Adjoint Optimization of Wind Farm Layouts for Systems Engineering Analysis

Wind is an important renewable energy resource, but in order for it to be competitive with other energy sources, wind farm layouts must be optimized to reduce the levelized cost of energy (LCOE). This requires an analysis that integrates high-fidelity flow models with physical turbine and cost models. We present a new flow model and turbine layout optimization tool, WindSE, that optimizes wind turbine locations as part of the National Renewable Energy Laboratory open source wind energy systems engineering software tool WISDEM. WindSE enables gradient-based layout optimization by solving the discrete adjoint equations corresponding to the forward flow model. This provides a computationally efficient way to calculate gradients used in the optimization process. We discuss the development of WindSE and provide optimization results based on simulations of single and multiple inflow directions. It is found that, where possible, the optimal layouts take advantage of flow curvature and speedup effects that are not generated by standard industry linear flow models. In multiple inflow direction optimizations, speedup effects are found to be less beneficial and the optimal layouts instead minimize wake losses. With evenly weighted inflow directions, the optimal layouts are typically symmetric about the axis of rotation of inflow directions. The effects of inflow direction binning and weighting are also discussed.