Robust wind power capacity planning under fuel price uncertainty using conic duality theory and piecewise McCormick relaxation

Journal Article

2024

Published in: https://www.sciencedirect.com/science/article/pii/S0378779624010125?via%3Dihub=

Increasing the proportion of renewable energy sources (RESs) in power generation is crucial due to fossil fuel
depletion and rising environmental pollution. In this regard, identifying the most lucrative sites and sizes for
installing wind farms, as one of the fastest-growing types of RESs, is imperative. This paper presents a robust
profit-oriented wind power capacity planning (WPCP) considering long- and short-term uncertainty. The model
forms a two-stage min-max-min hierarchical structure. The first stage minimizes the investment cost plus
maximum regret, while the second stage maximizes the profit under the worst-case uncertainty realization.
Unlike the existing approaches where uncertainty in fossil fuel prices is neglected, we model fuel price uncertainty
using both polyhedral and ellipsoidal uncertainty sets. In this respect, the third level is formulated as a bilevel
program, with the upper level being the profit maximization and the lower level being the locational
marginal price (LMP) calculation. In the case of the ellipsoidal set, the conic duality theory is employed to
dualize the lower level. The piecewise McCormick relaxation (PMR) technique linearizes the bilinear terms. The
nested column-and-constraint generation (NCCG) technique solves the formulated problem. A clarifying case
study is employed to demonstrate the efficacy of the proposed model.