Semi-Definite Programming for Power Output Control in a Wind Energy Conversion System

One of the key issues in wind energy is the control design of the wind energy conversion system to achieve an expected performance under both the power system and mechanical constraints which are subject to stochastic wind speeds. Quadratic control methods are widely used in the literature for such purposes, e.g., linear quadratic Gaussian and model predictive control. In this paper, the chance constraints are considered to address the stochastic behavior of the wind speed fluctuation on control inputs and system outputs instead of deterministic constraints in the literature. Also considered are the two different models: the first one assumes that the wind speed measurement error is Gaussian, where the chance constraints can be reduced to the deterministic constraints with Gaussian statistics; whereas the second one assumes that the error is norm bounded, which is likely more realistic to the practicing engineers, and the problem is formulated as a min-max optimization problem which has not been considered in the literature. Then, both of the models are formulated as semi-definite programming optimization problems that can be solved efficiently with existing software tools. Finally, the simulation results are provided to demonstrate the validity of the proposed method.