Optimal placement of wind farms via quantile constraint learning

Wenxiu Feng, Antonio Alcántara Mata and Carlos Ruiz Mora

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: Wind farm placement arranges the size and the location of multiple wind farms within a given region. The power output is highly related to the wind speed on spatial and temporal levels, which can be modeled by advanced data-driven approaches. To this end, we use a probabilistic neural network as a surrogate that accounts for the spatiotemporal correlations of wind speed. This neural network uses ReLU activation functions so that it can be reformulated as mixed-integer linear set of constraints (constraint learning). We embed these constraints into the placement decision problem, formulated as a two-stage stochastic optimization problem. Specifically, conditional quantiles of the total electricity production are regarded as recursive decisions in the second stage. We use real high-resolution regional data from a northern region in Spain. We validate that the constraint learning approach outperforms the classical bilinear interpolation method. Numerical experiments are implemented on risk-averse investors. The results indicate that risk-averse investors concentrate on dominant sites with strong wind, while exhibiting spatial diversification and sensitive capacity spread in non-dominant sites. Furthermore, we show that if we introduce transmission line costs in the problem, risk-averse investors favor locations closer to the substations. On the contrary, risk-neutral investors are willing to move to further locations to achieve higher expected profits. Our results conclude that the proposed novel approach is able to tackle a portfolio of regional wind farm placements and further provide guidance for risk-averse investors.

Keywords: Constraint; learning; Optimal; investment; Quantile; neural; network; Wind; generation; Stochastic; optimization (search for similar items in EconPapers)
Date: 2025-09-30
New Economics Papers: this item is included in nep-cmp
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