Systems, methods, and non-transitory computer-readable storage media for a fast power network simulator. A system configured per this disclosure can use identify a power network, the power network comprising generators, transmission lines, and loads, and receive a model of the power network. The model of the power network can include: models of the generators modeled as differential equations, and models of the transmission lines and the loads modeled as algebraic equations. The system can convert, via a processor, the algebraic equations of the models of the transmission lines and the loads to additional differential equations, then combine, via the processor, the differential equations and the additional differential equations, to yield combined differential equations. The system can then iteratively solve linear equations, via the processor, associated with the combined differential equations, to yield solutions, and output the solutions as part of a power simulation of the power network.