Physics-informed graph neural network for carbon emission flow analysis in power systems

High-resolution carbon emission flow (CEF) modeling is critical for carbon-aware power system scheduling and market operations. Conventional analytical methods are accurate but computationally demanding, whereas existing data-driven methods are fast yet often compromise physical consistency and robustness under varying operating conditions. To mitigate the practical trilemma among computational efficiency, physical consistency, and robustness, this paper proposes a physics-informed graph neural network (PI-GNN) for fast yet physically reliable CEF analysis. We formulate the CEF analysis as a graph completion problem, integrating prior knowledge of carbon emission intensity (CEI) reference buses via a bus-type-aware mask encoder and enforcing physical consistency by embedding AC power flow and CEF equations into a physics-consistent residual loss. Case studies on IEEE 14-, 39-, and 118-bus systems demonstrate that PI-GNN reduces prediction error by 61%–86% relative to multilayer perceptron and graph convolutional network baselines, and delivers millisecond-level inference—only 1.66–17.71% of the runtime of analytical methods. With an increasing number of islanded buses, PI-GNN limits the error increase to within 28%, whereas the baselines exhibit a 90%–330% increase. Within a reinforcement-learning-based framework for optimal CEF dispatch, the pretrained PI-GNN accelerates training convergence and reduces daily generation cost by 9.5% and CEF losses by 4.9%, indicating its potential for real-time carbon-aware operations. • A physics-informed GNN is developed for fast, high physical fidelity CEF analysis. • The CEF analysis is cast as a graph completion task with configurable prior knowledge. • Bus-type-aware mask encoder adapts network to dynamic system operating conditions. • Self-supervised physics-consistent residuals enhance physical fidelity and accuracy.