This paper analyzes the small-signal impedance of three-phase grid-tied inverters with feedback control and phase-locked loop (PLL) in the synchronous reference (d-q) frame. The result unveils an interesting and important feature of three-phase grid-tied inverters - namely, that its q-q channel impedance behaves as a negative incremental resistor. Moreover, this paper shows that this behavior is a consequence of grid synchronization, where the bandwidth of the PLL determines the frequency range of the resistor behavior, and the power rating of the inverter determines the magnitude of the resistor. Advanced PLL, current, and power control strategies do not change this feature. An example shows that under weak grid conditions, a change of the PLL bandwidth could lead the inverter system to unstable conditions as a result of this behavior. Harmonic resonance and instability issues can be analyzed using the proposed impedance model. Simulation and experimental measurements verify the analysis

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Small-signal stability is of great concern for electrical power systems with a large number of regulated power converters. In the case of dc systems, stability can be predicted by examining the locus described by the ratio of the source and load impedances in the complex plane per the Nyquist stability criterion. For balanced three-phase ac systems the same impedance-based method applies, for which this paper uses impedances in the synchronous rotating reference (d-q) frame. Small-signal stability can be determined by applying the Generalized Nyquist stability Criterion (GNC). This approach relies on the actual measurement of these impedances, which up to now has severely hindered its applicability. Addressing this shortcoming, this paper investigates the small-signal stability of a three-phase ac system using measured d-q frame impedances. The results obtained show how the stability at the ac interface can be easily and readily predicted using the measured impedances and the GNC; thus illustrating the practicality of the approach, and validating the use of ac impedances as a valuable dynamic analysis tool for ac system integration, in perfect dualism with the dc case.

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