Physics-informed neural network for dynamic energy flow calculation in integrated electricity and gas systems

The global decarbonization is driving integrated energy systems (IES) toward more efficient and low-carbon operations, with tighter coupling between natural gas systems (NGS) and electric power systems (EPS) to accommodate diverse renewable sources and energy carriers. The bidirectional energy flow problem in IES with a partial differential algebraic equations (PDAE) form remains a challenge for model-based solvers due to privacy concerns and computational complexity, as it may require full parameters and dozens of minutes or hours to obtain a feasible solution in large-scale systems. To address this obstacle, this study proposes a physics-informed neural operator for energy flow calculations in IES. A novel Differential-Algebraic Gas Flow Neural Operator (DAGFNO) is proposed to embed physical constraints of PDAE into the neural operator, which not only obtains accurate heterogeneous gas states but also provides a privacy-preserved interface for EPS analysis. Besides DAGFNO, we also developed a novel Masked Differential and Algebraic Coupling Constraint Loss function (MDACloss) to represent the degree of constraint violation and enable its parallel computing ability through the masking technique. By doing so, the MDACloss could guarantee the satisfaction of constraints in the energy flow calculation of IES obtained by the DAGFNO as much as possible. Case studies on two NGS and EPS coupled IESs reveal the effectiveness of the proposed method.