Review on Set-Theoretic Methods for Safety Verification and Control of Power System

TL;DR

This paper reviews set-theoretic approaches for power system safety verification and control, highlighting their mathematical foundations, advantages, and practical applications amid renewable energy uncertainties.

Contribution

It provides a comprehensive categorization and comparison of set operation-based and passivity-based methods, including a benchmark example for validation.

Findings

Set operation-based methods are computationally efficient.

Passivity-based methods offer semi-analytical reachable set expressions.

Benchmark example confirms method consistency.

Abstract

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.