Nonlinear power system model reduction based on empirical Gramians

Zhao, Huiru; Xiaoming, Lan; Ren, Hui

doi:10.1515/jee-2017-0077

Cited by 7 publications

(5 citation statements)

References 22 publications

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“…This work has been primarily targeted towards finding a reduced equivalent model of external area. There are various techniques used including calculating observable and controllable Grammians, Hankel singular values [12], linearized models [13]- [15], and neural networks [16], [17].…”

Section: Related Workmentioning

confidence: 99%

Neuro-physical dynamic load modeling using differentiable parametric optimization

Abhyankar¹,

Drgoňa²,

August³

et al. 2022

Preprint

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In this work, we investigate a data-driven approach for obtaining a reduced equivalent load model of distribution systems for electromechanical transient stability analysis. The proposed reduced equivalent is a neurophysical model comprising of a traditional ZIP load model augmented with a neural network. This neuro-physical model is trained through differentiable programming. We discuss the formulation, modeling details, and training of the proposed model set up as a differential parametric program. The performance and accuracy of this neurophysical ZIP load model is presented on a medium-scale 350-bus transmission-distribution network.

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Section: Related Workmentioning

confidence: 99%

Neuro-physical dynamic load modeling using differentiable parametric optimization

Abhyankar¹,

Drgoňa²,

August³

et al. 2022

Preprint

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“…Now let q * in (38) be an equilibrium of (11). Then from (42), we obtain G(q * ) = J T F (X * ) = 0. Since the Jacobian (43) has full column rank, we have F (X * ) = 0, which by (39) yields that ( 36) is an equilibrium of (35).…”

Section: A Equilibrium Analysismentioning

confidence: 99%

“…Balanced truncation based on empirical controllability and observability covariances of nonlinear power systems is proposed in [30]. The empirical Gramians and balanced realization were also used in [42], [43] to build a nonlinear power system model suitable for controller design. In [29], real-time phasor measurements are used to cluster generators based on similar behaviors using recursive spectral bipartitioning and spectral clustering.…”

Section: Introductionmentioning

confidence: 99%

Structure-Preserving Model Reduction for Nonlinear Power Grid Network

Safaee¹,

Gugercin²

2022

Preprint

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We develop a structure-preserving system-theoretic model reduction framework for nonlinear power grid networks. First, via a lifting transformation, we convert the original nonlinear system with trigonometric nonlinearities to an equivalent quadratic nonlinear model. This equivalent representation allows us to employ the H2-based model reduction approach, Quadratic Iterative Rational Krylov Algorithm (Q-IRKA), as an intermediate model reduction step. Exploiting the structure of the underlying power network model, we show that the model reduction bases resulting from Q-IRKA have a special subspace structure, which allows us to effectively construct the final model reduction basis. This final basis is applied on the original nonlinear structure to yield a reduced model that preserves the physically meaningful (second-order) structure of the original model. The effectiveness of our proposed framework is illustrated via two numerical examples.

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“…B is the input matrix [13]. The reduced order model (ROM) of order k ≪ n, which approximates the original system from a subspace spanned by a reduced basis of dimension k in R n is obtained by using Galerkin projection.…”

Section: Podmentioning

confidence: 99%

A scheme for comprehensive computational cost reduction in proper orthogonal decomposition

Singh

Bazaz

Nahvi

2018

Journal of Electrical Engineering

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This paper addresses the issue of offline and online computational cost reduction of the proper orthogonal decomposition (POD) which is a popular nonlinear model order reduction (MOR) technique. Online computational cost is reduced by using the discrete empirical interpolation method (DEIM), which reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by POD: this is the POD-DEIM approach. Offline computational cost is reduced by generating an approximate snapshot-ensemble of the nonlinear dynamical system, consequently, completely avoiding the need to simulate the full-order system. Two snapshot ensembles: one of the states and the other of the nonlinear function are obtained by simulating the successive linearization of the original nonlinear system. The proposed technique is applied to two benchmark large-scale nonlinear dynamical systems and clearly demonstrates comprehensive savings in computational cost and time with insignificant or no deterioration in performance.

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Nonlinear power system model reduction based on empirical Gramians

Cited by 7 publications

References 22 publications

Neuro-physical dynamic load modeling using differentiable parametric optimization

Neuro-physical dynamic load modeling using differentiable parametric optimization

Structure-Preserving Model Reduction for Nonlinear Power Grid Network

A scheme for comprehensive computational cost reduction in proper orthogonal decomposition

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