An optimisation model based approach for power systems voltage stability and harmonic analysis

Abstract

This paper presents a novel optimisation problem formulation for power systems voltage stability and harmonic analysis. The purpose is to evaluate the maximum loadability of an electrical power system considering voltage magnitudes, active/reactive powers, total and individual harmonic distortion limits as inequality constraints. The impact of power quality on the maximum loadability margin is evaluated based on the results of the optimisation problem solved by interior-point method and the proposed indices in which Lagrange multipliers are used to identify sensitive buses of electrical systems due to power quality degradation and voltage instability. Simulations are carried out using IEEE 30-bus power system assuming the insertion of non-linear loads to validate the use of the proposed method and show the applicability of the indices based on Lagrange multipliers for the assessment of both voltage stability and harmonic distortion. Results are compared with the traditional modal analysis to validate the ability of the proposed method for identifying the most critical buses of the system.