Approximation error of the unit commitment relaxation in AC capacity expansion planning

Determine the approximation error introduced by the unit commitment relaxation that replaces binary on/off decisions with continuous online-unit and startup variables for synchronous generators in the alternating current capacity expansion problem by rigorously comparing outcomes against a formulation with explicit unit commitment, in order to quantify deviations in costs and AC-feasibility.

Background

The paper formulates a multi-period alternating current capacity expansion problem that includes operational constraints and simplified stability limits. To enable tractability at large scale, it employs a relaxation of unit commitment that models synchronous generator startup procedures using continuous variables representing the number of online units and startup actions with associated costs, instead of explicit binary on/off decisions.

While this relaxation permits inclusion of reactive power capabilities and startup-related costs without the combinatorial complexity of full unit commitment, the authors explicitly note that the magnitude of the approximation error relative to a true unit commitment formulation has not been assessed. Quantifying this error would clarify how much the relaxation may bias investment, dispatch, and AC-feasibility outcomes, and inform when a full unit commitment model is necessary.