Fast Wind Turbine Design via Geometric Programming

Abstract

Over the past two decades, applied mathematicians in the field of convex optimization have developed powerful new tools for solving certain classes of constrained optimization problems extremely reliably and efficiently. This paper introduces the (perhaps surprising) discovery that a number of prevailing physics-based models for wind turbine aerodynamics have an underlying convex mathematical structure that these new methods can exploit. In particular, they can be expressed via the functional forms that define Geometric Programs (GPs). Modern GP solvers are extremely fast even on large problems, require no initial guesses or tuning of solver parameters, and guarantee globally optimal solutions. In addition, for various models that cannot be manipulated into the forms required by GP, it is often possible to fit compact GP models which accurately approximate the original models. The combination of 1) fast solution methods, 2) GP-compatible aerodynamic models (presented herein), and 3) GP-compatibility of structural models (well established) makes the application of GP to large wind turbine design problems a promising approach.