Robust Optimization for Transmission Expansion Planning: Minimax Cost vs. Minimax Regret

Due to the long planning horizon, transmission expansion planning is typically subjected to a lot of uncertainties including load growth, renewable energy penetration, policy changes, etc. In addition, deregulation of the power industry and pressure from climate change introduced new sources of uncertainties on the generation side of the system. Generation expansion and retirement become highly uncertain as well. Some of the uncertainties do not have probability distributions, making it difficult to use stochastic programming. Techniques like robust optimization that do not require a probability distribution became desirable. To address these challenges, we study two optimization criteria for the transmission expansion planning problem under the robust optimization paradigm, where the maximum cost and maximum regret of the expansion plan over all uncertainties are minimized, respectively. With these models, our objective is to make planning decisions that are robust against all scenarios. We use a two-layer algorithm to solve the resulting tri-level optimization problems. Then, in our case studies, we compare the performance of the minimax cost approach and the minimax regret approach under different characterizations of uncertainties.