# Chance Constrained Optimal Power Flow with Primary Frequency Response

## TL;DR

This paper introduces a chance constrained optimal power flow model that explicitly incorporates nonlinear primary frequency response characteristics and uncertainty from renewable sources, improving power system reliability.

## Contribution

It develops a novel CCOPF formulation that models nonlinear governor dead zones and incorporates chance constraints for renewable uncertainty, enhancing accuracy over existing methods.

## Key findings

- The proposed CCOPF outperforms standard models in reliability.
- Explicit modeling of nonlinear frequency response improves control accuracy.
- The method is validated on a modified IEEE 118-bus system.

## Abstract

Primary frequency response is provided by synchronized generators through their speed-droop governor characteristic in response to instant frequency deviations that exceed a certain threshold, also known as the governor dead zone. This dead zone makes the speed-droop governor characteristic nonlinear and makes affine control policies that are often used for modeling the primary frequency response inaccurate. This paper presents an optimal power flow (OPF) formulation that explicitly models i) the primary frequency response constraints using a nonlinear speed-droop governor characteristic and ii) chance constraints on power outputs of conventional generators and line flows imposed by the uncertainty of renewable generation resources. The proposed chance constrained OPF (CCOPF) formulation with primary frequency response constraints is evaluated and compared to the standard CCOPF formulation on a modification of the 118-bus IEEE Reliability Test System.