Illustration of the voltage stability by using the slope of the tangent vector component

Abstract

This Paper is dedicated to the analysis of the evolution of the tangent vector during the Continuous Power Flow (CPF) iterations. The flow of the tangent slope (measured in degrees) is shown through the coefficient of lambda tangent vector component and the maximum voltage tangent vector component. A 17 Node Network was used for the purposes of this Paper. The system was modelled in MATLAB software. The admittance matrix of the node voltage equations was formulated and the functions in MATLAB were developed for the systematic formation of the node admittance matrix. Equations for the calculated network were generated in MATLAB. 32 Iterations were performed. Iterations and corrections of iterations were done manually. Firstly, the results for the tangent vectors calculated through the CPF program were compared to the results for the tangents directly calculated with mathematical formula for the tangent, and both results match. The chart, which contains the classical PV curve and the flow of tangent vectors during the CPF iterations, was developed based on the results obtained. The increase in the slope of the tangent in the PV diagram imposes a clear numerical stability limit by specifying an angle limit value, which can be used to trigger an alarm. In addition to the classic Power-Voltage (PV) curve, this serves as an additional indicator for ensuring voltage stability of the examined system.