  Recent shifts toward sustainable energy systems have witnessed the fast
deployment of carbon-free and carbon-efficient generations across the power
networks. However, the benefits of carbon reduction are not experienced evenly
throughout the grid. Each generator can have distinct carbon emission rates.
Due to the existence of physical power flows, nodal power consumption is met by
a combination of a set of generators, while such combination is determined by
network topology, generators' characteristics and power demand. This paper
describes a technique based on physical power flow model, which can efficiently
compute the nodal carbon emissions contributed by each single generator given
the generation and power flow information. We also extend the technique to
calculate both the nodal average carbon emission and marginal carbon emission
rates. Simulation results validate the effectiveness of the calculations, while
our technique provides a fundamental tool for applications such as carbon
auditing, carbon-oriented demand management and future carbon-oriented capacity
expansion.
