Convex-Hull of Locational Marginal Carbon Emission for Carbon Management Considering Emissions During Non-Steady-State Operation Hours

The increasing penetration of renewable energy, while essential for decarbonization, can intensify thermal-unit cycling and ramping, aggravate network congestion, and increase emissions during non-steady-state operating periods (i.e., start-ups, shutdowns, and fast ramping). Research indicates that carbon emissions during such hours could increase to 2–6 times those of steady-state operation hours. However, conventional studies often ignore the impact of intertemporal constraints on carbon measurements, leading to significant underestimation of carbon emission. To address this gap, this paper extends the locational marginal carbon emission (LMCE) framework by incorporating non-steady-state hours emissions through a convex-hull-based variant of LMCE (i.e., LMCE2) model. This approach clarifies the endogenous link between nodal prices and carbon intensity and ensures theoretical consistency between electricity pricing and carbon emission calculation. The LMCE2 can be efficiently computed using the Dantzig–Wolfe decomposition. We further derive LACE2 that mitigates carbon over-allocation. Our case studies demonstrate that rapid emission assessment during non-steady-state operation hours using LMCE2/LACE2, enables more trustworthy carbon accounting. Compared with traditional LMCE/LACE, the use of LMCE2/LACE2 reduces carbon measurement error by 83.5%–90.1%. The proposed framework offers practical tools for carbon management in electricity markets with high renewable shares.