Designing wind turbine rotor blades to enhance energy capture in turbine arrays
An inverse design approach is proposed to compute wind turbine blade geometries which maximize the aggregate power output from a wind farm. An iterative inverse algorithm is used to solve the optimization problem. The algorithm seeks to minimize the target function, f = -CP,av, where CP,av is the average normalized mechanical power of all the turbines in the wind farm. An upper bound on the blade planform area, representative of the blade weight, is imposed to demonstrate how to incorporate constraints in the design process. The power coefficients (CP) of the turbines in the farm are computed by solving the Reynolds Averaged Navier Stokes equations with the turbine rotors modeled as momentum sources using the actuator disk model. The inverse design is carried out using the trust-region-reflective method, which is a nonlinear least squares regression solver. The computation cost is reduced by computing the Jacobian once every few iterations and approximating it using Broyden's method in between. The proposed design approach is first demonstrated to maximize the isolated performance of single- and dual-rotor wind turbines and subsequently used to design the blades for a 3-turbine array and a ten-turbine array in which the downstream turbines operate directly in the wake of the upstream turbines. For a turbine-turbine spacing of four rotor diameters, the farm-optimized blade designs increase the farm power output by over five percent and the optimized blade geometries are found to be considerably different from the blade geometry optimized for isolated turbine operation. As the turbine-turbine spacing is increased to eight rotor diameters, the difference between the blade geometry optimized for farm operation versus that for isolated operation, is reduced.
This is a manuscript of an article published as Moghadassian, Behnam, and Anupam Sharma. "Designing wind turbine rotor blades to enhance energy capture in turbine arrays." Renewable Energy (2019). DOI: 10.1016/j.renene.2019.10.153. Posted with permission.