Calculation of the probability density function of critical clearing time in transient stability analysis

The critical clearing time, t_cc, in power system transient stability analysis is modeled as a random variable due to the random nature of the power system load. A linear approximation approach that mainly involves the sensitivity calculation of the derivative of t_cc to the system load is developed to obtain the probability density function (PDF) of t_cc based on the PDF of the system load. A Monte Carlo simulation method is used to verify that this approach is accurate under the condition of small load deviation. The probability of the system being transiently stable for particular disturbances is calculated based on the PDF of t_cc.