Abstract: The accurate and real-time carbon metering, as the driving force behind the 'double carbon" strategy, provides a quantitative basis for the carbon emission reduction, carbon markets and carbon trading. A carbon metering system depends on the robust carbon metering theories. However, the traditional calculation methods of carbon emission flow are insufficient to address the needs of the local carbon metering at the carbon emission sources. In response to the foregoing, this paper proposes an iterative calculation of carbon emission flow in the power system. Firstly, a mathematical model of the iterative method based on the adjacency characteristics of the buses is developed. The stability of convergence and the computability of the convergence times are then demonstrated based on the characteristics of the power grid flow. Furthermore, the practicality of utilizing the carbon meter devices to measure the carbon emission flow locally is analyzed, the synergy of the carbon meter devices in the source, network and load sides is investigated, and the applicability of the carbon meter devices in generalized bus scenarios is broadened. Finally, simulation examples of a 4-bus system and the IEEE 14-bus system are used to validate the high efficiency and accuracy of the proposed iterative method. The method proposed in this research provides a theoretical foundation for the hardware implementation of the distributed carbon meter system.