The large-scale integration of power electronicbased systems poses new challenges to the stability and power quality of modern power grids. The wide timescale and frequency-coupling dynamics of electronic power converters tend to bring in harmonic instability in the form of resonances or abnormal harmonics in a wide frequency range. This paper provides a systematic analysis of harmonic stability in the future power-electronic-based power systems. The basic concept and phenomena of harmonic stability are elaborated first. It is pointed out that the harmonic stability is a breed of small-signal stability problems, featuring the waveform distortions at the frequencies above and below the fundamental frequency of the system. The linearized models of converters and system analysis methods are then discussed. It reveals that the linearized models of ac-dc converters can be generalized to the harmonic transfer function, which is mathematically derived from linear time-periodic system theory. Lastly, future challenges on the system modeling and analysis of harmonic stability in large-scale power electronic based power grids are summarized.

This paper proposes a unified impedance model of grid-connected voltage-source converters for analyzing dynamic influences of the phase-locked loop (PLL) and current control. The mathematical relations between the impedance models in the different domains are first explicitly revealed by means of complex transfer functions and complex space vectors. A stationary (αβ-) frame impedance model is then proposed, which not only predicts the stability impact of the PLL, but also reveals its frequency coupling effect. Furthermore, the impedance shaping effects of the PLL on the current control in the rotating (dq-) frame and the stationary (αβ-) frame are structurally comapred. The frequency-domain case studies on a three-phase grid-connected converter are next presented, and subsequently validated in timedomain simulations and experimental tests. The close correlations between the measured results and theoretical analysis confirm the effectiveness of the stationary-frame impedance model. Index Terms-Grid, impedance model, phase-locked loop (PLL), stability, voltage-source converters (VSCs). 0885-8993

This paper addresses the harmonic stability caused by the interactions among the wideband control of power converters and passive components in an ac power-electronics-based power system. The impedance-based analytical approach is employed and expanded to a meshed and balanced three-phase network which is dominated by multiple current-and voltage-controlled inverters with LCL-and LC-filters. A method of deriving the impedance ratios for the different inverters is proposed by means of the nodal admittance matrix. Thus, the contribution of each inverter to the harmonic stability of the power system can be readily predicted through Nyquist diagrams. Time-domain simulations and experimental tests on a three-inverter-based power system are presented. The results validate the effectiveness of the theoretical approach.

The interconnection stability of a grid-connected voltage-source converter (VSC) can be assessed by the passivity properties of the VSC input admittance. If critical grid resonances fall within regions where the input admittance acts passively, i.e., has nonnegative real part, then their destabilization is generally prevented. This paper presents an overview of passivity-based stability assessment, including techniques for space-vector modeling of VSCs whereby expressions for the input admittance can be derived. Design recommendations for minimizing the negative-real-part region are given as well.

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