Normal Form Analysis of Complex System Models: A Structure-Preserving Approach

Martínez-Carrillo, Irma; Messina, A.R.; Vittal, Vijay

doi:10.1109/tpwrs.2007.907357

Cited by 21 publications

(15 citation statements)

References 12 publications

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“…Reference [29] proposes an extension of the method to deal with resonant cases. It has become a mature computational tool and other applications have been developed [30], [31], or are still emerging [32].…”

Section: Simplification Of a Maximum Number Of Nonlinear Termsmentioning

confidence: 99%

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An Accurate Third-Order Normal Form Approximation for Power System Nonlinear Analysis

Tian

Kestelyn

Thomas

et al. 2018

IEEE Trans. Power Syst.

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The inclusion of higher-order terms in small-signal (modal) analysis has been an intensive research topic in nonlinear power system analysis. Inclusion of second-order terms with the method of normal forms (MNF) has been well developed and investigated, overcoming the linear conventional small-signal methods used in the power system control and stability analysis. However, application of the MNF has not yet been extended to include third-order terms in a mathematically accurate form to account for nonlinear dynamic stability and dynamic modal interactions. Due to the emergence of larger networks and long transmission line with high impedance, modern grids exhibit predominant nonlinear oscillations and existing tools have to be upgraded to cope with this new situation. In this paper, first, fundamentals of normal form theory along with a review of existing tools based on this theory is presented. Second, a new formulation of MNF based on a third-order transformation of the system's dynamic approximation is proposed and nonlinear indexes are proposed to make possible to give information on the contribution of nonlinearities to the system stability and on the presence of significant third-order modal interactions. The induced benefits of the proposed method are compared to those afforded by existing MNFs. Finally, the proposed method is applied to a standard test system, the IEEE 2-area 4-generator system, and results given by the conventional linear small signal and existing MNFs are compared to the proposed approach. The applicability of the proposed MNF to larger networks with more complex models has been evaluated on the New England-New York 16-machine 5-area system. Index Terms-Interconnected power system, methods of normal forms, nonlinear modal interaction, power system dynamic, stability.

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Section: Simplification Of a Maximum Number Of Nonlinear Termsmentioning

confidence: 99%

“…Validated using 4th order or higher order generator models, the proposed method 3-3-3 also inherits the applicability to systems modeled by 2nd order generator models as method 3-3-1 used in [30], and 3rd order generator as method 3-2-3 used in [13].…”

Section: B Strong Resonance and Model Dependencementioning

confidence: 99%

An Accurate Third-Order Normal Form Approximation for Power System Nonlinear Analysis

Tian

Kestelyn

Thomas

et al. 2018

IEEE Trans. Power Syst.

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“…In sharp contrast with this, the bisection method required 12 to converge, whilst the first order NR method required 5 iterations to converge [13,14].…”

Section: [ ] [ ] [ ]mentioning

confidence: 94%

Dynamic stability analysis Using Percent Error of High-Order Lagrange method

Juarez

Martínez-Carrillo

2011

2011 8th International Conference on Electrical Engineering, Computing Science and Automatic Control

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A No-Lineal Model with robust precision for transient stability analysis in Multimachine Power Systems is proposed. The proposed formulation uses the interpolation of Lagrange and Newton's Divided Difference. The High-Order Interpolation technique developed can be used for evaluation of the critical conditions of the dynamic system. The High-Order procedure shows the ability to identify the Percent Error of Critical Stability Parameter. Numerical examples illustrate the method and demonstrate the ability of the High-Order technique to isolate and extract temporal modal behavior. The technique is applied in the 2-area 4-machine model of the IEEE.

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“…2) Taylor expansion: The algebraic equations are substituted into the differential ones and the resulting differential-only equations are expanded by Taylor series up to desired order around the SEP. The Taylor expansion can also be done on structure preserving power system DAEs [9]. 3) Linear analysis: The Jacobian of the system is used to extract the system eigenvalues and vectors.…”

Section: A General Idea Of Nf Application To Power Systemsmentioning

confidence: 99%

“…It is assumed in (1) that the algebraic equations are already substituted in the differential ones and (1) is differential-only. The application of NF to power system structure preserving DAE models has been addressed before [9], but that is outside the scope of the present paper and would be considered in future work. For small perturbation, (1) can be expanded in Taylor series around a particular SEP X 0 .…”

Section: B Normal Form Theorymentioning

confidence: 99%

A New Fast Track to Nonlinear Modal Analysis of Power System Using Normal Form

Ugwuanyi

Kestelyn

Thomas

et al. 2020

IEEE Trans. Power Syst.

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The inclusion of higher-order terms in small-signal (modal) analysis augments the information provided by linear analysis and enables better dynamic characteristic studies on the power system. This can be done by applying Normal Form theory to simplify the higher order terms. However, it requires the preliminary expansion of the nonlinear system on the normal mode basis, which is impracticable with standard methods when considering large scale systems. In this paper, we present an efficient numerical method for accelerating those computations, by avoiding the usual Taylor expansion. Our computations are based on prescribing the linear eigenvectors as unknown field in the initial nonlinear system, which leads to solving linear-only equations to obtain the coefficients of the nonlinear modal model. In this way, actual Taylor expansion and associated higher order Hessian matrices are avoided, making the computation of the nonlinear model up to third order and nonlinear modal analysis fast and achievable in a convenient computational time. The proposed method is demonstrated on a single-machine-infinitebus (SMIB) system and applied to IEEE 3-Machine, IEEE 16-Machine and IEEE 50-Machine systems.

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Normal Form Analysis of Complex System Models: A Structure-Preserving Approach

Cited by 21 publications

References 12 publications

An Accurate Third-Order Normal Form Approximation for Power System Nonlinear Analysis

An Accurate Third-Order Normal Form Approximation for Power System Nonlinear Analysis

Dynamic stability analysis Using Percent Error of High-Order Lagrange method

A New Fast Track to Nonlinear Modal Analysis of Power System Using Normal Form

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