Sizing Wind Farm and Energy Storage Considering Wake Effect

The wake effect within a wind farm can precipitate wind speed deficits, subsequently leading to a decline in the power generation of downstream wind turbines. This chapter proposes a bi-objective distributionally robust optimization (DRO) model, which aims to determine the capacities of wind power generation and energy storage while considering the wake effect. To encapsulate the uncertainties of wind power and demand, an ambiguity set, grounded in the Wasserstein distance, is established. It is worth noting that wind power uncertainty is directly impacted by the wind power generation capacity, which is determined in the first stage. Consequently, the proposed model typifies a DRO problem with endogenous uncertainty, also referred to as decision-dependent uncertainty. To solve the proposed model, a method utilizing the approximation of stochastic programming through Lipschitz moduli is developed. This method effectively transforms the DRO model into a linear programming problem. Following this, an iterative algorithm is formulated, which incorporates methods for evaluating the Lipschitz moduli.