Capacity Expansion and Unit Commitment with Reserve Requirements: A Comparative Analysis for an Italian Off-Grid Island

Accurate modeling of operational aspects of fuelfired generators (FFGs) is critical for off-grid energy planning, yet traditional capacity expansion models often oversimplify unit commitment. This paper compares two approaches for representing generator commitment in Mixed-Integer Linear Programming (MILP): (i) a binary-variable formulation that offers detailed, per-unit fidelity; and (ii) a modular framework that aggregates identical units into integer variables. Both methods are applied to the off-grid island of Pantelleria, Italy, incorporating operational aspects such as standby costs and upward/downward reserve constraints, alongside capacity expansion. The results show that the modular approach reduces the computational time by up to two orders of magnitude, without compromising fidelity. This efficiency supports broader scenario exploration, contributing to more reliable energy planning models for offgrid systems.