“…It's important to note that when it comes to the presence of clusters, the total sags do not exhibit the statistical characteristics of a Poisson distribution process, as observed for rare sags in Section C. In order to 4 If a cubic-square transformation is applied to handle the broad range of ttnek (from some seconds to 10 6 s), replaces the relation (4) characterize the random occurrence of ttne k over time, it is essential to employ a stochastic model for voltage sag events. As suggested in [16,20,21], when the sag rate decreases monotonically over time, the random variable ttne k representing the total sags at site k can be accurately described using a Gamma distribution: (5) where Γ represents the Gamma function, α k stands for the shape parameter, and β k is the scale parameter. The mean value of equation ( 5) can be expressed as equation ( 6): (6) To predict the total number of sags at a specific site denoted as k, we begin by calculating the mean value as described in equation ( 6).…”