Vector-Norm Based Truncation of Harmonic Transfer Functions in Black-Box Electronic Power Systems

Abstract

Power systems equipped with power electronic converters can be modeled by harmonic transfer functions (HTFs) in a black-box manner for dynamic analysis. This paper studies the truncation of HTFs. It is proposed to define the gain function of an HTF as the norm of its central-column vector. Then, the error bound of the gain function in relation to the truncation order is explicitly derived, which can be used as an indicator for the HTF truncation. Compared with existing solutions, the proposed method is practical in truncating black-box systems with unknown internal parameters, since the truncation error bound can be estimated by the central-column elements of the HTF, which can be easily measured through frequency scan. The truncation approach is finally verified on a three-phase electronic power system by electromagnetic transient simulations.INDEX TERMS Time-periodic system; harmonic transfer function; truncation; frequency scan; black-box system; frequency-domain analysis