Towards a Graph Signal Processing Framework for Modeling Power System Dynamics The conventional approaches for modeling dynamic systems are based on statespace 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 closedform 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 highorder DAEs poses a huge computational burden 1 .

Modeling and Recovery of Graph Signals and DifferenceBased Signals In this paper, we consider the problem of representing and recovering graph signals with a nonlinear measurement model. We propose a twostage graph signal processing (GSP) framework. First, a GSP representation is obtained by finding the graph filter that best approximates the known measurement function. The new GSP representation enables performing tractable operations over graphs, as well as gaining insights into the signal graphfrequency contents. Then, we formulate the signal recovery problem under the smoothness constraint and derive a regularized leastsquares (LS) estimator, which is obtained by applying the inverse of the approximated graph filter on the nonlinear measurements. In the second part of this paper, we investigate the proposed recovery and representation approach for the special case of graph signals that are influenced by the differences between vertex values only. Differencebased graph signals arise, for example, when modeling power signals as a function of the voltages in electrical networks. We show that any differencebased graph signal corresponds to a filter that lacks the zeroorder filter coefficient, and thus, these signals can be recovered up to a constant by the regularized LS estimator. In our simulations, we show that for the special case of state estimation in power systems the proposed GSP approach outperforms the stateoftheart estimator in terms of total variation.