Small-Signal Modeling of AC Power Electronic Systems: Critical Review and Unified Modeling

Abstract

The harmonic state-space (HSS), the dynamic phasor (DP), and the generalized dq (GDQ) modeling are three widely used methods for small-signal analysis of ac power electronic systems. By reviewing their principles and deriving their mathematical relationships, this paper proposes a unified framework for all the three approaches. The unified modeling reveals that the linearization and transformation can be exchanged flexibly in the modeling process, and the initial phase takes a role in transforming the GDQ model into the HSS or DP model. Case studies on a three-phase voltage-source converter in unbalanced power grids are provided for validation. The relationships of three modeling methods are verified by mathematical proofs and time-domain simulations. The unified frequency-domain model is further validated through the frequency scan in experiments. Insights of the unified modeling framework and recommendations from engineering perspectives are finally discussed.

Modeling Techniques and Stability Analysis Tools for Grid-Connected Converters

“…The multi-frequency DPM is for small signal analysis when the system is linearized to form a Linear Time-Invariant (LTI) system. Also, it is worth mentioning that when the initial phase is extracted from the DP model and expressed in the form of a generalized dq (GDQ) transformation, a GDQ model is then derived, which puts an emphasis on the phase difference so that the power transmission is more convenient to calculate accordingly [43]. Combined with the concept of sequence component, unbalance faults analysis can be performed [44].…”

“…In fact, harmonic linearization can be regarded as a combination of FD stabilization and perturbation linearization [25]. Thus, power electronic converters of any topology, which can be expressed by a state-space model, can be easily transferred to an HSS model: single-phase converters [54], transformers [55], three-phase converters under both balanced and unbalanced situation [43], [56] and especially modular multilevel converters that have the nature of nonlinear inter-resonance between sub-modules [40], [57]. Similar to the DPM, the selection of harmonics under consideration has been a critical concern for HSS regarding computational burden.…”

“…) , By reason of the foregoing, the derivation process of the two methods follows the same steps with different order and variable representation [43], thus leading to real states with the DPM while complex states with the HSS model [62]. The flow charts of the derivation processes are shown in Fig.…”

Modeling of Power Electronics Systems and PWM Modulators in Harmonic-State Space

“…9. Test Model for three-phase three-inverter system (18) (19) (20) (21) Based on equations ( 18)-( 21) and the principles derived in Section-2, the set of ODEs can be transformed into the HSS model. The state-space matrices of A and B are derived from the obtained HSS model are shown in (22) and (23).…”

“…A good modeling approach for AC systems is presented in [18] but ignores switching frequency harmonics to focus on low-frequency harmonics. A single Fourier series-based modulation method to predict the spectra generated by digital asynchronous PWM, including the nonintegral harmonics, is presented in [19].…”