A preconditioner for transient stability time domain simulation

Transient Stability analysis, which is one of the most important tasks of power system dynamic security analysis, determines the dynamic behaviour of the power system after a large disturbance. Differential and algebraic equations (DAEs) model the nonlinear dynamic power system. The conventional time domain solution process uses a Newton method to simultaneously solve the differential equations, discretized via an implicit integration method, alongside the non-linear algebraic network equations. Direct or iterative methods can be used to solve the resulting set of sparse linearized algebraic equations. A well-known and faster solution algorithm used in some popular transient stability packages is the Very Dishonest Newton Method (VDHN), which uses a current balance form and a very infrequent LU factorization in the solution of the algebraic equations. In order to prevent any trouble arising from VDHN in today´s complex power system models, an exact Newton method with a Preconditioned Generalized Minimal Residual (GMRES) iterative method forms the basis of this paper. A new incomplete LU based preconditioner is proposed to achieve solution speeds comparable to that of the VDHN method. Results are given for a power system with 1169 buses, 392 generators, 2855 branches. Thanks to the proposed incomplete LU based preconditioner, a full Newton method approach with preconditioned GMRES can be used in the simulation of transient stability behavior with negligible impact on the solution speed.