Reduced-order state-space systems in the dynamic harmonic domain

Abstract

This paper presents a methodology to simulate electric networks in the dynamic harmonic domain (DHD) via model order reduction. Initially, the full-order system of ordinary differential equations (ODEs), expressed in the DHD, is internally balanced in the state sense. Then, the balanced system is truncated by selecting the dominant subsystem, resulting in a reduced-order system of ODEs. The reduced system permits to reproduce the dynamics of the original full-size system with accuracy dictated by the Hankel singular values, also known as second-order modes, of the balanced system. Also, the reduced-order system permits to achieve computational savings. A sample network is used for the illustration of the proposed method.