Chance-constrained co-expansion planning for power systems under decision-dependent wind power uncertainty

Variability and uncertainty in wind resources pose significant challenges to the expansion planning of wind farms and associated flexible resources. In addition, the spatial smoothing effect, indicating the impact of wind farm scale on aggregated wind power prediction errors, further aggravates the challenge. This paper proposes a chance-constrained co-expansion planning method considering the spatial smoothing effect, where the expansion of wind farm capacity, batter energy storage capacity, and power transmission lines are co-optimized. Specifically, a decision-dependent uncertainty (DDU) model is established capturing the dependency of wind power uncertainties on wind farm expansion decisions under the spatial smoothing effect. Unlike traditional optimization diagram where decisions are made under only decision-independent uncertainty (DIU) with fixe properties, properties of decision-dependent uncertain parameters would be inversely altered by decisions. To effectively tackle the coupling relation between decisions and DDU, DDU-based chance constraints are formulated in an analytical manner, where the decisions and decision-dependent uncertain parameters are expressed in a closed form. Eventually, with piecewise linearization of the DDU model and the polynomial approximation of cumulative distribution function of uncertain parameters, the proposed chance-constrained optimization model with DDU is converted into a mixed-integer second-order cone program (MISOCP). Case studies verify the effectiveness of the proposed method.