Comparative Analysis of Critical Clearing Angle and Critical Clearing Time on the Odukpani–Adiabo 330/132kV Transmission Network using Fourth order Runge-Kutta and State Variable Analysis

Abstract

Transient stability remains one of the most important operational challenges in modern power systems due to increasing loading conditions, network expansion, and fault disturbances. This paper investigates the determination of Critical Clearing Angle (CCA) and Critical Clearing Time (CCT) of the Odukpani–Adiabo 330/132kV transmission system under transient fault conditions using the Conventional Swing Equation, Fourth-Order Runge-Kutta (RK4) numerical method, and State Variable Analysis technique (SVA). The swing equation was employed to model the electromechanical dynamics of the generator rotor during disturbances, while the RK4 method was utilized for accurate numerical integration of nonlinear differential equations. State variable analysis was further applied to represent the system in state-space form for transient stability assessment. The proposed state variable analysis technique was applied by declaring the variables that are changing with respect to time, which are the rotor angle and the angular speed. The existing study cases were modelled and simulated using electrical transient analysis software (ETAP). Comparative analysis demonstrated that not all techniques used in this paper provided dynamic recovery after transient instability, particularly during the cycle of incremental operations. The RK4 model could not achieve stability when faults are cleared to restore and sustain stability with a critical clearing angle and critical clearing time (169 degrees, 0.15 Secs). Similarly, for the conventional swing equation, the critical clearing angle and critical clearing time were (41.25 degrees, 0.07 Secs), while in comparison, the proposed state variable analysis model predicted a critical clearing angle and critical clearing time of (32.65 degrees, 0.06 Secs), respectively. The critical clearing angle and critical clearing time were determined as key indices for evaluating system stability margins. Simulation and analytical results showed that delayed fault clearing significantly increases rotor angle deviation and may lead to instability. The results emphasize the importance of fast fault-clearing mechanisms, protective relays, and efficient system control strategies in maintaining transmission system stability. The study contributes to transient stability assessment of Nigerian transmission networks and provides useful insights for power system planning, operation, and protection coordination.