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This paper presents a modification of the general analytical probabilistic load flow methodology, used primarily in the analysis of composite systems. Some appropriate approximations are introduced and radial operating structure of power distribution systems is also utilized. This has resulted in significant simplification of the general methodology. It is now much more easier to obtain sensitivity coefficients and matrix operation can be avoided if some sort of ordering scheme is used. However, difficulties with the evaluation of convolutions remain and Fast Fourier Transform is still the best tool to deal with that. The methodology is shown on a comparative example taken fiom the literature.

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Summary The paper presents an approach where traditional Power Transfer Distribution Factors (PTDF) matrix is reduced in size so that it reflects sensitivities of branch flows to changes in nodal power injections at generator buses only. The advantage of the reduced PTDF matrix is in both reductions of decision variables in the optimization procedure and number of columns in branch flow constraints matrix. Furthermore, the number of rows is also reduced on the basis of a simple check, which effectively detects non‐binding branch flow limits allowing corresponding rows of the matrix to be omitted. The reduced PTDF matrix was successfully applied in solving two direct current optimal power flow problems: cost minimization and total transfer capacity calculation. Copyright © 2014 John Wiley & Sons, Ltd.