemented and tested in an aeroelastic simulation environment. The controller performs slightly better than a conventional one and, most importantly, enables additional features that are difficult to implement with a more conventional controller. This work has focused on one of such features: directly enforcing load constraints.

The simulation results confirm that the proposed algorithm, which measures the sum of the out-of-plane blade root loads and enforces a constraint on them, is a promising technique to reduce structural loads. However, an optimal tradeoff between load reduction and energy production has to be found. Even with such inconvenient, the method can be considered as a useful technique to increase design flexibility.

As a maximum thrust constraint has non-negligible impact on the power production, different alternatives have been proposed. Thrust rate constraints seem particularly promising, because they do not affect significantly the power curve. However, other design limits can then be affected, like an increase in rotor speed, and a practical implementation of these algorithms requires some form of constraint prioritization.

Computational times, usually a major drawback of MPC, are well within current computer capabilities, and with an adequate implementation and a modern processor, real-time requirements can be met without problems.

Although the linear MPC controller has been successful in limiting the tower loads, an alternative can be a Nonlinear MPC (NMPC) controller, as proposed by different authors. An advantage of NMPC is that in principle, it could be able to limit the thrust without directly measuring the loads, as suggested in [10], but then the model used by the controller needs to be very accurate, because a significant model mismatch can lead to high loads or low power production. On the other side, the formulation with Linear MPC (LMPC) is its flexibility: it is quite simple to increase the complexity of the model, at the expense of a moderate increase in computing time.

**Learning objectives**

Using a well-established linear MPC formalism, it is possible to control a wind turbine with similar performance than a conventional controller.

MPC can easily include additional control features that further improve performance, like constraints.

An estimation of the thrust axial force is derived using blade loads and a limit is imposed by the MPC controller. Simulations clearly show the potential of this method for load reduction. Many variations of this setup are possible.

**References**

[1] L. Henriksen, Â«Model predictive control of a wind turbine,Â» Lyngby, Denmark, 2007.

[2] A. KÃ¶rber y R. King, Â«Model Predictive Control for Wind Turbines,Â» de EWEC, Warsaw. Poland, 2010.

[3] A. KÃ¶rber y R. King, Â«Nonlinear Moel Predictive Control for Wind TurbinesÂ».

[4] C. L. Bottasso y A. Croce, Â«Advanced Control Laws for Variable-Speed Wind Turbines and Supporting Enabling Technologies, Scientific Report DIA-SR 09-0,Â» Politecnico di Milano, Milano, 2009.

[5] D. Schlipf, D. J. Schlipf y M. KÃ¼hn, Â«Nonlinear model predictive control of wind turbines using LIDAR,Â» Wind Energy, 2012.

[6] M. Soltani, R. Wisniewski, P. Brath y S. Boyd, Â«Load reduction of wind turbines using receding horizon control,Â» de International conference on control applications (CCA), Denver, CO, USA, 2011.

[7] T. Barlas, G. van der Veen y G. van Kuik, Â«Model predictive control for wind turbines with distributed active flaps: incorporating inflow signals and actuator constraints,Â» Wind Energy, 2011.

[8] D. Castaignet, N. K. Poulsen, T. Buhl y J. J. Wedel-Heinen, Â«Model Predictive Control of Trailing Edge Flaps on a Wind Turbine blade,Â» de American Control Conference , San Francisco, CA, USA, 2011.

[9] D. Schlipf, F. Sandner, S. Raach, D. Matha y P. W. Cheng, Â«Nonlinear Model Predictive Control of FloatingWind Turbines,Â» de 23rd International Offshore and Polar Engineering, Anchorage, Alaska, USA, 2013.

[10] J. Schuurmans, E. Nederkoom, S. Kanev, R. Rutteman y E. Nguyen, Â«Optimised Aerodynamics and Control by Nonlinear Model based Predictive Control,Â» de EWEA, Vienna, Austria, 2013.

[11] R. A. Santos, Damage mitigating control for wind turbines, PhD Thesis, University of Colorado at Boulder, 2007.

[12] U. MÃ¤der, F. Borrelli y M. Morari, Â«Linear offset-free Model Predictive Control,Â» Automatica, vol. 45, nÂº 10, pp. 2214-2222, 2009.

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[14] K. R. Muske y T. A. Badgwell, Â«Disturbance modeling for offset-free linear model predictive control,Â» Journal of Process Control, vol. 12, nÂº 5, pp. 617-632, 2002.

[15] . B. Anderson y J. Moore, Optimal control: linear quadratic methods, Englewood Cliffs, New Jersey: Prentice Hall, 1990.

[16] N. K. Gupta, Â«Frequency-shaped cost functionals - Extension of linear-quadratic-Gaussian design methods,Â» Journal of Guidance Control and Dynamics, vol. 3, nÂº 6, pp. 529-535, 1980.

[17] E. Bossanyi, Â«Individual Blade Pitch Control for Load Reduction,Â» Wind Energy, nÂº 6, pp. 119-128, 2003.

[18] A. Domahidi, A. Zgraggen, M. Zeilinger, M. Morari y C. Jones, Â«Efficient interior point Methods for Multistage Problems Arising in Receding Horizon Control,Â» de Conference on Decision and Control (CDC), Maui, HI, USA, 2012.

[19] A. Kumar y K. Stol, Â«Scheduled model predictive control of a wind turbine,Â» de 47th AIAA Aerospace Sciences Meeting, 2009.

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