Nonlinear model reduction of dynamical power grid models using quadratization and balanced truncation

Ritschel, Tobias; Weiß, Frances; Baumann, Manuel; Grundel, Sara

doi:10.1515/auto-2020-0070

Cited by 8 publications

(17 citation statements)

References 48 publications

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“…However, for special classes of nonlinear systems such as bilinear and quadraticbilinear systems, one can indeed use well-established system theoretical methods; see, e.g., [3], [5], [6]. A large class of nonlinear systems, such as those with smooth nonlinearities, e.g., exponential, trigonometric, can indeed be represented as quadratic-bilinear systems by introducing new variables (in a lifting map) [22], [14], [4], [33], [31]. Converting a nonlinear model to its equivalent quadratic form provides an opportunity to perform input-independent model reduction techniques where a system-theoretic norm is defined [5], [6].…”

Section: Structure-preserving Mor Approachmentioning

confidence: 99%

“…In [40] an SVD-based approach for real-time dynamic model reduction with the ability of preserving some nonlinearity in the reduced model is presented. The recent work [33] presents the idea of transforming the swing equations into a quadratic system, lifts nonlinear swing equations to a quadratic one, and employs quadratic balanced truncation model order reduction technique. A non-intrusive data-driven modeling framework for power network dynamics using Lift and Learn [31] has been studied in [34].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Structure-preserving Mor Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Structure-Preserving Model Reduction for Nonlinear Power Grid Network

Safaee¹,

Gugercin²

2022

Preprint

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“…Zhu et al [16] have proposed a method for large-scale power system model reduction based on the extended Krylov subspace technique. Ritschel et al [17] have reported a balanced truncation model reduction approach for reducing two commonly used nonlinear and dynamical models of power grids.…”

Section: Literature Reviewmentioning

confidence: 99%

A Recursive Least-Squares Approach with Memorizing Factor for Deriving Dynamic Equivalents of Power Systems

Karami

2021

Adv. technol. innov.

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In this research, a two-stage identification-based approach is proposed to obtain a two-machine equivalent (TME) system of an interconnected power system for transient stability studies. To estimate the parameters of the equivalent system, a three-phase fault is applied near and/or at the bus of a local machine in the original multimachine system. The electrical parameters of the equivalent system are calculated in the first stage by equating the active and reactive powers of the local machine in both the original and the predefined equivalent systems. The mechanical parameters are estimated in the second stage by using a recursive least-squares estimation (RLSE) technique with a factor called “memorizing factor”. The approach is demonstrated on New England 10-machine 39-bus system, and its accuracy and efficiency are verified by computer simulation in MATLAB software. The results obtained from the TME system agree well with those obtained from the original multimachine system.

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“…Therefore, it can be beneficial to perform a quadratization first and then use the dedicated methods. For further details and examples of applications, we refer to [11,15,16,20].…”

Section: Introductionmentioning

confidence: 99%

Optimal monomial quadratization for ODE systems

Bychkov¹,

Pogudin²

2021

Preprint

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Quadratization problem is, given a system of ODEs with polynomial right-hand side, transform the system to a system with quadratic right-hand side by introducing new variables. Such transformations have been used, for example, as a preprocessing step by model order reduction methods and for transforming chemical reaction networks. We present an algorithm that, given a system of polynomial ODEs, finds a transformation into a quadratic ODE system by introducing new variables which are monomials in the original variables. The algorithm is guaranteed to produce an optimal transformation of this form (that is, the number of new variables is as small as possible), and it is the first algorithm with such a guarantee we are aware of. Its performance compares favorably with the existing software, and it is capable to tackle problems that were out of reach before.

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Nonlinear model reduction of dynamical power grid models using quadratization and balanced truncation

Cited by 8 publications

References 48 publications

Structure-Preserving Model Reduction for Nonlinear Power Grid Network

Structure-Preserving Model Reduction for Nonlinear Power Grid Network

A Recursive Least-Squares Approach with Memorizing Factor for Deriving Dynamic Equivalents of Power Systems

Optimal monomial quadratization for ODE systems

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