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• The coordinate transformation stability criterion (CTSC) is derived by constructing the SISO model of the GCI system in αβ domain. This approach provides a simple and intuitive form while minimizing conservatism. • The average parameter assessment metric (APAM) is proposed based on CTSC to evaluate the impact of each parameter over a wide range. • The joint parameter assessment metric (JPAM) is proposed to simultaneously adjust multiple parameters on stability. • System stability can be effectively improved by selecting parameter tuning through parameter assessment metrics. The negative resistance of grid-connected inverter (GCI) and the increasing number of GCI in power grid pose great challenges to the stability of GCI. This paper proposes a coordinate transformation stability criterion (CTSC) based on the single-input single-output (SISO) impedance model for GCI system. A low complexity fractional polynomial model of GCI is derived by the Pade approximation and the SISO impedance model in the αβ domain. CTSC is proposed by applying the Nyquist stability criterion, which simplifies the graph trajectory criterion to a numerical criterion. Since the effect of parameter on stability is usually limited to the neighborhood, average parameter assessment metric (APAM) is proposed based on CTSC to evaluate the impact of each parameter over a wide range. Additionally, joint parameter assessment metric (JPAM) is proposed to simultaneously adjust multiple parameters on stability. Finally, compared with the three criteria for conservatism analysis, CTSC possesses the lowest conservatism. The theory proposed in this paper is verified by experiment. [ABSTRACT FROM AUTHOR]