Order-reduction Strategy of Non-linear Differential-algebraic Equation Models with Application on Power Systems

Abstract

The time evolution of many physical processes in power systems is described by non-linear differential-algebraic equations. In this article, a new reduced-order modeling technique for constructing explicit state-space approximations of non-linear power system models described by differential-algebraic equation models is developed. The proposed technique takes into account the interconnection structure and provides information on the effect of control actions on system behavior. A general second-order theory is presented for treating non-linear behavior in large non-linear power system models. In this approach, the algebraic equations are first reduced by projecting the original system model onto a truncated basis of the subspace generated by the right and left eigenvectors of the linear system model. A technique for constructing an explicit state-space approximation of the non-linear differential-algebraic equation model is then developed. The method is highly efficient and capable of developing state-space approximations of interest for non-linear simulation and control design while maintaining acceptable accuracy. Examples of the application of the developed procedures on a 50-machine test system are presented to estimate the validity of the reduction technique.

Keywords:

• proper orthogonal decomposition
• time-varying local modal approximation