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.
Highlights
Linearized modeling has been widely applied for dynamic analysis of electronic power systems [1]-[5]
If the harmonic transfer functions (HTFs) characterizes the dynamics of a multiple-input multiple-output (MIMO) linear time-periodic (LTP) system, the entire HTF can be seen as composed of block HTFs of multiple single-input single-output (SISO) LTP systems
The vector-norm based truncation method is verified on a three-phase converter-based power system, whose dynamics can be modeled as an LTP system using HTFs
Summary
Linearized modeling has been widely applied for dynamic analysis of electronic power systems [1]-[5]. Harmonic state-space (HSS) models or harmonic transfer functions (HTFs) can be used to characterize the dynamic behaviors of the linear time-periodic (LTP) system [7] These approaches enable the small-signal analysis of frequency-coupling dynamics of electronic power systems in the frequency domain. The conventional approach to the HTF truncation order selection usually considers the dominant harmonic components in the system steady states, such as in unbalanced grids [8], [13], [14] and in modular multilevel converter-based systems [12], [15]. The skew-rectangular truncation is the combination of skew and rectangular truncations [23], which keeps their advantages For these truncation methods, the truncation order can be determined if the error bound is smaller than a predefined threshold. The theory is validated on a three-phase converter-based power system through electromagnetic transient (EMT) simulations
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