Determination of Generator Angular Speed and Rotor Angle using Swing Equation, Runge-Kutta Fourth Order and State Variable Methods
Keywords:
Angular speed, Fourth-order Runge-Kutta, Rotor angle, State variable analysis, Swing equationAbstract
This study investigated the transient response of the generators in the Nigerian 330 kV grid network when a three phase is applied to perturb the system to determine the impact on the rotor angle and angular speed deviations in the network under investigation in a view to describe the behaviour of the 330/132kV Adiabo/Odukpani network with particular emphasis on the characteristics of 593MW synchronous generators after a large disturbance on the power system. To overcome these incessant disturbances on the network, which often result in outages and blackouts that can damage or hinder certain components of the network, there is a need to conduct transient stability evaluations on the power system to determine various network parameter conditions. This study proposed the determination of generator angular speed and rotor angle using the state variable analysis method in comparison to the existing Runge-Kutta fourth order (RK4) method, while benchmarking it against traditional swing equations numerical techniques to model power system behavior following a transient condition. This approach enables the simulation and prediction of whether the system will return to normal operation or become unstable by analyzing rotor angles and speeds over time. This study provides a comprehensive analytical and numerical examination of the determination of angular speed and rotor angle of synchronous generators through three methodologies: the traditional swing equation method, the Fourth-Order Runge-Kutta (RK4) method, and the State Variable Approach (SVA). Numerical iterations, comparative performance assessments, and in-depth mathematical derivations are provided. The results show that while the traditional approach offers a straightforward baseline solution, RK4 greatly improves accuracy, and SVA enables scalability for multi-machine systems with improved accuracy and stability. The results offer insights into their usefulness in power system stability studies and enhance modeling and simulation techniques in power system dynamics.
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