Comparative Assessment of Uncertainty Representation Methods for Bilevel Stochastic Wind Power Investment

In this paper, we address the problem of optimal investment in wind power within an existing transmission network, in an organized electricity market environment. A wind power investor decides which wind power units to install, as well as their size and loca-tion, with the objective of maximizing the investor's expected annual profit. The problem is formulated as a bilevel stochastic model, whose upper level describes the investment decisions and whose lower level represents market clearing. The bilevel model is succes-sively reformulated into a Mathematical Program with Equilibrium Constraints (MPEC) and then into an equivalent Mixed-Integer Linear Programming (MILP) problem. The main contribution of this paper is the systematic comparison of two methods for repre-senting the two sources of uncertainty considered in the model, namely electricity demand and wind power availability: (i) scenarios constructed from load and wind duration curves and (ii) correlated scenarios obtained through K-means clustering. Both methods are evaluated within a common optimization framework, with the same network, investment budget, candidate buses, and deterministic system data, enabling a controlled assessment of how the adopted uncertainty representation affects the resulting investment and network outcomes. The analysis considers a 3-bus verification system and the IEEE 24-bus Reliability Test System across nine case studies. The results show that the choice of uncertainty representation is not merely a technical preprocessing detail, but a substantive modeling decision that changes the optimal wind investment, wind curtailment, and locational marginal prices, while yielding distinct practical implications for both the wind power investor and the system operator.