TOPFARM: Multi‐fidelity optimization of wind farms

Abstract

A wind farm layout optimization framework based on a multi-fidelity optimization approach is applied to the offshore test case of Middelgrunden, Denmark as well as to the onshore test case of Stag Holt -Coldham wind farm, UK. While aesthetic considerations have heavily influenced the famous curved design of the Middelgrunden wind farm, this work focuses on demonstrating a method that optimizes the profit of wind farms over their lifetime based on a balance of the energy production income, the electrical grid costs, the foundations cost, and the cost of wake turbulence induced fatigue degradation of different wind turbine components. A multi-fidelity concept is adapted, which uses cost function models of increasing complexity (and decreasing speed) to accelerate the convergence to an optimum solution. In the EU-FP6 TOP-FARM project, three levels of complexity are considered. The first level uses a simple stationary wind farm wake model to estimate the Annual Energy Production (AEP), a foundations cost model depending on the water depth and an electrical grid cost function dictated by cable length. The second level calculates the AEP and adds a wake-induced fatigue degradation cost function on the basis of the interpolation in a database of simulations performed for various wind speeds and wake setups with the aero-elastic code HAWC2 and the dynamic wake meandering model. The third level, not considered in this present paper, includes directly the HAWC2 and the dynamic wake meandering model in the optimization loop in order to estimate both the fatigue costs and the AEP. The novelty of this work is the implementation of the multi-fidelity approach in the context of wind farm optimization, the inclusion of the fatigue degradation costs in the optimization framework, and its application on the optimal performance as seen through an economical perspective.

A Review of Methodological Approaches for the Design and Optimization of Wind Farms

“…The generalized WFDO problem includes all the mixed-integer variables described in Section 2.4. In addition, it considers the decision variable of designing auxiliary infrastructure (e.g., roads and/or electrical infrastructure), which can be viewed as an embedded NPO-complete problem (e.g., the auxiliary road and/or electrical infrastructure layout design problem can be viewed as a Minimum Spanning Tree problem [135,[163][164][165][166] or as a Steiner tree problem [167]; both problems have been categorized as NPO-complete problems [147,151]) or as an embedded NPO-hard problem (e.g., the wind farm array cable layout design problem can be viewed as a vehicle routing problem [168], which has been categorized as a NPO-hard problem). Currently, there is no defined computational complexity category for embedded NPO-complete/NPO-hard problems, and current solution procedures rely in multi-step, nested and hybrid approaches, which will be discussed in Section 3.3.4.…”

A Multi-Objective Optimization Framework for Offshore Wind Farm Layouts and Electric Infrastructures

“…The main goal of this EU-funded project, TopFarm, was the design of an optimization tool for wind farm developers [47]. The financial balance was used as the optimization goal, whereas the turbine coordinates were chosen as design variables.…”

“…This is because the optimization algorithm needs to capture the difference between the wind farm layouts [47].…”

“…Constraints on the location of turbines, such as minimum distance to existing power cables and shipwrecks, within the OWF area are automatically respected by not considering constrained places in the possible set of locations for the turbines [47]. Furthermore, the limited precision offered by the models used, such as the wake model, do not require the accuracy of continuous variables [33].…”

Development of a quantitative analysis system for greener and economically sustainable wind farms

“…TOPFARM is a system which optimises wind farm layout based on cost, power production and fatigue loads, developed by Réthoré et al (2014). This includes a sophisticated electrical grid connection cost model and the depreciation and replacement costs of components caused by wake-induced fatigue loads.…”