Power grid transient simulation in linear time based on transmission-line-modeling alternating-direction-implicit method

Abstract

This paper [1] develops a novel and efficient transient simulation algorithm for the power distribution networks. The 3D TLM-ADI method, with linear runtime and memory requirement, is also unconditionally stable which ensures that the time-steps are not limited by any stability requirement. Numerical experimental results show that the 3D TLM-ADI algorithm not only speeds up orders of magnitude over the SPICE but also reduces lots of the memory requirements and the results agree well with the SPICE’s. The power distribution networks are modeled by a three dimensional shunt node structure of the transmission line grids. Each wire segment is represented by resistors and inductors connected in series in x- and y-directions with a capacitor connected to the ground networks, and vias are modeled as resistors and inductors connected in series in z-direction. Once the circuit model has been set up, the system matrices are created by using the transient nodal analysis. Then, the size of each wire segment is shrunk to infinitely small and the original system equations can be transformed to the general three dimensional transmission line equations (3D-TLEs). The 3D-TLEs can be solved by the related techniques such as finite difference time domain (FDTD) method. The FDTD method discretizes the space domain into a finite number