Risk-averse wind farms placement via quantile constraint learning
提出一种概率神经网络作为代理模型，学习风速的时空相关性，并将其转化为混合整数线性约束，嵌入两阶段随机优化问题中，通过条件分位数决策帮助风险规避投资者优化风电场布局。
Wind farm placement arranges the size and the location of multiple wind farms within a given region. The power output is highly related to 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 constraints (constraint learning). We embed these constraints into the risk-averse placement decision problem, formulated as a two-stage stochastic optimization problem. Specifically, the conditional quantiles of 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 when we introduce transmission line costs into the problem, risk-averse investors favor locations closer to 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 can tackle a portfolio of regional wind farm placements and further provide guidance for risk-averse investors.