Towards a Graph Signal Processing Framework for Modeling Power System Dynamics

The conventional approaches for modeling dynamic systems are based on state-space methods using differential algebraic equations (DAEs). Such models not only require that the system dynamics can be precisely captured and expressed in mathematical equations, but also need detailed knowledge about the system parameters. Even when such DAEs are available, no closed-form solutions are available, and numerical solutions can be computationally expensive. As an example, modern power systems are typically large complex networks comprising of hundreds or even thousands of buses. The dimension of the mathematical models can easily reach the order of several thousands of state variables for dynamic simulation, trajectory sensitivity analysis, control, and so forth. Therefore, analyzing these extremely high-order DAEs poses a huge computational burden [1] .