Probabilistic Load Flow Analysis through Linearized Equations

Abstract

For real time operation, control and security assessment of power system, traditional load flow cannot be used because it operates with fixed load parameters. The consequences of variation in injected power at the buses due to variation in load and generation cannot be accounted. In this work, a probabilistic load flow method has been proposed which takes into account the load variation at the buses. The variations in load, resulting bus voltages and angles and injected power are represented by normal distribution and discrete distribution. Linearized load flow equation was used in a modified manner by generating random values from the PDF of injected active and reactive power at the buses to obtain the random values of bus voltage and its angle. The method was applied on IEEE 14-Bus, IEEE 30-Bus and IEEE 57-Bus systems. For IEEE 14-Bus system, two cases have been studied. In the first case, the loads are considered as continuous with normal distribution and in second case, the load has been considered discrete at 9th bus while continuous at other buses. The probabilistic load flow was analysed considering varying active and /or reactive load components and the performance has been analysed through distribution function PDF and CDF for bus voltage and angles having minimum and maximum deviation.