Frequency Stability-Constrained Unit Commitment: Tight Approximation using Bernstein Polynomials

TL;DR

This paper presents a novel approach for frequency-secured unit commitment under wind power uncertainty, using Bernstein polynomials to create tight approximations of frequency dynamics for improved security and economic efficiency.

Contribution

It introduces a Bernstein polynomial-based method to tightly approximate frequency dynamics in unit commitment, integrating distributionally robust chance constraints for wind uncertainty.

Findings

Method guarantees frequency security effectively.

Approximations are computationally efficient.

Case studies validate the approach's accuracy.

Abstract

As we replace conventional synchronous generators with renewable energy, the frequency security of power systems is at higher risk. This calls for a more careful consideration of unit commitment (UC) and primary frequency response (PFR) reserves. This paper studies frequency-secured UC under significant wind power uncertainty. We coordinate the thermal units and wind farms to provide frequency support, wherein we optimize the variable inverter droop factors of the wind farms for higher economy. In addition, we adopt distributionally robust chance constraints (DRCCs) to handle the wind power uncertainty. To depict the frequency dynamics, we incorporate a differential-algebraic equation (DAE) with the dead band into the UC model. Notably, we apply Bernstein polynomials to derive tight inner approximation of the DAE and obtain mixed-integer linear constraints, which can be computed in off-the-shelf solvers. Case studies demonstrate the tightness and effectiveness of the proposed method in guaranteeing frequency security.