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

Abstract

Sumsurooah, Sharmila and Odavic, Milijana and Bozhko, Serhiy (2017) A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription.For more information, please contact eprints@nottingham.ac.uk µ approach to robust stability domains in the space of parametric uncertainties for a power system with ideal CPL Sharmila Sumsurooah, Milijana Odavic, Member, IEEE, and Serhiy Bozhko, Member, IEEE Abstract-Power electronic systems are prone to instability. The problem, generally attributed to the constant power load (CPL) behaviour 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 work 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 the example CPL system.

Toward Robust Stability of Aircraft Electrical Power Systems: Using a μ-Based Structural Singular Value to Analyze and Ensure Network Stability

“…The input power P in is allowed to vary within Based on the technique of linear fractional transformation, the normalised uncertain parameters δ P in may be extracted from the state space system model and grouped in a diagonal matrix ∆ in feedback form [13]. In this case study, uncertainty matrix ∆ has the size of 3 × 3, as the uncertain parameter P in appears 3 times in the state space system model.…”

“…It implies that if the analysed system operates within the given boundary, the system is guaranteed robustly stable. By extrapolating on the ideas presented in this section, for a system subject to N parametric uncertainties, µ analysis provides the largest hypercube of dimension N centred about the nominal point and of coordinate size 1/µ, within which system robust stability can be guaranteed [13], [35].…”

“…6, the dc components of the supply voltage, supply current, input voltage and input current are clearly denoted as V g , I g , V in and I in respectively while their corresponding small-ac components are given byv g (t),î g (t), v in (t) andî in (t) respectively. R cpl is given by V in /I in [13].…”

Robust Stability Analysis of a DC/DC Buck Converter Under Multiple Parametric Uncertainties

“…In addition, this work demonstrates the significance of the robust stability measure µ for a practical PE system subject to multiple parametric uncertainties. In [47], the authors demonstrate the usefulness of µ by presenting the concept of the hypercube. It has been demonstrated that a system subject to N parametric uncertainties is guaranteed robustly stable within a hypercube of dimension N and of coordinate size 1/µ, centred about a nominal point [25], [47].…”

“…In [47], the authors demonstrate the usefulness of µ by presenting the concept of the hypercube. It has been demonstrated that a system subject to N parametric uncertainties is guaranteed robustly stable within a hypercube of dimension N and of coordinate size 1/µ, centred about a nominal point [25], [47]. This work applies the hypercube concept to demonstrate the significance of the µ results for the practical dc/dc buck converter system under investigation when it is subject to both single and multiple parametric uncertainties.…”