A Modeling Methodology for Robust Stability Analysis of Nonlinear Electrical Power Systems Under Parameter Uncertainties

Abstract

Abstract-This paper develops a modeling method for robust stability analysis of nonlinear electrical power systems over a range of operating points and under parameter uncertainties. Standard methods can guarantee stability under nominal conditions, but do not take into account any uncertainties of the model. In this study, stability is assessed by using structured singular value (SSV) analysis, also known as µ analysis. This method provides a measure of stability robustness of linear systems against all considered sources of structured uncertainties. The aim of this study is to apply the SSV method for robust small-signal analysis of nonlinear systems over a range of operating points and parameter variations. To that end, a modeling methodology is developed to represent any such system with an equivalent linear model that contains all system variability, in addition to being suitable for µ analysis. The method employs symbolic linearization around an arbitrary operating point. Furthermore, in order to reduce conservativeness in the stability assessment of the nonlinear system, the approach takes into account dependences of operating points on parameter variations. The methodology is verified through µ analysis of the equivalent linear model of a 4-kW permanent magnet machine drive, which successfully predicts the destabilizing torque over a range of different operating points and under parameter variations. Further, the predictions from µ analysis are validated against experimental results.Index Terms-Linear fractional transformation (LFT), µ analysis, robust stability analysis, structured singular value (SSV).

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

“…The authors in [4] have developed a software to make the process automatic in order to make the approach less laborious. Conversely, the SSV based µ method, that is presented in this work, has proven to produce reliable results in stability assessment of uncertain systems [9], [11], [12], [13]. Further, the µ approach excludes the need for extensive linearisation and parameter iterations.…”

“…3, over a range of operating points and parameter variations. To this end, the modelling methodology presented in [13] is employed to represent the EPS as an equivalent linear model that contains all system variability, in addition to being suitable for µ analysis. The method is based on symbolic linearisation around an arbitrary equilibrium point.…”

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

“…Hence, by working directly on an uncertain model, µ analysis eliminates the burden from a user of performing exhaustive parameter iterations and system linearisation [33], [34]. The µ approach has proven to produce reliable results in robust stability analysis of power systems subject to multiple simultaneous uncertainties [26], [31], [32], [29], [35].…”

“…The EMA was a standard vector-controlled PM motor drive [36], [37]. The detailed modelling and robust stability analysis of the system are presented in [33]. The aim of the study was to identify whether the system remains stable when the applied torque is allowed to vary within the uncertainty set [2 Nm, 38 Nm], (i.e 20 ± 18 Nm), where 20 Nm is the mean value of the torque on the given uncertainty set [33].…”

“…The system in Fig. 11 was analytically modelled to account for uncertainty in torque and system nonlinearities [33]. µ analysis was employed to predict boundary stability.…”