Abstract
The dq impedance stability analysis for a grid-connected current-control inverter is based on the impedance ratio matrix. However, the coupled matrix brings difficulties in deriving its eigenvalues for the analysis based on the general Nyquist criterion. If the couplings are ignored for simplification, unacceptable errors will be present in the analysis. In this paper, the influence of the couplings on the dq impedance stability analysis is studied. To take the couplings into account simply, the determinant-based impedance stability analysis is used. The mechanism between the determinant of the impedance-ratio matrix and the inverter stability is unveiled. Compared to the eigenvalues-based analysis, only one determinant rather than two eigenvalue s-function is required for the stability analysis. One Nyquist plot or pole map can be applied to the determinant to check the right-half-plane poles. The accuracy of the determinant-based stability analysis is also checked by comparing with the state-space stability analysis method. For the stability analysis, the coupling influence on the current control, the phase-locked loop, and the grid impedance are studied. The errors can be 10% in the stability analysis if the couplings are ignored.
Highlights
The integration of renewable energy sources is normally assisted by power electronic converters due to its ability for asynchronous connection and fully-AC voltage control
Based on the generalized Nyquist criterion, both eigenvalues of the impedance-ratio matrix need to be drawn as Nyquist plots for the stability analysis [8]
Based on the determinant-based dq impedance stability analysis, the analysis results with considering couplings or without considering couplings are shown as the pole map in Figure 4a under the 301-rad/s cut-off frequency of the phase-locked loop (PLL)
Summary
The integration of renewable energy sources is normally assisted by power electronic converters due to its ability for asynchronous connection and fully-AC voltage control. The determinant, rather than both eigenvalues of the impedance-ratio matrix, which is derived for including couplings, was used for the three-phase rectifier’s stability analysis [12,13] in the 1990s. Based on the generalized Nyquist criterion, both eigenvalues of the impedance-ratio matrix need to be drawn as Nyquist plots for the stability analysis [8]. The other elements of identified via (16) that Ydd adj(I − Yo Zg ) have no right-plane poles It can be concluded via the identification above and (9) that the system stability is determined only by the determinant det((I − Yo Zg )−1 ) of the impedance-ratio matrix. One Nyquist plot or one pole map can be used based on the determinant for the stability analysis by checking the right-plane poles
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