Transient Stability Analysis of a Transmission Network Using Eigenvalue Principles with Automated VAR Compensation: A Case Study of the Nigerian Eastern Grid

Power systems may encounter disturbances during operation as a result of switching of various components, etc. Such perturbations include transformer tap-changing action, load variations, and line outages due to various types of faults of which an earth fault is the most common. Stability analysis of a transmission system is necessary for us to determine the stability state of the system so that appropriate control measures can be implemented to guarantee system stability. This article presents the use of eigenvalue obtained from the system-linearized eigenvectors to analyze the stability state of the system. The choice of the eigenvalue principle is based on the strength of accuracy of the method to determine the actual state of the system providing adequate data for easy solution to the problem. The node admittance parameters computed from the line parameters is applied to the eigenvalue–eigenvector model to determine the system stability state. The state of the eigenvalue is used as an input to a control system, which utilized static volt-ampere reactive (VAR) compensators (SVC) to automatically stabilize the non-stable buses in the transmission network. The 6 × 6 nodal admittance matrix is formed and fed to the developed eigenvalue–eigenvector model via MATLAB in order to compute the right and left eigenvectors and the diagonal or eigenvalue of the network under steady-state and contingency condition. After this, the system stability state is determined, and necessary control actions by the SVC are implemented to guarantee system security. The developed model was tested on the 6 bus Eastern Grid Nigerian Transmission Network and validated using a 41 bus network of the same country. The compensated model showed considerable efficiency in improving the transient stability state of the transmission networks in terms of ease of operation, seamless integration into existing control system, and efficient utilization of SVS to compensate for reactive power imbalances. The results from the step response graph of the compensated model shows performance accuracy as the system regained stability in less than 0.5 s, which is a significant improvement over the uncompensated model.