This paper delved into in-depth modeling and analysis of locational marginal carbon intensity (LMCI) and developed a comprehensive set of indicators to assess carbon emission volatility from multiple perspectives. Firstly

starting from the locational marginal price and considering the characteristics of generator carbon emission intensity with load rate

a time-flexible definition of the LMCI was proposed along with corresponding fast computation methods. Subsequently

to explore the low-carbon driving force of the LMCI within the context of electricity and carbon markets

a bi-level low-carbon economic dispatch model based on the LMCI for transmission system operators and load aggregators was proposed. Then

three distinct indicators were introduced to capture carbon emission volatility from temporal

spatial

and market perspectives: locational marginal carbon intensity consistency probability

locational marginal carbon intensity volatility expectation

and producer carbon benefit volatility index. These depict the carbon emission volatility of each time interval

node

and system. Finally

an example analysis was carried out based on IEEE-30

IEEE-57

and IEEE-118 node systems to explore the characteristics of the LMCI and its effect on low carbonization and verify the effectiveness of the indicator system proposed in this paper.