Developing a Weakly Nonlinear Power System Model Using the Carleman Bilinearization Procedure

Dushin, Sergey V.; Abramenkov, Alexander; Kutyakov, Evgeniy Yu.; Iskakov, Alexey B.; Salnikov, A. M.

doi:10.1109/summa50634.2020.9280713

Cited by 2 publications

(1 citation statement)

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“…Many practical systems have been modelled by bilinear systems, such as the population of biological species [2], heat transfer process [3], FitzHugh-Nagumo system [4], channel equalization and echo cancellation [5], and activated sludge process [6]. Also, weakly non-linear systems can be approximated by a bilinear system using Carleman bilinearization [7,8]. However, the Carleman bilinearization approaches usually result in high-order bilinear models.…”

Section: Introductionmentioning

confidence: 99%

H₂model order reduction of bilinear systems via linear matrix inequality approach

Soloklo

Bigdeli

2023

IET Control Theory & Appl

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This paper proposes an H2‐optimal model order reduction (MOR) method for bilinear systems based on the linear matrix inequality (LMI) approach. In this method, to reduce the computational complexity, at first, a reduced middle‐order approximation of the system is derived based on common bilinear MOR methods. Next, the H2 norm of the error system is minimized to obtain the reduced‐order bilinear model. Generalized Lyapunov equations are added to the optimization problem as LMI constraints to guarantee the specification of type II Gramians of the bilinear system to improve accuracy. Besides, two stability conditions are included to the optimization problem as its constraints to preserve stability of reduced‐order bilinear model. One of advantages of the proposed method is the need for only one of the Gramians of controllability or observability. Since the proposed H2‐optimal MOR problem is a polynomial matrix inequality (PMI) problem, an iterative method is used to convert the PMI to the LMI problems and solve the optimization problem. Three bilinear test systems are considered to show the proposed method's efficiency, while its performance is compared with some classical methods. Results show that the proposed methods lead to a more accurate reduced‐order model than other MOR methods.

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Section: Introductionmentioning

confidence: 99%

H₂model order reduction of bilinear systems via linear matrix inequality approach

Soloklo

Bigdeli

2023

IET Control Theory & Appl

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Taylor Series Decomposition of Nonlinear Model of Two-area Four-generator Power System

Kutyakov

Dushin

Iskakov

et al. 2021

2021 3rd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA)

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Developing a Weakly Nonlinear Power System Model Using the Carleman Bilinearization Procedure

Cited by 2 publications

References 7 publications

H₂model order reduction of bilinear systems via linear matrix inequality approach

H₂model order reduction of bilinear systems via linear matrix inequality approach

Taylor Series Decomposition of Nonlinear Model of Two-area Four-generator Power System

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Developing a Weakly Nonlinear Power System Model Using the Carleman Bilinearization Procedure

Cited by 2 publications

References 7 publications

H2model order reduction of bilinear systems via linear matrix inequality approach

H2model order reduction of bilinear systems via linear matrix inequality approach

Taylor Series Decomposition of Nonlinear Model of Two-area Four-generator Power System

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H₂model order reduction of bilinear systems via linear matrix inequality approach

H₂model order reduction of bilinear systems via linear matrix inequality approach