2019/12/31 by Yichen Zhang, Zhang, Yichen, Yan Li +7 · 1 citation
Engineering · #Algebraic Geometry (math.AG) #FOS: Electrical engineering #FOS: Mathematics #Optimal Power Flow Distribution #Optimization and Control (math.OC) #Power System Optimization and Stability #Real-time simulation and control systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2001.00080
openalex publication_date 2019/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Increasing penetration of renewable energy introduces significant uncertainty into power systems. Traditional simulation-based verification methods may not be applicable due to the unknown-but-bounded feature of the uncertainty sets. Emerging set-theoretic methods have been intensively investigated to tackle this challenge. The paper comprehensively reviews these methods categorized by underlying mathematical principles, that is, set operation-based methods and passivity-based methods. Set operation-based methods are more computationally efficient, while passivity-based methods provide semi-analytical expression of reachable sets, which can be readily employed for control. Other features between different methods are also discussed and illustrated by numerical examples. A benchmark example is presented and solved by different methods to verify consistency.