Probabilistic load flow solution using method of moments

This paper presents a simple method for obtaining a probabilistic load flow solution using the method of moments. Bus voltages, line currents, line admittances, generated power and bus loads are considered as complex random variables. These complex random variables are known in terms of probability density functions. The probability density functions of bus voltages and line currents are evaluated using well known load flow equations in terms of moments and cumulants. Expressions for the convolutions of complex random variables in terms of moments and cumulants have been derived. All combinations of generator and/or transmission line outages are considered in the evaluation of quality of bus voltages indices and in determining the suitability of the transmission system to adequately carry the generated powers to the customer load points. The proposed method is very fast because the process of convolution of various complex random variables is performed in the moment and cumulant domain. Further, the method may be applied to the security analysis of bulk power systems.<
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