Numerical-Stiffness-Based Simulation of Mixed Transmission Systems

Inclusion of power electronics allows increased controllability and stability in power systems. The simulation of such systems on a large-scale is challenging due to the presence of a large number of switches and nonlinear devices. This paper presents an advanced simulation algorithm to solve the aforementioned problem. The algorithm considers separation of differential algebraic equations (DAEs) on the basis of numerical stiffness and applies hybrid discretization algorithms to simulate the DAEs. The DAEs, in this paper, represent the nonlinear nonautonomous switched system dynamics of power systems. Stability analysis is performed on a general class of nonlinear nonautonomous switched systems to show the constraints under which the proposed algorithm is stable. To show the validity of the proposed algorithm, two case studies are considered: 1) single high-voltage direct current (HVdc) substation based on the modular multilevel converter (MMC); and 2) an example three-terminal MMC-HVdc system. Relaxation techniques are introduced to create a stable interface for the separated DAEs. The developed algorithms are also validated with PSCAD/EMTDC-detailed reference models.