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Gros S.,Optimization in Engineering Center | Chachuat B.,Imperial College London
Wind Energy | Year: 2014

This paper describes an optimization-based approach to reducing extreme structural loads during rapid or emergency shutdown of multi-megawatt wind turbine generators. The load reduction problem is cast into an optimal control formulation, and a simple, low-order model is developed in order for this optimization problem to be tractable in reasonable time using state-of-the-art numerical methods. To handle the variations in wind speed and turbulence inherent to wind turbine operation as well as the presence of model mismatch, a real-time optimization strategy based on fast sensitivity updates is also considered, whose online computational burden is limited to the repeated solution of quadratic programs that are designed offline. The low-order model and both the open-loop and closed-loop optimal control strategies are validated against a high-fidelity model in the simulation environment Bladed™ for an industrial 3 MW wind turbine. Under favorable shutdown scenarios, i.e. when the wind turbine is operating properly and the actuators and sensors are not faulty, large reductions of the first compressive peak and subsequent compressive/tensile peaks of the tower load pattern are obtained at various above-rated wind speeds compared with normal pitch control shutdown. Extension to more challenging shutdown scenarios are also discussed. Copyright © 2013 John Wiley & Sons, Ltd. Copyright © 2013 John Wiley & Sons, Ltd. Source


Sternberg J.,Catholic University of Leuven | Goit J.,Optimization in Engineering Center | Gros S.,Catholic University of Leuven | Meyers J.,Optimization in Engineering Center | Diehl M.,Catholic University of Leuven
IFAC Proceedings Volumes (IFAC-PapersOnline) | Year: 2012

Power-generating kite systems extract energy from the wind by periodically pulling a generator on the ground while flying fast in a crosswind direction. Kite systems are intrinsically unstable, and subject to atmospheric turbulences. As an alternative to closed-loop control, this paper investigates the open-loop stabilization and robustification of a kite system using techniques based on the solution of Lyapunov differential equation. A wind flow is computed as a solution to a time-dependent three dimensional Navier-Stokes equation. Open-loop stable trajectories for the power-generating kite system are computed based on the statistical properties of the wind field, and are robustified with respect to the system constraints. The stability and robustness of the resulting trajectories are assessed by simulating the system using the computed time- and space-dependent turbulent wind flow. © 2012 IFAC. Source


Houska B.,Optimization in Engineering Center | Diehl M.,Optimization in Engineering Center
Mathematical Programming | Year: 2013

In this paper, we present a novel sequential convex bilevel programming algorithm for the numerical solution of structured nonlinear min-max problems which arise in the context of semi-infinite programming. Here, our main motivation are nonlinear inequality constrained robust optimization problems. In the first part of the paper, we propose a conservative approximation strategy for such nonlinear and non-convex robust optimization problems: under the assumption that an upper bound for the curvature of the inequality constraints with respect to the uncertainty is given, we show how to formulate a lower-level concave min-max problem which approximates the robust counterpart in a conservative way. This approximation turns out to be exact in some relevant special cases and can be proven to be less conservative than existing approximation techniques that are based on linearization with respect to the uncertainties. In the second part of the paper, we review existing theory on optimality conditions for nonlinear lower-level concave min-max problems which arise in the context of semi-infinite programming. Regarding the optimality conditions for the concave lower level maximization problems as a constraint of the upper level minimization problem, we end up with a structured mathematical program with complementarity constraints (MPCC). The special hierarchical structure of this MPCC can be exploited in a novel sequential convex bilevel programming algorithm. We discuss the surprisingly strong global and locally quadratic convergence properties of this method, which can in this form neither be obtained with existing SQP methods nor with interior point relaxation techniques for general MPCCs. Finally, we discuss the application fields and implementation details of the new method and demonstrate the performance with a numerical example. © 2012 Springer and Mathematical Optimization Society. Source


Houska B.,Optimization in Engineering Center | Diehl M.,Optimization in Engineering Center
Proceedings of the IEEE International Conference on Control Applications | Year: 2010

In this paper we formulate and solve optimal control problems for power generating kite systems. Here, the kite generates energy by periodically pulling a generator on the ground while flying fast in a crosswind direction. We are searching for an intrinsically open-loop stable trajectory such that the kite generates as much power as possible without needing feedback, while neither the kite nor the cable should touch the ground in the presence of wind turbulence. As the wind turbulences are unknown, robustness aspects need to be taken into account. The formulation of the associated optimal control problem makes use of periodic Lyapunov differential equations in order to guarantee local open-loop stability while robustness aspects are regarded in a linear approximation. The main result of this paper is that open-loop stable kite orbits exist and that open-loop stability only costs approximately 23% compared to the power-optimal unstable orbit. © 2010 IEEE. Source


Houska B.,Optimization in Engineering Center | Diehl M.,Optimization in Engineering Center
Proceedings of the IEEE International Symposium on Computer-Aided Control System Design | Year: 2010

In this paper, we discuss robust optimal control techniques for dynamic systems which are affine in the uncertainty. Here, the uncertainty is assumed to be time-dependent but bounded by an L-infinity norm. We are interested in finding a tight upper bound for the worst case excitation of the inequality state constraints requiring to solve a parameterized lower-level maximization problem. In this paper, we suggest to replace this lower level maximization problem by an equivalent minimization problem using a special version of modified Lyapunov equations. This new reformulation offers advantages for robust optimal control problems where the uncertainty is time-dependent, i.e. infinite dimensional, while the inequality state constraints need to be robustly regarded on the whole time horizon. © 2010 IEEE. Source

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