$\mu$ Approach to Robust Stability Domains in the Space of Parametric Uncertainties for a Power System With Ideal CPL

Power electronic systems are prone to instability. The problem, generally attributed to the constant power load (CPL) behavior of their power electronic controlled loads, can become more acute when the systems are subject to parametric uncertainties. The structured singular value (SSV) based μ method has proven to be a reliable approach for assessing the stability robustness of such uncertain systems. Despite its numerous benefits, the μ method is not often applied to electrical power systems (EPS) with multiple uncertainties. This may be due to the mathematical complexity underlying the μ theory. This paper aims to make the μ approach more application-friendly by providing clearer insights into the meaning and usefulness of the robust stability measure μ for EPS with multiple parametric uncertainties. This is achieved by presenting a methodology for translating μ analysis results from the frequency domain to the more perceivable uncertain parameters domain. The method directly demonstrates dependences of system stability on uncertain system parameters. Further, it clearly identifies robust stability domains as subsets of the much wider stability domains. The work is based on a representative EPS connected to an ideal CPL. μ analysis predictions are evaluated and validated against analytical results, for example, CPL system.