The power sector is a major contributor to carbon emissions. Deep and rapid decarbonization of electric power systems has emerged as an urgent priority. To address the complex mission of power system decarbonization, we develop a comprehensive framework for the "Carbon-Electricity Nexus":

• Carbon Accounting: using the Carbon Emission Flow (CEF) method for spatially and temporally granular demand-side carbon accounting and for physical grid alignment.

• Decarbonization Decision-Making: developing a novel fundamental decision-making methodology, termed "Carbon-Aware Optimal Power Flow (C-OPF)", to co-optimize electrical power flow and carbon emission flow in power grids and enable active demand-side carbon footprint management. It is applicable to carbon-aware grid planning, operation, and demand response.

• Carbon-Electricity Market: integrating carbon emissions into the electricity market design and price formation to incentivise low-carbon electricity generation and usage.