International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 12 Issue: 06 | Jun 2025
p-ISSN: 2395-0072
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Stability Analysis in Power System Using Energy Preserving Function Dipkumar Santoshkumar Trivedi1, Arpit Rajnibhai Joshi2, Krunalkumar Govindbhai Patel3 1Lecturer, K. D. Polytechnic Patan, Gujarat, India 2Lecturer, K. D. Polytechnic Patan, Gujarat, India 3Junior Engineer, UGVCL, Gujarat, India
---------------------------------------------------------------------***-------------------------------------------------------------------Abstract— Main purpose of this paper is to check the on this Critical Clearing Time (CCT) is calculated for different
Fault Locations. The method used for Transient Stability analysis in [5] is combination of Step by Step method with direct Methods. This method first calculates the potential and Kinetic energy of all machines in power system before and after occurrence of Fault. It finally compares Largest Group of Kinetic Energy to Smallest Group of Potential energy for Evaluation of Transient stability. If smallest group of Potential Energy is Greater than Largest Group of Kinetic Energy then System is Consider as stable.
stability of Multi machine power system with the help of Energy Preserving Function (Energy Based Direct Method). In this method first step is to compute Total Energy gained by the system during the Fault and by comparing this energy with Critical Energy CCT (Critical Clearing Time) can be estimated. Total Energy can be summarized as sum of Kinetic and Potential Energy during the fault. The Critical Energy can be Find out with the help of Closest Unstable Equilibrium Point method (C-UEP). For this analysis Considered Test System is Standard WSCC (Western System Coordinating Council) 3 machine 9 Bus System.
Transient Stability using Energy function can be analyzed with the help of Controlling UEP method which exclusively discussed in [12] whereas reference [13] mainly focus on the difficulty arise in the study of Energy based methods Like UEP, BCU, PEBS etc and prepare computational algorithms for finding out solutions.
Index Terms—Transient Stability, Critical Clearing Time (CCT), Energy Function, Critical Energy, Closest Unstable Equilibrium Point Method (C-UEP).
I. Introduction
II. Direct Method for Stability Analysis
Different forms of instability have emerged over the last century. Power System Stability is a complex problem that has challenged power system engineers for many years. Power system stability problems are solved with the help of computational tools, stability theories and advanced control strategies.
The transient energy approach can be understood by the example of rolling ball inside the bowl. The inside area of bowl is considered as stable region and outside area as the instable. Initially ball is at bottom that point is considered as the stable equilibrium point (SEP). When some kinetic energy is given to ball then ball starts to move in particular direction. The point where ball will stop that depends on initial given kinetic energy. The surface inside the bowl represents Potential Energy surface. The rim of the bowl represents the Potential Energy Boundary Surface (PEBS).Consider the potential energy at rim is PI, and given kinetic energy is KI.
The Direct Methods determines stability without solving the system of differential equations. Basic approach developed in [3, 5] is practical, enough accurate and apply to practical power system for better planning and operation. Direct methods without the solution of differential equations can be used to determine the transient stability analysis of power system. This method is the Lyapunov’s direct method (second method). The energy-based method is a special case of Lyapunov’s direct method. These techniques are extensions of the equal area criterion to power systems with more than two generators represented by the classical model.
If, KI > PI => Ball will cross the rim =>Unstable condition. KI < PI => Ball will not cross the rim => Stable Condition.
The authors of paper [4] proposed direct method that uses individual machine or group of machines energy function. The Energy function of each machine is compared to a Critical Energy which can be determined by Potential Energy Boundary Surface (PEBS) method or Boundary Controlling UEP (BCU) method or Closest Unstable Equilibrium point. If the individual Machine’s Energy is greater than Critical Energy then system is considered as unstable. Based
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Fig.1.A ball rolling on the inner surface of the bowl
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