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The relation between wind speed and electrical power-the power curve-is essential in the design, management and power forecasting of a wind farm. The power curve is the main characteristic of a wind turbine, and a procedure is presented for its determination, after the wind turbine is installed and in operation. The procedure is based on both computational and statistical techniques, in situ measurements, nacelle anemometry and operational data. This can be an alternative or a complement to procedures fully based on field measurements as in the International Electrotechnical Commission standards, reducing the time and costs of such practices. The impact of a more accurate power curve was measured in terms of the prediction error of a wind power forecasting system over 1 year of operation, whereby the methodology for numerical site calibration was presented and the concepts of ideal power curve and nacelle power curve introduced. The validation was based on data from wind turbines installed at a wind farm in complex topography, in Portugal, providing a real test of the technique presented here. The contribution of the power curve to the wind power forecasting uncertainty was found to be from 10% to 15% of the root mean square error.

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Abstract. We address sampled-data nonlinear Model Predictive Control (MPC) schemes, in particular we address methods to e ciently and accurately solve the underlying continuous-time optimal control problems (OCP). In nonlinear OCPs, the number of discretization points is a major factor a↵ecting the computational time. Also, the location of these points is a major factor a↵ecting the accuracy of the solutions. We propose the use of an algorithm that iteratively finds the adequate timemesh to satisfy some pre-defined error estimate on the obtained trajectories. The proposed adaptive time-mesh refinement algorithm provides local mesh resolution considering a time-dependent stopping criterion, enabling an higher accuracy in the initial parts of the receding horizon, which are more relevant to MPC. The results show the advantage of the proposed adaptive mesh strategy, which leads to results obtained approximately as fast as the ones given by a coarse equidistant-spaced mesh and as accurate as the ones given by a fine equidistant-spaced mesh.

An optimal control problem with state constraints based on a SEIR model to control the spreading of infectious diseases is considered. The main purpose is apply novel theoretical results to successfully validate the numerical solution, computed via direct method. The problem has simple but yet interesting features that we explore in our analysis. Of particular interest is the fact that the state constraint is of order one and that the solution is normal.

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