The Wind Farm Layout Optimization (WFLO) problem consists of determining the optimal spatial arrangement of wind turbines within a given wind farm terrain, so as to maximize the total energy generated by the facility, minimize the unit cost of energy, or generally maximize the net present value of the project. The WFLO has attracted a lot of attention from researchers and industry practitioners, as it has been proven that better placement of wind turbines can increase the overall efficiency and the total revenue of a wind farm. In addition, the environmental impact of wind farms has received increased attention, particularly regarding noise generation, land use, and infrastructure deployment. Common approaches found in the WFLO literature have focused on minimizing turbine wake interactions based on simplified mathematical models of wake behavior, and relying on optimization metaheuristics such as evolutionary algorithms to solve the non-linear, multi-objective, constrained WFLO problem.

In our work, we have addressed the WFLO problem with a two-pronged strategy, focusing on both the modelling and the optimization aspects. On the optimizaiton side, we have explored multi-objective formulations to characterize the trade-off between energy generation and noise levels around the wind farm. We have proposed efficient gradient-based formulations based on closed-form derivatives of the wake and wake combination models. These gradient-based formulations have been extended to include land-based objectives and constraints. We have also developed MIP models that solve efficiently and have convergence guarantees in the form of solution bounds. Overall, our results show that gradient-based formulations are the most efficient method for the WFLO problem, yielding the best solutions at the lowest computational cost, although this approach is restricted to differentiable, closed-form, simplified wake models.

On the modelling side, we are exploring simulation-based optimization formulations to improve the accuracy of our optimization results while reducing the associated computational cost. In this context, we have developed an advection-diffusion formulation to approximate the flow field for wind farms in complex terrains. We are currently developing a novel formulation using the Adjoint Method to determine the gradient of the flow field with respect to the turbine coordinates, based on full CFD simulations of the three-dimensional, trubulent flow field of wind farms in complex terrains. Preliminary results show the potential of this approach to solve the WFLO problem in its most general form.

Bio:

David A. Romero is currently a Senior Research Associate at the University of Toronto, Department of Mechanical & Industrial Engineering. David holds an undergraduate Mechanical Engineering degree (2000) from Universidad del Zulia, as well as M.Sc. (2003) and Ph.D. (2008) degrees in Mechanical Engineering from Carnegie Mellon University. Prior to joining the University of Toronto, he was an Associate Professor in Mechanical Engineering at the Universidad del Zulia, Venezuela.

David's research interests are in the intersection of applied computing, statistics and mathematics in support of engineering design, modeling and optimization, particularly in the thermal/fluid sciences. Current projects involve AI-based algorithms for global optimization, simulation-based design optimization, and modelling and optimization of renewable energy systems.