Optimization of wind farm portfolios for minimizing overall power fluctuations at selective frequencies – a case study of the Faroe Islands

Abstract. Hourly modeled wind turbine power output time series – modeled based on outputs from the mesoscale numerical weather prediction system Weather Research and Forecasting Model (WRF) – are used to examine the spatial smoothing of various wind farm portfolios located on a complex isolated island group with a surface area of 1400 km2. Power spectral densities (PSDs), hourly step-change functions, and duration curves are generated, and the 5th and 95th percentiles and the standard deviations of the hourly step-change functions are calculated. The spatial smoothing is identified from smaller high-frequency PSD amplitudes, lower hourly fluctuations, and more flat duration curves per installed wind power capacity, compared with single wind turbine outputs. A discussion on the limitation of the spatial smoothing for the region is included, where a smoothing effect is observed for periods of up to 1–2 d, although it is most evident at higher frequencies. By maximizing the smoothing effect, optimal wind farm portfolios are presented with the intention of minimizing overall wind power fluctuations. The focus is mainly on the smoothing effect on the 1–3 h timescale, during which the coherency between wind farm power outputs is expected to be dependent on how the regional weather travels between local sites, thereby making optimizations of wind farm portfolios relevant – in contrast to a focus on either lower or higher frequencies on the scale of days or minutes, respectively, during which wind farm power output time series are expected to be either close to fully coherent due to the same weather conditions covering a small region or not coherent as the turbulences in separate wind farm locations are expected to be uncorrelated. Results show that an optimization of the wind farm capacities at 14 pre-defined wind farm site locations has a minimal improvement on the hourly fluctuations compared with a portfolio with equally weighted wind farm capacities. However, choosing optimized combinations of individual wind farm site locations decreases the 1–3 h fluctuations considerably. For example, selecting a portfolio with four wind farms (out of the 14 pre-defined wind farm site locations) results in 15 % lower 5th and 95th percentiles of the hourly step-change function when choosing optimal wind farm combinations compared with choosing the worst wind farm combinations. For an optimized wind farm portfolio of seven wind farms, this number is 13 %. Optimized wind farm portfolios consist of distant wind farms, while the worst portfolios consist of clustered wind farms.
