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.
Highlights
AC power electronic systems are widely found in modern power grids, driven by the large-scale integration of renewable energy resources, flexible dc and/or ac transmission systems
In the presence of three-phase unbalanced or even harmonically distorted voltages, the time periodicity is still present in the dq frame, and their dynamics cannot be characterized as the linear time-invariant (LTI) model in the single dq frame
The framework summarizes the existing relationships among different modeling methods, and reveals some missing ones includingr The linearization and transformation can be exchanged r flexibly in the modeling process; The initial-phase impact needs to be considered for the generalized dq (GDQ) modeling in relation to the harmonic state-space (HSS) or dynamic phasor (DP) modeling
Summary
AC power electronic systems are widely found in modern power grids, driven by the large-scale integration of renewable energy resources, flexible dc and/or ac transmission systems. The linearization around their equilibrium points can be performed [33] This method has been widely applied to model power converters in three-phase unbalanced grids [19], [22] or with multiple harmonics [20], [21]. In [38], the equivalence of the two methods was verified through the eigenvalue analysis of the resulted state-space models, which was, merely based on numerical studies Their relationship is further revealed in [39], pointing out that the DP model can be transformed into the HSS model through the Laplace transformation. The unified modeling framework is further verified on a three-phase converter under unbalanced grids through mathematical proofs, simulations, and experiments
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