**Wind farm control algorithms for improved power grid integration**

Growing renewable energy production is putting increased stress on traditional electric power systems. By displacing conventional power sources, wind energy is reducing participation in important ancillary services that maintain grid stability. My research focuses on developing control algorithms to provide one type of ancillary service, secondary frequency regulation, where participating power plants track a power reference signal sent by the power grid operator.

*Block diagram of controlled wind farm showing receding horizon controller (top left block), wind farm (top right block), and state estimation (bottom block).*

We use a model-based receding horizon controller (also known as model predictive control) to track a secondary frequency regulation signal. Large eddy simulations (LES) are used as a computational test bed to test the performance of the control algorithm. Closed-loop feedback through ensemble Kalman filtering is used to correct modeling errors. Example results for a controlled 84-turbine wind farm are shown below.

*Total wind farm power output showing reference signal (—), controlled wind farm (—), and uncontrolled wind farm (—).*

**Wind farm wake modeling**

Design and control studies rely on engineering models that can be easily computed and optimized because high-fidelity simulations are too computationally expensive to be practical. Our wake model is derived directly from the Reynolds-averaged mean momentum equations, yielding a one-dimensional partial differential equation that governs the velocity deficit in the wake \(\delta u\)

\[ \frac{\partial \delta u_i}{\partial t} + U_\infty \frac{\partial \delta u_i }{\partial x} = - w(x) \,\delta u_i(x,t) + \,S_i \, G(x). \]

This model provides the basis for the wind farm control algorithms described above.

**Lifting line model of yawed wind turbines**

Yawing of wind turbines has the potential to increase wind farm power production by deflecting wakes away from downstream turbines. A practical, yet accurate, aerodynamic theory can be found by treating the yawed wind turbine as a porous lifting surface. This approach yields accurate predictions for the magnitudes of the transverse velocity and the axial velocity deficit, the circulation of the shed counter-rotating vortex pair.

*Comparison of (a) transverse velocity, (b) disk-averaged velocity, (c) streamwise velocity, and (d) skewness angle measured in simulations (squares) with present theory (solid black line) and prior models (other lines).*