Real-time electricity carbon flow computation based on physics-informed neural network

Accurate and efficient electricity carbon flow computation is crucial for electricity carbon emission tracing, low-carbon dispatch and responsibility allocation. However, analytical electricity carbon flow computation methods rely on explicit power flow computation, leading to high computational cost, whereas purely data-driven computation methods may violate physical constraints. To overcome these limitations, this paper proposes a Physics-Informed Neural Network (PINN)-based electricity carbon flow computation method, which embeds both power balance and carbon balance equations into the training objective function, enabling physically consistent and computationally efficient electricity carbon flow estimation. First, the nodal electricity carbon flow balance equations are derived under the carbon flow theory. Second, a PINN model is proposed with composite physical loss and data loss functions. The physical loss is based on the nodal electricity carbon flow balance and the nodal power balance. Finally, case studies on the IEEE 9-bus and IEEE 118-bus systems demonstrate that the proposed method achieves millisecond-level computation, enabling efficient real-time electricity carbon low analysis. © 2026 Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd.