Sequence operation theory and its application in power system reliability evaluation

The primary objective of this paper is to report a new mathematical approach named sequence operation theory (SOT) to handle the difficulty and complexity of power system reliability evaluation (PSRE) that arises from integrated resource planning or under deregulation environment. Enlighten by traditional discrete convolution, four type of discrete sequence operation (DSO) named addition-type-convolution, subtraction-type-convolution, AND-type-product and OR-type-product, are proposed in this paper. A special type of discrete sequence named probabilistic sequence (PS) has been studied in detail. In order to put SOT into practice, the definition of expected value of PS is presented according to Probability Theory. Moreover, some physical concepts of DSO between two PSs have been discussed. As a exact mathematical theory, all the properties of SOT are proved. SOT is a new general mathematical theory and wide application in many fields could be expected. A new PSRE method based on the theory of SOT is briefly reported in this paper. When dealing with traditional PSRE problems, such as IEEE Reliability Test System, the numeric example shows that the result of our approach is almost the same as that of traditional one. However, the new method can solve the newly emerging problem of PSRE in integrated resource planning or under deregulation environment, where the whole demand would be classified into several types and each type can be given a certain reliability index.