A sensitivity approach for computation of the probability density function of critical clearing time and probability of stability in power system transient stability analysis

This paper presents a linear approximation method to determine the probability density function (PDF) of the critical clearing time (CCT) and probability of stability for a given disturbance in power system transient stability analysis. The CCT is the maximum time interval by which the fault must be cleared in order to preserve the system stability. The CCT depends on the system load level and thus, is modeled as a random variable due to the probabilistic nature of system load demand. The proposed method first determines the sensitivity of the CCT with respect to the system load, and using these sensitivities it computes the PDF of the CCT based on the PDF of the system load. The probability of system being transiently stable for a particular disturbance and for a given fault clearing time is calculated using the PDF of CCT. This approach is verified to be accurate under the condition of small load deviation by Monte Carlo simulations method. Moreover, the proposed method reduces the computational effort significantly in Monte Carlo simulations indicating that it could be used in real-time on-line applications.