Distributed Extremum Seeking Control for Wind Farm Power Maximization

A cooperative extremum seeking control technique is employed to overcome the need for accurate models of aerodynamic wake interactions among wind turbines thereby providing an effective technique for farm wide power capture. In this paper, a time-varying extremum seeking control (TVESC) approach is employed in a distributed fashion to maximize the power production of an array of wind turbines under constant and varying free stream wind speeds and directions. Each wind turbine (identified as an agent) has access to the measurement of its unknown local power generation. The goal is to maximize the unknown total power capture in the wind farm. A cooperative approach is employed where the agents work together to maximize this overall objective function. This approach requires every agent to exchange information with its neighbours over an undirected connected communication network. Each agent is also expected to estimate the mean of the overall cost function and this is achieved using a dynamic average consensus estimator. The dynamics of each agent's cost estimate is parametrized and a parameter estimation routine is used to estimate the unknown gradient information. A distributed extremum seeking controller is designed to ensure that the overall cost is maximized. This problem is tackled via numerical simulations, results are provided to show the effectiveness of this technique.