Frequency disturbances caused by power system faults propagate in the form of electromechanical waves. This propagation process affects the frequency response analysis and decision-making of safety control measures such as frequency stability maintenance and under-frequency load shedding. The conventionally used offline simulation method offers high calculation accuracy

but it has limitations such as poor adaptability to complex and variable new power systems and insufficient online computing capability. An online calculation method is proposed for frequency propagation based on approximate analytical solutions and physics-informed neural network (PINN). Firstly

a partial differential equation model for the propagation of electromechanical disturbance frequencies is established. Through engineering simplifications

an analytical expression of frequency disturbance with respect to time and position is derived

which meets the requirement for fast calculation of frequency disturbances but suffers from reduced calculation accuracy due to the simplifications. Subsequently

PINN is introduced to improve calculation accuracy. A small amount of high-precision simulation data and a large amount of low-precision data quickly obtained from analytical solutions are used as samples

which solves the problem of excessive sample generation time. Furthermore

the electromechanical disturbance frequency propagation model before simplification is incorporated into the network layer as a physical constraint. This not only ensures fast calculation but also enhances the calculation accuracy and generalization performance across different operating scenarios. Finally

a case study system is built using RT-Lab and PyTorch. The feasibility and superiority of the proposed method are verified through simulation and comparative analysis.