Wind Turbines Electro-Mechanical System: Mathematical Modeling and Geometric Controllability

In recently published papers, we introduced mathematical modeling and analysis for wind turbines dynamics. The published results provided analytical proofs of boundedness, existence and uniqueness for the electro-mechanical system of wind turbines under the control limits. Also, we provided stability and simulation results for the system in challenging physical conditions, such as sudden wind speed changes or drop in the impedance of the power grid. Currently, we are working on formulating the wind turbines system in geometric framework to study controllability of the system in difficult physical situations. Differential geometric tools can capture some of the missing information in regular linearization analyses. We are searching for possible unconventional directions or interactions in the vector fields of the system using Geometric control theory. These new unconventional directions may lead to new control strategies or designs to improve our use and production of wind energy. In our presentation, we summarize the published work and the current progress in our research.