Abstract
This article proposes a multifrequency admittance model for voltage-source converters with three-phase unbalanced grid voltages. The model is derived with multiple complex vectors and harmonic transfer functions, which is merely dependent on its own input voltage trajectory, and can accurately capture the frequency-coupling dynamics. The dynamic effects of both the basic synchronous-reference-frame phase-locked loop (PLL) and its alternative with a notch filter of the negative-sequence voltage component are compared. It is revealed that the notch-filtered PLL significantly weakens the frequency-coupling effects, which leads to a reduced order of the admittance model. The developed model is validated by a frequency scan, and the frequency-coupling effects impacted by different PLLs and voltage unbalance factors are verified by the experimental tests. Finally, a case study on stability analysis in unbalanced grids proves the significance of the model.
Highlights
V OLTAGE-SOURCE converters (VSCs) are rapidly increasing in power grids, driven by the widescale use of renewable energy sources and flexible power transmission systems
The dq-frame model assumes that the VSC system is three-phase balanced, and the three-phase voltages that are time-periodic operating trajectories can be transformed as the time-invariant operating points in the dq frame [5]
The complex-valued model can intuitively interpret the frequency-coupling dynamics caused by the phase-locked loop (PLL) [5] and the dc-link voltage control [17], [18] in the αβ frame, since the Park/inverse Park transformations used in the VSC control can be seen as frequency shifts by complex vectors in the frequency domain
Summary
V OLTAGE-SOURCE converters (VSCs) are rapidly increasing in power grids, driven by the widescale use of renewable energy sources and flexible power transmission systems. The complex-valued model can intuitively interpret the frequency-coupling dynamics caused by the PLL [5] and the dc-link voltage control [17], [18] in the αβ frame, since the Park/inverse Park transformations used in the VSC control can be seen as frequency shifts by complex vectors in the frequency domain. Considering the coupling effect of an unbalanced operating trajectory on the PLL, this article proposes a generalized multifrequency admittance model for VSCs under unbalanced grid conditions. The concepts of base vectors in the complex space are introduced to rigorously characterize the frequency-coupling dynamics of VSCs. the dynamic impact of the SRF-PLL with a notch filter used for removing the negative-sequence voltage component is analyzed and further compared with that of the basic SRF-PLL. The significance of the proposed model for stability analysis in unbalanced grids is proved by a case study
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