Effects of Unsuccessful Transmissions of Measurements on Uncertainty in Power Flow Calculations

Using a linear DC power flow model, the power flow calculation can be determined by the bus susceptance matrix and the voltage angles. In this paper, we consider a power system where the voltage angle measurement at each bus is transmitted to a control center via a wireless communication channel. In order to model unsuccessful transmissions, we derive a two-component Gaussian mixture model to describe the probability density function of our knowledge of every voltage measurement at the control center. We investigate how the unsuccessful transmissions of each link affect the distribution of the quantities calculated by the power flow calculation at the control center.