82 SM 429-9 March 1983, p 527 factors are component structural importance measures, le Evaluation of Importance and Related Reliability Measures for Electric Power Systems G. J. Anders, Member IEEE Ontario Hydro Fsf=t, j 1 systems upgraded by improving components with relatively large importance Three importance measures are introduced in the paper 1 Structural importance, IST, defined as a partial derivative of probability of system failure (PSF) with respect to ponent failure probability (py) the com¬ /ylST, Thus, the frequency of system failure is obtained with minimal computational effort once the structural importance measures are computed Several examples are provided to illustrate the concepts intro¬ duced in this work and an application of a computer program to calculate the above reliability measures for power system problems is Evaluation of the probability and frequency of system failure has a relatively long history in power system reliability computations The information about system reliability described by those indices can be enhanced considerably by introducing measures of relative reli¬ ability importance of system components The component or cut-set's contribution to the system failure is termed its importance It is a function of component failure char¬ acteristics and system structure An importance analysis is akin to a sensitivity analysis and thus useful for system design, operation and optimization For example, we can estimate possible variation in system failure probability caused by uncertainties in component reliability parameters Inspection, maintenance and failure detection can be carried out in their order of importance for components, and , discussed in the paper 82 SM 434-9 March 1983, p 538 Optimal Network Bus Ordering in Power System State EstimationIts Consistency with That in Load Flow Hiroshi Sasaki, Member IEEE Department of Electrical Engineering, University of Hiroshima, Higashi Hiroshima, Japan State estimation technique provides a powerful tool for obtaining reliable data base for an on-line supervision of a very large and complicated power system As the static state estimation algorithm of an electric power system ultimately results in solving a system of linear equations of very large dimensions, it is mandatory to make the algorithm as efficient as possible The efficiency of the algorithm may be determined by the following three items (1) To clarify a basic rule for the ordering in state estimate calcula¬ tions, (2) To utilize the most optimum ordering scheme, and (3) To formulate the state estimate equation so that it requires less arithmetic operations and storage memory This paper discusses the above important factors, with the first a This measure is equal to the difference of two probabilities of system failure First probability is obtained by considering the system with component; removed The second probability is computed with component y replaced by a perfect com¬ 2 ponent Cnticahty importance, ICR, defined as a fractional sensitivity of system failu re with respectto changes in componentfailure probability PSF This measure considers the fact that it is more difficult to more reliable components than to improve less re¬ liable ones importance, IFV, defined as a conditional improve 3 Fussell-Vesely prob¬ ability that the system has failed based on the cuts containing element/ (this probability is denoted by Psf(D) given that the system is in the failed state Thus, ' PSF This measure reflects the importance of an element by the fact of its presence in several minimal cuts To evaluate the above importance measures, an algorithm com¬ puting probability of system failure is required For the purpose of computing measures 1 and 2 any algorithm will do For the third measure an algorithm utilizing minimal cuts of the system is re¬ quired In this paper an efficient computational algorithm to evaluate the exact probability of system failure given the set of minimal cuts is presented Using this algorithm a polynomial expression for system failure probability is obtained Given this expression the relative reliability importance of system components and the exact fre¬ quency of system failure will be easily evaluated The frequency of system failure {FSF) is shown to be a weighted sum of the component failure frequencies (fy) where the weighing PER MAR 1983 two being especially emphasized As is well known, the state estimate equation of a power system must be established by accounting for two different kinds of in¬ formation, that is, the system topology and measurement specifica¬ Hence, the network bus ordering for state estimation essen¬ tially differs from that in load flow T A Stuart compared ordering methods in state estimation [1], but he only took into account the topological information The author proposes a general rule of the optimal ordering in state estimation, which takes into consideration the measurement in¬ formation as well as network topology That is, the measurement information is translated into its topological equivalent and annexed to the network topology data, thus the unified reference information being obtained for the ordering The converting rule can be summarized as follows (A) For a node, at which its injection is measured, add additional 11 nes with zero admittance so that all of its adjacent nodes are completely interconnected These added lines are desig¬ nated as "imaginary lines" (B) Do nothing for line flow or voltage magnitude measure¬ ments (C) Delete an actual line, for which neither its line flows nor node injections are measured at either of its terminal nodes tion One of the most informative outcomes of the above rule is that we able to obtain a clear insight on changes in computational burden by altering measurement set For instance, the more node injections are chosen, the more imaginary lines are generated Then, seen from the viewpoint of computational efficiency only, a measare 23