A Hybrid Stochastic/Robust Model for Transmission Expansion Planning under an Ellipsoidal Uncertainty Set

• Published in: Electric power components and systems 2022-11, Vol.50 (19-20), p.1174-1185
• Main Authors: Alnowibet, Khalid A., Alshamrani, Ahmad M.
• Format: Article
• Language: English
• Subjects: Duality theorem; ellipsoidal uncertainty set; hybrid stochastic/robust optimization; Mathematical problems; Optimization; Parameter uncertainty; Robustness (mathematics); second-order cone program; System effectiveness; transmission expansion planning; Transmission lines
• ISSN: 1532-5008; 1532-5016
• DOI: 10.1080/15325008.2022.2148777

Over the last few years, the concept of robust optimization (RO) and its application to power system problems have been at the center of much recent research due to its successful implementation in handling uncertainties. In this regard, this paper presents a new approach for hybrid stochastic/robust transmission expansion planning (TEP), considering three sources of uncertainties, including demand growth, generation capacity, and thermal capacity of transmission lines. These uncertain parameters are modeled using an ellipsoidal uncertainty set, which can capture the correlation efficiently. The TEP problem is modeled as a bilevel mathematical optimization where the lower level is replaced by its Lagrange dual optimization problem using the duality theorem (DT). One main benefit of using the dual problem is that all uncertainties will appear in the objective function and thus can be converted to convex second-order cone constraints. The entire bilevel problem is then solved using the standard column-and-constraint generation (C&CG) technique by decomposing the mathematical problem into a master and a binary variable-free subproblem. Numerical studies on two test power systems validate the effectiveness of the proposed model. The results indicate that the presented methodology is more efficient than the existing models from the computational complexity perspective.