  As the penetration of distributed energy resources (DER) and renewable energy
sources (RES) increases, carbon footprint tracking requires more granular
analysis results. Existing carbon footprint tracking methods focus on
deterministic steady-state analysis where the high uncertainties of RES cannot
be considered. Considering the deficiency of the existing deterministic method,
this paper proposes two stochastic carbon footprint tracking methods to cope
with the impact of RES uncertainty on load-side carbon footprint tracing. The
first method introduces probabilistic analysis in the framework of carbon
emissions flow (CEF) to provide a global reference for the spatial
characteristic of the power system component carbon intensity distribution.
Considering that the CEF network expands with the increasing penetration of
DERs, the second method can effectively improve the computational efficiency
over the first method while ensuring the computational accuracy on the large
power systems. These proposed models are tested and compared in a synthetic
1004-bus test system in the case study to demonstrate the performance of the
two proposed methods
