Comparative Study of Modified Euler and 4th Order Runge Kutta Numerical Techniques for Transient Stability Prediction

Abstract

The focus of this study is to examine the transient response of synchronous machines in a 132KV transmission grid power system through the utilization of various numerical methodologies. In order to ascertain the critical clearing angle (CCA) and critical clearing time (CCT) of the transmission grid, a balanced 3-phase fault was implemented. The study and simulation were conducted using the data obtained from Transmission Company Nigeria (TCN). In order to examine the differential variations in generator rotor angles, generator bus voltage, and system frequency, the Electrical Transient Analysis Program (ETAP 19.1) was employed to simulate the time setting of circuit breakers and relays at intervals of 0.00, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, 0.14, 0.16, 0.18, and 0.2. The findings indicate that the 4th Order Runge Kutta numerical technique exhibits stability and accuracy. It demonstrates a rapid response critical clearing time (CCT) of 0.02s and a critical clearing angle of 76.9 degrees, which closely approximates 81.5 degrees. The average critical angle obtained from the simulation, along with a lower percentage error of -51% at the instant of disturbance, further supports these results. The utilization of the 4th Order Runge Kutta numerical algorithm demonstrates superior performance in maintaining stability during transient disturbances within the network under investigation, as compared to the Modified Euler method. In order to improve the stability margin of the network, it is crucial to promptly and effectively coordinate the circuit breakers and protective relays to promptly eliminate a symmetrical 3-phase fault at any bus.