On Stability of Voltage Source Inverters in Weak Grids

As the number of inverters increases in the power grid, the stability of grid-tied inverters becomes an important concern for the power industry. In particular, a weak grid can lead to voltage fluctuations at the inverter terminals and consequently cause inverter instability. In this paper, impacts of circuit and control parameters on the stability of voltage source inverters are studied using a small-signal state-space model in the synchronously rotating $dq$ -frame of reference. The full-order state-space model developed in this paper is directly extracted from the pulsewidth modulation switching pattern and enables the stability analysis of concurrent variations in the three-phase circuit and control parameters. This paper demonstrates that the full-order model of a grid-tied active (P) and reactive (Q) power (PQ)-controlled voltage source inverter (VSI) can be significantly reduced to a second-order model, preserving the overall system stability in the case of grid impedance variations. This paper also shows that a decrease in the grid inductance does not necessarily improve the stability of grid-tied VSIs. The system stability is a function of both the grid R/X ratio and grid inductance. Despite the grid-side inductor of the LCL filter is in series with the grid impedance, they have different impacts on the stability of a grid-tied PQ-controlled VSI, i.e., an increase in the filter inductance may improve the system stability in a weak grid. These findings are verified through simulated and experimentally obtained data.