Finding the reliability expression of different substation configurations can help design a distribution system with the best overall reliability. This paper presents a computerized and implemented algorithm, based on Disjoint Sum of Product (DSOP) algorithm. The algorithm was synthesized and applied for the first time to the determination of reliability expression of a substation to determine reliability indices and costs of different substation arrangements. It deals with the implementation and synthesis of a new designed algorithm for DSOP implemented using C/C++, incorporating parallel problem solving capability and overcoming the disadvantage of Monte Carlo simulation which is the lengthy computational time to achieve satisfactory statistical convergence of reliability index values. The major highlight of this research being that the time consuming procedures of the DSOP solution generated for different substation arrangements using the proposed method is found to be significantly lower in comparison with the time consuming procedures of Monte Carlo-simulation solution or any other method used for the reliability evaluation of substations in the existing literature such as meta-heuristic and soft computing algorithms. This implementation gives the possibility of RBD simulation for different substation configurations in C/C++ using their path-set Boolean expressions mapped to probabilistic domain and result in simplest Sum of Disjoint Product which is on a one-to-one correspondence with reliability expression. This software tool is capable of handling and modeling a large, repairable system. Additionally, through its intuitive interface it can be easily used for industrial and commercial Power systems. With simple Boolean expression for a configuration’s RBD inputted, users can define a Power system utilizing a RBD and, through a fast and efficient built-in simulation engine, the required reliability expressions and indices can be obtained. Two case studies will be analyzed in this paper. The effects of different substation configurations on the reliability are analyzed and compared. Then, the reliability of a radial distribution system will be evaluated using DSOP solution. The failure results will be combined with a load flow scenario, and indices such as SAIDI, SAIFI will be determined.

In this paper we present some properties of set-norm exhaustive set multi functions and also of atoms and pseudo-atoms of set multi functions taking values in the family of non-empty subsets of a commutative semi group with unity.

In this paper we define the Soft set Product as a product of many soft sets and afterwards we extend it to the HyperSoft set. Similarly, the IndetermSoft Product is extended to the IndetermHyperSoft set. We also present several applications of the Soft set Product to Fuzzy (and fuzzy-extensions)  Soft set Product and to IndetermSoft set and IndetermHyperSoft set.

A fuzzy-set based Power system stabilizer is proposed to enhance the stability of a Power system. The controller parameters are optimized using Genetic Algorithm (GA). An Artificial Neural Network (ANN) is then trained so that the controller parameters are selftuned based on operating conditions. The performance of the proposed approach has been assessed by simulating it on a single machine infinite busbar system.