Stochastic Dynamic Programming for Wind Farm Power Maximization

TL;DR

This paper develops a stochastic dynamic programming approach for wind farm power maximization, effectively incorporating wind variability and complex aerodynamic effects to improve control strategies.

Contribution

It introduces a multi-stage stochastic optimal control model that explicitly accounts for wind fluctuations and aerodynamic complexities, solved analytically via dynamic programming.

Findings

The approach outperforms deterministic models in numerical experiments.

Optimal policies incorporate wind fluctuation statistics.

The method links wind data directly to control strategies.

Abstract

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.