Abstract
This study introduces a flow network model to dynamically track carbon emissions in power grids, addressing limitations of traditional methods by transforming grids into directed graphs with virtual sink nodes for transmission losses. Using Markov chain-based probabilistic flow analysis, the model allocates emissions from generators to loads and power lines, incorporating life cycle emissions and eliminating matrix inversion. Validated via a 24-hour simulation on the IEEE 30-bus system, results demonstrate significant fluctuations in emission factors driven by renewable generation variability. Loads near renewables achieve near-zero emission factors during peak green generation, while loads remote from renewable sources exhibit weaker responses. The grid-level emission factor, inversely correlates with renewable output, reaching minimum during the highest renewable penetration. Furthermore, the model reveals that transmission losses contribute marginally to total emissions compared to loads, emphasizing the need for demand-side optimisation. This framework enables dynamic carbon-aware grid operations, such as aligning consumption with renewable availability and prioritizing low-loss pathways. By incorporating life cycle emissions, the model provides critical insights for sustainable grid planning, highlighting trade-offs between renewable deployment, storage integration, and emission reduction costs. The methodology's scalability and compatibility with both transmission and distribution networks position it as a robust tool for advancing analysis of low-carbon power systems.