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relative gain array and singular value decomposition in determination of PSS location

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER 2005年第5期15卷 397-412页

作者： Karimpour, A Asgharian, R Malik, OP Ferdowsi Univ Mashhad Dept Elect Engn Mashhad Iran Univ Calgary Dept Elect Engn Calgary AB T2N 1N4 Canada

In a multi-machine power system, it is important to determine the best location for the application of power system stabilizers. A number of techniques have been proposed to perform this selection. In this paper a new selection measure based on relative gain array and singular value decomposition is proposed. A comparison is made between the performance of the new measure and the older methods. The proposed methodology is based on the use of system transfer function. Copyright (c) 2005 John Wiley & Sons, Ltd.

关键词： singular value decomposition relative gain array power system stabilizer controllability observability

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relative gain array of Weakly Nonlinear Systems using a Nonparametric Identification Approach

Relative Gain Array of Weakly Nonlinear Systems using a Nonp...

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IEEE Conference on Control and Applications (CCA)

作者： Kadhim, Ali M. H. Castano, Miguel Birk, Wolfgang Gustafsson, Thomas Lulea Univ Technol Control Grp Lulea Sweden Kufa Univ Elect Engn Dept Najaf Iraq

ISBN: (纸本)9781479977871

This article presents a procedure to estimate the relative gain array (RGA) matrix for weakly nonlinear systems by means of nonparametric identification of the frequency response matrix (FRM). Specifically, the best linear approximation of nonlinear systems and the covariance of the nonlinear distortions are used in the relative gain array estimation. For the estimation neither process model nor model structure need to be known which is an advantage over methods that require accurate knowledge of a parametric process model. The proposed approach is compared with the original RGA and a nonlinear RGA calculation using the well-known quadruple tank process as a case.

关键词： approximation theory estimation theory frequency response identification matrix algebra nonlinear systems FRM RGA matrix estimation frequency response matrix linear approximation nonlinear distortion covariance nonparametric identification relative gain array weakly nonlinear system arrays Covariance matrices Estimation MIMO Nonlinear distortion Nonlinear systems Uncertainty Nonlinear systems Nonlinear distortion relative gain Linear approximation estimation theory Approximation Theory matrix algebra frequency response multiple input multiple output systems arrays variance covariance matrix residual gas analysis Covariance matrix

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relative gain array Application for a VSC Grid-Connected Converter 8

Relative Gain Array Application for a VSC Grid-Connected Con...

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8th Southern Power Electronics Conference and the 17th Brazilian Power Electronics Conference, SPEC / COBEP 2023

作者： Neto De Souza, Igor Dias Surerus Sarmento, Pedro Paulo De Almeida, Pedro MacHado Fogli, Gabriel Azevedo Universidade Federal de Ouro Preto Departamento de Engenharia Elétrica MG João Monlevade Brazil Universidade Federal de Juiz de Fora Núcleo de Automação e Eletrônica de Potência MG Juiz de Fora Brazil Universidade Federal de Minas Gerais Belo Grupo de Eletrônica de Potência MG Horizonte Brazil

ISBN: (纸本)9798350321128

This study investigates the behavior of a voltage source converter in abc,αβ and dq-coordinate frame, adopting a multivariable approach. Given the lack of functional controllability in the plant, an analysis of the frequency-dependent relative gain array is conducted to assist in determining the most suitable variables to be controlled within a specific frequency range. This analysis plays a critical role in selecting appropriate low- and high-frequency controllers for the system. © 2023 IEEE.

关键词： and dq-coordinate frame grid-connected converter multivariable systems relative gain array

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Integral-Square-Error Based Normalized relative gain array for the Input-Output Pairing and Equivalent Transfer Function Design of MIMO Processes

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IETE JOURNAL OF RESEARCH 2023年第9期69卷 5975-5985页

作者： Verma, Bharat Padhy, Prabin Kumar LNM Inst Informat Technol ECE Dept Jaipur Rajasthan India PDPM Indian Inst Informat Technol Design & Mfg ECE Dept Jabalpur India

Input-output pairing effectively minimizes the loop interaction in MIMO processes and avoids integral instability. In this article, a modified relative Normalized gain array is proposed for the Input-Output Pairing and design of the First-order and Second-order Equivalent Transfer function. The proposed modified relative gain array (mRNGA) matrix is derived by Normalizing the relative gain array matrix with a normalization factor, which is calculated by minimizing the Integral Square Error of the given MIMO process. After that, the first order and second order Equivalent Transfer function is design by the derived mRNGA matrix, which offers an improved estimation of the Effective open-loop transfer function of the given MIMO process. The proposed method is corroborated with the help of the Input-Output pairing examples up to the 5 x 5 MIMO processes and three ETF design example.

关键词： Equivalent Transfer function Integral Square Error MIMO process relative gain array RNGA

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THE ROLE OF THE CONDITION NUMBER AND THE relative gain array IN ROBUSTNESS ANALYSIS

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AUTOMATICA 1994年第6期30卷 1029-1035页

作者： CHEN, J FREUDENBERG, JS NETT, CN UNIV MICHIGAN DEPT ELECT ENGN & COMP SCI ANN ARBOR MI 48109 USA UNITED TECHNOL RES CTR E HARTFORD CT 06108 USA GEORGIA INST TECHNOL SCH AEROSP ENGN ATLANTA GA 30332 USA GEORGIA INST TECHNOL SCH ELECT ENGN ATLANTA GA 30332 USA

This paper studies deviations of open-loop properties in the presence of modeling uncertainties. Our aim is to gain insights into how open-loop properties and thus potentially closed-loop properties may vary in the face of a diagonally structured uncertainty. We give several estimates for the worst case deviations of the open-loop transfer function in terms of certain structured singular values and their bounds, and also in terms of certain scaled plant condition numbers, the relative pin array, and the block relative gains. Our analysis shows that the estimates in terms of the structured singular values and bounds are tight in general, so are those in terms of the condition numbers for certain cases studied previously in the literature. We show that the worst case deviation will be large when the estimates stated in terms of the structured singular values, or under certain circumstances in terms of the condition numbers, are large. On the other hand, an example is constructed to show that the relative pin array and block relative pins may be optimistic measures in assessing these deviations. The developments here support and reinforce previous conjectures and results which assert that plants with large condition numbers and/or relative gains are potentially difficult to control.

关键词： LINEAR MULTIVARIABLE SYSTEMS SENSITIVITY ROBUSTNESS ANALYSIS CONDITION NUMBER relative gain array BLOCK relative gain STRUCTURED SINGULAR VALUE STRUCTURED UNCERTAINTY

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Identification of electromechanical modes and placement of PSSs using relative gain array

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IEEE TRANSACTIONS ON POWER SYSTEMS 2004年第1期19卷 410-417页

作者： Milanovic, JV Duque, ACS Univ Manchester Inst Sci & Technol Dept Elect Engn & Elect Manchester M60 1QD Lancs England Empresarios Agrupados Madrid 28015 Spain

The paper investigates the possibility to use relative gain array (RGA) for power system small-disturbance stability analysis. The RGA has been successfully used in the past as steady state measure of interactions for multivariable, decentralized control in chemical and process engineering. The effectiveness of the RGA in identifying electromechanical modes and selecting the optimal location for placement of PSSs is compared with the conventional approach that uses transfer function residues, eigenvalues and participation factors. Two different multimachine power systems are used for the case studies. Limitations and advantages of the use of RGA in this purpose are clearly indicated in the paper.

关键词： damping electromechanical oscillations relative gain array stability

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CMMSE algorithms for constructing doubly stochastic matrices with the relative gain array (combined matrix) A○A^-T

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JOURNAL OF MATHEMATICAL CHEMISTRY 2019年第7期57卷 1700-1709页

作者： Fuster, Robert Gasso, Maria T. Gimenez, Isabel Univ Politecn Valencia Dept Matemat Aplicada Valencia Spain Univ Politecn Valencia Inst Matemat Multidisciplinaria Valencia Spain

The Combined matrix of a nonsingular matrix A is defined by phi(A)=A T where degrees means the Hadamard (entrywise) product. If the matrix A describes the relation between inputs and outputs in a multivariable process control, phi(A) describes the relative gain array (RGA) of the process and it defines the Bristol method (IEEE Trans Autom Control 1:133-134, 1966) often used for Chemical processes (McAvoy in Interaction analysis: principles and applications. Instrument Society of America, Pittsburgh, 1983;Papadourakis et al. in Ind Eng Chem Res 26(6):1259-1262, 1987;Wang et al. in Chem Eng Technol, 10.1002/ceat.201500202, 2016;Kariwala et al. in Ind Eng Chem Res 45(5):1751-1757, 10.1021/ie050790r, 2006;Golender et al. in J Chem Inf Comput Sci 21(4):196-204, 10.1021/ci00032a004, 1981). The combined matrix has been studied in several works such as Bru et al. (J Appl Math, 10.1155/2014/182354, 2014), Fiedler and Markham (Linear Algebra Appl 435:1945-1955, 2011) and Johnson and Shapiro (SIAM J Algebraic Discrete Methods 7:627-644, 1986). Since phi(A)=(cij) has the property of Sigma kcik=Sigma kckj=1,i,j, when phi(A)>= 0, phi(A) is a doubly stochastic matrix. In certain chemical engineering applications a diagonal of the RGA in wchich the entries are near 1 is used to determine the pairing of inputs and outputs for further design analysis. Applications of these matrices can be found in Communication Theory, related with the satellite-switched time division multiple-access systems, and about a doubly stochastic automorphism of a graph. In this paper we present new algorithms to generate doubly stochastic matrices with the Combined matrix using Hessenberg matrices in Sect.3 and orthogonal/unitary matrices in Sect.4. In addition, we discuss what kind of doubly stochastic matrices are obtained with our algorithms and the possibility of generating a particular doubly stochastic matrix by the map phi.

关键词： Hadamard product Combined matrix Doubly stochastic matrix Hessenberg matrix Householder matrix Orthogonal matrix Unitary matrix relative gain array

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A NEW RESULT ON relative gain array, NIEDERLINSKI INDEX AND DECENTRALIZED STABILITY CONDITION - 2 X-2 PLANT CASES

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AUTOMATICA 1991年第2期27卷 419-421页

作者： CHIU, MS ARKUN, Y GEORGIA INST TECHNOL SCH CHEM ENGN ATLANTA GA 30332 USA

This note discusses the decentralized stability condition for a 2-channel decentralized control system where each channel is a single-input-single-output (SISO) control loop. Stabilization of each individual loop (with the other loop open) is not required, which had been the case in previous work on the relative gain array (RGA) and the Niederlinski Index (NI). Therefore this new result is a generalization of previous RGA and NI stabilization conditions.

关键词： DECENTRALIZED STABILITY relative gain array NIEDERLINSKI INDEX

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Research on interaction of APFs based on relative gain array

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ARCHIVES OF ELECTRICAL ENGINEERING 2018年第1期67卷 165-177页

作者： Feng, Xingtian Sun, Tiantian Ma, Wenzhong China Univ Petr East China Coll Informat & Control Engn 66 West Changjiang Rd Qingdao Peoples R China State Grid Shandong Elect Power Co Dongying Power Supply Co 66 West Changjiang Rd Qingdao Peoples R China

Different APFs (Active Power Filter) interact with each other when multiple APFs are connected to the grid, and the interactions deteriorate the control performance of APFs and even lead to system instability. This paper presents a method to analyze the dynamic interaction of multiple APFs in a weak grid. This method uses the Norton equivalent principle to establish the mathematical model of a single APF. The mathematical model of the multiple APFs connected to the grid is set up based on the single APF mode. The RGA (relative gain array) principle is used to analyze the interactions among multiple APFs. Besides, this paper analyzes the effect of changing circuit parameters and controller parameters on the change of the interactions. The strategy of weakening and eliminating the interaction is proposed based on rational selection and combination of parameters. Analysis, along with time domain simulation and experimental results, is presented to verify the feasibility and effectiveness of the proposed method and strategy.

关键词： interaction effect relative gain array active power filter Norton equivalent LCL filter

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Sensitivity of relative gain array for processes with uncertain gains and residence times

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IFAC-PapersOnLine 2016年第1期49卷 486-491页

作者： Jain, Amit Babu, B.V. 333031 India 203201 India

The large scale industrial plants are often multivariable in nature. The preferred choice for the control of such plants is the decentralized multi-loop control system. The performance of a multi-loop control system depends strongly on the proper selection of control configuration. The most popular tool for control configuration selection is probably the steady-state "relative gain array (RGA)". It has later been extended to consider the effect of process dynamics. A very few attempts have been made towards the sensitivity of RGA analysis to model uncertainty and is majorly limited to the steady-state systems only. The aim of this paper is to gain insights into how process dynamics can affect control configuration decision based on RGA analysis in the face of model uncertainty. For the study, parametric uncertainty in gain and residence time of the process has been considered. Analytical expressions for worst-case bounds of uncertainty in steady-state and dynamic RGA are derived for two-input, two-output (TITO) plant models. A simulation example which has been used in several prior studies is considered here to demonstrate the applicability of the proposed approach. The simulink based closed-loop response has also been obtained to show the accuracy of results. The obtained bounds of uncertainty in RGA provide valuable information pertaining to the necessity of robustness and accuracy in the model of decentralized multivariable systems. © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： Process control Control systems Industrial plants Multivariable control systems Multivariable systems Uncertainty analysis Control configuration Parametric uncertainties relative gain array Residence time Worst case bounds

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