The multi-area systems reliability estimation using probabilistic load flow by Gramm-Charlier expansion

The paper presents the development of new possibilities to evaluate the reliability of multi-area power systems using the probabilistic load flow. One solution to estimate the probabilistic load flow is to approximate the probabilistic density function of fines load flow with the Gramm-Charlier expansion using the concept of Cumulants for nodal powers. The paper used a simple method to obtain the equivalent probabilistic density function for all power flow lines from one hypothetic generating source to each system node. Finally, the loss of load probabilistic values for nodes and system are estimated considering the probabilities of transmission lines outages and their capacitive powers. The analytical results are compared with Monte Carlo simulation and one '' exact '' analytical method.