Development of distributionally-robust optimization methodologies for electrical transmission operation problems with uncertainties

Electrical transmission operation problems such as unit commitment problems face many uncertainties including demand response and fluctuation, renewable energy integration, and contingencies. Traditionally, the stochastic optimization approach is considered to address the uncertainty issues, and more recently, the application of robust optimization methods is also studied for the unit commitment problems with uncertainty. The stochastic optimization can provide the system operators a sense of ‘expected’ cost of operation, but it requires the complete stochastic modeling of many uncertain parameters, which is prohibitive in practice. On the other hand, robust optimization requires simpler uncertainty sets, but it is often criticized of being too conservative. The goal of the proposed task is to develop distributionally-robust optimization methodologies for electrical transmission operation problems. Distributionally-robust optimization is a robust counterpart of stochastic programming where the uncertainty set for the probability distributions are considered. The distributionally-robust optimization identifies the worst-case probability distributions among the uncertainty set and finds the operation solution that minimizes the expected cost under the worst-case probability distributions. From the user’s perspective, the most beneficial aspect of distributionally-robust optimization is that one can model the uncertainty set of probability distributions with easy-to-obtain partial statistical information, such as mean and variances.