Stochastic carbon footprint tracing for power systems with uncertainty

The increasing penetration of distributed energy resources (DERs) and renewable energy sources (RESs) requires more granular analysis for accurate carbon footprint tracing. Traditional tracing methodologies primarily utilized deterministic steady-state analyses, which inadequately addressed the significant uncertainties inherent in RESs. To address this gap, this study introduces two stochastic carbon footprint-tracing approaches that incorporate RES uncertainties into load-side carbon footprint assessments. The first method embeds a probabilistic analysis within the carbon emissions flow (CEF) framework, providing a comprehensive reference for the spatial distribution of carbon intensity across power system components. Recognizing that the CEF network complexity increases with higher DER penetration, the second method extends the initial approach to enhance computational efficiency while maintaining accuracy, thus ensuring scalability for large-scale power system topologies. The proposed models were validated and benchmarked using a synthetic 1004-bus test system in a case study, demonstrating their enhanced performance and advancements over conventional deterministic methods. The results underscore the effectiveness of the stochastic approaches in delivering more precise and reliable carbon footprint tracing, thereby contributing to the sustainable management of decarbonized power systems.