Security assessment for bus voltages using probabilistic load flow

Probabilistic load flow (PLF) solution based on the method of moments is used for security assessment of bus voltages in power systems. Bus voltages, line currents, line admittances, generated real and reactive power, and bus loads are treated as complex random variables. These complex random variables are known in terms of probability density functions (PDF). Also, expressions for the convolutions of complex random variables in terms of moments and cumulants have been derived. PLF solution using the method of moments is fast, because the process of convolution of various complex random variables is performed in moment and cumulant domain. The paper proposes the method using PLF solution for the security assessment of bus voltages, so that the PDF of bus voltages readily provide probabilities of threshold violations for a whole planning period, reflecting the random variation of loads, generation uncertainties, dispatching effects and outages. Consequently, as a part of a power system security assessment, monitoring bus voltages in system become necessary to detect dangerous situations as soon as possible. Analysis task should be informed whether the current state is stable, critical or unstable with respect to a possible fault in a particular system component. Also, system operator can utilize the information of security assessment to improve reliability of power systems using the proposed method in this paper.