# Inverse Stability Problem and Applications to Renewables Integration

## TL;DR

This paper introduces the inverse stability problem in power systems, focusing on characterizing the set of operating conditions a grid converges to under renewable fluctuations, with applications in stability assessment and control.

## Contribution

It proposes a novel inverse stability framework using quadratic energy function approximations, addressing a rarely studied problem in power system stability analysis.

## Key findings

- Estimate of inverse stability region using quadratic energy functions
- Application to robust stability assessment with renewables
- Application to stability-constrained optimal power flow

## Abstract

In modern power systems, the operating point, at which the demand and supply are balanced, may take different values due to changes in loads and renewable generation levels. Understanding the dynamics of stressed power systems with a range of operating points would be essential to assuring their reliable operation, and possibly allow higher integration of renewable resources. This letter introduces a non-traditional way to think about the stability assessment problem of power systems. Instead of estimating the set of initial states leading to a given operating condition, we characterize the set of operating conditions that a power grid converges to from a given initial state under changes in power injections and lines. We term this problem as "inverse stability", a problem which is rarely addressed in the control and systems literature, and hence, poorly understood. Exploiting quadratic approximations of the system's energy function, we introduce an estimate of the inverse stability region. Also, we briefly describe three important applications of the inverse stability notion: (i) robust stability assessment of power systems w.r.t. different renewable generation levels, (ii) stability-constrained optimal power flow (sOPF), and (iii) stability-guaranteed corrective action design.