  As the electrification process advances, enormous power flexibility is
becoming available on the demand side, which can be harnessed to facilitate
power system decarbonization. Hence, this paper studies the carbon-aware demand
response (C-DR) paradigm, where individual users aim to minimize their carbon
footprints through the optimal scheduling of flexible load devices. The
specific operational dynamics and constraints of deferrable loads and
thermostatically controlled loads are considered, and the carbon emission flow
method is employed to determine users' carbon footprints using nodal carbon
intensities. Then, an optimal power dispatch model that integrates the C-DR
mechanism is proposed for low-carbon power system operation, based on the
carbon-aware optimal power flow (C-OPF) method. Two solution algorithms,
including a centralized Karush-Kuhn-Tucker (KKT) reformulation algorithm and an
iterative solution algorithm, are developed to solve the bi-level power
dispatch optimization model. Numerical simulations on the IEEE New England
39-bus system demonstrate the effectiveness of the proposed methods.
