Flexibility metrics predominantly focus on low-order statistical measures, only reflecting the system’s average flexibility level and concentration while overlooking the higher-order characteristics of flexibility. In response to these limitations, this paper introduces a portfolio high-order moment analysis theory to characterize the flexibility of power systems. The objective is to unveil the adjustment potential and risks associated with system flexibility. First, by analyzing the mean-variance-skewness-kurtosis model (MVSK Model) of the portfolio, the definition of a flexible unit portfolio is given. A flexible element probability model considering spatial correlation is constructed based on the multivariate Copula function. Secondly, a flexibility evaluation index is established based on each order moment of the flexible element combination, and the index calculation method based on kernel density estimation and Monte Carlo simulation is given. Finally, the proposed index is measured and verified by the FTS-213 test system and the historical data of a power grid in Germany. The example shows that the proposed index can reflect the average level, stability degree, potential and risk of the system flexibility adjustment ability. It can also quantify the impact of the types of flexible resources and the construction area on system flexibility, providing theoretical support for subsequent flexible resource planning.