A hybrid extended pattern search/genetic algorithm for multi-stage wind farm optimization

This purpose of this work is to explore means of optimizing multi-stage wind farms using two derivative-free optimization methods: a hybrid Extended Pattern Search/Genetic Algorithm (capitalizing on the benefits of each), and a multi-objective Extended Pattern Search. Large onshore wind farms are often installed in discrete phases, with smaller sub-farms being installed and becoming operational in succession, creating the completed large wind farm in a piece-wise fashion over multiple years. Multi-stage wind farms present a complex and relevant optimization challenge in that in addition to accounting for the site-specific objectives of a wind farm (such as power development and profit), optimization of both the discrete sub-farms and the completed farm must be jointly considered. Two different problem formulations are explored: the first uses the optimal layout of a complete farm and then systematically “removes” turbines to create smaller sub-farms; the second uses a weighted multi-objective optimization over sequential, adjacent land that concurrently optimizes each sub-farm and the complete farm. For both problem formulations, two wind test cases are considered for both a square and a rectangular field: a constant wind speed from a predominant wind direction, and a multidirectional test case with three wind speeds and a defined probability of occurrence for each. The exploration of these resulting layouts indicates the value of the advanced multi-objective EPS and the hybrid EPS/GA, and gives insight into how to approach optimizing both completed wind farms and sub-farm stages. The behavior exhibited in these tests cases suggests strategies that can be employed by wind farm developers to facilitate predictable, optimal performance of multi-stage wind farms throughout their useful life.