Distributionally Robust Low-Carbon Energy and Reserve Dispatch with Renewable Energy Uncertainty

This paper presents a distributionally robust low-carbon energy and reserve dispatch with renewable energy uncertainty. The carbon market is implemented to fully leverage the environmental benefits of power systems. Additionally, the uncertainty of renewable energy probability distributions is established based on expected values and covariances to ensure system operational safety. To solve this model, the infinite programming duality theory is employed to handle probability distribution uncertainties, and dual vertices are utilized to relax the optimal adjustment cost in the second stage, thus the distribution uncertainty is reduced to the scenario uncertainty. Secondly, by leveraging the S-lemma and matrix transformations, constraints with scenario uncertainties are converted into deterministic semidefinite constraints. Finally, a dual vertex generation method is proposed to solve the transformed model through an alternating optimization procedure of the master and sub problems. Case studies validate the performance of the model in ensuring the economic, low-carbon, and secure operation of power systems under renewable energy uncertainties.