Progressive Hedging Augmentations for Stochastic Frequency-Constrained Unit Commitment

Abstract

This paper develops a two-stage stochastic frequency-constrained unit commitment (FCUC) model for low-inertia grids with wind-based synthetic inertia (SI) and solves it using Progressive Hedging (PH). Frequency-security limits on RoCoF, nadir and steady-state deviation are embedded through separable-programming linearisations. In the model, SI is not a free always-available input: its realised contribution is capped at 20% of wind-plant nameplate and linked to curtailment-gated SI power variables. The formulation is tested on the IEEE RTS-96 system under a high-wind, high-demand case with exogenous wind scenarios. Deterministic FCUC restores frequency security relative to conventional UC, while increasing SI from 0 s to 6 s reduces operating cost without losing non-negative frequency margins. For the stochastic FCUC, the extensive-form MILP is compared with two PH variants whose scenario subproblems become MIQPs because of quadratic proximal penalties on commitment variables. PH preserves the extensive-form frequency behaviour and cuts wall-clock time from 4451 s to 594–611 s, while keeping expected RoCoF and nadir margins non-negative. Index Terms-Frequency-constrained unit commitment (FCUC), synthetic inertia (SI), wind power integration, lowinertia power systems, mixed-integer linear programming (MILP), mixed-integer quadratic programming (MIQP), stochastic optimisation, progressive hedging (PH)