# Stochastic Unit Commitment in Low-Inertia Grids

## TL;DR

This paper develops a stochastic unit commitment model for low-inertia power grids, incorporating nonlinear frequency constraints and proposing an efficient linearization method, demonstrating significant impacts on operational decisions and costs.

## Contribution

It introduces a novel approach to linearize nonlinear frequency nadir constraints in stochastic UC models for low-inertia grids, improving computational efficiency.

## Key findings

- Inertia constraints significantly affect UC decisions.
- Including inertia constraints increases total operational costs.
- The proposed linearization method outperforms existing piece-wise linearization techniques.

## Abstract

In this paper, the Unit Commitment (UC) problem in a power network with low levels of rotational inertia is studied. Frequency-related constraints, namely the limitation on Rate-of-Change-of-Frequency (RoCoF), frequency nadir and steady-state frequency error, are derived from a uniform system frequency response model and included into a stochastic UC that accounts for wind power and equipment contingency uncertainties using a scenario-tree approach. In contrast to the linear RoCoF and steady-state frequency error constraints, the nadir constraint is highly nonlinear. To preserve the mixed-integer linear formulation of the stochastic UC model, we propose a computationally efficient approach that allows to recast the nadir constraint by introducing appropriate bounds on relevant decision variables of the UC model. For medium-sized networks, this method is shown to be computationally more efficient than a piece-wise linearization method adapted from the literature. Simulation results for a modified IEEE RTS-96 system revealed that the inclusion of inertia-related constraints significantly influences the UC decisions and increases total costs, as more synchronous machines are forced to be online to provide inertial response.