Model reduction of LTI systems using spectral projection with application to power systems

The present work deals with the problem of order reduction using balanced singular perturbation approximation. Direct truncation and singular perturbation approximation are two fully compatible order reduction method for a linear time invariant system, and both methods yield a stable, minimal, and internally balanced reduced model with the equal error bound. This paper presents an efficient technique for computation of full rank approximation of Gramians by matrix sign function which allow to reduce models of order up to O(10
⁴
). Model reduction of unstable system can be performed by system decomposition via block diagonalization of the sign function method. Further, the effectiveness of the algorithm is validated with application to power system.