Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis

Anghel, Marian; Milano, Federico; Papachristodoulou, Antonis

doi:10.1109/tcsi.2013.2246233

Cited by 128 publications

(156 citation statements)

References 40 publications

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“…Further, ability to often determine Lyapunov functions of variable degrees enables the technique to overcome the limitation of traditional quadratic common Lyapunov methodologies. In a recent paper [16], the authors, by following [17], [18] have demonstrated a preliminary work on the utility of this approach for power system TSA. It converts the typical swing equation model (which has a nonpolynomial from) to a polynomial form by using translation as well as transformation.…”

Section: Simulation In Time Domain Encounters Two Major Problemsmentioning

confidence: 99%

Transient stability analysis of power system using polynomial Lyapunov function based approach

Mazumder

Fuente

2014

2014 IEEE PES General Meeting | Conference &Amp; Exposition

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Transient stability analysis (TSA) of power system is gaining significant importance given the dwindling gap of power generation and demand as well as increasing penetration of intermittent renewable energy sources. Traditional approach to TSA has been primarily based on time-domain analysis or energy-function-based approach or based on common-Lyapunov function-based approach. In this paper, exploration of a polynomial-Lyapunov-function based approach is outlined. It promises to overcome the key weaknesses of the traditional approaches with regard to eliminating the need for extensive time-domain simulation or determining specific energy-function or common-Lyapunov forms which is highly intuitive and in several cases are non-existing or do not conform to the definition of Lyapunov's stability.Index Terms-Transient stability analysis, polynomial Lyapunov function, power system, optimization I.

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Section: Simulation In Time Domain Encounters Two Major Problemsmentioning

confidence: 99%

Transient stability analysis of power system using polynomial Lyapunov function based approach

Mazumder

Fuente

2014

2014 IEEE PES General Meeting | Conference &Amp; Exposition

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“…The estimation of stability regions of nonlinear systems is of fundamental importance in a wide range of applications, such as autonomous systems [1], [2], control of robotic manipulators [3], and transient stability of power systems [4], [5]. This problem is continuously receiving a lot of attention in literature as it still remains unsolved.…”

Section: Introductionmentioning

confidence: 99%

Estimating the region of attraction via forward reachable sets

El-Guindy

Han

Althoff

2017

2017 American Control Conference (ACC)

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Abstract-We propose and implement an algorithm based on reachability analysis to estimate the region of attraction (ROA) of an equilibrium point for nonlinear systems. The stability region is obtained via the computation of forward reachable sets. We compare our results with well-established techniques in this area. In particular, we consider the optimization of the Lyapunov function (LF) sub-level set using sum-of-squares (SOS) decomposition, and the computation of backward reachable sets of a target set using the viscosity solution of a time-dependant Hamilton-Jacobi-Isaacs (HJI) formulation. Our method can overcome many limitations imposed on the applicability of Lyapunov-based approaches, such as conservatism in estimating the stability region, and difficulties associated with choosing a suitable LF. This is due to the fact that our reachability algorithm does not require a LF in order to provide an estimate of the ROA. Various numerical examples show that our proposed approach can estimate the exact ROA quite accurately, and more importantly, scales moderately with the system dimension compared to alternative techniques.

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“…The applications of SOS programming methods in power engineering have been recently reported in the literature [1]- [3] where SOS-based techniques for the algorithmic construction of Lyapunov functions for the transient stability analysis of power systems are introduced. Reference [4] investigates the stabilization of the discrete-time bilinear systems by using SOS decomposition method.…”

Section: Introductionmentioning

confidence: 99%

Lyapunov-based proportional-integral controller design with guaranteed region of convergence for dc-dc power converters

Vatani

Hovd

2017

2017 12th IEEE Conference on Industrial Electronics and Applications (ICIEA)

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Abstract-In this paper, Lyapunov stability of dc-dc power converters controlled with proportional-integral (PI) controllers is investigated. The class of dc-dc converters with discrete-time bilinear averaged dynamic model is considered. An integral action on the output voltage is introduced for robust output regulation in case of model parameter uncertainties and external disturbances. An algorithmic method, using sum of squares programming, is introduced to calculate a candidate Lyapunov function, and the coefficients of P and PI controllers are calculated to guarantee a decrease in the Lyapunov function in each time step while input constraints are fulfilled. The controller design method is iterated in order to improve the region of convergence of the state trajectories. The resulting controller designs are evaluated through simulations of detailed switching models for a boost and a cuk converter.

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Algorithmic Construction of Lyapunov Functions for Power System Stability Analysis

Cited by 128 publications

References 40 publications

Transient stability analysis of power system using polynomial Lyapunov function based approach

Transient stability analysis of power system using polynomial Lyapunov function based approach

Estimating the region of attraction via forward reachable sets

Lyapunov-based proportional-integral controller design with guaranteed region of convergence for dc-dc power converters

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