  To facilitate effective decarbonization of the electric power sector, this
paper introduces the generic Carbon-aware Optimal Power Flow (C-OPF) method for
power system decision-making that considers demand-side carbon accounting and
emission management. Built upon the classic optimal power flow (OPF) model, the
C-OPF method incorporates carbon emission flow equations and constraints, as
well as carbon-related objectives, to jointly optimize power flow and carbon
flow. In particular, this paper establishes the feasibility and solution
uniqueness of the carbon emission flow equations, and proposes modeling and
linearization techniques to address the issues of undetermined power flow
directions and bilinear terms in the C-OPF model. Additionally, two novel
carbon emission models, together with the carbon accounting schemes, for energy
storage systems are developed and integrated into the C-OPF model. Numerical
simulations demonstrate the characteristics and effectiveness of the C-OPF
method, in comparison with OPF solutions.
