Probabilistic Power System Production Cost and Reliability Calculation by the Z-Transform Method

Abstract

The authors describe a novel method of probabilistic power system production cost and reliability calculation using the Z transform. In the proposed method, the generating unit available capacity probability density functions (PDFs) are represented by probability impulses. These PDFs are convolved using the Z transform to produce equivalent capacity PDFs. By operating the equivalent capacity PDFs on the system demand, the unit energies, loss of load probability (LOLP), and expected unserved energy (EUE) can be calculated for each load level and the total demand. The method is compared with the cumulant method and Calebrese's traditional direct convolution procedure in terms of accuracy and computing time using the IEEE Reliability Test System. The main advantage of the new method is that actual load and generator availability data can be used directly, rather than via a mathematical representation such as cumulants. An efficient recursive algorithm using the Z transform procedure has been formulated to allow fast evaluations of convolution and deconvolution of PDFs. In terms of computing time, the new method is not much slower than the cumulant method. LOLP and EUE are also calculated more accurately. >