Analysis of rare events for AC power flow models

Abstract

We present an analytic approach for evaluating rare event probabilities for several specific AC power flow networks. First we analyze a three-cycle without the small-angle assumption, and compare the results obtained with the DC approximation. Next we analyze a line network powered from a single source at one end with variable voltages. We prove that in the most likely situation at which an overload occurs, nodes further away from the source consume more power. We also provide explicit bounds for the likelihood of this overload. Finally we add a new line to the former system to close the line into a loop, and show that the probability of an overload is considerably lower in this new system.