# Dynamic Polytopic Template Approach to Robust Transient Stability Assessment

## TL;DR

This paper introduces a reachability analysis method using a dynamic polytopic template to efficiently assess transient stability in power systems with uncertainties, improving scalability and reliability over traditional methods.

## Contribution

It presents a novel eigenvalue-based polytopic template approach for robust transient stability assessment that handles uncertainties efficiently and scales to large power systems.

## Key findings

- Successfully certifies stability on IEEE test cases.
- Provides bounds on state trajectories under uncertainties.
- Scalable linear programming-based implementation.

## Abstract

Transient stability assessment of power systems needs to account for increased risk from uncertainties due to the integration of renewables and distributed generators. The uncertain operating condition of the power grid hinders reliable assessment of transient stability. Conventional approaches such as time-domain simulations and direct energy methods are computationally expensive to take account of uncertainties. This paper proposes a reachability analysis approach that computes bounds of the possible trajectories from uncertain initial conditions. The eigenvalue decomposition is used to construct a polytopic template with a scalable number of hyperplanes that is guaranteed to converge near the equilibrium. The proposed algorithm bounds the possible states at a given time with a polytopic template and solves the evolution of the polytope over time. The problem is solved with linear programming relaxation based on outer-approximations of nonlinear functions, which is scalable for large scale systems. We demonstrate our method on IEEE test cases to certify the stability and bound the state trajectories.