# Fragility of Decentralized Load-Side Frequency Control in Stochastic Environment

## TL;DR

This paper analyzes how small stochastic uncertainties in power network parameters, especially due to renewable energy sources, can destabilize decentralized load-side frequency control algorithms, highlighting their fragility.

## Contribution

It introduces an analytical framework to determine the critical variance of stochastic uncertainties that cause instability in decentralized frequency control.

## Key findings

- Small variance in bus voltages can cause instability.
- Critical variance decreases with higher renewable penetration.
- Simulation confirms analytical predictions.

## Abstract

In this paper, we demonstrate the fragility of decentralized load-side frequency algorithms proposed in [1] against stochastic parametric uncertainty in power network model. The stochastic parametric uncertainty is motivated through the presence of renewable energy resources in power system model. We show that relatively small variance value of the parametric uncertainty affecting the system bus voltages cause the decentralized load-side frequency regulation algorithm to become stochastically unstable. The critical variance value of the stochastic bus voltages above which the decentralized control algorithm become mean square unstable is computed using an analytical framework developed in [2], [3]. Furthermore, the critical variance value is shown to decrease with the increase in the cost of the controllable loads and with the increase in penetration of renewable energy resources. Finally, simulation results on IEEE 68 bus system are presented to verify the main findings of the paper.