Selection of Membership Functions Based on Fuzzy Rules to Design an Efficient Power System Stabilizer

This paper presents an evaluation of membership functions on a single-machine infinite-bus and two-area four-machine ten-bus power system with power system stabilizers (PSSs). The PSS is added to an excitation system to enhance the damping during low-frequency oscillations. In this paper, the system is analysed for fuzzy logic power system stabilizer (FPSS) with different membership functions (MFs). The speed deviation (Δω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \omega$$\end{document}) and acceleration (Δω˙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta \dot{\omega }$$\end{document}) of the rotor of a synchronous generator are taken as the input to the fuzzy logic controller to improve small signal stability by enhancing damping. The effect of these variables on damping at the generator shaft mechanical oscillation is very significant. The stabilizing signals were computed using the different fuzzy membership functions in the Mamdani inference system. The general membership functions under consideration are triangular, trapezoidal, Gaussian, bell, sigmoid and polynomial types. The performance of the fuzzy logic PSS with different membership functions is compared to get best-suited MF to design an FPSS. The best-performing MF is found based on simulation study with both power systems and with varying no. of linguistic variables as well. It is found that, If the number of linguistic variables is 3 or 5, the preferred best-suited membership function appears as the Gaussian type, while with increased linguistic variables as 7 or above, then the triangular MF is preferable as the performance is better in comparison with Gaussian MF.