  Wind farms can increase annual energy production (AEP) with advanced control
algorithms by coordinating the set points of individual turbine controllers
across the farm. However, it remains a significant challenge to achieve
performance improvements in practice because of the difficulty of utilizing
models that capture pertinent complex aerodynamic phenomena while remaining
amenable to control design. We formulate a multi-stage stochastic optimal
control problem for wind farm power maximization and show that it can be solved
analytically via dynamic programming. In particular, our model incorporates
state- and input-dependent multiplicative noise whose distributions capture
stochastic wind fluctuations. The optimal control policies and value functions
explicitly incorporate the moments of these distributions, establishing a
connection between wind flow data and optimal feedback control. We illustrate
the results with numerical experiments that demonstrate the advantages of our
approach over existing methods based on deterministic models.
