A unified framework for co-optimization of PFR and FFR reserves using linearized tri-criteria frequency constraints

The increasing penetration of inverter-based resources reduces system inertia and heightens concerns about frequency stability. This paper proposes a systematic methodology for jointly optimizing primary frequency response (PFR) and fast frequency response (FFR) reserves so that three critical stability metrics—rate of change of frequency (RoCoF), frequency nadir, and quasi-steady-state (QSS) frequency—are simultaneously satisfied within linear constraints. Based on a simplified system frequency response (SSFR) model, dynamic simulations are used to derive multi-criteria PFR-FFR equivalency ratios and establish corresponding linear reserve requirement constraints that add no integer variables to existing optimization models. In tariff-based ancillary service markets like Korea’s, the methodology identifies optimal reserve combinations using the derived multi-criteria equivalency ratios and tariff levels. In security-constrained economic dispatch (SCED)-based co-optimization, integrating these linear reserve constraints ensures that RoCoF and QSS criteria are also satisfied across varying inertia conditions while enabling more efficient reserve procurement, compared with ERCOT’s current approach, which considers only the nadir and a fixed FFR ratio limit. The framework therefore offers a practical, market-ready tool for optimizing frequency reserves procurement in low-inertia power systems.